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UBC Theses and Dissertations

The economics of transmission and distribution of electric energy Smith, Allan James 1933

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THE ECONOMICS Of TRANSMISSION AND DISTRIBUTION of ELECTRIC ENERGY by A l l a n James Smith A T h e s i s submitted for the Degree of MASTER OF APPLIED SCIENCE In the Department of ELECTRICAL ENGINEERING THE UNIVERSITY OF BRITISH COLUMBIA A p r i l , 1933 ' - -PREFACE -/// ' The tra-hsmi^^ of e l e c t r i c energy hag been for: t f e mpat;; p a r t undertaken: by- P u b l i c U t i l i t y Companies. 'The. Pub-' ••'': l i e . : ' U t i l i t y .Company operates under a .••franchise granted by a l e g l s - l a - . t i v e : a u t h o r i t y I n the t e r r i t o r i e s considered. The method of o p e r a t i o n , > b y r f r a n c M s e r i g h t f l , : e l i m i n a t e s d i r e c t c o m p e t i t i o n . In order, there-•'• //fore;,;;that : the r a t e s p a i d for* e l e c t r i c energy may n^ot be, e x o r b i t a n t , •/;/ soffie/forni a f r e g u l a t i o n i s -generally inwogue. The concept of such I . ;-reg-u:^^l.on: hag- ..for, i t s ' t h e o r e t i c a l , "b'a-sis. & " f a i r r e t u r n on a f a i r ? '..vaiue:" . : ;The d e t e r m i n a t i o n of t h i s " f a i r value" i s the subject of /// . / ' this-^ i t a p p l i e s t o t r a n s m i s s i o n and .dis-t r i b u t e r e a l b a s i s of " f a i r v a l u e " , apart from intangibles., '•'"•': i n " the •.•"'rate:base",: • and t i e " r a t e base" i s i n t u r n a f u n c t i o n of the *' yaluat-loh' of the p h y s i c a l p l a n t equipment. The " r a t e base" I s the ; ; ;furidamehtal subject; i n r a t e problems, and to t h a t end the Importance '-•;. o f I t s c b r r e c t d e t e r m i n a t i o n I s paramount. How important the i m p l i c --•/ai'ions//^^ s u b j e c t matter are, may be r e a d i l y , a p p r e c i a t e d from a i -perusal of an a r t I c l e i n the New, York Times of January 23rd 1933-• T h i s v & r t i c l e has been i n c o r p o r a t e d i n t h i s work as Appendix "B" and : ; ought : t o ^be: r e a d - i n the f i r s t p l ace as an I n d i c a t i o n of the i s s u e s Involved;/in t h i s study. ; " F a i r v a l u e " and "Rate base" cannot be s t u d i e d without the ;•'/;'/' a p p r o p r i a t e ^ a n a l y s i s : Of ..data r e p r e s e n t a t i v e of the range of problems ,:^studied^ / I n t h i s cdrihection the data f o r t h i s t h e s i s have come from ":.•'• two Sources.whi.ch.^ r e p r e s e n t a t i v e of the range of yr.vpr^bXems covered In. t h i s i n v e s t i g a t i o n . The two extremes have been . .4''V;.;o:6*'h;S.'l4ei,ed>, l . e - . , - .minimuffl'and maximum-.'density per square m i l e e e r v i c - '. i ; %d.- :T from the p o i n t ' o f view of number of customers', l o a d i n k.w. or k.w. h r s . per s q u a r e m i l e . For c o n -..v/c-entrat-ea loads and h e a v i l y , loaded, c i r c u i t s of the d i f f e r e n t types yyv$^&^&&Ye&:%Xub data were . accumulated, r e c o n c i l e d and checked by the •/;:{writer and h i s a s s o c i a t e s when he was C h i e f Engineer of the Columbus ••/^Railways/Power -and L i g h t Company, 1923-1926, at Columbus,- Ohio, U.. S. A. '•' /This/ u t i l i t y s e r v i c e s a ; p o p u l a t i o n of 400,000 people. The data f o r • / ' / l i g h t l y ;ioade'd . c i r c u i t s due to s p a r s e l y populated t e r r i t o r i e s were ;[•^^ined[-lk-T^x&B,, Hew .Mexico, L o u i s i a n a and Alabama, U. S. A.,. / •wfieM'ttie • W i t e r was JGefieral Manager and C h i e f Engineer of the Texas- \ 'j^  ^ L ouisiana: Power Company I 9 2 6 - I 9 3 O . This u t i l i t y s e r v i c e d a p o p u l a t i o n ,// of ^ approximately 250> 00Q, d i s t r i b u t e d among 172 small communities. The w r i t e r wishes to' acknowledge the debt "he owes to Dr.. H• • /: V i c k e r s 5 Head of /the Be par tment of Mechanical and E l e c t r i c a l Engin-eering; o f t h ^ h i s ' / s t i m u l a t i n g encouragement i n the w r i t I h g of t h i s t h e s i s , but a l s o f o r Wie;"advanced--; t r a i n i n g which a p r a c t i c a l engineer coming back to-/// the.: academic world has been a b l e to: o b t a i n ; and t o P r o f e s s o r G-. F. I)rm of the * U n i v e r s i t y of B r i t i s h :/ of the manuscript and'the ,;,: c o h s t r u c t i v e suggestions made; t h e r e i n , of which the w r i t e r has: >•/un&esitatirigly" taken'; advantage i n t h i s t h e s i s . '/ /' The : U n i v e - r s i t y / o f B r i t i s h Columbia, / / V a n c o u v e r , - B r i t i s h . Co /////.Canada./-' •..••''/' '//-March 1933- - • - ' TABLE OF CONTENTS CHAPTER PAGE I n t r o d u c t i o n - • : . PART I I A p p l i c a t i o n of Engineering Economics t o ''Transmission and D i s t r i b u t i o n Problems 1 I I Costs 7 "III Energy Cost 18 IV Load C h a r a c t e r i s t i c s 33 V General Equation 44 VI 'Power Loss and Voltage Drop 50 PART I I VII Transmission'Line Problems - Trunk L i n e s . 57 V I I I ' ' transmit s e l o n t L i n e Problems - Secondary L i n e s 66 IX Power C i r c u i t s ' 7 7 X L i g h t i n g C i r c u i t s 92 XI Secondary D i s t r i b u t i o n - S i n g l e Phase 100 X I I Power Secondaries 127 X I I I Underground L i n e s 133 ' X I V .The System as a Whole . 140 XV I n d u s t r i a l P l a n t Problems 142 App.A Method of Approximating Energy Cost 146 App.B Current Press A c t i o l e 150 B i b l i o g r a p h y 154 .Diagrams and Tables -:- • THE ECONOMICS . ' o f ; TRANSMISSION AND DISTRIBUTION  ELECTRICAL.ENERGY  INTRODUCTION The- r a p i d g r o w t h . o f t h e e l e c t r i c l i g h t and power i n d u s t r y w i t h i n t h e l a s t d e c a d e has c a u s e d a n enormous i n c r e a s e i n b o t h t h e number and l e n g t h o f t r a n s m i s s i o n and d i s t r i b u t i o n l i n e s . . From a c o m p a r a t i v e l y u n i m p o r t a n t d e t a i l - - o f l i t t l e i n t e r e s t e v e n t o t h e o w n e r - - t h e power l i n e s have d e v e l o p e d i n t o q u i t e p r e t e n t i o u s systems whose r e l a t i o n t o o t h e r I n d u s t r i e s and t o t h e p u b l i c must be t a k e n I n t o c o n s i d e r a t i o n . The o c c a s i o n a l t r a n s m i s s i o n systems d e s i g n e d f o r 11,000 v o l t s and c o n s i s t i n g o f wood p o l e l i n e s w i t h spans o f 120 f t . have d e v e l o p e d i n t o 250,000 v o l t l i n e s on s t e e l t o v e r s w i t h spans from 500 t o 800 f t . l o n g , w h i l e the l i g h t wooden p o l e s s u p p o r t i n g a few s t r e e t l i g h t i n g c i r c u i t s have b e e n s u p e r s e d e d i n some c a s e s by v e r y heavy t r u n k l i n e s o f many c a b l e s . As I s t o be e x p e c t e d i n a g r o w i n g i n d u s t r y , no s e t o f s t a n d a r d s has b e e n u n i v e r s a l l y a d o p t e d . M o r e -o v e r , i t i s I m p o s s i b l e t o a p p l y any one s p e c i f i c a t i o n or s t a n d a r d o f c o n s t r u c t i o n u n i v e r s a l l y , u n l e s s s u c h a s t a n -d a r d has some e l a s t i c i t y and i s i n t e r p r e t e d and e n f o r c e d i n t e l l i g e n t l y . I n any a t t e m p t a t s t a n d a r d i z a t i o n , e i t h e r f o r one o p e r a t i n g company o r i n a n a t i o n a l s p e c i -f i c a t i o n , i t i s n e c e s s a r y t o c o n s i d e r c a r e f u l l y t h e c o s t and t h e o p e r a t i n g p r o b l e m s i n v o l v e d i n t h e a d o p t i o n o f any g e n e r a l m e c h a n i c a l r e q u i r e m e n t s . An a p p a r e n t l y h a r m l e s s r e q u i r e m e n t may become a v e r y s e r i o u s m a t t e r i f a p p l i e d t o a l l f u t u r e c o n s t r u c t i o n . E l e c t r i e a l l e n g i n e e r i n g d e s i g n has t h r e e n e c e s s a r y c o m p o n e n t s , i . e . e l e c t r i c a l d e s i g n , s t r u c t u r a l d e s i g n and e c o n o m i c a l d e s i g n . They a r e e q u a l l y i m p o r t a n t a n d no e l e c t r i c a l e n g i n e e r i n g p r o b l e m c a n be s o l v e d p r o p e r l y v l t h o u t c o n s i d e r a t i o n o f a l l t h r e e components i n a t h o r -ough m a n n e r . The s o l u t i o n o f any" p r o b l e m w i l l come n e a r e s t t o p e r f e c t i o n as e a c h o f t h e s e forms o f d e s i g n i s more s o u n d l y a n a l y s e d and t h e c o m b i n a t i o n o f t h e t h r e e more I n t e l l i g e n t l y a p p l i e d . S t r u c t u r a l d e s i g n c a l l s f o r t h e s t u d y o f m a t e r i a l s u s e d and t h e i r c o m b i n a t i o n i n t o t h e d e s i r e d s t r u c t u r e s V i n s u c h a way t h a t p r o p e r f a c t o r s o f s a f e t y may be o b -t a i n e d . E l e c t r i c a l d e s i g n c a l l s f o r a knowledge o f e l e c t r i c a l phenomena and t h e a p p l i c a t i o n o f t h i s know-l e d g e t o a c h i e v i n g r e s u l t s s a t i s f a c t o r y from an o p e r a t i n g s t a n d p o i n t . E c o n o m i c a l d e s i g n c a l l s f o r t h e knowledge o f c o s t s and t h e i r a p p l i c a t i o n t o t h e d e t e r m i n a t i o n o f t h e most e c o n o m i c a l d e s i g n p o s s i b l e . I t i s e v i d e n t t h a t t h e r e must be o v e r l a p p i n g between t h e s e t h r e e f i e l d s . S t r u c t u r a l d e s i g n depends i n most c a s e s on t h e s i z e o f e l e c t r i c a l a p p a r a t u s , c o n d u c t o r s , e t c . , w h i c h i n t u r n i s g o v e r n e d b y t h e e l e c t r i c a l d e s i g n . B o t h s t r u c t u r a l a n d e l e c t r i c a l f e a t u r e s , on t h e o t h e r h a n d , s h o u l d be p l a n n e d w i t h a v i e w t o w a r d economy. Where t h e r e i s a c h o i c e o f more t h a n one p o s s i b l e d e s i g n w h i c h i s s a t i s -f a c t o r y from a s t r u c t u r a l and an e l e c t r i c a l s t a n d p o i n t , t h e d e c i s i o n s h o u l d be b a s e d on s t u d y o f t h e r e l a t i v e economy o f a l l t h e a l t e r n a t i v e s c o n s i d e r e d . I t i s p r o p o s e d i n t h i s t r e a t i s e t o c o n s i d e r e l e c t r i c a l t r a n s -m i s s i o n a n d d i s t r i b u t i o n from t h e s t a n d p o i n t o f economy p r i n c i p a l l y . T h e r e I s no i n t e n t i o n however o f m i n i m i z i n g t h e I m p o r t a n c e o f s t r u c t u r a l and e l e c t r i c a l d e s i g n . E c o n o m i c a l d e s i g n has p r o b a b l y r e c e i v e d l e s s a t t e n t i o n t h a n t h e two o t h e r forms and t h e e m p h a s i s b r o u g h t on I t h e r e may h e l p t o g i v e I t i t s p r o p e r p l a c e i n the work o f o b t a i n i n g c o r r e c t s o l u t i o n s t o e l e c t r i c a l t r a n s -m i s s i o n and d i s t r i b u t i o n p r o b l e m s . T r e a t i s e s I n g e n e r a l may be d i v i d e d i n t o two c l a s s e s . The f i r s t c l a s s g i v e s f a c t s and d a t a o b t a i n e d from p r a c t i c a l e x p e r i e n c e . The s e c o n d c l a s s g i v e s methods and s u g g e s t i o n s o f means o f a t t a c k i n g t h e s t u d y o f c e r t a i n p r o b l e m s . T h i s t r e a t i s e b e l o n g s t o t h e s e c o n d c l a s s . I n work w i t h d i s t r i b u t i o n systems t h e c o n d i t i o n s met w i t h i n d i f f e r e n t l o c a l i t i e s a r e d i v e r s e . C o s t s o f m a t e r i a l a n d l a b o r and methods o f c o n s t r u c t i o n and o p e r a t i o n a r e v a r i e d a n d c h a n g e a b l e . I t f o l l o w s . t h a t i f d e f i n i t e f i g u r e s and r e s u l t s a r e g i v e n w h i c h m i g h t a p p l y t o one system a t one p a r t i c u l a r t i m e , t h e s e same f i g u r e s m i g h t be v e r y m i s l e a d i n g i f a p p l i e d i n d i s c r i m i n a t e l y to any o t h e r l o c a l i t y , system o r p e r i o d o f t i m e . I t i s n e c e s s - . a r y , t h e r e f o r e , t h a t any f i g u r e s g i v e n h e r e , p a r t i c u l a r l y t h o s e r e f e r r i n g t o c o s t s , s h o u l d be c o n s i d e r e d o n l y a s , e x a m p l e s o f t h e methods p r e s e n t e d and n o t a s m a t e r i a l on w h i c h t o b a s e any c a l c u l a t i o n s . F u r t h e r m o r e , t h e r e i s no I n d e n t i o n t o c o v e r f u l l y e i t h e r i n d e t a i l , o r i n a g e n e r a l d e s c r i p t i v e manner a l l V I the p r o b l e m s , w h i c h m i g h t be e n c o u n t e r e d i n e l e c t r i c a l t r a n s m i s s i o n and d i s t r i b u t i o n , v i e w e d from the economic s t a n d p o i n t . . I t i s d e s i r e d t o p r e s e n t some g e n e r a l methods t h a t c a n be a p p l i e d t o the s o l u t i o n o f most o f t h e s e p r o b l e m s , t o g i v e examples o f the a p p l i c a t i o n o f t h e s e p r i n c i p l e s to some o r d i n a r y c a s e s , a n d to i n d i c a t e the t y p e s o f q u e s t i o n s most o f t e n a r i s i n g i n t h i s w o r k . The t h e s i s i s made up o f two p a r t s * The f i r s t p a r t I n c l u d i n g C h a p t e r s I t o V I i s i n t e n d e d to g i v e w o r k i n g methods, o r i n o t h e r w o r d s , to f u r n i s h the t o o l s t o be u s e d i n s o l v i n g e l e c t r i c a l t r a n s m i s s i o n a n d d i s t r i b u t i o n p r o b l e m s e c o n o m i c a l l y . The a u t h o r has t r i e d to p r e s e n t the u n d e r l y i n g p r i n c i p l e s w h i c h a r e the b a s i s o f an economic s t u d y o f t h i s k i n d . The f u n d a m e n t a l s a r e n o t new b u t t h e i r a p p l i c a t i o n to the d e s i g n o f t r a n s m i s s i o n a n d d i s t r i b u t i o n systems i s n o t so g e n e r a l l y u n d e r s t o o d , , The u s e o f a c c u r a t e a n n u a l c o s t s I n s t e a d o f f i r s t c o s t s ( c r l o o s e e s t i m a t e s ) as a b a s i s f o r d e t e r m i n i n g the most e c o n o m i c a l i n s t a l l a t i o n goes b a c k to L o r d K e l v i n and f u r t h e r , B u t many e n g i n e e r s t o d a y i g n o r e the e c o n o m i c a l f a c t o r s o f the p r o b l e m e n t i r e l y w h i l e o t h e r s b a s e a l l c o m p a r i s o n s on f i r s t c o s t o n l y , o r a t t e m p t t o a p p l y the s o - c a l l e d K e l v i n ' s Law i n d l s c r i m i n a t e l y » A know-l e d g e o f the f u n d a m e n t a l s i s a b s o l u t e l y e s s e n t i a l i f any such s t u d y i s t o be w o r t h the t i m e s p e n t upon 1 to O t h e r -w i s e the e n g i n e e r may be g u i l t y o f d e l u d i n g h i m s e l f a n d o t h e r s w i t h f i g u r e s w h i c h a r e e n t i r e l y i n a p p l i c a b l e to the c a s e I n h a n d * The f i r s t c h a p t e r i s an a p p r o a c h to a p o i n t o f v i e w r e g a r d i n g the s u b j e c t a t h a n d . T h e n i n s u c c e s s i o n a r e t a k e n up means o f a n a l y z i n g a n d t a b u l a t i n g c o s t s o f m a t e r i a l and l a b o r , o f d e t e r m i n i n g the c o s t o f e n e r g y to be u s e d u n d e r v a r i o u s c o n d i t i o n s , o f s t u d y i n g the c h a r a c t e r i s t i c s o f l o a d s t o be h a n d l e d , a n d of" f o r m i n g g e n e r a l e q u a t i o n s f o r s o l v i n g p r o b l e m s i n e c o n o m i c a l d e s i g n . F i n a l l y a c h a p t e r on power l o s s and v o l t a g e d r o p i s i n c l u d e d to p r o v i d e c o n -v e n i e n t means o f h a n d l i n g t h e s e most I m p o r t a n t e l e c t r i c a l phenomena w h i c h must a l w a y s be c o n s i d e r e d i n c o n n e c t i o n w i t h e c o n o m i c a l d e s i g n s The s e c o n d p a r t o f the t h e s i s c o n s i s t s i n p r e s e n t i n g t h e a p p l i c a t i o n o f the m e t h o d s , o r the use o f the t o o l s d e s c r i b e d i n the f i r s t p a r t . F o r c o n v e n i e n c e a d i v i s i o n o f the s u b j e c t has b e e n made i n t o t r a n s m i s s i o n l i n e s , power c i r c u i t s , l i g h t i n g c i r c u i t s , s e c o n d a r i e s and u n d e r -g r o u n d l i n e s „ U n d e r e a c h h e a d i n g some o f the g e n e r a l V I I p r o b l e m s e n c o u n t e r e d , a r e I n d i c a t e d and some p a r t i c u l a r p r o b l e m s a r e s o l v e d i n d e t a i l as d e f i n i t e examples,. S p e c i a l o r u n u s u a l p r o b l e m s have n o t b e e n c o n s i d e r e d ; the work f o r the most p a r t d e a l s w i t h the p r o b l e m s o f . d a l l y p r a c t i c e . C h a p t e r XIV I n c o n c l u s i o n , t o u c h e s on a few o f the g e n e r a l p r o b l e m s w h i c h a p p l y to the system as a w h o l e , s u c h as the l o c a t i o n o f the g e n e r a t i n g s t a t i o n a n d s u b s t a t i o n s , the r e l a t i o n o f one p a r t o f the system to the r e m a i n d e r , e t c . I t w i l l be seen t h a t the p o s s i b i l i t i e s f o r s t u d y i n t h e f i e l d o f d i s t r i b u t i o n e c o n o m i c s a r e b o u n d l e s s . The d e e p e r one goes i n t o the s u b j e c t the more p r o b l e m s p r e s e n t t h e m s e l v e s a n d the more e v i d e n t becomes the n e e d f o r c a r e f u l and a c c u r a t e I n v e s t i g a t i o n . The o b j e c t i o n may be r a i s e d t h a t the c h a n g e a b l e c h a r a c t e r o f the l o a d s c a r r i e d , a n d t h e f l u c t -u a t i o n s , o f p r i c e s make a t o o d e t a i l e d study o f e c o n o m i e s i m p r a c t i c a b l e a T h a t i s no d o u b t t r u e s o m e t i m e s , as r e g a r d s i n d i v i d u a l p r o b l e m s . I n the l o n g r u n , however, the knowledge g a i n e d i s a l w a y s v a l u a b l e a n d o f g r e a t a s s i s t a n c e i n d e c i d i n g g e n e r a l p o l i c i e s . As our i n f o r m a t i o n on the b e h a v i o r o f m a t e r i a l s and on the c h a r a c t e r i s t i c s o f the v a r i o u s t y p e s o f l o a d s becomes more a c c u r a t e , , the p r a c t i c a b i l i t y o f the a p p l i c a t i o n o f d e -t a i l e d e c o n o m i e s w i l l i n c r e a s e . W i t h t h e i n c r e a s i n g demand f o r e f f i c i e n c y and economy i n a l l l i n e s o f e n d e a v o r , the n e c e s s i t y f o r the e c o n o m i c a l o p e r a t i o n - o f t r a n s m i s s i o n a n d d i s t r i b u t i o n systems becomes more i m p e r a t i v e <. I n any c a s e , an e x a c t knowledge o f the t r u e c o s t w i l l a l w a y s l e a d t o e f f o r t s t o r e d u c e t h a t c o s t I f p o s s i b l e . , V I I I THE ECONOMICS of. . TRANSMISSION AND DISTRIBUTION • • • ''-""Of •. •• E L E C T R I C A L ENERGY • PART ; I CHAPTER I *y/f: . APPLICATION OE ENGINEERING ECONOMICS TO  TRANSMISSION AND DISTRIBUTION PROBLEMS-As s t a t e d I n the I n t r o d u c t i o n , the p u r p o s e o f t h i s t h e s i s I s t o p r e s e n t some o f t h e p r o b l e m s e n c o u n t e r e d i n t h e d e s i g n o f l i n e s f o r t r a n s m i t t i n g e l e c t r i c a l e n e r g y and to a p p r o a c h t h e i r s o l u t i o n from an economic p o i n t o f v i e w . More s p e c i f i c a l l y i t Is p u r p o s e d to a p p l y e n g i n -e e r i n g e c o n o m i c s to t r a n s m i s s i o n - a n d d i s t r i b u t i o n - l i n e l a y o u t s i n d i c a t i n g how t h e most e c o n o m i c a l i n s t a l l a t i o n c o n s i s t e n t w i t h g o o d s e r v i c e c a n be d e t e r m i n e d . A t : t h e o u t s e t i t i s o b v i o u s t h a t the a p p l i c a t i o n o f economic p r i n c i p l e s to the p r o b l e m s o f e n g i n e e r i n g d e s i g n i s n o t o n l y a d v a n t a g e o u s b u t a l s o n e c e s s a r y i n t h e m a j o r i t y o f e a s e s * E n g i n e e r i n g s h o u l d make f o r e f f i c i e n c y b u t t h e r e c a n be no r e a l e f f i c i e n c y u n l e s s t h e r e a l s o I s a c c o m p l i s h e d economy, l . e » a maximum o f c o m m e r c i a l e f f i c i e n c y . Economy c a n n o t o f t e n be r e c o g n i z e d a t f i r s t g l a n c e . A w o r k i n g knowledge o f i t s f u n d a m e n t a l s a t l e a s t i s r e q u i r e d . E n g i n e e r i n g and e n g i n e e r i n g e c o n o m i c s a r e t h e r e f o r e synonymous i n a l l p r o b l e m s d i r e c t l y I n v o l v e d i n . the p r o d u c t i o n o r d i s t r i b u t i o n o f a c o m m e r c i a l c o m m o d i t y . T h i s i n c l u d e s t h e g r e a t m a j o r i t y o f our p r e s e n t e v e r y d a y e n g i n e e r i n g p r o b l e m s and n a t u r a l l y t h o s e o f t r a n s m i s s i o n and d i s t r i b u t i o n . . I t I-s n o t w i t h i n the scope o f t h i s t h e s i s to c o n s i d e r u n u s u a l p r o b l e m s s u c h as v e r y h i g h - v o l t a g e t r a n s m i s s i o n s f o r e x a m p l e , o r I n s t a l l a t i o n s o f s p e c i a l a p p a r a t u s whose use has n o t become a m a t t e r o f a c c e p t e d p r a c t i c e . R a t h e r , the g e n e r a l p u r p o s e w i l l be to make a few a n a l y s e s t h a t w i l l i n d i c a t e methods o f f i n d i n g the most e c o n o m i c a l d e s i g n u n d e r u s u a l c o n d i t i o n s w i t h m a t e r i a l o f known c h a r a c t e r i s t i c s and a t known p r i c e s . I t I F e s p e c i a l l y f o r the Improvement o f the d e s i g n o f the l a r g e c l a s s o f e v e r y d a y j o b s t h a t t h i s t r e a t i s e i s d e v e l o p e d . S u c h a n a l y s e s w i l l , n a t u r a l l y , n o t o n l y i n d i c a t e the most e c o n o m i c a l I n s t a l l a t i o n w i t h m a t e r i a l s a n d c o n s t r u c t i o n methods already i n use but w i l l make i t , p o s s i b l e to de-termine -"here any economy can be e f f e c t e d by changes i n t h e s e methods or m a t e r i a l s . T t must be recognized t h a t the major! 'y of the t r a n s m i s s i o n and. d i s t r i b u t i o n l i n e s have been l a i d out b y rule-of-thumb method, and by d u p l i c a t i o n of e x i s t i n g designs to new problems, w i t h no d e f i n i t e c o n c e p t i o n of a c t u a l c o s t s per u n i t of to.-a, t r a n s m i t t e d or d i s t r i b u t e d , or t h e economy e f f i c i e n c i e s . The laetho&F here p r e s e n t e d have- been developed by the studjr o f a c t u a l p r o b l e m s encountered i n p r a c t i c e . I t i s hoped t h a t these methodR w i l l on t h e one hand show the magnitude of the F-svingo p o s s i b l e by the use of engi n e e r i n g economics and on the other hand be simple enough In t h e i r a p p l i c a t i o n t o be considered w o r t h u s i n g i n many p l a c e s where empir-l e a l , methods. a r e used today. HETHOD OF TREATMENT P r a c t i c a l l y a l l such p r o b l e m s of engineering, d e s i g n r e q u i r e t r e a t m e n t i n three d i s t i n c t stager- f o r a c o m p l e t e s o l u t i o n . At. f i r s t a l l the data must be obtained t h a t can.be determined ""'1th e v a c t n e B R. Such elements as mater-i a l c o p t p , s t r e n g t h of p a r t s of c o n s t r u c t i o n , load t e n t s , e t c . , are here i n c l u d e d * S e c o n d , t h o s e elements which a r e not subject to exact measurement or computation rrust be decided, upon. These are u s u a l l y s development from p r a c t i c a l experience over a number of years and are o f t e n as t t e r r of a c c e p t e d standard o r s . c t . i c e * They are •such items as probable i n c r e a s e i n l o a d , a l l o w a b l e v o l t s g e r e g u l a t i o n , p a f e t y f a c t o r * ? , standardo of c o n -s t r u c t i o n , e t c . E m p i r i c a l methods must h e r e be e m p l o y e d I n t e l l i g e n t l y . The t h i r d element i s t h e most i n t a n g i b l e — the good judgment of the engineer b a s e d on h i s knowledge and experience and a p p l i e d t o the p a r t i c u l a r ' p r o b l e m i n hand to GO u t i l i s e the f i r s t two elements a? to c r e o t e an e f f i c i e n t and economical de s i g n best adapted t o the s i t u a t i o n . A l l thes?e e l e m e n t s i n LtheIT proper p r e p a r a t i o n s arc ecmally important In a t t a i n i n g t h e mopt s a t i s f a c t o r y s o l u t i o n f o r any problem. E m p i r i c a l methods i f 'applied b l i n d l y may l e a d f a r away from the purpose f o r which they were o r i g i n a l l y i n t e n d e d . Judgment based on e x -p e r i e n c e a l o n e i s l i a b l e t o become a mere guess u n l e s s supported by exact knowledge and good p r a c t i c e s I t would appear t h e r e f o r e , t h a t the f u r t h e r the exact data can be c e r r i e d I n a problem, t h e l e s s dependence need be placed on t h e more i n t a n g i b l e " elementG and h e n c e the g r e a t e r 3 c e r t a i n t y of t h e beat, s o l u t i o n . The exte n s i o n of t h i s exact knowledge I s the c h i e f purpose of the study o f the economic f e a t u r e s o f a problem. I n many casec-economy may be made t h e d e c i d i n g f a c t o r between two or more designs apparently e q u a l l y good from other p o i n t s o f ..view. EXACT DATA. - -For any g i v e n By stem t h e r e are a number of l i m i t i n g c o n d i t i o n s which reduce the unknown f a c t o r s i n the d e s i g n . There are c e r t a i n standards such as t r a n s -f o r m e r p'lsen, wire and cable sizes,, e t c . , which are e s t a b l i s h e d by the manufacturer* Other l i m i t a t i o n s are e s t a b l i s h e d by the accepted, good, p r a c t i c e of the p r o f e s s i o n I n g e n e r a l . A l s o each company has c e r t a i n standards of m a t e r i a l s and c o n s t r u c t i o n to which i t I s wise to adhere u n l e s s there I R E c l e a r advantage I n making a change. The- most complete I n f o r m a t i o n o b t a i n a b l e on a l l such .-da-ta' r e l a t i n g to the p a r t i c u l a r syetem i n hand, should be kept a v a i l a b l e f o r r e a d y r e f e r e n c e . The e y e t e a e l e c t r i c a l o p e r a t i n g c h a r a c t e r i s t i c s must foe c l e a r l y understood and d e f i n e d . A l s o o t h e r items which can be obtained ex-a c t l y f o r only t h e one l o c a l i t y or company such c.s c o s t s of m a t e r i a l s l a b o r and energy should be determined as a c c u r a t e l y as p o s s i b l e and be r e v i s e d from time to time t o conform t o changing p r i c e s , rage s c a l e s and coe s o f p r o d u c t i o n . T h i s I n f o r m a t i o n can be r e a d i l y k e p t up t o date and t a b u l a t e d or drawn up i n curves. Then o n l y such f a c t o r s s»s a r e inherent t o t h e p a r t i c u l a r l i n e i t s e l f need be determined i n making the design* EMPIRICAL DATA.--Some of the e m p i r i c a l elements of the prob-lem of t r a n s m i s s i o n and d i s t r i b u t i o n of energy are worthy of c o n s i d e r a b l e a t t e n t i o n . ' One of these I s -the element of "good s e r v i c e . " I t i s understood t h a t i n any desig n or l a y o u t the g r e a t e s t economy " c o n s i s t e n t w i t h good service' 8 I s the o b j e c t . J u s t what i s good s e r v i c e may be a matter of c o n s i d e r a b l e q u e s t i o n . Good S e r v i c e .-«&ood s e r v i c e In n o t d e p e n d e n t on t h e i d e a s of the engineer or the " s e r v e r " as t o what I t should be." S e r v i c e I s good when I t s a t i s f i e s the one t h a t i s served." That man who a* the r e c e i p t of h i s b i l l f e e l s t h a t he has g o t t e n a l l t h a t was due him i s r e c e i v i n g good.service* He. i s w i l l i n g to. exchange M s money, f o r what he has r e c e i v e d from the s e r v e r . The humeri element I s t h e r e f o r e the most important one i n determining good s e r v i c e . Customers w i l l expect as good or- b e t t e r o p e r a t i n g c o n d i t i o n s ? t h a n they have been I n the habit of g e t t i n g . Companies have, so t o speak, educated t h e i r p u b l i c t o c e r t a i n , ebcpec t a t lone and they must' l i v e up to- such- e x p e c t a t i o n s . '--it I P evident- however th a t i t i s Impossible t o e l i m i n a t e a l l i n t e r r u p t i o n s or* c o n d i t i o n s of poor r e g u l a t i o n . I n t h i c k l y populated d i s t r i c t p. w i t h a h i g h - l o a d d e n s i t y , p r a c t i c a l l y continuous s e r v i c e at good v o l t a g e i s e a s i l y g i v e n . In o u t l y i n g , s c a t t e r e d d i s t r i c t s the c o s t of the .same' d u a l i t y o f s e r v i c e would be p r o h i b i t i v e . From the c o m p a n y ' s p o i n t of view t h e s e r -v i c e s u s t be of good enough q u a l i t y to i n s u r e e a r n i n g s s u f f i c i e n t t o g i v e an adequate r e t u r n OR the investment necessary t o serve. I t i e t h e r e f o r e n e c e s s a r y , b e f o r e attempting t o s o l v e a t r a n s m i s s i o n or d i s t r i b u t i o n prob« lera e c o n o m i c a l l y , t o a s c e r t a i n what q u a l i t y of s e r v i c e i s r e q u i r e d both from the customer's and the company's p o i n t o f view. - . • • . Good s e r v i c e can t h e r e f o r e only be determined i n a g e n e r a l way and w l l T n r s r y w i t h l o c a l i t y , company, k i n d of l o a d , e t c * I t m i g h t be s a i d , .however, t h a t w i t h the modern refinement of methods and equipment and the n e a r l y u n i v e r s a l h i g h requirement of the customer- we are approach-i n g more and more a c o n d i t i o n when wide v a r i a t i o n of vo3.ta.ge and long or frequent i n t e r r u p t i o n s ^111 h a r d l y be p e r m i s s i b l e . Increase i n Load.--A second c u a n t i t y which must be e m p i r i c a l l y determined I F that of load I n c r e a s e . The v a r i a t i o n of the loads t o be c a r r i e d and the growth of energy demand t h a t I P p r e v a l e n t i n n e a r l y a l l l o c a l i t i e s are always mattern f o r c o n s i d e r a b l e study i n connection w i t h a l a y o u t . There are some capes where i t i e p o s s i b l e to design f o r a c e r t a i n demand t h a t can be asrumed t o remain constant f o r a p e r i o d o f y e a r s , p o s s i b l y f o r the l i f e of some p a r t of the equipment. S u c h would be the case i n plarrn'ng l i n e s t o a l a r g e power i n s t e 1 1 a tion where g r o w t h - c o u l d be t a k e n care of b y new c i r c u i t s . On the other hand such load as house l i g h t i n g i n c r e a s e s con-t i n o u s l y and i t s i n c r e a s e can only be estimated from the f i g u r e s f o r the p a r t fe*' years" and g e n e r a l business conditions.. I n any case we must design f o r a system t h a t w i l l be most economical over i t ? u s e f u l l i f e , i n other words when the sum o f the annual c o s t s f o r a l l years under con-s i d e r a t i o n , w i l l be a minimum. I t i s f u r t h e r necessary to study as e x a c t l y as p o s s i b l e the number of years;, to be c a r e d f o r by the present design and minor changes that can be made at v a r i o u s times during, t k a t p e r i o d f o r - t a k i n g care of the- changes i n l o a d . G e n e r a l l y the design should cover the expected l i f e o f t h a i part of the e a ulna-ant whose l i f e -it* the s h o r t e s t and which would r e q u i r e l?.Tge ©spend-i t u r e f o r I t s replacement. Any conpiderehle change necessary t o care f o r Isr-ger load could then be made at the same time r i t h r e l a t i v e l y s m e l l e r cost<• I n some cases, h o r e v e r , where the probable i n c r e a s e i n load i s more d e f i n -i t e l y known, the economical l i f e of the oresent d e s i g n can be a c c u r a t e l y determined even r e l l w i t h i n the expected l i f e of e l l the important p a r t s . F i n a n c i a l Condit.ions.**-The c o n d i t i o n of t h e money market may be another determining f a c t o r I n an economical d e s i g n . O f t e n the d i f f i c u l t y i n s e c u r i n g necessary funds f o r a job may r e q u i r e the engineer to spend l e s s at the time of i n s t a l l a t i o n than i s c o n s i s t e n t w i t h economy over the p e r i o d the design c o v e r s . However the c o n d i t i o n should be c a r e f u l l y considered i n order t o s t i l l o b t s i n the best d e s i g n as l i m i t e d by the money a v a i l a b l e . Re 1st i o n of P a r t s t o f n o l e System.--The f a c t that the t r a n s m i s s i o n or d i s t r i b u t i o n l i n e i s only one part of the system transmi' t i n g energy from the pov/er pl'-nt to the customer must be kept In mind. I t s desi g n w i l l a f f e c t and be a f f e c t e d by e x i s t i n g or planned c o n d i t i o n s I n the other p a r t e . I t i s t h e r e f o r e a r r a y s n e c e s s a r y t o t r e a t a l i n e not o n l y ap sn Independent u n i t f o r some s o e c i f i c purpose b u t a l s o as a working part of the r h o l e system. B e a r i n g i n mind the g e n e r a l c o n s i d e r a t i o n s brought out above, the o u t l i n e g i v e n belo*- w i l l show the most im-portant riointe to c o n s i d e r I n studying the layout of an economical l i n e . The f o l l o w i n g chapters r i l l d i s c u s s I n more d e t a i l the methods of o b t a i n i n g t h i s data and I t s a p p l i -c a t i o n to p a r t i c u l a r c l s s s e s of problems such as t r a n s -m i s s i o n l i n e s , porer l i n e s , secondaries, e t c . A. Load. L o c a t i o n . • Present s i z e . Probable i n c r e a s e ana r a t e of. i n c r e a s e . . . - C h a r a c t e r i s t i c s : : . 1 - Phase requirements. 2 . Power f a c t o r * 3* V a r i a t i o n , d a i l y , weekly, seasonal,, etc and r e l a t i o n t o stat 1 on v a r i a t i o n s and peak.- D i v e r s i t y . A , Unbalance f a c t o r . 5» Maximum demand, approximate time.of day 6. Load F a c t o r i B* Route of l i n e . I n v e s t i g a t i o n of a d v i s a b i l i t y of p o s s i b l e r o u t e s , a f f e c t e d by: 1. A v a i l a b l e pole or duct ,«pace. 2. Pur-chase .of rip.ht«of-vay . - l i m i t a t i o n s imposed. 3 « M f f l c u l t l e r I n c o n s t r u c t i o n . 4. I n t e r f e r e n c e r i t h or from other l i n e s , • p h y s i c a l l y o r - e l e c t r i c a l l y - . -5« Convenience of o p e r a t i o n . P o s s i b l e f u t u r e e x t e n s i o n s . 7- E f f e c t on system as a whole. 8. Ooprb: Co compered w i t h other p o s s i b l e r o u t e s '* ' P h y s i c a l c o n s t a n t s . - ;! Length of l i n e Spacing' V o l t a g e : d e s i r e d , a v a i l a b l e .-R e s i s t a n c e of l i n e . Reactance Voltage drop R e g u l a t i o n : d e s i r e d , a v a i l a b l e . Under v a r i o u s l i n e c o n d i t i o n s as :- l i m i t e d •  • 1. By good o p e r a t i o n . 2. By standard p r a c t i c e . 3- Ey r o u t i n g * 4. By economical c o n s i d e r a t i o n s . 5« By good, s e r v i c e . F o r a l l c o n d i t i o n s c o n s i d e r e d I). C o s t s . 1. Determination of l a b o r c o s t s , :.- ; m a t e r i a l c o s t s , and , ... energy l o s e c o s t s 2. A p p l i c a t i o n of those c o s t s to determine the best l i n e f o r the purpose-. E. R e l a t i o n to System. General c o n s i d e r a t i o n s t h a t may a f f e c t most economical l i n e found above under (D) due to i t s being a p a r t of e. large•system. F i n a n c i a l c o n s i d e r a t i o n e . From ah I n s p e c t i o n of t h i s o u t l i n e I t i s seen t h a t the f i v e d l i s i o n s i n i t are i n one *?ay or another interdependent, so t h a t each one must be considered In r e l a t i o n to a l l the o t h e r s . I t i s only by a c a r e f u l study of the problem from a l l angles and c o o r d i n a t i o n of r e s u l t s t h a t a s a t i s f a c t o r y s o l u t i o n can be o b t a i n e d . I n t h i s t h e s i s , however, the economic f e a t u r e s of the d e s i g n have been emphasized-rather than the mechanical or e c t r i c a l . These l a t t e r have been covered q u i t e thoroughly i n other •works. . ' 7 - . CHAPTER-II COSTS P r i n c i p l e s U n d e r l y i n g the Determination of True Costs-*. Formulas f o r U n i t Labor Costs--Cost Records—• Annual Costs The fundamental b a s i s u n d e r l y i n g the whole q u e s t i o n of economic design Is the accurate d e t e r m i n a t i o n of c o s t s , i . e . , c o s t s of c o n s t r u c t i o n and c o s t of energy. These c o s t s are obtained, (1) from accounting records as com-p i l e d i n an accepted standard c l a s s i f i c a t i o n of accounts as s p e c i f i e d by a recognised a u t h o r i t y or i n s t i t u t i o n ; or (2) from a reasonable estimate based on a c t u a l p r a c t i c a l experience. I f these c o s t s are not c o r r e c t l y determined any c o n c l u s i o n s drawn from t h e i r use w i l l have l i t t l e v a l u e * F u r t h e r i t i s g e n e r a l l y I n a d v i s a b l e to accept f o r t h i s puli|>of-s% any c o s t data which have n o t been l o c a l l y d e r i v e d , as every power company has i t s own methods and standards of con-s t r u c t i o n , i t s ; o w n l a b o r c o s t s , i t s own c o e f f i c i e n t of e f f i c i e n c y . Wide d i f f e r e n c e s are p o s s i b l e i n these. Hence, I t i s a b s o l u t e l y necessary to make as complete a d e t e r m i n a t i o n of l o c a l c o s t s as p o s s i b l e as a b a s i s f o r any economic study. E v i d e n t l y when i t i s decided to e s t a b l i s h a cost r e c o r d on c o n s t r u c t i o n , m a t e r i a l and l a b o r , d i f f i c u l t i e s w i l l be encountered i n o b t a i n i n g c o r r e c t i n f o r m a t i o n r e g a r d i n g a l l d e t s i l s o Much v a l u a b l e I n f o r m a t i o n w i l l be found i n a p p r a i s -a l s and wttglKKM from the accounting records by a s k i l l f u l economlstT However, i n most cases i t w i l l take s e v e r a l years to e s t a b l i s h a complete r e c o r d and s p e c i a l s t u d i e s w i l l be necessary; when obtained, t h i s r e c o r d can e a s i l y be kept up to date and i n convenient form f o r use. I n the meantime c e r t a i n makeshifts w i l l be necessary:. I f a complete r e c o r d of imlt.^ovrntr c o n s t r u c t i o n and o p e r a t i n g c o s t s i s not o b t a i n a b l e o r when l a c k of= time or of a v a i l a b l e records r e q u i r e s any item of c o s t to be estimated, the estimate should be based.on known c o n d i t i o n s as f a r as p o s s i b l e . F u r t h e r , an estimate should be made of the e f f e c t which a reasonable v a r i a t i o n In the computed c o s t w i l l have on the f i n a l r e s u l t and t h i s p r e f e r a b l y In percentage form.. For example, the c o s t of energy a t any p o i n t may be assumed to be 1 cto per k i l o w a t t - h o u r . I t i s an obvious f a c t that the c o s t of energy i s not the same at. any two places i n ,a system due to the v a r i a t i o n s i n investment a t each p o i n t ; and a g a i n ; i n g e n e r a l , no two loads have the .same e l e c t r i c a l c h a r a c t e r i s t i c s ; t h e r e f o r e , the.cost of,energy i s a d i f f e r e n t i a l , i n commercial p r a c t i c e what i s used i s the "system average c o s t " . The a c t u a l determina-t i o n of the c o s t elements.that enter i n t o the t o t a l c o s t s , and 8 : p a r t i c u l a r l y ; the theory as t o whether the item of " i n t e r e s t , ! i s a c o s t item, or not, are not w i t h i n the province of t h i s •treatiseo • I f the c o s t of energy Is not an a c c u r a t e l y d e t e r -mined f i g u r e however., i t would be well--to• a s c e r t a i n how the r e s u l t would be a f f e c t e d i f the cost of energy were say •§ ct» or I f c t s . per k i l o w a t t - h o u r . Such, a comparison w i l l at l e a s t place the s o l u t i o n of the problem w i t h i n d e f i n i t e l i m i t s . I t i s a g e n e r a l l y r e c o g n i z e d f a c t t h a t the•computation of f i r s t c o s t i s only a step i n the i n v e s t i g a t i o n of the r e a l cost of a p r o p o s i t i o n . The economy i n comparison w i t h any other a l t e r n a t i v e p r o p o s i t i o n can only be determined when the annual c o s t i s i n v e s t i g a t e d . The annual c o s t must i n c l u d e a l l f i x e d charges i»e#, i n t e r e s t , d e p r e c i a t i o n , insurance and t a x e s ; a g a i n s t the Investment i t s e l f and a l l o p e r a t i n g c o s t s , l a b o r , maintenance^.repairetc» 9 Of course annual c o s t s cannot always be c o n s i d e r e d the determining factor,, s i n c e on items I n v o l v i n g l a r g e expenditure the p o s s i b l e d i f f i c u l t y of o b t a i n -i n g c a p i t a l may have c o n s i d e r a b l e weight. U s u a l l y , however, annual c o s t may be accepted as the c r i t e r i o n . Before annual c o s t s on a piece of property such as a t r a n s -m i s s i o n l i n e can be obtained I t i s necessary to determine I t s t o t a l value or f i r s t c o s t . FIRST COST<•»-*The d e t e r m i n a t i o n of c o s t f i g u r e s f o r g e n e r a l use i s g r e a t l y f a c i l i t a t e d i f l i n e c o n s t r u c t i o n , m a t e r i a l s and methods are s t a n d a r d i z e d . This a l l o w s a f a i r l y a ccurate' f i g u r e to be obtained f o r standard u n i t s as per p o l e , or per 1,000 f t * or per mile of l i n e f o r any type of c o n s t r u c t i o n . Otherwise s m a l l e r u n i t s must be depended upon such as per crossarm # per i n s u l a t o r , per 100 f t . of wire^ e t c . I n any case i t w i l l be found exceedingly v a l u a b l e to have as complete a r e c o r d as p o s s i b l e of i t e m i z e d c o s t s from the s m a l l e s t p a r t , such as a b o l t 9 up to an average cost f o r . a l a r g e assembled u n i t such as per m i l e of l i n e * T h i s should i n c l u d e both m a t e r i a l and l a b o r c o s t s w i t h overhead expense a l l shown s e p a r a t e l y . These c o s t s should b e l a b e l e d as of a r e f e r e n c e year such as i s g e n e r a l l y accepted by economists i n t h e i r commodity index tabulations,, This p r a c t i c e makes i t p o s s i b l e f o r estimates on a c t u a l determined c o s t s of c o n s t r u c t i o n to be reasonably compared. This t i e s , i n a l s o w i t h the changing value or purchasing power of the d o l l a r . P r o v i s i o n should, however, be raa made f o r easy r e v i s i o n of c o s t s as p r i c e s change.. T h i s r e v i s i o n should be f r e q u e n t l y made when p r i c e s of l a b o r and m a t e r i a l are f l u c t u a t i n g to any extent s i n c e a l a r g e p a r t of an economic study deals w i t h p o s s i b l e new c o n s t r u c t i o n which r e p r e s e n t s a value equal to new c o n s t r u c t i o n l e s s a d e p r e c i a t i o n percent-age f o r i t s age. C e r t a i n types of problems r e q u i r e the con-s i d e r a t i o n of the a c t u a l c o s t of the o l d c o n s t r u c t i o n at the time i t was" i n s t a l l e d but these are not so g e n e r a l * 9 T h e r e a r e a number o f Items w h i c h must be i n c l u d e d i n a d d i t i o n t o c u r r e n t q u o t a t i o n s on m a t e r i a l o r a c t u a l l a b o r t i m e i n e r e c t i n g . To m a t e r i a l p r i c e may be a d d e d s u c h i t e m s as f r e i g h t , t r e a t i n g m a t e r i a l f o r p o l e s , t i e w i r e s on l i n e , e t c . To a c t u a l u n i t l a b o r c o s t s s h o u l d be added a p r o p o r t i o n a l amount f o r u n o c c u p i e d t i m e , r a i n y d a y s , v a c a t i o n s , t r a n s p o r t a t i o n i n s p e c t i o n , u n f o r e s e e n d e l a y s , e t c . F o r e x a m p l e : No» 2 S o l i d W i r e . Weight i ;'per/; ; * v .'•• ; ^ i n l l e i : >;one -• w i r e , •, .'pounds C o s t a t 21 c t s . .'-'-per-, • • > l b • . i n c l u d ~ i n g „;,'-. f r e i g h t F r e i g h t on ;, re--,,'.-; t u r n e d V •---reels ,-I n j u r y t o r e e l s T i e s p e r m i l e T o t a l p e r m i l e P e r c e n t o f w i r e c o s t 1,066 l b . $223,86 1.86 2.32 3 .63 1231.67 '.; 103.4 N a t u r a l l y t h e s e a d d i t i o n a l i t e m s v a r y f o r e a c h u n i t and e a c h l o c a l i t y . I t i s u s a l l y p o s s i b l e t o o b t a i n a p e r c e n t -age w h i c h may be a d d e d t o a c t u a l p r i c e t o i n c l u d e s u c h i n c i d e n t a l m a t e r i a l . O V E R H E A D . - - T h e i t e m o f o v e r h e a d expense i s one w h i c h must be I n c l u d e d i n n e a r l y a l l p r o b l e m s i n v o l v i n g c o s t s . T h e r e a r e v a r i o u s methods o f a p p l y i n g t h i s l o a d i n g b u t f o r t h e p u r p o s e u n d e r c o n s l d e r a t i n g ' t h e m e t h o d . o f u n i t l o a d i n g i s p r o b a b l y t h e most s a t i s f a c t o r y , i . e . , a p p o r t i o n i n g t o e a c h i n d i v i d u a l i t e m i t s p r o r a t a c o s t f o r d i f f e r e n t i t e m s o f o v e r h e a d e x p e n s e , b o t h on m a t e r i a l a n d l a b o r . I t i s e v i d e n t f o r e x a m p l e , t h a t t h e i t e m o f b r e a k a g e w i l l be g r e a t e r f o r i n s u l a t o r s t h a n f o r w i r e . The i t e m s , w h i c h may l e g i t i m a t e l y be i n c l u d e d i n l o a d i n g and t h e i r p e r c e n t o v e r h e a d a r e as f o l l o w s : C o n s t r u c t i o n C o s t s D i r e c t L a b o u r $ A 1 - M a t e r i a l : . B T o t a l L & M = $> A+ B O m i s s i o n s and C o n t i n g e n c l e s *= 2|-^ ( A + B) S p e c i f i c C o n s t r u c t i o n C o s t s — 1.025(A-*-B) 10 O v e r h e a d . — Minimum Maximum A v e r a g e A d m i n i s t r a t i o n a n d " L e g a l 1% • 2% E n g i n e e r i n g and S u p e r v i s i o n 3 10 '6>5 I n s u r a n c e and Damages ' 1 ' " ". 5 :•. 3 - 0 " T a x e s 1 3 2 , 0 I n t e r e s t ( d u r i n g c o n s t r u c t i o n ) 3 8 5-5 F i n a n c i n g 10 7 . 5 14 : 38 •• 2 6 . 0 T h e s e % f i g u r e s a r e on t h e S p e c i f i c C o n s t r u c t i o n C o s t s . The p e r c e n t a g e t o be a p p l i e d t o any u n i t t o c o v e r any one o f the above i t e m s w i l l depend e n t i r e l y on l o c a l c o n d i t i o n s and no f i g u r e s c o u l d be g i v e n h e r e w h i c h w o u l d be o f any v a l u e . The t o t a l l o a d i n g p e r c e n t a g e i s u s u a l l y between 1 5 & 2 5 p e r c e n t d e p e n d i n g upon t h e c l a s s o f p r o p e r t y and upon l o c a l c o n d i t i o n s . As w i l l be s e e n l a t e r a l l p r o b l e m s ' do n o t r e q u i r e a d e t a i l e d a p p l i c a t i o n o f loading© Many p r o b l e m s i n v o l v i n g t h e com-p a r i s o n o f r e l a t i v e l y s m a l l amounts o f c o n s t r u c t i o n may be s a f e l y c o n s i d e r e d from t h e p o i n t Of a c t u a l m a t e r i a l and l a b o r c o s t s a l o n e , c o n s i d e r i n g o v e r h e a d t o be e q u a l I n b o t h cases-, The q u e s t i o n o f w h e t h e r o r n o t t o a p p l y l o a d i n g must be d e t e r m i n e d by t h e c o n d i t i o n s i n v o l v e d i n t h e p a r t i c u l a r p r o b l e m u n d e r c o n s i d e r a t i o n * I n g e n e r a l where good c o s t r e c o r d s a r e k e p t i t w i l l be j u s t as e a s y and more a c c u r a t e t o i n c l u d e i t I n a l l p r o b l e m s . . L a b o r c o s t s on any u n i t may u s u a l l y be r e d u c e d t o „ a n e q u i v a l e n t f o r m u l a o f man h o u r s f o r v a r i o u s c l a s s e s o f l a b o r as f o r e m a n , l i n e m a n , groundman, e t c . , f o r e a c h u n i t p l u s a p e r -centage" f o r i n c i d e n t a l e x p e n s e s as a b o v e . S u c h f o r m u l a s f a c i l i t a t e r e v i s i o n o f p r i c e s when n e c e s s a r y as t h e c u r r e n t wages may be s u b s t i t u t e d and t h e l a b o r c o s t on t h e u n i t e a s i l y o b t a i n e d * F o r e x a m p l e , i f a gang c o n s i s t i n g o f 1 f o r e m a n , 1 t r u c k , . 1 c h a u f f e u r , 4 l i n e m e n and 3 groundmen c a n s t r i n g 1 . 6 m i l e s o f N o . 0 b a r e s t r a n d e d w i r e p e r d a y t o n a n a v e r a g e , t h e c o s t per m i l e o f w i r e w i l l be . 7 2 8 t i m e s t h e c o s t o f the gang p e r d a y ~ - t h e c o e f f i c i e n t . 7 2 8 i s , e q u a l t o . 6 2 5 + - ±6%% f o r o v e r -head—* . 7 2 8 ( 1 F + IT + ICh + 4 L + 3<3-r) Where t h e symbols r e p r e s e n t t h e d a l l y wage o f t h e v a r i o u s c l a s s e s o f l a b o r I n c l u d e d , f o r e m a n , t r u c k , c h a u f f e u r , l i n e m e n a a d groundmen. Some o f t h e l a b o r f o r m u l a s a r e more c o m p l i c a t e d b u t a l l a r e 1 1 computed on t h e same b a s i s « F o r p o l e s , f o r e x a m p l e , s e v e r a l d i f f e r e n t gangs a r e i n c l u d e d i n t h e l a b o r c h a r g e , I . e . , u n l o a d -i n g , d i s t r i b u t i o n , f r a m i n g a n d r o o f i n g , d i g g i n g h o l e , and s e t t i n g and t h e gangs f o r e a c h o p e r a t i o n may be d i f f e r e n t f o r d i f f e r e n t s i z e s o f p o l e s « A f o r m u l a s i m i l a r t o t h e above may be d e t e r m i n e d f o r e a c h o p e r a t i o n and t h e t o t a l l a b o r f o r m u l a f o r the p o l e I s a c o m p o s i t e o f t h e s e . i f G l r e p r e s e n t s t h e d a l l y c o s t o f t h e u n l o a d i n g gang • • « ( I T r -+- I C h + 3 G r ) , G-2 " « " " •"• t h e d i s t r i b u t i n g gang = ( I T r •+• ICh. •+- 3 G r ) , . G3 " " " " f r a m i n g and r o o f i n g - > ( f L + 2G-r), G4 " " " " " t h e d i g g i n g gang ••- ( 1 / 7 F •+- l / 7 T r + l / 7 C h +- l G r ) , G5 " " " " " t h e s e t t i n g gang • • - ( 5 / 7 F + 5 / 7 T r + 5 / 7 C h -+• 5Gr) (The 1/7F, 5 / 7 T r , e t c . , a r e o c c a s i o n e d by t h e f a c t t h a t one f o r e m a n and one t r u c k s e r v e s e v e r a l gangs a t one t i m e . ) T h e n t h e t o t a l l a b o r c o s t on one 3 5 - f t . p o l e e q u a l s -.0160G-1 .1403G2 '-K.063G3 + ° 2 2 4 3 G 4 . + .0468G5 COST R E C O R D S . - - F o r a c o m p l e t e r e c o r d o f l i n e c o s t s t h e r e a r e n e c e s s a r y t h e f o l l o w i n g i t e m s : (a) C u r r e n t p r i c e s o f m a t e r i a l and l a b o r o f a l l k i n d s . (b) L a b o u r f o r m u l a s and c o n s t a n t m u l t i p l i e r s f o r v a r i o u s c l a s s e s o f m a t e r i a l s w i t h l o a d i n g p e r c e n t a g e s f o r b o t h . (c) C u r r e n t m a t e r i a l a n d l a b o r c o s t s on u n i t s o f c o n s t r u c -t i o n , a s p e r c r o s s a r m , p e r p o l e , p e r l n s u l a t o r , e t c « (d) C u r r e n t c o s t s o n a s s e m b l i e s . A s s e m b l i e s may r a n g e from s m a l l i t e m s s u c h as a c r o s s a r m e r e c t e d w i t h b r a c e s , b o l t s , e t c , o r a g r o u n d c o n n e c t i o n w i t h w i r e , g r o u n d r o d , wood m o u l d i n g , e t c . , up t o l a r g e - i t e m s s u c h as c o s t p e r m i l e o f t r a n s m i s s i o n l i n e on c o s t o f a r a i l -r o a d c r o s s i n g , e t c . Some examples from s u c h a r e c o r d a r e g i v e n i n t h e f o l l o w i n g ' . ; (a) P r i c e s ( a t warehouse)(1) N o . 3 P o r c e l a i n I n s u l a t o r s . . . . . . . . . . . $ . 1 6 e a c h N o . 2 T.B.W .P. w i r e . .2348 p e r l b . P r i m a r y f u s e b o x e s . . 3 «94 e a c h 3 0 - f t . 6 - i n . p o l e , r o u g h . 7 .28 e a c h e t c . (1) (The f i g u r e s g i v e n below must n o t be t a k e n as r e p r e s e n t i n g c u r r e n t p r i c e s . They a r e g i v e n f o r example o n l y « 12 (b) L a b o r f o r m u l a s . W i r e s t r i n g i n g ( s i n g l e w i r e ) Gang = ( I F -+ l T r -+ l C h + 4L +• 3Gr) G ; L a b o r c o s t P l u s 16.55 M i l e s p e r p e r m i l e p e r c e n t day ; w i t h o u t f o r l o a d i n g i l o a d i n g No 0 6 S o l i d 2.8 , • -3575G .4165G Nov 0 S t r a n d e d . . . . . . . . . . . 1.6 : :*S25G .728G G r o u n d c o n n e c t i o n s Gang - ( l T r +' l C h + 3 L + l G r ) - G l a b o r c o s t e a c h w i t h o u t P l u s 18.75 p e r l o a d i n g c e n t 2 3 , 0 0 0 - v o l t g r o u n d c o n n e c t i o n s .02075G .0248G A n c h o r s a n d g u y s Gang = ( 2 / 7 F + 2 / 7 T r +• 2/7Ch + 2 L •*- l G r ) G L a b o r c o s t e a c h w i t h o u t l o a d i n g P o l e t o p o l e one 3 / 8 i n P o l e t o a n c h o r two 3 / 8 i n . . •..... . . . Stub t o a n c h o r one A- i n . .0833G •2833G .25G P l u s 1 7 . 6 5 p e r c e n t f o r l o a d i n g .098G • 3 3 3 3 G .2941G C r o s s a r m s Gang == 1/3F -f- l / 3 T r -*- l / 3 C h L Gr) « G L a b o r c o s t P l u s 1 7 065 p e r e a c h w i t h o u t c e n t f o r l o a d i n g l o a d i n g 2 3 , 0 0 0 - v o l t , s i n g l e - a r m , 36 i n . . 2 3 , 0 0 0 - v o l t , d o u b l e - a r m , 64 i n . . 2 3 , 0 0 0 - v o l t , d o u b l e - a r m , 64 i n - , ( s t r a i n i n s u l a t o r s , b o t h ways) .04G >131G .047G .154G I 1 3 (c) U n i t C o s t s . M a t e -r i a l 3 No.. 6 —S e c o n d a r y , 1,000 f t . . $99 .00 2 N o . ^ - - P r i m a r y , 1,000 f t . . . . 91.40 3 i 4f 9 2 i n . , s i x - p i n .74) c r o s s a r m and h a r d w a r e .54/ N o . 3 p o r c e l a i n i n s u l a t o r . . 16 • P i n — I f - 101/8 1 i n .06 P o l e s — 4 0 f t . 7 i n 16.70 • • • • e t c . _____ P l u s p e r c e n t . l o a d i n g ( 2 1 . 1 5 ) !$ 1 2 0 * 0 0 1 1 0 . 8 0 1.64 (21.80) .21 (26.08) .076 (16.91) 19-50 L a b o r ^ 3 4 . 3 5 2 5 . 4 6 P l u s p e r c e n t l o a d i n g (16.55) $40.00 2 9 .70 (17.65) 1.04 1.22 T o t a l $160.00 140.50 2.86 ^ b o r i n c l u d e d i n c o s t o f s t r i n g i n g w i r e (20.95) .10 .48 (12.16) 10.26 1 12.48 . 1 9 6 3 1 - 9 8 . (d) A s s e m b l i e s . 15 k v a . S^  t r a n s f o r m e r i n s t a l l a t i o n P l u s l o a d -i n g , p e r c e n t © • • • « 9 - - M O . 3 P o r c e l a i n i n s u l a t o r s a t 6§ « G l a s s i n s u l a t o r s , a t .043. 1 5 — S c r e w b r a c k e t s a t . 2 2 2 — S i x - p i n c r o s s a r m s a t <>74* • • 2 — B l o i s k s > a t #48 •... •.. *.> .... 6 —B r a c e s a t . 1 2 7 5 1 0 — 3 / 8 i n . b o l t s a t . 0 2 * 4—'I i n * b o l t s a t . 1 2 . 3«-Lags a t . 0 3 8 , 2 - - P r i m a r y f u s e boxes- a t 3.94< « 0 o * • * * • Q 0 o • © • • • • e * • • • 16.. e • • 0 © • o « 0 e « « « « « • e 1.44 31.80 .258 31.80 3 O 0 2 6 . 0 8 1.48 22.64 • 9 6 22.64 »765 22.64 . 2 0 : 22.64 .48 22.64 .114 2 2 . 6 4 7.88 2 2 * 6 4 M S 4.16 1.82 1.18 .94 .245 .59 .14. 9.67 1 14 2 — S e c o n d a r y f u s e b o x e s a t l . O O . . . . . . . | 2 . 0 0 2 2 . 6 4 $ 2.45 2 — L i g h t n i n g a r r e s t e r s 4 . 8 6 * . . . . . . . . . . • 9 * 7 2 2 2 . 6 4 • 11.91 G r o u n d - r o d , c a p and m o u l d i n g . . . . . . . 1.58 2 3 * 7 9 1 * 9 5 1.395 2 1 . 1 5 1 . 9 6 1 . 7 8 2 1 . 1 5 2 . 1 6 3 0 - - f t . 5/16 i n - , g a l v a n i z e d - i r o n • 525 2 2 . 6 4 . 6 3 w i r e , s t a p l e s , s c r e w s , e t c * .17 2 2 . 6 4 .21 |34»05 - © 0 • * 0 # 4 1 . 9 9 L a b o r l / 5 ( l F + I T r + 3 L •#- J.Gr) - &13.90 p l u s 15.45 % 1 6 . 1 0 •. ' loading'.. ..• 1 5 - k v a . t r a n s f o r m e r $ 1 8 5 • 9 0 n p l u s 16.91 % | 5 8 . 0 9 # © • 0 • • 9 • • • • • * « « • 217.00 9 9 9 9 -9 0 • | , # 2 7 5 . 0 9 C o s t p e r 1 , 0 0 0 f t o o f l i n e w i t h 1 2 5 - f t . s p a n . C r o s s - --- W i r e , a r m s , P i n s I n s u l a - W i r e p i n s , P l u s P l u s 3ne p e r t o r s i n s u l a - c r o s s - 3 5 - f t . p o l e t o r arms p o l e s P r i m a r y 2 $ 6 . . . . c~ jf c • e . . $ 2 2 . 8 0 . 2 2 . 8 0 $ 3 . 1 4 3.14 $ 3 * 3 6 . 3 . 3 6 $ 1 0 6 . 8 0 . 186.15 $ 1 1 3 * 3 0 -192.65 $136.10 - 215.45 $ 3 3 5 . 2 2 414.57 S e c o n d a r y 3T{^4 » « . . 2 2 . 8 0 4 . 7 0 1.37 2 1 0 . 0 0 216.87 2 3 9 . 6 7 4 3 8 . 7 9 The above a r e m e r e l y examples s e l e c t e d hat-- random- : and i n no way i n d i c a t e t h e c o m p l e t e r e c o r d . I t i s e a s i l y s e e n t h a t t h e c o m p i l i n g o f s u c h a r e c o r d i s a m a t t e r o f c o n s i d e r a b l e l a b o r and i n v e s t i g a t i o n . Once o b t a i n e d , however, i n t h i s form a r e v i s i o n i s a c o m p a r a t i v e l y s i m p l e m a t t e r . W h i l e t h e c o s t s t h u s g i v e n a r e a v e r a g e f i g u r e s , e s p e c i a l l y f o r l a b o r , t h e y may be a p p l i e d i n the l o c a l i t y i n w h i c h t h e y were d e r i v e d w i t h o u t g r e a t e r r o r f o r e s t i m a t i n g i n d i v i d u a l Jobs u n l e s s some u n u s u a l f i e l d c o n d i t i o n s i n d i c a t e s e x t r a -o r d i n a r y a d d i t i o n s t o some p a r t o f t h e c o s t . F o r economic s t u d i e s r o f c o u r s e a v e r a g e f i g u r e s a r e u s u a l l y d e s i r a b l e . : v ANNUAL COSTS The d e t e r m i n a t i o n o f a n n u a l c o s t s as u s e d i n t h i s work i s n a t u r a l l y d i v i d e d i n t o two p a r t s , t h a t p e r t a i n i n g t o t h e p h y s i c a l p r o p e r t y i t s e l f s u c h as c o n s t r u c t i o n a n d m a i n t e n a n c e c o s t s and t h a t p e r t a i n i n g t o t h e l o a d c a r r i e d , i . e . , c o s t o f e n e r g y . (See n e x t c h a p t e r ) ANNUAL COSTS ON PHYSICAL P R O P E R T Y . — T h e i t e m s t o he c o n -s i d e r e d u n d e r t h e f i r s t h e a d i n g , i . e . , a n n u a l c o s t s on t h e p h y s i c a l p r o p e r t y , w i l l e a c h he d i s c u s s e d b r i e f l y o They i n c l u d e , i n t e r e s t , t a x e s , i n s u r a n c e , m a i n t e n a n c e , r e p a i r a n d d e -p r e c i a t i o n . I n t e r e s t . — W h e n e v e r money i s i n v e s t e d i n a p i e c e o f p r o p e r t y a l e g i t i m a t e r a t e o f i n t e r e s t must be e x p e c t e d as p a r t o f t h e e a r n i n g s o f t h a t p r o p e r t y u n l e s s i t be r u n a t a l o s s . I n t e r e s t must be f i g u r e d on t h e t o t a l i n v e s t m e n t i n -v o l v e d i n c l u d i n g a l l m a t e r i a l , l a b o r a n d o v e r h e a d c o s t s . The r a t e a t w h i c h i n t e r e s t s h o u l d be charged, may v a r y w i t h t h e p r o b l e m u n d e r c o n s i d e r a t i o n . F u n d a m e n t a l l y i t s h o u l d be t h e c u r r e n t r a t e o f i n t e r e s t on sound i n v e s t m e n t s o r t h e r a t e a t w h i c h t h e company c o u l d b o r r o w money u n d e r o r d i n a r y c o n d i t i o n s . Sometimes the a v e r a g e r a t e p a i d on t o t a l c a p i t a l i z a t i o n may be t a k e n b u t i n c a s e the d i v i d e n d on c a p i t a l s t o c k i s f a i r l y l a r g e , p a r t o f i t m i g h t be c o n s i d e r e d a s a p r o f i t i n e x c e s s o f a f a i r rate* o f i n t e r e s t * i n some c a s e s , due t o p o o r f i n a n c i a l c o n d i t i o n s o r f o r a n emergency a company m i g h t have t o pay a h i g h e r r a t e f o r money, e v e n on b o n d s , t h a n t h e m a r k e t r a t e . A l l s u c h f a c t o r s s h o u l d be c o n s i d e r e d i n d e t e r m i n i n g t h e i n t e r e s t r a t e t o be u s e d * Taxes«.*~Taxes a r e a n e v e r - p r e s e n t c h a r g e on any p r o p e r t y and u s u a l l y t h e d e f i n i t e p e r c e n t a g e may be e a s i l y d e t e r m i n e d from t h e c o m p a n y ' s a c c o u n t i n g r e c o r d s * I n s u r a n c e . - - I n s u r a n c e a g a i n s t l o s s b y f i r e I s t h e most common form b u t on some c l a s s e s o f p r o p e r t y I n s u r a n c e a g a i n s t t h e f t , s t o r m , e t c * i s a l s o c a r r i e d . I n any p r o b l e m t h e k i n d and amount o f i n s u r a n c e c h a r g e a b l e t o e a c h c l a s s o f p r o p e r t y s h o u l d be i n v e s t i g a t e d . I n many c a s e s no " i n s u r a n c e " c h a r g e i s n e c -e s s a r y . M a i n t e n a n c e and R e p a i r . - - M a i n t e n a n c e and r e p a i r w i l l be d i f f -e r e n t f o r e a c h u n i t c o n s i d e r e d . No two t r a n s f o r m e r s f o r e x -ample w i l l r e q u i r e the same amount o f a t t e n t i o n d u r i n g t h e i r l i f e e v e n t h o u g h s i m i l a r l y l o c a t e d ; b r e a k s i n a l i n e c a n r a r e l y be a n t i c i p a t e d , e t c • A l a r g e p a r t o f m a i n t e n a n c e i s o c c a s i o n -ed by i m p e r f e c t i o n i n m a t e r i a l . M a i n t e n a n c e a n d r e p a i r s due t o s u c h c a u s e s on any i n d i v i d u a l p i e c e o f equipment c a n n o t be f o r e s e e n . I n s u c h c a s e s a v e r a g e f i g u r e s o n l y c a n be o b -t a i n e d from a c t u a l e x p e r i e n c e o v e r a number o f y e a r s , o t h e r i t e m s o f m a i n t e n a n c e s u c h as i n s p e c t i o n , t e s t i n g , e t c . , c a n be q u i t e d e f i n i t e l y d e t e r m i n e d f r o m p a y r o l l a n d t i m e r e p o r t s . 16 D e p r e c i a t i o n * ' " - No d e t a i l e d d i s c u s s i o n o f d e p r e c i a t i o n c a n . b e , h e r e - i n c l u d e d « S t r i c t l y s p e a k i n g , d e p r e c i a t i o n i s t h e p e r c e n t a g e b y w h i c h a p i e c e o f p r o p e r t y i s r e d u c e d I n v a l u e e a c h y e a r o f I t s l i f e (by v a l u e i s n o t meant n e c e s s -a r i l y s e l l i n g p r i c e ) . From a n a c c o u n t i n g p o i n t o f v i e w , on t h e o t h e r h a n d , a c e r t a i n amount must be s e t a s i d e e a c h y e a r t o r e p l a c e t h e p r o p e r t y when worn out© Sometimes t h e u s e f u l n e s s o f t h e p r o p e r t y i n s e r v i c e I s c o n s i d e r e d as a measure o f . I t s v a l u e . A l l t h e s e d i f f e r e n t v i e w p o i n t s g i v e r i s e to d i f f e r e n t methods o f f i g u r i n g d e p r e c i a t i o n , a n d a d i s c u s s i o n o f t h e s e may be f o u n d i n o t h e r w o r k s . F o r t h e p u r p o s e o f t h i s t h e s i s however what i s known a s t h e s i n k i n g f u n d method i s p r o b a b l y t h e most e q u i t a b l e and s a t i s f a c t o r y . The c o s t i s o b t a i n e d from t h e t o t a l f i r s t c o s t o f t h e p r o p e r t y i n p l a c e I n c l u d i n g m a t e r i a l , l a b o r a n d o v e r h e a d c h a r g e s , l e s s t h e s a l v a g e v a l u e a t t h e e n d o f I t s l i f e , p l u s t h e l a b o r c o s t n e c e s s a r y t o s a l v a g e I t * T h i s c o s t I s a m o r t i z e d o v e r tfee e s t i m a t e d number 6 f y e a r s o f l i f e on a s e m i - a n n u a l compoundingr:^ b a s i s and the p e r c e n t a g e o f d e p r e c i a -t i o n t a k e n a s t h e p e r c e n t a g e o f t h e t o t a l f i r s t c o s t t h u s o b t a i n e d . N a t u r a l l y t h i s w i l l v a r y w i t h d i f f e r e n t c l a s s e s o f p r o p e r t y . Some w i l l have l i t t l e i f any s a l v a g e v a l u e s u c h as . c r o s s a r m s , f o r e x a m p l e . A p o l e , when r o t t e d a t t h e b a s e , on t h e o t h e r h a n d c a n be sawed o f f a n d u s e d a g a i n e i t h e r as a s h o r t e r p o l e o r a s t u b . B a r e c o p p e r w i r e w i l l have p r a c t i c a l l y no p h y s i c a l d e p r e c i a t i o n , t h e c o s t o f s t r i n g i n g and r e m o v i n g t o g e t h e r w i t h t i e w i r e s and o t h e r i n c i d e n t a l s mak-i n g up t h e d e p r e c i a t i o n . The y e a r s o f l i f e t o use f o r any u n i t may depend on o t h e r t h i n g s t h a n i t s own l i f e * F o r a t r a n s m i s s i o n l i n e , f o r e x -a m p l e , i t i s p r o b a b l e t h a t no d e f i n i t e l i m i t c a n be f i x e d a t w h i c h t h e whole l i n e must be r e p l a c e d * P o l e s a n d c r o s s a r m s w i l l be r e p l a c e d from t i m e to t ime when n e c e s s a r y as l o n g as t h e l i n e i s i n s e r v i c e * I n s u c h a c a s e I t I s p r o b a b l y s i m p l e s t t o assume a d e f i n i t e l i f e f o r the whole l i n e , p o s s i b l y t h e assumed l i f e o f a p o l e , a n d f i g u r e ' d e p r e c i a t i o n on a l l u n i t s , w i r e , i n s u l a t o r s , e t c . on t h a t b a s i s * Thus any c l a s s o f p r o p e r t y may have a d i f f e r e n t p e r c e n t a g e o f d e p r e c i a t i o n d e p e n d i n g on where I t i s u s e d * f' A s i m p l e example o f a c o m p u t a t i o n f o r d e p r e c i a t i o n on i n s u l a t e d w i r e w o u l d be as f o l l o w s ; A s s u m i n g new i n s u l a t e d w i r e a t 30 c t s . and s c r a p c o p p e r a t l O c t s . p e r l b . S e r v i c e l i f e assumed 20 y e a r s . C o s t o f #0 w i r e p e r 1 ,000 f t . - 4 2 0 l b s . @ 30 c t s . . . = 4 1 2 6 . 0 0 L a b o r o f s t r i n g i n g . . . . . . . . . . . . . . . . . . . . . . . . =» 10.00. • T o t a l . . . D i r e c t l a b o u r and m a t e r i a l . == 136° .00 Over h e a d 15% o f D i r e c t L a b o u r and M a t e r i a l - 2 0 . 4 0 $156.40 $156.40 T o t a l s b r o u g h t f o r w a r d . . $ 1 5 6 . 4 0 $156.40 ..Less:'. S a l v a g e v a l u e o f s c r a p c o p p e r . S a l v a g e v a l u e 319 l b . ( i n s l . removed) @10 c t s . l b . - 3 1 . 9 0 L a b o u r t o remove i n s u l a t i o n . . . ^ 1 0 . 0 0 N e t C r e d i t t o P r o p e r t y A c c o u n t . ~— 2 1 . 9 0 21 .90 Amount o f D e p r e c i a t l on F u n d • » • • • • • • • * • • • • • » • • • • »»• ^13^ *»5Q Y e a r l y A n n u a l D e p r e c i a t i o n C o s t - - S i n k l n g F u n d b a s i s ( a s s u m i n g y e a r l y c h a r g e s i n v e s t e d © 5% and .compounded s e m i - a n n u a l l y . ) (I) , ... On a $1 b a s i s t h e a n n u a l y e a r end payment t o a c c u m u l a t e $ 1 . 0 0 i n 20 y r s . when compounded s e m i - a n n u a l l y .0148 d o l l a r s . Hence y e a r l y d e p r e c i a t i o n c h a r g e i s .0148 x 134.50 = $1.9906 and as e x p r e s s e d as a p e r c e n t o f o r i g i n a l I n v e s t m e n t I s : -The m a t t e r o f o b s o l e s c e n c e w h i c h i s sometimes c o n s i d e r e d a s a s e p a r a t e f i g u r e may, f o r t h i s w o r k , be c o n s i d e r e d as a p a r t o f d e p r e c i a t i o n . Where I t i s a n t i c i p a t e d " t h a t m a t e r i a l s w i l l become o b s o l e t e a n d rea_uire r e p l a c e m e n t b e f o r e worn o u t on a c c o u n t o f improvement i n d e s i g n , t h e assumed l i f e and s a l v a g e v a l u e u s e d I n c o m p u t i n g d e p r e c i a t i o n s h o u l d be a d j u s t e d a c c o r d i n g l y « Many s p e c i a l p r o b l e m s a r i s e i n f i g u r i n g a n n u a l c o s t . One w h i c h a l s o I n c l u d e s t h e i d e a o f o b s o l e s c e n c e i s e n c o u n t e r e d when t h e r e p l a c e m e n t o f a s e r v i c e a b l e l i n e w i t h one o f l a r g e r c a p a c i t y I s b e i n g c o n s i d e r e d . The v a l u e r e m a i n i n g i n the o l d l i n e must be I n c l u d e d I n t h e c o m p u t a t i o n s and t h e t o t a l I n -v e s t m e n t r e p r e s e n t e d i n the new l i n e must i n c l u d e , i n a d d i t i o n • t o t h e c o s t t o b u i l d i t , t h e p r e s e n t v a l u e o f the l a b o r n e c e -s s a r y t o b u i l d t h e o l d l i n e , i . e . , f i r s t c o s t f o r l a b o u r l e s s d e p r e c i a t i o n f o r y e a r s o f age and the l a b o r c o s t n e c e s s a r y t o d i s m a n t l e t h e o l d l i n e . Such p r o b l e m s w i l l be d i s c u s s e d i n more d e t a i l l a t e r . (I) See T a b l e E — page 247 - P i s h - E n g i n e e r i n g E c o n o m i c s . CHAPTER I I I ENERGY COST P r i n c i p l e s and Methods Involved In the Determination of the Cost of Energy and of Energy Losses Since any economic study of t r a n s m i s s i o n or d i s t r i b u t i o n i s , fundamentally, a c o n s i d e r a t i o n of the cost of energy or energy l o s s e s as compared w i t h other c o s t s ( i n g e n e r a l , f i x e d charges i n c r e a s e as energy l o s s decreases), i t i s of the utmost Importance that the c o s t of energy be a c c u r a t e -l y determined. The value assigned to the u n i t c o s t of energy may be the d e c i d i n g f a c t o r i n a problem. T h i s v a l u e , moreover, may vary c o n s i d e r a b l y according to the assumptions, methods:;and p r e c i s i o n employed i n i t s c a l c u l a t i o n . I t i s evident t h a t the c o s t per k i l o w a t t - h o u r of the energy used by a 5-h.p. motor running 1 hr» per day, 25 m i l e s n o r t h of the g e n e r a t i n g s t a t i o n may be q u i t e d i f f e r e n t from the u n i t c o s t f o r r e s i d e n c e - l i g h t i n g l o a d , 5 m i l e s west of the s t a t i o n and both of these may be f a r from the average u n i t c o s t over the whole system. The question of the d e t e r m i n a t i o n of energy c o s t o f f e r s an e x t e n s i v e f i e l d f o r study and one that g e n e r a l l y has been only touched upon. This chapter w i l l g ive some of the fundamental p r i n c i p l e s I n v o l v e d , a few methods of a t t a c k i n g the g e n e r a l problem and suggestions as to c o n d i t i o n s governing v a r i a t i o n s i n the g e n e r a l cost as a p p l i e d to p a r t i c u l a r uses a I n studying energy c o s t , the fundamental d i f f e r e n c e between the c o s t of energy f o r rate-making purposes and the c o s t of energy economical study must be r e c o g n i z e d . I n determining the c o s t o energy for: the purpose of adopting a r a t e scale., I t may be s u f f i c i e n t t o c o n s i d e r the system as a whole and determine the average c o s t per u n i t f o r each of a few g e n e r a l e l a s s e s of l o a d which laave markedly d i f f e r e n t c h a r a c t e r i s t i c s . The c h i e f p o i n t t o be.kept i n mind i s the amount which the customer pays, and t h a t t h i s , on an average should at l e a s t equal the expense of the company, p l u s a reasonable p r o f i t . U s u a l l y about the same r a t e must be a p p l i e d to s i m i l a r customers w i t h i n a reasonable area, unless there i s a marked d i f f e r e n c e . In the i n d i v i d u a l c o s t of s e r v i n g each. There are a l s o f a c t o r s other than a c t u a l p r o d u c t i o n , t r a n s m i s s i o n and d i s t r i b u t i o n c o s t which must be considered i n r a t e making, such as p u b l i c o p i n i o n , r e g u l a t i o n s and f r a n c h i s e agreements, previous p r a c t i c e , c o m p e t i t i o n , e t c . On the other hand, In making an economic study., we are i n t e r e s t e d i n the actual-, amount which the energy d e l i v e r e d to the point under c o n -s i d e r a t i o n i s c o s t i n g the company and hence, how much money, i f any, can be saved by reducing energy l o s s e s . I f energy 19 c o s t s more --per u n i t 5 m i l e s from the s t a t i o n than I t does 1 mile,, f o r example, the amount saved w i l l be correspondingly-more important«. For t h i s purpose, then, i t would seem de-s i r a b l e to i n v e s t i g a t e the c o s t of energy as f u l l y as Is warranted by the amount and 'accuracy of the i n f o r m a t i o n a v a i l -able on c o s t s of c o n s t r u c t i o n and o p e r a t i o n and on loads c a r r i e d . Even w i t h f a i r l y complete.data a t hand i t Is a d i f f i c u l t matter to determine d e f i n i t e f i g u r e s f o r energy costs*. The c o s t i s a f f e c t e d by many q u a n t i t i e s of a v a r i a b l e nature and these: l i m i t the e x tent to which I t i s p r a c t i c a b l e t o c a r r y • -.<• the study. At any, given p o i n t the c o s t of energy i s l a r g e l y -dependent on the f i x e d charges and o p e r a t i n g expenses of the c e n t r a l -station*., t r a n s m i s s i o n . system,, s u b - s t a t i o n and d i s t r i b u t i o n system, between, the s t a t i o n and that p o i n t . I t i s a l s o a f f e c t e d by- the s i z e and c h a r a c t e r i s t i c s of the l o a d a t the p o i n t i n q u e s t i o n i n r e l a t i o n to a l l the other loads on the system. Hence, s t r i c t l y speaking, energy c o s t may be con-ceived as having, a d i f f e r e n t value at every p o i n t on the system: and f o r every d i f f e r e n t l o a d at any g i v e n p o i n t . Loads of the same type may show, a d i f f e r e n t u n i t c o s t accord-in g to t h e i r s i z e and the u n i t c o s t may vary a t d i f f e r e n t times d u r i n g the day or even f o r d i f f e r e n t p a r t s of the same l o a d . The-length to which the d e t e r m i n a t i o n of c o s t of energy might be c a r r i e d : i s almost i n f i n i t e . I n p r a c t i c e I t w i l l depend not only on the accuracy of the data a v a i l a b l e but a l s o on how.this c o s t i s to be used. . CLASSIFICATION.OF COSTS OF A CENTRAL*STATION SYSTEM.—The v a r i o u s items e n t e r i n g i n t o the t o t a l annual cost of a c e n t r a l s t a t i o n to s e r v i c e a customer, may be c l a s s i f i e d as f o l l o w s : '. ^ ..  1. Costs dependent on the number of customers. 2 . Costs dependent on the peak load c a r r i e d or the demand. 3« Cos+s dependent on the t o t a l output In k i l o w a t t - h o u r s during the y e a r . I t must not be assumed that a l l expenses come s t r i c t l y under one of these three c l a s s i f i c a t i o n s . There are a g r e a t number of other minor d i v i s i o n s which might be made. For example, there are c e r t a i n o p e r a t i n g expenses at the s t a t i o n which are dependent on the e f f i c i e n c y and s i z e of the machines and the r e l a t i o n of the l o a d a t any time to the c a p a c i t y of the generators i n use and to the method of operating the s t a t i o n and the system. I t does not appear p r a c t i c a l however to attempt to i n c l u d e a l l such c l a s s i f i c a t i o n s . The above three are.the most important and other coPts can be i n c l u d e d i n one of them without great e r r o r . HOPKINSON METHOD.-D r . J o h n H o p k i n s o n was f i r s t to d e v i s e a r a t e system d e p a r t i n g from t h e f l a t - r a t e method* H i s method was p u t i n t o o p e r a t i o n i n M a n c h e s t e r , E n g l a n d , i n 1892o The H o p k i n s o n r a t e i n c l u d e s two f a c t o r s : The demand f a c t o r b a s e d on the c o n n e c t e d equipment o r " l o a d " and the e n e r g y f a c t o r b a s e d on e n e r g y c o n s u m p t i o n m e a s u r e d w i t h a ' w a t t h o u r meter., I n p r i n c i p l e t h i s system p e r m i t s an e q u i t a b l e c h a r g e to be made f o r t h e i n v e s t m e n t r e q u i r e d t o meet the maximum demand f o r e a c h c u s t o m e r . However, i n p r a c t i c e u n l e s s s a i d c h a r g e t a k e s the d u r a t i o n o f the maximum demand i n t o c o n s i d e r a t i o n a n d , i n a l t e r n a t i n g - c u r r e n t s y s t e m s , a l s o t h e p o w e r - f a c t o r o f the l o a d , i t does n o t make a f a i r d i s t r i b u t i o n o f c o s t s * M o d e r n r a t e s a l m o s t w i t h o u t e x c e p t i o n t a k e c a r e o f f a c t o r s f i r s t p o i n t e d out by H o p k i n s o n a n d to him b e l o n g s the c r e d i t o f m a k i n g the f i r s t s c i e n t i f i c a n a l y s i s o f r a t e m a k i n g . WRIGHT DEMAND SYSTEM»-A r t h u r W r i g h t f o l l o w e d i n H o p k i n s o n ' s s t e p s . He i n s t a l l e d a demand, s y s t e m i n B r i g h t o n , E n g l a n d , i n 1895 • B a s i c a l l y the H o p k i n s o n and the W r i g h t systems a r e s i m i l a r . The p r i n c i p a l improvement o f the W r i g h t s y s t e m was t h e use o f an i n s t r u m e n t f o r m e a s u r i n g t h e demand* H o p k i n s o n o r i g i n a l l y e s t i m a t e d , t h e demand f a c t o r from the c u s t o m e r ' s c o n n e c t e d l o a d ; W r i g h t , however, u s e d a c t u a l measurements as t h e b a s i s o f h i s c a l c u l a t i o n s . E x p e r i e n c e has"shown t h a t s e r v i c e r a t e s w h i c h i n v o l v e c a l c u l a t i o n s b a s e d o n e s t i m a t e s u s u a l l y e n c o u n t e r a c e r t a i n amount o f r e s i s t a n c e w i t h c u s t o m e r s who do n o t u n d e r s t a n d t h e p u r p o s e o f the c a l c u l a t i o n s and r e g a r d w i t h s u s p i c i o n a n y -t h i n g w h i c h c a n n o t be d e f i n i t e l y p r o v e n i n terms c o m p r e h e n s i b l e them'. •••••./•. P r o b a b l y the most I m p o r t a n t c o n t r i b u t i o n o f W r i g h t t o t h e s c i e n c e o f r a t e making was h i s demand i n d i c a t o r , w h i c h f u r n i s h e d means o f m e a s u r i n g f o r the f i r s t t i m e the a c t u a l demand and p e r m i t t e d t h e e s t a b l i s h m e n t o f r e l a t i o n s between demand and c o n n e c t e d l o a d t h a t p r e v i o u s l y had b e e n l a r g e l y a m a t t e r o f guess w o r k . In the W r i g h t demand s y s t e m , the c u s t o m e r i s c h a r g e d a t a c o m p a r a t i v e l y h i g h r a t e f o r a c e r t a i n number o f h o u r s o f use o f h i s maximum demand as i n d i c a t e d by t h e W r i g h t Demand I n -d i c a t o r , a n d t h e n f o r the s u c c e e d i n g t i m e i n t e r v a l s , e a c h b l o c k o f e n e r g y i s b i l l e d a t a- d e c r e a s i n g r a t e . THE DOHERTY THREE-PART R A T E . — ' I n 1900> H e n r y L . D o h e r t y I n t r o d u c e d i n t o M a d i s o n , W i s * , and D e n v e r , C o l o . , h i s now famous t h r e e - p a r t r a t e system o f c h a r g i n g f o r e l e c t r i c s e r v i c e . The D o h e r t y p l a n d i v i d e s t h e c h a r g e s i n t o t h r e e f a c t o r s t h a t a u t o m a t i c a l l y v a r y the r a t e s to f i t the c o s t o f the s e r v i c e , and thus f o s t e r p r o f i t a b l e b u s i n e s s . See F i g . I« The t h r e e f a c t o r s o f c h a r g e a r e : " C u s t o m e r ' s c h a r g e " ^ w h i c h c o v e r s the c o s t o f i n s t a l l i n g and m a i n t a i n i n g the s e r v i c e e n t r a n c e , i n c l u d i n g upkeep and r e a d i n g o f meter and b i l l i n g f o r the s e r v i c e . A l l o f t h e s e f a c t o r s e x i s t whether o r n o t the c u s t o m e r u s e s . e n e r g y . "Demand C h a r g e " , w h i c h i s d e t e r m i n e d by m a g n i t u d e o f c u s t o m e r ' s i n s t a l l a t i o n i n k . w . c a p a c i t y r e p r e s e n t s the i n v e s t m e n t i n e q u i p m e n t by the C e n t r a l S t a t i o n n e c e s s a r y to a s s u r e the a b i l i t y to s u p p l y the maximum demand f o r energy whenever the c u s t o m e r may w i s h i t . " K i l o w a t t - h o u r c h a r g e " , w h i c h i s d e t e r m i n e d by t h e e n e r g y u s e d and r e p r e s e n t s t h a t p a r t o f t h e e l e c t r i c energy c o s t t h a t v a r i e s w i t h the q u a n t i t y o f e n e r g y p r o d u c e d . The f i r s t o f the f a c t o r s I s a d i r e c t o p e r a t i n g e x p e n s e - - t h e l a s t two c a n "he a c c u r a t e l y m e a s u r e d and b i l l e d i n e x a c t a c c o r d w i t h a c t u a l u s e . The Maximum-demand W a t t h o u r M e t e r measures b o t h t h e maximum demand and t h e e n e r g y c o n s u m p t i o n f o r t h e p e r i o d between r e a d i n g s , and i s t h e r e f o r e p a r t i c u l a r l y s u i t e d t o use where the D o h e r t y T h r e e - p a r t R a t e System i s employed as i t removes a l l guesswork and p e r m i t s the b i l l i n g f o r s e r v i c e a c c o r d i n g to a b a s i c s t a n d a r d o f c h a r g e , w h i c h c a n be examined and t e s t e d i n s u c h c l e a n - c u t f a s h i o n t h a t d i s p u t e s a r e i m p o s s i b l e once the system I t s e l f i s a c c e p t e d . Some i t e m s o f t h e t o t a l a n n u a l c o s t c l e a r l y b e l o n g o n l y t o demand c o s t w h i l e o t h e r s w h i c h m i g h t seem to depend o n l y o n , o u t p u t have some p e r c e n t a g e o f demand c o s t i n c l u d e d . I n the f i r s t g r o u p come i n t e r e s t , t a x e s , I n s u r a n c e , d e p r e c i a t i o n , e t c . on the g e n e r a t i n g ^ s t a t i o n b u i l d i n g , I n t e r e s t , t a x e s , e t c * on b o i l e r s t u r b i n e s ^ g e n e r a t o r s a n d o t h e r equipment and a l a r g e p a r t o f t h e i r d e p r e c i a t i o n and m a i n t e n a n c e . A l s o f i x e d c h a r g e s on l i n e s and s u b s t a t i o n e q u i p m e n t a r e h e r e i n c l u d e d . Under 22 the s e c o n d g r o u p comes p a r t o f the c o s t o f c o a l , o i l and o t h e r e x p e n d a b l e m a t e r i a l s , p a r t o f the l a b o r o f o p e r a t i n g , a l s o p a r t o f t h e e n e r g y l o s s e s on l i n e s a n d t r a n s f o r m e r s due t o t h e f a c t t h a t t h e y a r e k e p t e n e r g i s e d a t a l l t i m e s . The a p p o r t i o n i n g o f s u c h c o s t s i s a m a t t e r f o r c o n s i d e r a b l e s t u d y * The method o f o p e r a t i o n may e f f e c t the amount c h a r g e a b l e t o demand i n c e r t a i n c a s e s . L a r g e m a c h i n e s a r e l e s s e f f i c i e n t a t s m a l l l o a d s . H e n c e , i f l a r g e u n i t s a r e employed, a n d a r e r u n f a r b e l o w t h e i r most e c o n o m i c a l l o a d f o r t h e g r e a t e r p a r t o f t h e d a y , t h e e x t r a expense due t o d e c r e a s e d e f f i c i e n c y may be c h a r g e d t o demand. I n a l a r g e , e f f i c i e n t l y o p e r a t e d s t a t i o n t h i s c o n d i t i o n w o u l d n o t o c c u r t o any g r e a t e x t e n t , b u t i t s u g g e s t s some o f t h e i t e m s w h i c h must be c o n s i d e r e d . I n f a c t , t h e r e must be i n c l u d e d i n demand c o s t a l l c h a r g e s d i r e c t l y or i n d i r e c t l y o c c a s i o n e d by t h e t o t a l c a p a c i t y o f t h e s y s t e m . The r e m a i n i n g a n n u a l c o s t s , a s i d e from the consumer c o s t b e f o r e m e n t i o n e d , may be c o n s i d e r e d as dependent on the o u t p u t * T h e s e c o m p r i s e the k i l o w a t t - h o u r c o s t * METHODS OF MAKING CLASSI FT C A T I O N . — T h e a c t u a l d i v i s i o n o f the t o t a l a n n u a l c o s t o n any p a r t o f the system i n t o t h r e e c l a s s i f i -c a t i o n s w i l l d e p e n d l a r g e l y on l o c a l c o n d i t i o n s . The r e l a t i v e p e r c e n t a g e s w i l l p r o b a b l y be d i f f e r e n t f o r e a c h company. S e v e r a l g e n e r a l methods o f a t t a c k i n g t h e p r o b l e m a r e i n u s e . I n t h e g e n e r a t i n g p l a n t , f o r e x a m p l e , an e m p i r i c a l a n a l y s i s c a n be made o f e a c h i t e m o f c o s t , s u c h as c h a r g e s on b u i l d i n g , on steam e q u i p m e n t , on e l e c t r i c a l e q u i p m e n t , f u e l , l a b o r , e t c . The p r o p o r t i o n b e l o n g i n g t o e a c h c l a s s i f i c a t i o n may be e s t i m a t e d from known c o n d i t i o n s , k e e p i n g I n m i n d t h e g e n e r a l d e f i n i t i o n s o f demand c o s t , k i l o w a t t - h o u r c o s t and consumer c o s t . One method o f s e p a r a t i n g demand and k i l o w a t t - h o u r c h a r g e s on f u e l , l u b r i c a n t s a n d s u c h i t e m s i s by c o m p a r i n g c o s t s u n d e r a p e r i o d o f l i g h t l o a d a n d one o f heavy l o a d — a month a t d i f f e r e n t s e a s o n s o f t h e y e a r . F o r .example, .. i f C demand c o s t , p e r u n i t demand C k i l o w a t t - h o u r c o s t , D . s t a t i o n demand, F l k i l o w a t t - h o u r s a t low p e r i o d , *2 =• k i l o w a t t - h o u r s a t h i g h p e r i o d , °1 = T t o t a l c o s t a t IOY? p e r i o d , ° 2 SEW t o t a l c o s t a t h i g h p e r i o d , °1 C . D + C f F l ° 2 C a D + C f F 2 C f °2 "~ C l ° 1 — c : G d F 2 - F l 2 f % 23 This should give s a t i s f a c t o r y r e s u l t s I f there were enough difference between the loads at the two periods to give a good comparison of cost. Another somewhat s i m i l a r method, W that may be applied to items such as t o t a l s t a t i o n or system costs, (which involve a l l three c l a s s i f i c a t i o n s ) , considers the t o t a l cost over three given periods, three years, for example, or three d i f f e r e n t months* Using s i m i l a r symbols to the above with C — customers cost. ,c ' N =; number of customers, c 1 = ° d D l +• C f F l +• C c N l C 2 " C dD 2 + C f F 2 +• C c N 2 °3 - C d D 3 C f F 3 + C c N 3 I f these are solved simultaneously the values of C^, C f and C c can be determined. An example of a t y p i c a l d i v i s i o n of costs between demand and kilowatt»hour of some of the items for the generating s t a t i o n i s as follows: Demand, Kilowatt-per cent hour, per cent Superintendence.. • • a • t o o • • 100 10 75 25 75 Station supplies, etc ..... 100 These general methods may be adapted to other parts of the system, transmission l i n e s , substations, etc., as well as to the generating plant. In analyzing the cost of a hydro-electrie plant, the a v a i l a b l e supply of water i s an important factor i n the consideration. I t i s evident tht the kilowatt-hour cost w i l l depend considerably on whether the supply i s unlimited or whether storage i s resorted to for regulating the flow* It appears then that the f i r s t step i n the study of energy cost i s the determination as accurately as possible of the t o t a l annual costs on each subdivision of the system and the proportion of these costs, i n each case, belonging to demand and to' output. Naturally the more d e t a i l e d the accounting record on various parts of the system, the easier the determination of these costs w i l l be. I f an e n t i r e l y new system i s being con-sidered, the various quantities can only be estimated from data of other s i m i l a r systems and present prices on construction materials, equipment, e t c . For the purpose under consideration, i f the ^ "Central S t a t i o n Rates i n Theory and P r a c t i c e , " by H.E. Eisen-menger, " E l e c t r i c a l Review", V o l . 7 5 , Aug. 23, 1919, p.305. 24 s t u d y o f e n e r g y c o s t i s t o be c a r r i e d to any d e g r e e o f e x a c t n e s s , i t i s p r o b a b l y b e t t e r t o p r e p a r e s e p a r a t e f i g u r e s on e a c h o f the t h r e e c l a s s i f i c a t i o n s o f c o s t s as r e l a t e d to d i f f e r e n t p a r t s o f the s y s t e m , g e n e r a t i n g s t a t i o n , v a r i o u s s u b s t a t i o n s , u n d e r -g r o u n d - c a b l e l i n e s , o v e r h e a d power l i n e s , f e e d e r s , e t c J u s t how much o f s u c h d e t a i l i s n e c e s s a r y w i l l be d e t e r m i n e d by the method w h i c h i s to be u s e d i n a p p o r t i o n i n g the c o s t s amoung the v a r i o u s c l a s s e s o f l o a d s a n d l o c a l i t i e s . APPORTIONING- OF DEMAND AND OUTPUT COSTS TO VARIOUS TYPES OF LOADS When the p r o p o r t i o n s o f the t o t a l c o s t c h a r g e a b l e to demand and to o u t p u t have b e e n d e t e r m i n e d , t h e r e a r i s e s the p r o b l e m o f : f i n d i n g what p a r t o f t h a t demand c o s t o r o f t h a t k i l o w a t t -hour c o s t b e l o n g s to any p a r t i c u l a r l o a d o r type o f l o a d . The " K i l o w a t t - h o u r " c o s t may be s i m p l y d i s p o s e d o f f o r t h e p r e s e n t by c o n s i d e r i n g t h a t t h e k i l o w a t t - h o u r c h a r g e a t any p o i n t i the system i s e q u a l t o the sum o f t h e k i l o w a t t - h o u r c o s t s i n -c u r r e d on a l l p a r t s o f the s y s t e m from t h a t p o i n t b a c k t o t h e g e n e r a t i n g s t a t i o n * C o n s i d e r a b l e s t u d y may be i n v o l v e d i n d e t e r m i n i n g t h e k i l o w a t t - h o u r c o s t s on such p a r t s as t r a n s m i s s i o n l i n e s or power l i n e s , s i n c e a g r e a t p a r t o f t h e c o s t depends on the e n e r g y l o s s e s and t h e c o s t o f t h e s e l o s s e s i n t u r n i n c l u d e s t h e demand a n d k i l o w a t t - h o u r c h a r g e s up t o t h a t . p o i n t . . The t h e o r y i s n o t complex h o w e v e r . M o d i f i c a t i o n o f t h i s method f o r s p e c i a l p u r p o s e s w i l l be e x p l a i n e d l a t e r . The a p p o r t i o n i n g o f the demand c o s t however p r e s e n t s a more d i f f i c u l t q u e s t i o n . Demand C o s t o - - I f a l l l o a d s had s i m i l a r c h a r a c t e r i s t i c s , i . e . , s i m i l a r l o a d c u r v e s , w i t h the peak coming a t the same t l m e . i t i s - e v i d e n t , t h a t t h e demand c h a r g e f o r each w o u l d be s i m p l y p r o -p o r t i o n a l t o i t s peak l o a d . T h i s a s s u m p t i o n i s sometimes u s e d i n f i g u r i n g e n e r g y c o s t b u t i s o b v i o u s l y n o t c o r r e c t e x c e p t i n c a s e s where a l l l o a d s a r e s i m i l a r or n e a r l y s o , s u c h as f o r a p l a n t s e r v i n g r e s i d e n c e l i g h t i n g o n l y . On t h i s a s s u m p t i o n , t h e demand c h a r g e x*Kk±±K p e r k i l o w a t t may be r e d u c e d t o a f i g u r e p e r k i l o w a t t - h o u r , i n v e r s e l y p r o p o r t i o n a l t o t h e l o a d f a c t o r , a n d t h i s added to t h e k i l o w a t t - h o u r c h a r g e d e t e r m i n e s the t o t a l c o s t o f e n e r g y . Where b o t h l i g h t i n g and c o m m e r c i a l power or o t h e r l o a d s a r e c a r r i e d , h o w e v e r , i t i s e v i d e n t t h a t , t h e demand r e s p o n s i b i l i t y o f e a c h c a n n o t be a c c u r a t e l y o b t a i n e d i n t h i s way as t h e peaks come a t d i f f e r e n t t i m e s a n d the l o a d s show d i f f e r e n t c h a r a c t e r i s t i c s t h r o u g h o u t the d a y . F o r example the power peak m i g h t come a t the same time as the s t a t i o n p e a k a t p e r h a p s 2 P c M . , whereas t h e l i g h t i n g peak comes a t 8 P . M . , the l i g h t i n g l o a d a t 2 P . M . b e i n g o n l y 30 p e r c e n t o f i t s p e a k . • A g a i n t h e s a s s u m p t i o n m i g h t be made t h a t t h e demand c h a r g e o f any l o a d i s p r o p o r t i o n a l t o I t s demand a t t i m e o f s t a t i o n p e a k . T h i s m i g h t sound r e a s o n a b l e i n a s m u c h as t h e demand c o s t o f the s t a t i o n i s f i g u r e d on t h e b a s i s o f i t s peak l o a d . 25 The demand r e s p o n s i b i l i t y f o r any c u s t o m e r i s sometimes computed on t h i s b a s i s by m u l t i p l y i n g h i s t o t a l c o n n e c t e d l o a d by h i s demand f a c t o r to g e t h i s i n d i v i d u a l demand, d i v i d i n g t h i s I n t u r n by the d i v e r s i t y f a c t o r o f t h e , s u b s t a t i o n and so on b a c k to the g e n e r a t i n g s t a t i o n , t h u s d e t e r m i n i n g t h a t c u s t o m e r ' s p r o p o r t i o n o f the s t a t i o n p e a k . Of c o u r s e a c a r e f u l d e t e r m i n a t i o n o f d i v e r s i t y and demand f a c t o r s i s n e c e s s a r y f o r t h i s . H e r e a g a i n the v a r i a b l e c h a r a c t e r i s t i c s o f the d i f f e r e n t l o a d s make t h i s assump-t i o n e r r o n e o u s e x c e p t i n s p e c i a l c a s e s . . Take f o r a s i m p l e example a s m a l l s t a t i o n o f 1,000 kw. s e r v i n g two c u s t o m e r s A and B . A t a k e s 1 ,000 kw. f o r 6 hr» e a c h d a y . B t a k e s 600 kw. f o r the r e m a i n i n g 18 h r s . b u t does not, o v e r l a p A . On the a s s u m p t i o n , o f demand p r o p o r t i o n a l to i n d i v i d u a l peak l o a d , A ' s c o s t would be 10/16 a n d B ' s 6/16 o f the t o t a l demand c o s t . On the a s s u m p t i o n o f demand p r o p o r t i o n a l t o l o a d a t time o f s t a t i o n p e a k , A ' s p r o p o r t i o n w o u l d be the whole s t a t i o n demand and B ' s n o t h i n g * ( s e e F i g . 2 a ) . I f , - h o w e v e r , the s t a t i o n may be c o n s i d e r e d as c o n s i s t i n g o f two p a r t s , one o f a c a p a c i t y o f 600 kw. and one o f 400 kw. " i t w l l l ' b e r e a d i l y ' s e e n t h a t the 600 may be assumed to o p e r a t e 6 h r . f o r A and 18 f o r B w h i l e the 400 o p e r a t e s o n l y 6 h r . f o r A (see F i g . 2 b , ) . li .'. 400 6 600:. ^ I n t h i s c a s e t h e n A ' s c o s t would be f X - o f t h e 1 ,000 24 1 ,000 18 600 9 t o t a l , w h i l e B ' s w o u l d be — X o f t h e t o t a l . 24 1 ,000 20 o T h i s t h e o r y c a n be e x t e n d e d to c o v e r any number o f l o a d s w i t h v a r i o u s l y shaped c u r v e s . I t may be s t a t e d i n g e n e r a l t h a t the c o s t o f e a c h - u n i t ( k i l o w a t t ) o f the t o t a l demand s h o u l d be d i v i d e d i n a c c o r d a n c e w i t h the l e n g t h o f time o r number o f h o u r s i t i s i n u s e , t o o b t a i n a n a c c u r a t e a p p o r t i o n i n g o f demand c o s t . O r d i n a r i l y s u f f i c i e n t d a t a i n r e g a r d to the v a r i o u s l o a d c u r v e s may n o t be a v a i l a b l e o r the degree o f a c c u r a c y d e s i r e d i n the r e s u l t v - m n o t w a r r a n t a n e x t e n s i v e a n a l y s i s on t h i s b a s i s . T h e r e Is no d o u b t t h a t t h e o r e t i c a l l y i t w i l l g i v e a more a c c u r a t e d i s t r i b u t i o n o f the demand c o s t f o r most p u r p o s e s t h a n e i t h e r o f the o t h e r methods m e n t i o n e d and the p r i n c i p l e s i n v o l v e d may o f t e n be u s e d to a d v a n t a g e , even i n a more a p p r o x i m a t e d e t e r m i n a t i o n . F o r some s p e c i a l u s e s , as w i l l be e x p l a i n e d l a t e r , the s e c o n d method g i v e n above i s p r e f e r a b l e , GENERAL METHOD FOR DETERMINING DEMAND COST AT ANY P O I N T . ' — I n order-to d e t e r m i n e , t h e demand c o s t a t any p o i n t on the system o t h e r t h a n the g e n e r a t i n g s t a t i o n the f o l l o w i n g g e n e r a l s t e p s s h o u l d be 26 followed (see F i g . 3) : 1» Apportion the •generating-statlon demand cost among the various substations by one of the • above methods, i n accordance with t h e i r loads. 2• For any substation, add to i t s portion- of the generating s t a t i o n cost the demand costs on -its transmission l i n e s and cables and on the substation i t s e l f . 3* The t o t a l demand cost - for the substation can now be d i s t r i b u t e d among the various l i n e s feeding out from i t and by repeating the same method the cost at any point or forany customer may be determined. I f more general figures only are-desired the t o t a l demand cost for the substation may be-divided among various classes of load such as, l i g h t i n g , commercial power, -street l i g h t i n g , s t r e e t railway, e t c . By assuming average figures-on l i n e costs, the cost at any distance from the substation for each class of load can be determined. The analysis may be extended i n a sim i l a r manner to cover suburban transmission l i n e s , substations and d i s t r i b u t i o n even where several substations i n -tervene ». •  Any such analysis .should give a f a i r l y accurate demand charge at any point. It requires however quite a large amount of accurate data for i t s . accomplishment* Detailed annual costs on each subdivision of the system must be known. Al s o the load curves through the year, for each load considered such as substations, power l i n e s , etc., must be studied to obtain one or more c h a r a c t e r i s t i c curves for each as a basis of analysis* Where a load shows an appreciable seasonal v a r i a t i o n several curves may be necessary as for high load, low load and average load* In-many cases i t w i l l be found prac t i c a b l e to determine a general c h a r a c t e r i s t i c curve for each type of load, such as residence l i g h t i n g , street l i g h t i n g , street railway, large power, small power, etc., and r e f e r a l l -toads of that type to i t , assuming that the curve, w i l l be always proportional to the peak load* The c o l l e c t i o n , c l a s s i f i c a t i o n and proper s e l e c t i o n of data w i l l be found to be a large part of the whole problem of determination of energy cost and requires the a p p l i c a t i o n of a high degree of s t a t i s t i c a l knowledge and engineering judgment. In order to make such a d e t a i l e d analysis as proposed above the following information should, be a v a i l a b l e . 1. Cost of Generating S t a t i o n . (a) F i r s t cost and present value of various parts i n 2?r s u f f i c i e n t d e t a i l so t h a t demand, energy and c u s t o m e r ' s c o s t s c a n be s e p a r a t e d . (b) The p r o p e r , p e r c e n t a g e s o f i n t e r e s t , t a x e s , d e p r e c i a t i o n : e t c a, c h a r g e a b l e t o e a c h p a r t o (©.) O p e r a t i n g c o s t s i n some d e t a i l . (d) D e t e r m i n a t i o n o f p r o p e r p e r c e n t a g e o f e a c h i t e m o f f i x e d and o p e r a t i n g c h a r g e s b e l o n g i n g to e a c h o f the t h r e e d i v i s i o n s o f c o s t « 20 C o s t o f t r a n s m i s s i o n - L i n e C a b l e s . (a.) F i r s t c o s t a n d p r e s e n t v a l u e o f c a b l e l i n e s t o e a c h s u b s t a t i o n w i t h p r o p o r t i o n a l c o s t o f the l i n e s between , •. s t a t i o n s a fb^ As above•• . (oj S u c h o p e r a t i n g c o s t as may be c h a r g e a b l e to c a b l e s , r e p a i r s , , e t c . (d) As above« 3<> C o s t o f S u b s t a t i o n s . (a.) F i r s t c o s t a n d p r e s e n t v a l u e o f e a c h s u b s t a t i o n i n s u f f i c i e n t d e t a i l . ( b , c , d , ) as above» 4» C o s t o f O v e r h e a d L i n e s » (a) F i r s t c o s t a n d p r e s e n t v a l u e o f a v e r a g e l i n e o f e a c h c l a s s , t r a n s m i s s i o n , power l i n e , c i r c u i t , d i r e c t - c u r r e n t f e e d e r , a n d s e c o n d a r y d i s t r i b u t i o n i n c l u d i n g t r a n s f o r m e r s , p e r u n i t l e n g t h * . ( b , c , d) As a b o v e . 5 . C h a r a c t e r i s t i c C u r v e f o r G e n e r a t i n g S t a t i o n . (May be t a k e n f o r s e a s o n s o r months i n s t e a d o f f o r y e a r *) 6. C h a r a c t e r i s t i c C u r v e s f o r e a c h s u b s t a t i o n * ( C o r r e s p o n d i n g w i t h g e n e r a t i n g - s t a t i o n c u r v e s . ) 7s C h a r a c t e r i s t i c C u r v e s f o r E a c h c l a s s o f L o a d out o f E a c h S u b s t a t i o n . fOr f o r e a c h l i n e . ) TOTAL CHARGE PER KILOWATT-HOUR»»-A11 the f o r m u l a s w h i c h w i l l be d e v e l o p e d l a t e r i n c l u d e t h e c o s t o f e n e r g y as one t o t a l c h a r g e per k i l o w a t t e h o u r » The c o m p u t a t i o n s might be made w i t h t h e demand c h a r g e a n d the k i l o w a t t - h o u r c h a r g e as two s e p a r a t e q u a n t i t i e s , b u t i t i s f o u n d more c o n v e n i e n t t o use a s i n g l e c h a r g e p e r k i l o w a t t - h o u r . I f the above a n a l y s i s i s c a r r i e d o u t i n d e t a i l the demand c h a r g e f o r e n e r g y w i l l be d e t e r m i n e d a s a d i f f e r e n t amount f o r e a c h t y p e o f l o a d and f o r any d i s t a n c e from e a c h s u b s t -a t i o n . The k i l o w a t t - h o u r c h a r g e w i l l be t h e same f o r a l l l o a d s o f a p a r t i c u l a r c l a s s i f i c a t i o n i n any one l o c a l i t y . S i n c e the a v e r a g e l o a d f a c t o r f o r any type of l o a d c o n s i d e r e d may be d e t e r m i n e d , the demand c h a r g e c a n be r e d u c e d t h e r e b y t o a c h a r g e p e r k i l o w a t t - h o u r , s i n c e k i l o w a t t h o u r s == k i l o w a t t s X l o a d f a c t o r X 24 X 365 p e r y e a r . T h i s added t o t h e o u t p u t o r k i l o w a t t - h o u r 28 c h a r g e w i l l g i v e t h e t o t a l c h a r g e p e r k i l o w a t t - h o u r f o r t h a t c l a s s o f f l o a d a t ; t h a t , p o i n t . - : -., -: -' ; F U R T H E R .yARIATIONS: IN ENERGY COST * - - U p t o t h i s p o i n t t h e r e has been c o n s i d e r e d , f o r any t y p e o f l o a d and l o c a l i t y , o n l y t h e a v e r a g e u n i t c o s t o f the t o t a l energy d e l i v e r e d , w i t h o u t a t t e m p t i n g t o d i f f e r e n t i a t e between c o s t s f o r l a r g e l o a d s and s m a l l l o a d s o f the same t y p e , h i g h power f a c t o r s and low power f a c t o r s , l o s s e s and u s e d power, e t c • T h e r e w i l l now be i n d i c a t e d some o f the p o s s i b l e , v a r i a t i o n s I n t h i s c o s t and methods o f s t u d y i n g them w i l l be s u g g e s t e d . I t may be shown t h a t a l l u n i t s o f e n e r g y even o f the same c l a s s and l o c a l i t y do n o t c o s t t h e same. F o r e x a m p l e , e n e r g y l o s t has a h i g h e r u n i t c o s t t h a n energy u s e d . A g a i n , n o t o n l y does t h e t o t a l k i l o v o l t - a m p e r e s o f any l o a d I n c r e a s e as power f a c t o r d e c r e a s e s b u t t h a t I n c r e a s e c o s t s more " p e r u n i t " t h a n t h e a v e r a g e c o s t hf a 100^ power f a c t o r w e r e -o b t a i n e d . F u r t h e r , u n d e r some c o n d i t i o n s a n I n c r e a s e i n a l o a d w i l l c o s t more p e r u n i t t h a n t h e f o r m e r a v e r a g e * The u n d e r l y i n g t h e o r y i n v o l v e d may be r e a d i l y s e e n I f we c o n s i d e r the c o s t o f l o s t or waste energy f o r e x a m p l e . M o s t s u b s t a t i o n s a r e r e g u l a t e d i n some way, and i f the energy l o s s e s -between t h e s u b s t a t i o n and t h e c u s t o m e r c o u l d be reduced, t h e c u r r e n t I n the t r a n s m i s s i o n c a b l e to the s u b s t a t i o n w o u l d be a l s o r e d u c e d . S i n c e l o s s e s a r e p r o p o r t i o n a l t o t h e s q u a r e o f t h e c u r r e n t , the c a b l e l o s s e s e l i m i n a t e d by t h i s r e d u c t i o n o f the- l o a d on t h e c a b l e w o u l d be p r o p o r t i o n a l t o the d i f f e r e n c e , i n the s q u a r e s o f the c u r r e n t s b e f o r e and a f t e r r e d u c t i o n . Hence i t w i l l be s e e n t h a t " r e d u c t i o n i n l o s s $ p e r u n i t " r e d u c t i o n i n l o a d " I s g r e a t e r t h a n t h e a v e r a g e l o s s p e r u n i t o f the t o t a l l o a d , a f t e r r e d u c t i o n . I n o t h e r w o r d s , the l o s s I n the c a b l e due ...to the u p p e r p a r t o f the l o a d , w h i c h may be e l i m i n a t e d and hence may be c o n s i d e r e d w a s t e , i s g r e a t e r p e r u n i t t h a n the l o s s due to u s e f u l l o a d a n d t h e c o s t w i l l hence be more-. T h i s may b e . s h o w n m a t h e m a t i c -a l l y as f o l l o w s : Suppose a s u b s t a t i o n B I s s u p p l i e d t h r o u g h c a b l e s from a g e n e r a t i o n - s t a t i o n ' / ; • • • ; ..-h . . / -.. ; (B) W = l o a d I n w a t t s a t B P = p e r c e n t a g e o f W l o s t b e y o n d B , w h i c h may be c o n s i d e r e d . waste power w h i c h m i g h t be c o n s e r v e d i n some way, p = P / 1 0 0 - t E v o l t a g e a t B , R = r e s i s t a n c e o f c a b l e . - - o n e w i r e . 29. F o r s i m p l i c i t y assume s i n g l e - p h a s e c a b l e , u n i t y power f a c t o r , 'Then-''.:"'.;' r ' : - " ' ! : \ ' : '•; " " -v-y /;...;.;• • : / ? V z . I 2 R l o s s e s I n AB due" t o t o t a l l o a d W = 2i^jR» / (1 « P) W \ g 1 1 l o s s e s i n AB due t o power l o a d o n l y ~ 2 l — - : - -J R , T % l o s s e s i n AB due t o l o s s e s b e y o n d B - pW = / W \ ^ 7Wf /Wf p o r e x p r e s s e d i n p e r c e n t a g e o f t o t a l l o s s ^ i n AB *»100(2p. - p 2 ) - (2P - - — I p e r c e n t . .- \ 100/ (1) I f the l o s s o r waste power a t B i s a , c o m p a r a t i v e l y s m a l l p e r c e n t a g e o f W I t w i l l be s e e n that, the l o s s e s i n AB due t o t h a t waste a r e n e a r l y t w i c e t h a t p e r c e n t a g e o f the t o t a l l o s s e s : ( T e n p e r c e n t waste a t B means t h a t 19 p e r c e n t o f l o s s e s i n AB a r e due t o t h a t w a s t e * ) I f Q, p e r c e n t a g e o f •Till, l o s t between A and B , ' • j ^ - - t o t a l l o s s i n c a b l e , M _ / 2 P - _ P ? J 1/100 - l o s s I n c a b l e due to waste b e y o n d B* 1 0 0 V • 100/ B u t waste b e y o n d B -M0 H e n c e , t h e l o s s i n the c a b l e due to waste b e y o n d B p e r u n i t waste = QW / 24 " loV) 1 / 1 0 0 , ' % 100 \ 100/ (2) PW 100 S i n c e t h e a v e r a g e t o t a l l o s s I n c a b l e p e r u n i t t o t a l l o a d a t j ^ - I f c o s t o f e n e r g y p e r k i l o w a t t a t A - C e A v e r a g e c o s t a t A o f t o t a l energy a t B = ^ l + C e (3) A v e r a g e c o s t a t A o f energy waste b e y o n d B = ^ l - H ^ 2 - JQO^  (A) I n o t h e r words a l o s s o f Q, p e r c e n t i n l i n e AB I n c r e a s e s the 30 a v e r a g e c o s t o f t o t a l energy d e l i v e r e d a t B by Q, p e r c e n t * B u t i f P p e r c e n t o f t h a t t o t a l e n e r g y r e p r e s e n t s l o s s e s 'Which may be assumed t o be r e d u c i b l e or w a s t e , the a v e r a g e c o s t o f s u c h l o s s e s i s i n c r e a s e d by 0,12 - ) p e r c e n t . The d i f f e r e n c e i n a v e r a g e u n i t t o t a l v 1 0 0 / 0- / P \ c o s t and a v e r a g e u n i t waste c o s t i s t h e n (1 «* J 0 e or 100* 1 0 0 ' _ i . f i ~ J L J i o o Q ( I - __L) 1 0 0 v 100^ V... 1 0 0 ' -,x. .' : — — = —— p e r c e n t o f a v e r a g e c o s t . 1 + • •• ,1.+ — 100 1 0 0 a t A o f t o t a l amount o f e n e r g y d e l i v e r e d a t Bo (5) F o r e x a m p l e , i f 1,000 kw. were t r a n s m i t t e d o v e r a l i n e f o r 1 hr» w i t h a l o s s o f 6 p e r c e n t — i f 10 p e r c e n t o f t h a t 1,000 r e p r e s e n t s r e d u c i b l e l o s s e s o r energy w a s t e d b e y o n d the end o f the l i n e -P •« 10 Q - 6 I f energy a t A c o s t s Itf p e r k i l o w a t t - h o u r the a v e r a g e c o s t p e r k i l o w a t t - h o u r d e l i v e r e d a t B I n c l u d i n g l o s s e s i n AB b u t n o t f i x e d c h a r g e s on l i n e = ( 1 + ) 0 0 1 «* .0106 per k i l o w a t t hour ..V ••- I O O 7 ( from Eq» 3) • The a v e r a g e c o s t o f e n e r g y waste b e y o n d B i s / l-h — 1 2 - — J) .01 - .01114 ( f r o m K q . 4 ) . A 100 V 1007 The d i f f e r e n c e i s .00054 w h i c h i s 5 . 1 p e r c e n t o f the a v e r a g e . . The same p e r c e n t a g e o f i n c r e a s e w o u l d be o b t a i n e d from E q . 5* .6A. «; -H) ioo -•: . y , 1 0 0 / : 5 4 Q 1 ~ " : "—=-Q^ * ~ 5.1 p e r c e n t 100 -h 6 •• I t must be n o t e d t h a t the above d e a l s w i t h t h e a v e r a g e c o s t a t A o f e n e r g y d e l i v e r e d a t B . I n o r d e r t o d e t e r m i n e the a v e r a g e c o s t a t B o f e n e r g y d e l i v e r e d a t B the c h a r g e s on t h e - l i n e AB. must be i n c l u d e d . These s h o u l d be p r a c t i c a l l y p r o p o r t i o n a l t o W and hence w o u l d a v e r a g e the same p e r u n i t f o r b o t h u s e f u l l o a d a n d f o r l o s s e s . The above m e r e l y e s t a b l i s h e s the f a c t o f the i n c r e a s e d c o s t o f waste energy a n d must n o t be c o n s i d e r e d as i n d i c a t i v e o f the a c t u a l amount o f t h a t i n c r e a s e . I n d e t e r m i n i n g t h i s a number o f v a r i a b l e q u a n t i t i e s must be c o n s i d e r e d : 31 1. The demand charge f o r waste energy at any po i n t should he f i g u r e d by the second method given under th a t heading, I.e., making up the demand charge, f o r any l o a d , of charges p r o p o r t i o n a l to. the amount of t h a t l o a d at the time of peak l o a d on s t a t i o n , t r a n s m i s s i o n c a b l e , s u b s t a t i o n , e t c . The reason f o r t h i s i s seen when i t i s considered t h a t the demand, c o s t onlthbo s t a t i o n , f o r example, i s considered p r o p o r t i o n a l to the s t a t i o n peak* I f t h a t peak can be reduced by e l i m i n a t i n g waste energy f w i t h o u t - r e d u c i n g the u s e f u l load) the demand cost w i l l be l i k e w i s e reduced i n p r o p o r t i o n . This c o n t e n t i o n does not a P P l y t o u s e f u l l o a d s i n c e , f o r t h i s , the company i s r e c e i v -i n g a monetary r e t u r n * The a c t u a l demand c o s t should be d i s t r i -buted to- such loads by the more e q u i t a b l e t h i r d method. I n other words, a r e d u c t i o n of l o s s e s a t off-peak time would not a f f e c t the a c t u a l demand c o s t of the s t a t i o n nor the d i s t r i b u t i o n of that c o s t among the u s e f u l loads* A r e d u c t i o n of u s e f u l l o a d at o f f peak would reduce the revenue and hence increase the c o s t to other l o a d s . 2o The example above uses the energy charge as a s i n g l e t o t a l charge per k i l o w a t t - hour and the l o s s a t a d e f i n i t e percentages Since the percentage l o s s v a r i e s as the lo a d v a r i e s d u r i n g the day the i n c r e a s e i n c o s t w i l l not depend on the percentage l o s s e s a t maximum l o a d . The v a r i a t i o n i n l o s s w i l l a f f -e c t both the demand charge and the kilowatt«hour charge and each.in d i f f e r e n t p r o p o r t i o n . ,1' 3. I f s e v e r a l loads of d i f f e r e n t s i z e s - a n d c h a r a c t e r i s t i c s are considered the problem i s f u r t h e r complicated. 4* I f l i n e s are operated under the most economical load, t h e l o s s e s may be considered as u s e f u l l o a d r a t h e r than waste» V As has been'stated before the theory here explained' can a l s o be a p p l i e d to determination of the a d d i t i o n a l c o s t of low power f a c t o r , of load I n c r e a s e s ' ( I n some eases) and" other s i m i l a r problems. I t would appear that each -unit of energy comprising any load:misht be conceived as having a d i f f e r e n t c o s t * I n d e a l i n g w i t h l o s s e s h o w e v e r , a l a r g e percentage of l o s s may be assumed to c o s t more per u n i t than, a s m a l l percentage. T h i s idea o-fincrea.sed c o s t of l o s s e s and waste energy I s an important one to bear i n mind i n a l l economical s t u d i e s , s i n c e u s u a l l y such a study i s fundamentally the-; estab-l i s h i n g of the most economical r e l a t i o n between cos t of energy l o s s and other c o s t s . -This chapter i s intended to be more a suggestion as to how the problem of c o s t of energy and energy l o s s e s may be st u d i e d r a t h e r than a complete s o l u t i o n or a recommended method.-to cover a l l cases. I t may be e a s i l y seen that the study of energy c o s t might be c a r r i e d t o an almost i n f i n i t e degree of refinement. Many economical s t u d i e s are general f o r any p a r t of a system and are intended to cover a periodd of time, w e l l i n t o the f u t u r e * For these cases a very de~ t a i l e d d e t e r m i n a t i o n of energy cost would not seem necessary, I f the more accurate c o s t s are once determined however, they can e a s i l y "be averaged f o r a more general problem. Lack of time and of the necessary data w i l l , i n many cases, l i m i t the study to more ©r l e s s approximate r e s u l t s * • I t i s hoped, however, that the methods and p r i n c i p l e s here e x p l a i n e d ' w i l l g i v e a good i d e a of the nature of the problem* D e t a i l e d analyses of energy c o s t , when data i s a v a i l a b l e , w i l l w e l l repay the e f f o r t expended* Even a more approximate study w i t h these t h e o r i e s i n mind w i l l I n d i c a t e the r e l a t i v e c o s t s of en-ergy at v a r i o u s p a r t s of the system, of v a r i o u s types of l o a d s , and the r e l a t i o n between the c o s t of waste and u s e f u l energy* CHAPTER LV LOAD CHARACTERISTICS C o n s i d e r a t i o n o f the c o s t o f e n e r g y , i n t h e p r e v i o u s c h a p t e r b r o u g h t f o r t h some o f the q u a n t i t i e s t h a t a r e u s e d i n a n a l y z i n g t h e c h a r a c t e r o f a l o a d and i t s r e l a t i o n to o t h e r l o a d s * I t was a l s o i n d i c a t e d t h a t t h e r e a r e many k i n d s o f l o a d s and t h a t e a c h one o f t h e s e c a n be e x p r e s s e d i n terms o f i t s c h a r a c t e r i s t i c s * I t i s p r o p o s e d h e r e t o d e f i n e and b r i e f l y comment on some o f t h e s e t e r m s : power f a c t o r , b a l a n c e f a c t o r , l o a d f a c t o r , demand f a c t o r , d i v e r s i t y f a c t o r , and e q u i v a l e n t h o u r s . The d e f i n i t i o n o f e a c h one o f t h e s e terms w i l l be t a k e n , when a v a i l a b l e , from t h e " S t a n d a r d i z a t i o n R u l e s " o f the A * I . E * E . Power F a c t o r . - - " T h e r a t i o o f the power t o the v o l t - a m p e r e s o r a p p a r e n t power* I n the c a s e o f s i n u s o i d a l c u r r e n t and v o l t a g e , the power f a c t o r Is e q u a l t o the c o s i n e o f t h e i r d i f f e r e n c e i n p h a s e * " 1 (Power i n a n a l t e r n a t i n g - c u r r e n t c i r c u i t . The a v e r a g e v a l u e o f the p r o d u c t s o f t h e c o i n c i d e n t , i n s t a n t a n e o u s v a l u e s o f the c u r r e n t a n d v o l t a g e f o r a c o m p l e t e c y c l e , as i n -d i c a t e d by a w a t t m e t e r . ) I n a l t e r n a t i n g - c u r r e n t s y s t e m s , I t i s u n f o r t u n a t e t h a t t h e c o s t o f m e e t i n g a g i v e n demand and s u p p l y -i n g a g i v e n amount o f e n e r g y v a r i e s a l s o w i t h a l o a d c h a r a c t e r -i s t i c c a l l e d " p o w e r - f a c t o r , w h i c h i s imposed by the a p p a r a t u s t h a t u s e s the e l e c t r i c e n e r g y * The p o w e r - f a c t o r o f a g i v e n a p p a r a t u s i s i n r e a l i t y a measure o f t h e e f f e c t i v e n e s s w i t h w h i c h i t u s e s e l e c t r i c c u r r e n t , and i n v a l u e i t r a n g e s from 15 p e r c e n t i n c e r t a i n w e l d i n g t r a n s -f o r m e r s t o 100 p e r c e n t i n f i l a m e n t l a m p s . . The most I m p o r t a n t o f f e n d e r i s the i n d u c t i o n m o t o r , the power-f a c t o r o f w h i c h v a r i e s from 63 p e r c e n t a t l i g h t l o a d ^ Jt,o ...9„1...P?.F c e n t a t f u l l l o a d . "* "~~ • Low p o w e r - f a c t o r means e x c e s s i v e i n v e s t m e n t i n e l e c t r i c a l equipment t o p r o v i d e c a r r y i n g c a p a c i t y f o r c u r r e n t needed to m a g n e t i z e c u s t o m e r a p p a r a t u s , a n d t h i s c u r r e n t b e i n g 90 d e g r e e s out o f phase w i t h t h e v o l t a g e , c o n t r i b u t e s no a p p r e c i a b l e amount t o the e n e r g y l o a d upon w h i c h the b i l l i n g f o r s e r v i c e iT*^ased*T"^ T h e r e i s no u n i v e r s a l l y a c c e p t e d p r a c t i c e w i t h r e g a r d t o the h a n d l i n g o f t h i s p o w e r - f a c t o r i t e m i n the r a t e s y s t e m . Some companies d e t e r m i n e t h e p o w e r - f a c t o r , o f the c u s t o m e r ' s l o a d , t h e n p e n a l i z e him i f I t I s b e l o w : a . ; c e r taiftriamouftt-and-rewards him > i f - . ' i t i s above ;• o t h e r s I n s t a l l c o r r e c t i v e a p p a r a t u s i n t h e s u b - s t a t i o n s to r a i s e the s t a t i o n p o w e r - f a c t o r t o u n i t y , and l e t the c u s t o m e r do as he wishesJ= S t i l l o t h e r s i s s u e r e s t r i c t i v e r e g u l a t i o n s d i c t a t i n g the k i n d s o f a p p a r t u s t h a t c a n be u s e d w i t h o u t i n s t a l l i n g o f f s e t t i n g c o r r e c t i v e a p p a r a t u s . Look a t i t I n any way one w i l l , low p o w e r - f a c t o r I s a d e t r i m e n t t o good s e r v i c e . I t n o t o n l y o c c u p i e s v a l u a b l e e l e c t r i c a l " A . I . E . E . S t a n d a r d s #3242 34 c a p a c i t y b u t i t s e r i o u s l y d i s t u r b s v o l t a g e r e g u l a t i o n and t h e r e b y i n t e r f e r e s w i t h good s e r v i c e * From the p o i n t o f v i e w o f the d e s i g n e r o f a n e c o n o m i c a l l i n e the power f a c t o r i s u s u a l l y d e t e r m i n e d In advance by the l o a d a t the end o f the l i n e and i t i s n o t w i t h i n h i s . p r o v i n c e t o change i t s v a l u e - The i n t e r e s t i n g - p o i n t to him Is r e a l l y the k i l o v o l t - a m p e r e s h i s l i n e has to c a r r y , as i t i s the c u r r e n t o f a l o a d t h a t d e t e r m i n e s , on a c c o u n t o f t h e energy l o s s e s , n o t o n l y the e c o n o m i c a l l o a d i n g o f a n o l d l i n e , b u t t h e econom-i c a l s i z e ".of r w l r e f o r a new l i n e d e s t i n e d t o c a r r y a g i v e n known l o a d . I t I s e v i d e n t , however, t h a t w h i l e making s t u d i e s i n e c o n o m i c a l h a n d l i n g o f l o a d s the e f f e c t s o f power f a c t o r w i l l be .most f o r c i b l y b r o u g h t to v i e w and t h a t t h e d e s i r a b i l i t y o f h i g h power f a c t o r a n d g e n e r a l p o w e r - f a c t o r Improvement, p a r t i c u l -a r l y on l i n e s c a r r y i n g l a r g e amount o f power l o a d s , w i l l be shown to be most i m p e r a t i v e f o r i n c r e a s e d economy. BALANCE F A C T O R W h i l e b a l a n c e f a c t o r has n e v e r b e e n p o s i t i v e -l y d e f i n e d i t s h o u l d be r e g a r d e d as means o f e x p r e s s i n g the d i v e r -gence between a n u n b a l a n c e d l o a d on a p o l y p h a s e c i r c u i t and the same l o a d when p e r f e c t l y b a l a n c e d * W h i l e i t has b e e n assumed t h r o u g h o u t t h i s t r e a t i s e t h a t l o a d s were b a l a n c e d , I t Is e v i d e n t t h a t many p r o b l e m s w i l l a r i s e where i t w i l l be n e c e s s a r y , when s o l v i n g f o r e c o n o m i c a l d e s i g n , to make a l l o w a n c e f o r s u c h u n -b a l a n c e * L a r g e s i n g l e - p h a s e l o a d s on p o l y p h a s e c i r c u i t s w i l l o f t e n r e s u l t i n t h i s n e c e s s i t y * - .•.-DEMAND FACTOR "The r a t i o o f the maximum demand o f any s y s t e m , o r p a r t o f a s y s t e m , t o the t o t a l c o n n e c t e d l o a d o f the s y s t e m , o r o f t h e p a r t o f system u n d e r c o n s i d e r a t i o n . " (The demand o f an I n s t a l l a t i o n o r System i s the l o a d w h i c h i s drawn from the s o u r c e o f s u p p l y a t the r e c e i v i n g t e r m i n a l s a v e r a g e d o v e r a s u i t a b l e and s p e c i f i e d i n t e r v a l o f t i m e . Demand-i s e x p r e s s e d i n k i l o w a t t s , k i l o v o l t - a m p e r e s , o r o t h e r s u i t a b l e •units-.) ... • •'•••• (The Maximum Demand o f a n I n s t a l l a t i o n o r System i s the g r e a t e s t o f a l l t h e demands w h i c h have o c c u r r e d - d u r i n g a g i v e n p e r i o d . I t i s d e t e r m i n e d by measurement, a c c o r d i n g to s p e c i f i c a t i o n s , o v e r a p r e s c r i b e d : t ime i n t e r v a l . ) , Demand f a c t o r i s t h e r e f o r e t h e e x p r e s s i o n o f the r e l a t i o n between a p p a r e n t l o a d o r c o n n e c t e d l o a d and the l a r g e s t a c t u a l l o a d t h a t w i l l be e x p e c t e d a t any t ime on an i n s t a l l a t i o n . • F o r example, I f a house i s w i r e d f o r 30 o u t l e t s e a c h u s i n g a 4 0 - w a t t lamp and the g r e a t e s t number o f t h e s e o p e r a t i n g a t one t ime i s 9 n i n e , t h e demand f a c t o r i s — = . 3 or 30 p e r C e n t . On the o t h e r , 30 hand i f a s e r v i c e i s w i r e d f o r a r a n g e o f 5*5~kw. c a p a c i t y and i f a t any t i m e t h i s r a n g e i s o p e r a t e d w i t h a l l t h e e l e m e n t s '!)':. •:. '.: • ' , . • • • • • ' ' ' A . I . E . E . S t a n d a r d s #3460 t u r n e d on t h e demand f a c t o r y becomes u n i t y . The demand f a c t o r as above d e f i n e d s u f f i c e s ' f o r the g e n e r a l p u r p o s e s o f b u s i n e s s d e a l i n g s w i t h the c u s t o m e r , b u t to the d e s i g n e r I n the d e t e r -m i n a t i o n o f the i n v e s t m e n t t o s e r v e he has to c o n s i d e r t h i s demand o n l y as a n i n d e x w h i c h has t o be a d j u s t e d a c c o r d i n g to the " s t a r t i n g " k . v . a . o f the l o a d . P a r t i c u l a r l y i s t h i s so when.a l a r g e i n d u s t r i a l l o a d i s h e a v i l y m o t o r e d w i t h i n d u c t i o n m o t o r s w h i c h i n many c a s e s a r e o v e r s i z e d f o r t h e i n d i v i d u a l l o a d s t o be r e s p e c t i v e l y h a n d l e d * I n a l a r g e complex system t h i s c o e f f i c i e n t o f a d j u s t m e n t on t h e demand i n d e x I s r e a d j u s t e d by t h e d i v e r s i t y o f the l o a d , p r o v i d i n g s u c h d i v e r -s i t y o f t h e l o a d , p r o v i d i n g s u c h d i v e r s i t y e x i s t s . DIVERSITY F A C T O R . — " T h e r a t i o o f the sum o f t h e maximum-power demands o f the s u b d i v i s i o n s o f any s y s t e m o r p a r t s o f a system to t h e maximum demand o f the w h o l e / s y s t e m or o f t h e p a r t o f t h e s y s t e m u n d e r c o n s i d e r a t i o n , measured a t the p o i n t o f s u p p l y " - , ™ H e r e we e x p r e s s a l o a d r e l a t i o n between v a r i o u s l o a d s o f the same o r o f d i f f e r e n t demand f a c t o r * and o t h e r c h a r a c t e r i s t i c s . F o r i n s t a n c e , i f we take 10 h o u s e s e a c h h a v i n g 30 o u t l e t s as above and- the same demand f a c t o r o f . 3 , t h e t o t a l demand w i l l n o t be 10 x «3 x 30 x 40 0 r 3 . 6 kw. b u t some s m a l l e r amount 1 0 0 0 • due to t h e f a c t t h a t the maximum demand o f a l l t h e houses a r e n o t s i m u l t a n e o u s . T h e r e f o r e i f the maximum l o a d 04? t h e s e h o u s e s t a k e n t o g e t h e r i s 1.8 kw. the d i v e r s i t y f a c t o r i s -f-£§. = 2 . Hdre t a k e , f o r e x a m p l e , s e v e r a l e l e c t r i c r a n g e s as above t h e n the d i v e r s i t y ^ f a c t o r may be »3 w h i l e e a c h r a n g e a t some time o r a n o t h e r w i l l be o p e r a t i n g a t a demand f a c t o r o f u n i t y . S i m i l a r l y the d i v e r s i t y f a c t o r between t r a n s f o r m e r s , between s u b s t a t i o n s , between l i n e s c a n be o b t a i n e d . LOAD F A C T O R . — " T h e l o a d f a c t o r o f a m a c h i n e , p l a n t o r s y s t e m . The r a t i o o f the a v e r a g e power t o the maximum power d u r i n g a c e r t a i n p e r i o d o f t i m e . " ^ - n e a v e r a g e power i s t a k e n o v e r a c e r t a i n p e r i o d o f t i m e , s u c h as a d a y , a month, o r a y e a r , and the maximum i s t a k e n as the a v e r a g e o v e r a s h o r t i n t e r v a l o f the maximum l o a d w i t h t h a t p e r i o d . " i n e a c h c a s e , the i n t e r v a l o f maximum l o a d a n d t h e p e r i o d o v e r w h i c h t h e a v e r a g e i s t a k e n s h o u l d be d e f i n i t e l y s p e c i f i e d , s u c h as a " H a l f - h o u r m o n t h l y " l o a d f a c t o r . The p r o p e r i n t e r v a l and p e r i o d a r e u s u a l l y d e p e n d e n t upon l o c a l c o n d i t i o n s and upon t h e p u r p o s e f o r w h i c h t h e l o a d f a c t o r i s to be u s e d . " (3/ S i n c e i n e c o n o m i c a l d e s i g n a n n u a l c o s t s a r e g e n e r a l l y the b a s i s o f - a n a l y s i s I t i s e v i d e n t t h a t the p e r i o d o f t ime t o be (V A . I . E . E . S t a n d a r d s // 3464 I2) A . I . E . E . S t a n d a r d s # 3438 O) A . I . E . E . S t a n d a r d s § 3438 u s e d w i l l be 1 y e a r . I n t h i s t r e a t i s e e q u i v a l e n t h o u r s have b e e n u s e d f o r d e t e r m i n i n g e n e r g y l o s s e s o v e r a l i n e as shown b e l o w . EQUIVALENT H O U R S . - — I t i s u s u a l l y c o n v e n i e n t i n s t u d y i n g a g i v e n t y p e o f l o a d , s u c h as r e s i d e n c e l i g h t i n g , f o r e x a m p l e , t o o b t a i n the e n e r g y l o s s e s p e r y e a r i n terms o f the l o a d c a r r i e d . By " l o a d c a r r i e d , " t h e peak l o a d f o r the y e a r w i l l be meant, s i n c e i t i s f o r t h a t l o a d t h a t the s i z e o f the w i r e a n d t r a n s f o r m e r s must be d e t e r m i n e d . S i n c e t h e - e n e r g y l o s s o v e r a l i n e i s d e p e n d e n t on the s q u a r e o f the c u r r e n t a t any t i m e , i t i s e v i d e n t t h a t the t o t a l l o s s i s not. p r o p o r t i o n a l t o t h e l o a d f a c t o r s i n c e the l o a d f a c t o r I s d e t e r m i n e d from the a v e r a g e l o a d and hence I n v o l v e s o n l y the f i r s t power o f the l o a d a t any t i m e . The c o m p u t a t i o n o f t o t a l energy l o s s i n terms o f peak l o a d must be b a s e d on the s q u a r e o f the l o a d s a t any t i m e . I t i s t h e r e f o r e c o n v e n i e n t f o r t h i s p u r p o s e to d e t e r m i n e f o r e a c h o f v a r i o u s c l a s s e s o f l o a d c o n s i d e r e d a q u a n t i t y w h i c h has b e e n c a l l e d the " e q u i v a l e n t h o u r s . " " E q u i v a l e n t h o u r s " may be d e f i n e d as " t h e a v e r a g e number o f h o u r s p e r day w h i c h i t w o u l d be n e c e s s a r y f o r the peak l o a d o f the y e a r to c o n t i n u e i n o r d e r to g i v e the same t o t a l e n e r g y l o s s as t h a t a c t u a l l y g i v e n by the v a r i a b l e l o a d t h r o u g h -o u t the y e a r . " I t i s a q u a n t i t y w h i c h , i f m u l t i p l i e d by t h e l o s s a t peak loa.d on any l i n e g i v e s the a v e r a g e l o s s p e r day o v e r the y e a r . I f t h i s a v e r a g e d a i l y l o s s i s t h e n m u l t i p l i e d by 365 t h e t o t a l y e a r l y l o s s i n k i l o w a t t - h o u r s i s o b t a i n e d . T h i s t i m e s the c o s t o f e n e r g y p e r k i l o w a t t - h o u r g i v e s t h e a n n u a l c o s t o f e n e r g y l o s s . I t i s e v i d e n t t h a t i f the e q u i v a l e n t h o u r s f o r any l o a d and t h e peak demand o f t h e y e a r a r e known, t h e t o t a l y e a r l y c o s t f o r l o s s e s would be I 2 R x t x 365 x G o . where I i s t h e c u r r e n t a t peak l o a d , H I s the r e s i s t a n c e o f the c i r c u i t , t i s t h e e q u i v a l e n t h o u r s , • C i s t h e c o s t o f e n e r g y p e r k i l o w a t t - h o u r » The q u a n t i t y , e q u i v a l e n t h o u r s , i s a l s o o f use i n d e t e r m i n i n g the c o s t o f e n e r g y p e r k i l o w a t t - h o u r p r e v i o u s l y d i s c u s s e d s i n c e the c o s t o f e n e r g y l o s s e s i s a component o f t h a t c o s t . I f the c h a r a c t e r i s t i c c u r v e f o r any type o f l o a d were a v a i l -a b l e f o r a whole y e a r , the sum o f the s q u a r e s o f t h e c u r r e n t f o r e a c h hour t a k e n from t h a t c u r v e t i m e s t h e r e s i s t a n c e o f t h e c o n d u c t o r , w o u l d g i v e the t o t a l y e a r l y l o s s I n w a t t h o u r s . T h i e , . i ' h o w e v e r , w o u l d be a t e d i o u s c o m p u t a t i o n and i n most c a s e s i m -p r a c t i c a b l e . I t I F u s u a l l y s u f f i c i e n t l y a c c u r a t e to O b t a i n c h a r a c t e r i s t i c c u r v e s f o r e a c h month or a t l e a s t a t y p i c a l l y c h a r a c t e r i s t i c c u r v e a p p l i c a b l e to any month w i t h a l l o w a n c e f o r the v a r i a t i o n s i n the peak from month to m o n t h . An example o f a n a c t u a l c a l c u l a t i o n o f e q u i v a l e n t h o u r s on r e s i d e n c e l i g h t i n g c i r c u i t s w i l l i n d i c a t e a method w h i c h c a n be f o l l o w e d In such c o m p u t a t i o n s . The c h a r a c t e r i s t i c v a r i a t i o n o f the l o a d on a r e s i d e n c e -o 0 o -p o o -p © CO bo r-1 1-3 ft <*1 CO -p ^ •H CD o .0-• H S 3 O LQ O w o t o O LO O o o o o o*HcoHcr>LococoLQ<tfLoto O O O O O O i O O O ' Q ' f l ' O c r ) O a D O c o l O c x ) c o * # w t Q • ^ , H W H W H H W W W ft! H H I O L O L Q L Q L Q ' I Q L Q O L O L O L Q L O E- CTs CO O tO ^  CO tO CO W £0 r l r l r l r l r l r l M N N H H r l -O O O l O O O i f l O i O O O l O H W H H H H W W N H H - H I Q O LQ o O O O L O O O O O c x f t o H t g t o c o ^ o c - ^ o o i H H H H H i—I N H H H H O O O I O O O O O L O O O I O N r i a i o o o i w u j i f l w a i c o H i—S H H H r l H r l L Q O L O O O O O L Q L Q O L Q O ( O ^ W ^ K l O C O C O C - ' v P O O H H H r—I H H rH rirlrl H H O L O O O LO o O O LO O LQ o <£> -^ H CQ C O H O O ' C - i O O O H H H H H H H W H H H H LO LO O © O LQ O O LO 10,0.10.. ri'HH H H H W W W H H ' H O LO O O LO LO O LO LO LO LO O CO C~ LO GO LQ tO H W H C O H H H H H H r l r l W O J W r l r l H O O L Q L O i O O L O L O i O i O O O GO CO U 3 > lO'^jf CVJ W C\J CO N <N} H r H H H r - l r - I W N C v J H H H \ O O LO LO LQ O LO LO LO LO LO O cn O C~ CO LO LO sl« tO W CO N tO H W H H H H W W W H H H H 03 tO ^  LOXO !S CO © O H W H H H O •0 LO. O LO to w CX2 O CO o C\2 LO <£> LO L O w t o H L O O t o O t o cn LO t o o -LO o CM.. o o CM ,<M r-1 03 -P o EH O 03. O o CM co H t o H O .: to r-i i—I t o H H H H O H LO to -1 el CM H CD. (3 & U «a3 -P 3 7 38 l i g h t i n g c i r c u i t from month t o month was o b t a i n e d from T a b l e I o f m a x i m u m - o u r r e n t r e a d i n g s f o r e a c h month d u r i n g 1 y e a r on 12 t y p i c a l c i r c u i t s i n v a r i o u s d i s t r i c t s and w i t h v a r i o u s l o a d s * The c u r v e ( F i g . 4 ) p l o t t e d from the above a v e r a g e v a l u e s i n -d i c a t e s c l e a r l y the v a r i a t i o n o f the m o n t h l y peak l o a d s on a t y p i c a l c i r c u i t * S i n c e the peak f o r the y e a r o c c u r s i n December, the peak f o r any month may be e x p r e s s e d as a f r a c t i o n o f t h i s y e a r l y peak as f o l l o w s : - U s i n g the a v e r a g e o f 12 C i r c u i t s - - ; J a n . j F e b . M a r . Apr. . May J u n e ©.884 0 . 8 4 5 0 . 8 2 0 0*778 0*695 0 . 6 6 2 J u l y A u g . S e p t . O c t . . N o v . D e c . 0*536 0 . 6 2 8 0 . 8 3 5 0 . 8 9 8 0 . 9 6 5 1 .00 H e n c e , f o r e x a m p l e , t h e maximum c u r r e n t f o r F e b r u a r y e q u a l s .845 m u l t i p l i e d : b y • t h e maximum c u r r e n t f o r the y e a r , •etc. •••• F o r c o n v e n i e n c e the I e R l o s s f o r any month may be c o n s i d e r e d e q u a l , t o the l o s s f o r a_. t y p i c a l day i n the month t i m e s the number-..:of d a y s i n the month, s i n c e the v a r i a t i o n o f l o a d from one month t o t h e n e x t i s n o t enough to w a r r a n t more d e t a i l e d com-p u t a t i o n . The I e R l o s s i n a f e e d e r f o r any one day w o u l d be v e r y n e a r l y e q u a l to t h e sum o f the s q u a r e s o f "the c u r r e n t r e a d i n g s f o r e a c h hour d u r i n g the day m u l t i p l i e d by R . F o r a g r e a t p a r t o f the d a y , however, the. l o a d on a l i g h t i n g c i r c u i t i s v e r y l i g h t , t h e h e a v y l o a d a n d hence most o f the l o s s o c c u r i n g w i t h i n a few h o u r s . i n the e v e n i n g . By a d d i n g the s q u a r e s o f t h e h o u r l y c u r r e n t r e a d i n g s t h r o u g h o u t a day and d i v i d i n g by t h e s q u a r e o f the maximum c u r r e n t f o r t h e d a y a f i g u r e i s obtained" w h i c h r e p r e s e n t s the number o f h o u r s f o r w h i c h t h e peak l o a d f o r t h e day w o u l d have to be c a r r i e d s t e a d i l y to p r o d u c e the same I 2 R l o s s . F o r a s t r i c l t y a c c u r a t e c a l c u l a t i o n , e n o u g h d a t a s h o u l d be a v a i l a b l e t o d e t e r m i n e the shape o f the l o a d c u r v e On a t y p i c a l c i r c u i t f o r one t y p i c a l day f o r e a c h month i n the y e a r . I f t h i s i s n o t p o s s i b l e , however, a f a i r l y a c c u r a t e a p p r o x i -m a t i o n may be a r r i v e d a t i f the l o a d c u r v e s f o r o n l y one o r two months a r e a v a i l a b l e . I f t h e e a u i v a l e n t number o f h o u r s a t peak l o a d f o r a t y p i c a l day f o r t h e s e months i s d e t e r m i n e d t h e e q u i v a l e n t h o u r s f o r t h e o t h e r months may be c a l c u l a t e d more or l e s s a c c u r a t e l y by making them p r o p o r t i o n a l t o t h e number o f h o u r s between s u n s e t a n d a b o u t 10 P . M . a l l o w i n g a l i t t l e 39 a d d i t i d n a l c i i t l m e o i n " : the ".winter' i isonths f o r the m o r n i n g l i g h t -i n g p e a k . The f i g u r e s o b t a i n e d i n t h e p r e s e n t c a s e f o r t h e s e monthly e q u i v a l e n t h o u r s a t peak l o a d w i l l be f o u n d i n the f i r s t column o f the a c c o m p a n y i n g t a b l e . T a b l e 2. The l o s s f o r any day i n a month i s p r o p o r t i o n a l to the square o f the maximum c u r r e n t f o r the day m u l t i p l i e d by t h e e q u i v -a l e n t h o u r s p e r day a t peak l o a d as o b t a i n e d a b o v e . I f now we assume t h a t t h e a v e r a g e d a i l y peak w i l l be 95 p e r c e n t o f t h e peak f o r t h e month, the l o s s f o r t h i s day i s p r o p o r t i o n a l to the s q u a r e o f the maximum c u r r e n t f o r t h e month m u l t i p l i e d by •95 2 , m u l t i p l i e d . b y the e q u i v a l e n t h o u r s p e r day a t d a i l y peak l o a d as d e t e r m i n e d a b o v e . The monthly peak however i s e q u a l to a c e r t a i n f r a c t i o n o f the y e a r l y peak as shown b e f o r e . Hence t h e l o s s f o r t h i s day i n terms o f the y e a r l y peak I s p r o p o r t i o n a l to maximum c u r r e n t f o r the- y e a r , s q u a r e d , m u l t i p l i e d by t h i s f r a c t i o n f o r t h e month, s q u a r e d m u l t i p l i e d by (»9$? , m u l t i p l i e d by t h e e q u i v a l e n t h o u r s p e r day a t d a l l y peak l o a d . I f t h i s f i g u r e i s m u l t i p l i e d by the r e s i s t a n c e o f t h e c i r c u i t , R , t h e a c t u a l l o s s Is o b t a i n e d . F o r e x a m p l e , the e q u i v a l e n t h o u r s p e r day i n terms o f d a i l y peak l o a d as d e t e r m i n e d f o r F e b r u a r y a r e 4f-. The peak f o r F e b r u a r y i s .845 o f the y e a r l y p e a k . Hence f o r a t y p i c a l day I n F e b r u a r y the I 2 R l o s s e q u a l s ( y e a r l y maximum c u r r e n t ) 2 x .8452 x .952 x 4.5 x R . The t o t a l y e a r l y l o s s would be the sum o f the d a i l y l o s s e s t h u s o b t a i n e d . An a v e r a g e o f t h e f i g u r e s f o r e a c h month w o u l d t h e n g i v e t h e a v e r a g e l o s s p e r d a y . S i n c e the q u a n t i t y ( y e a r l y maximum c u r r e n t ) 2 x R Is the l o s s due to t h e y e a r l y peak l o a d , t h e a v e r a g e , number o f h o u r s . p e r day w h i c h t h a t l o a d must c o n t i n u e may be o b t a i n e d by a v e r a g i n g the o t h e r f a c t o r s e n t e r -i n g i n t o t h e c o m p u t a t i o n o f a v e r a g e d a l l y l o s s i n terms o f y e a r -l y p e a k . T h e s e a r e the q u a n t i t i e s ( e q u i v a l e n t h o u r s p e r day a t ^monthly peak I 2 d a i l y peak l o a d ) x< —->x 95 2 as d e t e r m i n e d f o r e a c h ( y e a r l y peak J m o n t h . The r e s u l t i n g a v e r a g e I s the v a l u e o f " e q u i v a l e n t h o u r s " f o r t h a t l o a d , and as i n d i c a t e d i n T a b l e 2 w h i c h shows the d a t a worked o u t from t h e above example o f r e s i d e n c e l i g h t i n g the e q u i v a l e n t h o u r s i s e q u a l to 2 .27* C o r r e c t i o n s f o r S p e c i a l C o n d i t i o n s . - - T h e f i g u r e s i n T a b l e 2 a r e s u b j e c t t o c o r r e c t i o n u n d e r c e r t a i n c o n d i t i o n s . A c t u a l l o a d s on c i r c u i t s were u s e d and no a l l o w a n c e was made f o r t h e n o r m a l i n c r e a s e w h i c h m i g h t be e x p e c t e d on l i g h t i n g l o a d , due to a d d i t -i o n a l c u s t o m e r s , the i n c r e a s e d use o f c u r r e n t by o l d c u s t o m e r s , etc. . T h i s .might be a s a t i s f a c t o r y f i g u r e f o r use i n many c a s e s b u t - t h e r e , w i g h t , b e o c c a s i o h s o i n l w h ' i c h n a . . l o a d showing o n l y s e a s o n a l v a r i a t i o n s would be e n c o u n t e r e d . f c - F o r e x a m p l e , i f d i s t r i b u t i o n t r a n s f o r m e r s a r e k e p t loadfvnearly t o c a p a c i t y , new i n s t a l l a t i o n s w o u l d c a r e f o r t h e y e a r l y i n c r e a s e a n d e a c h 40 i n d i v i d u a l t r a n s f o r m e r w o u l d show n e a r l y the same l o a d from y e a r to y e a r , i n c a s e the a n n u a l r a t e o f i n c r e a s e i s known, a c o r r e c t i o n c a n be a p p l i e d to the f i g u r e s g i v e n f o r e a c h month t o r e d u c e i t to the same maximum l o a d f o r the y e a r . . I n t h e example - g i v e n , t h e a v e r a g e y e a r l y I n c r e a s e o v e r a number o f y e a r s was f o u n d to be 2 0 . 3 per c e n t o r 1*69 p e r c e n t p e r m o n t h . A s s u m i n g December as the y e a r l y p e a k , t h e r a t i o o f t h e peak f o r e a c h month t o the y e a r l y peak was c o r r e c t e d b y a p r o p o r t i o n a l p a r t o f the y e a r l y i n c r e a s e , i » e „ f o r November i t was i n c r e a s e d by 1.69 p e r c e n t , f o r O c t o b e r 3*38 p e r c e n t , e t c . TABLE 2 e-s i s o E-i to < 5 <q > TO M CC P D & <q c o o W tE t4 Sal o o Pi CM ft; O &« fc O to . <5 • x 5 J a n u a r y . F e b r u a r y M a r c h . . " A p r i l . • May J u n e • ' • J u l y . A u g u s t . September O c t o b e r . . November. December. T o t a l . . . . A v e r a g e . « 54 4 f a t 2 i 2 2* 3 i 4 5 5-1 .884 .845 •820 .778 ?695 .662 .536 0 628 .835 .898 .965 1 .00 .781 •714 .672 .606 . 4 8 3 .438 .287 o395 «697 «806 .931 loOO 6 9 • • 0 9 » t> » • 9. 9 9 * 4 . 1 0 3 . 2 1 2.185 1.67 1*088 «767 »574 -987 3o224 4 , 6 5 5 5 - 5 0 0 30 . 2 2 3 2.519 2.519 x ( .95) — 2.27 e q . h r . p e r day a t peak l o a d . The above i n d i c a t e s t h a t f o r the example u s e d o f p u r e l y l i g h t -i n g l o a d the t o t a l l o s s f o r the y e a r w i l l be the same as i f the peak l o a d were c a r r i e d 2„27 h o u r s p e r day t h r o u g h o u t the y e a r . TABLE 3 M o n t h l y r a t i o 1 . . . C o r r e c t i o n f a c -Jan«. , .  •• F e b . I M a r . A p r . May June .884 1.177 1.040 .845 1.160 .981 .820 1.143 .937 .778 1.126 '•.876 <-695 1.119 .778 .662 1.102 .729 C o r r e c t e d r a t i o . . "I • M o n t h l y r a t i o . • . C o r r e c t i o n f a c - . C o r r e c t e d r a t i o . . J u l y A u g . . S e p t • -O c t . Nov.' Dee « .536 1.085 .581 .628 1.068 .571 .835 1.051 .878 .898 1.034 .930 .965 1.017 .980 1.00 1.00 . 1.00 peak l o a d f o r month M o n t h l y R a t i o u n c o r r e c t e d . peak l o a d f o r y e a r The above i n d i c a t e s what the a c t u a l c o r r e c t e d peak on s u c h l o a d i s i n J a n u a r y b u t n o f enough d i f f e r e n c e w i l l be i n t r o d u c e d to n e c e s s i t a t e a r e v i s i o n o f the f i g u r e s t o t h a t b a s i s . I f now the e q u i v a l e n t h o u r s a r e computed on t h e b a s i s o f the above r a t i o s a new f i g u r e Is o b t a i n e d f o r a l o a d i n g w i t h no y e a r l y i n c r e a s e . I n t h i s c a s e the e q u i v a l e n t h o u r s t h u s c o r r e c t e d a r e computed to be 2.65 i n s t e a d o f 2.27 as d e t e r m i n e d f o r a c t u a l l o a d i n g , w i t h a y e a r l y i n c r e a s e . A f u r t h e r c o r r e c t i o n may be a p p l i e d i f , " as i n e a s e o f t r a n s f o r m e r s , t h e f u l l - l o a d c a p a c i t y i s to be u s e d i n s t u d y i n g l o s s e s r a t h e r t h a n the a c t u a l l o a d c a r r i e d . ' I f , f o r e x a m p l e , on t h e above c i r c u i t s the t r a n s f o r m e r s were c a r r y i n g , on an a v e r a g e , 89 per c e n t o f t h e i r f u l l - l o a d c a p a c i t y , the e q u i v a l e n t h o u r s b a s e d on c o n n e c t e d c a p a c i t y w o u l d be 2.65 x . 8 9 2 = 2 . 0 7 - T h a t i s to s a y , t h e y e a r ' s l o s s i n energy w o u l d be e q u a l to the f u l l l o a d c u r r e n t on the t r a n s -f o r m e r c a r r i e d 2 .07 h r . p e r day t h r o u g h o u t the y e a r . O t h e r c o r r e c t i o n s may be n e c e s s a r y to meet p a r t i c u l a r c o n d i t i o n s . The above w i l l g i v e an i n d i c a t i o n o f how s u c h c o r r e c t i o n s s h o u l d be a p p l i e d . The m a t t e r o f e q u i v a l e n t h o u r s s h o u l d be c a r e f u l l y 42 s t u d i e d and as a c c u r a t e , f i g u r e s as p o s s i b l e o b t a i n e d f o r v a r i o u s c l a s s e s o f l o a d . The v a l u e s w i l l v a r y , n a t u r a l l y , f o r d i f f e r e n t s e c t i o n s o f the c o u n t r y as w e l l as f o r d i f f e r e n t l o c a l i t i e s i n the same s e c t i o n o r on the same s y s t e m . The h a b i t s ©faa. community, as to h o u r s o f r i s i n g a n d ' r e t i r i n g , e t c . , w i l l a f f e c t the v a l u e f o r l i g h t i n g l o a d s . On p o w e r l l o a d s , o f c o u r s e , t h e n a t u r e o f the i n d u s t r y w i l l be a c o n t r o l l i n g f a c t o r , i n g e n e r a l f o r t h e c a s e s coming w i t h i n the e x p e r i e n c e o f t h e w r i t e r the v a l u e s l i e w i t h i n the r a n g e g i v e n b e l o w : Power Load»-from 0 t o 10 e q . h r . R e s i d e n c e l i g h t i n g — f r o m 2 t o 3 e q . hr« S t o r e l i g h t i n g ( s m a l l ) — 2 t o 3 e q . h r . S t o r e l i g h t i n g ( l a r g e ) — f r o m 2 to 5 e q . h r . S t r e e t l i g h t i n g - > - f r o m 5 t o 10 e q . 'hr* RELATION BETWEEN LOAD FACTOR AND EQUIVALENT H O U R S . — I t i s ' i n t e r e s t i n g t o f i n d what t h e r e l a t i o n between l o a d f a c t o r and' e q u i v a l e n t h o u r s i s , " e s p e c i a l l y as one o r the o t h e r q u a n t i t y may be . ' a v a i l a b l e i n a p r o b l e m , w h i l e the o t h e r i s n e c e s s a r y f o r t h e : s o l u t i o n a t h a n d . F o r our p u r p o s e i t w i l l be f o u n d p a r t i c u l a r l y u s e f u l i n making an a p p r o x i m a t e d e t e r m i n a t i o n o f e q u i v a l e n t h o u r s i f the l o a d f a c t o r i s known. L i m i t s may be e s t a b l i s h e d w i t h i n w h i c h t h e v a l u e o f t h e r e l a t i o n between l o a d f a c t o r a n d e q u i v a l e n t h o u r s w i l l l i e i n a l l : c a s e s . The. extreme c a s e s a r e as f o l l o w s . : . • •"£* The peak l o a d Is on f o r a s h o r t t ime o n l y . The r e m a i n d e r o f t h e l o a d c u r v e i s f l a t f o r the r e s t o f the d a y . See F i g . 5 a I n t h i s c a s e the amount o f the c o n t i n u o u s l o a d d i v i d e d by the momentary peak g i v e s t h e l o a d f a c t o r . The I 2 R l o s s - T r 2 R x 24 = ( L F x T ) 2 R x 2 4 . • a v . •• .•••.• : max' •• - • ( L F ) 2 x I 2 R x 24 E q u i v a l e n t : h o u r s a t peak load=— — - — ^ a x ^_E :{X,F) 2 x 24. I max R I I . The peak l o a d i s c o n t i n u o u s f o r a p a r t o f the d a y — T h e l o a d i s t h e r e a f t e r . See F i g . 5 b . I n t h i s c a s e the l o a d f a c t o r I s the number o f h o u r s t h e l o a d Is o n , d i v i d e d by 2 4 . -The I 2 R l o s s = I 2 R x ( L F x 2 4 ) . max E q u i v a l e n t h o u r s = L F x 24 I I I . F o r any I n t e r m e d i a t e a r r a n g e m e n t o f l o a d . See F l g i 5 c . A t any t i m e , , t „ , l e t the v a l u e o f I = p I * J * n» n * n max The l o a d f a c t o r =• / n m a * = / p „ d t . •^ max I e R l o s s = / ( p i ) 2 R d t » E q u i v a l e n t h o u r s — /p,_ d t max 2 , t , 0 fc> y?n I t i s e v i d e n t from the n a t u r e o f the c u r v e s t h a t f o r any l o a d f a c t o r C a s e s I , a n d I I a r e l i m i t i n g c a s e s s i n c e no g r e a t e r d i s t r i b u t i o n o f l o a d c a n be o b t a i n e d t h a n Case I and no g r e a t e r c o n c e n t r a t i o n than. Case I I . The r u l e c a n be s t a t e d as f o l l o w s g " F o r - a n y g i v e n : l o a d f^^  the c o r r e s p o n d i n g v a l u e o f e q u i v a l e n t h o u r s w i l l be somewhere between the l i m i t s o f ( l o a d f a c t o r x 24) and ( l o a d f a c t o r ) 2 x 2 4 . CHAPTER V 44 GENERAL EQUATION K e l v i n ' s L a w — G e n e r a l Method o f S o l v i n g P r o b l e m s -P r e s e n t a t i o n o f R e s u l t s The p r e v i o u s c h a p t e r s have d e a l t l a r g e l y w i t h t h e d a t a n e c e s s a r y f o r t h e e c o n o m i c a l s t u d y o f d i s t r i b u t i o n p r o b l e m s , and the methods o f o b t a i n i n g the n e c e s s a r y d a t a * The c o s t o f m a t e r i a l and l a b o r , the a n n u a l c h a r g e s on t h e s e i t e m s , the u n i t c o s t o f e n e r g y f o r d i f f e r e n t l o a d s a n d t h e a n n u a l c o s t o f energy l o s s e s have a l l b e e n t a k e n up I n some d e t a i l s Once the data, a r e c o l l e c t e d , t h e r e s t i l l r e m a i n s the p r o b l e m o f so u t i l i z -i n g them as t o o b t a i n the most e c o n o m i c a l c o n d i t i o n s f o r the l i n e o r l i n e s u n d e r c o n s i d e r a t i o n . A l s o , means must be found f o r so e x h i b i t i n g the r e s u l t s , by e q u a t i o n s , g r a p h s , t a b l e s , e t c * , t h a t t h e y w i l l be c o n v e n i e n t o f a p p l i c a t i o n to p r e s e n t p r o b l e m s and to s i m i l a r p r o b l e m s I n the f u t u r e and s u b j e c t to e a s y r e -v i s i o n w i t h c h a n g i n g p r i c e s * A l t h o u g h e v e r y p r o b l e m o f t h i s n a t u r e t h a t i s c o n s i d e r e d w i l l p r e s e n t c e r t a i n c h a r a c t e r i s t i c s o f i t s own w h i c h make i t d i f f e r e n t from a l l o t h e r s , t h e r e a r e c e r t a i n u n d e r l y i n g p r i n c i p l e s a n d methods o f p r o c e d u r e w h i c h a r e a p p l i c a b l e t o a l l . A b r i e f d i s c u s s i o n o f t h e s e w i l l be g i v e n h e r e . A good u n d e r s t a n d i n g o f t h e s e g e n e r a l methods w i l l s i m p l i f y the s t u d y o f t h e i r a p p l i c a . -t i o n to p a r t i c u l a r p r o b l e m s , w h i c h w i l l f o l l o w I n s u b s e q u e n t c h a p t e r s • K e l v i n ' s L a w , - - To S i r W i l l i a m Thompson ( L o r d K e l v i n ) i s g e n e r a l l y a t t r i b u t e d t h e b a s i c s tudy o f e c o n o m i c a l c o n d u c t i o n o f e l e c t r i c a l c u r r e n t s ? I n 1881 he e x p r e s s e d the p r i n c i p l e t h a t " t h e most e c o n o m i c a l s i z e o f c o p p e r c o n d u c t o r f o r - t h e t r a n s m i s s i o n o f e l e c t r i c a l energy would be f o u n d by c o m p a r i n g t h e a n n u a l I n t e r e s t on t h e money v a l u e o f the c o p p e r w i t h the money v a l u e o f t h e energy l o s t In I t a n n u a l l y I n t h e h e a t g e n e r a t e d i n i t by. the e l e c t r i c c u r r e n t « » . C o n t r a r y t o a v e r y p r e v a l e n t i m p r e s s i o n and b e l i e f , t h e gage t o be c h o s e n f o r t h e c o n d u c t o r does n o t depend on t h e l e n g t h , o f i t t h r o u g h w h i c h t h e e n e r g y i s t o be t r a n s m i t t e d . I t depends s o l e l y on t h e s t r e n g t h o f t h e c u r r e n t t o be u s e d s u p p o s i n g the c o s t o f the m e t a l and o f a u n i t o f e n e r g y t o be d e t e r m i n e d . " I n e x p r e s s -i n g t h i s m a t h e m a t i c a l l y , the t o t a l a n n u a l c o s t was e x p r e s s e d a s " t h e sum o f t h e f i x e d c h a r g e s o n : t h e c o n d u c t o r and the c o s t o f energy l o s s . The s i z e o f w i r e f o r w h i c h t h i s w o u l d be a. minimum was t h e n d e t e r m i n e d , n a m e l y , t h a t s i z e f o r w h i c h t h e two component c h a r g e s a r e e q u a l . What i s g e n e r a l l y known as K e l v i n ' s Law has b e e n f o r m u l a t e d from t h i f , i . e . , . t h a t the most e c o n o m i c a l s i z e o f c o n d u c t o r i s t h a t f o r w h i c h t h e a n n u a l c h a r g e on the I n v e s t m e n t i e e a u a l to the a n n u a l c o s t o f e n e r g y . l o s e . Under modern c o n d i t i o n s w i t h t h e use o f a l t e r n a t i n g c u r r e n t s , wide r a n g e o f v o l t a g e s , l a r g e v a r i e t y o f w i r e s i z e s , w i t h and w i t h o u t i n s u l a t i o n , e t c . , a n i n d i s c r i m i n a t e use o f K e l v i n ' s Law ae t h u s s t a t e d i s l i a b l e t o l e a d t o c o n s i d e r a b l e e r r o r . I t w i l l a p p l y s t r i c t l y o n l y t o p r o b l e m s f o r w h i c h the c o s t o f c o n d u c t o r s u p p o r t s c a n be n e g l e c t e d ( o r I s d i r e c t l y p r o p o r t i o n a l t o t h e s i z e o f w i r e ) , when t h e c o s t o f any s i z e o f w i r e i s d i r e c t l y p r o p o r t i o n a l t o the c r o s s - s e c t i o n a l a r e a o f the c o p p e r , when no t r a n s f o r m e r s , c o n d e n s e r s , o r o t h e r equipment need be c o n s i d e r e d and when t h e c o s t o f energy l o s s i s i n v e r s e l y p r o p o r t i o n a l t o t h e w i r e s i z e . F o r e x a m p l e , w i t h t h e f o l l o w i n g known d a t a ' a s o l u t i o n i n g e n e r a l i s had as f o l l o w s : F i g . 7 a . g r a p h i c a l l y I n d i c a t e s the method o f s o l u t i o n as o b t a i n e d m a t h e m a t i c a l l y by t a k i n g the f i r s t d e r -i v a t i o n o f t h e r e s u l t a n t e x p r e s s i o n w i t h r e s p e c t t o one o f the v a r i a b l e s , and e q u a t i n g I t t o z e r o , Ce = C o s t p e r kw. h r . f o r w a s t e d e n e r g y . P = P r i c e p e r 100# c o n d u c t o r , a == I n t e r e s t and d e p r e c i a t i o n i n % 21 - F t . o f l i n e w = w t . o f c u . f t . o f w i r e - 3-03 x 10 - 6 l b s . I = E f f e c t i v e c u r r e n t , t = f E f f . h r s . p e r y e a r o p e r a t i o n A.- A r e a o f c o n d u c t o r /=* = S p e c i f i c c o n d u c t i v i t y — 10.8 C ~= t o t a l C o s t s K - M i s , C o s t = C o n s t a n t . P a 2tf Ce C = 2<TAw- x H ld t + K 100 100 A 1000 dc 2±* I 2 t Ce 1 0 " 5 = 2 t w aPIO = 0 dA A 2 0 1 0 P l 2 t C 2 • • e - 4 . 2 < f .2 A * 2£wpa 10 =- ^ — I t C e 10~-^  and A = ; where / 10 x P g 0 0 Q ; W v^-; (7) A « 6000 I / « 6000 IK" a From e q u a t i o n (7) a u s e f u l q u a n t i t y i s d i r e c t l y o b t a i n e d w h i c h g i v e s the e c o n o m i c a l c u r r e n t d e n s i t y a t w h i c h a c o n d u c t o r s h o u l d be o p e r a t e d . T h i s f a c t o r i s o f i n e s t i m a b l e v a l u e to d e s i g n e r s o f t r a n s m i s s i o n l i n e s . E q u a t i o n (7) when r e 46 s t a t e d by d i v i d i n g b o t h terms by I . C u r r e n t d e n s i t y * the c u r r e n t , g i v e s t h e A •= 6000 K" where K"= • ' (7a) N e e d l e s s t o s a y , few p r o b l e m s c o u l d be i n c l u d e d under the above* I n most c a s e s i t i s n e c e s s a r y to r e v e r t t o K e l v i n ' s o r i g i n a l method w h i c h was to d e t e r m i n e a n e x p r e s s i o n f o r the t o t a l a n n u a l c o s t and from t h i s to d e t e r m i n e the most e c o n o m i c a l c o n d i t i o n d e s i r e d * T h i s w i l l i n c l u d e n o t o n l y the i n v e s t i g a t i o n o f the most e c o n o m i c a l w i r e s i z e b u t a l s o o f the most e c o n o m i c a l v o l t a g e , the most e c o n o m i c a l r o u t e , the most e c o n o m i c a l s i z e ••and•• s p a c i n g o f t r a n s f o r m e r s , and o t h e r s i m i l a r q u e s t i o n s * F r o m ' t h i s c a n l i k e w i s e be d e t e r m i n e d the a c t u a l a d v a n t a g e , i n d o l l a r s , o f one i n s t a l l a t i o n o v e r a n o t h e r , where i t w o u l d be e c o n o m i c a l t o change from one type o f i n s t a l l a t i o n to a n o t h e r , and a g r e a t many o t h e r e x t r e m e l y u s e f u l c o n s i d e r a t i o n s . G e n e r a l E q u a t i o n * — A g e n e r a l e x p r e s s i o n f o r t o t a l a n n u a l c o s t w h i c h w i l l be a p p l i c a b l e to most o f the. p r o b l e m s i n e l e c t r i c a l d i s t r i b u t i o n l i n e s c a n be s e t down. N a t u r a l l y e a c h o f the i t e m s i n c l u d e d w i l l be somewhat d i f f e r e n t f o r d i f f e r e n t p r o b l e m s and a l l p r o b l e m s w i l l n o t i n c l u d e a l l o f t h e s e i t e m s , the symbol "g" w i l l be u s e d t h r o u g h o u t to i n d i c a t e p e r c e n t a g e o f f i x e d c h a r g e s on i n v e s t m e n t * I t w i l l v a r y , o f c o u r s e , w i t h d i f f e r e n t k i n d s o f p r o p e r t y * I n t h i s g e n e r a l e q u a t i o n , " g " w i l l be u s e d as a g e n e r a l s y m b o l , i . e . , the e x p r e s s i o n (*g* x a q u a n t i t y ) i n d i c a t e s t h a t the a n n u a l c h a r g e s r a t h e r t h a n the f i r s t c o s t a r e c o n s i d e r e d . Then we h a v e : ' T o t a l a n n u a l A = F i x e d C h a r g e s c o s t = + g 6 + g ( c o s t o f r i g h t * * o f - w a y ) ( c o s t o f p o l e s and f i x t u r e s o r u n d e r -g r o u n d d u c t s I n - p l a c e ) ( c o s t o f c o n d u c t o r s i n p l a c e ) ( c o s t o f t r a n s f o r m e r s and t r a n s f o r m e r equipment i n s t a l l e d ) ( c o s t o f any s p e c i a l equipment used) O p e r a t i n g C h a r g e s + + c o s t o f m a i n t e n a n c e , I n s p e c t i o n , t e s t -i n g e t c « c o s t o f a n n u a l energy l o s s on l i n e c o s t o f a n n u a l e n e r g y l o s s on t r a n s « f o r m e r s a n d o t h e r e q u i p m e n t * (7b) I n d i v i d u a l c a s e s may p r o d u c e o t h e r c h a r g e s w h i c h must be added b u t the above i s c h a r a c t e r i s t i c . U n i t s « « - I n some s p e c i f i c p r o b l e m s , s u c h as the c o m p a r i s o n o f economy between two s i z e s o f c o n d u c t o r f o r some p a r t i c u l a r l o c a t i o n and d e f i n i t e l o a d , a c t u a l v a l u e s f o r v o l t a g e , r e s i s t -a n c e , c o s t s o f m a t e r i a l s and e n e r g y and o t h e r c o n s t a n t s c o u l d be i n t r o d u c e d a t once i n t o t h i s e q u a t i o n and the t o t a l a n n u a l 47 c o s t o f e a c h i n s t a l l a t i o n d e t e r m i n e d i n d o l l a r s . I n the u s u a l c a s e , however, i t Is d e s i r a b l e t o make t h e . s t u d y more g e n e r a l , c o v e r i n g a more o r l e s s wide v a r i a t i o n i n c o n d i t i o n s , so t h a t i t c a n be u t i l i z e d to r e d u c e c o m p u t a t i o n on f u t u r e p r o b l e m s or i n the d e t e r m i n a t i o n o f s t a n d a r d s f o r a g i v e n c l a s s o f i n s t a l l a t i o n s • F o r t h i s p u r p o s e i t i s a d v i s a b l e to r e p r e s e n t as many o f the q u a n t i t i e s as p o s s i b l e by symbols and to c a r r y t h e s e symbols t h r o u g h the c o m p u t a t i o n s as f a r as p o s s i b l e . . T h i s a l s o f a c i l i t a t e s r e v i s i o n o f the f o r m u l a s , g r a p h s , e t c . , i f a change i n p r i c e s make t h i s a d v i s a b l e . F o r example, the f o l l o w i n g a r e some o f t h e symbols most commonly u s e d i n t h i s t h e s i s ; W . - l o a d i n w a t t s K kw*« l o a d i n k i l o w a t t s E , ~ v o l t a g e cos 0 I - amperes A R » r e s i s t a n c e o f c i r c u i t X - i n d u c t a n c e o f c i r c u i t W r - u n i t r e s i s t a n c e o f c o n -d u c t o r T x •= u n i t i n d u c t a n c e o f c o n -d u c t o r » - 6 R^ = E q u i v a l e n t r e s i s t a n c e i o f t r a n s f o r m e r s C r = c o s t o f r i g h t - o f - w a y t i' per u n i t v . CQ~ c o s t o f c o p p e r per l b . P C - c o s t o f s t r i n g i n g c o n -s r d u e t o r s C e ~ C o s t o f e n e r g y ( s u b -s c r i p t 1, 2, 3 , e t c . . i n d i c a t e v a r i a t i o n s . ) = r e s i s t i v i t y o f c o n d u c t o r m a t e r i a l - power f a c t o r = c r o s s - s e c t i o n a l a r e a o f c o n -d u c t o r * - w e i g h t o f c o n d u c t o r p e r u n i t l e n g t h - t r a n s f o r m e r s i z e i n k i l o v o l t -a m p e r e s . - p e r c e n t f i x e d c h a r g e s , ( i n t e r e s t , d e p r e c i a t i o n , t a x e s , and i n s u r a n c e . ) " e q u i v a l e n t h o u r s - p e r c e n t v o l t a g e d r o p = p e r c e n t power l o s s I n any g i v e n c a s e , most o f t h e s e Q u a n t i t i e s w i l l be f i x e d by the c o n d i t i o n s o f t h e p r o b l e m s a n d may be c o n s i d e r e d as c o n s t a n t s so t h a t the g e n e r a l e q u a t i o n f o r a n n u a l c o s t may u s u a l l y be r e d u c e d , i n i t s f i n a l f o r m , to one c o n t a i n i n g o n l y two o r t h r e e v a r i a b l e s , s u c h as l o a d i n k i l o w a t t s o r a m p e r e s , c r o s s - s e c t i o n a l a r e a o f w i r e , power f a c t o r , o r e q u i v a l e n t h o u r s . Examples o f t h i s w i l l be shown l a t e r . PRESENTATION OF RESULTS :-When the e q u a t i o n f o r t o t a l a n n u a l c o s t has b e e n once o b t a i n e d t h e r e s t i l l r e m a i n s t h e q u e s t i o n o f g e t t i n g from i t the i n f o r m a t i o n d e s i r e d i n the b e s t p o s s i b l e form f o r c o n v e n i e n t u s e . I t i s f o u n d t h a t t h e r e a r e , i n g e n e r a l , t h r e e ways i n w h i c h i t i s c o n v e n i e n t t o a c c o m p l i s h t h i s . C o n d i t i o n s o f the p r o b l e m and. t h e r e s u l t s d e s i r e d w i l l d e t e r m i n e w h i c h one o f t h e s e Is most a p p l i c a b l e i n any c a s e . 1* . The a c t u a l a n n u a l c o s t i n d o l l a r s may be p l o t t e d i n a c u r v e 1 o r s e r i e s o f c u r v e s . Where the e q u a t i o n f o r a n n u a l c o s t i s e x p r e s s e d i n more t h a n one v a r i a b l e , s u c h as s i z e o f w i r e and l o a d , f o r e x a m p l e , one o f t h e s e v a r i a b l e s must be h e l d c o n s t a n t i n p l o t t i n g any one c u r v e . S u f f i c i e n t number o f s u c h c u r v e s must t h e n be p l o t t e d to show the r e q u i r e d v a r i a t i o n i n t h a t q u a n t i t y . I n t h i s way a s e r i e s o f c u r v e s may be o b t a i n e d , f o r example, one c u r v e f o r e a c h s t a n d a r d s i z e o f w i r e , showing the r e l a t i o n between a n n u a l c o s t and l o a d on a l i n e w i t h t h a t s i z e . An example o f t h i s method I s shown i n P i g . 6,.when the e x p r e s s i o n f o r a n n u a l c o s t c o n t a i n s more t h a n two s u c h v a r i a b l e s , however, t h i s method i s u s u a l l y n o t a p p l i c a b l e . • 2 . I n some c a s e s w i t h t h r e e v a r i a b l e s e n t e r i n g I n t o t h e t o t a l a n n u a l c o s t the f o l l o w i n g method w i l l be f o u n d Convenient. S u p p o s e , f o r e x a m p l e , the a n n u a l c o s t depends on a v a r i a b l e v a l u e f o r e q u i v a l e n t h o u r s , v a r i a b l e l o a d and v a r i a b l e w i r e s i z e . I f the e x p r e s s i o n f o r a n n u a l c o s t f o r two s t a n d a r d s i z e s o f w i r e a r e e q u a t e d , the r e s u l t i n g e q u a t i o n p l o t t e d between l o a d and e q u i v a l e n t h o u r s shows t h e d i v i d i n g : . l i n e between economy f o r one s i z e o r the o t h e r . The accompany-i n g f i g u r e ( F i g . 7). shows s u c h a s e r i e s o f c u r v e s as d e t e r m i n e d f o r t h r e e - p h a s e s e c o n d a r y f o r a c e r t a i n type o f l o a d . Any p o i n t l y i n g between two c u r v e s i n d i c a t e d economy f o r t h e c o r r e s p o n d i n g s i z e o f w i r e . T h i s method has the d i s a d v a n t a g e o f n o t e x h i b i t i n g q u a n t i t a t i v e economy. The r e s u l t s a r e q u a l i t a t i v e o n l y , s i n c e the n e a r e r p o i n t s l i e s t o e i t h e r l i m i t o f the a r e a the l e s s the r e l a t i v e d i f f e r e n c e between the c o s t w i t h the s i z e o f w i r e i n d i c a t e d and t h e n e x t a d j a c e n t s i z e . 3» A t h i r d method g i v e s r e s u l t s t h a t a r e n e i t h e r q u a n t i t -a t i v e n o r q u a l i t a t i v e . A l s o , i t s a p p l i c a t i o n i s u s u a l l y somewhat l i m i t e d . I n c e r t a i n c a s e s , however, i t i s p r e f e r -a b l e to any o t h e r m e t h o d . Where the e x p r e s s i o n f o r a n n u a l c o s t c o n t a i n s s e v e r a l v a r i a b l e s , I f t h e s e c a n a l l be r e d u c e d to terms o f two v a r i a b l e s (as p e r c e n t a g e v o l t a g e d r o p and l o a d , f o r example) and the f i r s t d e r i v a t i v e o f the r e s u l t i n g e x p r e s s -i o n ^ ' i t h r e s p e c t t o one o f t h e s e v a r i a b l e s be s e t e q u a l to 0 , the e q u a t i o n t h u s o b t a i n e d w i l l g i v e t h e most e c o n o m i c a l r e -l a t i o n between the two v a r i a b l e s (as most e c o n o m i c a l v o l t -age d r o p f o r any l o a d u n d e r the g i v e n c o n d i t i o n ) . The accompany« i n g f i g u r e g i v e s a n example o f a c u r v e d e r i v e d i n t h i s manner F i g . \ 6 . As was s u g g e s t e d b e f o r e , i t w i l l be f o u n d o f c o n s i d e r a b l e a d v a n t a g e t o p r e p a r e the e q u a t i o n s from w h i c h the f i n a l c u r v e s a r e p l o t t e d i n as g e n e r a l terms as p o s s i b l e , i . e . , w i t h as many o f the c o n s t a n t q u a n t i t i e s as p o s s i b l e r e p r e s e n t e d by s y m b o l s . I t i s , t h e n , a c o m p a r a t i v e l y e a s y m a t t e r t o r e v i s e t h e c u r v e s t o meet c h a n g i n g p r i c e s o f m a t e r i a l and l a b o r , or o t h e r c o n -d i t i o n s o f l o a d , v o l t a g e , power f a c t o r o r m a t e r i a l s o f c o n -s t r u c t i o n than t h o s e o r i g i n a l l y c o n t e m p l a t e d . I n some c a s e s i t . may be f o u n d u s e f u l to ' d e v e l o p the r e s u l t s 49 In numerical t a b l e s or sometimes merely by a, simple formula,, Such cases are not the most u s u a l , however, and the above methods w i l l probably be found s u f f i c i e n t f o r most purposes» On some more ext e n s i v e problems, a l l three methods of exhib-i t i n g data w i l l be used. I n f u t u r e chapters, a number of problems met w i t h i n p r a c t i c e w i l l be taken up and t h e i r treatment In accordance w i t h these methods w i l l be described,, Some of the d e t a i l s n e c e s s a r i l y omitted i n the previous d i s c u s s i o n of these methods w i l l be brought out i n the i n d i v i d u a l problems and the procedure h e r e t o f o r e d e s c r i b e d i n general terms w i l l be a c t u a l l y c a r r i e d through* CHAPTER VI POWER LOSS AND VOLTAGE PROP Charts f o r S i m p l i f i e d S o l u t i o n f o r Power l o s s and Voltage Drop Power L o s s . - - In most of the s o l u t i o n s of problems i n economy appearing: i n t h i s t r e a t i s e , the power l o s s i s introduced as f u n c t i o n of the l o u d , the wire s i z e , . t h e e q u i v a l e n t hours, e t c . The reason f o r t h i s i s evident from the nature of the methods' used and t h e r e s u l t s d e s i r e d . There are often cases, however, where the "power l o s s alone i s wanted. There w i l l be given ••In " t h i s chapter s i t p l e curves, w i t h t h e i r d e r i v a t i o n , which enable the power l o s s t o be q u i c k l y solved i n the great m a j o r i t y of problems. :. The most u s u a l case of power l o s s i s t h a t due t o the r e s i s t a n c e of the conductor, i . e . , the I £ R l o s s . I n High-t e n s i o n t r a n s m i s s i o n l i n e s , leakage l o s s e s and corona l o s s e s become important. Charging c u r r e n t a l s o has an e f f e c t on I R l o s s . Buch problems, however, are comparatively r a r e i n the-.work of most engineers and. warrant s p e c i a l treatment when encountered. Methods of s o l v i n g f o r corona l o s s , leakage, e t c . are given i n the handbooks and elsewhere 'and a d i s c u s s -i o n of them i s beyond the province of t h i s work. In the g r e a t e r m a j o r i t y of problems, the I 2 R l o s s i s a l l that need be con-sidered,•-;.and i f t h i s . i s i n t e l l i g e n t l y handled, the - other l o s s e s r e f e r r e d t o w i l l be-at a minimum, then again they are •only c o n s e q u e n t i a l i n the higher range of v o l t a g e s . . I i D = l e n g t h of l i n e i n f e e t , W -• the l o a d at the r e c e i v e r end i n watts { k i l o w a t t s X 1,000). E = the r e c e i v e r v o l t a g e , A _. c r o s s - s e c t i o n a l area of conduct or l i n e c i r c u l a r m i l s , p = r e s i s t i v i t y of conductor m a t e r i a l i n ohms per m i l •:• f o o t , / cos & = the power f a c t o r of the l o a d I Z R l o s s ^ J I — 2 2 w/atts ( f o r s i n g l e - p h a s e ) (8) \E cos 9 /A\ , / w  3 ^/3E c:bs;0/A I Z R losssf-z; 1 x 3 watts ( f o r three-phase) (9) A I f P = per cent power l o s s i n terms of power d e l i v e r e d , .-. P 2W«J> I 3 100 (E cos df A W. 200 W^D P = ( f o r single9phase) (10) (E cos d)A W^, D 1 51 x 100 (E c o s e ) a A v; 100W D p = - — — — — — — ( f o r t h r e e - p h a s e ) (11) CE c o s e ) s A F o r t h e same l o a d , same v o l t a g e between c o n d u c t o r s , and. t h e same c o n d u c t o r s i z e t h e l o s s w i t h s i n g l e - p h a s e i s t w i c e t h a t w i t h t h r e e - p h a s e . I f i t i s d e s i r e d t o c o n s i d e r t h e l o a d , v o l t a g e and power f a c t o r a t t h e s o u r c e i n s t e a d o f a t the r e c e i v e r , i f "W' =» l o a d a t s o u r c e i n w a t t s , E' — v o l t a g e a t s o u r c e , c o s 0 ' = power f a c t o r a t s o u r c e . The l i n e l o s s i n p e r c e n t a g e o f l o a d a t s o u r c e F ' ~ ( f f i ° ? o C e ' )*A ( f 0 r s i n S l e - p h a s e ) (12) P 1 - ( E ^ c o s ' ^ e M ^ A ( f 0 r t h r e e - P h a R e ) (13) F o r Gopper c o n d u c t o r /o- 10.8 a p p r o x i m a t e l y . I f l o a d i s e x p r e s s e d i n k i l o w a t t s (kw)., the f o r m u l a b e c o m e s - -r ~ g ' 1 ( / e o i 6 e ] t ) » W A P ( f o r '^M-Phaoc) (14) F" ool°t ¥I,J> ^ t h r e e - P h a s e , ( 1 5 ) These f o r m u l a s a r e c o m p a r a t i v e l y e a s y t o u s e . However, i t i s b e l i e v e d the work may be somewhat s i m p l i f i e d , e s p e c i a l l y where a l a r g e number o f s u c h c o m p u t a t i o n s a r e to be made, by use o f the a c c o m p a n y i n g c h a r t ( F i g . 10) . The use o f t h i s c h a r t r e d u c e s the c o m p u t a t i o n t o a s i m p l e m u l t i p l i c a t i o n o f r o u n d n u m b e r s . The c h a r t i s p l o t t e d as f o l l o w s : A s e r i e s o f c i r c u l a r a r c s ( w i t h the c e n t e r a t 0 ,0) a r e drawn, e a c h r e p r e s e n t i n g a g i v e n v o l t a g e . V o l t a g e s r a n g e from 0 to 150, b u t as w i l l be shown b e l o w , the same a r c s may be u s e d f o r any v o l t a g e . D i a g o n a l s t r a i g h t l i n e s a r e drawn t h r o u g h 0 , 0 a t v a r i o u s s l o p e s , e a c h r e p r e s e n t i n g a g i v e n power f a c t o r . I t i s e v i d e n t t h a t the a b s c i s s a , o f the i n t e r s e c t i o n o f any a r c w i t h any d i a g o n a l g i v e s the c o r r e s p o n d i n g v a l u e o f E c o s 0 . F o r e a c h s t a n d a r d w i r e s i z e c o n s i d e r e d a c u r v e i s now p l o t t e d between E - — — — and E c o s © g i v i n g f o r any v o l t a g e , power kw. D/ 1 , 0 0 0 f a c t o r , and w i r e s i z e the p e r c e n t a g e power l o s s p e r k i l o w a t t p e r 1,000 f t . C u r v e s f o r o t h e r s i z e s o f w i r e c a n be e a s i l y added, i f d e s i r e d . The upper p a r t o f t h e s e c u r v e s ^'S,s drawn to a c o n d e n s e d 5 2 s c a l e t o g i v e a g r e a t e r r a n g e o f v a l u e s i n the more u n u s u a l c a s e s . The c u r v e s h e r e shown a r e f o r t h r e e - p h a s e . The power l o s s f o r s i n g l e - p h a s e w o u l d be t w i c e the v a l u e s shown f o r t h r e e - p h a s e . The use o f t h e s e c u r v e s i s as f o l l o w s : 1. Reduce t h e v o l t a g e c o n s i d e r e d to any e q u i v a l e n t s e c o n d -a r y v o l t a g e w i t h i n the s c a l e o f the c h a r t ( l e s s t h a n 150 v o l t s ) by d i v i d i n g by some c o n v e n i e n t t r a n s f o r m a t i o n r a t i o s u c h as 2, 4, 10, 20, 200, 400, 1,000, e t c . 2 . L o c a t e i n t e r s e c t i o n o f v o l t a g e a r c and power f a c t o r d i a g o n a l . 3« The i n t e r s e c t i o n o f the v e r t i c a l t h r o u g h t h i s p o i n t w i t h the c u r v e f o r t h e p r o p e r w i r e s i z e g i v e s the v a l u e o f P on t h e s c a l e a t l e f t . 4. D i v i d e t h i s s c a l e r e a d i n g by t h e square o f the t r a n s f o r m -a t i o n r a t i o u s e d , to g i v e p e r c e n t a g e power l o s s per k i l o w a t t p e r 1,000 f t . f o r the g i v e n v o l t a g e . M u l t i p l y by the number of k i l o -w a t t s and b y t h e l e n g t h o f l i n e i n t h o u s a n d s o f f e e t o f t o t a l p e r c e n t a g e power l o s s I n terms o f power d e l i v e r e d . ( I f l i n e i s s i n g l e - p h a s e m u l t i p l y t h i s q u a n t i t y by 2.) Take f o r example t h e f o l l o w i n g p r o b l e m s -L o a d - — 1 , 2 0 0 kw. t h r e e - p h a s e -: Power f a c t o r - - 7 5 per c e n t V o l t a g e a t r e c e i v e r - - 4 , 4 0 0 W i r e s i z e - - 3 N o . 0 D i s t a n c e — 8 ,000 f t . 4 400 '^Q = 1 1 0 ( t r a n s f o r m a t i o n r a t i o = 40) • 38 3 ' Power l o s s — — x x 8 =- 9-12 p e r c e n t o r 109.4 kw. #0 x 0 VOLTAGE DROP. — I n s t u d y i n g t h e economy o f a l i n e , i t must n o t be f o r g o t t e n t h a t the e l e m e n t o f good s e r v i c e i s a l s o i m p o r t a n t . Good s e r v i c e depends l a r g e l y on :gi>o&vregatta t . l o n p w h l ' c % e 1 M t a r n -depends a g r e a t d e a l on t h e v o l t a g e " d r o p o f the l i n e . M o r e o v e r , as i s o f t e n p o i n t e d o u t , a l l o w i n g the v o l t a g e to f a l l by a c e r t a i n p e r c e n t a g e a t peak l o a d p r o d u c e s t w i c e as g r e a t a p e r c e n t a g e d e c r e a s e i n power consumed by b o t h lamps and m o t o r s . T h i s i s a n n o y i n g to a c u s t o m e r , s i n c e he w i s h e s f u l l power and i s w i l l i n g t o pay f o r i t , b u t i t Is a d i r e c t money l o s s t o the power company, whose income i s b a s e d on the amount o f energy r e g i s t e r e d by t h e m e t e r s . O f t e n , a l i n e e c o n o m i c a l l y l o a d e d w i l l have t o o g r e a t a v o l t a g e d r o p . I f i t i s a r t i f i c i a l l y r e g u l a t e d , the c o s t o f the r e g u l a t o r e n t e r s i n t o t h e c o n s i d e r a t i o n o f economy. I n some c a s e s the use o f l a r g e c o n d u c t o r s w i t h o u t a r e g u l a t o r may be more e c o n o m i c a l than s m a l l e r c o n d u c t o r s w i t h a r e g u l a t o r . The c o m p u t a t i o n o f v o l t a g e d r o p i s a p t t o be a t e d i o u s opera-* t i o n i f c a r r i e d o u t o f t e n . S e v e r a l means o f s i m p l i f y i n g t h i s 53 have h e e n p u b l i s h e d , s u c h as the w e l l - k n o w n Mershon D i a g r a m and ,the .Droight c h a r t . Vvhen r e l a t i n g t o h i g h - t e n s i o n l i n e s . , the p r o b l e m of v o l t a g e d r o p i n v o l v e s c o n s i d e r a t i o n of l i n e c a p a c i t y , e t c . These p r o b -lems a r e u s u a l l y of s u f f i c i e n t i m p o r t a n c e to w a r r a n t d e t a i l e d c o m p u t a t i o n . F o r m u l a s , f o r t h i s a r e g i v e n i n t h e handbooks a n d e l s e w h e r e . E , = E . c o s h V Z Y + IC -MTl s i n h JZT. . I, - I t c osh y z T + E . £ / Y / Z sinh: */2T Where I , and E 4 a r e v o l t a g e s f r o m phase t o n e u t r a l a t t h e s e n d -i n g and r e c e i v i n g ends r e s p e c t i v e l y ; Z i s t h e impedance p e r w i r e ; Y i s t h e a d m i t t a n c e f r o m phase w i r e t o n e u t r a l . E o r medium and l o w - v o l t a g e p r o b l e m s , i t i s u s u a l l y s u f f i c i e n t t o c o n s i d e r i n d u c t i v e r e a c t a n c e and r e s i s t a n c e o n l y . The method a n d c h a r t s f o r c o m p u t i n g v o l t a g e d r o p , g i v e n b e l o w , a r e ^ b a s e d on t h e s e q u a n t i t i e s . They a r e d e r i v e d f r o m t h e e q u a t i o n o r d i -rcarily u s e d f o r s u c h c o m p u t a t i o n s , i . e . V J(E cos 6+ v/3RID) a ^ (E s i n 9 + S3 X ID)Z - E 100 E ( f o r t h r e e - p h a s e l i n e s ) s 9 + — — — / f l a i n 6 +- I -1 (16) Where V - p e r c e n t v o l t a g e d r o p i n terms of r e c e i v e r v o l t a g e , S r e s i s t a n c e = i n ohms p e r f o o t , X - i n d u c t i v e r e a c t a n c e i n ohms p e r f o o t , D = d i s t a n c e from s o u r c e t o r e c e i v e r i n f e e t , P - c u r r e n t p e r w i r e . : But 100 W D 10073 RID P ;ss .-per scent :power 1 oss_-(E cos e ^ A E cos 6 (see a b o v e . ) (17) S u b s t i t u t i n g O S ©j. 4 - • JM.fi 00 R tan 0-f-100 (18) ( Y 100 cos 0 [J p ve / " 1 i \ 2 — m B m : / / l + j+ (tan 9 -f- — P P * s / . \ 1 0 0 / \ 100 R / (The above d o m p u t a t i o n i s f o r t h r e e - p h a s e "but t h e r e s u l t i n g e x p r e s s i o n f o r B i s t h e same f o r s i n g l e - p h a s e . ) B t h e n i s a q u a n t i t y e x p r e s s i n g t h e r e l a t i o n between p e r c e n t v o l t a g e d r o p and p e r c e n t power l o s s . I t depends on t h e power f a c t o r (cos 0 ) , s i z e and s p a c i n g of c o n d u c t o r s ^ - AMD p e r c e n t power l o s s (P) , but i s i n d e p e n d e n t of l o a d or v o l t a g e . I t i s e v i d e n t t h a t i f B i s known t h e p e r c e n t v o l t a g e d r o p may be e a s i l y o b t a i n e d f r o m t h e p e r c e n t power l o s s by t h e d i m p l e r e l a t i o n V - BP (20) B may be p l o t t e d as shown i n the a c c o m p a n y i n g c u r v e s ( F i g . 1 £ ) (a) and (b,},. S i n c e t h e v a r i a t i o n of B w i t h P i s n o t g r e a t e x c e p t i n g f o r h i g h - p o w e r f a c t o r and l a r g e , c o n d u c t o r s , t h r e e f i x e d v a l u e s of p were c h o s e n w h i c h c o v e r t h e u s u a l range of p r o b l e m s , i . e . , 1 p e r c e n t , 10 p e r c e n t and £0 p e r c e n t . F o r e a c h power f a c t o r , a c u r v e between 3 a n d . x / R i s p l o t t e d f o r e a c h of t h e s e v a l u e s of P . O t h e r v a l u e s of P may be i n t e r p o l -a t e d i f n e c e s s a r y . The v a l u e o f X / R i s shown d i r e c t l y by t h e c u r v e s on t h e r i g h t f o r s t a n d a r d s i z e s of c o n d u c t o r and any s p a c i n g . •. Use of C u r v e s . — T h e use of t h e c u r v e s i s a s f o l l o w s : l o c a t e t h e p o i n t on t h e X / R c u r v e f o r t h e g i v e n w i r e s i z e and s p a c i n g . (E*or t h r e e - p h a s e u n e q u a l s p a c i n g use t h e e q u i v a l e n t - s p a c i n g , S N/S-^SpS..,- . P a s s a c r o s s t h e s h e e t to t h e l e f t on the h o r i z o n t a l t h r o u g h t h i s p o i n t u n t i l i t i n t e r s e c t s t h e c u r v e f o r the -g i v e n power f a c t o r and v a l u e of P . The c o r r e s p o n d i n g v a l u e o f B i s f o u n d on the s c a l e a t t h e b o t t o m . ' I f t h i s i s " m u l t i p l i e d b y t h e v a l u e o f P computed f r o m F i g . 1 0 , t h e . d e s i r e d v a l u e oi V ( p e r c e n t v o l t a g e drop) i s o b t a i n e d . E x a m p l e . — I n t h e example g i v e n above f o r t h e d e t e r m i n a t i o n of P , l e t t h e s p a c i n g between t h e w i r e s be 28 i n . , 28 i n ; , 56 i n . The e q u i v a l e n t s p a c i n g =\/ 28 x 28 x 56 = 3 5 i n . I n t e r p o l a t i n g between t h e 70 p e r c e n t and 80 p e r c e n t p o w e r -f a c t o r c u r v e s • B - 1.18 V = 1 . 1 8 x 9.12 = 1 0 . 7 5 p e r c e n t or 473 v o l t s . The c u r v e s g i v e n h e r e a r e g e n e r a l and may be u s e d f o r any v o l t a g e , l o a d , l e n g t h of l i n e and s p a c i n g between, c o n d u c t o r s . The range o f w i r e s i z e s and power f a c t o r i s more l i m i t e d but t h e c u r v e s c o u l d be e a s i l y e x t e n d e d t o c o v e r any d e s i r e d v a l u e . F o r e v e r y d a y u s e on t h e p r o b l e m s a r i s i n g on any g i v e n system l e s s g e n e r a l c u r v e s may be d e r i v e d from t h e s e w h i c h s t i l l f u r t h e r 54 100C P (19) 55 s i m p l i f y c o m p u t a t i o n s . As an example, F i g . 13 (a) ana (h) shows % a s e t of c u r v e s p l o t t e d f o r work on 4 , 6 0 0 ^ 0 ^ l i n e s . Three c u r v e s a r e shown f o r each w i r e s i z e g i v i n g a range f r o m 4 , 4 0 0 t o 5 ,000 v o l t s . F o r any power f a c t o r ( l o w e r s c a l e ) t h e s c a l e on t h e l e f t g i v e s t h e ' p e r c e n t power l o s s - p e r - k i l o w a t t p e r 1 ,000 f t . F i g u r e 13 (b) shows how s c a l e s f o r o t h e r v o l t a g e s can he-added . F i g u r e 14 shows a n o t h e r s p e c i a l c u r v e g i v i n g . p e r cent v o l t a g e d r o p p e r 1 , 0 0 0 f t . of l i n e f o r - 4 , 6 0 0 v o l t s , t h r e e - p h a s e , 80 p e r cent power f a c t o r , . 2 7 9 i n . s p a c i n g . F i g u r e 15, c a l l e d "Load Curve f o r Power L i n e s " / g i v e s t h e d i s t a n c e t o w h i c h any l o a d can he c a r r i e d on a t h r e e - p h a s e , - " 4 , 6 0 0 - v o l t l i n e a t 80 p e r c e n t power f a c t o r w i t h a 10 p e r c e n t d r o p i n v o l t a g e . F i g u r e 16 i s a s i m i l a r c u r v e f o r s i n g l e - p h a s e l i n e s w i t h a power f a c t o r .of 95 p e r c e n t . . F i g u r e 17 i s a l o u d c u r v e f o r 2 2 0 - v o l t , t h r e e - p h a s e s e c o n d -a r y w i t h ' 10 p e r c e n t d r o p . . F i g u r e 18 i s a l o a d c u r v e f o r 2 2 4 / l l 2 - v o l t , s i n g l e - p h a s e s e c o n d a r y - w i t h 3 p e r c e n t d r o p . I t i s c o m p a r a t i v e l y s i m p l e m a t t e r t o d e r i v e any s u c h s p e c i a l c u r v e s d e s i r e d b y u s e of t h e g e n e r a l c u r v e s f o r power l o s s and © g i v e n a b o v e . A p p r o x i m a t e Method f o r S e c o n d a r i e s . — F o r l o w - v o l t a g e p r o b l e m s , s u c h as f o r s e c o n d a r i e s , an a p p r o x i m a t e d e t e r m i n a t i o n i s u s u a l l y as a c c u r a t e . a s one more d e t a i l e d . I t w i l l be f o u n d t h a t t h e e x p r e s s i o n V ^ - = v o l t s d r o p p e r ampere = R cos 9 + X s i n 9 (21) I w h i l e an . a p p r o x i m a t i o n , i s s u f f i c i e n t l y a c c u r a t e f o r most p r o b l e m s of t h i s c l a s s . .. As a n example f o r t h e u s e of t h i s e x p r e s s i o n , t h e c u r v e s i n F i g . 19 ( a . b . c . ) a r e g i v e n . The l o ^ d c o n s i d e r e d i s r e s i d e n c e l i g h t i n g on t h r e e - w i r e , 1 1 0 / 2 2 9 - v o l t s e c o n d a r y . The a v e r a g e p e r r e s i d e n c e i s assumed t o range from 13.5 t o 200 w a t t s . T w o d i f f ^ e r e n t l e n g t h s , of a v e r a g e span a r e t a k e n as shown. The t o t a l v o l t a g e d r o p from the t r a n s f o r m e r t o t h e end of t h e s e c o n d a r y i s computed by m u l t i p l y i n g t h e number o f c u s t o m e r s at each p o l e b y t h e spans between t h a t p o l e and t h e t r a n s f o r m e r and u s i n g t h e sum of t h e s e m u l t i p l i c a t i o n s t o f i n d t h e d r o p i n v o l t s w i t h t h e p r o p e r c u r v e and s c a l e . The s c a l e s a r e so a r r a n g e d t h a t f o r t h r e e - w i r e s e c o n d a r y , i . e . , 220 v o l t s w i t h l o a d b a l a n c e d t h e b o t t o m and r i g h t - h a n d s c a l e s s h o u l d be u s e d . F o r t w o - w i r e s e c o n d a r y , 110 v o l t s , t h e b o t t o m and l e f t hand s c a l e s or the t o p and r i g h t - h a n d s c a l e s g i v e t h e r e q u i r e d r e s u l t . F o r example c o n s i d e r a s e c o n d a r y as shown below: F i g . 2 0 . of ler/lce5 X /fa Jechons) 56 S e c t i o n s 150 f t . , a v e r a g e l o a d 135 w a t t s F i r s t p o l e l x l .as 1 Second p o l e 2 x 2 as 4 T h i r d p o l e . F o u r t h p o l e 1 x 4 = 4 F i f t h p o l e 3 x 5 15 S i x t h p o l e 1 x 6 = 6 S e v e n t h p o l e ... E i g h t h p o l e 2 x 8 16 ....Ninth p o l e 3 x 9 — 27 T e n t h p o l e E l e v e n t h p o l e 2 x l l l = 22 T o t a l 95 V p l t a p ^ d r o p i r o m curve, 3 . 9 3 v o l t s . Which I s , hlgnferr-than i t s h o u l d ^ e ^ 3 t : v o l t s b e i n g a b o u t t h e l i m i t t o "be u s e d In case: t h e d r o p t o t h e e i g h t h p o l e Is d e s i r e d . Sum of f i r s t seven above = 30 . E i g h t p o l e , 7 x 8 = 5 6 86 V o l t a g e d r o p , 3 . 5 6 v o l t s . Troths former . • •• ' * At9 o o. ... o f Q ( S o Q .....JB o^"_ F'J 20. P. ' • .. . O (3 :Q •• •• Cf O Q P „.,;57 FART lit CHAPTER V I I TRANSMISSION-LIME PROBLEMS Method o f D e t e r m i n i n g Most E c o n o m i c a l D e s i g n f o r M a i n or — " T r u n k " T r a n s m i s s i o n L i n e s . — " T r u n k " T r a n s m i s s i o n L i n e s I n c o n s i d e r i n g t h e e c o n o m i c a l d e s i g n o f t r a n s m i s s i o n l i n e s two g e n e r a l t y p e s o f l i n e s a r e e n c o u n t e r e d . These may be c a l l e d f o r c o n v e n i e n c e : ; 1 » m " T r u n k " t r a n s m i s s i o n l i n e s . 2 . " S e c o n d a r y " t r a n s m i s s i o n l i n e s . To t h e f i r s t c l a s s i f i c a t i o n b e l o n g s t h a t l i n e or system o f l i n e s w h i c h forms the " t r u n k " o f any system l a r g e or s m a l l . I t i s u s u a l l y a l i n e w h i c h t r a n s m i t s a c o m p a r a t i v e l y l a r g e l o a d ( r e l a t i v e to t h e t o t a l l o a d on the s y s t e m ) , t o some c o n -s i d e r a b l e d i s t a n c e , a t a r e l a t i v e l y h i g h . v o l t a g e . S e c o n d a r y t r a n s m i s s i o n ones on t h e o t h e r hand p a r t a k e more o f t h e n a t u r e o f d i s t r i b u t i o n l i n e s . They d i s t r i b u t e the e n e r g y from t h e c e n t r a l f e e d i n g p o i n t s , s e r v e d by the " t r u n k " l i n e , to a u x -i l i a r y s t a t i o n s from w h i c h i t may be d i s t r i b u t e d by the o r d i n a r y -:\ d i s t r i b u t i o n l i n e s . F o r e x a m p l e , i n a l a r g e system t h e r e may be s e v e r a l g e n e r a t i n g s t a t i o n s t i e d t o g e t h e r by a 1 1 0 , 0 0 0 - v o l t l i n e , " t h e t r u n k " . A t v a r i o u s p o i n t s a l o n g t h i s l i n e , s u b s t a t i o n s a r e l o c a t e d , s t e p p i n g the v o l t a g e down t o 2 2 , 0 0 0 v o l t s , t h e s e c o n d a r y t r a n s m i s s i o n . T h e s e r u n t o the v a r i o u s c o m m u n i t i e s to be s e r v e d where the v o l t a g e i s t r a n s f o r m e d , I n l o c a l s u b -s t a t i o n s , , t o o r d i n a r y d i s t r i b u t i o n v o l t a g e . E a c h o f t h e s e t y p e s o f l i n e s p r e s e n t c e r t a i n d i s t i n g u i s h i n g c h a r a c t e r i s t i c s w h i c h a f f e c t t h e method u s e d I n d e t e r m i n i n g the most e c o n o m i c a l d e s i g n . The p r o b l e m o f a " t r u n k l i n e " i s u s u a l l y a s p e c i f i c o n e , i . e . , a d e f i n i t e l o a d o f known c h a r a c t -e r i s t i c s i s t o be t r a n s m i t t e d from one g i v e n p o i n t t o a n o t h e r . F u t u r e s m a l l e x t e n s i o n s a r e n o t a n t i c i p a t e d , t h e s e b e i n g c a r e d f o r by t h e s e c o n d a r y . t r a n s m i s s i o n . l i n e s . On t h e o t h e r , h a n d c e r -t a i n c o n d i t i o n s s u c h as v o l t a g e , w i r e s i z e , and span a r e not l i m i t e d e x c e p t by c o n s i d e r a t i o n s o f economy and good o p e r a t i n g c o n d i t i o n s . S e c o n d a r y t r a n s m i s s i o n l i n e s on the o t h e r hand must c a r e f o r a v a r i e t y o f l o a d s and d i s t a n c e s . They a r e s u b j e c t t o s h o r t e x t e n s i o n s to c a r e f o r a d d i t i o n a l l o a d s . They a r e apt t o be t i e d t o g e t h e r i n a n e t w o r k . A l l t h e s e p o i n t s must be c o n s i d e r e d and the b e s t v o l t a g e , s p a n , e t c . to f i t the a v e r a g e c o n d i t i o n s must be a d o p t e d a s " a s t a n d a r d . Wire s i z e s may a l s o be s t a n d -a r d i z e d to one or two s i z e s . F u r t h e r p r o b l e m s a r e t h e n l i m i t e d t o c o n s i d e r a t i o n s o f the e c o n o m i c a l l o a d f o r any l i n e , number o f l i n e s f o r any l o a d , most e c o n o m i c a l r o u t e s , e t c . The profe-l e m s o f u n d e r g r o u n d t r a n s m i s s i o n l i n e s f a l l m o s t l y under t h i s c l a s s i f i c a t i o n but.*wi-W«sfee t o u c h e d on s e p a r a t e l y w i t h o t h e r u n d e r g r o u n d p r o b l e m s . 58 N a t u r a l l y t h e above d i v i s i o n i s somewhat e l a s t i c . I n some systems t h e r e a r e n o r t r u e " t r u n k l i n e s " , the h i g h - v o l t a g e l i n e s b e i n g so e x t e n s i v e as to be s i m i l a r t o s e c o n d a r y t r a n s -m i s s i o n l i n e s . On the o t h e r h a n d , i n s m a l l systems t h e r e may be no s e c o n d a r y t r a n s m i s s i o n l i n e s , one or two l i n e s c o m p r i s -i n g the whole t r a n s m i s s i o n system* I n s u c h c a s e s t h e t r u n k l i n e s a r e o f s u c h a v o l t a g e , l o a d , e t c . t h a t on a. l a r g e system they would p r o b a b l y be c l a s s e d as s e c o n d a r y t r a n s m i s s i o n or e v e n d i s t r i b u t i o n . They a r e t r u n k l i n e s , however, i n r e l a t i o n to the s m a l l system-, and t h e i r v o l t a g e , , w i r e s i z e , e t c . may u s u a l l y be d e t e r m i n e d by e c o n o m y w i t h o u t : any- l o c a l l i m i t i n g c o n d i t i o n s * I n t h i s - c h a p t e r , t h e p r o b l e m o f t h e t r u n k l i n e w i l l be t a k e n up and the v a r i o u s e l e m e n t s a f f e c t i n g i t s s o l u t i o n w i l l be d i s -c u s s e d * A l i n e o f r e l a t i v e l y h i g h v o l t a g e and heavy, l o a d w i l l be assumed b u t the same p r i n c i p l e s m i g h t be a p p l i e d to any t r u n k l i n e « . The: r e g u l a t i o n o f - t r u n k t r a n s m i s s i o n l i n e i s dependent upon the s y s t e m i n u s e , s u c h a s v a r i a b l e v o l t a g e o r c o n s t a n t v o l t a g e a t t h e r e c e i v e r e n d . The c h a r a c t e r i s t i c s of- c o n s t a n t v o l t a g e , t r a n s m i s s i o n a n d summarized as f o l l o w s by D w l g h t : Advantages**-, • , 1. S t e a d y v o l t a g e . 2. S t e a d i e r f r e q u e n c y i n s m a l l w a t e r - p o w e r p l a n t s . : :3« Lower t o t a l c o s t where v o l t a g e i s l e s s t h a n a b o u t 1,000 v o l t s p e r - m i l e . The low v o l t a g e per m i l e may be c a u s e d by e x -t e n s i o n s , . c i t y c o n d i t i o n s , c o r o n a , or a l a r g e number o f s u b s t a t i o n s . 4 . O v e r l o a d s a r e b e t t e r h a n d l e d . 5* L a r g e c o n d u c t o r s r e d u c e . c o s t o f towers and l a n d . •6* W i d e . s p a c i n g s and l a r g e c o n d u c t o r s e x t e n d c o r o n a l i m i t . 7 . I n c r e a s e i n e c o n o m i c a l d i s t a n c e o f t r a n s m i s s i o n . 8 . B e t t e r p r o t e c t i o n , due t o h i g h r e a c t a n c e . 9* T e n d e n c y t o use 60 c y c l e s . 1 0 . The method c a n be g r a d u a l l y a d o p t e d . 11. I n c r e a s e d R e v e n u e s . 12. U n i t c o s t p e r m l l e . p e r k i l o w a t t t r a n s m i t t e d l o w e r . D i s a d v a n t a g e s 1» Tendency o f s y n c h r o n o u s machines t o d r o p out o f s t e p . 2. P o s s i b l e l a r g e a c c i d e n t a l v a r i a t i o n s In v o l t a g e . 3. I n c r e a s e i n s h o r t - c i r c u i t c u r r e n t , u n l e s s r e a c t a n c e i s i n c r e a s e d * 4 . D e c r e a s e i n r e s e r v e , due to fewer l i n e s . 5» H i g h e r t o t a l c o s t f o r s h o r t , h 3 g h - v c l t a g e l i n e s . 6 . Lower e f f i c i e n c y . O b v i o u s l y from the above summary, the d i s a d v a n t a g e s o f t h e c o n s t a n t v o l t a g e s y s t e m a r e the a d v a n t a g e s o f the v a r i a b l e v o l t a g e system, and t h e s e must be c o n s i d e r e d I n any e c o n o m i c a l s t u d y o f t r u n k t r a n s m i s s i o n l i n e s . 59 The type o f s y s t e m l l » e » , c o n s t a n t o r v a r i a b l e v o l t a g e , halving b e e n d e t e r m i n e d , and b e i n g g i v e n the l o a d t o be c a r r i e d , w i t h i t s p r o b a b l e f u t u r e i n c r e a s e , the p o i n t s from and t o w h i c h t h e l o a d i s t o be t r a n s m i t t e d , a n d t h e c h a r a c t e r i s t i c s o f i t h a t l o a d , i . e . , i t s v a r i a t i o n s d u r i n g the day and s e a s o n s , and the a v e r a g e c o s t p e r k i l o w a t t - h o u r a t the g e n e r a t i n g s t a t i o n , the p r o b l e m r e m a i n s to d e t e r m i n e the most e c o n o m i c a l r o u t e , the most e c o n o m i c a l v o l t a g e , the most e c o n o m i c a l w i r e s i z e and t h e most e c o n o m i c a l s p a n and a r r a n g e m e n t o f s u p p o r t i n g s t r u c -t u r e s . I t may be stated, a t once t h a t no method o f s o l v i n g f o r any o f t h e s e unknown q u a n t i t i e s has y e t b e e n p r e s e n t e d w h i c h i s s i m p l e and a t t h e same time a c c u r a t e enough f o r the b a s i s o f a f i n a l d e s i g n * . S e v e r a l w r i t e r s have p u b l i s h e d a p p r o x i m a t e methods o f making such, d e t e r m i n a t i o n s . I n t h e s e , however, t h e v a r i a b l e q u a n t i t i e s a r e so numerous t h a t i t i s n e c e s s a r y t o make c e r t a i n a s s u m p t i o n s f o r s i m p l i c i t y and thus the r e s u l t s o b t a i n e d a r e s u b j e c t t o c o n s i d e r a b l e q u e s t i o n . I t i s b e l i e v e d t h a t t h e s e a r e v a l u a b l e i n e s t a b l i s h i n g the l i m i t s o f a p r o b l e m b u t t h a t • t h e a c t u a l d e s i g n , e s p e c i a l l y f o r a l i n e o f any c o n s i d e r a b l e i m p o r t a n c e , s h o u l d be c h e c k e d up by a summation o f a c t u a l c o s t f i g u r e s as compared w i t h the c o s t o f s e v e r a l o t h e r p o s s i b l e a l t e r n a t i v e s * S o m e . o f the a p p r o x i m a t e methods a r e g i v e n i n t h e r e f e r e n c e s b e l o w i - ' -I n t h e p a p e r on " P r o b l e m s o f 220 k v . Power T r a n s m i s s i o n " by A . E . S i l v e r i n t h e A . I . E » E * P r o c e e d i n g s , J u n e , 1919, i s g i v e n one o f the most c a r e f u l and c o m p l e t e s t u d i e s o f a h i g h - t e n s i o n t r a n s m i s s i o n l i n e , from an economic p o i n t o f v i e w , y e t p u b l i s h -e d . I n t h a t p a p e r , the v o l t a g e i s assumed, the e c o n o m i c a l w i r e s i z e i s d e t e r m i n e d from c o n s i d e r a t i o n o f f i x e d c h a r g e s and l o s s e s , and t h e most e c o n o m i c a l s p a n d e t e r m i n e d by a c o m p l e t e c o m p a r i s o n o f c o s t f i g u r e s on a c t u a l tower d e s i g n s . (1) " E c o n o m i c V o l t a g e o f L o n g T r a n s m i s s i o n L i n e s " , by Henry H P l u m b , J o u r n a l A . I . E . E . , A p r i l , 1920* " T r a n s m i s s i o n L i n e D e s i g n , " by F . K . K l r s t e n , A . I . E . E * P r o c -e e d i n g s , v o l . 37, 1917, p . 685*" " E l e c t r i c Power T r a n s m i s s i o n , " by A * E . S t i l l , p . 64, a p p r o x -imate e c o n o m i c a l v o l t a g e W k i l o w a t t s , . , /distance-f - . .an e m p i r i c a l formula» "Notes on t h e C a l c u l a t i o n o f T r a n s m i s s i o n L i n e s f o r Maximum E c o n o m y , " by E . B a t i c l e , Revue G e n e r a l e de L ' E l e c t r l c l t e , O c t * 3 0 , 1920. 60 G e n e r a l E q u a t i o n . - In t h i s p r o b l e m , as i s the c a s e w i t h most economic p r o b l e m s , the d e s i g n - sought f o r i s , i n g e n e r a l , t h a t one f o r w h i c h the t o t a l a n n u a l c o s t w i l l be a minimum. The t o t a l a n n u a l c o s t may be e x p r e s s e d as f o l l o w s l e t t i n g "g x (any q u a n t i t y ) " i n d i c a t e t h a t the a n n u a l c o s t i s to be u s e d : T o t a l a n n u a l c o s t = g ( c o s t o f r i g h t - o f - w a y ) + g ( c o s t o f towers and f o u n d a t i o n s i n p l a c e ) . + g ( c o s t of i n s u l a t o r s i n p l a c e ) 4-g ( c o s t o f c o n d u c t o r and g r o u n d w i r e i n • • p l a c e ) -t-g ( c o s t o f t r a n s f o r m e r s i n p l a c e ) +• g ( c o s t o f l i g h t n i n g a r r e s t e r s i n p l a c e ) •+• g ( c o s t o f s w i t c h e s I n p l a c e ) +• g ( c o s t o f s p e c i a l a p p a r a t u s , r e g u l a t o r s , c o n d e n s e r s , e t c • i n p l a c e ; 4- g ( c o s t o f s u b s t a t i o n s t r u c t u r e s ) •+- a n n u a l c o s t o f energy l o s s on t h e l i n e - f - a n n u a l c o s t o f energy l o s s on the t r a n s -f o r m e r s +- a n n u a l c o s t o f p a t r o l i n g , t e s t i n g a n d o t h e r m a i n t e n a n c e . E l e m e n t s A f f e c t i n g C o s t s . - E a c h o f t h e s e s u b d i v i s i o n s o f c o s t i s a f f e c t e d by one or more o f the v a r i a b l e q u a n t i t i e s whose s o l u t i o n i s b e i n g s o u g h t , some i n an e x t r e m e l y c o m p l i c a t e d manner. The manner i n w h i c h t h e -costs a r e a f f e c t e d w i l l be d i s c u s s e d b r i e f l y . (a) C o s t o f R i g h t - o f - w a y . - - - R i g h t - o f - w a y may have a d e f i n i t e c o s t f o r the whole l i n e r e g a r d l e s s o f tower s i z e o r s p a c i n g , In -which: ease, i t i s a f f e c t e d o n l y by the r o u t e c h o s e n . A g a i n , ' i t may v a r y w i t h t h e number o f towers o n l y , r e g a r d l e s s o f t h e i r s i z e . In o t h e r p l a c e s , i t may v a r y b o t h w i t h t h e number and base d i m e n s i o n s o f the t o w e r s . The l o c a l i t y t h r o u g h w h i c h the l i n e . w i l l pass- a n d the v a l u e o f l a n d w i l l d e t e r m i n e w h i c h o f the above i s a p p l i c a b l e t o the p r o b l e m i n h a n d . (b) C o s t o f T o w e r s . - - T h e c o s t o f towers i s a f f e c t e d by a g r e a t number of. c o n d i t i o n s and i t s r e l a t i o n t o t h e economy o f a l i n e i s a, d i f f i c u l t p r o b l e m . The type o f tower to be u s e d , wide b a s e or n a r r o w , o n e , two o r more c i r c u i t s , e t c . , i s o f p r i m a r y i m p o r t a n c e . The t y p e o f b a s e , i n t u r n , depends somewhat on the r i g h t - o f - w a y a v a i l a b l e . The number o f c i r c u i t s depends on the e c o n o m i c a l s i z e , o f c o n d u c t o r , t h e l i m i t s f o r corona, v o l t a g e on c o n d u c t o r and the e x p e c t e d i n c r e a s e i n l o a d . The h e i g h t , o f the tower I s a l s o a d e t e r m i n i n g f a c t o r . T h i s depends on the minimum c l e a r a n c e r e q u i r e m e n t s f o r t h e s p a n , and the sag i n the c o n d u c t o r ( w h i c h i n t u r n depends on the s p a n , w i r e s i z e a n d t h e a s s u m p t i o n s f o r h e a v i e s t l o a d i n g ) . I t a l s o i s a f f e c t e d by t h e v e r t i c a l s p a c i n g between c o n d u c t o r s , w h i c h i s a f u n c t i o n o f the v o l t a g e . The h o r i z o n t a l s p a c i n g ( w h i c h v a r i e s w i t h the v o l t a g e ) 61 l i k e w i s e a f f e c t s the c o s t , s i n c e the w e i g h t and. t o r s i o n a l s t r e s s e s a r e i n c r e a s e d , by l o n g e r a r m s . The w i r e s i z e i n -f l u e n c e s ' t h e c o s t o f the tower s i n c e i n most c a s e s the tower d e s i g n d e p e n d s , to a c o n s i d e r a b l e e x t e n t , on t h e maximum' s t r e s s a l l o w a b l e o n ! t h e c o n d u c t o r , w h i c h i s p r o p o r t i o n a l t o i t s c r o s s - s e c t i o n a l a r e a . The s p a n i s a l s o a f a c t o r , s i n c e t h e l o n g e r the s p a n , the g r e a t e r the l a t e r a l w i n d p r e s s u r e on the c o n d u c t o r s , and t h i s i s a n i m p o r t a n t f a c t o r * i n the d e s i g n o f the s t r a i g h t l i n e t o w e r s . I t a p p e a r s t o be p r a c t i -c a l l y i m p o s s i b l e t o d e v e l o p a n y s i m p l e f o r m u l a w h i c h w o u l d i n d i c a t e the v a r i a t i o n i n tower c o s t , w i t h a l l t h e s e v a r i a b l e e l e m e n t s . T h e n a g a i n , t h e q u e s t i o n o f s p e c i a l t o w e r s I $ e \ .?o-i c a n n o t be o v e r l o o k e d ; f o r " d e a d e n d i n g " l i n e e v e r y h a l f m i l e o r m i l e o f l e n g t h t o b r a c e l i n e , i n event o f a b r e a k i n t h e c o n d u c t o r s ; f o r a n g l e t o w e r s f o r bends i n the t r a n s m i s s i o n l i n e due to change i n d i r e c t i o n ; f o r t r a n s p o s i t i o n s , i n p a r a l l e l o p e r a t i o n o f l i n e , t o m i n i m i z e t h e i n f l u e n c e s o f i n d u c e d v o l t a g e s from o t h e r c i r c u i t s i n o r d e r to g e t b e t t e r v o l t a g e r e g u l a t i o n ; f o r p o i n t s o f i n t e r - c o n n e c t i o n , t a p - o f f p o i n t s , a i r - d i s c o n n e c t f o r s p l i t t i n g l i n e and s u c h o t h e r o p e r a t i n g d e v i c e s - * , (c) C o s t o f I n s u l a t o r s . - - T h e c o s t o f t h e I n s u l a t o r s I n c r e a s e s w i t h the v o l t a g e b u t n o t I n d i r e c t r a t i o on a c c o u n t o f the d e c r e a s e d e f f i c i e n c y p e r u n i t i n a l o n g s t r i n g s o f i n s u l a t o r s . (d) C o s t o f C o n d u c t o r . - - T h e c o s t o f c o n d u c t o r i n p l a c e w i l l be v e r y n e a r l y p r o p o r t i o n a l t o i t s c r o s s - s e c t i o n a l a r e a . It, w i l l , o f c o u r s e , depend a l s o on t h e m a t e r i a l u s e d . I t may v a r y somewhat w i t h the number o f t o w e r s . The c o s t o f g r o u n d w i r e w i l l i n most c a s e s be p r a c t i c a l l y a c o n s t a n t f o r the l i n e , d e -p e n d i n g o n l y o n , i t s l e n g t h , and number, s i z e a n d m a t e r i a l o f g r o u n d w i r e s d e c i d e d u p o n . G r o u n d w i r e s i z e s are g e n e r a l l y d e t e r m i n e d by t h e u n b a l a n c e d c u r r e n t c a r r i e d f o r some assumed maximum s t a t e o f u n b a l a n c e , and t h i s g e n e r a l l y l e a d s to a w i r e s i z e o f sma-ller c r o s s - s e c t i o n t h a n t h e o t h e r c i r c u i t c o n d u c t o r s . The g r o u n d w i r e s a r e g e n e r a l l y always p l a c e d on . t o p o f towers., and i n t h a t p o s i t i o n the m e c h a n i c a l s t r e s s e s a r e g r e a t e r t h a n i n the o t h e r c o n d u c t o r s ; t h e r e f o r e I f c r o s s - s e c t i o n i s s m a l l e r , and same m a t e r i a l u s e d , t h e s e s t r e s s e s may exceed the e l a s t i c l i m i t , c a u s e a b r e a k i n l i n e w i t h an i n t e r r u p t i o n to s e r v i c e . I n g e n e r a l , t h i s , the d e t e r m i n a t i o n o f g r o u n d w i r e s i z e s h o u l d be d e t e r m i n e d - from t h e m e c h a n i c a l r e q u i r e m e n t s i n s t e a d o f the e l e c t r i c a l c h a r a c t e r i s t i c s . To t h i s e x t e n t t h e economy i s a f f e c t e d as to a q u e s t i o n o f f i r s t c o s t or i n c r e a s e d o p e r a t i n g expenses i n s u b s e q u e n t y e a r s (e) C o s t o f T r a n s f o r m e r s . — T h e t r a n s f o r m e r c o s t w i l l I n c r e a s e as the v o l t a g e i n c r e a s e s (but not i n d i r e c t r a t i o ) and a l s o d e p -ends on the s i z e o f u n i t to be u s e d and the type ( a i r - c o o l e d or w a t e r - c o o l e d ; s e c o n d a r y - v o l t a g e ; e t c . ) . I n most problems o f t h i s k i n d t h e s e c o n d a r y - v o l t a g e r e a u i r e m e n t s w i l l be e s t a b l i s h e d and the t y p e and s i z e o f t r a n s f o r m e r w i l l be i n d i c a t e d by the l o a d 62 and type o f - . s u b s t a t i o n t o be u s e d . C o n s i d e r a t i o n In t h i s r e s p e c t b e i n g f i r m as to whether t h r e e s i n g l e - p h a s e t r a n s -f o r m e r s a r e u s e d o r one t h r e e - p h a s e t r a n s f o r m e r , a l s o as t o whether s t a r o r d e l t a c o n n e c t e d ; t h e n , a g a i n , i t may be o n l y a s t e p - u p s u b s t a t i o n u s i n g a u t o - t r a n s f o r m e r s » A f t e r d e t e r -m i n a t i o n o f the type o f s y s t e m to be used, has been made, t h e c o s t w i l l t h e n v a r y w i t h t h e v o l t a g e o n l y . ( f ) C o s t o f L i g h t n i n g A r r e s t e r s . - - I f a g i v e n t y p e o f a -r r e s t e r : i s . - c h o s e n , the c o s t w i l l v a r y w i t h t h e v o l t a g e . (g) C o s t o f S w i t c h e s . — I f the type and s i z e o f s w i t c h i s d e t e r m i n e d by the l o a d , the c o s t w i l l a l s o v a r y w i t h the v o l t a g e . (h) C o s t o f S p e c i a l A p p a r a t u s . - - I f s p e c i a l a p p a r a t u s i s n e e d -ed t o m a i n t a i n p r o p e r v o l t a g e r e g u l a t i o n , i t s c o s t must be i n c l u d e d i n d e t e r m i n i n g economy, s i n c e i t might be e l i m i n a t e d i f l a r g e - e n o u g h c o n d u c t o r or enough l i n e s were u s e d . The c o s t w i l l v a r y w i t h the s i z e r e q u i r e d , w h i c h depends upon the amount o f r e g u l a t i o n , and a l s o w i t h t h e v o l t a g e . ( i ) C o s t , o f S u b s t a t i o n S t r u c t u r e s F o r a g i v e n s i z e t r a n s -f o r m e r , t h e c o s t o f t h e t e r m i n a l s t a t i o n p e r t a i n i n g t o t h e t r a n s m i s s i o n l i n e w i l l be p r a c t i c a l l y c o n s t a n t , v a r y i n g some-what w i t h t h e voltage;, on a c c o u n t o f the i n c r e a s e d s p a c i n g o f c o n d u c t o r s . I f r e g u l a t o r s c r c o n d e n s e r s a r e u s e d the c o s t o f the s u b s t a t i o n s p a c e . © c c u p i e d by them must be i n c l u d e d . ( j ) C o s t o f e n e r g y L o s s . - - T h e energy l o s t on a t r a n s m i s s i o n l i n e c o n s i s t s . , of• I Z.R l o s s due t o t h e r e s i s t a n c e o f the c o n d u c t o r , l e a k a g e , and c o r o n a l o s s . I f the i n s u l a t o r s a r e w e l l d e s i g n -ed- and t h e . - c o n d u c t o r Is: l a r g e r , t h a n t h e - c o r o n a l i m i t f o r - t h e v o l t a g e . u s e d , t h e l a t t e r two w i l l be- c o m p a r a t i v e l y s m a l l and i n most c a s e s may be n e g l e c t e d i n - d e t e r m i n i n g economy. The I S R l o s s n a t u r a l l y depends on the c r o s s - s e c t i o n a l a r e a o f c o n d u c t o r , on t h e m a t e r i a l u s e d , and on t h e c u r r e n t t r a n s m i t t e d . The c u r r e n t i s a f u n c t i o n o f the v o l t a g e , i f t h e l o a d , power f a c t o r , e q u i v a l e n t h o u r s , e t c . a r e f i x e d ( n e g l e c t i n g c h a r g -i n g c u r r e n t ) . I f c h a r g i h g r c u r r e n t must be. c o n s i d e r e d , the a v e r a g e between c u r r e n t a t s o u r c e and a t r e c e i v e r w i l l be s u f f i c i e n t l y c l o s e a p p r o x i m a t i o n i n most e a s e s . The c o s t o f the I 2 R l o s s c a n be computed from t h e I a R l o s s a t peak l o a d , e q u i v a l e n t h o u r s , and c o s t p e r u n i t o f energy l o s s . The l a t t e r two a r e u s u a l l y f i x e d by l o c a l c o n d i t i o n s and a r e n o t v a r i a b l e s ' , f o r -the p r o b l e m . The e n e r g y . l o s s e s on t r a n s f o r m e r s c o n s i s t o f c o r e l o s s e s and c o p p e r l o s s e s . S i n c e t r a n s f o r m e r e f f i c i e n c i e s do not v a r y g r e a t l y w i t h s i z e o r v o l t a g e , t h e v a r i a t i o n s i n the l o s s e s w i l l n o t be c o n s i d e r a b l e . I n g e n e r a l t h e s e l o s s e s d e c r e a s e some-what as t h e s i z e o f t r a n s f o r m e r i n c r e a s e s and i n c r e a s e s l i g h t -l y as the v o l t a g e I n c r e a s e s . The e x a c t amount o f v a r i a t i o n must be d e t e r m i n e d ^for-^tHe p a r t i c u l a r t r a n s f o r m e r s t o be u s e d * 63 Other energy l o s s e s w i l l be encountered i f s p e c i a l apparatus such as r e g u l a t o r s - or condensers are used and the cost of t h i s l o s s must be i n c l u d e d * (k) Cost of P a t r o l i n g , e t c * — T h e cost of t e s t i n g i n s u l a t o r s • w i l l depend somewhat-on the number of u n i t s used i n a s t r i n g and hence on the voltage.. .The c o s t of p a t r o l i n g w i l l vary w i t h t h e : l e n g t h of the l i n e and the nature of the country to be covered. Other maintenance and- r e p a i r c o s t s can only be e s t i -mated and w i l l probably be roughly p r o p o r t i o n a l to the l e n g t h of the l i n e . S o l u t i o n by Equation I m p r a c t i c a b l e T h e above Is an i n d i c a -t i o n of the v a r i o u s -number"of elements which a f f e c t the c o s t of each of the f a c t o r s t h a t go t o make up the t o t a l annual cost on a t r a n s m i s s i o n l i n e . I t i s e v i d e n t , t h a t , w i t h so many v a r i a b l e q u a n t i t i e s , there i s no simple s o l u t i o n f o r minimum annual c o s t , which w i l l be g e n e r a l f o r a l l cases* I t i s true t h a t * f o r any given problem, when a l l the c o n d i t i o n s are f i x e d excepting:the. f o u r - c h i e f v a r i a b l e s mentioned above, i . e . , v o l t a g e , wire s i z e , timer spacing, and r o u t e , equations can be w r i t t e n f o r each of. the elements of c o s t i n terms of these v a r i a b l e s , which w i l l approximate q u i t e c l o s e l y : t h a t c o s t under any ^ c o n d i t i o n . For ex-ample, . the cost of a g i v e n type of transformer can be represent-ed w i t h s u f f i c i e n t accuracy by the ex p r e s s i o n Cost = K, + K e E " where Kj", ,K2 and'"n" are constants and E i s the v o l t a g e . Some of the' c o s t s are very d i f f i c u l t to represent, the cos t of towers fo r example. I f a l l these expressions are determined, however, and.are combined i n t o the; g e n e r a l equation of annual c o s t , i t w i l l be found t h a t t h i s equation i s so complicated and con-t a i n s the v a r i a b l e s In so many d i f f e r e n t powers, that a s o l u t i o n i s impossible except by t r i a l * There i s then no apparent advantage over the method of assuming a.number: of a l t e r n a t i v e designs, u s i n g d e f i n i t e v a l u e s f o r each of the v a r i a b l e s , and computing the a c t u a l annual cost of each of these designs. A comparison of these c o s t s w i l l i n d i c a t e the most economical. • Method of S o l u t i o n O u t l i n e d . - - I n order to systematize the computation and to f a c i l i t a t e the determination of the e f f e c t on the t o t a l c o s t , of changes or a d d i t i o n s to any design, the . f o l l o w i n g method i s suggested.,' 1. F i x e d Q u a n t i t i e s . — A s many as p o s s i b l e of the elements a f f e c t i n g the problem should be f i x e d . These w i l l be: (aj The maximum l o a d . The expected increase should a l s o be determined. In case of more than one feeding p o i n t each load must-be Considered s e p a r a t e l y . (b) The load f a c t o r and eq u i v a l e n t hours of the loa d . (C) The power f a c t o r of -load. 64 (d) The c o s t o f energy per k i l o w a t t hour*, (e) The l e n g t h and c o s t o f r i g h t - o f - w a y ( a t l e a s t a p p r o x -i m a t e l y ) f o r t h e v a r i o u s p o s s i b l e r o u t e s . ,(f) The, type o f tower to be u s e d f o r each r o u t e . (g) The p e r c e n t a n n u a l c h a r g e s a p p l i c a b l e t o the v a r i o u s k i n d s o f p r o p e r t y e n t e r i n g i n t o a t r a n s m i s s i o n l i n e * 2 . L i m i t s o f P r o b l e m « - ~ I t i s e s s e n t i a l to d i s c o v e r a p p r o x i -m a t e l y the. l i m i t s o f t h e p r o b l e m so t h a t t i m e w i l l not be w a s t e d i n c o n s i d e r i n g v o l t a g e s and w i r e s i z e s w h i c h a r e f a r from t h e f i n a l r e s u l t * I n c a s e the d e s i g n e r ' s e x p e r i e n c e i s n o t s u f f i c i e n t t o t e l l h i h t h i s , the a p p r o x i m a t e f o r m u l a s f o u n d i n the r e f e r e n c e s g i v e n above w i l l be found u s e f u l * 3« C o s t D a t a . — T h e n e c e s s a r y c o s t d a t a , q u o t a t i o n s , e t c * , must be c o l l e c t e d . These w i l l b e : (a) C o s t o f t r a n s f o r m e r s , o f the s i z e d e t e r m i n e d by the l o a d f o r v a r i o u s v o l t a g e s w i t h i n t h e range o f the p r o b l e m (more t h a n one s i z e may be n e c e s s a r y e s p e c i a l l y i f t h e r e a r e s e v e r a l f e e d i n g p o i n t s w i t h d i f f e r e n t s i z e d l o a d s . ) C o r e l o s s and c o p p e r l o s s s h o u l d - , a l s o be a s c e r t a i n e d . (b) C o s t o f s w i t c h e s , o f p r o p e r s i z e , f o r v a r i o u s v o l t a g e s * (ej C o s t o f l i g h t n i n g a r r e s t e r s , f o r v a r i o u s v o l t a g e s . (d) C o s t o f i n s u l a t o r s , f o r v a r i o u s v o l t a g e s . The l i m i t i n m e c h a n i c a l l o a d f o r any s t r i n g o f I n s u l a t o r s s h o u l d a l s o be d e t e r m i n e d . I n c a s e s where p i n i n s u l a t o r s a r e c o n s i d e r e d i n c o m p a r i s o n t o s u s p e n s i o n t y p e , t h e c o s t o f b o t h must be o b -t a i n e d . The c o s t o f p l a c i n g i n s u l a t o r s s h o u l d be i n c l u d e d . (e) The c o s t p e r pound o f c o n d u c t o r s of d i f f e r e n t m a t e r i a l s -c o p p e r , c o p p e r - c l a d s t e e l , and aluminum w i t h s t e e l c o r e * I n c a s e the p r i c e p e r pound v a r i e s c o n s i d e r a b l y w i t h t h e s i z e , t h e c o s t f o r a v a r i e t y o f s i z e s w i t h i n t h e r a n g e o f the problem s h o u l d be o b t a i n e d * The c o s t o f s t r i n g i n g t h e c o n d u c t o r s h o u l d be e s t i m a t e d o r d e t e r m i n e d fr:om p r e v i o u s e x p e r i e n c e . ( f ) The c o s t o f v a r i o u s s i z e s o f tower f o r e a c h t y p e * I f p o s s i b l e s u f f i c i e n t c o s t s on towers s h o u l d be O b t a i n e d t h a t the v a r i a t i o n o f c o s t w i t h s p a n , w i r e ;;size and v o l t a g e may be d e t e r m i n e d . . T h i s c o u l d be a c c o m p l i s h e d i f t h r e e v o l t a g e s , t h r e e w i r e s i z e s , a n d , t h r e e d i f f e r e n t s p a n s , c o v e r i n g the p r o b a b l y r a n g e o f the p r o b l e m , a r e . c o n s i d e r e d . . By p l o t t i n g Curves^vthe i n t e r m e d i a t e v a l u e s c o u l d be d e t e r m i n e d w i t h s u f f i c i e n t a c c u r a c y . The c o s t o f f o u n d a t i o n s h o u l d be i n c l u d e d w i t h e a c h t o w e r . A n c h o r towers' and s e m i - a n c h o r towers s h o u l d a l s o be c o n s i d e r e d and s i m i l a r c o s t s o b t a i n e d . (g) The c o s t o f t e r m i n a l s u b s t a t i o n s o f the r e q u i r e d s i z e . , . :65a./ The v a r i a t i o n i n t h i s c o s t w i t h v o l t a g e s h o u l d be d e t e r m i n e d ^ . i f p o s s i b l e , , . I n ease, .other, s p e c i a l t e r m i n a l a p p a r a t u s , s u c h as c o n d e n s e r s or r e g u l a t o r s a r e c o n s i d e r e d , the a d d i t i o n a l s u b -s t a t i o n c o s t f o r these" .must be e s t i m a t e d . (h) Q u o t a t i o n s on s p e c i a l a p p a r a t u s c o n s i d e r e d , r e g u l a t o r s , c o n d e n s e r s , . e t c . , s h o u l d be o b t a i n e d w i t h v a r i a t i o n s i n t h i s c o s t with-, s i z e and v o l t a g e - . (1) Annual. , c o s t o f . m a i n t e n a n c e , t e s t i n g , p a t r o l i n g , e t c . must -be e s t i m a t e d . ' 4« A r r a n g e m e n t o f C o s t D a t a . — A f t e r the d a t a i s c o l l e c t e d , :r I t s h o u l d be a r r a n g e d f o r c o n v e n i e n t u s e . T h i s p r o b a b l y c a n b e s t be done by means - o f c u r v e s . S u c h c u r v e s a r e i l l u s t r a t e d i n t h e f i g u r e s . They s h o u l d g i v e : (a) A n n u a l c o s t o f t r a n s f o r m e r s ( i n p l a c e ) i n terms o f v o l t a g e ( F i g . 2 1 ) . (b) A n n u a l c o s t o f s w i t c h e s ( i n p l a c e ) i n terms o f v o l t a g e ( F i g . 2 2 ) . (c) A n n u a l c o s t o f l i g h t n i n g a r r e s t e r s ( i n p l a c e ) i n t e r m s o f v o l t a g e ( F i g . . 22) . (d) A n n u a l c o s t o f i n s u l a t o r s p e r s t r i n g In terms o f v o l t a g e * (e) A n n u a l c o s t p e r m i l e o f c o n d u c t o r s o f d i f f e r e n t m a t e r i a l s i n p l a c e i n terms o f c r o s s - s e c t i o n a l a r e a . ( f) A n n u a l c o s t o f towers i n p l a c e . These c a n be a r r a n g e d ( f o r example) as a s e r i e s o f c u r v e s f o r e a c h s t a n d a r d v o l t a g e showing f o r e a c h s t a n d a r d w i r e s i z e (and m a t e r i a l ; ) t h e v a r i a t i o n , o f c o s t w i t h s p a n . (g) A n n u a l c o s t on t e r m i n a l s u b s t a t i o n i n terms o f v o l t a g e * (h) A n n u a l c o s t o f t r a n s f o r m e r e n e r g y l o s s e s i n terms o f .' v o l t a g e . .'••••• '"-•••' ( i ) A n n u a l c o s t o f l i n e energy l o s s e s p e r m i l e f o r e a c h m a t e r i a l o f c o n d u c t o r c o n s i d e r e d , i n terms o f c r o s s - s e c t i o n a l a r e a . 5* Most E c o n o m i c a l - D e s i g n * — I t now r e m a i n s t o a p p l y t h e s e c o s t s to d e t e r m i n e t h e most e c o n o m i c a l d e s i g n . The r o u t e Is . u s u a l l y t h e most l i m i t e d o f a l l the v a r i a b l e s , t h e r e o r d i n a r i l y b e i n g no more than two o r t h r e e p o s s i b l e r o u t e s a t m o s t . L i k e -w i s e , on any r o u t e , t h e l a y o u t I s somewhat l i m i t e d . L o c a t i o n s o f a n c h o r towers and s e m i - a n c h o r towers a r e u s u a l l y more o r l e s s f i x e d . On s t r a i g h t r u n s the span c a n o f t e n be v a r i e d . I f two or t h r e e p o s s i b l e l a y o u t s a r e made f o r each r o u t e , v a r y i n g the span where p o s s i b l e , a s u f f i c i e n t c o m p a r i s o n w i l l be o b t a i n e d . I f , now, f o r e a c h o f t h e s e l a y o u t s , a s h e e t o f c u r v e s i s p r e -p a r e d , showing f o r e a c h s t a n d a r d c o n d u c t o r c o n s i d e r e d , a c u r v e , g i v i n g t h e v a r i a t i o n i n t o t a l a n n u a l c o s t w i t h the v o l t a g e , a c o m p l e t e and a c c u r a t e s t u d y o f the economy may be made. Not o n l y w i l l t h e most e c o n o m i c a l v o l t a g e , w i r e s i z e , r o u t e and layout-be o b t a i n e d , b u t t h e c o m p a r a t i v e e f f e c t o f v a r i a t i o n i n t h e s e q u a n t i t i e s may be s t u d i e d , , C u r v e s may be added to show c o m p a r i s -on o f two or more c i r c u i t s w i t h a s i n g l e c u r x z u l t • I f a d e s i g n , c h o s e n t e n t a t i v e l y , p r o v e s , on f u r t h e r i n v e s t i g a t i o n , t o be i m p r a c t i c a b l e on a c c o u n t o f c o r o n a l i m i t , t o o g r e a t r e g u l a t i o n , e t c . , t h e c o s t o f c o r r e c t i n g the f a u l t by a change i n d e s i g n , a d d i t i o n o f r e g u l a t o r , e t c • , as compared w i t h one o f t h e o t h e r d e s i g n s n o t h a v i n g t h a t f a u l t , may be e a s i l y determined,* Space does n o t p e r m i t d w e l l i n g on the s u b j e c t o f " t r u n k " t r a n s m i s s i o n l i n e s more i n d e t a i l . Any p r o b l e m o f t h i s k i n d i s , one w h i c h w i l l b e a r a n a l m o s t i n f i n i t e amount o f s t u d y . N a t u -r a l l y the d e t a i l t o w h i c h s u c h a s t u d y s h o u l d b e c a r r l e d w i l l depend somewhat on t h e s i z e a n d n a t u r e o f the p r o j e c t . As a r u l e , however, t i m e spent on a n e c o n o m i c a l d e t e r m i n a t i o n i s w e l l r e p a i d , I n many c a s e s some o f t h e v a r i a b l e s a r e l i m i t e d -v o l t a g e may be d e t e r m i n e d by o t h e r t h a n e e o n o m i c a l c o n s i d e r a t i o n s , r o u t e and l o c a t i o n f o r t o w e r s may be f i x e d , e t c . T h i s s i m p l i f i e s t h e p r o b l e m b u t i n any c a s e some s u c h study as t h a t o u t l i n e d above i s e s s e n t i a l to an a c c u r a t e d e t e r m i n a t i o n . V a r i a t i o n s i n t h e method w i l l , o f c o u r s e , be f o u n d t o accommodate s p e c i a l c o n d i t i o n s . I n any c a s e , i t i s t o be e m p h a s i z e d t h a t t h e p r o b l e m i s a c o m p l i c a t e d one a n d u s u a l l y does not b e a r s o l u t i o n by any e a s y , a p p r o x i m a t e m e t h o d . CHAPTER VIII 66 TRANSMI3SION-LINE PROBLEMS  SECONDARY TRANSMISSION-LINES Determination-of Most Economical Standards of Construction Conductor Size, Loading, Route, E t c . on Lesser or Secondary Transmission •Lines. In the preceding chapter the points of d i s t i n c t i o n between "trunk" transmission l i n e s and "secondary" transmission l i n e s were discussed. I t i s proposed here to consider the problems a r i s i n g i n connection with- secondary transmission l i n e s and to indicate t h e i r economic s o l u t i o n . . The "secondary" transmission l i n e s of any system must be considered as a c l a s s instead of as one or more s p e c i f i c problems. Their service i s v a r i e d . They are c a l l e d upon to feed loads of various sizes, and various power factors and load f a c t o r s . They may have a considerable diversity- i n leng-ths, types of route, etc*- I t i s obviously impracticable to consider each l i n e as a s p e c i a l problem. It i s necessary to adopt c e r t a i n standards•which w i l l best f i t a l l cases on an average, allowing some v a r i a t i o n i f necessary i n wire sizes, .etc. ; There then remains.the problem of how best to adapt these standards to f i t . a n y given condition. In t h i s study, therefore, there are two separate d i v i s i o n s . The f i r s t i s of a somewhat sim i l a r nature to that of the "trunk" transmission l i n e , excepting that the problem i s general rather.than s p e c i f i c . I t deals with the establishment of standards wiie-h w i l l best f i t average conditions, such as a standard voltagey one or more standard wire sizes (the v a r i e t y depending .somewhat on the range of loads handled) and a stand-ard span. • The -second d i v i s i o n includes problems r e l a t i n g to the proper' use and. combination of these standards. Such problems as the most economical route, the economical d i v i s i o n of .load among several l i n e s , the load at which wire size should be changed or an a d d i t i o n a l l i n e run, and reconstruction prob-lems are i n this c l a s s . I t would be impossible i n a reasonable amount of space to attempt to cover i n any d e t a i l a l l the problems which might arise i n connection with secondary transmission l i n e s . The f f i e l d of study i s very large and new problems are constantly appearing. Some of the problems commonly met with under each of the -two d i v i s i o n s w i l l be discussed, however, and the elements a f f e c t l t l n g t h e i r solution w i l l be indicated. The general method of attacking any. problem of this kind i s to determine an -expression for annual cost and then to discover under what conditions that cost w i l l be a minimum. Since the r e s u l t s are to be of general application, i t i s necessary 67 t h a t t h e d a t a u s e d he g e n e r a l , f o r the whole system^ Average c o s t s o f p o l e l i n e p e r m i l e s h o u l d be u s e d , f o r e x -ample, r a t h e r t h a n a n e s t i m a t e d c o s t f o r a c e r a t i n l i n e o v e r a g i v e n r o u t e . S i m i l a r l y , the B e s u l t s o b t a i n e d s h o u l d be d i s p l a y e d i n f o r m u l a s , c u r v e s o r t a b l e s w h i c h may be o f g e n e r a l a p p l i c a t i o n . D a t a N e c e s s a r y . - - T h e d a t a n e c e s s a r y f o r s o l v i n g s u c h p r o -blems on s e c o n d a r y t r a n s m i s s i o n l i n e s i n c l u d e the f o l l o w i n g : (a) Range o f s i z e s o f l o a d s c o n s i d e r e d . (b) C h a r a c t e r i s t i c s o f v a r i o u s t y p e s o f l o a d c a r r i e d , l o a d f a c t o r , power f a c t o r , e q u i v a l e n t h o u r s , e t c . I f the c h a r a c -t e r i s t i c s o f t h e g e n e r a l t y p e s o f l o a d a r e t h o r o u g h l y u n d e r -s t o o d any i n d i v i d u a l l o a d c a n be s t u d i e d as a c o m b i n a t i o n o f s e v e r a l g e n e r a l t y p e s i n d i f f e r e n t a m o u n t s . A l o a d may c o n s i s t o f p a r t l i g h t i n g , p a r t power, p a r t s t r e e t r a i l w a y , e t c . and i t s I n d i v i d u a l c h a r a c t e r i s t i c s a r e a c o m b i n a t i o n o f t h e c h a r a c t e r i s t i c s o f a l l these- t y p e s . (c) A v e r a g e m a t e r i a l and l a b o r c o s t s on s t a n d a r d com-s t r u c t i o n ; a v e r a g e r i g h t - o f - w a y c o s t s i f s u c h f i g u r e s a r e o b -t a i n a b l e • (d) C o s t o f energy f o r v a r i o u s t y p e s o f l o a d i n v a r i o u s i p a r t s . o f t h e -system. " S t a n d a r d V o l t a g e . " - - T h e s o l u t i o n o f the f i r s t c l a s s o f problems m e n t i o n e d above i s v e r y o f t e n l i m i t e d by o t h e r c o n -s i d e r a t i o n s t h a n s t r i c t economy. E x t e n s i v e systems r a r e l y s p r i n g i n t o b e i n g s u d d e n l y . U s u a l l y they a r e d e v e l o p m e n t s from c o m p a r a t i v e l y s m a l l b e g i n n i n g s . H e n c e , what was y e s t e r d a y the t r u n k t r a n s m i s s i o n l i n e o f the s m a l l s y s t e m , becomes today p a r t o f t h e s e c o n d a r y t r a n s m i s s i o n network o f the l a r g e s y s t e m . I t h a p p e n s , t h e r e f o r e , t h a t the s e c o n d a r y t r a n s m i s s i o n v o l t a g e i s r a r e l y c h o s e n as s u c h , b u t i s r a t h e r a development from p a s t p r a c t i c e . T h e r e I s always the q u e s t i o n o f the economy o f c h a n g i n g the s t a n d a r d v o l t a g e , u s u a l l y to one h i g h e r . T h i s c a n o n l y be d e t e r m i n e d by a c a r e f u l study o f p r e s e n t and p r o b a b l e f u t u r e c o n d i t i o n s , t a k i n g i n t o c o n s i d e r a t i o n the a d d i t i o n a l c o s t f o r t r a n s f o r m e r s and s t a t i o n equipment and. the c o s t o f making the c h a n g e - o v e r , as compared w i t h the s a v i n g i n l i n e l o s s e s , the s m a l l e r c o n d u c t o r u s e d , and the i n c r e a s e i n c a p a c i t y i n the system w i t h the p r o p o s e d h i g h e r v o l t a g e . Such a change c a n sometimes be made e c o n o m i c a l l y , where s i n g l e - p h a s e . t r a n s f o r m e r s a r e u s e d t o a l a r g e e x t e n t , by c h a n g i n g from a d e l t a t o a s t a r c o n n e c t e d s y s t e m . I n c a s e s where t h e v o l t a g e c a n be c h o s e n i n advance on the b a s i s o f economy, an a n a l y s i s s i m i l a r t o t h a t , s u g g e s t e d f o r t r u n k t r a n s m i s s i o n l i n e s w i l l be n e c e s s a r y . " S t a n d a r d S p a n " The s t a n d a r d span t o be c h o s e n w i l l depend l a r g e l y on .the type o f c o n s t r u c t i o n u s e d . C o n d i t i o n s may v a r y from the use o f a ' s t e e l - t o w e r l i n e on p r i v a t e r i g h t - o f - w a y to t h a t o f w o o d - p o l e l i n e s ' a l o n g the highway, c a r r y i n g d i s t r i b u t i o n i n a d d i t i o n . F o r the f i r s t , p r e b a b l y the most advantageous span c a n be c h o s e n somewhat as o u t l i n e d f o r t r u n k l i n e s 68 and n e e d n o t n e c e s s a r i l y "be u n i f o r m n o r t h e same f o r a l l l i n e s * F o r t h e l a t t e r , t h e span w i l l he d e t e r m i n e d p a r t l y by the s t r e n g t h o f t h e . p o l e s and p a r t l y by the needs o f the d i s t r i b -u t i o n l i n e s * These spans c a n he f a i r l y u n i f o r m , n o t e x c e e d -i n g a d e f i n i t e maximum o f 300 f t * o r d i n a r i l y * C o n d u c t o r S i z e * — T h e q u e s t i o n o f s t a n d a r d i z a t i o n o f c o n -d u c t o r s i z e w i l l depend l a r g e l y on t h e k i n d o f l o a d s c a r r i e d and t h e i r d i s t r i b u t i o n o v e r the s y s t e m . I n some c a s e s i t w i l l be found a d v a n t a g e o u s t o s t a n d a r d i z e on o n e • o r two s i z e s a n d c a r e f o r a d d i t i o n a l l o a d by more l i n e s * I n o t h e r s , i t may be b e t t e r t o use a w i d e r v a r i e t y o f c o n d u c t o r s , accommodating t h e s i z e to t h e l o a d c a r r i e d . A method o f s t u d y i n g c o n d u c t o r economy i s g i v e n b e l o w . By i t s means,: t h e most e c o n o m i c a l w i r e s i z e f o r any l o a d .may be c h o s e n a n d , under p r o p e r c o n d i t i o n s , s t a n d a r d s i z e s may be f i x e d . T h i s method o f s tudy a l s o a i d s i n the s o l u t i o n o f s e v e r a l o f the p r o b l e m s o f the s e c o n d c l a s s as w i l l be p o i n t e d out l a t e r . Example o f s t u d y o f C o n d u c t o r Economy: L e t a s t a n d a r d i z e d t y p e o f c o n s t r u c t i o n w i t h g i v e n v o l t a g e and s t a n d a r d span be a s s u m e d . The t o t a l a n n u a l c o s t o f s u c h a t r a n s m i s s i o n l i n e i s composed o f : : * . A n n u a l c o s t on c o n s t r u c t i o n e x c l u s i v e o f c o n d u c t o r . 2, A n n u a l c o s t o f c o n d u c t o r I n p l a c e * 3* A n n u a l c o s t o f e n e r g y l o s s . F o r t h i s e x a m p l e , a \". rood-pole l i n e w i l l be assumed w i t h a maximum s p a n o f 175 f t . ' t o accommodate d i s t r i b u t i o n . The a n n u a l c o s t o f p o l e s and f ' x t u r e s p e r 1,000 f t . o f l i n e w i l l , o f c o u r s e , v a r y w i t h t h e w i r e s i z e , i f the l i n e i s p r o p e r l y d e s i g n e d f o r s a f e t y , p r o b a b l y a f t e r some s u c h f o r m u l a s as K, +• K 2 A , where K, and Kg a r e c o n s t a n t s and A Is the c r o s s - s e c t i o n a l a r e a o f t h e c o n d u c t o r . The a n n u a l c o s t o f the c o n d u c t o r per 1,000 f t . w i l l v a r y a p p r o x i m a t e l y w i t h A as a l s o w i l l t h e c o s t o f s t r i n g i n g , i . e . c o s t i n p l a c e = K3•+• K 4 A» The a n n u a l c o s t o f energy l o s s per 1,000 f t * w i l l v a r y w i t h t h e s q u a r e o f the l o a d , the f i r s t power o f the e q u i v a l e n t h o u r s , and t h e c o s t o f e n e r g y , and i n v e r s e l y w i t h the c r o s s - s e c t i o n a l a r e a . , : • •• - •: T h e n the t o t a l a n n u a l c o s t p e r 1,000 f t * o f d i n e Y = K 7 + K3 + ( K 2 + K4)'A+ R>kw g tCe Where t - e q u i v a l e n t h o u r s , Ce c o s t o f e n e r g y l o s s p e r k i l o w a t t -h o u r , k w . » l o a d i n k i l o w a t t s S i m p l i f i e d 2 y ~ Ka +- KbA +• Ec kw tCe (24) A 69 Where K a = K K. and K b = K 2^ and Kc K< o s t E c o n o m i c a l C o n d u c t o r S i z e . . - - T h e most e c o n o m i c a l t h a t f o r w h i c h the v a l u e o f Y i s a by s e t t I h g t h e f i r s t -der» e q u a l t o 0 c o n d u c t o r s i z e " i l l be minimum. T h i s c a n be o b t a i n e d i v a t i v e o f Y w i t h r e s p e c t t o A dY dA k w g t C e A £ A = (25) Most^Ee :onomica 1 • •  L o a d * I f i t i s d e s i r e d to d e t e r m i n e t h e most e c o n o m i c a l l o a d f o r any l i n e , t h e d e r i v a t i v e o f Y must be t a k e n w i t h r e s p e c t to the l o a d , kw, I t I s e v i d e n t t h a t , w i t h t h e e q u a t i o n I n t h e above f o r m , t h e r e s u l t would be kw. = 0 , s i n c e •the minimum l i n e l o s s i s o b t a i n e d w i t h no l o a d * However, the l i n e must 'be c o n s i d e r e d as a w o r k i n g u n i t . H e n c e , i f t h e above e x p r e s s i o n i s c h a n g e d to r e p r e s e n t the a n n u a l c o s t per k i l o w a t t t r a n s m i t t e d , a n d the minimum v a l u e o f t h a t Q u a n t i t y f o u n d , the most e c o n o m i c a l l o a d f o r the l i n e w i l l be o b t a i n e d . • I f Y r = t h e a n n u a l c o s t per k i l o w a t t t r a n s m i t t e d + K b A kw K c kwtC, (26) •ay * akw - k — kw2 kw K b A A (27) [KctC&J-M u m e r l e a l E x a m p l e . — The v a l u e s o f t h e c o n s t a n t s must be o b t a i n e d t o a c c o r d w i t h l o c a l c o n d i t i o n s * Kc i s e v a l u a t e d as f o l l o w s : Ye as a n n u a l c o s t o f energy l o s s per 1,000 f t . — 3 I a R x t x 365 x ° e . 1,000 Where I =-R « I = T h e n Y e Where/? - r e s i s t i v i t y per m i l f o o t A .., . . .... / c u r r e n t p e r w i r e r e s i s t a n c e , p e r 1 , 0 0 0 f t . , one w i r e , ^ . /ox 1 ,000 A kw x 1 ,000 vs/T E c o s e 1,000 kw\2 1,000/C E COB 67/ X A x t x 365 2. Where 71,000 V2 C \ E coa/ 1,000 K c k w " t C A x 365 70. I f * - 10.8, K a ^ 9 4 ° * ^ ; 7 G (E eos<<? )--2 L e t us assume f o r example a 2 2 , 0 0 0 - v o l t l i n e . F o r •which K-j_ = 39 • v K 2 « 12.2 . .' 105 • . ' ' ."• K-2 = ' i .715 - ' P_ \_ . _ c o s t o f c o n d u c -K A « p « 2 1 1 4 7 . 5 C c u j B h e r e C c u  t o r p e r pound I f C — ^ 0 . 2 0 c u ••• Kcr = 11*3 KI — 40.72 Kb -43.9 - I O 5 K 6 , = 11.3: 2 . - 4 3 . 9 kw t Op (From E q . 24) Y± 4 0 . 7 2 - — — A -f- 11.3 — -10^ '•..•'A / l l . 3 x 10^t Ce . — — ( f r o m E q . 25) A-= kw /• — - — - — = 1 6 0 . ^ kw / tC *J 43*9 ( f r o m E q . 26) Y ' = 4 0 . 7 2 4- 4 3 ° 9 A 1 0 5 kwtC + 11.3 -kw : A r 43*9 (From E q . 27) k w = / 4 0 . 7 2 - l ^ A 1 10 D A l l - 3 t G ^ The f o r e g o i n g a r e a l l s i m p l e e q u a t i o n s I n terms o f the l o a d c a r r i e d , t h e c r o s s - s e c t i o n a l a r e a o f c o n d u c t o r , t h e equiv** a l e n t h o u r s and the c o s t o f e n e r g y . The l a t t e r two q u a n t i t i e s a r e more or l e s s i n t e r « r e l a t e d . A s t u d y o f energy c o s t w i l l show t h a t the c o s t per k i l o w a t t - h o u r v a r i e s , among other" t h i n g s , w i t h the l o a d f a c t o r and hence w i t h the e q u i v a l e n t h o u r s . The v a l u e o f " t C " may t h e n be o b t a i n e d a p p r o x i m a t e l y f o r any v a l u e o f "t" w i t h a n y e t y p e o f l o a d . I t w i l l be f o u n d advantageous f o r study t o p l o t c u r v e s o f a l l t h e e q u a t i o n s g i v e n a b o v e . I f d i f f e r e n t v a l u e s o f t C e are c h o s e n , as t c e — . 0 2 , t C e - . 0 4 , t C e - = . 0 6 , t C e — .08 and t C Q = 71 -» d i s p l a y e d ; s i m i l a r l y E q . 26, F o r E q s . 25 and 27, a c u r v e , p l o t t e d between A a n d kw f o r e a c h d e s i r e d v a l u e o f tC~c mav be o b t a i n e d . e * F o r a n u m e r i c a l example t h e v a l u e o f e q u i v a l e n t h o u r s I s t a k e n as 6 and the c o r r e s p o n d i n g v a l u e o f " t C e assumed ae • 0 6 , The c u r v e s f o r Y ' t h e a n n u a l c o s t p e r k i l o w a t t per 1,000 f t . , a r e p l o t t e d as shown i n F i g . 23- The c u r v e s f o r Y t h e t o t a l a n n u a l c o s t per 1,000 f t . a r e e a s i l y o b t a i n e d i f d e s i r e d b u t a r e n o t shown here.. These c u r v e s f o r Y ' a r e i n t e r e s t i n g i n t h a t t h e y show d e f i n i t e l y t h e p o i n t o f minimum-c o s t or t h e l o a d o f g r e a t e s t economy f o r any g i v e n c o n d u c t o r "~cost o r the l o a d o f g r e a t e s t economy f o r any g i v e n c o n d u c t o r s i z e . L i k e w i s e , t h e y show, f o r any l o a d , the most e c o n o m i c a l c o n d u c t o r and j u s t how much c h e a p e r one s i z e i s t h a n a n o t h e r f o r any l o a d . F i g u r e s 24 and 25 a r e a l s o p l o t t e d from E q s . 25 and 27, u s i n g v a r i o u s v a l u e s f o r t C e * F i g u r e 2§ g i v e s the most e c o n o m i c a l l o a d f o r any w i r e s i z e * The c u r v e s f o r t C e = *06 might have b e e n d e r i v e d d i r e c t l y from F i g . 23, F i g * 24 b e i n g a b o u n d i n g c u r v e f o r a l l the c u r v e s shown and F i g . 25 the l o c u s o f a l l t h e minimum p o i n t s . I t i s i n t e r e s t i n g to n o t e t h a t t h e most e c o n o m i c a l s i z e o f w i r e f o r any l o a d I s n o t the same as t h e s i z e f o r w h i c h t h a t i s the. most e c o n o m i c a l l o a d . The r e a s o n f o r t h i s i s a p p a r a n t from F i g . 2 3 ; f o r #0 w i r e a p p e a r s a t 2,500 ; k . w v t o be most e c o n o m i c a l , t h o u g h when l o a d e d t o 3 , 8 0 0 k . w . i t g i v e s an a n n u a l c o s t o f o n l y .0473 c e n t s p e r k i l o w a t t p e r 1 ,000 f t . , as compared to .051 per k l l o w a t p e r 1,000 f t . Use o f C u r v e s . — By means of s u c h c u r v e s as t h e s e , a number o f the problems' 6'f s e c o n d a r y t r a n s m i s s i o n l i n e s may be r e a d i l y s o l v e d . I f the s i z e and " c h a r a c t e r i s t i c s o f a l o a d a r e known, the most e c o n o m i c a l c o n d u c t o r may be f o u n d from the p r o p e r c u r v e . I f some o t h e r s i z e t h a n the most e c o n o m i c a l i s u s e d , i t s a d d i t i o n a l c o s t i s g i v e n by t h e c u r v e s . I f s t a n d a r d s i z e s a r e to be d e t e r m i n e d , the r a n g e o f l o a d s , and t h e i r c h a r a c t e r i s t i c s , to be h a n d l e d may be s t u d i e d i n c o n n e c t i o n w i t h the c u r v e s a n d the most e c o n o m i c a l s i z e o r s i z e s to f i t t h e m a j o r i t y o f -cases may be c h o s e n . I f the p r o b l e m i s one o f c h a n g i n g c o n d u c t o r s i z e s , the l o a d a t w h i c h the a n n u a l c o s t a f t e r t h e change ( i n c l u d i n g the a n n u a l c h a r g e s on the c o s t o f changes) w i l l be l e s s t h a n the a n n u a l c o s t w i t h the p r e s e n t s i z e , may be t a k e n from s u c h c u r v e s as F i g . 2 3 . S l m i l a r l y , i f c u r v e s f o r two ( o r more) c i r c u i t l i n e s a r e p r e p a r e d , the economy o f a d d i n g a second c i r c u i t , o f b u i l d i n g a n a d d i t i o n a l l i n e , e t c . , may be s t u d i e d . I f s e v e r a l l i n e s o f d i f f e r e n t s i z e s a r e f e e d i n g one s t a t i o n , the e c o n o m i c a l d i v i s i o n o f l o a d i s shown by c u r v e s s i m i l a r to F i g . 2 5 . M n s t E c o n o m i c a l R o u t e . A n o t h e r p r o b l e m w i c h Is e c o u n t e r e d i n the d e s i g n o f n e a r l y ~ a l l t r a n s m i s s i o n l i n e s i s the c h o i c e o f t h e b e s t r o u t e . I t is*' seldom p o s s i b l e t o f o l l o w a n y t h i n g l i k e a d i r e c t " a i r l i n e " r o u t e on a c c o u n t o f the d i f f i c u l t y i n o b -t a i n i n g r i g h t - o f - w a y « I f wooden p o l e s o r s t e e l s t r u c t u r e s w i t h s m a l l b a s e a r e u s e d , a r o u t e i s o r d i n a r i l y c h o s e n w h i c h f o l l o w s t h e highway i n s u c h a way as t o a r r i v e a t t h e d e s t i n a t i o n w i t h 7 2 The least possible length of l i n e and the fewest possible d i f f i c u l t i e s i n construction. I t often occurs, however, that t h i s choice i s not a simple matter. There may be two or more routes, each of which has advantages and disadvantages which more or less o f f s e t each, other, and there i s no self-evident choice between them. I t i s then necessary to make a. c a r e f u l cost an-a l y s i s to determine the most economical route. The r e l a t i v e economy of the various routes can be weighed against any other features which are not subject to a tangible cost comparison, and the most practicable route w i l l usually be made evident. Probably one of the most usual and simple problems of t h i s kind Is the choice between two routes, one of which i s shorter than the other but necessitates the purchase of a eertainnamount of right-of-way, while the other i s longer but follows the highway and Is not subject to right-of-way charges. It i s the purpose here to show how the cost of two such routes can be r e a d i l y compared and a general equation derived which w i l l cover a l l such problems on any p a r t i c u l a r system. This equation can be used to determine curves that give a more tangible method of choesing the best s o l u t i o n . -As a c o r o l l a r y to t h i s problem we have the condition where there i s a choice of a longer route, c l e a r of trees and other obstructions, and a shorter one which w i l l require extra high structures, a d d i t i o n a l guying, etc. In fact, the problem resolves i t s e l f into the question of "How much can we a f f o r d to spend i n addition to the normal cost of construction in order to shorten a route?" The basis, for such a cost comparison w i l l n aturally be the annual cost of the two routes. I f we can determine what w i l l be the saving i n annual cost of the shorter route over the longer when only- normal l i n e construction cost i s considered, we can then t e l l what i s the maximum amount which we would be j u s t i f i e d i n expending .for right-of-way or a d d i t i o n a l material, etc., i n order to use that shorter route. I f the longer route should also require some extra construction expenses these should natur-a l l y be included i n the comparison. The annual cost of any route Is made;up of the annual charges against the construction i t s e l f and the annual charges for the energy loss, the l a t t e r depending on the load c a r r i e d and the size of the wire used. It i s f i r s t necessary to determine as accurately as possible what the-unit annual charges w i l l be on a normal l i n e , i . e . one without exceptional d i f f i c u l t i e s . Determination of Normal-Line C o s t . — The annual charges against the construction w i l l depend upon TEe standard type of construction used and. on the cost of materials and labor i n the l o c a l i t y under consideration. There must be obtained the t o t a l cost per mile of the l i n e i n place including both material and labor costs on poles, crossarms, pins, Insulators, wire, grounds, guying, etc. In doing t h i s , the sizes and quantities of the various materials which would, constitute an average normal mile 73 of l i n e must f i r s t be determined. The annual, cost may then be obtained by f i g u r i n g i n t e r e s t , insurance, taxes and depreciation on t h i s f i r s t cost allowing for the difference In depreciation between the dif f e r e n t - m a t e r i a l s used. A certain'amount per year should also be added for maintenance, p a t r o l l i n g etc* The r e s u l t i n g annual cost w i l l be a constant for any condition of loading, providing the size of the wire i s fixed, and may be represented -by K 6 * -..-.-U.sua-liy-.-when. a-., shorter-route Is selected a number of corners are eliminated* The cost of a corner construction, e s p e c i a l l y on high-tension lines,, may be quite an appreciable addition to the normal cost of the l i n e * It can be figured, however, i n the ' same manner as the, normal l i n e cost* This annual cost per corner may be represented by Eg* : "Annual cost of Energy Losses."--The annual charges due to loss of energy may be determined as shown above i n the study of conductor economy. Then, Annual cost of energy l o s s = K kws" per mile* 365*000 r t C . Where Kf=— '••' •'. (E cos e)£ Where " r " = resistance of conductor i n ohms per mile* When these constants have been evaluated for the p a r t i c u l a r conditions of the problem In hand, i t . i s then possible-to. determine the t o t a l annual cost per mile with normal l i n e con-struction- and the t o t a l annual cost for any p a r t i c u l a r length including/the corners* Determination- of General Equation*-- I f we l e t L represent the difference i n length between the shorter route and the longer, -the savings i n annual cost of the shorter route over the longer would be L times the annual cost per mile i f normal l i n e con-st r u c t i o n o n l y . i s considered* This, then, represents the addit-ional, maximum' amount which i t would be economical to spend i n addi-t i o n to the normal annual cost of the l i n e i n order to u t i l i z e the shorter route* I f the a d d i t i o n a l cost i s for right-of - w a y , this annual amount Is the maximum rent which we could afford to pay for i t or I f the right-of - w a y i s bought outright, t h i s amount represents the i n t e r e s t and taxes on the maximum amount which could be paid for the necessary land* In. the case where the addi t i o n a l cost would be for extra poles and other l i n e material, the above savings would represent the interest, taxes and de-pr e c i a t i o n on the maximum amounts which could be so expended*. I f L = the length i n miles which would be saved by - • using the shorter route, C/ ~ the maximum extra expenditure allowable i n C - ? K l e S x l P a u l l p ^ a i ! ^ g t P r r M l ' saved =CL, , L 9 74 N . = the number o f c o r n e r s s a v e d b y u s i n g the s h o r t e r r o u t e , g = p e r c e n t a n n u a l c h a r g e s on a d d i t i o n a l e x p e n d i t u r e ( i n t e r e s t , i n s u r a n c e , t a x e s , d e p r e c i a t i o n ) , K 6 - . t h e a n n u a l c o s t , o f n o r m a l l i n e c o n s t r u c t i o n p e r m i l e , K^kw2 =• a n n u a l c o s t o f e n e r g y l o s s per m i l e , K s = a n n u a l c o s t o f a c o r n e r i n a d d i t i o n t o n o r m a l l i n e c o s t , Then The a n n u a l c h a r g e s on t h e a d d i t i o n a l e x p e n d i t u r e f o r r i g h t -o f - w a y , e x t r a p o l e s e t c . would be gC/ ; gC, ~ L(KA +•"• K 7 k w e ) + K 8 N (28) w h i c h i s a g e n e r a l e q u a t i o n and c a n be a p p l i e d t o any such r c a s e . i f -the p r o p e r v a l u e s f o r - . t h e - v a r i o u s c o n s t a n t s a r e o b t a i n e d . I f t h e n t h e c o n t e m p l a t e d s h o r t e r r o u t e c a n be u s e d w i t h a l e s s e x p e n d i t u r e t h a n Cf i t would be an e c o n o m i c a l p r o p o s i t i o n t o use i t . The above e q u a t i o n can be made even more g e n e r a l and be shown g r a p h i c a l l y by means o f a c u r v e i f we r e d u c e i t t o terms o f C or the maximum a l l o w a b l e e x p e n d i t u r e per m i l e o f l e n g t h s a v e d , o m i t t i n g f o r the -present t h e amount s a v e d on c o r n e r s * . . K« + K 7 k w 2 •' • • ' C * g/100 (29.) The v a l u e o f "g"as I n d i c a t e d above depends upon t h e n a t u r e o f the a d d i t i o n a l e x p e n d i t u r e . I f i t i s f o r r i g h t - o f - w a y , i n t e r e s t and t a x e s must be c h a r g e d b u t no d e p r e c i a t i o n need be c o n s i d e r e d , We may take- i n t e r e s t a t 6 p e r c e n t , i n s u r a n c e and t a x e s a t 2 • p e r c e n t or g*g per c e n t . T h i s r e p r e s e n t s y e a r l y r e n t a l . I f e x t r a l i n e m a t e r i a l I s t o be p u r c h a s e d d e p r e c i a t i o n a l s o must be a d d e d . C o n s i d e r i n g the l i f e o f s u c h m a t e r i a l as 20 y e a r s , d e p r e -c i a t i o n 5 per c e n t a n d g = 13 per c e n t . - D a t a f o r C u r v e s . — T h e accompanying c u r v e s , F i g . 2 6 , were p l o t t e d a s s u m i n g v a l u e s f o r K 6 , K r and Ka as f o l l o w s : K t t = $350 (wood p o l e c o n s t r u c t i o n ) r =. .539 f o r N o , 0 w i r e • t = 6 hr« . E = 4 6 , 0 0 0 v o l t s c o s . &.==* .90 . '• . Ce ~ .01 p e r k i l o w a t t - h o u r - K = 3 6 5 , 0 0 0 r t C e _ 0 . 6 9 :. : CE C O S ^ ) 2 . ~ io5 Ks = $40 . g « 8 ' a n d 13 320 + 320 + •69 kwg 105 .08 ; and. C f 75 .13 These equations are plotted for various values of the load, kw.. The lower curve A i s plotted for g = 8 per cent £>r when the a d d i t i o n a l expenditures to he.made i n using the shorter route w i l l he for such property as right-of-way which has no depreciation. In case the right-of-way i s obtained on a yearly r e n t a l basis, Q% of the amount shown by the curve would be the allowable..yearly rent. The upper curve Is' to be used when the extra cost w i l l be for extra l i n e material such as poles, stubs, guys, etc. for which the l i f e was assumed to be 20 years and g = 13%. I f any corners w i l l be saved by using the shorter route, the cost, of these may be added to the amount shown by the curve |500 for g = 8 per cent and $308 for g — - ; Discussion :of Curves .—These curves, then, show the .amount which .could be spent i n constructing a l i n e i n addition to the normal cost of construction under average conditions i n order to. shorten the length of the route 1 mile. The value of C when the load i s 0 represents annual charges on the normal'construction cost of 1 mile of l i n e c a p i t a l i z e d at the percentage g, which i s the percentage of annual charge against a d d i t i o n a l property, acquired and depends on i t s nature. As the load Increases the value of C Increases due to the i n -creasing cost of the l i n e l o s s . The slope of the l i n e away from the v e r t i c a l i l l u s t r a t e s g r a p h i c a l l y the importance of knowing as accurately as /possible.the load and the load factor that It i s intended to carry on the line,, i n order t o . c o r r e c t l y make the choice of routes. Though.an accurate determination may be p r a c t i c a l l y impossible, i t i s usually possible to work between some assumed.limits that w i l l represent a wide range of conditions and s t i l l lend,themselves to analysis by means of the curves. •Further more, as the load Increases, the point which stands out.plainly i s the great economy which w i l l o r d i n a r i l y be achieved, by the use of a shorter route. For example I f right-of-way can be,obtained for a yearly r e n t a l of $1 per. pole, at 8 per, cent t h i s would represent.$12.50 per pole or at 35 poles per mile, $437*50 per mile. With a load of 4 ,000 kw. the/curves show that we could spend,.according to curve A, | 5 , 3 0 0 for each mile saved, which would purchase right-of-way, at the above rate for 12 miles. Or, from curve B we could expend $3,300 for a d d i t i o n a l material i n order to save 1 mile. ;If--anv corners were eliminated the amount would be s t i l l more. Hence,. i f the actual expenditure necessary i s any less than the 'above figures, the difference would represent a r e a l saving and .It would be economy to use the shorter route. K 8 or g/100 for each corner. I f K = $40, t h i s amounts to 76 Naturally the -curves here given could not he used for any but the p a r t i c u l a r type of c o n s t r u c t i o n , l l o c a t i o n and voltage for which they were, computed. I t Is a simple matter, however, to develop s i m i l a r curves to f i t any other case from the equations given* The economy shown by such a curve, however, -cannot be used as an- absolute c r i t e r i o n i n the choice of a route* There are other factors which do not lend themselves to such an exact cost a n a l y s i s . . The matter of. p a t r o l l i n g a l i n e and making . repa i r s might be. considerably more expensive along private right-of-way than along a main highway. The proximity to a r a i l r o a d might be considerably' af-fec-t>-phencosts©flnerect'ton* The matter of protection against severe storms must be considered. Many other d e t a i l s w i l l , i n any construction project, present themselves for -analysis. I f , however, we have a concrete comparison of the r e l a t i v e economy of one route over another, we have gone a long way toward an exact determination of which w i l l be the most advantageous under a l l conditions. . • As brought out at the beginning of t h i s discussion, only one s p e c i f i c point i n economies of routes has been covered here, that i s , where the choice between two routes i s to be made, the shorter one requiring purchase of right-of-way or i n s t a l l a t i o n of higher structures and s p e c i a l reiflforcements. The many other .problems i n the choosing of the economical route for a trans-mission l i n e could be treated i n a very similar manner. The above^will give an idea of the kind of problems In connection with a secondary transmission system which require a solution for economy. It must always be kept i n mind, of course, that economy i s not the only consideration i n designing a l i n e . Mechanical'strength i s an Important feature. Good . regulation i s e s s e n t i a l . While the economical conductor size i s usually Independent of the length- of the l i n e , regulation depends on the length. In determining the economy of a l i n e from, the point of view of regulation; the regulation should be determined between maximum and-minimum load— n o t zero load. This l a t t e r figure Is of academic interest only i n comparative analysis and estimating work. Often, on a long l i n e , a larger size than the most economical must be used to give good voltage. , In case a r t i f i c i a l means of imporving regulation are considered, t h e i r cost w i l l tend to o f f s e t the economy of the smaller con-ductor and a study of the l i n e as a whole. Including a l l such Items i s necessary. The problem i s s t i l l one of economy. In any case the determination of the most economical conductor size, voltage, span, route, etc. w i l l serve as a s t a r t i n g point.for the study of'the most advantageous design f o r f i n a l adoption. CHSPirERP.IX." • • , . . 77 • POWER CIRCUITS P r o b l e m s R e l a t i n g t o L i n e s C a r r y i n g Power L o a d C h i e f l y V o l t a g e - - E c o n o m i c a l C o n d u c t o r S i z e — - U s e o f Two L i n e s i n P l a c e o f - D i e t r l b u t i o n o f Load Over S e v e r a l L i n e s The s t u d y o f p r i m a r y l lnrvs w i l l be d i v i d e d I n t o two p a r t s , i . e . , the c o n s i d e r a t i o n o f c i r c u i t s c a r r y i n g cower c h i e f l y a n d o f t h o s e d e v o t e d l a r g e l y t o l i g h t i n g l o a d . ' I f i s r e a l i z e d t h a t on most s y s t e m s , the e i s no s h a r p d i v i s i o n , between t h e r e two CM, c l a s s e s . In most c a s e s , where t h e power l o a d i s c o m p a r a t i v e l y s m e l l , power l o a d s come o n , the d i f f i c u l t i e s o f r e g u l a t i o n u s u a l l y c a l l f o r a s e p a r a t i o n o f c i r c u i t s , even though the l o a d f a c t o r on t h e l i n e s i s t h e r e b y r e d u c e d somewhat. The f a c t s t h a t l i g h t i n g l o n d r e q u i r e s a c l o s e r r e g u l a t i o n t h a n power, and t b e t , when large- power l o a d s a r e c o n s i d e r e d , l i g h t i n g and nower l o a d u s u a l l y o v e r l a p c o n s i d e r a b l y d u r i n g t h e heavy l o a d i n g s e a s o n , j u s t i f y such a p r a c t i c e . • On some s y r t e m s , the power and l i g h t i n g c i r c u i t s a r e kept e n t i r e l y d i s t i n c t . On o t h e r s , where t h r e e - or two-phase c i r c u i t s a r e used f o r l i g h t i n p , s m a l l - and m e d i u m - s i z e d power l o a d s a r e t a k e n on t h e same c i r c u i t s , w h i l e s e p a r a t e l i n e s a r e r u n f o r l a r g e power l o a d s . I n the f i r s t c a s e , i t i s v e r y o f t e n the p r a c t i c e t o r u n a t h r e e - p h a s e l i n e t o some c e n t r a l f e e d i n g p o i n t end t h e r e s e p a r a t e the phases i n t o i n d i v i d u a l s i n g l e - p h a s e c i r c u i t s f o r l i g h t i n g . I n the l a t t e r c a s e , a l l b r a n c h e s c a r r y i n g l i g h t i n g o n l y a r e o r d i n a r i l y s i n g l e - p h a s e . I t a p p e a r s , t h e r e f o r e , t h a t t h e p r o b l e m s r e l a t i n g t o power o n l y , to power and l i g h t i n g combined and to l i g h t i n g o n l y may be v e r y s i m i l a r up to a c e r t a i n p o i n t , d i f f e r i n g o n l y . i n l o a d f a c t o r 1 . On t h e o t h e r h a n d , I f l i g h t i n g o n l y Is c o n s i d e r e d the q u i t e d e f i n i t e l o a d f a c t o r s i m p l i f i e s t h e s t u d y s o m e - h a t . A l s o the s i n g l e - p h a s e l i n e s a r e problems i n t h e m s e l v e s . T h i s c h a p t e r w i l l be d e v o t e d t o the problems o f power o i r e u i t s . K i n d o f P r o b l e m s E n c o u n t e r e d : The q u e s t i o n s a r i s i n g In c o n n e c t i o n w i t h power c i r c u i t s have t o do m o s t l y w i t h v o l t a g e and c o n d u c t o r s i z e . Such l i n e s are n e a r l y a l w a y s r u n on r o a d s , - i; s t r e e t s , a l l e y s o r l o t l i n e s and t h e p o l e spac'np; and l o c a t i o n i s l i m i t e d by" t h e m e c h a n i c a l s t r e n g t h o f the p o l e , by the arrangement o f s t r e e t and l o t l i n e s , by p r o v i s i o n s f o r f u t u r e e x t e n s i o n s , e t c , P o l e h e i g h t s a r e g o v e r n e d by s t a n d a r d p r a c t i c e , by c i t y o r d i n a n c e s and by h e i g h t s n e c e s s a r y t o c l e a r o b s t r u c t i o n s . O c c a s i o n a l l y t h e r e may a r i s e q u e s t i o n s as to t h e economy o f u s i n g p r i v a t e r i g h t - o f - w a y i n s t e a d o f the p u b l i c highway f o r s h o r t d i s t a n c e s b u t s u c h p r o b l e m s a r e u s u a l l y s m a l l ones and a r e e a s i l y s o l v e d by a c o m p a r i s o n o f t h e a n n u a l c o s t o f the two a l t e r n a t i v e s . V o l t a g e . - - T h e v o l t a g e f o r use on power c i r c u i t s 1s u s a l l y a development from p a s t p r a c t i c e , a l t h o u g h i t i s o f t e n found e c o n o m i c a l t o i n c r e a s e the v o l t a g e when the l o a d i n c r e a s e s beyond a c e r t a i n amount. The v o l t a g e s I n common use have' "fceen p r e t t y w e l l s t a n d a r d i z e d a t 2 , 2 0 0 , 4 , 4 0 0 , 6 , 6 0 0 and 11,000 v o l t s . T h e r e i s a tendency a t p r e s e n t t o go even h i g h e r f o r power l i n e s w i t h heavy l o a d s , b u t s u c h l i n e s p a r t a k e wore o f the n a t u r e Of t r a n s m i s s i o n l i n e s . On any l i n e , t h e h i g h e r the v o l t a g e t h e l e s s the l i n e l o s s e s and the l a r g e r the l o a d s w h i e h c a n be c a r r i e d on the l i n e w i t h a g i v e n r e g u l a t i o n . On the o t h e r hand, t h e , c o s t o f I n s u l a t i o n o f t h e l i n e and the c o s t o f t r a n s f o r m e r s i s i n c r e a s e d . The a d d i t i o n a l p r e c a u t i o n s w h i c h i t i s n e c e s s a r y f o r c o n s t r u c t i o n m e n . t o t a k e i n w o r k i n g w i t h a h i g h e r v o l t a g e I s a l s o a f a c t o r > t o b©' c o n s i d e r e d . To g i v e a c o m p a r i s o n , 6 , 6 0 0 - v o l t t r a n s f o r m e r s c a n be o b t a i n e d f o r a b o u t 18 o r 20 p e r c e n t more t h a n 2 , 2 0 0 - v o l t . T h e r e b y t h e v o l t s a g e i s m u l t i p l i e d by t h r e e , hence the l i n e l o s s i s / d i v i d e d by n i n e f o r any g i v e n l o a d and w i r e s i z e . O r , f o r the s a m e . p e r c e n t v o l t a g e d r o p a n d c o n d u c t o r , ' n i n e t i m e s t h e . l o a d c a n be c a r r i e d , .Where los»&s a r e n e t heavy, s u c h a n I n c r e a s e i n c a p a c i t y may n o t be d e s i r a b l e as compared w i t h the i n c r e a s e d c o s t o f c o n s t r u c t i o n , "'here heavy l o a d s a r e h a n d l e d , however, a v o l t a g e o f 6 , 6 0 0 o r 11 ,00 may o f t e n be f o u n d v e r y advantageous:. .When t h e p r o b l e m i e one o f c h a n g i n g the v o l t a g e o f system a l r e a d y i n o p e r a t i o n to a. h i g h e r v o l t a g e , the c o s t o f making the change must be t s k e n i n t o a c c o u n t . The o l d l i n e t r a n s f o r m e r s must be d i s p o s e d o f , o r the change m a d e . g r ? d u a l l y , u s i n g t h e o l d t r a n s -f o r m e r s •In c e r t a i n d i s t r i c t s u n t i l they a r e worn o u t . S t a t i o n '. t r a n s f o r m e r s a n d o t h e r a p p r a t u s , s u i t s M . e f o r the h i g h e r v o l t a g e , • \.l must be p r o v i d e d . O f t e n , c a b l e s must be r e p l a c e d w i t h those o f h i g h e r - r e t i n g . The i n c r e a s e i n a n n u a l c h a r g e s due t o a l l t h e s e i t e m s muet be c a r e f u l l y s t u d i e d i n c o n n e c t i o n with, the v a l u e o f t h e i n c r e a s e d c a p a c i t y , and r e d u c t i o n i n l o s s e s a c h i e v e d , i n o r d e r to-., t o " d e t e r m i n e t h e economy o f any s u c h a l t e r a t i o n . I n t h i s c o n n e c t i o n , t h e p r o b a b l e i n c r e a s e c f l o s d on the system f o r some time i n the • f u t u r e must be e s t i m a t e d and what f u r t h e r changes w i l l have to be made e v e n t u a l l y t o c a r e f o r p r o b a b l e . f u t u r e c o n d i t i o >ns V o l t a g e D r o p — The p r o b l e m o f v o l t a g e d r o p i s an i m p o r t a n t one t o c o n s i d e r i n c o n n e c t i o n - " i t h power c i r c u i t s . The a l l o w a b l e r e g u l a t i o n a t the c u s t o m e r i s more or l e s s f i r e d by c o n s i d e r a t i o n s o f good s e r v i c e o r by c o n t r a c t . The s u b s t a t i o n bus v o l t a g e may be k e p t w i t h i n c e r t a i n known l i m i t s . The q u e s t i o n i s then one o f whether, t o s e r v e t h e c u s t o m e r by a c i r c u i t o f s m a l l o r medium* s i z e d c o n d u c t o r w i t h a r e g u l a t o r , o r o f l a r g e - s i z e d c o n d u c t o r w i t h o u t a r e g u l a t o r . • The -.annual c o s t o f - the i n s t a l l a t i o n as a w h o l e , i n c l u d i n g c o s t o f e n e r g y l o s s e s , w i l l be the c r i t e r i o n . On a l a r g e system w i t h a s t e a d i l y i n c r e a s i n g l o a d i t i s o f t e n t h e p r a c t i c t o s t a n d a r d i z e on one or two c o n d u c t o r s i z e s . A new l i n e i s b u i l t o f s t a n d a r d s i z e and a l l o w e d to o p e r a t e a t low l o a d s u n r e g u l a t e d . L o a d i s added from time to t ime u n t i l , when i t becomes t o o heavy, a r e g u l a t o r i s a d d e d . From a p r a c t i c a l s t a n d p o i n t t h i s method has I t s a d v a n t a g e s . A study o f the economy o f the I n s t a l l a t i o n , how-e v e r , w i l l s t i l l be o f r e a l advantage In i n d i c a t i n g the s t a n d a r d s i r e s to u s e , when the l i n e s become l o a d e d beyond the e c o n o m i c a l l i m i t . , etc-.- • 79 P o w e r - f a c t o r Improvement . — The q u e s t i o n o f power f a c t o r i s a p r o m i n e n t one a t p r e s e n t . A s i d e from the p r o p o s i t i o n o f i n -d u c i n g the c u s t o m e r to improve h i s power f a c t o r by u s i n g t h a t a s a b a s i s f o r r a t e s , t h e r e i s a f u r t h e r i n t e r e s t i n g p r o b l e m f o r t h e c e n t r a l s t a t i o n . Poor power f a c t o r means i n c r e a s e d l o s s e s f o r the same d e l i v e r e d l o a d i n k i l o w a t t s . T h e r e w i l l b e , t h e n , a p o i n t a t w h i c h i t w i l l be e c o n o m i c a l t o i n s t a l l s t a t i c o r s y n c h r o n o u s c o n d e n s e r s In o r d e r t o r e d u c e t h e s e l o s s by i m p r o v i n g t h e power f a c t o r . T h i s p o i n t c a n be d e t e r m i n e d by a c o m p a r i s o n o f the a n n u a l cost, o f the c o n d e n s e r i n p l a c e , w i t h t h e v a l u e o f the e n e r g y c o n s e r v e d , c o n s i d e r i n g a l s o the improvement i n r e g u l a t i o n ' , v •. Most E c o n o m i c a l C o n d u c t o r S i z e . ° ~ T h e d e t e r m i n a t i o n o f the most e c o n o m i c a l s i z e o f w i r e f o r any l o a d , Is c l o s e l y c o n n e c t e d w i t h t h e c o n s i d e r a t i o n s o f v o l t a g e and v o l t a g e d r o p , as i s e v i d e n t f r o m the above d l s c r i p t i o n . I f the most e c o n o m i c a l c o n d u c t o r s i z e , c o n s i d e r i n g t h e l i n e o n l y , Is known, however, i t s e r v e s as a s t a r t i n g p o i n t f o r t h e f u r t h e r s t u d y o f the economy o f the c i r c u i t as a w h o l e , i n c l u d i n g r e g u l a t o r s . , e t c . An example w i l l b e g i v e n h e r e o f the method o f a t t a c k i n g t h i s p r o b l e m o f most e c o n o m i c s ! w i r e s i z e f o r power c i r c u i t s . A n n u a l C o s t E q u a t i o n . - - F o r a three=phase l i n e the a n n u a l c o s t per.•1 ,000 f t . 'of l i n e =* g ( c o s t o f w i r e +• c o s t o f s t r i n g i n g ) + g ( c o s t o f p o l e s f i x t u r e s , g u y s , e t c . ) -f- c o s t o f energy l o s s . g = p e r c e n t I n t e r e s t , i n s u r a n c e , t a x e s , d e p r e c i a t i o n , e t c . ( C o s t o f r i g h t - o f - w a y i s o m i t t e d as i t i s n o t a l w a y s p r e s e n t on s u c h l i n e s , a n d , i n any c a s e , i s the same f o r a l l s i z e s o f c o n d u c t o r I n t h i s c a s e , i n s t e a d o f d e v e l o p i n g t h e above e q u a t i o n i n terms o f the c r o s s - s e c t i o n a l a r e a o f c o n d u c t o r and them, by means o f t h e f i r s t d e r i v a t i v e , d e t e r m i n i n g t h e most e c o n o m i c a l s i z e , i t h a s been found more u s e f u l t o i n v e s t i g a t e the r a n g e o f l o a d s f o r w h i c h any g i v e n s t o c k w i r e s i z e 5 s more e c o n o m i c a l t h a n any o t h e r • • • ' The method, u s e d i s as f o l l o w s : The a n n u a l cost, p e r 1,000 f t . o f l i n e f o r each s t a n d a r d c o n -d u c t o r s i z e i s o b t a i n e d i n terms o f the cost, o f c o p p e r , t h e l o a d , v o l t a g e , power f a c t o r , e q u i v a l e n t h o u r s , and c o s t -.f- e n e r g y . T h i s e q u a t i o n i s o f the form _ ("50) 80 • Cos 9 = power f a c t o r • ' ;.t = e q u i v a l e n t h o u r s , ' ': C e = c o s t o f energy p e r k i l o w a t t - h o u r , K, , ' Z9 j=-constants, ' ' . : Combined Equation>->°If t h e •"equation f o r any s t o c k s i z e o f w i r e i s combined w i t h t h a t o f the n e x t a d j a c e n t s i z e by e q u a t i n g the a n n u a l c o s t s , a n o t h e r e q u a t i o n i s obtained, w h i c h e x p r e s s e s t h e c o n d i t i o n s u n d e r .-which-.- ther©v.i-8.:<:not.-ehoice.• i n economy .between the two-. • i f ; for~--exawple, i n th© above- e a u a t L o n . E , a n d Cct> a r e .fixed,- the combined e x p r e s s i o n w o u l d -xl-vct f o r any v a l u e o f tCe , t h e l o a d a t w h i c h t h e economy changes from one s i z e o f c o n d u c t o r t o t h e n e x t . I f s u c h e x p r e s s i o n s a r e determined, a n d p l o t t e d f o r N o , 6 to Po A and f o r "Wo. 4 t o WQV ' 2, f o r exampie 1 , t h e ' v a l u e s o f k^!7cos0 between tfte two - c u r v e s . f o r any. val.d.e o£ t C e , i n d i c a t e s t h e range o f l o a d s ' f o r ' w h i c h ?f4 vi'Hs j a more e c o n o m i c a l t h e n " e i t h e r a d j a c e n t s i z o 1 . F o r s m a l l e r l o a d s , //6 i s more e c o n o m i c a l , f o r l a r g e r loads. , #2 ( ;see. F i g . 27. -. V a l u e o f C o n s t a n t s . - - I n t h e above e q u a t i o n (30)': the c o n s t a n t s K, a n d Tfe depend on w i r e s i z e , l o c a l e o s t s f o r s t r i n g i n g w i r e , a n d l o c a l s t a n d a r d s o f c o n s t r u c t i o n a n d c o s t s f o r use w i t h e a c h w i r e s i z e . I t , m a y be assumed i n t h i s c a s e . t h a t t h e p o l e s w i l l b e t h e same f o r any s i z e o f c o n d u c t o r , and hence t h e i r c o s t w i l l c a n c e l o u t when t h e e q u a t i o n s f o r two w i r e s i z e s a r e c o m b i n e d . . - .Thecssstvof p o l e - - f i x t u r e s ( c r o s s a r m s , .etc.:) ;doee n o t i n c r e a s e •.•.•proportionally••'•with w i r e s i z e b u t w i l l be t h e same; f o r s e v e r a l s i z e s and t h e n change a b r u p t l y f o r t h e n e x t l a r g e r g r o u p . The c o s t o f c o n d u c t o r i n p l a c e , i n c l u d i n g i n c i d e n t a l m a t e r i e l and l a b o r e o s t o f s t r i n g i n g , w i l l f o l l o w s u c h a n e x p r e s s i o n as X a + K b C e 0 j K d and ••'•Kb' b e i n g s e p a r a t e l y d e t e r m i n e d f o r e a c h s i z e o f w i r e These c o n s t a n t s , p r o p e r l y combined g i v e the v e l u e s o f K, and ]T a . Cost" o f - E n e r g y L o s s . - - T h e c o s t o f energy l o s s i s d e t e r m i n e d from t h e e q u a t i o n : A n n u a l c h a r g e f o r energy l o s s p e r 1 ,000 f t . 3 I * r x 365 x t * C c = 3 6 5 , 0 0 0 McJ — — \ * . (31) • . 1 , 0 0 0 , I E c o s ey f h e r e r =• r e s i s t a n c e o f c o n d u c t o r p e r 1 ,000 f t . T h e n f i n E q . 3 0 ) = 3 6 5 , 0 0 0 r , f o r any s i z e o f c o n d u c t o r . -.3 T a b l e 5 - - - E q u a t i o n s o f T o t a l .Annual C o s t S i z e o f ^ i r e — ; — : — — — — — - • : ' - — 6 • • 6.7 + 56 .20^+147 ,000 A t C e 4 8 . 4 1 + 8 0 . 0 C W + 9 2 , 5 0 0 A t C e 11 .30+-126.0C c o + 58, IOC A t C e 0 12.43 + 204. 0C c t )+ 3 7 , 3 0 0 t C e 00 14 .624- 251. 0C c o + 20 1 500 A t C € - • 000 1 6 . 4 3 + 313-r.)Ceo+ 1 8 , 6 0 0 Ate* oooo 17 • 32 + 3 8 2 . 0 C c o + 18,600 A t C . Note I\J kw \ g "(E c o s e/ E q u a t i n g the e x p r e s s i o n s f o r c o s t f o r each a d i a c e n t p a i r o f wire- s i z e s , the f o l l o w i n g e x p r e s s i o n s a r e " o b t a i n e d T a b l e 6 S i z e o f w i r e 6 t o 4 5 4 , 5 0 0 AtC« - ?3.8Q„ + 1.71 h - to 2 3 4 ,400 AtO, = 4 6 . 1 Q , + 2-91 2 to © 2 0 , 8 0 0 A t C e - 7 8 . 0 ^ + 1.13 0 t o 00 7 , 8 0 0 A t C c 4 7 . 4 ^ + 1.19 00 t o 000 6 , 1 0 0 A t q . s = = 6IL • + 1.81 000 to 0000 4 , 8 0 0 AtC^ - 69.0C C „ + 0 . 8 9 0 t o 0000 18,700 A t C e = 1 7 8 . 0 C c o . 4 . 8 9 Note A J kw \ g ^E c o s e)' * Assuming t h e v o l t a g e o f 4 , 6 0 0 and two p r i c e s f o r c o p o e r 30 c t s . and 30 c t s . , w h i c h r e p r e s e n t a good ranpe <->? v a l u e s ' the e q u a t i o n s become. . ' T a b l e 7 — For- 4 , 6 0 0 V o l t s 82 S i z e o f Wire-S i z e o f W i r e 6 4 2 6 06 000 0 t o t o t o t o 4 2 •0 00 t o 000 t o 0000 t o 0000 t c e 884 tce = tc e tc e = tc c = to. = 3 0 - c t . Copper 2 0 - c t , Copper 3 , 4 3 0 ID*? 290 '""' • f , ?60 \ 24 i 00 R " i l . s o n 70^000 B 9 5 , 2 0 0 B . 66,000 B _ 177lOO ^ . B ' -28 s 900 _ 48^750 ~ • B _ 64,750 ~ B • _ 4 5 , 3 0 0 "* B N o t e : B„( kw \ g ^cos ej F o r 2 ,300 v o l t s the n u m e r a t o r s o f the above cos e x p r e s s i o n s f o r 4,6CC v o l t s s h o u l d be d i v i d e d by 4 as H o . 6 t o Wo. 4 , t C c 3 5 7 . 5 (kw/coe e) & The c u r v e s p l o t t e d f o r 4 ,600 v o l t s c a n be used f o r 2 ,300 v o l t s i f t h e ; g i v e n l o a d . f o r 2,-300 v o l t s i s m u l t i p l i e d by 2 b e f o r e a p p l y i n g c u r v e . • P l o t t i n g P e s u l t s i n C u r v e s . - - As was mentioned b e f o r e i n C h a p . V i l l o n " S e c o n d a r y T r a n s m i s s i o n L i n e s , " the c o s t o f e n e r g y l o s s e s -per k i l o w a t t - h o u r , Ce , and the e q u i v a l e n t h o u r s , "t^ a r e i n t e r r e l a t e d . F o r any typo o f l o a d , such as t h a t 'on a t y p i c a l power c i r c u i t - , t h e v a l u e o f C e c o r r e s p o n d i n g t o any va.lue oft" may be d e t e r m i n e d a p p r o x i m a t e l y . F o r power c i r c u i t s i n h e a v i l y l o a d e d d i s t r i c t s , such a s the i n d u s t r i a l a r e a s i n a l a r g e c i t y , the l o a n f a r - t o r , e n u i v a l e n t ' h o u r s , and power f a c t o r n>ay be p r a c t i c a l l y the same f o r n e a r l y a l l l i n e s . In t h a t c a s e , the p r o b l e m i e s i m p l i f i e d and the range o f l o a d s f o r w h i c h any w i r e s i z e i s most e c o n o m i c a l Is more &imply d e f i n e d . F o r the g e n e r a l c a s e o f power c i r c u i t s , however, the l o a d may v a r y from a s i n g l e m o t o r s - w i l l v a r y t h r o u g h a l a r g e r a n g e , and the e q u i v a l e n t h o u r s f o r the same l o a d f a c t o r w i l l be d i f f e r e n t f o r d i f f e r e n t l o a d s , d e p e n d i n g on the o p e r a t i o n . The above e q u a t i o n s t h e r e f o r e have b e e n p l o t t e d u s i n g t C e as one c o o r d i n a t e , F i g s . 27 and 2 8 . The method o f d e t e r m i n i n g * to a large manufacturing plant load, from a few hours per week operation to continuous 24 hr. per day. N a t u r a l l y the load f a c t o r , —-t h e v a l u e o f t c 0 f o r any l o a d w i l l be e x p l a i n e d l a t e r , i n o r d e r to make the c u r v e s a p p l i c a b l e t o l o a d s o f v a r i o u s power f a c t o r s , t h e kw o t h e r c o o r d i n a t e was made c o l T F - The c o a r o u t a t i o n o f c o s 8 f o r any v a l u e o f e i t h e r q u a n t i t y c a n be made g r a p h i c a l l y by u s e o f t h e c u r v e s on the l o w e r h a l f o f the f i g u r e . The i n t e r s e c t i o n o f the c u r v e f o r any l o a d w i t h the h o r i z o n t a l f o r t h e d e s i r e d power i a c t o r g i v e s the v a l u e o f — o n the s c a l e b e l o w . Use o f C u r v e s . - - S i n c e the e q u a t i o n s were so "developed as to 'Show t h e p o i n t s where economy changes from one s i z e o f w i r e t o a n o t h e r , i t f o l l o w s t h a t the a r e a between two c u r v e s i s the l o c u s o f a l l p o i n t s f o r w h i c h the s i z e o f w i r e shown i s most e c o n o m i c a l . , m ThuP, ' on" F i g . 28, f o r — — - 600 a n d t C c 0 .06 ; No-.-CO ' p r i m a r y c o s 9 i s more e c o n o m i c a l t h a n N o . 2 o r N o . 00- S i m i l a r l y i t i s more e c o n o m i c a l t h a n N o . 2 f o r a l l v a l u e s o f t C c g r e a t e r t h a n .045 and i s more e c o n o m i c a l t h a n No, 00 f o r a l l v a l u e s o f t C c l e s s t h a n . 0 8 . The d o t t e d c u r v e shews the d i v i s i o n between N o . 0 a n d N o , 0000 w h i c h c a n be u s e d I n c a s e N o . 00 and: $0.. .000 a r e n o t u s e d a s s t a n d a r d s f o r s u c h l i n e s . T w o s e t s o f c u r v e s a r e g i v e n , one f o r 20 c t . c o p p e r and one f o r 3 0 - c t . I n t e r m e d i a t e v a l u e s c a n be i n t e r p o l a t e d . The use o f t h e c u r v e s , then i s as f o l l o w s : 1. L o c a t e the i n t e r s e c t i o n o f the c u r v e f o r the l o a d I n k i l o w a t t s w i t h t h e h o r i z o n t a l o f I t ? power f a c t o r . 2. L o c a t e t h e i n t e r s e c t i o n o f t h e o r d i n a t e t h r o u g h t h i s p o i n t w i t h t h e p r o p e r v a l u e o f t Q ( s c a l e on L e f t ) • 3- ^he a r e a i n w h i c h t h i s p o i n t l i e s i n d i c a t e s the tnost e c o n o m i c a l w i r e s i z e . The d i s t a n c e o f the p o i n t from the c u r v e d i v i d i n g t h a t a r e a from the n e x t a d j a c e n t a r e a i s an I n d i c a t i o n o f the amount o f e c o n o m i c a l advantage o f the one s i z e o v e r the o t h e r . D e t e r m i n a t i o n o f tCg . . - - T h e ' p r o p e r v a l u e o f t C e to j s e f o r any l o a d may be d e t e r m i n e d as f o l l o w s : I t was .shown in. C h a p . IV i n the d i s c u s s i o n o f e q u i v a l e n t h o u r s , t h a t the v a l u e o f e q u i -v a l e n t h o u r s c o r r e s p o n d i n g to any l o a d f a c t o r may v a r y between c e r t a i n l i m i t s . The u p p e r l i m i t ( l o a d f a c t o r X 24) would be c o r r e c t o n l y f o r a l o a d , s u c h as a s i n g l e m o t o r , . w h i c h has a c o n s t a n t v a l u e f o r I t s whole time o f o p e r a t i o n . The minimum v a l u e would be ( l o a d f a c t o r ) . X 24 f o r a l o a d w i t h a momentary peak and t h e r e m a i n d e r o f the d a y ' s c u r v e f l a t . W i t h power l o a d s , i t i e p r o b a b l e t h a t " t " v a r i e s from somewhere n e a r the f i r s t 84 a u a n t i t y f o r s m a l l l o a d s , s u c h as one o r two m o t o r s , t o soffie where - n e a r .the - average- between t h e two f o r large, l o a d s w i t h a number o f m o t o r s not r u n n i n g s i m u l t a n e o u s l y . P r o b a b l y f o r roost l o a d s e n c o u n t e r e d , " t " w i l l be n e a r e r the l e t t e r f i g The l i m i t s of '""t" would be as f o l l o w e r T a b l e 8 Load F a c t o r - . C o n t i n u o u s L o a d Ifomentary Peal? Average 0 • '0 0 0 . 10 2. k i 1 .32 .20 k. 8 -'• . 06 2.38 . , ^ 0 7 . ? 2.16* 4.68 .40 9 . 6 3 . a b 6 .72 .50 12. re 6 . 0 9 - 0 0 .60 - 1 4 . 4 8 .6* 11 .52 .70 i 6 ' . a 11.76 14.28 .80 19-2 ' 15-36 17.28 .90 21 . 6 19.4* 20-52 1 .00 2 4 . 0 24.00. 2 4 . 0 0 An approximate d e t e r m i n a t i o n of the v a r i a t i o n of the cost o f energy I O P F S ? with load f a c t o r can be mi&.e, auite- e a s i l y , as In d i c a t e d In " A p p e n d i x A . " Of course, i f more accurate c o s t figures have been determined they are preferable. The f o l l o w i n g i n d i c a t e s such a c h a r a c t e r i s t i c v a r i a t i o n . T a b l e 9 Load. F a c t o r . Cost of Energy L o s s P e r Kilowatt-Hour .10' .0278 .20' . 0184 •30 : .0150 .40 . • .0133 ' »5Q .0121. .60 .0113 ' .70 • .0107 .«30 .0101. .QO .0096 l.no : .0092 U s i n g t h e s e f i g u r e s i n c o n n e c t i o n w i t h the t a b l e g i v e n above t h e c u r v e ? shovn on F i g . 29 e r e p l o t t e d which show 1 he v a l u e s of . t c r c o r r e s p o n d i n g to any l o a d f a c t o r . A second s c a l e i s shown at t h e t o p g i v i n g the a v e r a g e number o f h o u r s per day o f ' p e a k - o p e r a t i o n , c o r r e s p o n d i n g t o a n y l o a d f a c t o r , w h i c h , . i s u s e f u l / , e s p e c i a l l y i n c o n n e c t i o n w i t h ems 11 l o a d s . I f the l o a d • f a c t o r o f a .load-:-Is known and. t h e -approximate-, shape - o f i t s ., •-. t y p i c a l c u r v e , the v s l u e o f t C e way be s e l e c t e d . F o r s s i n g l e motor a v e r a g i n g 3 h r . a d a y , f o r example, t.C« would be eVout . 0 7 2 . F o r a l a r g e r l o a d wit ha d e f i n i t e peak and an average l o a d c u r v e , w i t h - a l o a d f a c t o r o f 30 per c e n t , t h e v a l u e o f tCe would be 85 somewhere n e a r . 0 8 . I n g e n e r a l i t may he s a i d t h s t : T a b l e 10 Load F a c t o r Load Curve e t c e S n a i l power 0 t o 20 C o n t i n u o u s t o a v e r a g e 0 . 0 4 t o 0 . 0 6 Medium power 10 to 30 Near a v e r a g e 0 . 0 4 t o 0 . 0 7 L a r g e power PO to 40 Wear A v e r a g e 0 . 0 5 t o 0 . 0 9 These f i g u r e s a r e i n d i c a t e d on the c u r v e s , F i g s . 27, 28, and b y t h e b r a c k e t s on the l e f t . F o r l i n e s c a r r y i n g l i g h t i n g o n l y , t h e v a l u e o f t C e would be between .03 and .05 b e i n g n e a r e r the l a t t e r f o r r e s i d e n c e l i g h t i n g o n l y , and approaching: t h e former f i g u r e f o r heavy s t o r e l i g h t i n g , e t c . , w i t h a f a i r overage o f a b o u t . 0 4 . F o r a l o a d w h i c h combines power and l i g h t i n g the v a l u e o f t-C c w i l l depend on t h e p r o p o r t i o n o f e a c h , " h e r e the power p r e d o m i n a t e s , the l i g h t i n g l o a d w i l l have the e f f e c t o f i n c r e a s i n g the l o a d f a c t o r . «nere l l g b t l n g p r e d o m i n a t e s t h e power l o a d w i l l have the sarae e f f e c t . I n e i t h e r c a s e a h i g h e r v a l u e o f tCc s h o u l d be used t h a n would be assumed f o r the p r e d o m i n a t i n g , type o f l o a d a l o n e . The amount o f i n c r e a s e must be e s t i m a t e d from a c o n s i d e r a t i o n o f t h e p r o b a b l e l o a d f a c t o r f o r the p a r t i c u l a r c a s e . S i m i l a r C u r v e s S h o u l d be D e r i v e d L o c a l l y . - - C u r v e s such as those i l l u s t r a t e d , h e r e , may be worked o u t f o r any s y s t e m , u s i n g l o c a l cost, f i g u r e s . (The examples g i v e n h e r e o u s t n o t be c o n s i d e r e d a p p l i c a b l e t o any b u t the system from which they were d e r i v e d . ) By t h e i r use the most e c o n o m i c a l w i r e s i z e for- any l o a d may he d e t e r m i n e d a n d , from t h a t p o i n t , the p r o b l e m becomes one o f o b t a i n i n g p r o o e r r e g u l a t i o n .in the most e c o n o m i c a l way. Power C i r c u i t s w l t h " t " C o n s t a n t As was i n d i c a t e d above, f o r power c i r c u i t s i n h e a v i l y l o a d e d m a n u f a c t u r i n g d i s t r i c t s where t h e r e i s c o n s i d e r a b l e d i v e r s i t y o f l o a d on each l i n e , t h o u g h the g e n e r a l c h a r a c t e r i s t i c s o f a l l l o a d s a r e somewhat, s i m i l a r , t h e v a l u e of e q u i v a l e n t h o u r s w i l l be n e a r l y t h e same f o r a l l l i n e s . I f an a v e r a g e v a l u e o f " t " i s dieter m i n e d , the p r o b l e m o f e c o n o m i c a l c o n d u c t o r s i z e may be s i m p l i f i e d and i t i s p o s s i b l e t o study the ^ e f f e c t o f v a r i a t i o n s i n the c o s t o f c o p p e r and o f . e n e r g y t o b e t t e r a d v a n t a g e . 5teterm i n s t i o n o f " t " . - - T h e d e t e r m i n a t i o n o f average e q u i v a l e n t h o u r s f o r a number o f . c i r c u i t s was e x p l a i n e d i n C h a p . I V w i t h a n example o f l i g h t i n g c i r c u i t s . F o r po^er c i r c u i t s the method i s s i m i l a r . Tn a s p e c i f i c I n s t a n c e , b i - m o n t h l y c u r v e s were t a k e n f o r a number o f p o * e r c i r c u i t s f o r 13 months and the e q u i v a l e n t h o u r s f o r each such c u r v e i n terms o f the c u r v e ' s ; peak was . d e t e r m i n e d . T h i s was assumed t o be the a v e r a g e f o r the h a l f month c o v e r e d , " a c h o f t h o s e f i g u r e s was r e d u c e d t o a v a l u e o f 86 e q u i v a l e n t h o u r s i n terms o f the y e a r ' s peak by m u l t i p l y i n g i t by t h e s q u a r e o f t h e r a t i o between the peak f o r the d a y f o r w h i c h the f i g u r e was d e r i v e d and the y e a r ' s p e a k . The 26 v a l u e s t h u s o b t a i n e d were a v e r a g e d and the r e s u l t was assumed t o be a f a i r l y a c c u r a t e f i g u r e f o r the e q u i v a l e n t h o u r s f o r t h e whole y e a r , c o n s i d e r i n g days o f o p e r a t i o n o n l y , e x c l u s i v e o f Sundays and h o l i d a y s . I n t h e example t a k e n , the v a l u e o f e q u i v a l e n t h o u r s was f o u n d t o be 9.69. T h i s i s h i g h f o r o r d i n a r y p u r p o s e s , b e i n g o b t a i n e d a t a time o f n i g h p r o d u c t i o n d u r i n g t h e p o s t - w a r p e r i o d , b u t w i l l s e r v e as an i l l u s t r a t i o n o f t h e method:. E q u a t i o n s f o r A n n u a l C o s t . - - T h e f o r m u l a s f o r a n n u a l c o s t w i t h any s i z e o f c o n d u c t o r were a l t e r e d somewhat f o r c o n v e n i e n c e , and to b r i n g out a n o t h e r method o f r e p r e s e n t i n g the r e s u l t s . I t ?*as assumed, as a n a p p r o x i m a t i o n , t h a t a l l c h a r g e s on c o n s t r u c t i o n , w h i c h a r e n o t p r o p o r t i o n ? 1 to t h e c o s t o f c o p p e r , a r e the same f o r a l l s i z e s , and h e n c e , c a n c e l o u t when t h e e q u a t i o n s f o r t^o s i z e s are c o m b i n e d , The e r r o r t h u s i n t r o d u c e d I s s m a l l f o r any two s i z e s n e a r t o g e t h e r , such ss H o . 6 and N o . 4, b u t becomes g r e a t e r f o r such- c o m b i n a t i o n s a s N o . 0 and N o . 0 0 0 0 . I n any c a s e , however, i t can be k e p t In mind and compensated f o r ^ h e n u s i n g the r e s u l t i n g c u r v e s . Then* the a n n u a l c h a r g e c e r 1,000 f t . on the above b a s i s Y=JT$~ ( 3 , 0 0 0 - ; Ccc> ) + * 2 * - j ^ * 3 , 0 0 0 * t * 300 * fytb -, ?om, Cco+ 9 0 0 i z - f - t e f t 02) f o r a c o n d u c t o r w e i g h t i n g w, pounds per f o o t and o f cross=> s e c t i o n a l a r e a A, , u s i n g 300 w o r k i n g days p e r y e a r t o c o r r e s p o n d t o M t " a s . d e r i v e d above . T f t h i s e x p r e s s i o n Is combined w i t h a s i m i l a r one f o r a c o n d u c t o r o f w e i g h t \~z and a r e a Az> the r e s u l t i n g e q u a t i o n may be r e d u c e d to 30p(A., - A • • • ' ' •• • 8? Curves . for TTconogilcal ^ i r e 51'2.e.--The curves shown In • F i g . 30 have been .plotted from th i s equation. Their use Is s i m i l a r to that,.: of Figs-. 27- and 2 8 , the ' aro.fiB between the curves b e l o n p i n p : to the conductor s i7 .es Indicated. I t i s • c l e a r l y evident t h a t , as the r a t i o between copper price and energy cost increases, by c o p p e r price Increasing or energy cost decreasing, the smaller w i r e • b e c o m e s more economical"^' As .was explained shove, in using the curve between No. 0 and TJo. 0 0 0 0 , t h e e x c e s s cost of s t r i n g i n g the larger size must be kept 5,n mind. T h i s would' have the "sarae e f f e c t as -an increase in n r i c e o f c o p p e r , i.e., to r a i e e the curve somewhat. Use of Two l i n e s i n P i e c e of One.--The study of economical!',-;, conductor elsse-may'., he.' further extended, i n a s i m i l a r manner, to the consideration of the economy of the use of two l i n e s In P l a c e 1 o f one. A s s u m i n g that, for mechanical reasons, Ho. 0 0 0 0 . -. wire i s the largest nige- which i s used as a standard on a given overhead system, there i s a load at which I t becomes e c o n o m i c a l to use sore than one Wo. 0000 c i r c u i t . Another c i r c u i t of any s i z e o f conductor might be added, according to the load. For s i m p l i c i t y , the problem here w i l l "be l i m i t e d to that of discov*» •er-jng . a t what load two *7o. 0000 l i n e s are sore e c o n o m i c a l than one., assf-uminft the mme c o n d i t i o n s of load as i n .the previous ex- -a m p l e / w i t h H M . c o n s t a n t . In t h i s case, the c h a r g e s on construction cannot be as fussed to be the satce f o r both"-.-conditions since twice as much pole space Is occupied ,by. twp.-eircultec-as by one. In some e a e e e , t h i s would- 'simnly cause the a d d i t i o n of a n extra a r o s s a r m . I t very often occurs, however, t h a t , in d i s t r i c t s where such large loads are: f o u n d , the poles are heavily loaded end a l l available-Pin positions are v a l u a b l e . In such a case, the c i r c u i t s h o u l d be charged with that proportion of the t o t a l cost of poles and-. f i x t u r e s equal to the p r o p o r t i o n of the t o t a l available pole, apace w h i c h i t occupies» I f , for example, such s n • a r r a n g e m e n t ap shown on F i g . 31 i s assumed to represent average l i n e conditions, one o f the three-phase line?? occupies one-fourth t h e pole space. If the average cost of a pole and four- c r o s s -arms with other f i t t i n g s i s #60 th© cost o f pole space for the l i n e In q u e s t i o n Is t-15 p e r pole, or about §150 per 1 ,000 f t . - I f Op =: cost o f -pole . s p a c e p e r 1,000 f t . . and c c «= c o p t of s t r i n g i n g , conductor., insulators and pins per 1 , 0 0 0 f t . :' The t o t a l annus! cost for one c i r c u i t and f o r two c i r c u i t s S f - ( 3 , 0 0 0 w C U - C r + Ccy 2 * 900 ( I ) 2 - § - t C » (36) -V = ~ z 100 • 88 The i n v e s t m e n t c o s t i e d o u b l e d w h i l e the e n e r g y l o s s i s h a l v e d . EquatlRg"/*^/ . and Yz ' '' ;' • - | _ ( 3 , 0 0 ( > C L W + CF + c e ) « 4 5 0 I 2 - f - ^ (37) In o r d e r t o put the c u r v e s i n t h e same form as t h o s e f o r s i n g l e l i n e s , t h i s e q u a t i o n must be r e d u c e d to an e v a l u a t i o n for- : C c e ' T o o 3000wC C o k I f k = 1 + . :j = 4501 3 , 0 0 0 ^ 0 (38) I f P, t , g , w and h a r e c o n s t a n t and Ji is e v a l u a t e d f o r s e v e r a l v a l u e s o f cco , - t h i s e o u s t i o n c?-n bp p l o t t e d i n s s r l e e o f c u r v e s a s shown on F i g . 32, one c u r v e f o r each v a l u e o f Cca T h i s c o u l d h.?ve been added t o ^ i g . 30, i f d e s i r e d , as I t Is o f the sstsp form-. Improvement o f R e g u l a t i o n by Two C l r c u i t s . - - A n i n t e r e s t i n g P o i n t a r i s e s i n c o n n e c t i o n w i t h the use o f two c i r c u i t s i n s t e a d o f one when a low power f a c t o r I s e n c o u n t e r e d , ^ h ' l e the r e s i s t a n c e d r o p o f a c o n d u c t o r d e c r e a s e s p r o p o r t i o n a l l y w i t h the i n c r e a s e In s i z e , the- i n d u c t a n c e d r o p d e c r e a s e s s l o w l y . Hence', f o r - power f a c t o r s below a c e r t a i n v a i u e , l i t t l e improvement i n r e g u l a t i o n i s a c c o m p l i s h e d by i n c r e a s i n g the s i z e o f c o n d u c t o r . On the o t h e r hc<nd, the a d d i t i o n o f a s e c o n d c i r c u i t m a t e r i a l l y r e d u c e s the i n d u c t a n c e d r o p and hence the r e g u l a t i o n . As a c o n c r e t e e x a m p l e , eostpare the volte?-© d r o p on a F o . 0000 c i r c u i t c a r r y i n g 3 , 0 0 0 TCw., 7 , 5 0 0 f t . , w i t h two F c . 0 c i r c u i t s , b o t h a t 4.60G- v o l t s , t h r e e - p h a s e , w i t h 2 8 - i n . s p a c i n g . The r e s i s t a n c e o f S o . O w i r e b e i n g a b o u t t w i c e that o f $ 0 . 0 0 0 0 , t h e e q u i v a l e n t , r e s i s t a n c e o f b o t h i n s t a l l a t i o n s i s about the same. The power l o s e and v o l t a g e . d r o p , a t d i f f e r e n t power f a c t o r s , ©s f i g u r e d by the c h a r t s i n f h a p . VI? ere- se f o l l o w s : T a b l e . 11 Power f a c t o r Per c e n t Power l o s s , V o l t a g e d r o p ~ne "No. 0000 Two N o . C One N o . 0000 Two N o . 0 Per c e n t Per c e n t 50 85 OR 14 . 6 5 ' 0 3 4 .05 14 .25 4 . 8 7 3.97 18.05 8 -78 6.64 10.97 6.04 5 . 0 5 89 I t I s v e r y e v i d e n t , from the a b o v e , t h a t , a t a low power f a c t o r , c o n s i d e r a b l e a d v a n t a g e i n r e g u l a t i o n 3« g a i n e d by u s i n g two c i r c u i t s of s m a l l c o n d u c t o r r a t h e r than one c i r c u i t of t w i c e t h e s i z e . T h i s would be e c o n o m i c a l ) f the inr.rove^.pnt i n r e g u l a t i o n Is w o r t h more t h a n the I n c r e a s e d c o s t o f c o n s t r u c t i o n , -it h i g h power f a c t o r s , the a d v a n t a g e d i s a p p e a r s s i n c e the v o l t a g e d r o p Is p r a c t i c a l l y e q u a l to the r e s i s t a n c e d r o p . E c o n o m i c a l D i s t r i b u t i o n o f Load o v e r S e v e r a l L i n e s . - - O n e more t y p i c a l p r o b l e m w i l l be i n c l u d e d i n t h i s d i s c u s s i o n o f power c i r c u i t s . I n e s s e s where t h e r e a r e s e v e r a l d i f f e r e n t L i n e s , o f d i f f e r e n t l e n g t h s and c o n d u c t o r s i z e , f e e d i n g a l a r g e l o a d , i t ' i s d e s i r a b l e t o detertplne the most e c o n o m i c a l d i v i s i o n o f t h e l o a d amoriP" tnone l i n e s . F o r s i m p l i c i t y c o n s i d e r two c i r c u i t s o n l y . I f 7 . t h e t o t a l l o a d c u r r e n t , . T«.= the e c o n o m i c a l c u r r e n t on l i n e a , T t = the ecr-noTiical c u r r e n t on l i n e b , T = la.-4" ly, (approximatelyV. S i n c e the T i n e s a r e a l r e a d y i n p i e c e , the annual c h a r g e s on c o n s t r u c t i o n v i 1 1 bo c o n s t a n t f o r e a c h KA-= a n n u a l c h e r p e s on c o n s t r u c t i o n f o r l i n e a . Kj, = a n n u a l c-hsrpes on c o n s t r u c t i o n f o r l i n e h. The a n n u a l c o s t of energy l o s s on each c i r c u i t w i l l v a r y w i t h T* s n d C9 , and w i t h r e s i s t a n c e , 1 ! t " b e i n g f i x e d . Kc l l C c - c o s t o f e n e r g y l o s s i n l i n e a . K c Vb Ca P.h « c o s t o f energy l o s s i n l i n e b . Then the t o t a l annual, c h a r g e s on l i n o 1 a , and on l i n e b , end on t h e t o t a l i n s t e l l s t i o n , + Y * = Y-S X c < " * ( £ it *b) S u b s t i t u t i o n f o r ^ i t s v a l u e I - I * , V = <£3f7f7c&/ traj/jZfr-ampere cra^r/ec/. .,r The c o n d i t i o n of maximum economy Is r e a c h e d when"f" becomes a minimum* The v a l u e o f 1^ t o a c c o m p l i s h t h i s may be d e t e r m i n e d 90 by t a k ' n g t h e f i r s t d e r i v a t i v e o f w i t h r e s p e c t t o l ^ ; s i n c e I is^ c o n s t a n t • , d y / i /PR^ . S i m i l a r l y and I 3 . 3 . " 5ft (45) I n c a s e more than two l i n e s a r e c o n s i d e r e d , two o r more l i n e s c a n be r e p r e s e n t e d t o g e t h e r as one e q u i v a l e n t c i r c u i t and the same m a t h e m a t i c s a p p l y . From the a b o v e , t h e r e f o r e , the r u l e can be f o r m u l a t e d t h a t : "The 'iiost e c o n o m i c a l d i s t r i b u t i o n o f a l o a d o v e r s e v e r a l c i r c u i t s I s e f f e c t e d , by making the l o a d on e a c h c i r c u i t i n v e r s e l y p r o p o r t i o n a l t o I t s r e s i s t a n c e , i . e . , b ^ making the IR d r o p e q u a l on a l l > l i n e s . / T h i s I s what m i g h t have b e e n e x p e c t e d i f I t i s c o n s i d e r e d , t h a t 'the t o t a l a n n u a l c h a r g e s on c o n s t r u c t i o n w i l l be the same, r e g a r d -l e s s o f the d i v i s i o n o f the l o a d , and h e n c e , the o b j e c t IS to make t h e t o t a l energy l o s s e s a minimum. -The accompanying F i g . 33 i n d i c a t e s how the t o t a l c o s t o f energy l o s s on two c i r c u i t s w i t h d i f f e r e n t d i v i s i o n s o f l o a d c a n be d i s p l a y e d g r a p h i c a l l y . The p o i n t - o f minimum c o s t Is c l e a r l y d e f i n e d . . D i v i s i o n o f Load. Between L i n e s i n p a r a l l e l . — - F o r d i r e c t - c u r r e n t c i r c u i t s the l o a d would n a t u r a l l y d i v i d e i t e e i f i n - p r a c t i c a l l y t h e most e c o n o m i c a l p r o p o r t i o n s i f the l i n e s are p a r a l l e l e d , ^ o r a l t e r n a t i n g c u r r e n t , _however, the ' n d u c t i v e r e a c t a n c e has a n e f f e c t , and t h e n a t u r a l d i v i s i o n o f c u r r e n t would, be somewhat d i f f e r e n t . The c u r r e n t s w o u l d d i v i d e so t h a t the r a t i o o f the c u r r e n t i n any c i r c u i t t o the load, c u r r e n t i s the same as t h e r a t i o o f t h e a d m i t t a n c e o f that c i r c u i t t o the combined e q u i v a l e n t a d m i t t a n c e s o f a l l the c i r c u i t s . F o r example w i t h a Mo. 0 and a $ o . 0000 o v e r h e a d c i r c u i t , o f the same l e n g t h , s p a c i n g , e t c . F o r Wo. 0 , R„ ~ .539 ohm p e r m i l e - N o . 0000, R c o a o = , ? 6 9 ohm p e r m i l e The most e c o n o m i c a l d i v i s i o n o f c u r r e n t would then be T = — — — 0 2 6 9 — 1= 0.3331 or 1/3 the t o t a l c u r r e n t 0 . 5 3 9 * 0.269 °»<»> = - — • I - 0 .6671 or 2/3 t h e t o t a l c u r r e n t 0 . 5 3 9 X 0.269 91 The n a t u r a l d i v i s i o n , i f the c i r c u i t s were p a r a l l e l e d would b e I „ — - I = 0 .4441 o r 4 4 . 4 per c e n t o f the l o a d c u r r e n t T = I = 0.5661 o r 5 6 . 6 p e r c e n t o f the l o a d c u r r e n t The f a c t t h a t the a r i t h m e t i c a l sum o f I „ and \ * e . 0 i s n o t e q u a l t o I I s due to t h e f a c t t h a t they a r e n o t I n phase w i t h e a c h o t h e r , n o r w i t h I . L a r g e E c o n o m i e s P o s s i b l e on Power C i r c u i t s . - - T h e f i e l d o f s t u d y o f the e c o n o m i c s o f power c i r c u i t s w i l l be found q u i t e e x t e n s i v e and v e r y f r u i t f u l o f r e a l r e s u l t s . Such c i r c u i t s i n m a n u f a c t u r i n g d i s t r i c t s , u s u a l l y h a n d l e l o a d s many t imes as l a r g e as t h o s e on the o r d i n a r y l i g h t i n g c i r c u i t s , s i n g l e l o a d s a m o u n t i n g t o s e v e r a l t h o u s a n d k i l o w a t t s i n some p l a c e s . The l o a d f a c t o r Is a l s o c o m p a r a t i v e l y h i g h i n most c a s e s . The c o s t o f p o l e s p a c e , on the o t h e r h a n d , i s o f t e n c o n s i d e r a b l y l e s s p e r c i r c u i t on a c c o u n t o f the f a c t t h a t power c i r c u i t s a r e u s u a l l y r u n on p o l e s w h i c h would be s e t f o r l i g h t i n g c i r c u i t s i n any c a s e . I t i s e v i d e n t , t h e r e f o r e , t h a t the s a v i n g o f a few p e r c e n t i n l i n e l o s s on s u c h a l i n e may .mean the s a v i n g o f a c o n s i d e r a b l e sum o f money d u r i n g the y e a r . H e n c e , the o p e r a t i o n under t h e most e c o n o m i c a l c o n d i t i o n s p o s s i b l e i s p r o b a b l y p r o d u c t i v e o f more r e a l s a v i n g i n money t h a n on any other- p a r t o f the s y s t e m . A s t u d y o f the e c o n o m i e s o f any type o f i n s t a l l a t i o n i s a l w a y s b e n e f i c i a l , b u t i n the c a s e o f power c i r c u i t s i t i s i m p e r a t i v e . The p r o b l e m s e x e m p l i f i e d i n t h i s c h a p t e r i n d i c a t e the t y p e o f Q u e s t i o n o f t h i s k i n d w h i c h ^111 a r i s e most o f t e n and ;• I l l u s t r a t e methods w h i c h have b e e n found u s e f u l f o r a t t a c k i n g t h e i r s o l u t i o n . . CHAPTER X LIGHTING- CIRCUITS Economical Studies on Ci r c u i t s ' C a r r y i n g . L i g h t i n g O n l y — Prediction of Load—Conductor S i z e — I n c r e a s i n g Capacity of Overloaded-Systems .The preceding chapter indicated that i n general there were three, classes of. primary c i r c u i t s , those carrying l i g h t i n g load only, those carrying power loads only and those carrying loads jj made, up of a combination of the two. It. i s here planned to . ' deal with c i r c u i t s c a r r y i n g . l i g h t i n g load only, and p a r t i c u l a r l y i n reference to residence l i g h t i n g . ' The problemsvencountered i n general can be divided into, three cl a s s e s . ' In the f i r s t class are those pertaining to the design of a new. system to. handle a given or predicted -load, such as would be found where i t i s planned to b u i l d a d i s t r i b u t i o n system i n a town where no e l e c t r i c service has been furnished before. In t h i s case we meet a.problem somewhat s i m i l a r i n c h a r a c t e r i s t i c s to the one encountered under "trunk", transmission l i n e s . Here our purpose i s to design the most economical system possible with few of the factors of design previously established. The only l i m i t i n g features would be accepted practice, equipment ob -tainable, and the general knowledge of the subject as recorded i n other work.of the same c l a s s . The problem would therefore ' resolve i t s e l f into one of compiling costs on materials and labor,, and working out, as pointed out previously, comparative costs for several d i f f e r e n t a l t e r n a t i v e designs using d i f f e r e n t voltages, d i f f e r e n t types of primaries, such as single-phase, three-phase, four-wire, etc- The method of determining an economical conductor: size w i l l be discussed l a t e r on i n this chapter. I t i s a matter o f - f i n d i n g the lowest annual charges (investment and'energy losses) within the- l i m i t s of the quality of service desired. The second class 'of problems would be that of operating and extending.an e x i s t i n g system of primary l i g h t i n g l i n e s i n the most economical manner. This class of problems would be the most commonly encountered^ i n p r a c t i c e . Here c e r t a i n l i m i t a t i o n s are found prescribed by the c h a r a c t e r i s t i c s of the system at hand which would, i n general, prevent any considerable change from the practice l a i d out at the Inception of the project. However i t i s advisable to be prepared always to contemplate 'the possibi-litv of a r a d i c a l change i n such a system. This brings : i n the t h i r d c l a s s of .problems... They c a l l , f o r a. study of the a d v i s a b i l i t y of making such changes as r a i s i n g the voltage, changing from to 3^ , three-wire or four-wire, etc. Predicting load on Residence Lighting C i r c u i t s — T h e problem o f : p r e d i c t i n g load on c i r c u i t s does not involve economics. How-ever, a correct estimate of what should be expected i n the subsequent - .. . • 93 years, i s e s s e n t i a l as a basis for economical design. If the" demands for e l e c t r i c service which are made each vear are to be met economically,, they must be anticipated, f a r enough i n advance to enable provisions f o r servicing to be rendered • economically;, they must also be anticipated far enough i n advance-:to enable provisions for serving to be made when I t i s .moat^economicalto do so. About the only way to make i n t e l l i g e n t • --.;• -estima.tes^-of f u t u r e '.requirements i s to couple an analysis of past rates of load Increase with a far-sighted judgment which w i l l take Into account the e f f e c t on future conditions of the . past^rate of growth.-. Predicting the load on c i r c u i t s carrying a load consisting of .residence and store l i g h t i n g is-usually' s i m p l i f i e d by the fact , . that, .the growth. i s r e l a t i v e l y constant and that the other factors .• :.(tome <4,ri-:'5t0emadJfy.f.the..te,sfeimates can be analyzed and allowance : '•can .be made for them. '. .-..•••.._•..;. " ->In :-the.-following I t w i l l be shown- how an analysis of-the- con*-' d i t i o n s causing the increase has been attempted for a-number.of .-sing le*ph age. c i r c u i t s fed by 200,OOO-cire. mil* underground cables' and No. 0 or No, 0000 overhead wires. The data a v a i l a b l e f o r such a study consist of a set of curves, : one for each, c i r c u i t y showing the monthly maxima over a period of 4 years. These curves are not a l l of the same outline, yet there i> . are c e r t a i n c h a r a c t e r i s t i c s pertaining to a l l which could be expressed i n one curve to be considered t y p i c a l . A t y p i c a l curve : would; serve as a f a i r l y firm foundation on which tp base estimates for •Jthe:- future. r • The .changes i n e i r c u i t loads, shown by an inspection of the v';--aion:tMwaiiiaxi!iia, are caused by a' number of e a s i l y defined f a c t o r s . - :The'firsf A s a? ggayionalyeondition due to the change i n the length of days a n d t h e . r e s u l t of cold weather keeping people indoors; .•>: .the--:seeo-nd>-;-i«='an--increase i n the use of e l e c t r i c i t y by each eustomery ©aused by the greater appreciation of the uses of e l e c t r i c a l energy i n the home;, the t h i r d Is due to increase of , j-population within the boundaries of each c i r c u i t ; the fourth i s due tfo losseof old t e r r i t o r y caused by switching of load on account of . overload o r other operating necessities^ cor the embracing of , .new--territory by the c i r c u i t . .... . • ... The f i r s t two' faetors are constants i n their own p a r t i c u l a r sense«-that i s to say,' the rate of increase due to these factors ....... •.-'••: is: a - f a i r l y constant'value-^and the third. Is: partly so, for i t may be .subdivided into two, the f a c t o r of normal increase i n pop-: : u l a t i o h and that of abnormal Increase. Normal increase w i l l be enco : encountered i n p r a c t i c a l l y every section of the: c i t y , abnormal only , -' In:'- sections:-'hot"'yet " c l o s e l y ' b u i l t up and to which people are attracted -:•"••-: by ^  r e a l - e s t a t e ' a c t i v i t y or the circumstances of i n d u s t r i a l r-idevelopment. The fourth factor i s a r e s u l t of the preceding three and must be 94 considered as i n d e f i n i t e , as i t appears both f o r and against increases-of load. It i s a f a c t o r y however, for which correcti o n may be made, since i t s use l i e s within the control of the operating company. The ordlnates of curve I, F i g • 34 are' proportionate to the -sums of the maximum monthly loads on the c i r c u i t s , averaged : over 3 years. It was considered that the indeterminate factor .-. of changes i n t e r r i t o r y would not a f f e c t the curve, Inasmuch as •they appeared In d i f f e r e n t c i r c u i t s at different/vof the year and t h e i r effeet would be reduced to a 'comparatively'small value with ah average equal e f f e c t on- a l l the ordlnates of the curve, i n view c f of the long period of time covered. This assumption i s borne out by the comparison of curve I with curve I I . This l a s t curve-..covers a period of only.one year and was corrected for changes i n -.- t e r r i t o r y . , The" corrections were made-by deducting from the t o t a l s • .of each month the amount representing the load i n the same t e r r i t o r y appearing:in two c i r c u i t s i n the.same month. This condition of d u p l i c a t i o n of load Is due to the f a c t that when.a change i n boundary for.the r e l i e f of any c i r c u i t i s made, the load on the section: cut o f f appears In the maxima of both the c i r c u i t s r e l i e v e d and r e l i e v i n g . It would be possible naturally to take a. well-built—up d i s t r i c t including several c i r c u i t s and e s t a b l i s h a curve,, showing the growth, per year, of that nature of load, leaving the new' " c i r c u i t s , with abnormal growth, for a s p e c i a l study. This refinement Is hardly necessary, as - the percentage of growth * would not be: much diminished. In the method used here there i s introduced a small factor of safety. : In order to make the curve more e a s i l y applicable i t has been reduced•-•to' a table of percentages. Table 12 i n which the load : •': for each month In the year appears as a percentage of every other month.in the year. I t i s possible by the use of this table to take the load on any c i r c u i t for any given month and predict on that c i r c u i t the load for any future date, always-considering that the boundaries of the c i r c u i t remain unchanged and/that there, are no p a r t i c u l a r conditions i n that c i r c u i t which w i l l cause an,abnormal increase or decrease i n the load. ,It i s not:the. intention.that t h i s curve, or the percentage table developed from i t , s h a l l figure as an absolute method for estimating future loads, but merely as a basis on which are to be imposed the p a r t i c u l a r conditions obtaining for each t e r r i t o r y under consideration.. The table contains no allowances for abnormal conditions, and the r e s u l t s derived from i t may, i n some cases have to be considerably modified by such conditions as changing of - ' . c i r c u i t boundaries, r a p i d increase i n rate of settlement,- and others. However, the table i s s u f f i c i e n t l y accurate to serve as a basis i n estimates on the necessity for future work, unless the speed of growth of the c i t y i s greatly diminished or increased from the average rate maintained for the years considered. t*4 o CO i-r< ( » C5 a-to rH ha K A C O o CM O V O V O C O O rH O O ft •» OJ CM o ' •/ rH O O O K A O A O A V O O Y o o CM t— V D rH o rH CM i n G O A C O C O G ft • ft o o O o rH K A C O O A O o o V O CM V O C O CM V D •- K A -3" o o C O O A rH rH C O C O ... -^J-' C O co o o C O rH CM CM rH rH rH O O A O A o rH . « • • ft . « . . . <e> • * . fc . .. « a rH rH rH rH rH rH rH o o rH •H C O ov o KA OJ o K A K A C O •3" KA rH CM i n h"A A • rH CM C M K A K A o o CM K A rH o O A o rH CM K A K A CM CM o o rH . K A ft . ft ' . ft a. rH rH rH rH rH rH r-l rH O rH o rH . . » - ' c*4 rH V O rrH rCM rH V O 00 O . K A o . O •3- co r n t n O o V O o o rH rH o CM CM CM C M rH rH o O A o CM • • « « • a H H rH rH rH rH o :rH rH crj - rH 05, a O KA H O rH K M r © •» :1—* rH V O CO VO O VO OA CM vo rH CU OA CO O O CM -CM OA H Hi o o o O OA C O OA o « a 6 . « •ft .• « rH H H H H H o o o rH CM 1 C O CM V O i n i n co OA O o • a * o O r-l rH V O o V O co CM vo K A O A o i n C O t>- K A o O O o O A C O t>- C O O - m A ' ft . » ft a rH rH rH r-l O o o o r-1 : f : _ ... •< ' u V D H CM V O OS . V O o O C O K A rH V O vo • -crj- r n H CM CM O o rH K A V O o - m ; C O O A O O o O o O A O A co b- C O o •-* * « * • • « * * • • * -• -o o rH .H H rH rH o o o o o H « rH in- vo co CM O K A CM !>- vo rH O CD K \ CM o . rH CM o O A V O rH CM i n O co O A - o O O o O A O A O A C O C O o • • • * • • * - i * - - "• « • e « * « o o rH rH rH rH O o o o o o rH < d CM K A V O O -^ CM K A CM O A O A CM - E v . co •H o co O A o t>- O A o K A CM " C O O A O A O A o O A O A C O co co O A ft « a * * • « a ft . « a « o o . o o rH o o o a o O o o O i n t>- V O o K A o m i n CM CM i n o 0) rH o C O o o co O A H as C O Q f>CO O A O A o o O A G A C O . co t - 00 O A ft . » • .• * . • « . I . ft o o o rH r-l o Q : O o o o O o • • • > • i n m o CM i n - K A vo vo CM C M i n K A o CM rH o rH r-i O A C O m o CM U A K A O A •CO O A o o o Ch •o\; O A O A C O C O o-\ » «- a . « a ft a * o o rH rH rH o' o o o O . o o o • "P CM o r-i : m rH K A rH - V O . -^ f C O C O rH G O A o C O O . o C O t~ O A rH o C O CD C O o o rH • - o O o O A C O C O O A O -* • • - * * ' * * : ' » 10 * ~. o rH r-l rH H rH rH rH O: o o o r-t o K A o V O O O m O A V O i n o o K A o H . H CM- K A K A O A i n O A O A & rH O o rH CM CM - CM CM r-l rH o O A O A o CM ft • . * ft ft ft ft a . -. ft -..Hi- a « rH rH H rH rH rH rH rH rH o o rH rH ft +3 • . • • ft -P V o CirC 6) O O <D crj C Tfi O ft t-3 fe ft -ft !>> * u U a-. rH ft ft 0$ > f^ H © <4 1 - 3 r-D 03 The t a b l e g i v e s , t h e load.on any of any other month, and by c o r r e c t p o s s i b l e :.to. p r e d i c t w i t h reasonable l o a d i n amperes on any c i r c u i t i f a t h a t c i r c u i t i s g i v e n . For example is-2 2 3 amp., and i t , i s d e s i r e d to e two years l a t e r . Taking," the Novemb the load, f o r the f o l l o w i n g . Septemb.e then t a k i n g t h i s September.load as January i s 1.23 of t h i s c a l c u l a t e d t h e r e f o r e , -the January maximum l o a d 223 X .993 X 1.23 272 amp. This f o r p r e d i c t i n g f u t u r e load, ; upward ($5) c i r c u i t f o r any month i n terms s e l e c t i o n of f a c t o r s ' I t i s accuracy the f u t u r e maximum present or previous reading oh , the November load on a c i r c u i t stimate i t s l o a d f o r January, er load as; 1 i n the t a b l e , r i s .993 of .the November l o a d ; 1, the l o a d f o r the f o l l o w i n g September l o a d . I n , t h i s case, of t h i s c i r c u i t w i l l be ta b l e .should read downward i f past loads are to be determined. Ha v i n g . e s t a b l i s h e d a t a b l e f o r p r e d i c t i n g loads i t Is a p p l i e d ,-to the planning of the-necessary.: new equipment r e q u i r e d to take care of the-expected, loads . I t w i l l serve not only as a b a s i s f o r designing new overhead or underground feeders, but a l s o f o r the i n c r i m e n t o f ' a d d i t i o n f o r s u b s t a t i o n , t r a n s m i s s i o n and power l i n e requirements. I t I s . e v i d e n t t h a t proper p r e d i c t i o n of l o a d i s of great Importance i n the work of economies' of d i s t r i b u t i o n as i t a f f e c t the growth of the c o n s i d e r a b l e study of l o c a l c o n d i t i o n s . w i l l be w e l l r e p a i d in: b r i n g i n g about the: p o s s i b l e economies of the system. • Economical wire S i z e f o r Single«phase L i g h t i n g Primaries.-~-I n extending an e x i s t i n g system the problem of the proper s i z e f o r l i g h t i n g p r i m a r i e s w i l l present i t s e l f . Loads to be handled-w i l l he .estimated as shown above. A method of o b t a i n i n g the eq u i v a l e n t hours f o r those loads was g i v e n i n Chap. IV. With -.these two factors-known we can proceed, as an example, to determine the. economical w i r e s i z e for.-. single*phase.,. 4- ,700*-volt-primaries.:; .In the. preceding chapter on power c i r c u i t s a complete a n a l y s i s . of'a . s i m i l a r problem was' gi v e n . Here i t i s proposed b r i e f l y to .give the' equations and the constants that apply p a r t i c u l a r l y ^ to l i g h t i n g c i r c u i t s . -.- •'.';.':- ' .the- - • . For single-phase;<-lihe<s'cost :§frcpnductor w i l l be two-thirds t h a t f o r three-phase. The c o s t f o r pole f i x t u r e s w i l l be more than two*-thirds on account, of the fa c t : t h a t the. crossarm c o s t i s i n c l u d e d . - . - • JTae f o l l o w i n g equations were obtained i n a s p e c i f i c i n s t a n c e * Table 13."-Equations of T o t a l Annual Cost Size of Wire 6 5-70 r 3 7.50 C O 294,000 AtC e 4 6,17 + 5 3 . 3 C C „ 185,000 'AtCe 2 8 . 1 0 + 8 4 . 0 C * * — 116,200 AtC e , 0' 8 . 8 6 + 1 3 6 . 0 C « 74,600 AtC,. 00 10.58 + 167 .4C«, 59,000 AtC e 000 11.80 + 208 ,5Cco = 46,800 AtC e 0000 12.39-f 2 5 5 . 0 C ^ 37,200 AtC e Note A = i kw IE cos G Equating the expressions for cost for each adjacent pair of Wire sizes the following equations are obtained. Size of Wire Size o f l i r e -6 ' to 4 109,000 AtCe=- 15.8C„ + 0.47 A to 63 ,800 AtC e - 30 ..7Cco -t- 1.93 c to 0 41 ,600 At(L = 52.0Cco -t- 0.76 0 to 00 15,600 Atq.« 3i.4c c„ 1.72 -oo. - to 000 " 12,200 AtC e = 41 . lCca X » 2 d 000 : to • .0000 9 ,600 AtC^- 46,5CCW -h 0.59 o - to 0000 37,400 AtC e =119.0C C £ , 3-53 Note A kw IE cos e Table 15- "-For 4,600 Volts Size of Wire • S ize of Wire Ob-PpeE-/ -. .' • 3©i 2CW 6 to ' '4 t c & 1,010 705 B B 4- -• to 2 t c e 3,420 2,480 . 2 to 0. ' . to. =• B B 8 ,320 5,670 B B 0 to • 00 t c e •• ••==• 15,100 , 10,850 B.. . • • . . B> 00 . , to 000 t c e .-.'•=• "23,500_ 16,380 B B 000 to ' 0000 tC e 32.100 _ 21.800 - B B 0 ' to 0000 ' t c e = 22,200 • 15,470 B B' Note B »J f kw Y cos el For 2,300"volts the same formulas can be used i f the load i n k w i s m u l t i p l i e d by two. The factor tC„ s t i l l remains to be evaluated i n order to plot 97 the curves. In the case of l i g h t i n g c i r c u i t s the load factor can he taken as p r a c t i c a l l y a constant and the shape of the load curve can be also assumed to remain uniform. Hence a simple value" for t C e can be used instead of keeping i t a variable i n the equation, as was done with power c i r c u i t s . This- factor, as used i n F i g . 35, was assumed as . 0 4 . The eauivalent hours for l i g h t i n g were determined previously. The cost, of energy combined with this was found to give the above figure as an average. ".The curve i s plotted for two values of the cost of copper ( 2 0 . c t s . and 30 c t s . ) . The area-in which the load ordinate i n t e r -sects the curve for copper cost indicates the wire size.to be •used. The economical advantage of the size given i s indicated by the distance to the adjacent areas. This method of exhibiting r e s u l t s has the advantage of showing graphically the l i m i t s between which one can work and w i l l show r e a d i l y the e f f e c t of an increase or decrease of load. Use of Regulators.-—.In connection with the determination of the most economical wire size for a l i g h t i n g c i r c u i t i t i s sometimes necessary to include a consideration of the- cost of a regulator. As with power c i r c u i t s , i t may be desirable to determine whether i t i s more economical to use large conductors without a regulator -than.smaller conductors with a regulator. The annual charges on investment and losses for the regulator must be included with those of the l i n e i n t h i s case. With l i g h t i n g c i r c u i t s , however, i t i s usually more necessary to have good regulation than with, power c i r c u i t s to prevent f l u c t u a t i o n In the i l l u m i n a t i o n . The demands of the radio appliance, have made the degree of r e g u l a t i o n more exacting; Hence It i s often preferable to use a regulator i n any case, regard-less of the exact economy, in order to -keep the voltage at or near the center of the load as nearly constant as possible. Other Problems on Lighting Circuits.--With l i g h t i n g c i r c u i t s there appear also some of the same problems met with i n the preceding chapters, such as the economical load, which can be c a r r i e d on a line, already In place,_ when an a d d i t i o n a l c i r c u i t should be i n s t a l l e d or the wire size increased, etc. As the s o l u t i o n , i s not e s s e n t i a l l y d i f f e r e n t from that for other types of l i n e s , these questions need not be discusred i n d e t a i l here. Increasing Capacity of an Overloaded System.--It has been the case i r many, i f not a l l , large c i t i e s , and also In a number of small communities, that the systems of lighting, c i r c u i t s , which a few years ago were apparently perfectly s a t i s f a c t o r y for a long time to' come, have become inadequate on account of the large increase i n the u t i l i z a t i o n of e l e c t r i c i t y and i n view of the prospective further increases i n the future.. This i s e s p e c i a l l y true where comparatively low primary voltages are i n use, such as 1,100 or 2,300 v o l t s , and where single-phase c i r c u i t s , running from the usual type of. main sub-stations, i s the practice. The change to be made i n such a system i s a problem warranting -the mbst c a r e f u l considerations, It i s quite probable that future developments may, i n a few years, raalte any provision, which could now be made i n the l i g h t of present conditions, again inadequate. This cannot be foreseen as yet ho ever. The best that can be done i s to previde for an Increase at -the samerate /as at It -^present for .a-, reasonable number of years, leaving, i f possible, a | i good opportunity for further 'changes' at the end of that time, to I| care for the unforeseen developments. Several methods of providing | •-..-•for this Increase i n capacity have been t r i e d i n d i f f e r e n t c i t i e s with good success. The p r i n c i p a l ones w i l l be noted here with i : /brief notes, on the advantages' claimed and some factors which / a f f e c t the making of such changes, *: Probably the ; simplest method i s that of increasing the voltage . used. • The advantage of such a change was mentioned i n the chapter i ; : on "Power /Circuits " I.e., the Increase i n load c a r r i e d , with the j: •.••same . per cent voltage drop, w i l l be equal to the sauare of the fr Increase/in voltage^ A. change i n st a t i o n Transformers, st a t i o n ;; .equipment and l i n e transformers i s necessary, The economical ad-f:] svantage Ecan be studied by' a c a r e f u l consideration of the annual . costs of making the change. j • Another method i s to change from a single-phase to a. three-f; phase system for the main l i g h t i n g c i r c u i t s . / The advantage gained i s the well-known advantage of three-phase over single-1/ phase. Twice the load can be c a r r i e d for the same per cent power |; loss and per cent voltage drop. Balanced against t h i s advantage u. is the'-cost of making s t a t i o n changes, of i n s t a l l i n g the t h i r d |; conductor, etc. A combined increase in voltage and a change from single-to three-phase is.sometimes used, such as a change, from a 2,300-volt, single-phase to a 4,600 v o l t , three-phase system.. This method/has.• the advantage of obtaining an increase i n capacity, due to both changes with the cost of making the change very ii l i t t l e .greater -than for .either change alone. A method which has been'used recently i n a number of places with apparent s a t i s f a c t i o n i s the 3 n s t a n a t i o n of a four-wire, three-phase system,- with grounded neutral. For example, i f 2^300-volt, single-phase c i r c u i t s have been i n use, the change i s made to three-phase, with a voltage of 2,300 v o l t s from eaeh phase to 'neutral. Some of the advantages claimed are: h The reduction In voltage drop and power loss due to'" three-phas ..transmission from substation to feeding points or. branches. . 2. The reduction i n t o t a l number /of conductors due to the com-bination of three former single-phase c i r c u i t s with six conduce tors into one three-phase c i r c u i t with four conductors. 3. The u t i l i z a t i o n of the same branch single-phase c i r c u i t s and -distribution transformers without change. 4. The load need not be so well balanced as with three-phase, three-wire c i r c u i t s on account of the use of a neutral conductor. Also the"shutting down of one phase w i l l not cut o f f service on the other phases. . 99 5 - The s t a t i o n changes are somewhat simpler than for a straight fj;- increase In voltage or change to a three-phase, t h r e e - w l r e - system. 6 . The a b i l i t y to carry three-phase loads on the same c i r c u i t i f desired. -Some disadvantages noted are the increase i n voltage from phase wire to ground on single-phase branches, the concentration of f a i r l y large:, loads on one c i r c u i t , and'the f a c t that the increase i . In voltage :.ls; not as great as could, be made by a - s t r a i g h t doubling | of voltage. Another method which has also been t r i e d out i n a few places : i s tha.t- of extending, the secondary transmission, system. Instead of attempting to carry the load a l l out .of main substations, on heavy feeder circuits-;- at .primary voltage, small automatic or j semi-automatic substations are established at desirable feeding points and these are supplied through high»voltage l i n e s or cables. The- primary c i r c u i t s running from, these substations are .comparatively short and a corresponding advantage i n regulation• .. is accomplished. Ho- one of the above methods of increasing the capacity of the l i g h t i n g c i r c u i t system can be recommended as most advantageous for a l l cases. The,.one best applicable to any system must be chosen by a c a r e f u l study of present loads, conditions i n the substations and on the lines,'probable future loads,- the cost and p r a c t i c a l d i f f i c u l t lea. of making the change, and •adaptability.•-••of the new system to s t i l l further changes when necessity- demands. This study should be based on' as complete a determination as possible of annual costs before and .after the change and the comparative annual costs with various a l t e r n a t i v e changes. • importance of/good service .--The importance of good service in,' connection with l i g h t i n g c i r c u i t s should be emphasized. I t i s here e s p e c i a l l y that a desire for economy should not lead the engineer to practices which w i l l endanger the q u a l i t y or continuity', of the service rendered. A f l u c t u a t i o n of voltage i s e a s i l y .discernible• in the e f f e c t s on l i g h t i n g and gives r i s e to many complaints. An i n t e r r u p t i o n of service, e s p e c i a l l y i f for any considerable length of time, inconveniences a great number of customers, sometimes with very serious .consequences. ..Economy i s -always desirable, but i t . i s fa l s e economy to save a few d o l l a r s on construction and thereby.lose customers. The-aim should be to reduce-cost to.a minimum which.is consistent with service, at least as good as that to which the customers have been accustomed. . V CHAPTER XI 100 SECONDARY DISTRIBUTION — SINGLE PHASE Study .of Most Economical Design for Secondaries - Voltage • Drop -•.Conductor Size - Transformer Size-.- •  . Length of Secondary , . :-..;.-..., Since the f i n a l objective i n evolving an e f f i c i e n t and econom- • • l e a l design for the central.-station system i s the delivery of energy to the consumer at the least possible coat per uni t and with continu-ously good-service,- no l i n k in the chain connecting the consumer with :the coal supply ought to be overlooked. The ultimate purpose of a l l , study.,;In this d i r e c t i o n i s to enable'energy to be delivered to the customer .at the l e a s t ..possible cost per unit and to render at the same time'cohtihuausly good service. To t h i s end considerable atten-t i o n "has been pa,id to generating plant, transmission l i n e s and sub-stations, but on the f i n a l l i n k i n contact with the customer,, namely, • the;: d i s t r i b u t i o n : l i n e s , the tendency has been to apply ' cut-and-dry' methods i n place of a s c i e n t i f i c evaluation•of the factorsinvolved" i n the layouts. It may be observed that even i n a well-designed system energy losses on t h e i r l i n e s may be. equal to or somewhat more than one-half of the total-loss- between the generator and the customer; -how important and p r o f i t a b l e , therefore, a study of the economical design of d i s t r i b u t i o n l i n e s i s cannot be gainsaid. There are several conditions pertaining to the secondary system which make the c a r e f u l layout of such a system e s p e c i a l l y important-.. The number of transformer-Installations i s so'large and the area .covered ?by the: l i n e s ;so great that constant or very frequent inspect-ion- i s impossible., The load i s subject to irregular: Increases. In :districts-, which are newly b u i l t up new services are constantly being added. In old. d i s t r i c t s , new appliances are being purchased and the •load on old services thereby increased. On t h i s account any design must be made to," forecast a- period of. years- and the increase i n load for ... that period estimated from --.-past experience • On the, other: hand, care must be taken .-not to i n s t a l l too much capacity and thereby" increase the cost beyond.the l i m i t s of economy. The problem must be c a r e f u l l y studied to obtain the balance between low cost and good service for any p a r t i c u l a r ;ease. The problems of secondary d i s t r i b u t i o n economies dea l . c h i e f l y with the wire s i z e and the size and arrangement of transformers. The voltage i s usually l i m i t e d to'-,, a small range of values by past practice, -transformer standards, lamps, motor and other appliance standards, etc. The layout of pole locations, while requiring a con-siderable amount of engineering s k i l l and experience, i s usually dependent on l o c a l conditions, the arrangement of l o t lines,- convenience i n reaching services, .-probable future business, and so on,,. r a t h e r than oh purely economic considerations. Of course, many l o c a l problems:: arise i n the layout and construction o f secondary l i n e s , i n the solution of which economics should be considered. Changes i n type of construction should be. looked at from an economic view point as well~ as' from that of the mechanical-design only. There are several general types of problems r e l a t i n g to second-a r i e s " They might be c l a s s i f i e d i n general as those.of: 101 (a) - S i n g l e - p h a s e . s e c o n d a r i e s i n c i t i e s a n d - l a r g e t o w n s ; (tO - S i n g l e - p h a s e s e c o n d a r i e s i n s m a l l towns a n d c o u n t r y ; (c) T h r e e - p h a s e ' s e c o n d a r i e s on l a r g e power i n s t a l l a t i o n s ; - (d) T h r e e - p h a s e s e c o n d a r i e s on s m a l l power i n s t a l l a t i o n s . , In t h i s c h a p t e r t h e p r o b l e m o f s i n g l e - p h a s e s e c o n d a r i e s w i l l •;. be d i s c u s s e d , e s p e c i a l l y In r e f e r e n c e t o d i s t r i c t s a l r e a d y w e l l b u i l t - u p , where t h e l o a d may be c o n s i d e r e d t o have p r a c t i c a l l y a u n i f o r m : d i s t r i b u t i o n . S e c o n d a r i e s f o r U n i f o r m l y . D i s t r i b u t e d L o a d . - I n a t t a c k i n g such-a: p r o b l e m we c a n o f t e n d e t e r m i n e from t e s t s a n d from p a s t ex-p e r i e n c e :what;.the d e n s i t y o f t h e l o a d i n g i s a n d how i t w i l l i n c r e a s e - f o r some y e a r s , i n a d v a n c e . . - W e a r e . u s u a l l y l i m i t e d o n . a n y system t o c e r t a i n s t o c k s i z e s o f t r a n s f o r m e r and o f w i r e , due t o p r a c t i c a l c o n s i d e r a t i o n s ..of m a n u f a c t u r i n g and; s t o c k - k e e p i n g - . The p r o b l e m . t h e n i s -to d e t e r m i n e t h e p r o p e r c o m b i n a t i o n , o f w i r e , t r a n s f o r m e r :: a n d t r a n s f o r m e r - s p a c i n g i n o r d e r to g i v e g o o d c o n d i t i o n s o f o p e r a t i o n a n d a l s o t o show t h e l e a s t c o s t p e r y e a r f o r t h e l o a d d e n s i t i e s e x -p e c t e d - d u r i n g t h e p e r i o d .of t i m e under c o n s i d e r a t i o n . I t i s c l e a r l y : u n d e r s t o o d t h a t no d e f i n i t e , r u l e s c a n be e s t a b l i s h e d w h i c h w i l l f i t a l l c o n d i t i o n s . The v a r i a t i o n s i n t h e p r o b l e m a r e t o o many. The . -most-that c a n be done i s t o f u r n i s h means f o r r e a d i l y d i s c o v e r i n g t h e l i m i t a t i o n s o f a n y p r o b l e m a n d o f p r o c e e d i n g w i t h i n t h e s e l i m i t -a t i o n s t o t h e most e c o n o m i c a l design.. . The s t u d y h a s - b e e n c a r r i e d , f o r w a r d from t h r e e d i f f e r e n t a n g l e s . F i r s t , . from . t h e . t h e o r e t i c a l ; s e c o n d , from a s e m i - p r a c t i c a l , , t h a t i s , by a d o p t i n g c e r t a i n s t a n d a r d s a n d s t u d y i n g t h e i r b e h a v i o r ; t h i r d , from a p u r e l y p r a c t i c a l , ' g i v i n g t h e d e s i g n e r d a t a on t h e c o s t s o f v a r i o u s t r a n s f o r m e r s a n d w i r e s i z e s under t h e c o n d i t i o n s o r d i n a r i l y e n c o u n t e r e d ' i n p r a c t i c e . -I t i s assumed; i n - t h e f o l l o w i n g d i s c u s s i o n t h a t t h e l o a d i n g i s s u c h t h a t i t may,be c o n s i d e r e d a s u n i f o r m l y d i s t r i b u t e d a l o n g t h e l i n e . The u n i t u s e d i s c a l l e d l o a d d e n s i t y , g i v e n i n k i l o w a t t s per 1,000 f t . The l i n e i s assumed t o be t h r e e - w i r e s e c o n d a r y s p a c e d 42 i n . between o u t s i d e w i r e s . The c o s t o f r i g h t - o f - w a y , p o l e s , c r o s s a r m s a n d ; i n s u l a t o r s I s n o t i n c l u d e d i n any o f the c o m p u t a t i o n s as i t i s assumed t h i s w o u l d be the same under any g i v e n c o n d i t i o n . Nor i s t h e d i f f e r e n c e i n l e n g t h o f p r i m a r y f o r d i f f e r e n t t r a n s f o r m e r s p a c i n g s ' c o n s i d e r e d . In a c t u a l d e s i g n under known c o n d i t i o n s a c o r r e c t i o n s h o u l d be made f o r t h i s . The l o a d i n g c o n d i t i o n s a r e t a k e n as t h o s e o f r e s i d e n c e - l i g h t i n g d i s t r i c t s . a l t h o u g h t h e same methods c o u l d be a d a p t e d t o any o t h e r c o n d i t i o n s o f l o a d i n g i f i t s c h a r a c t e r i s t i c were, known. T r a n s f o r m e r s a r e assumed t o be i n t h e c e n t r e o f t h e s e c o n d a r y . s e r v e d , f e e d i n g b o t h ways. 102 DISCUSSION OF METHODS USED IN DERIVING EQUATIONS AND THEIR APPLICATION. T h e o r e t i c a l . I n t h e t h e o r e t i c a l d i s c u s s i o n I d e a l c o n d i t i o n s a r e assumed w h i c h w i l l - r a r e l y i f ever, be met w i t h i n p r a c t i c e , b u t i t c a n - b e shown by a s t u d y o f t h e r e s u l t s how t h e y may be a p p l i e d t o p r a c t i c a l c o n d i t i o n s , . These a s s u m p t i o n s a r e , t h a t t h e l i n e i s i n d e f i n i t e i n l e n g t h so t h a t t h e t r a n s f o r m e r s may be . p l a c e d a t ,any e x a c t l y d e t e r m i n e d s p a c i n g and t h a t t h e s p a c i n g w i l l change w i t h the l o a d ; t h a t the. t r a n s f o r m e r I s a lways o f a s i z e j u s t e q u a l t o t h e . l o a d t o be c a r r i e d , t h a t i s , e q u a l t o t h e l o a d d e n s i t y a t peak l o a d t i m e s t h e s p a c i n g ; t h a t t h e . w i r e may be o f any c r o s s -s e c t i o n a l a r e a a n d v a r y w i t h t h e l o a d . Such a c o n d i t i o n c o u l d o n l y be o b t a i n e d i n a c a s e where the l o a d showed o n l y s e a s o n a l v a r i a -t i o n s a n d no y e a r l y i n c r e a s e . However, i n p r a c t i c e we u s u a l l y d e s i g n , f o r . a c e r t a i n p e r i o d a t t h e end o f w h i c h i t i s assumed t h e l o a d d e n s i t y w i l l be a c e r t a i n amount. The g e n e r a l method has b e e n t o o b t a i n a n e x p r e s s i o n f o r t h e a n n u a l c o s t p e r .1,000 f t . o f l i n e a n d t o d e t e r m i n e by f i n d i n g t h e f i r s t d e r i v a t i v e a n d s e t t i n g i t e q u a l t o z e r o , t h e c o n d i t i o n under w h i c h t h i s a n n u a l c o s t i s a minimum. T h i s i s t h e most e c o n o m i c a l G o n d i t i o n . A n n u a l C o s t o f S e c o n d a r y D i s t r i b u t i o n - The g e n e r a l e q u a t i o n f o r t h e a n n u a l c o s t Is f i r s t o b t a i n e d as f o l l o w s ; A n n u a l c o s t .per 1,0.00 f t . o f ' I n s t a l l a t i o n — Y Y = ( T o t a l a n n u a l c h a r g e s ' on t r a n s f o r m e r s per 1,000 f t . o f l i n e ) + ( T o t a l a n n u a l c h a r g e s on l i n e p e r 1,000 f t . o f s e c o n d a r y ) r (4,6.) •-. /gr_ ( P u r c h a s e p r i c e + c o s t of h a n d l i n g + c o s t o f I 100 • ' • ' . • i n s t a l l a t i o n s - c o s t ' o f l i g h t m i n g a r r e s t e r s and equipment) +• C o s t . - o f c o r e a n d c o p p e r l o s s •+• c o s t -o f . i n s p e c t i o n \ 1000. S '•. Where Y r g r P e r c e n t i n t e r e s t + d e p r e c i a t i o n - • - t a x e s on t r a n s f o r m e r . -••-• '. S = S p a c i n g of. t r a n s f o r m e r s i n f e e t . . T h e c o r e l o s s i s p r a c t i c a l l y a c o n s t a n t q u a n t i t y f o r 24 h r . p e r day t h r o u g h o u t t h e y e a r . The c o p p e r l o s s - oh t h e o t h e r hand depends -on t h e l o a d . I f t h e v c h a r a c t e r i s t i c . v a r i a t i o n o f t h i s l o a d from h o u r t o h o u r , day t o day a n d - m o n t h t o .month i s known, t h e a v e r a g e l o s s per day c a n be d e t e r m i n e d i n terms o f t h e y e a r ' s peak l o a d . I n t h i s .case t h e peak l o a d v i s assumed t o be j u s t e q u a l t o t h e c a p a c i t y , o f the t r a n s f o r m e r . - T h e . c o s t ' o f energy a t the t r a n s f o r m e r must, a l s o be c a r e f u l l y d e t e r m i n e d . ' ' The c o s t f o r c o p p e r l o s s w i l l be c o n s i d e r -a b l y h i g h e r t h a n t h a t f o r c o r e - l o s s on a c c o u n t o f - t h e l o w e r l o a d f a c t o r . . T h e sum o f a l l t h e s e Items makes up the a n n u a l c o s t on a - ; t r a n s f o r m e r . • • . : : 103-I t was found, that i f the value of the transformer annual cost i s plotted against the transformer size that the curve f o r values between 0 and 25 kg/, may- be approximated by a straight "line of the formula Y 1 = K, + KT, T being the transformer size and K, and K^constanls t o be determined for any p a r t i c u l a r combination of transformer cost, energy cost, etc. (see Pig. 36). This: becomes Y r •», \1»-00Q , +.; KT) per 1,, 000 f t w h e r e S i s the; length of secondary belonging to any one transformer on the distance : between'transformers where -banked - : then Assuming a transformer size just s u f f i c i e n t to carry the load, T - L '°1,000 Where Lj,= load density i n kw. per 1,000 f t . m , ' „ 1,000 /_ . T . L - S \ Then Y y ^ > :: I E/-*-.-:-Ka • D ) . r ( M M S V 1,000/ The annual cost on.the l i n e included i n t e r e s t , depreciation, insurance, and taxes on the Investment cost of the wire i n place, including p u r c h a s e s p r i c e and cost,of i n s t a l l a t i o n , also the cost of annual energy loss due to resistance. The copper loss i s ar r i v e d at by the same method as the copper loss on the transformer,, that i s , by use of the equivalent average number of hours per day a t f u l l load or eouivalent hours. ' • Y £= Investment cost of material per 1,000 f t . of l i n e + instal,-' 1,000 l a t i o n charges perl,000 f t . of, l i n e + — x cost of copper loss in-'-secondary. -'- -' : v*- , ^ = £ ^ ( 3 * L O G O - , * ,,.« + S X 2 x t x 365 X ^ e a . 1,000 Where g / . p e r , cent interest' ^ d e p r e c i a t i o n ±.. taxes on lxne, •••• weight of insulated wire-in' pounds per-foot, , - (V = cost of insulated wire per pound -"cost of stringing 1,000 f t . " o f - l i n e , . I « t o t a l current i n secondary at transformer rV:::>Vi,re:sl.st-ivlty^-o:f;: wire,per,: mil ' ^ o t ^ ' , - -' C - c o s t ' o f copper loss in' secondary per-kilowatt-hour •• •' * t Ii^ulvaient per day which jS*r i r peak^ o a d _ - - should .continue..in order to give : an. l aR. loss ; e q u a l to the t o t a l a c t u a l I 2R' loss for'the year, -• 104 Where A =cross-sectional area of wire i n c i r c u l a r mils, E ' - voltage between outside wires of secondary, Cos 6 = power factor -of load. I = E cos e ' . and y^--A-(3,ooo wc r os- csri + Ml 100 x *° * t * 6 0 ? 8 3 C A « 2 i (48) The total, annual cost per 1 , 0 0 0 f t . of i n s t a l l a t i o n i s low obtained by adding .these two quantities, annual cost of trans« •former and annual.cost on l i n e , and the equation obtained as shown below* • ' Then T = 1 , 0 0 0 S ( K,+ K ^ S -1 , 0 0 0 / 100 1 s 0 0 0 wCco+ 60.83 AE ecos e$ Eauatlon 49 gives the t o t a l annual_cost per 1 , 0 0 0 f t l a t i o n as a function of the spacing and load density.. (49) of I n s t a l -Mo.st Economical Voltage Drop..— One of the most important con-t r o l l i n g factors i n determining the length of a. secondary or the &p spacing of transformers i s the maximum allowable voltage drop. It has usually been considered that the most economical condition of operation would be with a voltage drop higher than would be allow* able for good service.. In. our case,33 per per cent diiopshas been considered the l i m i t i n g value, as'luminosity curves for'Mazda lamps show a reduction as high as 18 per" cent with 5 .per cent . voltage drop while 3 per cent shows over 10 per cent reduction. Considering the voltage loss In the service drops, which cannot be figured, c l o s e l y on account. of variable conditions and the fact,,, that the load i s not absolutely uniformly d i s t r i b u t e d , 3 per cent '• is accepted: as the highest, value commensurate with .good operation. It must be determined, then, i f under c e r t a i n conditions, a* smaller, voltage drop than t h i s w i l l be more economical. In order to obtain the most economical per cent voltage drop i t i s necessary to obtain Y as a function of the per cent voltage drop. ' • This Is done as follows: W = t o t a l load on secondary In watts, V = voltage drop on secondary i n per cent of delivered voltage, B = constant rel a t i o n , between per cent voltage drop . . , and the per cent power loss.-10§ ....... g Then W « L S= A E V * 300 BS E Whence S = 17.32 Blip ..Substituting this value for S i n Eq . 49. Then Y = 1 > 0 0 ° K' v T ^ &u f ' x 17»32 E 2 AV r T*,/- Cez I ( 1 7 .32) 2 BL, 5 0 ' 8 3 A E * c o s * 9 > ' v ...... J i 7 f 3 2 o - 5 i 7 B p v ^ + e . 2 0 2 a f ^ C e i l L j 3 V E \ A . B c o s 2 9 •^••'A1**—(3»ooo*> cw+ c^ r) ; (50) 100 • ' The most economical per cent voltage drop i s obtained when.the, ' f i r s t . d e r i v a t i v e of Y.with respect to V eaua 1:0 •..,,.'• • :. 0 •/'.••• A V = ' K 17,320-1' & v ; / £ . + 0,2028 •/^ C" -Solving for. V_r ( c o s 2 e ) % ' BK,^ 5 1 5 - .. 1,223 J / 3 > (5D .Equation 51/gives "the most .economical per cent voltage drop ;as a,function of the load d e n s i t y : . . , , , ; .": ':-.-/. :''.•.By- :assuming values for; the constants to f i t p a r t i c u l a r conditions. , th i s .expression for V can be plotted against load density for various standard wire s i z e s . These curves show that, as load density Increases, the most economical voltage drop decreases and, under the conditions assumed In the curves here plotted, the most economical voltage 'drop- falls:.below. 3 per cent, at; load densities, which are often : encountered with such loads-, (see F i g . 37) • -. ,. 106 Most Economical Transformer.Spacing^-In order to obtain the most economical length of secondary or spacing of transformers i t i s necessary to have:y- as a function of-S» This i s , obtained from En. 49 • S — ~ : 1 • ! • •.•••AB-o-oB-'e-' The most economical spacing i s obtained when the . f t e s t derivative of y with respect t o . S equals 0 »-dy = 0 dS . .'• r « — f 2 * 60.83 — r % c - o ; S* AE 2cos* 9 * c Solving for S e c " ^ ^ ( 5 2 ) (K,E cos 6 1 A S e c = 2,02 — ; J> Enuatlon 52 gives the most economicallspacing of transformers ' as a function.of the load density.. It i s necessary to l i m i t the range of a p p l i c a t i o n of Eq. 52 to conditions where,the voltage drop i s less.than 3 per cent. A-second equation must be ..developed for 3 per cent drop to apply where the, most economical drop, would be greater than 3 per cent. P r a c t i c a l , considerations l i m i t the. drop to that value. From above S = • E '300031^  using V= 3 per cent ; S ~ 10 j B L p 7 (53> -^Transformer spacing for 3 per cent. drop. . Then,: summarizing:, x z „ K, E cos e S e c = 2.02 { 7 — -:./«^#&4f which i s general for a l l cases. I f now the constants are evaluated these curves may be plotted for various sizes of wire, using, for any p a r t i c u l a r load density, the equation which shows the shortest spacing. 107 We obtain the ;set of.curves, F i g . 38, giving'the transformer, spacing which -will, g i v e w i t h any wire size, the greatest economy, prov-iding good operating conditions are maintained by having no voltage drop greater than 3 per. cent. Most.Economical: Transformer. Size . - - I t Is a simple matter with th i s data, at hand to derive the curves showing the most economical transformer size, for any load density, providing the transformers are spaced most.economically. Since I t was assumed in the beginning . that the transformer would: be . lust large enough to carry the load, ,.. • T = L (Eq . 55) w&ere S_ i s the" value taken from the curves . -21,000 for most economical spacing., v.This i s the most, economical s i z e - f o r .-any: load since, the annual charges on the investment represented by the transformer i s a much greater proportion of the t o t a l annual charge than the cost of energy losses, Therefore, the use of a larger transformer,: even though under-loaded, would be more costly :\ (see Fig. ; 39) . Most Economical wire S i z e . - " I t i s no?/ possible to attack the • problem of.'the---most economical size of wire for any load: density , We s h a l l assume that i t Is f e a s i b l e ' t o use'the. most economical • transformer size-: at i t s most economical - spacing for - any load density,.:. modified by the l i m i t i n g 3 per cent voltage drop requirement. Then ; i f we ;,.substitute i n our o r i g i n a l .equation (Eq. 49): the expressions for S used In'plotting the curves for most economical spacing and f o r spacing l i m i t e d by, 3 rper cent-drop i n voltage,..we obtain-two express-ions for the annual cost' per 1,000 f t . In terms of load density and crossse'ctional 'area of wire (A) * -It i s necessary to introduce two approximations;. -The' weight per foot, of wire (w) enters the equation, ; .also the. quantity"B which Is the constant r e l a t i o n between per cent voltage drop,and per cent power loss for any size of wire* It i s found by p l o t t i n g values of "w" for standard sizes of wire of.the range -of sizes, which "would be ..used, in-::-'Secondaries that the expression •W'«*-K^ '"'^ A'- i s avvery close, approximation, K and.K: being constants . (see F i g . 40). It i s also found thattthe value.of B for any size of wire may be approximated very c l o s e l y by the straight l i n e function B= ••:]&+•&, where K> and'Ke are' eonstants (see F i g . 40) . These must > be derived-from the p a r t i c u l a r values of B which apply to the con-di t i o n s being studied, since these, values vary for different, spacing? between wires* Substituting these expressions i n the equations referre d to above;-we •obtain-.- the-- two - general expressions for annual cps: per 1,000 f t . i n terms of wire s i z e - f o r maximum economy of t r a n s -former spacing . and for 3 per cent .voltage dropv-Ea s. 56*. & 5&. These are d i f f e r e n t i a t e d with respect to A and the Eqs. 57 & 59 are obtained between the most economical wire size and the load density for most- economical spacing and. for 3 Per Cent voltage -drop. &•§§§§8851 m 108 / S u b s t i t u t i n g the, value Sec (Eq- 52) for\S In Eq • 49 [, E cos 9| # A # ; 100 /2.02[ , L j p t G e a f 2 / K / E 2 c o s 2 e 60.83 — —<2.02 ' \ — — 1 , A E e c o s £ e j V ^ t c e 2 K 3 + EAA V If,-w «• „/./;, '.v.: ' ; ; (see^ curve 40) . -' 100 •,<. /•/.''The' equation for annual costs per 1,000 f t . becomes y ™ ^ ?t%* Y *** A - ^ K g L ^ / 3 0 ( K 3 + K , A ) C c o + C K 1 1 '<jw**Y*r.# A 4 + 248.5 I L_" A S*eos 2e ' /Si m p l i f y i n g ' ••/. / • '._ • E ^ c p s 2 # ) •"'-••v. . + A) r +- c s i : (56) :'/ , Equation 56/gives-the annual c o s t per 1,000/ f t . of; l i n e / u s i n g the. most economical, spacing of transformers. The most, economical c r o s s - s e c t i o n of wire i s obtained when the " f i r s t - d e r i v a t i v e of Y w i t h r e s p e c t to A equals 0 or dY .: .'.' • :;dA ;/; / •• : . _ 1 x W . 5 * ^  ^ „ life J • ,-//'./ 3 :|B*COS*e j ^ 10O ) 4 I ... ?'---; ' / S o l y l h g - f o r A ^ - -^ ^ _1_54 f K / p t C ^ ^ V * ? |E cos e ; L / * ; ( 5 7 ) Equation 57 gives the/most economical• .cre-sBisection of wire , using the most economical spacing of transformers. I t i s necessary to l i m i t the a p p l i c a t i o n of Eq . 57 t o l e s s than per cent v o l t a g e drop'and l e v e l o p the eauatlon f o r most economical wire s i z e w i t h 3 per cent drop.'. This i s done as f o l l o w s $ Prom Eq. 53 , the- spacing which w i l l give a 3 per cent v o l t a g e .drop i s , • >,' -.-•i E n s =— 10/ BLp • ' B may be expressed as a f u n c t i o n . o f A as f o l l o w s : B = K3.+ K.A (see curve 40) . A - J C . -S u b s t i t u t i n g the value of S i n Eq. 49, the ex p r e s s i o n f o r annusl c o s t s per 1,000 f t . of l i n e (the spacing being l i m i t e d f o r a 3 per cent v o l t a g e drop) becomes 1,000K, Y3% = %t PtCeg. E £ A +• 60.83 x AE c o s 2 G 100, (Ks -*- E^A) L-S i m p l i f y i n g Y 5 % — • / E * K z L p + loo: 3 p ( K * - + K*A)G<* + ptC f f t + 0.6083 r — 7 - T — ; - (58) cos GjKj. •+• K 6 A J J Equation 58 gives annual c o s t per 1,000 f t . of l i n e using a spacing which l i m i t s the v o l t a g e drop to 3 per cent a t f u l l l o a d . The-most,economical c r o s s - s e c t i o n a l area i s obtained when the f i r s t d e r i v a t i v e of Y 3y e w i t h r e s p e c t to A i s equal to 0 . From which 5,000K, K^ L^  ' K*?tCe, L p + -6083 — — — r - OOg^K^C^ ; (59) « c o s 2 e ^ K ^ A ^ ec Equation 59* gives the most economical c r o s s ^ s e c t i o n a l area of wire when the spacing i s l i m i t e d by a 3 per cent v o l t a g e drop. The constants were evaluated and these curves p l o t t e d , the 3 per cent curve 'for low load d e n s i t i e s and, the maximum economy curve f o r h i g h l o a d i n g . They f u r n i s h a graphic r e p r e s e n t a t i o n of the most.economical s i z e of wire to use under any load d e n s i t y ' p r o v i d i n g ; i d e a l c o n d i t i o n s o b t a i n i n the way of transformer s i z e and.spacing* See F i g . 41 . Purpose of T h e o r e t i c a l C u r v e s A t f i r s t glance i t may appear as I f these curves, being obtained on the b a s i s of such t h e o r e t i c a l assumptions,- c o u l d have very l i t t l e p r a c t i c a l v a l u e . However, when a t t a c k i n g a ' p r a c t i c a l problem of t h i s nature the data from these curves may be,,used as the b a s i s -upon which to s t a r t the c a l c u l a t i o n s of annual c o s t s under operating c o n d i t i o n s . I f , for example, the present load d e n s i t y ,and .the load d e n s i t y which i s to be expected a t some c e r t a i n f u t u r e time are known, by going to the t h e o r e t i c a l curves, we may determine (a) whether the v o l t a g e drop i s to be l i m i t e d by" the 3 per cent maximum, '(b) what would •be the most economical c o n d i t i o n s of transformer s i z e and spacing for present o p e r a t i o n and f o r o p e r a t i o n a t t h a t f u t u r e time, and (c) what standard s i z e of wire w i l l , be most economical over the p e r i o d . The curve f o r the most economical wire s i z e covers, for each standard s i z e , sucha range of load d e n s i t i e s that we . -should be a b l e to s e l e c t a t once ou& wire s i z e without f u r t h e r computation., Having determined t h i s and knowing what stock s i z e s of transformers and p r a c t i c a l spacings come the nearest to f i t t i n g the i d e a l c o n d i t i o n s over .the p e r i o d under,consideration, we can then i n v e s t i g a t e , as w i l l be shown -later,, the comparative economf of such v a r i o u s methods of i n s t a l l a t i o n as c o u l d be used i n t h i s .particular-'-case.. i n other words,. these t h e o r e t i c a l curves ... I l l u s t r a t e l i m i t i n g f a c t o r s to be considered i n more p r a c t i c a l i n v e s t i g a t i o n s . S e m i - p r a c t i c a l , - - l n order to present o u r . r e s u l t s I n a l i t t l e more concrete and p r a c t i c a l form and to show the exact comparative •economy between v a r i o u s types o f i n s t a l l a t i o n , e s p e c i a l l y w i t h . r respect to the s i z e of wire to be used, a s e r i e s of curves, was developed showing the exact annual c o s t under v a r i o u s conditions*. These are c a l l e d - the s e m i * p r a c t i c a l curves ( F i g s . 42 and 43). /// I l l Annual Cost of Standard Wire S i z e s Working under I d e a l C o n d i t i o n s . The f i r s t conditions-was assumed to be that i n which the most economical s i z e of transformer c o u l d be used, spaced the most economically or, where necessary, f o r .3 per cent maximum vo l t a g e . drop. A curve was p l o t t e d f o r each of the three standard s i z e s ;.of wire, No. 6, No.4 and.No.. .'2,- showing the annual c o s t a t v a r i o u s l o a d d e n s i t i e s (see- F i g . 42). .This i s , i n r e a l i t y , simply p l o t t i n g Eqs. 56 & 58. as developed above. Annual Costs per kl^OOO; f t o f I n s t a l l a t i o n f o r Any Combination  of Standard S i z e s of Wire and Transformers.—As the next step i n proceeding from .the g e n e r a l problem to the concrete example v a r i o u s combinations of standard s i z e s of.transformers w i t h standard s i z e s of wire were assumed and curves developed showing the annual c o s t -of each of-these-combinations a t v a r i o u s l o a d d e n s i t i e s . The tran s f o r m e r , s p a c i n g was s t i l l assumed to be always the t h e o r e t i c a l l y :best s p a c i n g : f o r e a c h ' p a r t i c u l a r l o a d . This enables us to compare, f o r example,, the economy of a 10-kw>y transformer and No. 4 wire w i t h tha of a 15*.kw. and No. 6 wire a t any load d e n s i t y . The method .of developing these curves has some p o i n t s of - i n t e r e s t although the equations are merely v a r i a t i o n s of our general equations : f o r annual, cost perl,000 f t . I t i s seen that f o r any s i z e of transformer, as the .load d e n s i t y increases a c e r t a i n p o i n t i s reached where the spacing i s no longer governed by the allow a b l e •••voltage drop but. by the s i z e of the transformer i t s e l f . Hence each curve w i l l c o n s i s t of two p a r t s , the lower where the v o l t a g e drop governs the spacing, and excess transformer c a p a c i t y i s provided, the upper where the-transformer s i z e governs the spacing and the volta g e -drop i s Vies-s than the a l l o w a b l e . .'The t o t a l annual,cost i s •made up of f i v e Items: : i r . Transf ormer. core^.ioss:. 2. Transformer copper l o s s . 3- Copper, l o s s on -the l i n e i t s e l f . 4. - General charges on the transformer ( i n t e r e s t ^ depreeeation, taxes,: i n s p e c t i o n and'testing) . 5. F i x e d charges on the l i n e . ( I n t e r e s t and depreciation.-') Each of these f i v e elements was analyzed as to constants and v a r i a b l e s , c o n s i d e r i n g the . load-density. Lp as the c h i e f v a r i a b l e , and the transformer • aad wire sizes-.- constant f o r any given c o n d i t i o n . I t was found that the equations took the following' form: Y - K g L j S Lp- +• (-+• K / o ) I > * K„ . when the v o l t a g e drop and wire s i z e governs, and Y - (K l z +• K „ + K|Y )L P* (K|(+ K ; 4 ) When transformer s i z e governs. 112 Tbe~ f i r s t i s an equation of a t h i r d degree curve i n Lp breaking -Into a s t r a i g h t l i n e (the second equation) at the c r i t i c a l p o i n t where the spacing f o r 3 per cent drop f u l l y loads the t r a n s -former . The equation f o r each constant was then developed and evaluated f o r each combination of'wire and transformer. The express-Ions f o r c o s t s here g i v e n d i f f e r from those g i v e n i n the t h e o r e t i c a l d i s c u s s i o n i n / t h a t here a c t u a l stock s i z e s of transformers and standard w i r e ' s i z e s are used. The r e s u l t s were then p l o t t e d as shown i n F i g . 4-3• The d e r i v a t i o n of these curves i s a,, good example of; the method of developing a gen e r a l curve by. the use. of symbols f o r a l l constants and then e v a l u a t i n g these symbols t o f i t . a g i v e n Condition••. The d e r i v a t i o h f o l l o w s --The load possible: on a gi v e n wire w i t h a 3. per cent drop i s gi v e n by the formula: 3AE • AS 2 B * 3 0 0 * S 1 0 0 B S . L p S W^L^S and I = - — -E, cos 8 •" E Fk~ - - . . ...S= — /-—when l i m i t e d by v o l t a g e drop (see Eq-53) . The t o t a l l o a d on the transformer «=. - L^S 1 , 0 0 0 1 , 0 OCT S ==•—;'".;•-- ' -when l i m i t e d by transformer c a p a c i t y Lj? . . . . . The f o l l o w i n g i t e m s e n t e r i n t o the t o t a l annual charges per - 1 , 0 0 0 f t . o f I n s t a l l a t i o n s -{&) Transformer Gore.Loss - This i s assumed constant f o r . a - g i v e n t r a n s f o r m e r . f o r a l l loads. Core Loss = constant. 'V'-" 1 , 0 0 0 : ' core l o s s Annual charge per , 1 , 0 0 0 f t . = - -—* C * 24 x 365 x ^ ; : • - . s e / . . 1 , 0 0 0 . _ CLt * 2h » 365 * 1 0 core l o s s ,| • •• -. • • lA-r - •, l i m i t e d by vo l t a g e drop) or -_ _Q^, *-24-;.'?*,:.• 365 " core l o s s K:l^ 1 , 0 0 0 T :'• ^ , ^ l i m l ' f c e d f c y transformer: s W h e n . e e > . . • 1 1 3 -P*, ..«•• 24 y, ,365 « Ip ;,; >core l o s s , r •A G^x , 24 • * 365 * core l o s s ::[:-:r'-K,r ; If000 T - >; ••?</.•.*•: Cost of cor e . l o a s per ki l o w a t t - h o u r • Gore, l o s s In watts, (h) Transformer Oo'p'per Loss -1,000 1,000 •3j55:^.;^ : « 365 tS E e c o s £ e k-j, - we have 10E.<cos 0 Lp .-(Limited by v o l t a g e drop) l e o c T ' Where S == -—- — \ we have L D R TG e ^-365 * 1,000 * t,;* T -• ' - — - L p ( i l m i t e d by transformer s i z e ) ;'••-' •; :-\ . - E cos 9 Where /; • : "' . /A RTG*«365t, '. . :10E COB'•:$»'• R;T;:Ge/;365>OOQt-.T ••••'•',\ .•. E acos*e (c) .Seeondary 0opper ;Loss• -. R 7 * — j • v.' : IA-:.-; .•' 1,000 / i \ 2 s c Secondary copper l o s s - - — — 21—W^L x — "2 « t < 365 e a t2/. "A;: ,y6v 1,000 Where 1= — ; we have E cos 0 "365- C„ S^ ; E a e o a a © A6 e e pt365C e £ 'cos 2 ©E '600 = K L Lj?'(When l i m i t e d by v o l t a g e drop)} o r . •: - : ~ • (when l i m i t e d by transformer s i z e ) y E c o s ^ 8A . . .. .Where ' pt365C eos a0 B600 P t 3 6 5 0 ^ ' l 0 6 T £ ^ E z c 6 s 2 6 A (d-)" iFlxedvOharges on Transformer --'- Constant f o r any s i z e of transformer.;, 1,000/' g^ _ (Transformer cost - t - l i g h t n i n g a r r e s t e r :, S [100 +cost of. ins t a l l a t i o n ] + - ' i n s p e c t i o n p o s t : r 10 •"/"'•'•'•'• (Transformer eost.+ l i g h t n i n g a r - 1 f / g r rester+cost of i n s t a l l a t i o n ) * i n - ( 1100'': speet ion'-"cost f ( (when l i m i t e d by"voltage drop) / • • • , : : '£ fgy; (Transformer c o s t + l i g h t n i n g arrester+'T '•'"• or * i — cost of i n s t a l l a t i o n ) * i n s p e c t i o n cost/ ? v/ T^ Vr 100 (when l i m i t e d by t s i z e ) ' j Where K/5. K 10^r>g r (Transformer costv*- l i g h t n i n g a r r e s t e r 70 fA~| 100 4-eost of i n s t a l l a t i o n ) + i n s p e c t i o n cost) E ~ ; 115 •t l &T- /^Transformer cost + l i g h t n i n g a r r e s t e r • o."W'v :--'.:?;:'^{100; : : * ? d s t ' ; o f I n s t a l l a t i o n ) + i n s p e c t i o n • costf (e) :Flxed Charges ;on lire.:. 100 • - K/, v • . • ( f ) T o t a l Annual Cost - The t o t a l y e a r l y p. opt, p e r i . noo ft.. of l i n e i s t h e summation of t h e s e ' f i V e i t e m s . ; Y 3 per cent - K,LJ - Ka L * + \ 1^ + K Q L J + K„ K*L^ + W + ( K T - lQl£ - K„ > (69) : (When; l i m i t e d by the v o l t a g e olrop) . . - (K,2+K3 - K / r ) L X , + (K,4 +• K,) ; (when "'0:'~,•',;./ :,'"'':^ ;':;;:v l i m i t e d by transformer s i z e ) (.6.1) Purpose .of S e m i - p r a c t i c a l Curves. ^ These s e m i - p r a c t i c a l curves, , although reducing the v a r i a b l e elements, s t i l l r e t a i n enough of the I d e a i c o n d i t i o n so th a t they cannot be used as.an absolute c r i t e r i o n but merely as,a guide. They do show however c o n c r e t e l y the r e l a t i v e economy, of the, v a r i o u s standard s i z e s of wire when used under the most/favorable; c o n d i t i o n s and,-this may. be taken as a; guide to, t h e i r eomparative behavior under a l l c o n d i t i o n s . The/second set of curves a l s o shows: c o n c r e t e l y the r e l a t i v e economy of the v a r i o u s transformer sizes: w i t h any one s i z e of wire as w e l l as the r e l a t i v e economy of .various s i z e s of wire w i t h any s i z e of transformer. This comparison of economy i s v a l u a b l e in'showing, the exact amount by, which the •annual .cost of one i n s t a l l a t i o n i s greater or l e s s .than another. I t of t e n occurs that.where the d i f f e r e n c e i n cost i s not great, other advantages, a r e , s u f f i c i e n t to more than o f f s e t i t and lead.to the choice of the more costly-.'The s p a c i r ^ of 'transformers i s here con-•••aidered;''to be the maximum a l l o w a b l e throughout, w i t h the transformer c a r r y i n g i t s maximum al l o w a b l e load. This l i m i t s the g e n e r a l a p p l i c a t i o n of .these -curves'',in p r a c t i c e and hence l i k e the f i r s t s e r i e s they are. c h i e f l y u s e f u l i n e s t a b l i s h i n g l i m i t s and as a b a s i s f o r the design. . . 116 P r a c t i c a l We now, come t o the development .of, the -curves which the : designer may use i n t e s t i n g the economy of. any design and thereby choose the most economical from s e v e r a l a l t e r n a t i v e s . -Here no "most economical" c o n d i t i o n s need be assumed-. The curves simply represent annual cost as they occur under any c o n d i t i o n -which may be encountered., ,-. • ., Load Curves f o r Secondaries - The f i r s t - curve i s a development .from the two t h e o r e t i c a l curves, the most economical transformer •spacing and most -/economical t r a n s f o r m e r s i z e . . -By p l o t t i n g the., transformer s i z e a g a i n s t the spacing we o b t a i n f o r each s i z e of wire a curve showing the most economical spacing or the spacing l i m i t e d by 3 per cent, v o l t a g e drop for any t o t a l l o a d on the transformer (See 'Pig . 44) ./ By - drawing diagonal l i n e s, one f o r each l o a d ' d e n s i t y d e s i r e d , we can now show f o r any p a r t i c u -l a r load d e n s i t y , the maximum economical : spacing, and the minimum ; transformer, s i z e w i t h that., d e n s i t y and/spacing. This curve merely, -s i m p l i f i e s , the former two and serves the same purpose, not i n t r o d u c -ing any new p r i n c i p l e s . I t i s evident that any poin t below the curve w i l l i n d i c a t e a drop, l e s s than" the v a l u e used .on the curve.. This curve i s of use i n -determining what a l t e r n a t i v e designs may be fe a s i b l e , w i t h any load and standard equipment and what changes may be made t o care, f o r an i n c r e a s e . ,. . Line Cost Curves. - ,The equation f o r annual charges on the l i n e (Eq. 48) i s . next developed n u m e r i c a l l y . Lp * S 2x ptCez AE £ cos 2 9 / / - - A i l c o n s t a n t s were evaluated and a curve p l o t t e d f o r .each,., d e s i r e d spacing -5.00 f t . - i n t e r v a l s were used - showing the annual charges per 1,000 f t . , in'terms of the load d e n s i t y f o r each standard s i z e of wire (see P i g . 45, a. b.. c ) . Transformer: Cost, Curves,. - The t h i r d set of curves shows the annual cost on- the transformer f o r any loading (see P i g . 46). Annual cost of.the transformer = g (cost of transformer,* cost of l i g h t n i n g a r r e s t e r Y ' = — - +• cost of I n s t a l l a t i o n ) 4- i n s p e c t i o n T ioo * cost of core l o s s + cost of copper l o s s / g T' (eos t o f transformer * cost of / l i g h t n i n g a r r e s t e r . 100 + cost of i n s t a l l a t i o n ) + Cost of i n s p e c t i o n core l o s s + Ce, X 365 "* 24 x iRSfflB : Swisses I :::::: siisss :::: BH«55 85S53 •aaswE • • • • • • i B O P t l t f • M m n lt>MS I I :: :s I H I M H i s 1 iuHH ............ ::::: iHif|if|i|fsi BE 117. The equation f o r each of the standard s i z e s of transformers 2, 5, 10," 15 and 25 was' developed and p l o t t e d . Since t h i s curve whows t o t a l annual c o s t on a transformer and not cost per lj ' '000 f t ; . of i n s t a l l a t i o n , a scale was added on the diagonal a t the l e f t by use of which, w i t h a pair, of t r i a n g l e s , the cost per •1,000 f t . may be obtained by the p r i n c i p l e of s i m i l a r t r i a n g l e s . '. s • ' Y t' 1,000 Y r 1,000 ... Y ^ Y r , « . ' , . • s (Y T' = t o t a l . a n n u a l c o s t on a transformer .) (Y r = annual c o s t ,of transformers per 1,000- f t . of i n s t a l l a t i o n ) • (see f i g . 47) • - H e n c e by adding the diagonal s c a l e at,the l e f t , YT-may be obtained from Y r'as follows- by. the method of s i m i l a r t r i a n g l e s . Draw a l i n e from the value of Y r' obtained on the v e r t i c a l s c a l e •to the value of S used, on the diagonal s c a l e . Draw a p a r a l l e l l i n e through 1,000 f t . on the diagonal s c a l e and/where I t i n t e r s e c t s the v e r t i c a l s c a l e w i l l be found the d e s i r e d value of Y r . Cost of. R e p l a c i n g T r a n s f o r m e r s . — Two more items of cost are of i n t e r e s t . t o the designer and those are a r b i t r a r i l y f i x e d by l o c a l c o n d i t i o n s , the cos t of changing the s i z e of transformers i n the same l o c a t i o n and the cost- of changing the l o c a t i o n of a trans** -former. These w i l l be p r a c t i c a l l y constant f o r a l l s i z e s and may be determined i n . any case from l o c a l cost r e c o r d s . Application-'of P r a c t i c a l C u r v e s . — We are now ready to f u r n i s h the d e s i g n e r , w i t h t h e i n f o r m a t i o n .necessary to t e s t the r e l a t i v e economy of any two a l t e r n a t i v e designs. He f i r s t determines h i s wire s i z e from a study of the t h e o r e t i c a l and s e m i - p r a c t i c a l curves. Then, going to the load- curves he may determine h i s ^ a l t e r n a t i v e s i n transformer s i z e and spacing... Assume that c o n d i t i o n s point: t o the a l t e r n a t i v e of i n s t a l l i n g 10-kw. transformers a t a, long spacing, . changing, to 15-kw* a t a-shorter spacing a f t e r a c e r t a i n p e r i o d of years, or o f - i n s t a l l i n g the 10-kw. at the shor t e r spacing now and merely changing s i z e s a t tha t time. From our curves the exact c o s t per 1,000.-ft. f o r each year under considera-t i o n may be obtained by using the c o r r e c t l o a d i n g and spacing and, a t the'.proper time, adding the c o s t of e i t h e r changing l o c a t i o n or changing s i z e . The t o t a l of the annual c o s t s for, eachdde-sjgn gives the t o t a l cost over the per i o d under c o n s i d e r a t i o n and a comparison of the t o t a l s show e x a c t l y the r e l a t i v e economy of the designs over•• the whole p e r i o d . These curves may be a p p l i e d . to any such problem since they are based not on the assumption ;0f i d e a l c o n d i t i o n s but cover any a c t u a l c o n d i t i o n which might occur i n . p r a c t i c e . They can be used i n cases where the transformer, spacing cannot be uniform on account of l o c a l c o n d i t i o n s of pole spacing, secondary length, and s t r e e t and a l l e y arrangement, a very u s u a l case. 118 When there. I s .-doubt about the. wire s i z e a study of the various, possible.:combinations making; use of these curves w i l l , soon "deter -mine the s i z e f o r gr e a t e s t economy. 'Similar•curves can a l s o be developed to s u i t other c l a s s e s of problems such as concentrated -. Toads, l o a d s w i t h c h a r a c t e r i s t i c v a r i a t i o n s d i f f e r e n t from those of, the residence l o a d used, here, as i n business d i s t r i c t s , power •'loads.,-:'etc •' • • . . - ' . . ' 'Example, of - A p p l i c a t i o n -of P r a c t i c a l Curves .--A concrete example of the use. of the above ".curve's-1'may. be h e l p f u l . Assume th a t t e s t s on a d i s t r i c t show a load.'--density of 8 'kw....per 1,000 f t . , with...-' • N o 4 .secohdary, wire already i n pl a c e . Our load curves show f o r that l o a d i n g %" s i z e of wi r e , 12,8kw. l o a d a t 1,800 f t . spacing '•to'- -''-keep 'iwithln J> per cent drop i n v o l t a g e . We wish-to- provide-f o r an: i n c r e a s e - i n l o a d which we w i l l estimate may go to 15 kw. per;i,000-•ft...- in.:'-6; y e a r s . For the present -a 10-kw. .transformer -Bpacedg&t -.1,400' f t . would care f o r the l o a d / w h i l e at 15 kw*' per-1,000 f t . there would, be r e q u i r e d a. 15 kw. transformer at 1,000 ft/Spacing or a 25-kw, a t 1,200 f t . i n order t o ' a v o i d too many c changes, we may space lO-ksv transformers a t 1,000 f t . , changing :tes3g-ye;are .toyl^kw*6r--w.e may put i n 15-kw transformers now at '13-00 -trt'.,/'e-han^ "'ing-' the " l o c a t i o n i n 2 years to 1,000 f t . Other a l t e r n a t i v e s might be considered but. these two w i l l serve as an exa,mple;. For / the f i r s t . a l t e r n a t i v e . - assuming increase' i n load density of 1 2/5 kw. per year. ^ . F i r s t y e a r . 119 L i n e c o s t : 8 ' ' • ;::Sv-^l,.OO0 . ,$16.00:-pep, 1,00.0.. f t . i n s t a l l a t i o n Transformer: post-10- kw •.. • a t . Skw. loadf3 2 . 0 0 per, 1,000- f t . I n s t a l l a t i o n ''•••'"'For ••'•year • . . . . . . . . . .... ........ §48.00 /Second year., : /Line! c o s t-Lj,*' 9 '2/5 kw. ,S. ~ 1 , 0 0 0 . ... .' 16.50 per 1,000 f t . :-vT^h$'fbriner^-c'pst.--.^ 10 kw. at 91 2/5 -'. • 32-70 per 1,000 f t . -.-, ' , ,-; 'For//year:.,. . . . . . .•.•.•.. ' . .•. . . .; , ,- .•..•••-.. ' : 49*00 T'Kird/year* '.' / . ''.-:-Line, cost-1* , , * 10 ' 4/5 Kw . ,,S = 1,000... . . 16 .80-per 1,000. ft,. Transformer .cost - 10 kw. at 10 4/5-• 33-70 per 1,000 f t . "'•'/'For year i. • .50*50 Fourth y e a r . ,/ . •, , Line c o s t - L = 12 1/5kw'-. ,S =.1,000. .... 17-30 per. 1,000 f t . - Transformer .c'ost - 15 kw. a t 12 1/5. - 42.9© per 1,000 f t . • .'.'CO's't of: changing s i z e (10 kw.". to-15 kw. oh .,/:' /./same-pole,)'..;•.......•.,,..•..,..,..../•. -7.00 per 1,000 f t . , .;. ;'"". For year ............... . . 67.20 Fifth/year,/:' • . .-.•-/"^Llne'eostaL v~\l3 3/5 kw.,S = 1 ,000. . - 17.80 per 1,000 ft.. Transformer: c o s t iS-kw- a t 13 3/5 > - - : 43-60 per 1,000, ft.. -/For-yearv,,^. .* .-•. '.•..;'• .•,-.• • •'-• - •-•• ' • • . 61.40 S i x t h y.ear.':"•'•"• - • - • •''" "•-•"'" ///Llhe^cost^L/;^^ 15/kw>iS- =• 1,000,-. - • ../18.40 per 1,000 ,'ft. / - - T r a n s f o r m e r c o s t * 15 kw. a t - 1 5 • 44.40 p e r 1,000 f t . FOr^ year,;,...'.,.../. =. ri.... .'.. ., .-,,.-..•,.',. . / • . / / .; .62*. 86 Totai, ,for 6 y e a r s • .#338 «90/;// per 1,000 f t . 120 Second, a l t e r n a t i v e F i r s t year. Li n e coot - i ^ - 8.kw., S = 1,500 . | 17 .20 per 1,000 f t . Transformer.,cost 15 kw. a t 12 kw. , ; ;•: load..,.. 35.50 per 1,000 f t . ' ' T o t a l f o r y e a r . . . . . . . . . . . . . . . v - • • 52*70 •Second year. •'-.;• , •. •...-. /. • Line- c o s t L_= 9 2/5 kw., S<L,500 .. . . • 18 .00 per 1,000 f t . --v;:: Trans former- cost 15 kw ...at ,15 4/5 • • • -37-20 per 1,000 f t . •-.'•.-' .for- year .•..-...;.....*........; 55 »20 •Third-years. - • ' -Line c o s t 1 0 4/5 kw.,S-= 1,000... . 16 .80 per 1,000 f t . •:Transformer cost~;15 kw. a t 10 4 / 5 . .. 42-30 per 1,000 f t . Cost "of.Changing l o c a t i o n . , ..... ...... ,20-50 per 1,000 f t . f o r year . . . 79*60 Fourth year-same a s f i r s t a l t e r n a t i v e ( l e s s charge f o r changing s i z e ) - |60*20 per 1 1,000 f t F i f t h year-same as f i r s t a l t e r n a t i v e . . . . . . . . . . . . . . .. . . .. . .|6l*40 per M f t . S i x t h year -same as f i r s t a l t e r n a t i v e . §62.80 per M f t . T o t a l f o r 6 years ,.,. .$371»90 per ' . . 1 f t . A- saving of $33 per 1,000 f t . of i n s t a l l a t i o n , or approximately 10-per cent-of: the. t o t a l cost over a p e r i o d o f .6 year s "by the f i r s t method thus demonstrating i t s economy. I t i s w e l l to note that a -large p a r t of. the d i f f e r e n c e i n cos t i s due to.othe f a c t that i n the f i r s t case,, the size': of transformer i s changed while i n . the other the ,. : l o c a t i o n but not the s i z e i s changed. I f a f u r t h e r refinement of the comparison i s d e s i r e d , I n t e r e s t may be considered: on the year l y . i t e m s up t o the end of the p e r i o d under c o n s i d e r a t i o n . U s u a l l y such refinement i s not necessary however. .Conclusions — A study of a l l . t h e s e curves gives c o n s i d e r a b l e a i d i n determining c e r t a i n standards.: of design as w e l l as the f i n a l p a r t i c u l a r s f o r any s p e c i a l problem. There a l s o may be obtained a d e f i n i t e knowledge of-the behavior of secondaries under v a r i o u s con-d i t i o n s of l o a d i n g and op e r a t i o n . ' I t i s purposed here to take-up.-..each curve In d e t a i l , to b r i n g out i t s c h a r a c t e r i s t i c s and i t s p o s s i b l e use. Most Economical Voltage .Drop.--The curves on vo l t a g e drop show that the most economical c o n d i t i o n v a r i e s I n v e r s e l y as the cube r o o t of the wire s i z e , a l s o i n v e r s e l y as the cube r o o t of the load d e n s i t y . For low load d e n s i t i e s the economical drop i s high but decreases r a p i d l y , r w h i l e at high l o a d i n g the decrease i s comparatively slow. 121' I t Is c l e a r l y shown that, the most economical v o l t a g e drop may "be w e l l under- t h a t a l l o w a b l e f o r good s e r v i c e f o r loads which mayo oft e n be ecountered i n practice.. Under the c o n d i t i o n s and p r i c e s assumed.In the present case the 3 per cent l i m i t seems to have some j u s t i f i c a t i o n by economy f orordinary-Toads . -Two c o n d i t i o n s must be considered which might a f f e c t these curves, i-.e.,, t h e - p r i c e of m a t e r i a l s and cost, of energy and the f a c t that here . the -transformer was: c o n s i d e r e d Just s u f f i c i e n t to c a r r y the load 'while o r d i n a r i l y , when des i g n i n g f o r an i n c r e a s i n g load, the t r a n s - . formers; are underloaded. •;, I t is v: seen from the equation of the curves for - economical voltage, drop t h a t the c o s t of .copper does not a f f e c t thi& discussion.-- This is-due to the f a c t that the-annual cost i s based on a u n i t of 1,000 f t . hence f o r any given p r i c e of copper the. -annual cost, per 1,000 f t . - of. thr.ee»wire l i n e i-s - a constant no matter . what the load-. The- c o s t of energy enters as an i n v e r s e f a c t o r to the 2/3 power. In addit'ionifls a .small element In the f a c t o r K., which-is aiso-.to-the; .2/3 power but i n the; d i r e c t r a t i o . Hence an increase . i n the cost of energy would increase both the numerator and,the denominator - but the T a t t e r - s l i g h t l y more: than the numerator',, hence a l l the curves would, be r a i s e d . s l i g h t l y . T h i s e f f e c t would be s m a l l , however, f o r o r d i n a r y f l u c t u a t i o n s . In the case of an-increase i n the transformer p r i c e there would be no change i n the curves p r o v i d i n g the increase were p r o p o r t i o n a l to, the s i z e since the f a c t o r .K, would, not be a f f e c t e d by such an i n c r e a s e . In o r d i n a r y design f o r a n . i n c r e a s i n g load the transformer would be-ma;de l a r g e r •-than-'sufficient to c a r r y the present load to a l l o w f o r the a n t i c i p a t e d increase.. A study of the curves f o r the v a r i o u s components of, the annual charge on a,transformer and.the equation r e s u l t i n g therefrom, YT< =- ,K, •+- Kg,T,- w i l l show that i f they'are developed-with the transformer working below i t s r a t e d l o a d i n g , . and i f the: p e r c e n t a g e — ; — — •— : ;—.—_—_ . -of underloading i s kept the same f o r a l l s i z e s , the f a c t o r ,: K7- w i l l be very l i t t l e a f f e c t e d , the e f f e c t being s i m i l a r to an ., i n c r e a s e i n : p r i c e p r o p o r t i o n a l t o . s i z e . Since t h i s i s the only part of. t h i s equation that enters i n t o the equation for.most economical v o l t a g e drop i t f o l l o w s t h a t i f a design could be l i m i t e d to any given percentage of mnderloading throughout, the curves.would s t i l l show the most economical c o n d i t i o n of v o l t a g e drop.. - Most Economical Transformer Spacing These- curves f o r the ; - most-economical transformer -spacing ( F i g • 3-8) are d e r i v e d from the same general expression f o r annual cost per 1,000 f t . as those fo r economical v o l t a g e drop. Hence, the same r e s u l t s might be expected from the: use of e i t h e r of these s e t s of .'curves w i t h the exception that where the most economical spacing would give a maximum vo l t a g e drop of more than 3 per cent / a ' c o r r e c t i o n has been made f o r t h a t value, making i t such as;-to give 3• p e r cent-. These curves show f o r very low load d e n s i t i e s extremely high spacings which-are probably much greater than i t would be p r a c t i c a b l e to use, s i n c e , f o r such a distance and f o r l i g h t loads, the e f f e c t of the non-uniform l o a d i n g would be c o n s i d e r a b l e . As i s shown by the equation, the spacing f o r 3 -per cent drop v a r i e s as the square root of the wire s i z e , w h i l e f o r g g r e a t e s t economy i t . v a r i e s as the cube, root..--122 I t a l s o v a r i e s i n v e r s e l y w i t h the load d e n s i t y to the ^—— Square root i n : the f i r s t case and to; the 2/3 power i n the second.: . For ordinary loadings encountered In p r a c t i c e and the usual range of wire s i z e s i t i s seen t h a t spacing of f r o m l , 0 0 0 : t o 2 ,000 f t . -i s the most, economical and p r a c t i c a b l e . For the higher loadings the most economical spacing decreases'very slowly, remaining over 500 f t . up to hi g h values of Lip. • Changed c o n d i t i o n s would have a s i m i l a r e f f e c t on these curves as on those f o r economical v o l t a g e drop, i n the; range of value s f o r which the most economical v o l t a g e drop governs the spacing. That i s , a r i s e i n the p r i c e of energy would lower: the curves s l i g h t l y •while the p r i c e s of wire; and transformers would not have a n o t i c e - , able e f f e c t - For the c o n d i t i o n of underloaded transformers, i f the p r o p o r t i o n of underloading were f i x e d there would be s l i g h t change., I n - p r a c t i c a l ; d e s i g n i n g , however,; when c o n s i d e r i n g the ' amount 'of t h i s margin In transformer c a p a c i t y to be used, i t might be found r e l a t i v e l y more economical to use a transformer s i z e some-where near the t h e o r e t i c a l l y most economical and o b t a i n the margin i n capacltyvby using a spacing less: than the most economical spacing. T h i s may have some advantage over using the most economical spacing, as shown by the" curves, and a l a r g e r s i z e of transformer than the most economical, when the design i s to cover s e v e r a l years -and the cost of. changing s i z e s and l o c a t i o n s i s taken i n t o account. Hence ; care must be used i n p l a c i n g too much dependence on the s t r i c t l y t h e o r e t i c a l values i n p r a c t i c a l design. The choice must be t e s t e d by, the a c t u a l year to year c o s t s as shown by the cost Curves. • Most Economical Transformer S i z e . - The curves f o r the most economical transformer, size:, simply show the s i z e of transformer which w i l l c a r r y the lo a d when the spacing I s the most economical or j u s t enough to giv e 3 per cent v o l t a g e drop.; They have r e l a t i v e -ly, l e s s p r a c t i c a l v a l ue excepting that i t i s from these and the spacing curves combined th a t the p r a c t i c a l load chrves are obtained. Most Economical Wire S i z e . - The wire s i z e i s the f i r s t t h i n g to determine i n a design.and must be chosen to cover long periods o f increase i n l o a d as replacement of secondary wire i s very c o s t l y . . Hence f o r secondaries a standard must be chosen f o r i n s t a l l a t i o n i n new-work which w i l l show good economy through the greatest, range of co n d i t i o n s to be encountered; The curves seem to i n d i c a t e c l e a r l y that under the c o n d i t i o n s and p r i c e s assumed No.6 wire should be used as a•standard i n a l l new work, i n d i s t r i c t s where ordinary residence l i g h t i n g l o ad i s expected. The economy curve r i s e s very r a p i d l y a t low d e n s i t i e s up to about 20,000 c i r . m i l . or nearly No «7 at about 7 kw. per 1,000 ft-.- • prom here the r i s e i s l e s s r a p i d feut s t i l l c o n s i d e r a b l e u n t i l i t crosses the value of No.6 wire at •'15-kw. load d e n s i t y . The load density of 15. i s a' normal .loading. I t would not be a d v i s a b l e to use any s i z e l e s s than a -No «7. since the loadings at the smaller values are subject to such r a p i d i n -crease. Even at No-7 the economical load i s f a i r l y small (7 kw. per 1,000 f t . ) . On the other hand, the curve r i s e s slowly a f t e r .passing No.6 and only reaches No .5 at a l o a d i n g - o f about 31 kw. and No.4 at 40 kw. which are h i g h d e n s i t i e s and t o be encountered o n l y i n s p e c i a l cases .:.: I t i s i n t e r e s t i n g to note . th a t f o r a l l values below a No.6 wire the economical s i z e I s governed by 3 per. cent v o l t a g e drop while above that the most economical drop governs, -the curves c r o s s i n g a t 19-kw. load density ..-••-.,. , :.: 123 Since the curves were f i g u r e d ' a t a low copper p r i c e , i n case of an increase i n prKiee, the curves would be lowered, i . e . , a smaller wire s i z e would be i n d i c a t e d f o r any p a r t i c u l a r l o a d i n g . An ; increase i n energy cost would be i n d i c a t e d f o r any p a r t i c u l a r loading-. An inc r e a s e i n energy co s t would s l i g h t l y r a i s e the curve;' an, Increase I n transformer p r i c e i f p r o p o r t i o n a l to s i z e would-not a f f e c t the d i s c u s s i o n . Since the curves were f i g u r e d on the assumption that the transformer spacing was the most economical and the e i z e .just equal to the loadj a change i n these c o n d i t i o n s m i g h t - a f f e c t .the most economical, wire, s i z e somewhat. A f i x e d pro-p o r t i o n o f .under l o a d i n g as ".above shown would-have l i t t l e e f f e c t but i f d i f f e r e n t c o n d i t i o n s of spacing were assumed, the design should be t e s t e d by use of the cost curves f o r v a r i o u s s i z e s of wire-.-- ••.<•:•-'•.. - , S e m i - p r a c t i c a l Curves• - The curves which we c a l l s e m i - p r a c t i c a l show a l i t t l e ' more c o n c r e t e l y the r e l a t i v e economy of i n s t a l l a t i o n s with, the v a r i o u s s i z e s of wire, - i n d o l l a r s per year per . 1,000 f t . They show the a c t u a l annual c o s t f o r ..different types. . The excessive cost of. No .2. wire f o r ordinary loads i s -clearly-•.demonstrated-being from. $3.50 t o |6.00 per year more-than No.4 f o r loadings -up to. 15, -kw.-per,-1,000 f t . , ' • -•When-we go from the i d e a l s i z e -of transformer t o , p r a c t i c a l stock sizes,, s t i l l assuming the best--spacings to be used,: there are some c o n d i t i o n s i n which the r e l a t i v e wire economy Is somewhat d i f f e r e n t ..These curves a l s o give an i n d i c a t i o n of transformer .economy., I t : seems .to be q u i t e c l e a r l y shown t h a t , under the assumed c o n d i t i o n s , the use of larg e transformers such as 25 kw. i s . n o t j u s t i f i e d except, w i t h very heavy l o a d i n g , even c o n s i d e r i n g the p o s s i b l e r e d u c t i o n In the number of transformers and hence i n the • core l o s s . The increase i n the investment cost more than e q u a l i z e s such saving-.: . •• ---; . P r a c t i c a l Curves . - The use.of the cost . curves i n designing has, already --been e x p l a i n e d I t may now be . r e a d i l y seen how a study of the t h e o r e t i c a l and semimpractical curves a p p l i e d to any problem w i l l g i v e a b a s i s upon which to formulate a design.which can then be t e s t e d f o r a c t u a l economy by a p p l i c a t i o n of.the exact costs to be expected. We can determine from t h i s , i n case of a new l i n e , the s i z e of wire and then the spacing.and s i z e of transformers which w i l l care f o r s e v e r a l years of Increase. The exact number of years w i l l be determined by the r a t e . o f increase together w i t h the economy of the design, i n c l u d i n g cost of changing s i z e s and l o c a t i o n s . Or, i n case of remodeling an o l d d i s t r i c t , we s t a r t w i t h a g i v e n s i z e of wire which, although perhaps not" the most economical, w i l l not -j u s t i f y the cost of change. We can then choose and space our transformers most economically w i t h regard to.that s i z e of wire. In a s p e c i a l , case where no increase i n load i s expected the theoret-i c a l curves w i l l give e x a c t l y the design to use- In other cases where the l o a d i n g , v o l t a g e , e t c , are somewhat d i f f e r e n t , by proper s u b s t i t u t i o n i n - t h e t h e o r e t i c a l formulae,... curves could'be p l o t t e d which would apply to t h a t . p a r t i c u l a r c o n d i t i o n . General. - The curves given here should not be accepted f o r general- a p p l i c a t i o n - to design problems.. The-costs and c o n d i t i o n s 124 of loading used were of l o c a l d e r i v a t i o n and apply only to the - o r g a n i z a t i o n and the time for, -which they were obtained". S i m i l a r curves should.be: developed f o r the study of c o n d i t i o n s i n any . o t h e r l o c a l i t y and they, should be r e v i s e d from time to time t o meet changing c o n d i t i o n s . These examples are given here merely t o i n d i c a t e the c h a r a c t e r i s t i c s of such c u r v e s . -I t i s evi d e n t that no very simple means of d e s i g n i n g . c o r r e c t l y a d i s t r i b u t i o n system i n regard to transformers and secondary wire can,be made a v a i l a b l e due to the many v a r y i n g c o n d i t i o n s encountered and the large.number.of f a c t o r s to be taken Into account. , . The elements o f good judgment and experience are as necessary In the .'solution o f these problems as i n any other problem of engin-e e r i n g . The object of t h i s study has been to, analyze and evaluate -; the f a c t o r s of the design of, a single-phase secondary system of the -type considered, f a c t o r s , t h a t l e n d themselveB to such d e f i n i t e a n a l y s i s and' that present r e s u l t s to be used as a i d s i n the a p p l i c a - ' ••tion of good judgment and. experience to the best p o s s i b l e s o l u t i o n o f the.: problem... This problem has been dwelt on In some d e t a i l s i nce i t Is thought t h a t the methods used, and the p r i n c i p l e s brought out- a r e t y p i c a l f o r a l a r g e number.of such types of problems. Secondaries, f o r S c a t t e r e d Load. --A very common que s t i o n a r i s i n g I i n r u r a l ' d i s t r i c t s where the load i s s c a t t e r e d , is- t h a t of how f a r i t Is economical to' extend secondary from a present transformer l o c a t i o n to reach a new customer r a t h e r than to hang a new transformer I t i s thought t h a t t h i s problem i s of s u f f i c i e n t i n t e r e s t to warrant a b r i e f mention here. The comparison should be made, of course, on the b a s i s of annual c o s t s . • - , The. ap.nuaT cost on the I n s t a l l a t i o n i n case t h e secondary i s extended i s y s = annual charges on Investment on l i n e of leng t h • D - D 5 - - ' ' + cost of I R l o s s on extended secondary _ + co-st of increase i n I R l o s s i n transformer ,' ,..'--cost of. i n c r e a s e d copper l o s s In transformer Where D = d i s t a n c e from, present transformer to new load, Dy = d i s t a n c e from present transformer end of present - •:- secondary, ( I t Is assumed that the present transformer i s lar g e .enough to c a r r y the in c r e a s e d load.). . - The" annual 'cost i n . case the primary i s extended and .a new , transformer' used,.-,-is,. , Y - annual charge on investment on. l i n e of length P D — Dp -+ I Z R l o s s i n t o t a l l ength of primary D ; +. T o t a l annual charges on new transformer i n c l u d i n g " f i x e d charges and energy l o s s e s . 125 : / ' ^ l i e r e /D^//^,/distance, from present transformer : to end of primary. / / - . / . / " ' V ; < • / " . ' " / ' '•'•///.In the problem: eonsidered, i t i s assumed that the cost of right-of-way, poles, crossarms,. e t c . would be the same, i n e i t h e r case.. • ////-; I f : the .expressions f o r f ? . - a n d T r are put i n the form of equations ih/terms; • of. the, load, v o l t a g e , wire s i z e , cost of; energy,.:,etG^; and equated to Y p , a s o l u t i o n ; may be obtained fbr/D^/the distance, at which economy changes from a secondary t o a. p r i m a r y ' e ^ The f o l l o w i n g e x p r e s s i o n was obtained using constants apply-i n g , to a p a r t i c u l a r system. / ; VZ\ IT •': T \ • , : . . W J 2 I . 6 L p 3 s +- (W +.2W>/): R^- - ' WE^ '-* K \. \ vvv/Where- W «= new. load i n watts, I '; ; / / / - , ; ; ; , ; • E = the/; secondary voltage;:, /- /;/;Vv ; ; / ; ; : ,E / ^:ther/pr imary voltage,; .,-'•/'/-;,:.-;,-;; w-a* weight; -per foot: of conductor (primary: and'secondary;), -•.•:;,: >aa'Sumel same s i z e ; f o r small l o a d ) , //-/W, «*present load on present transformer, /:;;;// ; !Rf.' •' equi v a l e n t r e s i s t a n c e of present transformer, -/ ; : / - ; ; / / / R^ « e q u i v a l e n t .resistance of new transformer, r K * = f i x e d charges and annual c o s t l o s s cost on transformer, -v./"If/both'primary-ahd secondary were/two No .6; wire and E y = 4,6O0,; /E ;/^': i l2-| : ; theteq-uatipn.'becomes . .... ;.W'"-:Y: / W \ (0.823 1V382D;••• ; 1 - ^ — : * 8 > 3 5 ' (D 5- D j , - 1,680 ( — — /• .1. „.:.;,/%i£ \I,OG0.// ' 5 ; ^ /.„; .,; \l,ooo7; /V 10* W •• 2W, "R^.- P y^ •+- 1,000 E •i-,doo' i,oooy 1,000 In the ./.limiting ca'se> where D^f , D and % .. ~ . 0 the cost of primary e x t e n s i o n would be, a minimum' and of secondary extension a maximum 18,550 - 4,180 1,000, ' • '•/ •.•w.-'.-'V'. . 1.382 ,/ -;.; /I * 8 . 3 5 • : 1 1 , 0 0 0 / ' (65) 126 This i n d i c a t e s the dis t a n c e to which i t i s economical to carr y any load, 7J, on secondary. , ; Since, f o r J : per cent v o l t a g e drop w i t h the'above c o n d i t i o n s 417 D= W/l,000 So l v i n g simultaneously . W = . 2kw. , , 1,000 This i n d i c a t e s that, f o r any load, over 200 watts, economy need not be' c o n s i d e r e d . i f the maximum al l o w a b l e v o l t a g e drop i s f i x e d at 'J, per cent,, since i t i s economical ,to c a r r y such a load on secondary to any d i s t a n c e at which the v o l t a g e drop.Is 3 per cent or l e s s . For loads l e s s than 200 watts, Eq.65"may be p l o t t e d In a curve i f desired., ' The above s o l u t i o n has been g i v e n very b r i e f l y and a l l . b u t the c h i e f - s t e p s , omitted. I t i n d i c a t e s the method which can.be f o l l o w e d i n s tudying a number of s i m i l a r problems. The r u l e e s t a b l i s h e d i n the p a r t i c u l a r case shown has been found very u s e f u l i n l a y i n g out. r u r a l e x t ensions. Space w i l l not permit the' e l a b o r a t i o n of more problems of s i n g l e phase secondaries.. Among the others o f t e n encountered are the f o l l o w i n g ; economy of : r e p l a c i n g a sm a l l secondary w i t h a l a r g e r s i z e Instead of hanging an a d d i t i o n a l transformer; r e p l a c i n g wire l a r g e r than the economical s i z e w i t h a smaller 1 s i z e ; the economical s i z e . of secondaries and arrangement of transformers f o r e l e c t r i c range loads, economy o f , l e a v i n g dead wire I n place i f i t i s t o be u t i l i z e d : l a t e r ; and many others.-CHAPTER X I I 127 POWER S E C O N D A R I E S Power: Secondary Vs. Separate Transformers - Economical S i z e of 3 0 Secondaries.. • 'T ?he' power- .secondaries.- on any system are,, as a r u l e , by no means as ext e n s i v e as the l i g h t i n g secondaries. I n d i s t r i c t s where the power l o a d i s very heavy., i t . i s very o f t e n a d v i s a b l e to supply each customer from separate transformers. In d i s t r i c t s where the, power load Is s c a t t e r e d , the distances are u s u a l l y too , great- to c a r r y more, than a very few customers on one secondary. There a r e , of." course, many cases where s e v e r a l small or medium s i z e d Toads are grouped i n a r e l a t i v e l y s m a ll area, such as a .number of small f a c t o r i e s or a. bl o c k of s t o r e s . For such c o n d i t i o n s , i t i s . u s u a l l y p r a c t i c a b l e to use a few l a r g e transformer I n s t a l l -a t i o n s with.power secondaries. While the p r o p o r t i o n of the t o t a l system investment represented i n power secondaries i s r e l a t i v e l y •-•small- n e v e r t h e l e s s the amount of load handled on any one i n s t a l l a -t i o n i s . u s u a l l y l a r g e compared w i t h that on a l i g h t i n g secondary. Hence, although a. c o n s i d e r a t i o n of t h e i r economy"as a general p r o p o s i t i o n , may not seem so important, i t - may be q u i t e p r o f i t a b l e -i n ••individual.' cases . • " '  • ,.. I t v e r y - r a r e l y happens that the load on a power secondary i s so arranged that i t may be considered as a d i s t r i b u t e d load, e i t h e r uniformly ."--or •..in: accordance w i t h any other d e f i n i t e law. N e i t h e r does i t o f t e n occur that power secondaries can be made continuous and-the transformers spaced as d e s i r e d . Hence, the problem I s u s u a l l y one of concentrated loads of a given s i z e to be t r a n s m i t t e d • a . d e f i n i t e d i s t a n c e . There must be a study of each p a r t i c u l a r case r a t h e r than of the type of i n s t a l l a t i o n i n g e n e r a l . Two kinds of,problems are q u i t e commonly met w i t h In connection : with: power/secondaries... I t must be decided, f o r any ease of a small or medium s i z e d l o a d , whether i t i s p r o f e r a b l e to c a r r y I t on a separate transformer or tap I t to a power secondary, p r o v i d i n g one I s a v a i l a b l e or can be i n s t a l l e d . . . I f i t i s to be thus handled,, . the most economical s i z e o f conductor should then be determined. R e g u l a t i o n and C o n t i n u i t y o f - S e r v i c e Important. - The de c i d i n g f a c t o r i s q u i t e l i k e l y to be some other c o n s i d e r a t i o n than that of economy onl y . I t must f i r s t be determined whether the load can be c a r r i e d from the - present i n s t a l l a t i o n w i t h -a ...reasonably, s i z e d , secondary," without exceeding the al l o w a b l e v o l t a g e drop:. Oftentimes, a,present t r a n s former, i n s t a l l a t i o n can be moved to a .new l o c a t i o n and the secondaries: rearranged to accommodate such a d d i t i o n a l . loads , >-. Even though i t i s found e a s i l y p o s s i b l e , t o c a r r y the load i n . t h i s way there are some cases where the -importance of c o n t i n u i t y of ser-v i c e may i n d i c a t e that a separate i n s t a l l a t i o n i s a d v i s a b l e . Any t r o u b l e on one customer's s e r v i c e or i n the transformer would d i s a b l e the* s e r v i c e s of a l l other customers. Hence, any customer whose s e r v i c e Is e s p e c i a l l y subject to i n t e r r u p t i o n , or any one 128 ;'Whom.'an: i n t e r r u p t i o n would s e r i o u s l y discommode should be given : separate transformer i n s t a l l a t i o n s -.".'..For. the same reason, I t i s w e l l hot to concentrate too many power s e r v i c e s on one secondary, / e s p e c i a l l y - s e r v i c e s to , Tmanufacturing' plants,./ _ , -"'Economy,,of Secondary i n s t e a d , of Separate Transformers • . -; i f " i t has. been decided: t h a t the l o a d i n Question can and should be / c a r r i e d ; on/secondary, i t . s t i l l remains, to determine "whether such : an , i n s t a l l a t i o n i s economical.- . i f the annual f i x e d charges plus '/-co.st/',':6;f •' e n e r g y l o s s on the secondary necessary to re.acfi the customer, . i s g r e a t e r than the annual charges on a separate transformer, i n s t a l l - , /'atiohi,/ then:; the . l a t t e r , should be used. I f the .whole I n s t a l l a t i o n '/is, to, be: rearranged, the annual charges on the whole cost- of making the/cha^ For" small Toads "or loads near/an --. e x i st-ihgk t r a p s f a r m e r . ;.a. s e c o n d a r y i n s t a l l a t i o n i s , i n most cases, more •economical,.. /The.'cases to/ be/questioned are those where heavy / / ,secphda;rles:-/c3;f/ c o n s i d e r a b l e • l e n g t h are necessary. ' ,,v;/: ./For/ examplev' suppose a. new: load o f 25 hp. ie to be served, which; i s .800; f't. from a present / i n s t a l l a t i o n . ' I n order to -get.. ... : 'proper- reguiation,. I t w i l l ; be- necessary to: s t r i n g No .0 secondaries .the whole-distance,.,;; The transformer, which,at present i s a, 75 kva., '.'- weTl-Toadedv changed to... a 100 kva . 11 w l l l . b e , assumed that the .necessary/poles w i l l be the same -.for e i t h e r a secondary or •'''prima'ry-'-ext.e.ns/idhv'tO' .the customer "'..//To' determine the most economical . i n s t a l l a t i o n we must : compare the annual costs of the two. a l t e r n a t i v e s . .These;-are made:,up:'as-follows': Seconds.ry I n s t a 11a11 on. - / / : i ' . / The annual; charges, on 800 f t . of three No.O secondary, IncTud-ing-.cost of conductor, crossarms, p i n s , i n s u l a t o r a n d labor c o s t . f o r i n s t a l l i n g , . , 2 , .Annual c o s t o f energy l o s s e s over the ;new secondary. . >3•''-":•: A n n u a l >,c-har:ge.s /on. cost to change transformers. , ..'•:•' :,:'"4/.-; Annual, charges on increase, i n transformer investment from a 75 t o a 100 kva. \ ' / '•/5 Annual/cost of 'increase-in-trans-former energy Tosses,/ 'Primary I n s t a l l a t i o n . -: I., Annual c o s t on 800 f t . of primary, unless the present primary :' extends, past the new l o a d . ' / . -'/, 2'.'''-•-•'•'Energy-losses-- on'the primary. / 3 - - Annual cost on a new transformer I n s t a l l a t i o n of 25 kva •- '//.- i n c l u d i n g l o s s e s 129 Some; such f i g u r e s as the f o l l o w i n g may be obtained: Secondary I n s t a l l a t i o n Primary I n s t a l l a t i o n . ' #1. • I' 3-9-00 §1 15.00 #2. 32.00 #2. . 2.50 #3 "• 2.00 #3 118.00 #4. • .'. ... • .-. . . . . . 35-00 # 5 . . . . . . . . - . . . / . . - . . . 14.00 1135-50 ' ' T o t a l . 412.2.00 The secondary i n s t a l l a t i o n w i l l have advantage of - $13.50 per year, which at:-15 per cent represents a c a p i t a l i z a t i o n of-$90.00. ..; I f the primary: i s already i n .place, the advantage would be s l i g h t l y w i t h the separate i n s t a l l a t i o n , although the d i f f e r e n c e In-cost: i s : s m a l l . . • • , . Economical S i z e of Secondaries. -~ When.it has been decided upon-that: a l o a d i s to' be c a r r i e d on secondary ,-• e i t h e r a f t e r some such c o n s i d e r a t i o n as the above, or when, w i t h a separate i n s t a l l a t i o n , i n order- t o [ l o c a t e the transformer conveniently, i t i s necessary to s t r i n g a-few spans of secondary from the transformer to the s e r v i c e , there- s t i l l remains the q u e s t i o n of the most economical s i z of .'/conductor-, t o be used. . Let us assume f o r t h i s example s m a l l 3<p power i n s t a l l a t i o n s f o r which the l o a d i s considered continuous, during the time of oper a t i o n . Equation of Annual.Cost. --Annual c o s t .on ~5<fr secondary =.< gfc o s t ' of wire -+-cost of s t r i n g i n g ! . per 100 f t '+g(cost of poles, f i x t u r e s and guys)) ? ;.--.'-.- cost of energy l o s s . J - - Where-g'srper cent i n t e r e s t , t a x e s .and d e p r e c i a t i o n ==13 per -cent f o r w i r e . . A s s u m e po l e s , f i x t u r e s and guys the same f o r a l l cases and neglect cost-,-in making comparison. No doubt -with a heavier s i z e of .'.wire/, a d d i t i o n a l .cost w i l l be found necessary f o r h e a v i e r cross arms, i n s u l a t o r s , e t c . and a d d i t i o n a l guying'. The study c o u l d be made so as.-: to inc l u d e ' these, a, s was, done i n the case:-of p r i m a r y - l i n e s - : i n Chap.IX but i n t h i s case t h i s .factor w i l l be l e f t out of the computations. In using- the r e s u l t i n g curves i t can be kept i n mind and w i l l have the e f f e c t of i n c r e a s i n g s l i g h t l y the economical l o a d -. on -those s i z e s . Annual charge f o r energy l o s s (3^) I 2 R * 365 * t -* = . 3 6 5 I aRtC. 1 1,000 1 130 z kw* x 1 0 * k w < I R = «3Dr - 10* A cr 12 „ „ ^ a r v • . / . 3E*cos ! ie ; , E ' c a s ' 0 -kW 2 ' - < '. Annual charge (-energy)-- 365,000 Br — — tG c 7 E z c o s z G . • . -.. In.:-, the'-.above* IT e q u i v a l e n t hours per day. I f - ' f ^ - e q u i v a l e n t hours per week which i s assumed i n t h i s case to be.hours per week which motor runs and power i s g i v e n i n horse-power. . : - • ' - • . -*- Let E' = 220 v o l t s ; cos 9 ~ .80 - - HP 2 * ( .746)* .;- Annual charge = 5 2 , 000 Br———-.,: - 1 C e 2 cos 0 " = -933 Drt.CL.HP2. • - ."••-"-'- B• ==• d i s t a n c e one way i n hundreds of f e e t . r = r e s i s t a n c e per wire per 100 f t . Annual charge per. 100 f t . (energy) === . 9 3 3 r t ^ C^ifP^-The. c o s t of the- conductor per 100 f t . was .determined from the number: of pounds, per 100 f t . , f o r d i f f e r e n t s i z e s , the cost . of t i e s , and the pr o p o r t i o n a l ; c h a r g e f o r f r e i g h t and i n j u r y t o returned r e e l s . ', This was put i n the form"•KinG~+ K„, so that the e f f e c t of a change i n p r i c e of copper eould^be s t u d i e d . The la b o r cost.was determined f o r average c o n d i t i o n s and reduced t o a cost, per 100 -ft • f o r each s i z e . The-proper overhead loading percentage was added t o both m a t e r i a l and labor... .Combining- these-. ywo charges, the expressions f o r annual charges on the conductor ••In place for' each size-were determined as shown i n Table 16, column 2. ' .. -Column 3 of the same t a b l e g i v e s the r e s i s t a n c e per 100 f t . of t h e v a r i o u s s i z e s of conductors and column 4 the corresponding expression f o r annual charge f o r energy loss,, found by i n s e r t i n g the proper value of r i n equation above. The-sum of columns 2 and 4 would g i v e the t o t a l annual- charges per 100. f t . f o r each s i z e of conductor. Equations of Equal Cost. " I f the ex p r e s s i o n f o r the t o t a l charges oh one s i z e o f wire i s equated to that f o r any other - s i z e , the r e s u l t i n g equation would represent the c o n d i t i o n s f o r which there i s no economical advantage of one.size over the other. This i s done'for each-adjacent s i z e i n the table'and the r e s u l t i n g ex-pressions are g i v e n i n column 5--If we consider two p r i c e s of copper, the r e s u l t s f o r any .1 rite mediate' p r i c e can be i n t e r p o l a t e d . In Table 17 the expressions f o r eriual annual cost are g i v e n w i t h the copper p r i c e s u b s t i t u t e d , using p r i c e s of 20 cts.. and 30 c t s . per pound.. CQ O o rs © C M O; o CO • d c pa w (Ci N CA r A o J>- O - r - rH CM . CO O'-. ' O H O c o H v o H in rH CO: o -y-+• + + + + 5 2 I S o o o o CM L A •vo r-1 •a u a v v o . L n m r A o o o o " o " d i o o b - • O CM O CO <f O OJ O O O I A Q A ' - O L A C O N ^ - ' - I H ' > O A O * A Q • • s r -- ^ j - • c o * t - ~ CM rH <f . J>- <H -5T.PJ.VO. tA'.VQ LTi to o b I O 60 co P4 11 I! II ii it i II .1 R H II «tl <j- <J' <t|' < <• CO o- CO rH O •. CC CVJ OA UA CXJ -4- c o " I O , r r ' rH \ .' rH rH O -'••-©-•''•' o Q. O O O , o o , o v o v o I A I A CVJ O o c o H O CVJ L A OA O o • HA ON CM LA L A O cvi rH t—i o o o • i<U L A t- v o m OA t-fc- L A o o © o o o rH - 3 - rH CO- v o LPl o o o o o © * * * VO H © rH , Q rH'l I A CD •O « a ! -p - P , CQ ^-). •H. • tn o CO o IA o •'•* o CM o •H - P O r-i •P CQ 53 O o sd • o © w «. o rH cS. 3 OA rH i n + o O A rH VO i n ha I A H rH m rH OA L A •o« LA OA . OA • • CVI • <-f LA rH r A LA LA CM OA c o VO c o H o H v o C^ • * * . * H rH + + + + • 2 o • J ou o Q . - ^ ' VO VO H v o H CM Cvl o LA H CO X CVI '•'JL CM Jl ' IA '!>-rH -.rH.' ' '•• O I A 1>- o t A , c o O rH , CM CM CM r A + , +, +, + d* ! A K A <t CM OA CM CM <T o t-t A L A VO CO OA •fDt '•' v ^ f A I A H A I A I A rH rH H rH rH • . • 0 » ,». o CM I A rH I A I A I A r A I A r A H © «H 03 •vo cvi »fc =& t A K A O O o o o o ..«fc r A I A K A a o o o t A Table 17 131 S i z e of Wire S i z e of • Wire I f C CO • 30 i f c c w - .20 6 ' to 4 \,C cHP e = 55-99 t,C eHP* - 39-04 4 to 2 tt 165 -77 11 _ 113.57 2 •..to 6 11 = 465-00 • i i ••.•• _ _ 317-20 0 t o ; 00 1! 788 .50 » = 547.50 00 to 000 If = 1276.80 it _ _ ' 889-80 000. • •to- 0000 tt — 1784.40 11 • • = 1214.40 - : Value'/-of-'t,,CJ'./. - In -previous, chapters the v a r i a t i o n of: the cost o-Penergv with the load factor and hence with the Equivalent ' hours ms ;sbeen ;expiained.// In;: ,,Appendix.A,t;: the; method, of approxi-mating the value of VCL i s c a r r i e d out, / In t h i s case, the loads : are"considered small, c o n s i s t i n g of not more than two or three motors, which, would give a. f l a t load curve. The value of equiva-l e n t hours per week, V , would, then be p r a c t i c a l l y equal-to the -average number of .hours per week which the -motors .are r u n I n case of loads/: of a / d i f f e r e n t character, a more, accurate determina-t i o n ^ o f - t ^ would "be- necessary'-. The values of t»,: for-any load : factor, and the. corresponding values of t a.C eused are given below., Tab le 18 the vffiSe°^Vi'cf^r a V v a l J i ^ t ^ f l 6 U r e S ' 6 i V l n S 132 Curves , f o r Economical Conductor S i z e • - The two; set s of curves given i n P i g . 49 and" F i g . 5 0 c a n "Be p l o t t e d from the equations i n Table 1 7 u s i n g - a s ; c o o r d i n a t e s the average number of hours of ope r a t i o n per week and the l o a d iri' horsepower (the load i s given i n horse-power f o r convenience i n use w i t h loads c o n s i s t i n g of one or two motors, which are so r a t e d ) . The curves are s i m i l a r to those g i v e n for " "Power L i n e s " i n Chap.IX.-/ The conductor s i z e s given p e r t a i n to the areas between the curves, s i n c e the curves themselves are the l o c i of p o i n t s of equal c o s t . For example (using 20-ct.copper) -three' No.-2- secondary: .is more economical than three. No>4 f o r a. 20-hp-load,' i t " 1-t operates more than 6-g- h r . per ?;eek. I t Is l e s s econom-i c a l than three- No• ©; i f . t h e 20-hp., motor operates more than 54 hr. per week. - S i m i l a r l y f o r a load operating A hr. per week, three No.2 i s the most economical secondary,.for loads between 21%-hp. and 38g- hp. i f h i g h e r - p r i c e d copper i s being" used, the corresponding '.-loads'- and hour's of o p e r a t i o n w i l l be i a r g e f ag-shown- by f i g 5 0 ' . The di s t a n c e .•which the point r e p r e s e n t i n g a g i v e n l o a d l i e s from-e i t h e r boundary curve i s : an i n d i c a t i o n of the amount of economical , advantage of the s i z e of wire shown, over the next adjacent s i z e . N a t u r a l l y , these curves apply - only to concentrated loads of the : character assumed. S i m i l a r curves: may be developed f o r any type of- l o a d - d e s i r e d by the i n c l u s i o n of the proper- f a c t o r s ' i n "making up, the equation. For,loads which are not concentrated, the secondary may be studied, by d i v i d i n g , i n f o s e c t i o n s . Curves f o r l a r g e power loads -can be s i m i l a r l y developed. I n that case, however, i t i s pro-bably b e t t e r to'designate the load i n k i l o w a t t s and use values- of ta* equivalent• hours" per day, as was done i n the case of power prim-a r i e s , Chap.' IX-Problems In Power Secondaries Comparatively Simple. - The problems r e l a t i n g t o power secondaries.are comparatively simple. With good cost data on the i n s t a l l a t i o n of such secondary and t r a n s - ; formers, load c u r v e s . f o r power secondaries as shown i n Chapter VI, and/curves :f o r ••economical conductor size,, n e a r l y a l l such .problems ..y as are d i s c u s s e d i n t h i s chapter may be r e a d i l y s olved. Power secondaries": may be, of course, a r e l a t i v e l y l e s s .important,; -.-part of the system, than transmission" l i n e s , p r i m a r i e s or l i g h t i n g secondaries .-.: Notwithstanding t h i s . f a c t , .however, the study of t h e i r economy should'not be overlooked. - '• S SIS Si if * ' 3 3 133 CHAPTER -XIII UNDERGROUND LINES Voltage - Cable S i z e - Route - Number of Duct .Line -Arrangement of Ducts and Cables • /'The'majer part of t h i s t h e s i s has been devoted t o the pro-•blems connected w i t h overhead l i n e s . This was done not because' the economic' study of underground l i n e s i s any l e s s important than t h a t of overhead. The o p p o r t u n i t i e s f o r e f f e c t i n g economies are j u s t as gr e a t , or perhaps g r e a t e r , on underground l i n e s on account of' the gr e a t e r cost of c o n s t r u c t i o n . I t i s a f a c t , however, t h a t on most of the c e n t r a l - s t a t i o n systems, the underground l i n e s are of s m a l l extent as compared w i t h the overhead. Overhead work i s preferred,where p o s s i b l e , underground being used c h i e f l y i n congested down-town areas and f o r t r a n s m i s s i o n l i n e s where h i g h voltage' i s not permitted by the m u n i c i p a l i t y , or i s considered unsafe. In some c o u n t r i e s , the case i s q u i t e d i f f e r e n t , underground work predominating. I n any case the p r i n c i p l e s employed i n s o l v i n g the problem of underground l i n e s are the same as those used f o r overhead which have been e x p l a i n e d and e x e m p l i f i e d . Only the con<-d i t l o n s of the i n d i v i d u a l problems are d i f f e r e n t . Some of the a f f e c t i n g f a c t o r s and s p e c i a l problems r e l a t i n g to underground l i n e s w i l l be. taken up-in t h i s chapter. The n e c e s s i t y r a r e l y a r i s e s to make a choice, on the b a s i s of economy, between an u n d e r g r o u n d - i n s t a l l a t i o n and an•••overhead- •' Overhead, as a r u l e , c o s t s only a f r a c t i o n of the amount necessary t o i n s t a l l underground f o r the same loa d . An overhead t r a n s m i s s i o n -l i n e , f o r . example, can be b u i l t f o r between $3,000 and $4 ,000 per mile to Garry the load which would r e q u i r e an underground i n s t a l l a t i o n c o s t i n g -$15.,.000 to f18,000 per m i l e . Overhead a l s o has the advantage of g r e a t e r f l e x i b i l i t y . w h e n changes are necessary to accommodate I n c r e a s e s - i n - l o a d . 'The choice of underground i s u s u a l l y based on con-s i d e r a t i o n s of n e c e s s i t y ( i n congested a r e a s ) , ' s a f e t y , s i g h t l i n e s s , e t c . ' ' The nature of the c o n s t r u c t i o n on underground l i n e s makes the n e c e s s i t y f o r s t a n d a r d i z a t i o n and f o r the best possible, workmanship im p e r a t i v e . -The comparative i n a c c e s s i b i l i t y and the high cost of i n s t a l l a t i o n - m a k e r e p a i r work very expensive, True economy l i e s i n using- a l l means p o s s i b l e to reduce- such r e p a i r work t o a minimum. ' Problems S i m i l a r to those of Overhead L i n e s . - A great many of the problems of underground' l i n e s are very s i m i l a r t o those already d i s c u s s e d f o r overhead. .There i s ^ f o r example, the same general c l a s s i f i c a t i o n i n t o t r a n s m i s s i o n l i n e s , p r i m a r i e s and secondaries, w i t h the s p e c i a l c u e s t i o n s a r i s i n g from each. The economy of any i n s t a l l a t i o n should be s i m i l a r l y s t u d i e d w i t h respect to v o l t a g e , voltage drop, conductor s i z e , transformer s i z e and l o c a t i o n , most economical ro u t e , e t c . The s o l u t i o n of these problems w i t h respect to underground l i n e s i s l i m i t e d by t h e i r c h a r a c t e r . I n f l e x i b i l i t y and h i g h cost of c o n s t r u c t i o n make i t necessary that o r i g i n a l i n s t a l l a t i o n s be designed w i t h s u f f i c i e n t thought toward probable ' 1 3 4 .future-GondiiIons, even at the expense of apparent present - ; economy-in some cases. There are some other problems concerning the c o n s t r u c t i o n i t s e l f , which 'apply only to underground l i n e s , -such as the .'number-and arrangement of • ducts In a r u n , and of cable i n the ducts, e t c . ' These w i l l be taken up a f t e r some of the questions of v o l t a g e , conductor s i z e , route, e t c . , have been b r i e f l y considered. Voltage.-. - The d e t e r m i n a t i o n of the most economical v o l t a g e i s rarely'''dependent on the economics of the underground system alone. I n t r a n s m i s s i o n , the v o l t a g e i s l i m i t e d by the type of • cables available'- At present, about ; 3 3 R 0 © 0 v o l t s f o r three 'con-ductors and 6 6 , 0 0 0 v o l t s f o r s i n g l e conductor i s the p r a c t i c a b l e l i m i t , although higher v o l t a g e s - 1 3 2 , 0 0 0 v o l t s - are being con-sidered, and w i l l probably be used i n the near, f u t u r e . There are a few- 1 3 2 , 0 0 0 v o l t s i n g l e conductor cable- i n s t a l l a t i o n ' i n New York, .London and --on-the c o n t i n e n t . The.economical advantage of..the use - . of 1 3 2 , 0 0 0 v o l t cables cannot be determined u n t i l operating s t a t i s -t i c s have been r e l e a s e d f o r a n a l y s i s , -meantime t h e i r use i s i n the .experimental'., stage .. For power lines', one: or two standard v o l t a g e s are u s u a l l y chosen f o r the whole system. While the economics of the- underground,lines should be considered In t h i s choice, i t i s by no,'-means .the only factor,- A study of the system as a whole i s necessary. ' Conductor" S i z e • - A new element i s i n t r o d u c e d i n the study of the most - economical cable t o carry any load or the most economical l o a d f o r any c a b l e . The l i m i t i n g f a c t o r i n t h i s case i s u s u a l l y the current carryihg'.capacity of the c a b l e . .- This, i s governed by the .heating of,.the c a b l e s . I t depends not" only on the s i z e . o f conductor . and on the I n s u l a t i o n but on the l o c a t i o n of the cable i n the duct run, the number of ducts, the c o n d i t i o n of the surrounding s o i l and the'shape of:, the curve of; the l o a d on, the-cable i t s e l f and on the -other cables i n adjacent ducts. The' q u e s t i o n of- the heating of cables has- been a t t r a c t i n g a great d e a l of", a t t e n t i o n ' r e c e n t l y and a number'of a r t i c l e s on t h i s subject have appeared in>the,-Journal o f the A,. I . ,"F. .B • and other - p u b l i c a t i o n s . The study i s s t i l l I n the making and, while much v a l u a b l e data have been c o l l e c t e d , there i s s t i l l much to be done. At present-there i s no g e n e r a l l y accepted standard on such matters. I t i s safe to say that i n p r a c t i c a l l y a l l cases of ordinary loads, - t h e ./appar^ht^eebnomleal load'-.for: a, c a b l e , basing: t h e - f i g u r e s on the normal l i f e of t h a t c a b l e , w i l l - b e considerably more than the safe -current c a r r y i n g c a p a c i t y , i f the cable i s t o f u l f i l l i t s normal ; l i f e - . For example, F i g . - - 5 1 shows, t h e annual c o s t of t r a n s m i t t i n g , loads over No. 0 0 underground cable at 2 3 , 0 0 0 v o l t s f o r v a r i o u s values of equivalent hours. In-making the computations, d e p r e c i a t i o n was f i g u r e d , on the b a s i s of a 2 0 - y e a r l i f e f o r the cable. I t i s seen that the most economical loadings on that b a s i s would be between • 2 0 0 ' and 3 O O -amp:.-depending on the l o a d f a c t o r ( o r the e q u i v a l e n t hours). 'Figure . 5 2 gives the average a l l o w a b l e load f o r such, a cable i n v a r i o u s combinations w i t h s i m i l a r cables^ based on the heating of the c a b l e . I t shows t h a t the safe loading In duct runs of the u s u a l s i z e i s i n the neighborhood of only 1 0 0 amp., or about • .• •••• •. • •JTi-'ilJii 135 50 per cent of the most-economical load, as shown by F i g . 51 . I t might be thought p o s s i b l e to r u n the cable at a higher average load than t h a t given as the safe load, l e t t i n g the increased d e p r e c i a t i o n -due to the shortening of the l i f e of the cable be balanced a g a i n s t the i n c r e a s e d economy of o p e r a t i o n . Not enough data are a v a i l a b l e on the extent to which a cable Is damaged by an o v e r l o a d to warrant any'figures on t h i s subject. I t : i s q u i t e probable t h a t the damage done would be greater than the economy ef f e c t e d , i n most cases. In the axample represented by F i g . 51,. i f the load, were such as to reduce the l i f e of the cable to 10 years, the apparent most economical l o a d at tC f i = «10 would be.about 225 amp. However, i f a load of 140 amp. or g r e a t e r c o u l d be c a r r i e d without reducing t h e . l i f e of the cable to '.less t h a n 1 0 years, the annual cost per ampere would be l e s s than that .at-100 amp. w i t h a 20-year l i f e f o r the cable. I f a cable is/to-be. run a t a load greater than that considered-as per-f e c t l y safe..-from a standpoint of h e a t i n g , there i s the f u r t h e r c o n s i d e r a t i o n . o f i n c r e a s e d d i e l e c t r i c l o sses and increased r e s i s -tance of:: conductor . The problem has great p o s s i b i l i t i e s when . • more: data become a v a i l a b l e . . / - - F i g u r e 51 a l s o shows how the most economical load increases -as the:: load f a c t o r , and hence the value of e q u i v a l e n t hours, decreases. Since cable- heating has somewhat of a cumulative " e f f e c t , i t i s -generally ./possible-to-carry higher loads at low than at h i g h load : f a c t o r s -.//The safe load w i l l , -therefore-,- bear somewhat the same : relation/'-.to. the most economical load, i n any case . Hence i t appears : t h a t , i n . most c o n d i t i o n s met w i t h • i n p r a c t i c e , the load c a r r i e d w i l l •be •governed/.by/-, the capacity of the" cable r a t h e r than by economy as u s u a l l y considered,/although, of course> economy i s r e a l i z e d by not overloading a:cable.to the point of i n j u r y . . Economical Route. - The most economical route f o r an under-ground-' line.-may.' be an important c o n s i d e r a t i o n i n - i t s l a y out. On account of t h e .high c o n s t r u c t i o n c o s t , the use of the shortest - p o s s i b l e r o u t e i s even more important i n t h i s case than, M t h over-head; l i n e s O t h e r things being equal, t h i s might o f t e n p o i n t to the -use of p r i v a t e right-of-way . T h e ' r e l a t i v e i n a c c e s s i b i l i t y of such • l i n e s on p r i v a t e property, the p o s s i b i l i t y of i n t e r f e r e n c e by f u t u r e • b u i l d i n g s , "etc (unless the property i s bought o u t r i g h t ) and the -d i f f i c u l t y o f . d r a i n i n g manholes i n many cases, g e n e r a l l y make i t preferable, to keep such l i n e s on the p u b l i c highway, The number and l o c a t i o n of manholes necessary may have considerable, bearing on the choice of a.route. In runs of only a few ducts, the cost of Manholes i s a l a r g e p r o p o r t i o n of the t o t a l and hence i s r e l a t i v e l y very important. In runs w i t h a large number of ducts'the manhole cost i s l e s s important compared w i t h the t o t a l cost of t h e - l i n e , but In any case, the "-route'requiring the fewest manholes, other t h i n g s being' equal,-has -considerable advantage. Secondary D l s t r I b u t i o n . - The problem of underground secondary d i s t r i b u t i o n Is q u i t e d i f f e r e n t from that on overhead l i n e s . Trans-former l o c a t i o n s are l i m i t e d to the manholes which i n t u r n must be 136 spaced f o r convenience In i n s t a l l i n g and maintaining the cable. • The' secondaries and s e r v i c e s must be designed to transmit the required,,load w i t h ample p r o v i s i o n f o r future contingencies. The changing of. secondaries of s e r v i c e s or of transformer l o c a t i o n s i s a con s i d e r a b l y more se r i o u s matter than on overhead l i n e s . In g e n e r a l the design of an underground secondary system Is a problem r e q u i r i n g a great, d e a l of care and good judgment i n p r e d i c t i n g .•-future loads and p r o v i d i n g f o r them i n an economical manner. ' v;. . • Number of ducts i n . a. Duct L i n e . - There are a number of-problems':'relating to the c o n s t r u c t i o n and arrangement" o f ducts : and cables.which are worthy of a t t e n t i o n . An example w i l l be gi v e n here, of a method of determining the most economical number of ducts,which should be placed together i n one duct run- While i t would not: always be p r a c t i c a b l e to l i m i t the number of ducts to t h e . f i g u r e s - w h i c h might r e s u l t from such a study, the knowledge thus gained.'would at l e a s t be an, a i d i n making the ch o i c e . For s i m p l i c i t y , i n t h i s example i t w i l l be assumed th a t the ducts are a l l f i l l e d , "the cables a.re a l l of, the same s i z e , and the loads c a r r i e d on a l l the cables, are of equal amounts a n d , i d e n t i c a l char-a c t e r isticS:. . N a t u r a l l y such a c o n d i t i o n would r a r e l y be found i n p r a c t i c e H o w e v e r , i f the • method of a t t a c k i n g the problem Is. once -established., it,.can be extended to. cover other: cases of d i s s i m i l a r cables and. loads .:-The ba;sis for- determining economical c o n d i t i o n s i s the annual cost-per ampere- t r a n s m i t t e d over the l i n e as a-whole . The equation . fo r annual- c o s t of: the l i n e i s . made up as follows:: . Annual cost per 1,000 f t .=H-g (cost, of 1,000 f t . of d u c t ' l i n e , ..,.. . . o f "n" conduits, i n place) ;: . - . - ' : . " - • : • " - • . : " - : - ' -j-g (average cost per 1,000 f t . f o r .-'.-:•.-•-• /..---.;. manholes complete w i t h sewer . . • . • . . .connections) r- - . •'; • +.g .-(cost per 1,000 f t •. of "n" cables i n s t a l l e d ) :.-" 4--cost-of energy l o s s e s per year over '. - w/-':- 1,000 f t . o f — n~ c a b l e s . ;." ; ;:.- : •;• . , ^ • (67) " Post :of Duct. Line . - The cos t of i n s t a l l i n g a duct l i n e i s -made- up o f : - •' - i . " - Cost of excavating, b a c k f i l l i n g , paving, e t c - , which Is ne a r l y p r o p o r t i o n a l to the wid t h of the duct l i n e . I f the- cross-s e c t i o n ; of the duct i s square, or nearly so, the width i s p r a c t i -c a l l y p r o p o r t i o n a l to the square r o o t of the number o f conduits, "n".• . 2 . C o s t o f - m a t e r i a l s used and l a b o r of . i n s t a i l i n g which i s p r a c t i c a l l y p r o p o r t i o n a l to the number of conduits, "n" . ,. 3 . Cost o-'f - t r a n s p o r t a t i o n , t o o l s , water connections, e t c . which i s , p r a c t i c a l l y the same f o r " a l l s i z e s . 137 The t o t a l cost of the duct i n place i s then represented approximately "by the expression K,+ K t / y T f K ; n " w h e r e K, , X t and •' K 3 are constants to "be determined from a c t u a l f i e l d costs on s e v e r a l jobs. Cost of Manholes . - The cost of b u i l d i n g a standard manhole i s u s u a l l y easy t o determine. The cost of- drainage and sewer connections w i l l vary, of course, w i t h d i f f e r e n t " c o n d i t i o n s en-' countered.. : An average f i g u r e must be assumed. By determining " the average number of manholes per 1,000 f t . of duct l i n e , the .. annual charges per 1,000 f t . f o r manholes completed may be e a s i l y computed. Cost of Cables. - The cost per foot of cable i s r e a d i l y de-termined from c u r r e n t p r i c e s and"average-labor cos t s of - the system under c o n s i d e r a t i o n . Energy -losses. - The energy l o s s depends on the current c a r r i e d . I f the number, of conduits i n the duct i s l a r g e , the all o w a b l e "current per cable w i l l be smaller than i n . a duct r u n of few.'conduits on account of the increa s e d heating e f f e c t . A study of .the Current c a r r y i n g capacities ;;-of . l e a d covered -cables under v a r i o u s ' c o n d i t i o n s i s g i v e n by Ralph W. Atk i n s o n , In the J o u r n a l c f the A. I . E- E. f o r September, 1920. By use of the f i g u r e s and c h a r t s .given: i n t h a t paper, the v a r i a t i o n of the >:•;. all o w a b l e current-on a cable w i t h the number of conduits i n the duct l i n e .was d e r i v e d , f o r three types of cables, and p l o t t e d i n ; F i g . 5 2 . F i g u r e 5 3 - i s derived' from F i g - 52 and gives' the t o t a l -allovjable' number of amperes c a r r i e d on the duct l i n e as a whole, f o r any number "of c o n d u i t s . I f I c • the a l l o w a b l e current per cable, and r-. = the r e s i s t a n c e per 1,000 f t . of one conductor- of one cable'-." The 'annual -cost of energy losses per 1,000 f t . f z ' C e «= n < 31 * r * t * 365 * / c 1,000 g. - The va l u e of 'g" i . e . , the per cent of i n t e r e s t , taxes, d e p r e c i a t i o n , e t c . w i l l vary f o r the d i f f e r e n t c l a s s e s of m a t e r i a l . Such f i g u r e s , as the f o l l o w i n g can be assumed f o r any-problem. I n t e r e s t 7 per cent '••--Taxes-.-'.:» .--*? . . i" .-.-.'.. . .' .•.••. . '• .-, . 2 per cent Depreciation,' etc . on-ducts . 2-per cent on manholes 5 per cent on cables ...:..-..'..:..... .-.5 per cent". .'•-, T o t a l Annual Cost. - A f t e r the v a r i o u s . i n d i v i d u a l c o s t s , as i n d i c a t e d above,' have been evaluated,, they may be combined to gi v e the t o t a l annual cost- Figures 5 4 , . 5 5 , and 56 show, f o r the ' three d i f f e r e n t types of. cable, -the v a r i a t i o n of the cost of the d i f f e r e n t Items: given above as a f u n c t i o n of the number of:-.ducts. i n the l i n e . The numerical v a l u e s , of course, apply only to the l o c a l c o n d i t i o n s f o r which they were, d e r i v e d . The curve f o r t o t a l ; 138 annual cost I s a summation of the separate-charges. I f the t o t a l annual c o s t f o r any given,number of-ducts a n d cables: i s , d i v i d e d . -by the t o t a l a l l o w a b l e c u r r e n t c a r r i e d , as given by F i g . 53- , the cost per ampere i s obtained.. This I s g i v e n In. the Upper curve : on F i g s . 54, 55 and 56 . R e s u l t s Shown. - The curves i n d i c a t e c l e a r l y the h i g h cost of l e s s than fouraducts I n a. run.. -For l a r g e r l i n e s , the point-of:-economy Is not; so p l a i n l y 'shown. There appears to be comparatively l i t t l e d i f f e r e n c e i n economy between duct runs of from 4 -to: 16 . . ducts. The curves f o r 2,300 - v o l t cable, F i g . 56, i n d i c a t e s a minimum point, at. about eight- ducts, /but the-curve :• i s - f a i r l y - f l a t . The reason f o r the small d i f f e r e n c e i n cost shown i s due t o the f a c t t h a t , as' the- number of ducts •••increases',"-, the a l l o w a b l e current per cable decreases. I t would seem to be i n d i c a t e d , i n t h i s case, , that .there, would-be co n s i d e r a b l e advantage/ i n not • b u i l d i n g duet, runs -to provide too f a r Into the f u t u r e . I f the t o t a l cost per ampere of a six-, or -eight.-duct .run i s . no more than that o f a 16, i t would-." .be b e t t e r t o b u i l d the smaller -size and when tha t Is f i l l e d , b u i l d another -of the same s i z e , thus saving the investment-on empty ducts .' f o r a c o n s i d e r a b l e p e r i o d . Of course, i f d i f f e r e n t cost f i g u r e s were, used or d i f f e r e n t assumptions as- to--cable-sizes and loadings were < -made, the points- of g r e a t e s t economy might pe more pronounced. Hence these curves must be considered as examples of the method only and not f o r g e n e r a l a p p l i c a t i o n . Arrangement of ducts.: - Another d e t a i l , of c o n s t r u c t i o n which •-, might o f f e r a p r o f i t a b l e f i e l d f o r i n v e s t i g a t i o n i s the arrangement . -of ducts i n a duct-run. I t Is r e a l i z e d that: the p r a c t i c a l , d i f f i c u l t - ; , i e s i n c o n s t r u c t i o n may be the d e c i d i n g f a c t o r i n t h i s matter. ,: However,, i t must be; kept. In mind t h a t the c a r r y i n g -capacity,of a. cable depends a great" d e a l upon i t s l o c a t i o n w i t h respect to other cables. The; c e n t r e cable i n - a nine duct, run, arranged i n , a. square , w i l l have co n s i d e r a b l y l e s s c a p a c i t y than the outside c a b l e s , while the corner c a b l e s , w i l l have-more -capacity than those between ( F i g . 5 7 a . ) . The nine duct system ( F i g . 5 7 a )'is about the most economical, arrangemehtAOf: duct f o r 3 'conductor cables used as, second© *; a r i e s connecting two. s u b s t a t i o n s . F i g - 57 b . - l 6 duct system - shows •the duct 'arrangement which-would, be-.used f o r primaries 1 where-single. conductor cables would be used f o r the higher v o l t a g e s 33,000 v o l t s t o .66",000 v o l t s ..- Each three-phase c i r c u i t , would occupy the. three . ducts I n each corner. This arrangement of c i r c u i t s g i ves approx-i m a t e l y t h e - ' e q U l l a t e r a l - t r i a n g l e arrangement of the three phases as, -d e s i r e d i n 3 phase t r a n s m i s s i o n . The remaining four inner ducts are -a v a i l a b l e ; f o r miscellaneous pi>/iposes, such.as one,or two 3-conductor c i r c u i t s , ground conducto-rs, as w e l l as l i g h t i n g and communication c i r c u i t s f o r , systems used., The v a r i a t i o n i n current c a p a c i t y . o f s i m i l a r cables i n d i f f e r e n t ducts p o s i t i o n s i s due t o the r e l a t i v e c a p a b i l i t y of heat d i s p e r s i o n of the, v a r i o u s p o s i t i o n s . I t would be . a n " i n t e r e s t i n g problem to determine.how much e x t r a expense would be j u s t i f i a b l e i n order to use some arrangement which would accomplish b e t t e r heat d i s p e r s i o n . The problems of i n c r e a s i n g the current 139 c a p a c i t y of a duet l i n e by lasing. the centre, ducts f o r some form of a cooling'/system or /of f l o o d i h g the- runs /are 'similar . No / d e f i n i t e - data .are at /present, /available on these questions . :// Arrangement/:of- Cables; i n / a . Duct Line/. - The /question/of the -/ r e i a t l ^ /arrahgeme:nt/,of^ eable/s i n a; given : duct run. I t . r a r e l y , happens . that//the ./cables- a r e a l l / o f /the -same '-size or :klnd. or c a r r y ' / /similar/loads:; : The , d i v e r s i t y 'between loads/ may have- considerable bearing ph the/mq 'Obviotisly /a/o-able- par-rying-a heavy l o a d / w i t h .a' h i g h - l o a d f a c t o r .';',. can :/qpehate/ more/ -e"'f f i e l e n t l y i f p l a c e d i n an-outside/: duct where-,-the/&a/t >P^ i f -a cable; -carrying':nigh%'''llfehtl:% ; l o a 'only -is- p l a c e d i n an / i n t e r i o r /duct, s u r r o u n d e d cables with'day power loads only, and the -peak-'loadS: do not.-' overlap- -the', l i g h t i n g cable ban /be : :operaterd/,at a. 'higher load' than would : be :bonsidered :-safe' /.with a l l - '-..cables-similarly- loaded--- . /-'./- ' ' / -: -•/;////./Bo s s l b l e , S a v i n g s///Large. -/The p o s s i b i l i t i e s f o r economic' investigations-/on /und/er ground l i n e s / a r e / l a r g e . The; loads'/carried' •/are: ,-fal'rly -heavy as - 'a r u l e , /Since /undergrduhd work 1 s" u s u a l l y : done ;in'/c/png/e'Stedydlstricts . /The:/construction'cost i s high/// The/possible ec/6^ .bml/e sV/in/Gap ,Expehdltures are- many/, not only-does t h i s mean a saving - i h r l n i t l a i / c a p also: 'means reduced f Ix-ed//charges' /to/operations i n ^ subsequent years..; / examples ••' : prese n t e d - , ^ problems /mentioned :arp Intended/, '•merely.'/as././sugge/stiqhs/'for s The- a v a i l a b l e ; / data'/ on .healing :- of •/'.'cables'.,.-/allowable p u r r e n i c a r r y I'ng capacity ,:; ageingp-etc are "as/yet so u n r e l i a b l e as / to render, the '/conclusive."'/ solutions//of,/apy/1^ CHAPTER XIV THE SYSTEM AS A WHOLE There s t i l l remain a great mania; problems, both la r g e and s m a l l , which are c o n t i n u a l l y c o n f r o n t i n g engineers i n charge of d i s t r i b u t i o n systems. Some of these are s p e c i a l cases but can be solved by an adaptation o f the p r i n c i p l e s i n d i c a t -ed herein*. Others apply to other parts of the system than the the d i s t r i b u t i o n l i n e s , such as to d e t a i l s i n the design of the generating s t a t i o n or the s u b s t a t i o n s . No attempt has been made to cover such questions s p e c i f i c a l l y , although the general methods co u l d be a p p l i e d . There are s t i l l other problems which d e a l w i t h the system as a. whole. While i t i s net w i t h i n the province of t h i s work to discuss such questions at lengthy a few of the most Important w i l l be mentioned here. A c o n s i d e r a b l e amount has been published at d i f f e r e n t times and at v a r i o u s places about the proper l o c a t i o n of a generating s t a t i o n * T h e o r e t i c a l l y , I t should- be l o c a t e d i n such a way, w i t h r e s p e c t to the loads to be.carried,' t h a t the t o t a l annual cost on the completed system w i l l be a minimum. This does not n e c e s s a r i l y mean tha t the best l o c a t i o n i s a t the center of g r a v i t y of the"loads as i s sometimes s t a t e d . I f we consider two equal loads, one o p e r a t i n g 24 h r . per day, and the other 1 h r . per day, i t i s ob v l o u s that the generating s t a t i o n should not be h a l f way between but, r a t h e r , nearer the load w i t h the high load f a c t o r * From a p r a c t i c a l standpoint, the l o e a t l o n t h e o r e t i c a l l y best i s r a r e l y a t t a i n a b l e . There are many other important c o n s i d e r a t i o n s such as t r a n s p o r t a t i o n f a c i l i t i e s f o r f u e l , a v a i l a b l e supply of c o o l i n g water, p r a c t i c a b l e b u i l d i n g s i t e s , e t c . , which govern the choice. I t might be s a i d that, w i t h the present-day design of s t a t i o n s and the large c a p a c i t i e s being a t t a i n e d , the matter of a v a i l a b l e water supply Is becoming a l l important. The question of generating energy a t the mouth of c o a l mines and t r a n s m i t t i n g to d i s t a n t points has been much t a l k e d about r e c e n t l y * Such a p r a c t i c e seems at present, to be limited,, however, to e x c e p t i o n a l cases where an ample water supply may be had. In such cases economy i s r e a l i z e d , i f the energy can be so generated and t r a n s m i t t e d to the point of u t i l i z a e t i o n at a l e s s c o s t per year, I n c l u d i n g investment charges and c o s t of" l o s s e s on t r a n s m i s s i o n l i n e s , than the cost of the same v energy generated a t the feeding p o i n t , I n c l u d i n g the c o s t of t r a n s p o r t i n g the c o a l by f r e i g h t . In any case the economy of any l o c a t i o n f o r a generating s t a t i o n i s determined only by a complete study of the annual c o s t s of . a l l aternatlves« The l o c a t i o n of a s u b s t a t i o n i s a somewhat s i m i l a r problem*. In t h i s case, however, the l i m i t i n g f a c t o r s are u s u a l l y not so many, and the choice, may be made on a more t h e o r e t i c a l b a s i s 0 A c a r e f u l c o n s i d e r a t i o n of the loads'to be c a r r i e d , the lengths of the necessary l i n e s , both underground and overhead, and the energy , l o s s e s Involved, w i l l u s u a l l y be very p r o f i t a b l e . I t o f t e n occurs that the expenditure of a l i t t l e more money i n the purchase of the best p o s s i b l e s i t e may be r e p a i d s e v e r a l .times over i n the * . economies e f f e c t e d on the d i s t r i b u t i o n system. :• The previous chapters i n t h i s t h e s i s have discussed the problems p e r t a i n i n g to each part of the system w i t h very l i t t l e r e g a r d f o r the r e l a t i o n of that p a r t fcc5 the system as a" wholes I f the study of the economies of the d i s t r i b u t i o n system i s to be made complete, t h i s I n t e r - r e l a t i o n ' m u s t - b e considered. For example, we may determine the most economical drop i n voltage on a tr a n s m i s s i o n l i n e and a l s o 'on a power l i n e . However, i n order to Pro p e r l y .serve the customer, the vo l t a g e r e g u l a t i o n must be maintained to a c e r t a i n standard* The problem is., then, to determine the most economical design and arrangement of t r a n s m i s s i o n l i n e s , s u b s t a t i o n , power l i n e s and r e g u l a t o r s to accomplish the d e s i r e d r e s u l t . This may p o s s i b l y be somewhat d i f f e r e n t than ..the s o l u t i o n s for. the I n d i v i d u a l parts*. Such a study i n v o l v e s a c a r e f u l determination of annual charges on a l l types of c o n s t r u c t i o n and a complete computation of the cos t o f energy l o s s . Immediate r e s u l t s should not n e c e s s a r i l y be expected from an a p p l i c a t i o n of engineering economics to an e s t a b l i s h e d d i s t r i b u t i o n systeme I n some cases the money saved on one or two l i n e s may prove the work w e l l worth w h i l e . In other cases, the r e s u l t s w i l l be evident only a f t e r some l e n g t h of time* I t i s r a r e that a. system can be brought up to an economical standard i n a short time* U s u a l l y the engineer must be content to Improve c o n d i t i o n s g r a d u a l l y , by designing new extensions and r e b u i l d i n g o l d work, here and there, i n accordance w i t h economical p r i n c i p l e s . The f i n a l r e s u l t s w i l l be shown i n the improved e f f i c i e n c y on the system as a whole. Often, t h i s w i l l take the form of ,a r e -d u c t i o n i n o v e r a l l l o s s e s on the system, a I t hough I t h i s i s "not n e c e s s a r i l y the case© The economical percentage o f l o s s w i l l depend on the r e l a t i o n between c o n s t r u c t i o n c o s t s and the cos t of energy, which may be very d i f f e r e n t f o r d i f f e r e n t systems• Hence the percentage of energy l o s t I s not a true measure of economy. The I d e a l c o n d i t i o n of maximum e f f i c i e n c y to which i t i s the pur-pose of a l l economic study to c o n t r i b u t e , i s that c o n d i t i o n s i n which every customer i s provided w i t h a reasonably good q u a l i t y of s e r v i c e a t the l e a s t p o s s i b l e c o s t over the whole system. CHAPTER XV INDUSTRIAL PLANT PROBLEMS A p p l i c a t i o n to i n d u s t r i a l p l a n t Problems of the P r i n c i p l e s of Economics O u t l i n e d f o r E l e c t r i c a l D i s t r i b u t i o n This t h e s i s has d e a l t p r i m a r i l y w i t h e l e c t r i c a l d i s t r i b u t i o n problems from the p o i n t of view of the c e n t r a l s t a t i o n * . The purpose, i n g e n e r a l , has been to i n d i c a t e means of studying a d i s t r i b u t i o n system w i t h the view to t r a n s m i t t i n g e l e c t r i c a l energy from the generating p l a n t t o the customer at the l e a s t p o s s i b l e o v e r f a l l c o s t . The second p a r t of the t h e s i s so f a r has d e a l t e n t i r e l y w i t h the problems encountered i n the v a r i o u s parts of such a d i s t r i b u t i o n system. The consumer, however, Is- I n t e r -ested but i n d i r e c t l y i n such problems, In t h a t a r e d u c t i o n i n c e n t r a l s t a t i o n c o s t s may l e a d to lower r a t e s or b e t t e r s e r v i c e . The consumer of any considerable amount of energy, however, such as a l a r g e I n d u s t r i a l p l a n t , has numerous problems of h i s own which may be classed, as problems of e l e c t r i c a l d i s t r i b u t i o n . These may be viewed from the standpoint of the producer or the buyer of e l e c t r i c a l energy according to whether he produces h i s own energy or buys i t from the c e n t r a l station.. I n some cases these problems are very s i m i l a r to those of the c e n t r a l s t a t i o n . I n other cases they may be q u i t e d i f f e r e n t . In any case, however, where the question of economy e n t e r s , the p r i n c i p l e s explained i n P a r t I w i l l be found fundamental,. Annual co s t i s the b a s i s of comparison f o r any a l t e r n a t i v e propositions,, In general, the s o l u t i o n of many of the problems may be s i m p l i f i e d by the use of a general equation such as t h a t d e s c r i b e d i n Chapter V» The most economical c o n d i t i o n w i l l be d i s c o v e r e d , only i f a l l Items of expense i n c l u d i n g the cost of energy l o s s e s as w e l l as the f i x e d charges on investment are considered. , Voltage Regulation.>--The problem c o n f r o n t i n g the e l e c t r i c a l engineer i n an i n d u s t r i a l p l a n t i s , e s s e n t i a l l y , the same as th a t of the d i s t r i b u t i o n -engineer as s t a t e d i n Chapter I , i . e . , to r e a l i z e the g r e a t e s t economy p o s s i b l e c o n s i s t e n t w i t h good s e r v i c e . I n t h i s case good s e r v i c e depends, upon two f a c t o r s . I n the f i r s t p l a c e , the c e n t r a l s t a t i o n must f u r n i s h reasonably good r e g u l a -t i o n a t the consumer* s service... This Is u s u a l l y more or l e s s r e g u l a t e d by c o n t r a c t but may depend somewhat on the character of l o a d imposed by the consumer as to power f a c t o r , load f a c t o r , d i v e r s i t y , maximum and minimum, f l u c t u a t l o n , " e t c . A customers l o a d may be of such a nature that I t i s p r a c t i c a l l y impossible to give good r e g u l a t i o n a t h i s s e r v i c e and other s e r v i c e s on the same l i n e may be s i m i l a r l y d i s t u r b e d . I n such, a ease i t i s u s u a l l y necessary f o r the customer to change h i s equipment or method of op e r a t i o n i n some way so as to remedy the d i f f i c u l t y . The. second f a c t o r i s the i n t e r i o r d i s t r i b u t i o n of the p l a n t i t s e l f . Assuming t h a t good r e g u l a t i o n I s f u r n i s h e d by the c e n t r a l s t a t i o n , i t i s - e s s e n t i a l t h a t the arrangement of the plant e l e c t r i c a l d i s t r i b u t i o n be such t h a t good -voltage c o n d i t i o n s are maintained a t the p o i n t s of u t i l i z a t i o n . By p l a n t d i s t r i b u t i o n i s meant a l l /43 p a r t s of the e l e c t r i c a l c i r c u i t i n c l u d i n g that of apparatus of u t i l i z a t i o n . A l l such-problems may a t f i r s t be more e l e c t r i c a l than economic. However, good s e r v i c e being accomplished,"it i s then e s s e n t i a l . t o • i n v e s t i g a t e the matter of economy. Problems of Power D i s t r i b u t i o n . - - T h e problems p e r t a i n i n g to the a c t u a l , w i r i n g ; i n an Indus t r i a l p l a nt; w i l l be very s i m i l a r to those of the l a r g e r d i s t r i b u t i o n system which as been heretofore d e s c r i b e d . For small p l a n t s i t w i l l be simply a case of secondary d i s t r i b u t i o n . The s i z e s of conductor can be r e a d i l y determined by a c o n s i d e r a t i o n of the annual charges on the cost of.the conductor i n place versus the c o s t of l o s s e s . In the case of the con-sumer, the u n i t c o s t of l o s t energy i s more e a s i l y determined than f o r the c e n t r a l s t a t i o n as i t appears very decidedly i n h i s month-l y bills« For l a r g e r p l a n t s , w i t h s e v e r a l separate b u i l d i n g s , i t may -.be;;,advlsable to d i s t r i b u t e p a r t l y a t primary v o l t a g e . For s t i l l l a r g e r ones, generating t h e i r own power, the problem of . high v o l t a g e t r a n s m i s s i o n may e n t e r . In any such case the problems of the c e n t r a l s t a t i o n are more n e a r l y approached and the examples c i t e d i n the preceding chapters w i l l apply* In many p l a n t s the question a r i s e s as to the comparative advantages of e l e c t r i c a l d i s t r i b u t i o n of power as compared w i t h mechanical,. I»e.., ..Individual motors on every machine i n s t e a d of l a r g e motors w i t h mechanical t r a n s m i s s i o n to a group of machines. Of course, there are many f a c t o r s i n such a problem, i n c l u d i n g the type of machines used and method of operations In general a study of the t o t a l annual c o s t of o p e r a t i o n i n c l u d i n g f i x e d charges, e l e c t r i c a l and. mechanical l o s s e s , and a c o n s i d e r a t i o n of any p o s s i b l e d i f f e r e n c e i n production, labor c o s t s , maintenance, e t c • w i l l be of g r e a t value i n determining the proper c h o i c e . Such a study w i l l be based on the p r i n c i p l e s explained i n P a r t I . Problems of Equipment .—The choice of proper equipment may have c o n s i d e r a b l e e f f e c t on the economy of p l a n t o p e r a t i o n . For customers buying energy a t primary voltage there i s f i r s t the s e l e c t i o n of"proper primary switch house equipment* Trans-formers must be s e l e c t e d w i t h the view of probable increase i n l o a d . However, i f too l a r g e u n i t s are i n s t a l l e d , not only i s there a waste of Investment but the a d d i t i o n a l core losses and the effect-on the power f a c t o r may be important. I t w i l l sometimes be found economical i n such a case to use an open d e l t a I n s t a l l a t i o n u n t i l the l o a d j u s t i f i e s the i n s t a l l a t i o n of the t h i r d u n i t . Where reserve transformers are r e q u i r e d i n case of t r o u b l e where a shut-down would be s e r i o u s , the choice of the s i z e of u n i t s w i l l be invluenced by that f a c t . In any such case as w e l l as i n the s e l e c t i o n of other equipment such as switches, e t c . , a study of the t o t a l annual c o s t i s e s s e n t i a l . A very common f a u l t i n the s e l e c t i o n of apparatus of u t i l i z a t i o n i s t h a t of overmotoring. Where c a r e f u l engineering has not been done the tendency o f t e n i s to I n s t a l l l a r g e r motors than are neces-sary* f o r the use r e q u i r e d w i t h the idea that the reserve power ob-t a i n e d i s advantageous. The investment charges i n such a case are l a r g e r than necessary* A l s o , any considerable underloading o f . I n d u c t i o n - . m o t o r s ' b r i n g s down the power f a c t o r and t h i s may have con s i d e r a b l e e f f e c t on the r e g u l a t i o n * In case poor power f a c t o r Is p e n a l i z e d i n the r a t e s i t i s Important to maintain as good a value as p o s s i b l e . A c a r e f u l study of the d i v e r s i t y f a c t o r between machines on. the same motor i s important i n i t s , proper s i z e . In some; cases- synchronous motors operated to improve power f a c t o r or s t a t i c condensers w i l l be found a d v i s a b l e . S i m i l a r . c o n s i d e r a t i o n s w i l l be. encountered w i t h other types of equip-ment* Old i n e f f i c i e n t - e q u i p m e n t may o f t e n be r e p l a c e d to advantage, although i t must be kept i n mind that beyond a c e r t a i n p o i n t e f f i c i e n c y i s not always economy* In a l l cases, the annual-cost must always be considered as an important f a c t o r along w i t h probably load Increase, r e g u l a t i o n , " r e s e r v e power, etc« Problems of Operation.~~In t h i s country the establishment of r a t e s . m o d i f i e d by power f a c t o r c o n s i d e r a t i o n s i s becoming more and more.-important and i s a t present r e c e i v i n g considerable a t t e n t i o n from the c e n t r a l s t a t i o n s * Poor power f a c t o r not only occasions a d d i t i o n a l power l o s s e s a l l the way back to the genera-t o r s but i t i n c r e a s e s the d i f f i c u l t i e s of maintaining good r e g u l a -t i o n . I t would, there f o r e seem j u s t that a customer w i t h a low power f a c t o r , should pay more per k i l o w a t t hour than one with a h i g h power f a c t o r . With t h i s i n mind i t i s e s s e n t i a l t h a t every • • user.:.obtain- as good a power f a c t o r as p o s s i b l e from h i s p l a n t * . This may be done by a s e l e c t i o n of equipment of proper s i z e and : type f o r the- load as mentioned above and a l s o by the use. of condensers, e i t h e r s t a t i c or synchronous. The expenditure j u s t i f i e d i n order to increase power f a c t o r can be determined by a study of the r e d u c t i o n i n the power b i l l s so r a f f e c t e d . In t h i s way i t w i l l be d i scovered whether i t w i l l be a paying, p r o p o s i t i o n to' e s t a b l i s h a power f a c t o r of say 95 per cent or of 80 per cent, etc o • • ' ' • • - . ' . The. p l a n t l o a d f a c t o r w i l l u s u a l l y be an.important considera-t i o n i n "-a -study to increase economy. At present most power r a t e s are based: on some form of demand charge and some form • of k i l o w a t t hour charge.. I-t i s obviously advantageous to reduee the demand charge i f p o s s i b l e , spreading the energy used at the peak-through the rest.-of the day.. This Is e s p e c i a l l y true, where the r a t e s are of such a form as, the demand load f o r "a" hours at "b" cents per .unit and. the reminder at "c" cents* The demand may o f t e n be. reduced by a c a r e f u l study.of the time of s t a r t i n g up motors and-of overlapping o p e r a t i o n of v a r i o u s equipment* In some cases-the r e d u c t i o n i n the annual b i l l s w i l l warrant the purchase of new equipment to reduce the demand. Other P r o b l e m s ^ - I t I s not w i t h i n the province of t h i s ;thesis- to attempt to d i s c u s s i n any d e t a i l a l l problems, i n e l e c t r i c a l d i s t r i b u -t i o n which occur i n an I n d u s t r i a l p l a n t . I t has been attempted a-bove to o u t l i n e some o f " t h e questions encountered and g i v e a general idea of the f i e l d of a p p l i c a t i o n of economic p r i n c i p l e s to such-problems. There are many others which are l e s s s t r i c t l y e l e c t r i c a l or not a t a l l e l e c t r i c a l which w i l l bear a s i m i l a r study. The questions of proper- i l l u m i n a t i o n as a f f e c t i n g - -production,-d e v i c e s ' e t c ° * ™ a l l more or l e s s „?Z ^  +V °^ B& T h e m a i n P o i n t must be always kept i n mind t h a t , once good s e r v i c e Is accomplished, the g r e a t e s t advan-tage l i e s w i t h any i n s t a l l a t i o n f o r which the t o t a l annual . p o s t , e v e r y t h i n g considered, i s l e s s than any other. APPENDI; METHOD OF APPR OX IMA TING- ENERGY POST I t very o f t e n happens t h a t I t i s d e s i r a b l e to study the eco^ nomies of d i f f e r e n t types of c i r c u i t s before i t has. been p o s s i b l e to undertake any d e t a i l e d determination of energy c o s t as o u t l i n e d - i n C h a p . H i e I t .has been customary, w i t h most .engin« eers doing, such work to assume i n : such a case,- an approximate average f i g u r e such as | .01 per k i l o w a t t - h o u r or some other-f i g u r e which i s kndwn to be somewhere, near the average-for the whole- outout of the system. A l i t t l e c l o s e r approximation .may. be made, keeping the p r i n c i p l e s set f o r t h i n Chap. I l l i n mind, by determining.roughly the v a r i a t i o n i n c o s t w i t h the load f a e t o r f o r the c l a s s o f load being considered* While not very accurate, such f i g u r e s are at l e a s t b e t t e r than a rough guess of a cost to cover a l l cases. An example of such a determination w i l l be worked out here to show how i t i s p o s s i b l e to handle such a problem. The general methods used may be adopted to other s i m i l a r cases. The loads consid.ered are power loads i n the suburban d i s t r i c t s , i . e . , such t h a t considerable t r a n s m i s s i o n - l i n e cost i s i n v o l v e d . As was e x p l a i n e d i n Chap. I l l , the demand c o s t f o r energy l o s s e s i s very n e a r l y p r o p o r t i o n a l to the amount of load at time of s t a t i o n peak. I t was assumed that the average demand c o s t at the g e n e r a t i n g - s t a t i o n switchboard equals $15©76 Per k i l o w a t t and the average k i l o w a t t - h o u r cost-$ .0036 per k i l o w a t t - h o u r e (These c o s t s : a r e u s u a l l y a v a i l a b l e and f a i r l y c o r r e c t i n most companies.) The demand cost per kilowatt-hour w i l l be i n v e r s e l y p r o p o r t i o n a l to the load f a c t o r , c o n s i d e r i n g load a t generating s t a t i o n o n l y . Reducing the demand cost to a c o s t per k i l o w a t t - h o u r ; : 15«76 At 100 per cent' load f a c t o r , demand charge= = 8760 ,0018 per k i l o w a t t - h o u r . .0018 For any other load f a c t o r , demand charge =-Load f a c t o r (expressed as a f r a c t i o n not as a per cent) I n order to determine the energy cost a t any point on the system beyond the g e n e r a t i n g - s t a t i o n , the c o s t s given above must be Increased by the -cost of d i s t r i b u t i o n . A l s o d i v e r s i t y f a c t o r s must be taken i n t o account. A study of the property c l a s s i f i c a t i o n of the system i n d i c a t e d a d i v i s i o n approximately as f o l l o w s : Per cent • Generating p l a n t . . . . . . . . 40.0 Underground c o n d u i t , e t c 6.5 Poles and f i x t u r e s . . . . . . . . . 7.0 Transmission l i n e s . . . . . . . . . . . . . . . 24.5 D i s t r i b u t i o n . .. . . , 19* 3 Transformers..... 2.7 We may then assume, roughly, that the demand charge e x c l u s i v e of the generating p l a n t i s 60per cent and of the generating p l a n t 40 per cent of the t o t a l e For a load of 100 per cent load f a c t o r the t o t a l demand charge would then be simply—= g e n e r a t i n g - s t a t i o n demand charge — 2«5 g e n e r a t i n g - s t a t i o n demand f o r 100 per cent load f a c t o r . For any other l o a d f a c t o r , the d i v e r s i t y between loads w i l l a f f e c t the c o s t . A k i l o w a t t load at the customer w i l l not mean a k i l o w a t t a t the generator unless the peaks happen to c o i n c i d e . The d i v e r s i t y f a c t o r s were assumed i n t h i s case to be those given In the "Standard Handbook" f o r general power loads as f o l l o w s : Per cent Between transformers.. 74 Between power l i n e s . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87. Between s u b s t a t i o n s . 91 I t I s assumed t h a t these f a c t o r s h o l d good f o r a load f a c t o r of 25 per Cent. Then, 1 kw. a t the customer becomes f 1 x 1 = 1 kw. a t the transformer. 8?4 x .1 = »74 kw. on the power l i n e . .87 x .74 = *61 kw. a t the s u b s t a t i o n * .91 x .61 == .586 kw. a t the generating**station. These r a t i o s combined w i t h the. percentages of the t o t a l prop-er ty values as given above, give the approximate share of each k i l o w a t t at the customer i n the t o t a l demand charge f o r the system. For example, i f the transformer investment i s 2»7 per cent of the t o t a l , and 1 kw. at the customer represents .1 kw. at the transformer, that k i l o w a t t should take 2*7 per cent of the t o t a l demand charge f o r I t s share i n the transformer investment. I f i t becomes only .586 kw. at the generating s t a t i o n and the generating s t a t i o n represents 40 per cent of the t o t a l Investment, the k i l o w a t t i n auestion should be charged w i t h 23.5 per cent.of the t o t a l demand "charge for i t s share i n the s t a t i o n . In order to make property and d i v e r s i t y f a c t o r c l a s s i f i c a t i o n s c o i n c i d e and « L ^ i P ^ X i m ^ i 0 n l 1 1 w a s a s s u m e d t h a t investmen? In , d l t r r l ^ p i ° n P 0 1 ^ ^ f l X t u r e S c o u l d b e taken t» represent power l i n e s , ana th a t the investment In tra n s m i s s i o n and underground c o u l d he a p p l i e d to s u b s t a t i o n s . _ T . V u • , U U V W W O % t o t a l investment share i n t o t a l demand cost On transformer At g e n e r a t i n g s t a t i o n . . . 1*0 kw. x 2,7 •74 kw. x ( 1 9 »3 +• 7.0) •64 kw. x (6.5 + 24.5) .586 kw.x 40 2»7 19*5 19*8 23«5 65*5 Then i f t o t a l demand f o r any load f a c t o r gen.-sta* demand for t h a t load f a c t o r *40 The demand charge f o r 1 kw« at the customer w i t h the load f a c t o r assumed (25 per cent) gen.-sta, demand at 25% load f a c t o r x 0*655 ,40 = 1,63 x gen,-sta, demand at 25 per cent load f a c t o r f o r 100 per cent and 25 per From the two valu e s thus obtained cent load f a c t o r s and the point f o r load f a c t o r equals zero, the curve shown on F i g . 58 was p l o t t e d showing by what amount the gene r a t i n g s t a t i o n demand cos t at any ?inload "factor should be m u l t i p l i e d to give the demand charge at the customers i n question. S i m i l a r l y the k i l o w a t t - h o u r charge must be increased t o account f o r l o s s e s i n tr a n s m i s s i o n and d i s t r i b u t i o n . I t was assumed that the t o t a l l o s s between generating s t a t i o n and customer would be not f a r from 30 per cent and, f o r the loads considered, i t was assumed that i t would be accurate enough to increase the g e n e r a t i n g - s t a t i o n , k i l o w a t t - h o u r charge 13y 30 per cent to give the charge at the oust omer. The average k i l o w a t t -hour charge would then «= ,036 x 1,30 = ,0047 The -following t a b l e may then be derived.' The f i r s t column gives the average number of hours of operation per week ( t ^ ) at f u l l load corresponding to any load f a c t o r . The l a s t column giv e s the corresponding values of t^Cg i f t chaps* IX and X I I . The values of twCc These are used as shown* are p l o t t e d i n F i g . 48 The cos, of energy obtained i n t h i s way i s very approximate but.may serve the purpose u n t i l some more accurate destina-t i o n can_be made. The f i g u r e s here- given must be considered a S examples only and not as r e p r e s e n t a t i v e of present-day cost on any system * J Table 19 t„ Load f a c t o r S t a t i o n Demand M u l t l " p l i e r Demand at load T o t a l at . Load •0, 16 .8 33.6 50 *4" 67*2 84.0 100*8 117.6 1^4.4 151.2 168 *0 .00 .10 .20 .30 .40 *50 .60 «70 .80 *90 1«00 i •0 . .018 .009 .006 .0045 .0036 .003 .0026 .00225 .002 .0018 1.00 1.28 1.52 1*72 1.90 2.05 2 e20 2,32 2.41 2 047 2.50 »00 o0231 .0137 .0103 .0086 .0074 .0066 ,0060 .0054 .0049 .0045 e0 .0278 .0184 .0150 .0133 .0121 .0113 .0107 .0101 .0096 .0092 1. 1. 1. 1 0 .0 .467 .619 6756 .894 015 139 258 358 1.450 1.543 APPENDIX B " t i d e Appearing.-in.New York Times of January 22nd 1953 ""On Power •- Cost*"~ F i n d s Power Cost Widely V a r i a b l e Samuel Ferguson Says.Factor of E l e c t r i c D i s t r i b u t i o n Precludes General F i g u r e . PINCHOT'S REQUEST FUTILE Information Asked by& Governor Held Impossible to Ascertain*—«Sp£cific Data Given* The p r i n c i p a l f a c t o r s i n the d i s t r i b u t i o n costs of e l e c t r i c i t y are the number of customers i n a given t e r r i t o r y and the average customer usage i n such an area, according to Samuel Ferguson, p r e s i d e n t of the H a r t f o r d (Conn.) E l e c t r i c L i g h t Company. For t h i s reason, Mr. Ferguson says, " d i s t r i b u t i o n " c o s t s are not capable of being expressed so a c c u r a t e l y i n gener a l terms as are "generation""'and"transmission" c o s t s . Mr. Ferguson made an/analysis, of d i s t r i b u t i o n c o s t s f o r s i x companies which he manages, In order to r e p l y to c r i t i c s of u t i l i t y accounting p r a c t i c e s , and plans to d i s t r i b u t e a r e p o r t on t h i s study to the persons who attended on Friday,, at the. H o t e l Pennsylvania, a meeting of the I n s t i t u t e on P u b l i c E n g i n e e r i n g devoted to d i s t r i b u t i o n , c o s t s . In d i s c u s s i n g the matter Mr• Ferguson r e f e r r e d to a recent a r t i c l e i n The New Republic by M o r r i s L l e w e l l y n Cooke, con-s u l t i n g engineer of P h i l a d e l p h i a and a member of the New York State, power- A u t h o r i t y , who handled the arrangements f o r F r i d a y ' s meeting and r e c e i v e d Mr. Ferguson's request to make a b r i e f . a d d r e s s too l a t e to arrange a place on the program f o r him. DEFINES. DISTRIBUTION COST t Quoting Mr* Cooke's statement that the e l e c t r i c companies i n 1931 had an estimated u n j u s t i f i a b l e charge of $330,000,000 f o r d i s t r i b u t i o n expense, Mr. Ferguson s a i d that Mr, Cooke covered generation and transmission together at 1.5 cents per k i l o w a t t hour and d i s t r i b u t i o n at another 1.5 cents-, and de-f i n e d a l l of the p r i c e r e c e i v e d above the sum of these two items not p a r t l y as other c o s t s but wholly as p r o f i t . "Thus, i f we accept the u s u a l d e f i n i t i o n f o r 'generation and t r a n s m i s s i o n 1 c o s t s , " Mr, Ferguson s a i d , "Mr. Cooke places a l l other c o s t s under the t i t l e of d i s t r i b u t i o n ' — t h a t i s to say, i n a d d i t i o n to l i n e , transformer and meter, f i x e d and operati n g c o s t s and s p e c i f i c customer c o s t s , t h i s convenient term must cover a t l e a s t i t s share of a d m i n i s t r a t i o n and general s a l a r i e s , l e g a l expense, a d v e r t i s i n g , employee welfare, s t a t i o n e r y and p r i n t i n g , expense of State and Federal question-n a i r e s j Insurance, telephone*•••store and purchasing expense, r e g u l a t o r y commission expenses, taxes and other items too numerous to mention, and a l l f o r 1*5 cents per kilowatt-hour« " i l i m i t my d e f i n i t i o n of ' d i s t r i b u t i o n c o s t s ' to f i x e d and,operating and maintenance costs on l i n e s , transformers, s e r v i c e s and meters,' together w i t h a l l d i r e c t expenses caused by the s e r v i c e of the i n d i v i d u a l customers,- such as b i l l i n g , c o l l e c t i n g , t r o u b l e and lamp s e r v i c e , i n s p e c t i o n , i n f o r -mation and complaint servioee I a l s o i n c l u d e d i r e c t taxes, b u t not Federal, or other income taxes, and such p u b l i c l i a b i l i t y insurance c o s t s as are a t t r i b u t a b l e wholly to d i s t r i b u t i o n l i n e s . I leave out a l l . l e g a l and a d m i n i s t r a t i o n expenses to be covered under some other c l a s s i f i c a t i o n or by a l l o c a t i o n . AN IMPOSSIBLE REQUEST. "Mr. Cooke and Governor Pinchot have discovered I n the supposed absence of Information c o v e r i n g d i s t r i b u t i o n costs a new s i n to p i n on our power companies, and i t i s one which we cannot shake o f f as e a s i l y as we have many others by the simple expedient of g i v i n g the requested i n f o r m a t i o n * We are asked to d i s c l o s e the f i g u r e of "the c o s t per kilowatt-hour of d i s t r i b u t i o n ' which we are accused of co n c e a l i n g ; t h i s can-not be done, and f o r the simplest of a l l . reasons, which i s t h a t 'there a i n ' t no such animal'«-you c o u l d as reasonably as/< "what i s the cost per g a l l o n of sewage d i s p o s a l ? ' without making your question any more s p e c i f i c . " i t i s , however, i n a way a n a t u r a l request, because as Mr* Cooke p o i n t s out, we do have a p r e t t y good general idea of gen-e r a t i o n and t r a n s m i s s i o n c o s t s , and t h e r e f o r e , why not d i s t r i b u t i o n c o s t as w e l l ? " The reason that the one i s capable of being expressed f a i r l y a c c u r a t e l y i n general terms wh i l e the other i s not l i e s , probably i n the f a c t t h a t ^generation* and 'transmission' c o s t s deal w i t h the combined requirements.of a l l customers, and the only m a t e r i a l v a r i a b l e s are those of p l a n t arid f u e l costs and plant e f f i c i e n c y . With d i s t r i b u t i o n ^ however, the., s i t u a t i o n i s e x a c t l y reversed,, and by by f a r the greater v a r i a b l e s are those of re u stonier density and average consumer usage, while the cost per mile i s r e l a t i v e l y constant except as between overhead and underground c o n s t r u c t i o n . v \ , r l t i s always p o s s i b l e to o b t a i n a f i g u r e which represents i n any t e r r i t o r y or s u b d i v i s i o n thereof the quotient of cost d i v i d e d by kilowatt«hours but such Q u o t i e n t i s o n l y - d i s t r i b u t i o n /ft c o s t I n b u t i o n m i l e ; r a t i o the l i m i t e d sense of. 'the bmJ^^flf ° f 1 « ' a spee.iflc number of customers i Of a s p e c i f i c average usage per customer: 3 overhead to underground c o n s t r u c t i o n . ' p a r t i c u l a r cost of distri« per a s p e c i f i c COST FOR SIX OOMPAWfFa, t h : - • • I S f e p t t1°- f^ 8 ' J i l t e d d e f i n i t i o n , I have l i s t e d i n a table the-cost,per Mlowatt^hour- of d i s t r i b u t i o n taken from the booke a n d d a t a of s i x companies together w i t h the p a r t i c u l a r c o n d i t i o n s p e r t a i s i n g te eaeh," ^  Tfie t a b l e follows': • D i s t r i b u t i o n Customers ' K i l o w a t t Cost per Kw. :\; \ Hours Per Hr, (i n c c e n t per ,mile .'•'•'Customer, Co. A° •• . .-93 - 682 2*7 'Cp'».'.: .:B?'. •.•*;'.* ....16 812 5*0 CO. - Qo • . • »• •••58 507 4.6 -Co. D • • • '. -8 678 9.2 Co. ;• E • • • .. .. 6 780 - : 8*5, c o ; . ; F • • • • • • 10 • 596 .. . 8.7 Town: - A I » . • • • 18 : 1*338. 3.0 Town .;A2<-. •-•*-39 ' 436 5 »8 Twoh. Bl- • --'• v l 4 1,:543 •481 3.1 Tbwrf B2- • . .. 4Q 5*2 "These f i g u r e s are taken from the books and data of companies A to F and from t h e data of companies and A and B i n the case of towns A-rl'to B«2. You w i l l note t h a t customer •density ranges from 6 t o 93 customers per mile and usage from 436 to 1*543 k i l o ~ watt«<hours per customer per annum; and that under these v a r y i n g c o n d i t i o n s the 1 d i s t r i b u t i o n cost per kilo w a t t ^ h o u r v a r i e s from 2»7 cents to 9£cents per k i l o w a t t hour. I n t h i s t a b l e I have gone-somewhat f u r t h e r and s t u d i e d 'Certain i s o l a t e d t e r r i t o r i e s of these same companies. I t i s i n t e r e s t i n g to note that the h i g h : use. I n the .low«density town B ~ l almost balances the low usage but higher d e n s i t y of company A. " l l i s true t h a t a mathematical average of these r e s u l t a n t / f i g u r e s might be made-9 but even 1 then i t would represent only, the cost of some one p a r t i c u l a r customer density between 9'"and JL3, when -combined w i t h some p a r t i c u l a r , customer usage between 436 and 1,543. Such a f i g u r e would be of no s i g n i f i c a n c e whatever as r e p r e s e n t i n g even an approximation of d i s t r i b u t i o n cost under d i f f e r e n t circumstances, as t h i s p a r t i c u l a r set of sireumstances would not be met again once i n a thousand times. LIST, OF DIAGRAMS Figure 22 1" Load Demand Diagram cc 2 a & b • Load Demand, Diagram 26 3 Diagram i n d i c a t i n g method of Studing • energy cost at' v a r i o u s p o i n t s on a 27 4-. Average of monthly "Maximum Loads on 39 Twelve T y p i c a l l i g h t i n g c i r c u i t s - C h a r t 5: a b c. Loading diagrams-for load f a c t o r 43 •determination. 6 Annual Cost of 3 #4 Secondaries' 49 7 a Determination of Most Economical Cross- 46 s e c t i o n of Wire. '8; '" • , Most Economical Voltage'Drop on L i g h t -ing Secondaries 49 .10.; '-Power Loss Curves - E Cos 0 52 12.a & b values of "B" Fa c t o r „ 55 13'a'-b' Power Loss.Curves - Power Factor 56 14- Voltage Drop .per cent 56 15- Load. Curves f o r Power Lines-3 phase 56 16 Load Curves f o r s i n g l e phase 56 17 .Load Curves f o r Power Lines 56 18? Load Curves f o r Secondaries 56 19 a b e "Voltage Drop Curves-secondaries 56 20 Approximate method f o r secondaries 57 21 Cost of S i n g l e Phase 60 c y c l e t r a n s - 65 b formers 22 Cost of L i g h t n i n g A r r e s t e r s and 65 b switches 23 . ; Annual Cost per K i l o w a t t per 1000 f t . 72 22000 V.. tr a n s m i s s i o n l i n e . -24 Most Economical Conductor s i z e 22000V- 72 . Line . 25 Most Economical lo a d i n g f o r 22000 V-Line 72 26 Curves Showing maximum Economical Ex- 75 penditure per mile of l i n e . 27 Economical wire s i z e f o r 3 phase primary 81 28 Economical wire s i z e f o r 3 phase primary 83 29 " Curves Showing V a l u e s of tCe for,Power 85 • loads 30 Economical wire s i z e f o r any r a t e s of 88 Cm/Ce 31 Poletop digram f o r C i r c u i t cost a s s i g n - 88 ment • 32 Economical c i r c u i t s ' f o r r a t i o Cm/Ce f o r 89 3 phase power.. In f r o n t of Page No . LIST OF DIAGRA MS ~ CONT IN USD In f r o n t of Page Fi g u r e • • Ko. 33 T o t a l Annual. Cost of Energy losses f o r 91 Various methods of D i v i d i n g a Load, "between two l i n e s 34 T y p i c a l curves to show v a r i a t i o n i n monthly 95 maximum f o r l i g h t i n g c i r c u i t s 35 ' Economical wire s i z e f o r Single-phase 98 p r i m a r i e s . 36 . . . Annual Charges on Transformer 104 36 . • Most Economical Voltage Drop. 106 38 Most Economical Spacing of Transformer 108 39 . ., Most Economical Transformer. Size ' 108 AO " Wire S i z e s Cm 108 41 Most Economical Wire S i z e 111 42 '." Comparative Economy of Various Wire S i z e s i l l 44 Load curve f o r Secondaries 117 45; a b c L i n e Cost Curves # 6, 4 and 2 ' 117 46 .Transformer Cost Curves 117 47 '• Scale f o r T r a n s f e r r i n g Y t o Y 117 48 ' Values'of t C f o r d i f f e r e n t v a l u e s of t 133 49 '•' M 0 s t Economical Wire S i z e f o r Secondaries 20^ / l b . 133 50 . Most Economical'Wire S i z e f o r Secondaries 30rf / l b . 133 51 ••-..' Annual. Cost per M f t . per ampere #00 Cable •  -13. 52 Current C a r r y i n g Capacity of cables Vs. § of Ducts. 53 '. .' Ducts and C a h l e s per Duct Line 138 54 ' Ducts and Cables - 23,000 V o l t s 138 55 Ducts and Cables 4600 V o l t s 138 56 . Ducts and Cables 2300 V o l t s 138 57 a and b Duct Arrangement #? and 16' 139 '58. Demand Charge A d j u s t i n g F a c t o r 149 '5 135' /S3c LIST OF TABLES 1. . Monthly Load v a r i a t i o n i n residence L i g h t I n ? C i r c u i t . 37 2. E q u i v a l e n t hours Determination 40 C o r r e c t i o n Factor f o r Future Growth 41 4. ' N o t a t i o n and Symbols . 47 . t .5 ' ' .- Table of Equations of TotalAAnnual Costs 81 6'. Table of Equating Adjacent Equations 81 T-7. •-Table f o r 4600 V and Copper at 30^ & 2 0 ^ f l b . 82 3:. . -Determination of " t " l i m i t 84 ; 9- Determination of "C^" 84 10. Determination of " t 0 C e " f o r General Purposes 85 •11. ' Table of Power Loss and Voltage Drop. 88 12. R a t i o 'of Each Month's Load to the T o t a l 94b 13. Equations of T o t a l Annual Cost . 95 14. Equations of Adjacent Wire S i z e s 96 15- t Ce values f o r 4600 v o l t s © 30$^ and. 20^ •' 96 16... Equations o f Equal Cost. 130b 17 - Equation of Equal Costs t w C c H P £ 131 ' i 8 . • Values of t C f o r t and Load Factor '131 119- Values of t C a - Approximate Method 149 Author . Elsenmenger,K•E• Seelye, H.P S t i l l , A Llnq-uist, R.A. Meyers, ' E-B.• . Dwight, H.B. Dwight, B'.B •Reyneau,P.0. De Imar, Wm .A . F i s h , J.CW. Nash, W-R • G i l l e t t e & Dana Reyneau & Seelye Gear, H.B-S a i l e r s , E.A. Fowle, F. F. Elden, L- I • M i l l s , F.C. Shelden & Housmann BIBLIOGRAPHY T i t l e C e n t r a l S t a t i o n Rates i n Theory and P r a c t i c e P u b l i c a t i o n D i s t r i b u t i o n Costs E l e c t r i c Power Transmission E l e c t r i c World v 0 1 . ( p E l e c t r i c World 1921 McGraw H i l l N-Y-1919 Transmission Line C o n s t r u c t i o n McGraw H i l l Underground Transmission and D i s t r i b u t i o n Constant Voltage Transmission Transmission Line Formula •Transmission Costs E l e c t r i c Cables Engineering Economics Economics of P u b l i c U t i l i t i e s E l e c t r i c a l & Mechanical Cost Data S i n g l e Phase Secondaries The A p p l i c a t i o n of the D i v e r s i t y Factor Accountant's Handbook Standard Handbook fo r E l e c t . Engineers Wiley & Co. N .Y . 1915 Wiley & Co .K.Y• E l e c t r i c World 1919-McGraw H i l l N•Y• 1924 McGraw H i l l 1923 McGraw H i l l 1925 McGraw H i l l 1918 A. I . E. E. N.E.L.A. p. 238 Ronald Fress Co 1923 McGraw H i l l 1922 A n a l y s i s of D i s t r i b u t i o n Losses A.I.E.E- 1907 i n a' Large System- p.665 S t a t i s t i c a l Methods E l e c t r i c T r a c t i o n and Trans-mission Engineering. Holt & Co. . Van Nostrand Co 

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