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UBC Theses and Dissertations

Fast control of power system transient stability Sawada, Jack Hisao 1974

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FAST CONTROL OF POWER SYSTEM TRANSIENT STABILITY Jack Hisao Sawada B.A.Sc, University of British Columbia, 1972 A THESIS SUBMITTED IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF APPLIED SCIENCE iri the Department o f Electrical Engineering We accept this thesis as conforming to the required standard THE UNIVERSITY OF BRITISH COLUMBIA September 1974 In p r e s e n t i n g t h i s t h e s i s i n p a r t i a l f u l f i l m e n t o f t h e r e q u i r e m e n t s f o r an a d v a n c e d d e g r e e a t t h e U n i v e r s i t y o f B r i t i s h C o l u m b i a , I a g r e e t h a t t h e L i b r a r y s h a l l m a k e i t f r e e l y a v a i l a b l e f o r r e f e r e n c e a n d s t u d y . I f u r t h e r a g r e e t h a t p e r m i s s i o n f o r e x t e n s i v e c o p y i n g o f t h i s t h e s i s f o r s c h o l a r l y p u r p o s e s may be g r a n t e d by t h e H e a d o f my D e p a r t m e n t o r by h i s r e p r e s e n t a t i v e s . I t i s u n d e r s t o o d t h a t c o p y i n g o r p u b l i c a t i o n o f t h i s t h e s i s f o r f i n a n c i a l g a i n s h a l l n o t be a l l o w e d w i t h o u t my w r i t t e n p e r m i s s i o n . D e p a r t m e n t o f y, •;.. c f X I i c-The U n i v e r s i t y o f B r i t i s h C o l u m b i a V a n c o u v e r 8, C a n a d a ABSTRACT This t h e s i s provides some guidelines of fast control application f o r t r a n s i e n t power system s t a b i l i t y , i n c l u d i n g the b r a k i n g r e s i s t o r , the forced e x c i t a t i o n , the f a s t - v a l v i n g , and combinations of them. M u l t i p l e a p p l i c a t i o n s of s i n g l e and combined f a s t c o n t r o l s of v a r i o u s r e s i s t o r c a p a c i t i e s , v a r i o u s c e i l i n g v o l t a g e s , f u l l or p a r t i a l v a l v e c l o s u r e s are a l s o examined. Chapter 2 gives the power system model f o r the t h e s i s i n v e s t i g a -t i o n . Computer s i m u l a t i o n r e s u l t s of i n d i v i d u a l b r a k i n g r e s i s t o r , f o r c e d e x c i t a t i o n , and f a s t - v a l v i n g f a s t c o n t r o l s are presented i n Chapter 3 ,and a l s o i n Chapter 4 , but of combined f a s t c o n t r o l s . Included i n Chapter 5 are the experimental r e s u l t s i n comparison w i t h computer s i m u l a t i o n r e s u l t s , and a l s o instrumentations of transducers and c i r c u i t s f o r implementing the f a s t c o n t r o l s . F i n a l l y , the main conclusions of the t h e s i s study and sug-gestions f o r f u t u r e i n v e s t i g a t i o n are summarized i n Chapter 6 . i i TABLE OF CONTENTS Page ABSTRACT i i TABLE OF CONTENTS . . . . i i i LIST OF TABLES ., v LIST OF ILLUSTRATIONS v i ACKNOWLEDGEMENT ' i x NOMENCLATURE . . . . . . . . . . . . . . . . . . . . . x 1. INTRODUCTION 1 2. POWER SYSTEM MODEL FOR COMPUTER AND MICRO-MACHINE SIMULATION . . . . . . . . . . . . . . . . . . 3 2.1 I n t r o d u c t i o n . . . . . . . . . . . . . . . . . . . 3 2.2 Synchronous Machine Model . . . . . . . . . . . . 5 2.3 Voltage R e g u l a t o r - E x c i t e r Model . . . . . . . . 5 2.4 Governor - Prime-Mover Model 5 2.5 E x t e r n a l System 5 • 2.6 V a l i d i t y of D i g i t a l S i m u l a t i o n and Lab Test Model 10 2.7 Load C o n d i t i o n f o r T r a n s i e n t S t a b i l i t y S t u d i e s . . 10 3. MERITS OF VARIOUS FAST POWER SYSTEM CONTROLS . . . . . . . 16 3.1 I n t r o d u c t i o n 16 3.2 Concept of Power System S t a b i l i t y . . . . . . . . 16 3.3 T r a n s i e n t Power System S t a b i l i t y w i t h . Braking R e s i s t o r c o n t r o l . . . . . . . . . . . . . 18 3»4 Power System w i t h Forced E x c i t a t i o n c o n t r o l . . . 28 3.5 Power System w i t h F a s t - V a l v i n g c o n t r o l . . . . . . 38 i i i Page 4. INFLUENCE OP COMBINED FAST CONTROLS IN TRANSIENT STABILITY . 54 4.1 I n t r o d u c t i o n . . . . . . . . . . 54 4.2 System S t a b i l i t y w i t h LOC and Fast C o n t r o l s . . . 54 4.3 Braking R e s i s t o r and Forced E x c i t a t i o n Combination . 55 4.4 F a s t - V a l v i n g and Forced E x c i t a t i o n Combination . . . 60 f 4.5 Braking R e s i s t o r , Forced E x c i t a t i o n , and F a s t - V a l v i n g Combination . . . . . . . . . . . . . . 63 5. FAST CONTROL TEST ON A LABORATORY TEST MODEL AND INSTRUMENTATION . . . . . . . . . . . . . . . 69 5.1 I n t r d d u c t i o n 69 5«2 Experimental R e s u l t s . . . . . . . . . . . . . . . 69 5.3 Speed, Torque-angle, and other transducers . . . . 75 5.4 Speed and Power S i g n a l L e v e l and Speed Slope D e t e c t i o n C i r c u i t . < , . . . < > . . . . • . . 77 5.5 Counting and I n h i b i t . C i r c u i t f o r A p p l i c a t i o n Number o f Fast C o n t r o l . . . . . . . . . . . . . . 77 5.6 The Bra k i n g R e s i s t o r c o n t r o l c i r c u i t . . . . . . . 80 5.7 The Forced E x c i t a t i o n c o n t r o l c i r c u i t . . . . . . 80 5.8 The F a s t - V a l v i n g c o n t r o l c i r c u i t 84 6. CONCLUSIONS . . . . . . 85 APPENDICES A. The 5th and the 3rd Order Synchronous Machine Models'in Park's Parameters 87 B. L i n e a r Optimal E x c i t a t i o n C o n t r o l Design . . . . . 89 REFERENCES . . 91 iv LIST OF TABLES Table Page I Parameters and Base Values f o r the Model . . . . . 6 I I Parameter Values o f a Governor-Turbine System f o r F o s s i l U n i t . 8 I I I E x t e r n a l System Parameters i n p.u. . . . . . . . . 11 IV 2 5 $ and 5 0 $ BR c o n t r o l D e t a i l w i t h M u l t i p l e S e l e c t i o n and M u l t i p l e A p p l i c a t i o n . . . . . . . . 2 5 V Parameter Values f o r the FE c o n t r o l . . . . . . . 3 2 VI - 6 . 0 p.u. FE c o n t r o l a p p l i c a t i o n d e t a i l . . . . . 3 6 v LIST OF ILLUSTRATIONS Fig u r e Page 2.1 A one machine I n f i n i t e - b u s system . . . . . . . . . . . 4 2.2 A 2-axis synchronous machine i n Park's dq coordinates . . . . . . . . . . . . . . . . . . . . 4 2.3 Block diagram of Voltage R e g u l a t o r - E x c i t e r system . . . 7 2.4 Block diagram of Governor-Steam Turbine system 7 2.5 P l u g type valve c h a r a c t e r i s t i c . . . . . . . . . . . . . 8 2.6 B u t t e r f l y type v a l v e c h a r a c t e r i s t i c . . . . 8 2.7 I d e a l i z e d l i n e a r v a l v e c h a r a c t e r i s t i c . . . 8 2.8 One phase of the Transmission L i n e . . . . . . . . . . . 9 2.9 The -re - Model 9 2.10 The e q u i v a l e n t c i r c u i t of the power system . . . . . . . 11 2.11 5th and 3rd order s i m u l a t i o n and l a b test, r e s u l t s . . . 12 2.12 System swing curve w i t h v a r i o u s loads . . . . . . . . . 14 3.1 Power and torque-angle diagram . . . . . . . . . . . . . 17 3.2 Power and torque-angle diagram w i t h B raking R e s i s t o r . . 17 3.3;- BR c o n t r o l procedure . . . . . . . . . . . . . . . . . . 19 3.4 S i n g l e BR a p p l i c a t i o n s ; 25$, 50$ and 75$ BR V 21 3.5 M u l t i p l e BR a p p l i c a t i o n s ; 1, 2 and 3 . . . . . . . . . . 24 3.6 System responses of 50$ BR c o n t r o l . . . . . . . . . . . 26 3.7 Power, speed and torque-angle diagram w i t h Forced E x c i t a t i o n . . . . . . . . . . . . . . . . . . . 29 3.8 FE c o n t r o l procedure . . . . . . . . . . . . . . . . . . 30 3.9 Speed- torque-angle phase plane diagram . . . . . . . . . 32 3.10 System responses of FE c o n t r o l . . . . . . . . . . . . . 33 3.11 FV c o n t r o l procedure . . . . . . . . . . . . . . . . . . 39 v i Figure Page 3.12 E f f e c t s of r e l a y time, IV c l o s i n g time and valv e c l o s u r e d u r a t i o n . . . . . . . 41 3.13 E f f e c t of IV and/or CV opening . . . . . . . . . . . . 42 3.14 Power vs speed r e - a p p l i c a t i o n s i g n a l w i t h two FV a p p l i c a t i o n s 45 3.15 Various f a s t - v a l v i n g c o n t r o l s . . . . . . . . . . . . . 47 3.16 Various v a l v e "closures . . . . . . . . . . . . . . . . 52 4.1 System swing curves w i t h and without LOC . . . . . . . 56 4„2 - I n d i v i d u a l f a s t c o n t r o l s w i t h and without LOC . . . . . 56 4.3 Combined BR ,and FE c o n t r o l w i t h LOC . . . . . . . . . . 58 4.4 Combined FE and FV c o n t r o l w i t h LOC . . . . . . . . . . 61 4.5 Combined BR, FE and FV c o n t r o l w i t h LOC . . . . . . . . 64 4.6 Second BR vs FV a p p l i c a t i o n w i t h o t h e r c o n t r o l s ; . . . 65 4.7 BR, FE and FV combination w i t h LOC ( P = 550 watts ) . 66 b 5.1 Test and computer r e s u l t s of a power system w i t h and without LOC; No f a s t c o n t r o l . 7 0 5 . 2 Test and computed r e s u l t s of BR c o n t r o l . . . . . . . . . 70' 5.3 Test and computed r e s u l t s o f FE c o n t r o l . . . . . . . . . 7 2 5.4 Test and computed r e s u l t s of FV c o n t r o l . . . . . . . . 72 5.5 Test and computed r e s u l t s of combined two f a s t c o n t r o l s . . . . . . . . . . . . . . 73 5.6 One and m u l t i p l e a p p l i c a t i o n s of combined three f a s t c o n t r o l s . . . . . . . . . . . . . 74 5.7 A schematic diagram of the speed transducer . . . . . . 76 5.8 Speed transducer t r a n s f e r c h a r a c t e r i s t i c . . . . . . . 76 5.9 A schematic diagram of speed s i g n a l l e v e l d e t e c t o r . . 78 5.10 A schematic diagram of speed slope d e t e c t o r . . . . . . 78 v i i F i g u r e Page 5.11 A schematic diagram of the counting and i n h i b i t c i r c u i t . . . . . . . . . . . » . . . » .>. . 79 5.12 A schematic diagram of the BR c o n t r o l c i r c u i t . . . . 81 5.13 A schematic diagram of the FE c o n t r o l c i r c u i t . . . . 82 5 .14 A schematic diagram of the FV c o n t r o l c i r c u i t . . . . 83 v i i i ACKNOWLEDGEMENT I am very g r a t e f u l to the many people who have g i v e n me i n v a l u a b l e a s s i s t a n c e i n completing t h i s t h e s i s . I n p a r t i c u l a r , I wish to express-my deepest g r a t i t u d e to my s u p e r v i s o r , Dr. Y. N. Yu, f o r h i s continuous i n t e r e s t , patience and guidance throughout t h i s e n t i r e t h e s i s p r o j e c t . A l s o , I would l i k e to thank Mr» B. N u t t a l l f o r h i s s k i l f u l t e c h n i c a l a s s i s t a n c e i n the hardware implementation and Mr. W. Walters, f o r h i s e f f i c i e n t h a n d l i n g and o r d e r i n g of a l l components t h a t were necessary f o r t h i s t h e s i s . I wish to thank Dr. H. Cheann, my co-reader, f o r h i s c o n s t r u c t i v e comments w h i l e r e v i e w i n g the d r a f t . My a p p r e c i a t i o n to the UBC E l e c t r i c a l E n g i n e ering o f f i c e s t a f f f o r t y p i n g the t h e s i s and t h e i r s i n c e r e c o - o p e r a t i o n . F i n a l l y , but not the l e a s t important, s e v e r a l members of the power group, f e l l o w graduate students and other f a c u l t y members are a p p r e c i a t e d f o r t h e i r h e l p f u l d i s c u s s i o n s and memorable experiences shared d u r i n g the past few yea r s . ix NOMENCLATURE Synchronous Machine i instantaneous value of c u r r e n t v instantaneous value of v o l t a g e y f l u x - l i n k a g e r r e s i s t a n c e x reactance £, torque angle, r a d i a n w e l e c t r i c a l angular v e l o c i t y , radian/second H i n e r t i a constant T e l e c t r i c a l torque e T mechanical torque m generator t e r m i n a l v o l t a g e i generator t e r m i n a l c u r r e n t Voltage R e g u l a t o r - E x c i t e r KA r e g u l a t o r - e x c i t e r g a i n TA r e g u l a t o r time constant,second ira e x c i t e r time constant, second U s t a b i l i z i n g s i g n a l hi Governor-Steam Turbine system reference angular v e l o c i t y f radian/second a>m mechanical angular v e l o c i t y f radian/second u > b a g e base angular v e l o c i t y f radian/second T per u n i t torque output of the h i g h pressure t u r b i n e Hr > T j p per u n i t torque output of the i n t e r m e d i a t e pressure t u r b i n e T T_ per u n i t torque output of the low pressure t u r b i n e hr T^ t o t a l per u n i t torque output of prime mover U p o s i t i o n o f c o n t r o l v a l v e (UQ V= 1«0 CV open; U = 0.0 CV closed) 0 V U j y p o s i t i o n of i n t e r c e p t o r v a l v e (^jy= 1 7 open; U I y = 0.0 IV closed) R speed r e g u l a t i o n T ^ , T 2, T^ time constant a s s o c i a t e d w i t h the governor x the time constant a s s o c i a t e d w i t h the main i n l e t volumes between the c o n t r o l v a l v e and the h i g h pressure t u r b i n e the time constant a s s o c i a t e d w i t h the h i g h pressure t u r b i n e , r e h e a t e r and p i p i n g volumes up to the i n t e r c e p t o r v a l v e the time constant a s s o c i a t e d w i t h the volumes between the i n t e r c e p t v a l v e and the intermediate:' pressure t u r b i n e the time constant a s s o c i a t e d w i t h the i n t e r m e d i a t e pressure t u r b i n e , cross-over p i p i n g and low pressure t u r b i n e i n l e t volume f r a c t i o n of t o t a l prime-mover torque d e l i v e r e d r e s p e c t i v e l y by h i g h , i n t e r m e d i a t e and low pressure t u r b i n e s e q u i v a l e n t s e r i e s impedance of t r a n s m i s s i o n system e q u i v a l e n t shunt admittance of t r a n s m i s s i o n system • x - - . — - i j XiXi.xxj.xuo u u o *wx u a 5 ^ z i 1. INTRODUCTION In e a r l i e r e l e c t r i c power development, the system was s m a l l and methods developed to maintain system s t a b i l i t y were adequate. 1•! However, w i t h modern l a r g e generator design of increased reactances and decreased i n e r t i a s , and the continuously growing i n t e r c o n n e c t i o n of power systems and the development of f a s t c i r c u i t breakers and r e l a y s , power system s t a b i l i t y becomes an i n c r e a s i n g l y c h a l l e n g i n g problem. In recent y e a r s , much experimental and a n a l y t i c a l work has been done, and has succeeded i n improving dynamic s t a b i l i t y , e s p e c i a l l y w i t h the phase-compensated e x c i t a -t i o n c o n t r o l . 1 * 2 The l i n e a r optimal c o n t r o l a l s o has been w e l l developed and p r o v i d e s , perhaps b e t t e r a l t e r n a t i v e to the e x c i t a t i o n c o n t r o l . 1 # 3 However, the t r a n s i e n t s t a b i l i t y of the f i r s t few swings of a power system remains as a very c h a l l e n g i n g problem when the system faces severe d i s -turbances. Many f a s t c o n t r o l s such as b r a k i n g r e s i s t o r , 1 # 4» 1 , 5 > ! • 6,1. 7,1.8, 1 , 9 forced e x c i t a t i o n , 1-10,1.11. 1.12 f a s t - v a l v i n g 1 * 1 3 ' 1 * 1 4 ' 1 * 1 5 ' 1 * 1 6 ' 1 * 1 7 s e r i e s c a p a c i t o r s w i t c h i n g } * 1 8 ' 1 , 1 9 ' 1 * 2 0 ' 1 * 2 1 and HVDC 1* 2 2' 1* 2 3' 1' 2^ con-t r o l s have been explored. Among them, the b r a k i n g r e s i s t o r c o n t r o l , the for c e d e x c i t a t i o n c o n t r o l , and the f a s t - v a i v i n g c o n t r o l nave aroused great i n t e r e s t s i n c e they are economically f e a s i b l e at p r e s e n t . 1 * 4 The b r a k i n g r e s i s t o r c o n t r o l has been presented i n many papers and s e v e r a l p r a c t i c a l a p p l i c a t i o n s were made.1***'1*7 In many cases, b r a k i n g r e s i s t o r of f i x e d c a p a c i t y i s a p p l i e d f o r a predetermined time. However, s i n c e v a r i o u s system disturbances w i t h d i f f e r e n t degrees of s e v e r i t y occur, the r e s i s t o r c a p a c i t y , the a p p l i c a t i o n and removal time, and other r e l e v a n t c o n t r o l parameters must be v a r i e d a c c o r d i n g l y as sug-gested by R.H. P a r k . 1 * 5 The concept of forced e x c i t a t i o n c o n t r o l has a l s o been e s t a b l i s h e d by many authors ,1«10»1«11,1.12 Many of them have concentrated on one or on c e r t a i n types of optimal c o n t r o l s . However, i n the case of severe d i s -turbances, more than one or two a p p l i c a t i o n s may be b e n e f i c i a l . A l s o , h i g h order n o n - l i n e a r optimal c o n t r o l design i s extremely d i f f i c u l t . Hence, a sound engineering approach of developing c o n t r o l s t r a t e g i e s on prototypes of power systems u s i n g measurable v a r i a b l e s such as torque angle, f i e l d c urrent and speed as c o n t r o l s i g n a l s seems t o be more ap p r o p r i a t e at the present time. 1 2 The f a s t - v a l v i n g c o n t r o l i s a l s o being developed and have been put i n t o practice.-*- 3,1.14,1.15,1.16 Some authors have developed f a s t -v a l v i n g from the equal area c r i t e r i o n w i t h speed s i g n a l as the c o n t r o l i n -put^"" w h i l e others have i n v e s t i g a t e d the e f f e c t of time delay of r e l a y , v a l v e c l o s u r e and duration.1.15,1.16 However, f o r s u c c e s s f u l f a s t - v a l v i n g a p p l i c a t i o n , more e f f e c t i v e c o n t r o l scheme w i t h both power and speed s i g -n a l s as c o n t r o l input and w i t h m u l t i p l e a p p l i c a t i o n f e a t u r e need to be explored. The foregoing d i s c u s s i o n n a t u r a l l y leads to another area of i n -v e s t i g a t i o n , namely two or more f a s t c o n t r o l s i n combination. This t h e s i s i s aimed at developing those f a s t c o n t r o l schemes. Computer s i m u l a t i o n and l a b o r a t o r y t e s t of these c o n t r o l schemes are d e t a i l e d . Chapter 2 models the power system i n c l u d i n g synchronous generator, voltage r e g u l a t o r e x c i t e r , steam t u r b i n e governor, t r a n s m i s s i o n l i n e and other components. 1 Chapter 3 i n v e s t i g a t e s the i n d i v i d u a l f a s t c o n t r o l s , the b r a k i n g i c s l b L u i (3R) c u u L r o l , cue forced e x c i t a t i o n (*£) control., ana the r a s t -v a l v i n g (FV) c o n t r o l to examine the e f f e c t i v e n e s s of BR c a p a c i t y , the FE c e i l i n g v o l t a g e l i m i t s , the f u l l and p a r t i a l FV c l o s u r e s and s i n g l e vs. m u l t i p l e a p p l i c a t i o n s on the t r a n s i e n t power system s t a b i l i t y . I n chapter 4, combinations of two or three f a s t c o n t r o l s are examined to f i n d whether there are advantages w i t h the combined f a s t con-t r o l over the i n d i v i d u a l f a s t c o n t r o l . Again, v a r i o u s degrees of c o n t r o l s of s i n g l e and m u l t i p l e a p p l i c a t i o n s are explored and compared. In chapter 5, the experimental r e s u l t s of f a s t c o n t r o l gathered from t e s t s on a l a b o r a t o r y micro-machine model developed by the UBC power group are presented and compared w i t h d i g i t a l s i m u l a t i o n s . F o l l o w i n g t h a t , schematic diagrams of the i n s t r u m e n t a t i o n f o r the f a s t c o n t r o l s and some improvement of the e x i s t i n g Dynamic Power System Test Model are recorded. 3 2. POWER SYSTEM MODEL FOR COMPUTER AND MICRO-MACHINE SIMULATION 2.1 I n t r o d u c t i o n I n a t y p i c a l power system, s e v e r a l generators supply power to the system' through t i e l i n e s . However, i n order to s i m p l i f y the study of the s t a b i l i t y of a p a r t i c u l a r generator, the r e s t of the system i s u s u a l l y represented as an i n f i n i t e bus to which t h i s s p e c i f i c generator i s con-nected through the l i n e s . A schematic diagram of a t y p i c a l one machine i n f i n i t e - b u s system w i t h v o l t a g e r e g u l a t o r and governor i s shown i n F i g . 2.1. I n t h i s chapter, major components of the one machine i n f i n t e - b u s system are described. System parameter values are a l s o i n c l u d e d . 2.2 Synchronous Machine Model The l a b o r a t o r y synchronous generator used f o r the i n v e s t i g a t i o n i n t h i s t h e s i s i s a s a l i e n t pole machine. In Park's c o - o r d i n a t e s , a con-v e n t i o n a l , s a l i e n t pole generator i s normally represented by f i v e windings, namely, the d i r e c t and quadrature a x i s armature windings (d & q ) , the f i e l d winding ( f ) , and the d i r e c t and quadrature damper windings (D & Q) as shown - - i n t i g . 2 . 2 . r o r - d i g i t a i s i m u l a t i o n s t u d i e s , a l l f i v e windings can be des-c r i b e d i n d e t a i l by d i f f e r e n t i a l equations. However, i n p r a c t i c a l s t a b i l i t y 2 s t u d i e s , synchronous machine equations of reduced order are normally used. * In t h i s t h e s i s , both the 5th and the 3rd order synchronous machine models i n Park's parameters, i n c l u d i n g the torque equations are s i m u l a t e d . Neg-l e c t e d are the e f f e c t s of s a t u r a t i o n , the v a r i a t i o n of parameters due to frequency and v o l t a g e changes, and the f a s t e l e c t r i c t r a n s i e n t s of the t r a n s m i s s i o n l i n e s . I n order to o b t a i n the 5th order model from the d e t a i l e d model, two assumptions are made, ( i ) the e f f e c t of transformer v o l t a g e s of the armature windings are n e g l i g i b l e . ( i i ) the e f f e c t of speed d e v i a t i o n on the speed v o l t a g e i s n e g l i g i b l e . The 5th order f l u x l i n k a g e equations of the generator are sum-marized i n equations ( A . l ) and (A.2) i n Appendix A. In order t o o b t a i n the 3rd order f l u x l i n k a g e model, an a d d i -t i o n a l assumption i s made th a t the e f f e c t of the two damper windings i s n e g l i g i b l e . The r e s u l t i n g 3rd order equations are summarized i n (A.3) VOLTAGE REGULATOR / INFINITE BUS BRAKING RESISTOR F i g . 2.1 A one machine i n f i n i t e - b u s system d-AXlS I I I I q-AXis F i g . 2.2 A 2-axis synchronous machine i n Park's dq-coordinates 5 and (A.4) i n Appendix A. The necessary synchronous machine parameters f o r the d i g i t a l s i m u l a t i o n s t u d i e s are obtained from previous t e s t s . 2 • 2 , 2 . 3 ^he parameters i n per u n i t , and t h e i r base q u a n t i t i e s are given i n Table I . 2.3 Voltage R e g u l a t o r - E x c i t e r Model The block diagram of the v o l t a g e r e g u l a t o r - e x c i t e r model used i n t h i s study i s shown i n F i g . 2.3. The parameter values are: KA = 50.0 TA = 0.05 sec. TE = 0.035 sec. V m a x = t 8.0pu The c e i l i n g v o l t age l i m i t s of the r e g u l a t o r e x c i t e r can be v a r i e d and w i l l be i n d i c a t e d when the change i s made. 2.4 Governor-Prime Mover Model Since f a s t v a l v i n g i s one of the major c o n t r o l s i n t h i s t h e s i s , the governor-prime mover system of a l a r g e steam t u r b i n e u n i t i s modelled i n d e t a i l . 2 ' 4 A b l o c k diagram r e p r e s e n t a t i o n of the governor and the f o s s i l f i r e d steam t u r b i n e u n i t i s shown i n F i g . 2.4. The f i r s t b l o c k from the l e f t i s a general r e p r e s e n t a t i o n of the e l e c t r i c a l - h y d r a u l i c or mechanical-hydra«ulic governor. The h i g h pressure torque THP, f o l l o w i n g the second b l o c k w i t h a time constant T4 }can be c o n t r o l l e d by the h i g h pressure c o n t r o l v a l v e , CV. Next, both the intermediate pressure torque, T i p , and the low pressure torque, TLp,are i n f l u e n c e d by the i n t e r c e p t o r v a l v e , IV,with time d e l a y s . In the b l o c k diagram, the e f f e c t of c o n t r o l v a l v e and that of i n t e r c e p t o r v a l v e are represented by m u l t i p l y i n g f a c t o r s . I t must be pointed out that although the f l o w - t o - s t r o k e r e l a t i o n s h i p of a p r a c t i c a l p lug type v a l v e or a b u t t e r f l y type v a l v e , i s n o n - l i n e a r as shown i n F i g . 2.5 and 2.6 r e s p e c t i v e l y , a l i n e a r r e l a t i o n s h i p F i g . 2.7 i s assumed f o r the t h e s i s study. This assumption i s considered t o be a good approximation by many i n v e s t i g a t o r s . 2 . 5 Table I I l i s t s t y p i c a l parameter values of a governor-turbine system of a f o s s i l f i r e d u n i t . 2.5 E x t e r n a l System A s i n g l e phase r e p r e s e n t a t i o n of the e x t e r n a l system i s shown i n F i g . 2.8, I t c o n s i s t s of a t r a n s m i s s i o n l i n e , c i r c u i t b r e a k e r s , b r a k i n g r e s i s t o r s , and an, i n f i n i t e bus. The r e a l t r a n s m i s s i o n l i n e i s three-phase d o u b l e - c i r c u i t , 576 m i l e s l o n g , and i n three s e c t i o n s . I t i s simulated by ir s e c t i o n s which a l s o i n c l u d e the e f f e c t of shunt r e a c t o r s (135 MVAR at 525 KVA) at both ends of each section.2.2 The Tr-model and i t s parametric MKS v a l u e s are 6 Table I Parameter and Base values f o r the Model Pbase = 6 3 3 ' ° w a t t s "e base = 3 7 7 ' ° r a d ' / eec. "m base = 1 8 8 , 5 r a d - / s e c . (4 p o l e s ) S t a t o r base V s base = 1 0 0 * ° v o l t s l i n e - t o - l i n e ZB base = 3 , 6 5 a m P s -Z = 15.8 ohms. s base Rotor base V. x .= 1758.0 v o l t s J r base = °* 3 6 ^ P 8 ' System parameters ( i n p.u. u n l e s s otherwise dimensioned) r - 0.0456 p . =0.0007 a f x,, = 1.025 x * = 0.173 x ' 1 = 0.153 d d d x = 0.614 x »* = 0.456 x . = 0.0253 q q a l T, » = 5.0 sec. T, »» = 0.027 sec. T f t = 0.0165 sec. do do qo H = 4.63 sec. D = 0.003 j o u l e s - s e c . / r a d . 7 KA 1 (1+sTA) • I, ,-.,l.|>L (1 + sTE) '•Fd F i g . 2.3 Block diagram of Voltage R e g u l a t o r - E x c i t e r system F i g . 2.4 Block..diagram o f Governor.;-Steam Turbine system 8 F i g . 2.5 Plug type valve F i g . 2.6 B u t t e r f l y type valve F i g . 2.7 Idealized l i n e a r valve c h a r a c t e r i s t i c c h a r a c t e r i s t i c c h a r a c t e r i s t i c Tabie I I Parameter values of a Governor-Turbine system f o r F o s s i l U n i t -r, KX> A w r r r p T ? T> - - l 1 R 0.05 T, 0.10 s e c . 1 T 0.20 s e c . 2 T3 0.03 s e c . T 4 0.20 s e c . T 5 10.0 s e c . T6 0.20 s e c . T7 0.40 s e c . Kl 0.30 K2 0.30 K3 0.40 h L 7 T r 77 T T FAULT SWITCH . 2.8 One phase of the Transmission L i n e 0.671 si 24.2 mh. -AW* WRP-298/* f =r 7.98 >«f F i g . 2.9 TheTT-Model 10 given i n F i g . 2.9. For the t h e s i s study, three banks of three-phase shunt b r a k i n g r e s i s t o r s of equal values are i n s t a l l e d at the l a b o r a t o r y machine t e r m i n a l s through three three-phase c i r c u i t breakers. Three r e s i s t a n c e values can be obtained w i t h the combination of one, two, or three r e s i s t o r banks. Thus, three d i f f e r e n t power r a t i n g s of b r a k i n g r e s i s t o r s can be achieved. 2.6 V a l i d i t y of D i g i t a l S i m u l a t i o n and Lab Test Models The v a l i d i t y of the model i s e s t a b l i s h e d f i r s t from a steady-s t a t e o p eration of the power system w i t h c o n v e n t i o n a l governor and e x c i t a -t i o n but w i t h a three-phase f a u l t d i s t u r b a n c e . Because no s p e c i a l f a s t c o n t r o l i s yet implemented on the micro-machine f o r the t r a n s i e n t s t a b i l i t y t e s t , the machine has approximately 50% l o a d so t h a t s e v e r a l o s c i l l a t i o n s of the swing curve can be observed. The disturbance i s a three-phase grounding of one c i r c u i t of the t r a n s m i s s i o n l i n e as shown i n F i g . 2.8. A f t e r 0.05 second, the c i r -c u i t breakers remove the f a u l t e d l i n e and approximately 0.45 second l a t e r the f a u l t i s c l e a r e d . The system i s r e s t o r e d at 0.5 second a f t e r the f a u l t i s i n i t i a t e d . The e q u i v a l e n t c i r c u i t - - o f the system under a l l c o n d i -t i o n s i s as i n F i g . 2.10 and the parameter values are given i n Table I I I . In F i g . 2.11(a) through ( e ) , comparisons are made of d i g i t a l s i m u l a t i o n of the 5th and the 3rd order synchronous machine w i t h an a c t u a l lab t e s t model, both w i t h conventional governor and v o l t a g e r e g u l a t o r . Except f o r some discrepancy w i t h the f i e l d v o l t a g e F i g . 2.11(c) and t e r -minal v o l t a g e F i g . 2.11(d), c l o s e agreement of torque angle F i g . 2.11(a) and speed F i g . 2.11(b) are observed between the computed and t e s t r e s u l t s i n the f i r s t swing and s l i g h t l y b e t t e r damping of the t e s t r e s u l t s i n the subsequent swings. I t i s a l s o observed t h a t there i s not much d i f f e r e n c e between the 5th and the 3rd order models i n the computed r e s u l t s of the f i r s t few swings. I t i s decided that the 3rd order model be chosen f o r the computer s i m u l a t i o n . 2.7 Load C o n d i t i o n f o r T r a n s i e n t S t a b i l i t y Studies Curves 1, 2, 3 and 4 of F i g . 2.12 show system swings f o l l o w i n g the disturbance w i t h generator l o a d of 550, 500, 400 and 300 watts r e s -p e c t i v e l y . Note that as the l o a d i n c r e a s e s , the system swings more ex-t e n s i v e l y as expected. 11 TI jl .— — A ' l r t ' - m l ; •-• ' - J „ .V-f __• - i x. - . - J ' . - . l . . - ' i . - i . »- -Table I I I E x t e r n a l system parameters i n p.u. SYSTEM CONDITION R X G B F a u l t e d one l i n e 0.109 1.610 0.127 -1.525 S i n g l e l i n e 0.109 1.610 0.000427 0.148 Double l i n e 0.055 0.805 0.000854 0.296 12 T 1 1.0 1.5 2.0 TIME (SECONDS) 2.5 3.0 1. 5 ^ order model F i g . 2.11(a) Power system swing curves 0.5 1.0 KS 2.0 . TIKE (SECONDS) 2. 3 r c* order model I . Lab Test r e s u l t 2.5 3.0 F i g . 2.11(b) Power system speed 13 14 0 . 5 5 -, 0 . 5 0 0 . 1 5 0.10 4 - f l . 3 5 r> t n 0 . 3 0 u i o <x -o • - 0 . 2 5 0 . 2 0 0 . J 5 0 . 1 0 / T L P (LOW pressure) X—Ov^ x /^if> (Intermediate X ^ - v ^ pressure) (High pressure) 0.05 -i o • ' i ' " " * * * * i *1 * * * 1 1 * * * 0 . 5 1 . 0 1 . 5 2 . 0 TIME (SECONDS) 2 . 5 ,rd 3 . 0 F i g . 2.11(e) Turbine torques w i t h 3 u order model i / Curves 1. E = 550 watt o 2. P =• 500 watt o 3. P = 400 watt o 4. P = 300 watt 0 . 5 • '•• 1 . 0 1 - 5 2 . 0 TIME (SECONDS) T 2 . 5 3 . 0 F i g . 2.12 System swing curves w i t h v a r i o u s loads 15 Curve 2 corresponds to the generator w i t h a l o a d of 500 watts and approaches very c l o s e l y to the t r a n s i e n t s t a b i l i t y l i m i t on t h e . f i r s t swing, whereas curve 1 w i t h an a d d i t i o n a l l o a d of 50 watts l o s e s synchron-ism on the f i r s t swing. Therefore, f o r the f a s t c o n t r o l study, the genera-t o r load of 500 watts i s chosen to f i n d out how the t r a n s i e n t s t a b i l i t y l i m i t can be improved. 1 6 3. MERITS OF VARIOUS FAST POWER SYSTEM CONTROLS 3 . 1 I n t r o d u c t i o n In t h i s chapter, three types of f a s t c o n t r o l s f o r t r a n s i e n t power system s t a b i l i t y are i n v e s t i g a t e d , the b r a k i n g r e s i s t o r (BR) c o n t r o l , the for c e d e x c i t a t i o n (FE) c o n t r o l , and the f a s t - v a l v i n g (FV) c o n t r o l . For each type of c o n t r o l , the general concept i s explored and a s p e c i f i c p o l i c y developed. The r e l a t i v e m e r i t s of these i n d i v i d u a l f a s t c o n t r o l s are a l s o i n d i c a t e d . 3.2 Concept of Power System S t a b i l i t y The b a s i c concept of power system s t a b i l i t y can be best i l l u s -t r a t e d by the use of a power-torque angle diagram f o r a one machine i n f i n i t e -bus system as shown i n F i g . 3 . 1 , i n c o n j u n c t i o n w i t h a s i m p l i f i e d swing equation ( 3 . 1 ) : d 2 6 V. V M 5 - « Pm - — sin $ ( 3 . 1 ) d+T m X In F i g . 3 . 1 , the s i n e curve shows the e l e c t r i c output power PQ under an i d e a l i z e d steady s t a t e and u n c o n t r o l l e d o p e r a t i n g c o n d i t i o n s , and the h o r i z o n t a l l i n e shows the mechanical i n p u t power P m which i s maintained constant. Under steady s t a t e o p e r a t i n g c o n d i t i o n , the system power i n p u t and output maintain an e q u i l i b r i u m at P Q. For a system under severe d i s -turbance and w i t h f a s t c o n t r o l s , the system behavior w i l l be q u i t e d i f f e r e n t and much more complicated. The system under study c o n s i s t s of a d o u b l e - c i r c u i t , t h r e e - s e c -t i o n t r a n s m i s s i o n l i n e . The type of system dis t u r b a n c e considered i s a temporary three-phase l i n e - t o - g r o u n d f a u l t a t the end of the f i r s t s e c t i o n of one c i r c u i t near the generator t e r m i n a l . This w i l l c r eate a momentary decrease i n generated power PQ and s i n c e the c o n v e n t i o n a l governor and e x c i t a t i o n c o n t r o l l e r s are unable to r e a c t w i t h adequate countermeasures immediately, the synchronous generator w i l l a c c e l e r a t e and r e s u l t i n system i n s t a b i l i t y . The most c r i t i c a l p e r i o d i s probably d u r i n g the f i r s t swing. E f f i c i e n t f a s t c o n t r o l means must be devised i n order t o reduce the power unbalance during the c r i t i c a l p e r i o d . Three types of c o n t r o l s , namely, the b r a k i n g r e s i s t o r c o n t r o l , the f o r c e d e x c i t a t i o n c o n t r o l , and the f a s t -v a l v i n g c o n t r o l w i l l be examined i n t h i s chapter. 17 F i g . 3.1 Power and torque-angle diagram © ® % F i g . 3.2 Power and torque-angle diagram w i t h Braking R e s i s t o r 18 3.3 Transient Power System S t a b i l i t y w i t h Braking R e s i s t o r C o n t r o l The b r a k i n g r e s i s t o r has proven to be one of the most e f f e c t i v e means of c o u n t e r a c t i n g power system disturbances.3.1,3.2 j t c a n q u i c k l y d i v e r t and absorb the excessive energy caused by the system d i s t u r b a n c e , thus, reducing the extent of generator a c c e l e r a t i o n and a v o i d i n g the l o s s of s t a b i l i t y . The br a k i n g r e s i s t o r has the g r e a t e s t e f f e c t when i t i s l o c a t e d near the generator t e r m i n a l s and may c o n s i s t of s e v e r a l banks i n p a r a l l e l f o r m u l t i p l e s e l e c t i o n . 3 , 3 The p r i n c i p l e of BR c o n t r o l can be ex p l a i n e d from f i g u r e 3.2. The i n t e r s e c t i o n of the mechanical i n p u t power Pm, and the generator output power curve S i , represents a p r e - f a u l t e q u i l i b r i u m . However, when the f a u l t occurs near the generator t e r m i n a l s on one c i r c u i t of the double c i r c u i t t r a n s m i s s i o n system, the generated power i s c o n s i d e r a b l y reduced and may be represented by a zero output power l i n e . When the f a u l t e d c i r c u i t i s c l e a r e d , the e l e c t r i c output of the system without any BR may be represented by curve S2- Although the system d i s t u r b a n c e may have a l -ready been detected through a f a u l t c u r r e n t sensor or power unbalance de-t c C u O i the f i i f o t " i.pplic~*"icn c f _f"hc BP ~££i~ be nadc c n 1 " ' is removed. 3* 3 A l s o , i t i s the time at which the r e s i s t a n c e value should be decided i f m u l t i p l e s e l e c t i o n i s a v a i l a b l e . A f t e r the b r a k i n g r e s i s t o r i s a p p l i e d , the system performance may be represented approximately by curve S 3 . The next step i s to determine the d u r a t i o n of the BR a p p l i c a t i o n . Since the BR can be removed very r a p i d l y , the peak torque angle can be used to s i g n a l the BR removal. The o v e r a l l p e r i o d of the BR a p p l i c a t i o n is governed by i t s c a p a b i l i t y of energy d i s s i p a t i o n and hence, the tempera-ture l i m i t of the design. One of the recommendations i s th a t a b r a k i n g r e s i s t o r must be capable of absorbing r a t e d generator output f o r at l e a s t 3 3 f i v e c y c l e s plus one h a l f of the output f o r ten c y c l e s . A f t e r the f i r s t swing a p p l i c a t i o n , there may be a need f o r f u r t h e r a p p l i c a t i o n of the BR, as w e l l as the m u l t i p l e magnitude s e l e c t i o n s , responsive to power unbalance, r o t o r a c c e l e r a t i o n , speed change, and/or r o t o r torque angle. The a l g o r i t h m to develop the BR c o n t r o l scheme i n t h i s t h e s i s is o u t l i n e d i n F i g . 3.3. A l l the f e a t u r e s of m u l t i p l e a p p l i c a t i o n and m u l t i p l e s e l e c t i o n of the b r a k i n g r e s i s t a n c e , and the time delays of open-19 F a u l t detected $ Delay BR a p p l i c a t i o n u n t i l f a u l t i s c l e a r e d BR CAPACITY SELECTION Monitor 3 BR banks w.r.t. magnitude of : AP or Ao 6 6 I At maximum torque-•angle remove a l l BR BR c o n t r o l r e q u i r e d R e - i n t i a t e BR c o n t r o l i f A u w ^ and u 0 . 0 e e r e f e BR c o n t r o l not r e q u i r e d End of BR c o n t r o l F i g . 3.3 BR c o n t r o l procedure 20 i n g or c l o s i n g c i r c u i t breakers are i n c l u d e d , although they are not a l l shown i n the o u t l i n e . For the BR study i n t h i s t h e s i s , the f o l l o w i n g parameters are chosen. Two c y c l e s or 0.03 second f o r the r e l a y and again two c y c l e s f o r the c i r c u i t breaker c l o s i n g or opening. For a l l s t u d i e s , a delay time of 0.1 second i s allowed f o r the b r a k i n g r e s i s t o r removal unless otherwise s p e c i f i e d , which corresponds to about one-tenth of the f i r s t swing. In p r a c t i c e , the l a s t parameter should be v a r i e d i n c o n j u n c t i o n w i t h the s i z e of the b r a k i n g r e s i s t o r to ensure that the generator w i l l not r e g a i n sub-s t a n t i a l a c c e l e r a t i o n . Each of the three banks of r e s i s t o r s i s assumed to be of equal value f o r s i m p l i c i t y i n m u l t i p l e s e l e c t i o n , which i s dependent upon the e l e c t r i c a l angular speed and upon the percentage of the power d e v i a t i o n as o u t l i n e d i n F i g . 3.3. The minimum a p p l i c a t i o n time i s chosen as 0.05 second a f t e r each s e l e c t i o n although c o n s i d e r a t i o n s must be given to the c i r c u i t breaker c a p a c i t y i n p r a c t i c a l a p p l i c a t i o n s . In the d i g i t a l s i m u l a t i o n , the f i r s t a p p l i c a t i o n of BR i s made a f t e r the clearance of f a u l t which i s detected by the t e r m i n a l c u r r e n t . The BR w i l l not be i n s e r t e d d u r ing the f a u l t because i t takes only 0.05 second t o c l e a r the f a u l t , i n c l u d i n g r e l a y time, and i t takes at l e a s t 0.06 seconds f o r the BR a p p l i c a t i o n . For the r e a p p l i c a t i o n of BR, the f o l l o w i n g two c o n d i t i o n s must be met: the speed must have exceeded a p r e s c r i b e d l i m i t a f t e r the f i r s t a p p l i c a t i o n , and the t o t a l number of a p p l i c a t i o n does not exceed the l i m i t allowed from temperature c o n s i d e r a -t i o n s . I n the f o l l o w i n g , d i g i t a l computer s i m u l a t i o n r e s u l t s of the e f f e c t of BR c o n t r o l are summarized. I n v e s t i g a t e d are the BR c a p a c i t y , s e l e c t i o n , d u r a t i o n of a p p l i c a t i o n and m u l t i p l e a p p l i c a t i o n s . F i g . 3.4 shows the e f f e c t of s i n g l e BR a p p l i c a t i o n w i t h no s e l e c t i o n but w i t h v a r i o u s c a p a c i t i e s , ( a ) , ( b ) , ( c ) , and, v a r i o u s a p p l i c a -t i o n d u rations 1, 2 and 3. Note t h a t without the BR c o n t r o l , the genera-t o r experiences a l a r g e i n i t i a l swing and e v e n t u a l l y l o s e s synchronism during the second swing f o r the disturbance s p e c i f i e d . However, w i t h the BR c o n t r o l , c o n s i d e r a b l e r e d u c t i o n i s achieved i n the i n i t i a l swing, which i s of v i t a l importance i n improving t r a n s i e n t s t a b i l i t y . B raking r e s i s t o r c a p a c i t i e s of 25%, 50%, and 75% generator 21 1.0 1.5 2.0 TIME ISECCNOSJ 3.0 F i g . 3.4(a) S i n g l e BR a p p l i c a t i o n , 25%.BR 0.5 1.0 1.5 2.0 2.5 3.0 TIME (SECONDS) F i g u r e s (a) 25% BR (b) 50% BR (c) 75% BR Curves NC-No c o n t r o l 1. 0.25 sec. 2. 0.50 sec. 3. 0.75 sec. F i g . 3.4(b) S i n g l e BR a p p l i c a t i o n , .50% BR F l g * 3 * 4 ( c ) S i n g l e BR a p p l i c a t i o n , 75% BR c a p a c i t y are chosen to i n v e s t i g a t e the e f f e c t of r e s i s t o r s i z e on the sy s -tem response f o l l o w i n g the d i s t u r b a n c e , and the r e s u l t s are shown i n F i g . 3.4(a), (b) and (c) r e s p e c t i v e l y . Even w i t h only 25% r e s i s t a n c e , the i n i t i a l swing of a l l cases w i t h d i f f e r e n t d u r a t i o n s of a p p l i c a t i o n are r e -duced by 50% approximately. With i n c r e a s e s of BR c a p a c i t y t o 50% and 75%, f u r t h e r r e d u c t i o n i n the i n i t i a l swing are achieved. These r e s u l t s r e v e a l that i n order to improve the f i r s t swing of the t r a n s i e n t s t a b i l i t y , i t i s b e n e f i c i a l to have a BR w i t h a c a p a c i t y as l a r g e as i t i s economically f e a s i b l e . To i n v e s t i g a t e the e f f e c t of r e s i s o r a p p l i c a t i o n time, d u r a t i o n s of 0.25, 0.50, and 0.75 seconds are chosen and they are shown as curves 1, 2 and 3 i n each f i g u r e r e s p e c t i v e l y . F i g . 3.4(a) r e v e a l s t h a t although the i n c r e a s e i n r e s i s o r a p p l i c a t i o n time from 0.25 to 0.50 seconds de-creases the magnitude of the i n i t i a l swing, f u r t h e r i n c r e a s e beyond 0.5 seconds has no n o t i c e a b l e improvement. In f a c t , continued a p p l i c a t i o n beyond the maximum torque angle has an adverse e f f e c t on the f i r s t swing as c l e a r l y shown i n 3.4(b) and ( c ) . The e x p l a n a t i o n f o r t h i s e f f e c t i s simple. Since the reverse swine of the g e n e r a t o r . i s caused by.the de^ ... . f i c i e n c y of the power output of the generator, any a d d i t i o n a l BR load must be s u p p l i e d at the expense of the generator's k i n e t i c energy, which makes the s i t u a t i o n even worse. Thus the l a r g e r the r e s i s t o r c a p a c i t y and the longer the r e s i s t o r a p p l i c a t i o n d u r ing t h i s p e r i o d , the worse w i l l be the reverse swing of the generator. Therefore, i n order to prevent excessive reverse swing without s e r i o u s l y damaging the t r a n s i e n t s t a b i l i t y l i m i t , the proper time to remove the BR i s at or near the maximum torque angle of each swing. The e f f e c t of BR c o n t r o l w i t h m u l t i p l e a p p l i c a t i o n , v i z . once, twi c e , or t h r i c e , and w i t h m u l t i p l e magnitude s e l e c t i o n , v i z . 1/3, 2/3, and 1 of 50%, 75%, and 100% BR c a p a c i t i e s are i n v e s t i g a t e d i n t h i s s e c t i o n . I t i s assumed th a t the r e s i s t o r i s d i v i d e d i n t o three banks of equal v a l u e . The c r i t e r i o n f o r s e l e c t i n g the number of banks i s based on the degree of power d e v i a t i o n and on the magnitude of speed d e v i a t i o n . For example, f o r each step i n c r e a s e or decrease i n power of 33.3% r e s i s t o r c a p a c i t y or speed l e v e l of 1 r q d . / s e c , one a d d i t i o n a l bank of r e s i s t o r , i f a v a i l a b l e i s added or removed. However, a l l banks of r e s i s t o r s must be removed simultaneously f o l l o w i n g the d e t e c t i o n of the peak torque angle. F i g . 3.5(a) shows the r e s u l t s of one PR a p p l i c a t i o n w i t h the s e l e c t i o n f e a t u r e . For the 50% c a p a c i t y , o n ly two of the three r e s i s t o r banks were a p p l i e d f o r 0.06 second and then one bank was l e f t i n f o r 0.49 second f o l l o w i n g the disturbance. For the 75% c a p a c i t y , o n ly one bank was i n s e r t e d f o r 0.53 second and f o r the 100% c a p a c i t y , again only one bank was i n s e r t e d f o r p e r i o d o f 0.51 second. Hence, from the r e s u l t s of F i g . 3.5(a) and p r e l i m i n a r y t e s t s , i t i s found t h a t by d i s t r i b u t i n g the r e s i s t a n c e i n t o s e v e r a l banks, l a r g e changes i n the system v a r i a b l e s due to BR s w i t c h i n g can be avoided thus a s s u r i n g a smooth system c o n t r o l . The e f f e c t of m u l t i p l e BR a p p l i c a t i o n on the system i s shown i n F i g s . 3.5(b) and 3.5(c). By comparing the two f i g u r e s , i t i s seen that w i t h the second a p p l i c a t i o n , the second p o s i t i v e swing i n a l l cases i s reduced by 50% approximately. S i m i l a r i l y , by comparing 3.5(b) and 3.5(c), f o r cases r e q u i r i n g a t h i r d a p p l i c a t i o n , the t h i r d p o s i t i v e swing i s e f f e c t i v e l y reduced. Along w i t h the m u l t i p l e a p p l i c a t i o n , a v a i l a b i l i t y of the m u l t i p l e s e l e c t i o n i s a l s o important. For example, i n the case of a 50% r e s i s t o r l i m i t e d to two a p p l i c a t i o n s , no more than two banks were used i n the f i r s t a p p l i c a t i o n , and i n the second a p p l i c a t i o n , combinations of three and one banks were employed i n su c c e s s i o n . In Table IV, d e t a i l s of the s e l e c t i o n and the a p p l i c a t i o n d u r a t i o n of r e s i s t o r c a p a c i t i e s of 25% and 50% w i t h m u l t i p l e a p p l i c a t i o n c o n t r o l are presented. The r e s u l t s i n d i c a t e that the BR c o n t r o l w i t h m u l t i p l e a p p l i c a t i o n and m u l t i p l e s e l e c -t i o n f e a t u r e s can smoothly and e f f e c t i v e l y dampen the secondary system swings. The e f f e c t of a 50% BR c o n t r o l w i t h m u l t i p l e s e l e c t i o n and m u l t i p l e a p p l i c a t i o n on system v a r i a b l e s are shown i n F i g . 3.6(a) through (e ) . I t i s c l e a r that the BR c o n t r o l can e f f e c t i v e l y r e s t r a i n l a r g e s y s -tem v a r i a b l e d e v i a t i o n s and r a p i d l y r e t u r n the system o p e r a t i o n to normal. To summarize, i t i s evident that the BR c o n t r o l i s v ery e f f e c t i v e i n reducing the f i r s t and second swings. I t should be a p p l i e d as soon as the f a u l t i s c l e a r e d and removed at the maximum torque angle. I t i s a l s o d e s i r a b l e to d i v i d e the BR i n t o p a r a l l e l banks so t h a t v a r i o u s s e l e c t i o n s can be made according to the s e v e r i t y of system d i s t u r b a n c e . F i n a l l y , when system s t a b i l i t y cannot be r e s t o r e d w i t h s i n g l e BR a p p l i c a t i o n , suc-c e s s i v e m u l t i p l e BR a p p l i c a t i o n i s necessary and proved e f f e c t i v e . 24 .0 1.5 2.0 T IHf (SECONDS) F i g . 3.5(a) BR a p p l i c a t i o n once (1) F i g . 3.5 M u l t i p l e BR a p p l i c a t i o n s w i t h m u l t i p l e s e l e c t i o n F i g u r e s (a) BR a p p l i e d once (1) (b) BR a p p l i e d twice (2) (c) BR a p p l i e d three times (3) 2.3 3.0 F i g . 3.5(b) BR a p p l i c a t i o n twice (2) Curves NC-No c o n t r o l 1. 50% BR 2. 75% BR 3. 100% BR F i g . 3.5(c) BR a p p l i c a t i o n three times (3) Table IV 25$ and 50$ BR control detail with multiple selection and multiple applications APPLICATION ,LIMIT FIRST APPLICATION SECOND APPLICATION THIRD APPLICATION 25$ BR 50$ BR . ; .25$ BR 50$ BR 25$ BR 50% BR Limit • 1 3 banks for (0.06) sec. 1 for (0.06) 2 for (0.06) 1 for (0.06) 2 for (0.18) 1 for (0.14)' 2 banks for (0.06) sec. and 1 bank for (0.04) sec. Not • Applicable (NA) , (NA) (NA) . (NA) 1 1 Limit = 2 Same as in Limit = 1 Same as in Limit = 1 3 banks for (0.42) sec. 1 for (0.19) 3 for (0.34) 1 for (0.19) (NA) (NA) Limit = 3 Same as in Limit = 1 Same as in Limit = 1 Same as in Limit = 2 Same as in Limit = 2 3 for (0.45) 1 for (0.80)-3 for (0.06) 1 for (0.06) 2 for (0.19) 1 for (0.19) 26 0.5 1.0 1.5 2.0 2.5 ' TIME (SECONDS) F i g . 3.6(a) 50% BR c o n t r o l (A £ response) 3.0 Curves NC-No c o n t r o l 1. 50% BR once (1) 2. 50% BR twice (2) 3. 50% BR " three times (3) 0.5 K O l ! s 2.0 TIME (SECONDS) F i g . 3.6(b) 50% BR c o n t r o l (AOJ- response) 28 3.4 Power System w i t h Forced E x c i t a t i o n C o n t r o l Forced e x c i t a t i o n (FE) c o n t r o l i s another e f f e c t i v e means of im-proving power system s t a b i l i t y . 3 . 4 , 3 . 5 This type of f a s t c o n t r o l i n v o l v e s e x c i t i n g the generator f i e l d w i t h maximum or minimum a l l o w a b l e v o l t a g e . I t i s made p o s s i b l e only w i t h the development of s o l i d - s t a t e or s t a t i c e x c i t e r which have not only f a s t response but a l s o h i g h c e i l i n g v o l t a g e s . When t h i s c o n t r o l i s p r o p e r l y designed, i t can a p p r e c i a b l y reduce both the i n i t i a l and succeeding system swings. The FE c o n t r o l scheme can be i l l u s t r a t e d by the power-torque angle diagram of F i g . 3.7(a), along w i t h the corresponding phase plane t r a j e c t o r y F i g . 3.7(b). When a f a u l t occurs near the generator, the s y s -tem moves from the steady-state o p e r a t i n g c o n d i t i o n 1 to the f a u l t p o i n t 2 and remains at that l e v e l u n t i l 3 where the f a u l t i s c l e a r e d . At t h i s c l e a r i n g time, a maximum p o s i t i v e f o r c e d e x c i t a t i o n i s a p p l i e d so that the system w i l l not only r i s e to p o i n t 4 but continue to p o i n t 5. I t w i l l remain on the curve u n t i l reaching 6. At 6, the system recovers i t s double c i r c u i t t r a n s m i s s i o n and w i l l approach p o i n t 7. But the p o s i t i v e f o r c e d - e x c i c a t i o n is - s f a L - l i on and- die system—will- move towards 5. - I t should "De-noted that the system does not change i n s t a n t a n e o u s l y from 6 to 8 s i n c e there are time delays i n the r e a l system. S h o r t l y a f t e r r e a c h i n g 9, the p o i n t of peak speed, the p o s i t i v e FE s h a l l be removed, a n t i c i p a t i n g a f i e l d delay and that by then the p o s i t i v e swing has been c o n t r o l l e d . At the maximum peak torque angle 10, the n e g a t i v e FE i s a p p l i e d i n order to reduce the excessive d e c e l e r a t i n g torque and thus p r e v e n t i n g a l a r g e r e -verse swing. At minimum speed 11, the negative FE i s removed and an appropriate l i n e a r e x c i t a t i o n c o n t r o l may take over i f p e r m i s s i b l e . F i g . 3.8 o u t l i n e s the FE c o n t r o l scheme developed i n t h i s t h e s i s . As shown, c r i t i c a l c o n t r o l d e c i s i o n s are dependent upon the measurable s t a t e v a r i a b l e s such as speed, torque angle, and f i e l d c u r r e n t , and a l s o , on the system f a u l t c o n d i t i o n . As i n d i c a t e d i n F i g . 3.8, the f i r s t p o s i -t i v e FE i s a p p l i e d immediately a f t e r the f a u l t i s removed and continued u n t i l s h o r t l y a f t e r d e t e c t i n g a maximum peak speed. I t i s assumed th a t the decay of p o s i t i v e e x c i t a t i o n i s s m a l l and w i l l not cause i n s t a b i l i t y . A t a maximum torque angle, the negative FE i s i n i t i a t e d and a p p l i e d u n t i l a minimum peak speed i s detected. Approximately, at t h i s 29 (normal double l i n e w i t h +FE) Sj (normal double l i n e ) ( s i n g l e l i n e w i t h +FE) 2 ( s i n g l e l i n e ) '5 (normal double l i n e w i t h -FE) F i g . 3.7(a) Power and torque-angle diagram w i t h Forced E x c i t a t i o n W maximum e minimum F i g . 3.7(b)- Speed and torque-angle diagram w i t h Forced E x c i t a t i o n 30 Large Disturbance w > w _ , e — e r e f 1 R e - i n i t i a t e next FE c o n t r o l c y c l e immediately FE c o n t r o l r e q u i r e d F a u l t detected Delay FE a p p l i c a t i o n u n t i l f a u l t i s c l e a r e d Apply p o s i t i v e FE I Remove P o s i t i v e FE a f t e r p r e s c r i b e d delay time f o l l o w i n g maximum speed d e t e c t i o n 1 At maximum torque-angle apply Negative FE I At minimum speed remove Negative FE Intermediate Disturbance W e r e f 1^ U e > "e r e f 2 • Apply P o s i t i v e FE u n t i l : - f i e l d c u r r e n t r e t u r n s to normal value OR -minimum torque-angle whichever occurs f i r s t R e - i n i t i a t e FE c o n t r o l i f : to > u „ and w > 0 . 0 e — e r e f e Small Di£ e ~~ e sturbance r e f 2 Apply P o s i t i v e FE u n t i l f i e l d c u r r e n t r e t u r n s to normal v a l u e FE c o n t r o l not r e q u i r e d End of FE c o n t r o l F i g . 3.8 FE c o n t r o l procedure 31 p o i n t , the torque changes from d e c e l e r a t i o n to a c c e l e r a t i o n and the next c o n t r o l step must be c a r e f u l l y chosen. The next c o n t r o l step taken i n t h i s t h e s i s a f t e r the removal of negative FE can be best explained w i t h the a i d of the speed-torque angle phase plane diagram of F i g . 3.9. Curves I , I I , a n d . I l l of 3.9 are t r a j e c t o r i e s of the system w i t h d i f f e r e n t degrees of i n s t a b i l i t y . For example, at curve I , the system i s more unstable than at curve I I I ; the torque angle and speed d e v i a t i o n s are c o n s i d e r a b l y l a r g e r i n the former than the l a t t e r . Two reference speeds W e r e f i and W e r e f 2 ( | W eref ]_| > | w e r e f 2 | ) are chosen to compare the s h a f t speed. I f the s h a f t speed i s l a r g e r than | w e r e f - J , a l a r g e secondary swing i s expected, and hence the next FE con-t r o l c y c l e must be prepared. On the other hand, i f the speed i s s m a l l e r i n magnitude than |W r e f 2 | the l i n e a r e x c i t a t i o n or other c o n t r o l s may ensue i f they can e f f i c i e n t l y s t a b i l i z e the system. However, l i m i t e d p o s i t i v e FE may be a p p l i e d to b r i n g the f i e l d current w i t h i n the range of the normal operating v a l u e . For speeds between the two r e f e r e n c e s , an intermediate FE c o n t r o l must be i n i t i a t e d and a p p l i e d u n t i l e i t h e r the - — f i e l d c u r r e n t s — r u m s tr> the* nnrma-l- 'ira or-—<r+"? ~? T T?t'?Tn 'reachesH Tf.iniir.um _ ' torque angle v a l u e , which ever occurs f i r s t . These options are necessary f o r system response c l o s e to curve I , adequate e x c i t a t i o n i s provided f o r r e - i n i t i a t i o n of the next c y c l e by b r i n g i n g the e x c i t a t i o n up to the normal v a l u e , or only a s m a l l p e r i o d of p o s i t i v e FE a p p l i c a t i o n between the m i n i -mum torque angle and the next r e - i n i t i a t i o n speed l e v e l i s missed. On the other hand, f o r system response c l o s e to curve I I I , over e x c i t a t i o n i s prevented by l i m i t i n g p o s i t i v e FE a p p l i c a t i o n u n t i l the f i e l d c u r r e n t has returned to normal. Here, the disturbance i s assumed s m a l l and the f i e l d c u rrent has returned to the normal value before the torque angle reaches i t s minimum value. In Table V, parameter values f o r the FE c o n t r o l are provided. The d i g i t a l s i m u l a t i o n r e s u l t s are shown i n F i g . 3.10(a) through (f ) and d e t a i l s of the FE c o n t r o l o p e ration f o r the "t 6 p.u. c e i l i n g l i m i t i s given i n Table VI. F i g . 3.10(a) r e v e a l s that the FE c o n t r o l a p p r e c i a b l y reduces the f i r s t and subsequent swings; e s p e c i a l l y the reverse or the negative p a r t of the f i r s t swing. With the i n c r e a s e of c e i l i n g v o l t a g e from i 6.0 to i 10.0 p.u., the system swing i s s u b s t a n t i a l l y reduced. ^ f?£F. F i g . 3.9 Speed-torque-angle phase plane diagram Table V Parameter values for the FE control Positive FE application: A u> > 1 . 0 rad./sec. and w > 0 . 0 r r e — e A P > P . and u > 0 . 0 e — e ref e Prescribed time delay for Positive FE removal after maximum speed detection: 0 . 0 5 second Speed reference to g (at minimum speed) : - 3 . 0 rad./sec. Speed reference u>e (at minimum speed) : -1.0 rad./sec. 1.0 1.5 2.0 TIME (SECONDS) " l " 2.5 3.0 F i g . 3.10(a) FE c o n t r o l ( A £ ) 12. 10 8 6. UJ 4 in CC £ 2 . -2 i > ! - 4 . -6 -8 -10 rl2 0 o-; o-i o o o 0-i o -i o-i o o us o.s 1.0 ' " l i s " 2.0 TIME (SECONDS) 2.5 3.0 Curves NC-No c o n t r o l 1. -6..0 p.u. (3) 2. -8.0 p.u. (3) 3. -10.0 p.u. (2 Fig. 3.10(b) FE c o n t r o l ( A W) 34 10.00 9 .00 8 .00 7 .00 6 .00 5 .00 4 .00 „ 3 .00 ^ 2 .00 Cl. " 1 0 n §-1.00 §-2.00 •* ^ - 3 . 0 0 - 4 . 0 0 - 5 . 0 0 - 6 . 0 0 - 7 . 0 0 - 8 . 0 0 - 9 . 0 0 - 1 0 . 0 0 A ' 3 O Ur'M i ' 5 <1 li -*•>• " 1 H ! /! / 1 < 1 > 1 ' 1-ii • I ' I J / I 1 ii ni l IPs • •/ 1 r 1 i i : ' '1 1 ; 1 i : 1 : i 1 . ; : ii 1 Ii 1-, '.1 /'I j l ' H I /iri/ i f i i i li J I I I 1 ! !'- > mrr s j .7 i ! Ii / Ii1 R / •  "i= / 11 / i 1 !•• I • • /• i i ; T ! ! M 1 i / i V . i I I I v# I ' M / 1 l! / i ' • 1!-' \ / I\Vf I \> 1 I A i 1 1 t i r- i 1 --Ii V 1 M; 1 I 1 I 1 v • ' 1 r 1 1 1 \l 1 \l VI (^ i i i i i 0 . 5 1.0 1.5 2 .0 TIME (SECONDS) • • i i 2 . 5 3 . F i g . 3.10(c) FE c o n t r o l (E •) rd Curves NC-No c o n t r o l 1. -6.0 p.u. (3) 2. -8.0 p.u. (3) 3. ^10.0 p.u. (3: 35 ] .30 1.20 ^1.10 -1 .00 0.80 -d 0.70 0.60 AY. lis \\ i V t M A , w/a/ \\//v w •11 • • 0.5 • • i i i •' 1.0 1.5 2.0 TIME (SECONDS) 2.5 3.0 F i g . 3.10(e) FE c o n t r o l (V ) Curves NC-No c o n t r o l 1. -6.0 p.u. (3) 2. -8.0 p.u. (3) 3. -10.0 p.u. (3 36 Table VI - 6.0 p.u. Forced E x c i t a t i o n c o n t r o l a p p l i c a t i o n d e t a i l FE .APPLICATION SYSTEM CONDITION AND SIMULATION • CYCLE FE CONTROL STEPS TIME (sec.) F a u l t detected 0.02 F a u l t c l e a r e d 0.07 F i r s t P o s i t i v e (+) FE a p p l i e d i 0.09 A p p l i c a t i o n + FE removed '; 0.41 Double l i n e s r e s t o r e d 0.51 Negative (-) FE a p p l i e d i 0.57 - FE removed + FE a p p l i e d (to . = -5.34 rad./sec.) r r e mm. next FE c o n t r o l r e - i n i t i a t e d 0.84 - - - - —r= -. h—F-R-removed— - — - 1.40 -- FE a p p l i e d 1.55 Second + FE a p p l i e d (to . = -2.45 rad./sec.) e min 0 = A p p l i c a t i o n i n t e r m e d i a t e FE c o n t r o l + FE removed min. 1.74 f i e l d c u r r e n t up to 91$ of normal value . 2.02 + FE c y c l e r e - i n i t i a t e d 2.17 + FE removed 2.35 T h i r d - FE a p p l i e d 2.48 A p p l i c a t i o n - FE removed + FE a p p l i e d (to . = -0.87 rad./sec.) r i r e min. 2.62 f i e l d c u r r e n t n o r m a l i z a t i o n c o n t r o l 2.62 + FE removed ( f i e l d c u r r e n t r e t u r n e d to normal value) 2.82 37 Although the FE c o n t r o l w i t h llO.O p.u. c e i l i n g i n d i c a t e s some i n s t a b i l i t y i n the succeeding swings, i t can be remedied by r e f i n i n g the speed r e f e r -ences of the c o n t r o l , or by app l y i n g i t w i t h the l i n e a r o p t i m a l c o n t r o l . The e f f e c t of FE c o n t r o l on.other system v a r i a b l e s are shown i n F i g . 3.10(b) through ( f ) . F i g . 3.10(b) records the speed v a r i a t i o n s c o r -responding to F i g . 3.10(a). From the f i e l d v o l t a g e response, F i g . 3.10(c), the FE c e i l i n g v o l t a g e s are c l e a r l y seen. Note that during the f i r s t p o s i t i v e swing when maximum p o s i t i v e e x c i t a t i o n i s r e q u i r e d , the FE c o n t r o l maintains the r e q u i r e d p o s i t i v e f i e l d v o l t a g e , and a l s o , d u r i n g the reverse swing when maximum negative FE i s r e q u i r e d , i t again r e t a i n s the r e q u i r e d l e v e l . In c o n t r a s t , i n the case without FE c o n t r o l , the f i e l d v o l t a g e a f f e c t e d by conventional voltage r e g u l a t o r responds e r r a t i c a l l y most of the time. The e f f e c t of FE c o n t r o l on the t e r m i n a l v o l t a g e i s recorded i n F i g . 3.10(e). When FE i s a p p l i e d , l a r g e r t e r m i n a l v o l t a g e d e v i a t i o n s occur which i s not d e s i r a b l e . But during the d i s t u r b a n c e , the hi g h e s t p r i o r i t y must be placed i n mai n t a i n i n g synchronism w i t h the r e s t of the power system, and some app r e c i a b l e v o l t a g e d e v i a t i o n s w i t h i n safe l i m i t s are g e n e r a l l y ' t o l e r a t e d . F i n a l l y , che input-output power d i f f e r e n c e i s recorded i n F i g . 3.10(f). From a l l those r e s u l t s , i t i s evident that the forced e x c i t a t i o n c o n t r o l can s u b s t a n t i a l l y reduce a l l system e x c u r s i o n s , e s p e c i a l l y the f i r s t two p o s i t i v e and negative swings. The f o l l o w i n g important aspects of the FE c o n t r o l were e s t a b l i s h e d i n t h i s s e c t i o n . The c o n t r o l can e f f e c t i v e l y improve power system damping i n the f i r s t few swings, e s p e c i a l l y the negative p a r t of the f i r s t swing. A f t e r the f i r s t a p p l i c a t i o n , the p o s i t i v e FE should be removed s h o r t l y a f t e r d e t e c t i n g a maximum peak speed. The a p p l i c a t i o n of the negative FE should be made at the maximum torque angle and continued u n t i l s h o r t l y a f t e r d e t e c t i n g a minimum peak speed. A f t e r the removal of the negative FE, the next c o n t r o l must be i n i t i a t e d i n accordance w i t h the s e v e r i t y of the system as can be determined by the magnitude of speed d e v i a t i o n . For the most severe c o n d i t i o n , r e - i n i t i a t i o n of the next c y c l e of FE c o n t r o l must be made immediately, f o r a l e s s severe c o n d i t i o n , only a l i m i t e d amount of p o s i t i v e FE need be a p p l i e d u n t i l e i t h e r the minimum torque angle i s reached or the f i e l d c u r r e n t r e t u r n s to the normal v a l u e , and f o r the l e a s t severe c o n d i t i o n , only a momentary p o s i t i v e FE c o n t r o l need be a p p l i e d t o r e t u r n the f i e l d current to i t s normal op e r a t i n g v a l u e . 38 3.5 Power System w i t h F a s t - V a l v i r i g C o n t r o l The aim of f a s t - v a l v i n g (FV) c o n t r o l i s to provide f a s t r e d u c t i o n of prime mover torque during the f i r s t p o s i t i v e swing and hence maint a i n s t a b i l i t y during the system disturbance. 3-6,3.7 Both the i n t e r c e p t o r v a l v e (IV) between the reheater and intermediate and low pressure stages of a steam t u r b i n e and the c o n t r o l v a l v e (CV) of the high pressure s i d e can be used. This c o n t r o l has been made p o s s i b l e by the i n t r o d u c t i o n of modern e l e c t r o - h y d r a u l i c governors to re p l a c e the mech a n i c a l - h y d r a u l i c types. With the former, the c l o s u r e time i s c o n s i d e r a b l y reduced to as short as 0.15 seconds. 3*** I t i s a l s o very important to have the f e a t u r e of f a s t reopening of the steam v a l v e to prevent system i n s t a b i l i t y on the reverse swing. The mechanism of f a s t - v a l v i n g i n v o l v e s the c o n t r o l of the i n t e r -ceptor (IV) and/br the c o n t r o l v a l v e (CV),according to the system r e q u i r e -ment. When the generator e l e c t r i c a l power output suddenly decreases due to a f a u l t near the t e r m i n a l , c o n s i d e r a b l e r e d u c t i o n i n mechanical power in p u t can be a t t a i n e d by immediately c l o s i n g e i t h e r of these two v a l v e s or both. When the f a u l t i s temporary, the system's quick v o l t a g e recovery w i l l c r e a t e a sudden demand f o r generated power" output." In such a case , ' these ' tw w "valvto' should be r a p i d l y reopened t o supply the necessary mechanical power i n p u t as re q u i r e d . A f t e r the f i r s t swing, there may be a need f o r another a p p l i c a -t i o n of FV but p a r t i a l c l o s u r e s of both or by the IV alone may be s u f f i c i e n t to m a i n t a i n s t a b i l i t y . In F i g . 3.11, the FV c o n t r o l scheme i s o u t l i n e d . A l l important f e a t u r e s such as r e l a y delay time, v a l v e opening and c l o s u r e time, and a l s o the p o s s i b i l i t y of m u l t i p l e a p p l i c a t i o n s are i n c o r p o r a t e d although not a l l of them are shown. In a d d i t i o n , although not i n d i c a t e d i n the o u t l i n e , f u l l and p a r t i a l c l o s u r e s of the IV, p a r t i a l c l o s u r e of the CV, and t h e i r combinations are a l s o i n v e s t i g a t e d . For the t h e s i s study, the FV c o n d i t i o n s are as f o l l o w s unless otherwise mentioned: 0.1 second f o r the r e l a y delay, 0.1 second f o r the IV f u l l opening and f u l l c l o s i n g and 0.05 seconds f o r 50% IV c l o s u r e . The only exception i s that i n the study of f a s t c o n t r o l u s i n g IV i n con j u n c t i o n w i t h CV, 0.1 second i s chosen f o r a 50% IV c l o s u r e . The CV i s never c l o s e d beyond 50% at any time, and i t s v a l v e opening, and c l o s i n g time f o r the com-bined CV and IV c o n t r o l i s 0.1 second. The v a l v e openings are i n i t i a t e d when the peak speed i s detected. For a l l v a l v e opening and c l o s i n g o p e r a t i o n s , 39 F a u l t detected Apply f u l l IV OR f u l l IV and 50$ CV immediately r At maximum speed begin v a l v e re-opening Apply e i t h e r : IV alone OR f u l l IV alone OR f u l l IV and 50$ CV OR 50$ IV and 50$ CV FV c o n t r o l r e q u i r e d R e - i n i t i a t e FV c o n t r o l i f : ( o n l y one of the f o l l o w i n g ) (a) A a) > u> _ and u > 0.0 ^ J e e ref. e •(b) A P e > A . P e r e f and & e>0.0 FV c o n t r o l 1 not r e q u i r e d End of FV c o n t r o l F i g . 3«11 FV c o n t r o l ' procedure 40 l i n e a r r e l a t i o n s h i p between steam fl o w and v a l v e c l o s u r e i s assumed. In F i g . 3.12(a), d i g i t a l computer s i m u l a t i o n r e s u l t s of the e f f e c t of r e l a y delay f o r FV u s i n g IV alone are shown. The graphs r e v e a l t h a t the f a s t e r the r e l a y response, the b e t t e r w i l l be the r e s u l t . Both the f i r s t p o s i t i v e and negative swing can be reduced w i t h f a s t r e l a y time. To i l l u s t r a t e the e f f e c t of IV c l o s i n g time, the r e s u l t s i n v o l v i n g only the f u l l IV c l o s u r e are shown i n F i g . 3.12(b). I t i s evident from the graph that a p p r e c i a b l e reduction, i n the f i r s t swing can be achieved w i t h the f a s t IV c l o s u r e . The e f f e c t of v a l v e c l o s u r e d u r a t i o n on the system s t a b i l i t y i s shown i n F i g . 3.12(c). Curve 1 corresponds to a v a l v e c l o s u r e u n t i l the system i s recovered (0.5 sec. duration) and curve 2 a c l o s u r e u n t i l a peak speed i s reached. Note that although an a d d i t i o n a l r e d u c t i o n i n the f i r s t p o s i t i v e swing i s achieved by the former, i t has an adverse e f f e c t on the negative reverse swing. The r e s u l t suggests that the peak speed i s the best time to i n i t i a t e the v a l v e reopening a f t e r a f a s t v a l v e c l o s u r e . A f t e r e s t a b l i s h i n g the best IV reopening time, the advantage of c o n t r o l l i n g both the i n t e r c e p t o r and the main c o n t r o l v a l v e s i s explored. I t can be seen by comparing curves 2 and 3 of F i g . 3.12(c) t h a t these are appreciable reductions both i n the i n i t i a l p o s i t i v e swing and i n the r e v e r s e negative swing. The e f f e c t of a p p l y i n g e i t h e r a f u l l or a 50% IV c l o s u r e w i t h a v a l v e opening time of 0.1 second on the system s t a b i l i t y i s compared i n F i g . 3.13(a) and 3.13(b). C l e a r l y , w i t h f u l l v a l v e c l o s u r e , g r e a t e r attenua-t i o n of the p o s i t i v e swings i s achieved. However, w i t h regard to the over-a l l improvement i n system s t a b i l i t y gained by FV c o n t r o l , 50% p a r t i a l v a l v e c l o s u r e seems to be almost as good as the f u l l v a l v e c l o s u r e . Hence, unless the system s t a b i l i t y i s very c r i t i c a l , o n l y 50% p a r t i a l v a l v e c l o s u r e c o n t r o l w i l l be a p p l i e d , f o r i t could be a good compromise between improving the s t a b i l i t y and reducing the s t r e s s on the t u r b i n e b o i l e r system. I t has been noted that the v a l v e opening time i s an important f a c t o r i n preventing excessive reverse swing as have been shown i n F i g . 3.13 ( a ) , 3.13(b), 3.13(c), and 3.13(d). As the opening time of IV and CV or IV alone i s i n c r e a s e d , there i s a corresponding i n c r e a s e i n the reverse swing. Therefore, the reopening of the v a l v e s should be accomplished as r a p i d l y as the t u r b i n e system permits. 41 140.0-120.0 4 ioo;o4 80.0 4 60.0 5 e 40.0 U J 0 1 -20.0 t — 5 -40.0 UJ £ -60.0 ° -80.0 -100.0 -120.0 -140.0 -160.0 0.5 1.0 1.5 TIME (SECONDS) 2.0 o!s 1!o 1.5 TIME (SECONDS) 2.0 F i g . 3.12(a) E f f e c t of r e l a y time F i g . 3.12(b) E f f e c t of IV cl o s u r e time 1. 0.05 sec. 2. 0.10 sec. 3. 0.20 sec. 0.5 1.0 1.5 2.0 TIME (SECONDS) 3.0 F i g . 3.12(c) E f f e c t of v a l v e c l o s u r e d u r a t i o n 1. O.SO sec. f u l l IV c l o s u r e 2. peak speed f u l l IV c l o s u r e 3 . peak speed f u l l IV and 50% CV c l o s u r e s 4 2 Curves 1. 0.1 sec. 2. 0.5 sec. 3. 1.0 sec. 4. 4.0 sec. 0.5 1.0 U5 2.0 TIME (SECONDS) 3.0 F i g . 3.13(a) E f f e c t of IV opening ( f u l l c l o s u r e ) Curves 1. 0.05 sec. 2. 0.10 sec. 3. 0.50 sec. 4. 4.0 sec. ' I I " I " I I I I I I I , ! m 0.5 1.0 1.5 2.0 2.5 3.0 TIME (SECONDS) F i g . 3.13(b) E f f e c t of IV opening (50% c l o s u r e ) 43 1.0 l^S 2.0 TIME (SECONDS) F i g . 3.13(c) E f f e c t of IV and CV opening (50% IV and 50% CV c l o s u r e ) Curves. 1. 0.05 sec 2. 0.10 sec 3. 0.50 sec 4. 4.0 sec. -160.0 | i 0.5 1.0 f .5 2.0 TIME (SECONDS) 2.5 n 3.0 F i g . 3.13(d) E f f e c t of IV and GV opening . ( f u l l IV and 50% CV c l o s u r e ) Curves 1. 0.1 sec. 2. 0.5 sec. 3. 1.0 sec. 4. 4.0 sec. 44 The r e s u l t s of m u l t i p l e f a s t - v a l v i n g a p p l i c a t i o n s are shown i n F i g . 3.14(a) through (d). In a l l cases, the maximum number of a p p l i c a t i o n s were l i m i t e d to two and more than that are considered redundant, e s p e c i a l l y when the FV c o n t r o l i s a p p l i e d i n c o n j u n c t i o n w i t h other f a s t c o n t r o l s . The e f f e c t s of two d i f f e r e n t i n i t i a t i o n s i g n a l s , the power and the speed, on the second swing i s shown i n F i g . 3.14(a). Since power un-balance of the system i s detected before the speed d e v i a t i o n s , the former s i g n a l i s more e f f e c t i v e than the l a t t e r as i n d i c a t e d by an a p p r e c i a b l e r e d u c t i o n i n the second swing. A comparison i s a l s o made between 50% and f u l l second IV c l o s u r e i n F i g . 3.14(b), both w i t h power d e v i a t i o n s i g n a l : f u l l second IV c l o s u r e i s more e f f e c t i v e than 50%. , The e f f e c t of 50% Instead of the f u l l v a l v e c l o s u r e f o r the second a p p l i c a t i o n w i t h v a r i o u s i n i t i a t i o n s i g n a l s i s f u r t h e r explored i n F i g . 3.14(c). A l l r e s u l t s i n d i c a t e l a r g e r second swings. However, there may be s i t u a t i o n s where only moderate t u r b i n e c o n t r o l , i . e . , o n ly p a r t i a l v a l v i n g and not f u l l v a l v i n g i s d e s i r e d . The d e c i s i o n i n p r a c t i c e should be based on the degree of excess power. The r e s u l t s of two 50% CV and IV f a s t - v a l v i n g s are shown i n F i g . 3.14(d). The r e s u l t s are not encouraging f o r t h i s p a r t i c u l a r d i s t u r b a n c e , suggesting that f a s t - v a l v i n g has to be a p p l i e d simultaneously w i t h other f a s t c o n t r o l s . ' The importance of r a p i d v a l v e re-opening w i t h m u l t i p l e a p p l i c a t i o n i s r e c o g n i z a b l e i n F i g . 3.14(d), when curves 1 and 2 are compared w i t h curves 3 and 4 r e s p e c t i v e l y . C l e a r l y , the system s t a b i l i t y i s enhanced w i t h the f a s t e r v a l v e re-opening time of 0.1 second than that of 0.5 second. The same f i g u r e a l s o shows IV and CV c o n t r o l s (curves 1 and 3) are b e t t e r than IV c o n t r o l alone (curves 2 and 4 ) . Responses of the t u r b i n e torques and the generator e l e c t r i c a l torque w i t h and without the FV c o n t r o l are shown i n F i g . 3.15(a) through ( i ) . Note that without FV, F i g . 3.15(a), the t u r b i n e torque i s c o n t r o l l e d mainly by the r e g u l a r speed governor which i s intended only f o r s m a l l speed and power v a r i a t i o n s and not f o r t r a n s i e n t s t a b i l i t y c o n t r o l . The t u r b i n e torque response, T m, of F i g . 3.15(a) i s f u r t h e r r e s o l v e d i n t o the HP, IP, and LP components as shown at the bottom of the same f i g u r e . The t o t a l t u r b i n e torque and i t s components w i t h the FV c o n t r o l s are shown i n F i g . 3.15(b) through ( i ) . In a l l cases, the t u r b i n e torque, Tm a t the end of 45 -120 .0 --140.0 --160.0 ] ( i i i i 0 0.5 1.0 1.5 2.0 2.5 3.0 TIME: (SECONDS' F i g . 3.14(a) Power vs speed r e - i n i t i a t i o n s i g n a l i n two IV cl o s u r e s - F u l l IV cl o s u r e s f o r two a p p l i c a t i o n s (curves 1 and 2) -120.0 --140 .0 --160-0 \ . . . . | , , , , 0 0.5 1.0 1.5 2.0 2.5 3.0 TIME ISEC0NDS) Power r e - i n i t i a t i o n s i g n a l i n two IV c l o s u r e s 1. F u l l IV cl o s u r e s f o r two a p p l i c a t i o n s 2. F u l l IV c l o s u r e f o r f i r s t and 50% IV c l o s u r e f o r second Fig. 3.14(b) Curves 1. AP s i g n a l e 2. At) . s i g n a l e 3 . AP s i g n a l e 4 . Ao s i g n a l Valve opening time =0.5 sec . 0 . 5 3.0 F i g . 3.14(c) 1 . 0 1 . 5 2 . 0 TIME (SECONDS) Power vs speed r e - i n i t i a t i o n s i g n a l i n two IV c losures -Ful ] j IV c losures for two a p p l i c a t i o n s (curves 1,2) - F u l l IV c losure for the f i r s t and 50% IV c lo sure for second (curves 3,4) 1 4 0 . 0 -q 1 II Curves 0. 5 s e c va lve opening 1. IV and CV 2. IV only 0.1 sec . valve opening 3. IV and CV 4. IV only 3.0 | i i i I i i i i i f r r i - r r r r n f rT 0 0.5 1.0 TIHE 1SEC0NDS1 F i g . 3.14(d) IV or IV and CV c o n t r o l w i th two a p p l i c a t i o n s —50% IV c losures (curves 2,4) -50% IV and 50% cV c losures (curves 1,3) 47 2.50 -i 2.00 A 1.50 1.00 . cnO.50 -\ -0.50 -1.00 - ] . 5 0 | i i i • M -0.0 0.2 0.4 O.C O.P 1.0 1.2 1.4 1.6 1.8 2.0 TIME I SECONDS) Torques T - e l e c t r i c a l e torque T -mechanical m torque 1.00 0.90 i 0.80 -3 0.70 -O.60-3 => a. i n 0 . 5 0 UJ § ° 0 . 4 0 -i 0.30 0.20-3 0.10-3 •Tup -Tie i i I . i . i i . i n i i ; " '"i 0 0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0 TIME '.SECONDS) I n d i v i d u a l Turbine Torque T T T )-Low pressure T IP-Intermediat« pressure T R p- High pressure F i g . 3.15(a) Turbine torques without FV c o n t r o l 48 2.50 1.00 - 0 . 5 0 -1.00 -1.50 H i r / I / -0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0 TIME ISECON0S) 2.00 1.S0H I.00H .nO.50 -O.SOH -1.00 '•••1 1 ' 1 1 1 1 1 " ) • ' " • -3.0 8.2 0.4 0.6 0.8 1.0 1.2 !.4 l . C 1.8 2.0 TIME -.SECONDS) 49 . 3.15(d) 50% IV and 50% CV c l o s u r e F i g . 3.15(e) F u l l IV c l o s u r e once (1) and 50% CV c l o s u r e once F i g . 3.15(f) 50% IV c l o s u r e twice (2) 51 F i g . 3.15(h) F u l l IV c l o s u r e f o r f i r s t F i g . 3.15(i) F u l l IV c l o s u r e a p p l i c a t i o n and 50% IV twice (2) c l o s u r e f o r second a p p l i c a t i o n 52 1.00 O.SO 0 . 0 0 0.70-3 „0.60 5 > 0 .30 0 . 1 0 1.00 -IV - cv 1.0 l . S 2 . 0 TIME ISECONDSI 2 . 5 3 . 0 0 . 2 0 . 3 0.4 T J f K {SECONDS) F u l l IV cl o s u r e and 50% CV c l o s u r e (b) Expansion of (a) 1.00 7 - 1 o.so .o.eo 0.70 J 1 . 6 0 Jr ? I.SO 'o.o 0.30 0.23 -0.10-0 k-zv o.s 1 .3 l . S 2 . 3 TIME ISECONOS) 2 . 5 3 . 0 1.33 O.SO o.eo -. 0.70-cJO.60 an &0.SO-J 0^.40 ' 0.30-3 0.20 0.10-3 U-xv 1 .3 l . S 2 . 3 TIME fSEI3N051. 2 . S 3 . 3 F u l l IV cl o s u r e s twice (2) (d) F u l l IV c l o s u r e f o r f i r s t and 50% IV cl o s u r e f o r second a p p l i c a t i o n F i g . 3.16 Various v a l v e c l o s u r e s 53 the f i r s t 0.5 second f o l l o w i n g the system disturbance has. been a p p r e c i a b l y reduced i n an attempt to match the decrease i n e l e c t r i c a l torque, and i n the cases of two FV a p p l i c a t i o n s , the second t u r b i n e torque r e d u c t i o n s are a l s o a t t a i n e d during the p e r i o d when the e l e c t r i c a l torque again decrease below i t s normal operating l e v e l . F i n a l l y , i n F i g . 3.16, some v a l v e c l o s u r e s during the system d i s -turbances are recorded. These graphs r e v e a l important f e a t u r e s such as valv e c l o s u r e and opening time, d u r a t i o n of c l o s u r e , 50% p a r t i a l v a l v e c l o s u r e , and m u l t i p l e a p p l i c a t i o n s . In t h i s s e c t i o n , many important aspects of FV c o n t r o l have been e s t a b l i s h e d . The study has shown that f a s t r e l a y and a l s o f a s t v a l v e c l o s u r e and opening times are d e s i r a b l e . A l s o , the use of the peak speed s i g n a l to i n i t i a t e the v a l v e reopening i n s t e a d of a p r e s c r i b e d d u r a t i o n of c l o s u r e , has proven to be more b e n e f i t i a l . Furthermore, the study i n d i c a t e s that system s t a b i l i t y can be improved by m u l t i p l e a p p l i c a t i o n and by c o n t r o l l i n g both the IV and the CV. F i n a l l y , a 50% p a r t i a l v a l v e c l o s u r e may be appro-p r i a t e f o r the secondary swings when only moderate c o n t r o l i s r e q u i r e d . 54 4. INFLUENCE OF COMBINED FAST CONTROLS IN TRANSIENT STABILITY 4.1 I n t r o d u c t i o n In Chapter 3, the e f f e c t i v e n e s s of improving t r a n s i e n t s t a -b i l i t y w i t h the b r a k i n g r e s i s t o r c o n t r o l , the fo r c e d e x c i t a t i o n c o n t r o l , and the f a s t v a l v i n g c o n t r o l s were e s t a b l i s h e d . But they were a p p l i e d s e p a r a t e l y . In t h i s chapter, these f a s t c o n t r o l s are combined and co-ord i n a t e d , and a p p l i e d simultaneously i n an attempt to f u r t h e r improve the t r a n s i e n t s t a b i l i t y of a system during the distu r b a n c e . For severe d i s t u r b a n c e s , f a s t c o n t r o l of both the mechanical input power w i t h FV and the generated e l e c t r i c output power w i t h BR and/or FE may be necessary. When the combined c o n t r o l s are designed, some t r a d e o f f s from cost c o n s i d e r a t i o n s are necessary, although i t i s beyond the scope of t h i s t h e s i s study. For example, the s i z e of BR can be reduced not o n l y to decrease the cost i t s e l f , but a l s o the a s s o c i a t e d c i r c u i t breaker c a p a c i t i e s and the c e i l i n g v o l t a g e l i m i t of the FE which determines the cost of cue s o i i d - s c a c e e x c i t e r . This a l s o a p p l i e s to r"v. c o n t r o l . P a r t i a l and s i n g l e v a l v i n g might prove to be s u f f i c i e n t . Of course, the co s t of inst r u m e n t a t i o n and the o v e r a l l r e l i a b i l i t y a l s o must be taken i n t o con-s i d e r a t i o n f o r the design. In t h i s chapter, however, the i n v e s t i g a t i o n of combined f a s t c o n t r o l s w i l l be r e s t r i c t e d to the t e c h n i c a l aspect. In a d d i t i o n , a l i n e a r o p t i m a l e x c i t a t i o n c o n t r o l (LOC) i s de-signed which can dampen sm a l l system dynamic o s c i l l a t i o n s . I t i s expected that a f t e r the f i r s t or the secondary swing f o l l o w i n g a s e r i o u s system disturbance when the system o s c i l l a t i o n has been harnessed and reduced by the f a s t c o n t r o l s to s m a l l o s c i l l a t i o n s , the LOC can q u i t e comfortably and e f f e c t i v e l y s t a b i l i z e the system, thus a v o i d i n g the unnecessary and pos-s i b l y i n e f f e c t i v e successive f a s t c o n t r o l r e - a p p l i c a t i o n s . 4.2 System S t a b i l i t y w i t h LOC and Fast C o n t r o l s The LOC designed i n t h i s t h e s i s i s based on the same p r i n c i p l e as developed by UBC power group. The process i s summarized i n Appendix B. The r e s u l t i n g optimal e x c i t a t i o n c o n t r o l i s : -Tj = (-0.27 AS + 0.09 Aa)g - 0.08 AY^ + 0.01 AI>e + 0.1 A i f + 0.005 A E f d ) p.u. E F D 55 I i i F i g . 4.1, the e f f e c t i v e n e s s of LOC i s r e - e s t a b l i s h e d . While curve NC i s the swing curve of the system without any a u x i l i a r y c o n t r o l f o l l o w i n g a f a u l t near the generator t e r m i n a l as d e s c r i b e d i n Chapter 3, curve LOC represents the swing curve of the system w i t h the l i n e a r o p t i -mal e x c i t a t i o n c o n t r o l which provides damping f o r the system. However, the system o s c i l l a t i o n s are r a t h e r prolonged, suggesting that the LOC may not be able to maintain the s t a b i l i t y i n case of more severe system d i s -turbances. Therefore, the f a s t c o n t r o l i s s t i l l r e q u i r e d p a r t i c u l a r l y i n improving the t r a n s i e n t s t a b i l i t y during the f i r s t few swings. The r e s u l t s of system behaviour w i t h both LOC and f a s t c o n t r o l s f o r the p a r t i c u l a r disturbance described i n Chapter 3 are shown i n F i g . 4.2 (a) through (c) . Although i t i s very d i f f i c u l t to d i s t i n g u i s h the n o n l i n e a r t r a n s i e n t s t a b i l i t y and the l i n e a r dynamic s t a b i l i t y , and the t r a n s i t i o n i s r a t h e r g radual, i t i s f a i r to say t h a t i n a l l cases, the f i r s t swing of the system which d e f i n i t e l y belongs to the t r a n s i e n t s t a b i l i t y r e g i o n , i s improved s p e c i f i c a l l y by the f a s t c o n t r o l s and the s t a b i l i t y of l a t e r swings are improved mainly by the LOC. This can be seen i n F i g . 4.2 ( a ) , ( b ) , and ( c ) . The d e t a i l s of f a s t c o n t r o l s of F i g . 4.2 are as f o l l o w s : (a) 25%. BR a p p l i e d three times (b) -8.0 p.u. FE a p p l i e d three times (c) 50% IV and 50% CV FV a p p l i e d two times 4.3 Braking R e s i s t o r and Forced E x c i t a t i o n Combination In t h i s s e c t i o n , combination of the BR and the FE c o n t r o l s w i l l be considered f i r s t . I t i s expected that t h i s combination w i l l reduce the f i r s t p o s i t i v e swing mainly w i t h the former and the f i r s t n e g a t i v e swing mainly w i t h the former and the f i r s t n egative swing mainly w i t h the l a t -t e r . The r e s u l t s are very encouraging as summarized i n F i g . 4.3 (a) through ( d ) . + In F i g . 4.3 ( a ) , curve 1 shows the r e s u l t of - 6.0 p.u. FE w i t h one a p p l i c a t i o n , curve 2, the r e s u l t of 25% BR w i t h one a p p l i c a t i o n , and curve 3, the combination of 1 and 2 w i t h one a p p l i c a t i o n of both FE and BR c o n t r o l s and a l l w i t h the LOC i n c l u d e d . I t i s obvious that the combined f a s t c o n t r o l , curve 3, gives b e t t e r r e s u l t than others f o r the f i r s t 5 6 0.5 1.0 1.5 2To TIME (SECONDS) 3.0 Curves 1. without LOC 2. w i t h LOC 1.0 l . S 2.0 TIME (SECONDS) 2.5 n 3.0 F i g 4.2(a) 25% BR a p p l i e d three times (3) 57 Curves 1. without LOC 2. w i t h LOC T 0.5 -Fig- 4 1.0 1 !s 2.0 TIME (SECONDS) .2(b) -8.0 p.u. FE applied'.three times..(3). ' I | 0.5 1.0 1.5 2.0 2.5 3.0 TIME (SECONDS) F i g . 4.2(c) 50% IV and 50% CV,, FV a p p l i e d two times (2) 58 Curves 1. -6.0 p.u. FE a p p l i e d once (1) 2. 25% BR applie. once (1) 3. 25% BR and -6.0 p.u. FE a p p l i e d once (1) -60.0 i f[ i r r r r I T i i | i i > i t i f T r p 1.0 1.5 2.0 TIME (SECONDS) 3(a) 25% BR and +6.0 p.u. FE combination w i t h LOC Curve's 1. -6.0 p.u. FE a p p l i e d once (1) 2. 50% BR a p p l i e once (1) 3. 50% BR and -6.0 p.u. FE a p p l i e d ' once (1) 0.5 1.0 ' 1.5 2.0 2.5 3.0 TIME ISEC0NDS) F i g . 4.3(b) 50% BR and ^ 6.0 p.u. FE combination w i t h LOC 59 Curves 1. - 6 .0 p . u . FE a p p l i e d three times (3) 2. 25% BR app l i ed three times (3) 3. Combination of 1 and 2 >'TtT"| I I I I I f H T [ T 0 0.5 1.0 1.5 2.0 2.5 3^ 0 TIME (SECONDS! 4.3(c) 25% BR and -6 .0 p . u . FE combination wi th LOC 1.0' Curves 1. - 6 . 0 p . u . FE a p p l i e d three times (3) 2. 50% BR a p p l i e d three twice (2) 3. Combination of 1 and 2 -60.0 1.0 1.5 2% TIME (SECONDS) 0 0.5 F i g . 4.3(d) 50% BR and ± 6 . 0 p . u . FE combination wi th LOC 60 p o s i t i v e swing but not n e c e s s a r i l y b e t t e r than curve 2 f o r the f i r s t n egative swing. F i g . 4 . 3 (b) i s s i m i l a r to F i g . 4 . 3 (a) except that a 50% BR i s used i n curves 2 and 3 . I t i s evident again that the com-bined c o n t r o l , curve 3 , i s f a r b e t t e r than the other two. The d i f f e r -ence between F i g . 4 . 3 (c) and (d) and F i g . 4 . 3 (a) and (b) i s that both FE and BR are a p p l i e d three times i n s t e a d of once. While i n F i g . 4 . 3 ( c ) , a 25% BR i s used, a 50% BR i s used i n F i g . 4 . 3 (d). In both cases, the combined c o n t r o l s , the curve 3's give the best r e s u l t s . Note t h a t f o r F i g . 4 . 3 (c) and (d) a - 6.0 p.u. FE i s used and the LOC i s a l s o i n c l u -ded. From the r e s u l t s given here, i t i s safe to conclude that the combined FE and BR c o n t r o l i s more e f f e c t i v e than the i n d i v i d u a l c o n t r o l s i n improving the f i r s t one or two swings. A l s o m u l t i p l e a p p l i c a t i o n s of t h i s combination i s b e n e f i c i a l to the system i n improving the l a t t e r swings. 4 . 4 F a s t - V a l v i n g and Forced E x c i t a t i o n Combination In Chapter 3 , FV has proved e f f e c t i v e i n reducing the f i r s t p o s i t i v e swing but not e f f e c t i v e i n reducing the f i r s t n e g ative swing. However, the s i t u a t i o n can be improved by i n c o r p o r a t i n g the FV c o n t r o l w i t h the FE c o n t r o l which i s very e f f e c t i v e i n reducing the f i r s t nega-t i v e swing. A l s o i n c l u d e d i s the LOC which can c o n t r o l the s m a l l o s c i l -l a t i o n s . The r e s u l t s of t h i s study are shown i n F i g . 4 . 4 (a) through ( d ) . In F i g . 4 . 4 (a) and ( b ) , a - 6.0 p.u. FE alone i s a p p l i e d o n ly once, but three times i n F i g s . 4 . 4 (c) and ( d ) ; curve l ' s . The curve 2's show' that of FV a p p l i c a t i o n alone, F i g . 4 . 4 (a) f u l l IV c l o s u r e once, (b) f u l l IV c l o s u r e and 50% CV c l o s u r e once, (c) f u l l IV c l o s u r e t w i c e , and (d) 50% IV and 50% CV c l o s u r e t wice. Curve 4's are the combined f a s t c o n t r o l s of curve l ' s and 2's of the r e s p e c t i v e ( a ) , ( b ) , ( c ) , and (d) f i g u r e s , and curve 5's are the combined f a s t c o n t r o l s of curve l ' s and 3's. I n a l l the f i g u r e s , the combined c o n t r o l s , curve 4's and 5's, a l l give b e t t e r r e s u l t s than that of the i n d i v i d u a l FV or FE c o n t r o l s , and the combined c o n t r o l s w i t h f u l l IV c l o s u r e once, F i g . 4 . 4 (a) curve ( 4 ) , or t w i c e , F i g . 4 . 4 (c) curve 4 , i s always b e t t e r than i t s counterpart curve 5's w i t h 50% IV c l o s u r e s . This i s a l s o true f o r F i g . 4 . 4 (b) and 61 - 6 0 . 0 + r 0 . 5 11" " " 1 1 11 1 1 . 0 1 . 5 2 . 0 TIME (SECONDS) Curves 1. -6.0 p.u. FE (1) 2. F u l l IV (1) 3.. 50% IV (1) 4. Combination of 1 and 2 5. Combination of L-and 3 F i e . b.4(~a) -6.0 r>.u. FE and FV combination w i t h LOC 0 . 5 11" " 1 " " i " " i 1 1 . 0 1 . 5 2 . 0 TIME (SECONDS) i 3.0 Curves 1. -6.0 p.u. FE (1) 2. F u l l IV (1) 50% CV (1) 3. 50% IV (1) 50%JCV (1) 4. Combination of 1 and 2 5. Combination of 1 and 3 F i g . 4.4(b) -6.0 p.u. FE and FV combination w i t h LOC 6 2 1.5 2.0 2.5 3.0 TIME ISECONDS) Curves 1. -6.0 p.u. FE (3) 2. F u l l IV (2) 3. 50% IV (2) 4. Combination of 1 and 2 5. Combination of 1 and 3 F i g . 4.4(c) -6.0 p.u. FE and FV combination w i t h LOC Curves 1. ±6.0 p.u. FE (3) 2. F u l l IV f i r s t 50% IV second 3. 50% IV (2) 50% CV (2) 4. Combination of 1 and 2 5. Combination of 1 and 3 -60.0 1 1 1 1 1 1 1 1 1 ' i " • • 1 1 11 1 1 1 1 1 1 1 1 11 1 • 1 1 1 1 1 1 111 1 n 1 1 1 1 11 1 1 1 1 1 n111 0 0.5 1.0 1.5 2.0 2.5 3.0 TIME (SECONDS) F i g . 4.4(d) ±6.0 p.u. FE and FV combination w i t h LOC 63 From these r e s u l t s , i t may be concluded that the combined FV and FE c o n t r o l i s b e t t e r than i n d i v i d u a l f a s t c o n t r o l s , f u l l IV c l o s u r e i s b e t t e r than 50% IV c l o s u r e s , and m u l t i p l e a p p l i c a t i o n of the combination i s b e t t e r than the s i n g l e a p p l i c a t i o n , provided that system disturbance s e v e r i t y i s the same. 4.5 Braking R e s i s t o r , Forced E x c i t a t i o n , and F a s t - V a l v i n g Combination In t h i s s e c t i o n , the combinations w i t h a l l three f a s t c o n t r o l s , i . e . , BR p l u s FE plus FV, are i n v e s t i g a t e d . A l s o i n c l u d e d i n each case i s the LOC f o r s m a l l o s c i l l a t i o n c o n t r o l s as described i n s e c t i o n s 4.3 and 4.4. In F i g . 4.5, the swing curves of the system w i t h the combined f a s t c o n t r o l s are shown, but each of them i s a p p l i e d only once. I n a l l the cases, there are i n general s i g n i f i c a n t improvements i n each f i r s t p o s i t i v e swing and negative swing when compared w i t h any of the i n d i v i d u a l or combination of two f a s t c o n t r o l s t u d i e s shown i n previous s e c t i o n s . Curve 1 of F i g . 4.5 (a) i s the r e s u l t s of the BR p l u s a - 6.0 p.u. FE p l u s a f u l l IV c l o s u r e , which i s not as good as curve 2 w i t h FE i n c r e a s e d to - 8.0.p.u.,. and a l s o i t i s not as good as curve 3 f o r which the FE remains at - 6.0 p.u. but i n c l u d e s a 50% CV c l o s u r e . The comparisons are made, of course, on the f i r s t p o s i t i v e and negative swings. Curve 4 corresponds to curve 2 but the BR i s i n c r e a s e d to 50% and curve 5 corresponds to curve 4 but w i t h a d d i t i o n a l 50% CV c o n t r o l . I t may be concluded that the c o n t r o l i n curve 5 i s b e t t e r than that of 4, which i s b e t t e r than that of 3, e t c . In F i g . 4.5 ( b ) , a - 6.0 p.u. FE i s a p p l i e d f o r a l l the cases. Curve 1 i s the r e s u l t of a d d i t i o n a l 25% BR p l u s 50% IV c l o s u r e , curve 2, t h a t of 50% BR p l u s 50% IV c l o s u r e , curve 3, that of 25% BR p l u s f u l l IV c l o s u r e , and curve 4, that of 50% BR and f u l l IV c l o s u r e . Here, the r e s u l t s i n d i c a t e that the greater the BR c a p a c i t y and/or the IV c o n t r o l , the b e t t e r w i l l be the t r a n s i e n t s t a b i l i t y . So f a r the r e s u l t s of combined three f a s t c o n t r o l s w i t h only one a p p l i c a t i o n have been presented. In F i g . 4.5 ( c ) , responses of v a r i o u s options of t h i s combination but w i t h s i n g l e and m u l t i p l e a p p l i c a -t i o n s are recorded. In a l l three curves, the FE i s a p p l i e d three times but only once f o r the BR and again only once f o r the FV c o n t r o l s . A l s o , i n these cases, the BR c a p a c i t y i s kept constant at 25%. I n curve 1, three 40.0 30.0 20.0 CO LU cn o CC 10.0 -j -10.0 CC X -20.0 4 -30.0 -40.0 64 Curves 1. 25$ BR ( l ) ±6.0 p.u. FE ( l ) F u l l IV ( l ) 2. Same as 1. except -8.0 p.u. FE 3 . 25$ BR ( l ) / ^  ±8.0 p.u. FE ( l ) / L-\ F u l l IV ( l ) 50$ CV ( l ) 4 . 50$ BR ( l ) -8.0 p.u. FE ( l ) F u l l IV ( l ) 5. 50$ BR ( l ) -8.0 p.u. FE ( l ) F u l l IV ( l ) 50$ CV ( l ) ' 2 ^ 5 3 . 0 i 11 r n i i [ r r i r i i i i i | i i m i n t ' | i r r r r r r r t f - i 0.5 1.0 1.5 2.0 TIME tSECONDS! Fig. 4.5(a) 25% BR, - 6.0 p.u. FE and FV combination 60.0 r. 50.0 -3 w i t h LOC Curves 1. 25$ BR ( l ) • ^6.0 p.u. FE ( l ) 50$ IV ( l ) 2. 50$ BR ( l ) ±6.0 p.u. FE ( l ) 50$ IV ( l ) 3. 25$ BR ( l ) -6.0 p.u. FE ( l ) F u l l IV ( l ) 4 . 50$ BR ( l ) -6.0 p.u. FE ( l ) F u l l IV ( l ) 1.0 1.5 2.0 TIME (SECONDS) F i g . 4.5(b) BR, +6.0 p.u. FE and FV combination with LOC 65 Curves 1. 25$ BR ( l ) ^8.0 p.u. FE (3) 50$ IV ( l ) 2. 25$ BR ( l ) ^8.0 p.u. FE (3) 50$ IV ( l ) 50$ CV ( l ) 3. 25$ BR ( l ) -6.0 p.u. FE (3) 50$ IV ( l ) 4. 25$ BR ( l ) ^6.0 p.u. FE (3) 50$ IV ( l ) 50$ CV ( l ) 0 0.5 1.0 1.5 2.0 2.5 3.0 TIME (SECONDS) F i g . 4.5(c) 25% BR, FE and FV combination w i t h LOC Curves 1. 25$ BR (2) -6.0 p.u. FE (3) 50$ IV ( l ) 2. 25$ BR (2) -6.0 p.u. FE (3) F u l l IV ( l ) 3. 25$ BR ( l ) ^6.0 p.u. FE (3) 50$ IV ( l ) 50$ CV ( l ) 1.0 ).5 2J3 TIKE (SECONDS) 0 0.5 F i g . 4.6(a) 25% BR, ±6.0 p.u. FE and FV combination w i t h LOC 66 60.0 Curves 1. 25$ BR ( l ) ±6.0 p.u. FE (3) F u l l IV (2) 2. 25$ BR ( l ) ±6.0 p.u. FE (3) 50$ IV (2) 3. 25$ BR ( l ) -6.0 p.u. FE (3) 50$ IV (2) 50$ CV (2) I | I I I * I I I I I | I I I I I I I I I j • 0 0.5 1.0 1.5 2.0 2.5 3.0 TIME (SECONDS) F i g . 4.6(b) 25% BR. ±6.0 p.u. FE and FV combination w i t h LOC Curves 1. 25$ BR ( l ) ±6.0 p.u. FE (3) 50$ IV (2) 2. 25$ BR (2) ±6.0 p.u. FE (3) 50$ IV ( l ) 3. 25$ BR ( l ) ±6.0 p.u. FE (3) 50$ IV (2) 50$ CV (2) 4. 25$ BR (2) ±6.0 p.u. FE (3) 50$ IV (2) 50$ CV (2) 0.5 1.0 1.5 2'.0 TIME (SECONDS) F i g . 4.7 BR, FE and FV combination w i t h LOC ( P e = 5 5 0 w a t t s ) a p p l i c a t i o n s of - 8.0 p.u. FE and one of 50% IV c l o s u r e i s made, w h i l e i n curve 2 an a d d i t i o n a l one.50% CV c l o s u r e I s a p p l i e d which gives b e t t e r r e s u l t s i n the f i r s t two swings. Next, curves 3 and 4 of F i g . 4.5 (c) correspond to curves 1 and 2 r e s p e c t i v e l y but w i t h l e s s FE c o n t r o l , i . e . + + re d u c t i o n from - 8.0 p.u. to - 6.0 p.u. The r e s u l t s of curves 3 and 4 are o b v i o u s l y not as good as curves 1 and 2, again suggesting that w i t h greater magnitude of f a s t c o n t r o l s b e t t e r r e s u l t s are achieved. S i m i l a r s t u d i e s are continued i n F i g . 4.6 (a) and (b). In F i g . 4.6 ( a ) , 25% BR i s a p p l i e d two times, - 6.0 p.u. FE a p p l i e d three times, and v a r i a t i o n s of FV a p p l i e d once. Curve 1 shows the r e s u l t of a 50% IV c l o s u r e , curve 2 a f u l l IV c l o s u r e , and curve 3 a 50% IV c l o s u r e plus a 50% CV c l o s u r e . Of the three curves, curve 3 gives the best r e -s u l t s . In F i g . 4.6 ( b ) , r e s u l t s of 25% BR a p p l i e d once, - 6.0 p.u. FE a p p l i e d three times and two a p p l i c a t i o n s of FV are shown. Curve 1 c o r -responds to 50% IV c l o s u r e s , curve 2 to f u l l IV c l o s u r e s , and curve 3 to 50% IV c l o s u r e plus 50% CV c l o s u r e s . Curve 3 which has the l a r g e s t f a s t c o n t r o l c a p a c i t y of the three mentioned again gives the best r e s u l t . F i n a l l y , a s p e c i a l set of t e s t s were c a r r i e d out and are summa-r i z e d i n F i g . 4.7. The generator power output during the steady s t a t e o p e r a t i o n i s increased from 500 watts to 550 watts. Although the-LOC was designed f o r 500 w a t t s , i t i s l e f t unchanged. A l s o the same system, d i s -turbance i s assumed as i n previous cases. Curve NC shows the swing curve of the system without any a u x i l i a r y c o n t r o l and the s t a b i l i t y i s l o s t im-mediately on the f i r s t p o s i t i v e swing. Curve 1 shows th a t w i t h the LOC, the system b a r e l y maintains i t s s t a b i l i t y i n the f i r s t swing and l o s e s i t i n the second swing. Fast c o n t r o l s are in t r o d u c e d and the r e s u l t s are shown i n curves 2 and 3 of F i g . 4.7; both w i t h three a p p l i c a t i o n s of - 6.0 p.u. FE, the former i n c l u d e s the e f f e c t of one a p p l i c a t i o n of 25% BR and two a p p l i c a t i o n of 50% IV c l o s u r e s , and the l a t t e r has one a p p l i c a t i o n of 50% IV c l o s u r e and two a p p l i c a t i o n s of the 25% BR. Curves 4 and 5 co r -respond t o curves 2 and 3 r e s p e c t i v e l y but w i t h a d d i t i o n a l 50% CV c o n t r o l i n c o n j u n c t i o n w i t h IV c o n t r o l , which f u r t h e r improves the t r a n s i e n t s t a b i -l i t y . T h e s e r e s u l t s again suggest that the BR c o n t r o l i s s l i g h t l y b e t t e r than the FV c o n t r o l f o r the c a p a c i t i e s chosen. 68 In g e n e r a l , the combination of BR, FE, and FV c o n t r o l has proved to be very e f f e c t i v e i n improving the system s t a b i l i t y , e s p e c i a l l y during the f i r s t c r i t i c a l swing. A l s o the r e s u l t s have i n d i c a t e d t h a t economic t r a d e o f f s can be made without s e v e r e l y h i n d e r i n g the e f f e c t i v e n e s s of s y s t s t a b i l i t y c o n t r o l . 69 5. FAST CONTROL TEST ON A LABORATORY TEST MODEL AND INSTRUMENTATION 5.1 Introduct ion In Chapters 3 and 4, computer s imula t ion r e s u l t s of the e f f e c t of BR, F E , and FV contro l s of various s e l e c t i o n s , s i n g l e and m u l t i p l e a p p l i c a -t i o n s , and the combination of the three fas t contro l s on t r a n s i e n t power system s t a b i l i t y were presented and some u s e f u l guide l i n e s and conclus ions were drawn. In t h i s chapter , evidences of experimental tes ts are sought to compare wi th the computer s imula t ions . The experimental r e s u l t s and the computer s imula t ion comparisons are summarized i n s ec t i on 5 .2 . I n -strumentation c i r c u i t s developed e s p e c i a l l y f or the fa s t c o n t r o l t e s t s and a l so some improvements of the e x i s t i n g l a b o r a t o r y Power System Dynamic Model which has been developed at U . B . C . are recorded i n sec t ions 5.3 through 5 .5 . 5.2 Experimental Results In t h i s s e c t i o n , the experimental r e s u l t s recorded as curves I , TT—T-T-T • — T . r r i i i-to „ — „—_~ J T.ii-fVio-nrmiTtTrfQ^— r ^ s w l t s ~ r e c a r d e d ~as~'C'_irT.Te"s~— 1, 2, 3 e t c . The experimental r e s u l t s are recorded b y , Brush Recorder Mark 200 which i s checked wi th the o s c i l l o s c o p e to ensure accuracy . The computed r e s u l t s are obtained from the same program developed f o r the s t u -dies of Chapters 3 and 4 us ing the 3rd order synchronous machine model as s ta ted i n Chapter 2. Since more than two or three a p p l i c a t i o n s of f a s t c o n t r o l s are not d e s i r a b l e , F i g . 5.1 again e s tab l i shes the e f f ec t ivenes s of LOC which can subdue smal l o s c i l l a t i o n s a f t er the fa s t contro l s are removed. Curves I and 1 are swing curves wi th LOC, and curves I I and 2 without fas t c o n t r o l s . The r e s u l t s c l e a r l y show the advantage of LOC i n the f i r s t p o s i t i v e swing but not i n the f i r s t negative swing. The d i screpanc ie s between the experimental and computed r e s u l t s are a t t r i b u t e d to the ins trumentat ion n o i s e s , parameter e r r o r s due to measurement techniques and a l so the temperature change of the machine and the imperfect mode l l ing . Never the le s s , there i s d e f i n i t e l y general agreement between the two sets of curves . In F i g . 5 .2 , system responses wi th three a p p l i c a t i o n s of the BR c o n t r o l are shown. Curves 1 and 2 are computer s i m u l t a t i o n r e s u l t s of 25% BR c o n t r o l wi th and without LOC and curves I and I I , t h e i r corresponding 70 L J 120 110 100 90 CO 70 60 50 40. 30 20 10. g -10 5 -20 S -30 £-40 ° - 5 0 -60 -70 -80 -90 -100 -110 -120 0 ? o -: o-j o ] o o -: o •; o -; o -: o '-. o \ o -: o -; o -; o \ o-il o 0 0 0 o-1 0 o-1 0 0 t. \ \: \ / A Computed 1. w i t h LOC 2. without LOC Lab Test Result I . w i t h LOC I I . without LOC S . I I " T T T T T T T r T T l I ' I I 0.5 1.0 1.5" 2.0 2.5 3.0 TIME (SECONDS) Test- and computed r e s u l t s of a power svstem w i t h and .without LOC; No f a s t c o n t r o l Curves 1 , 1 : 2 5 $ BR ( 5 ) with LOC 2 , 1 1 : 2 5 $ BR (3 ) without LOC III: 5 0 $ BR (2) with LOC TIME (SECONDS) Fig. 5.2 Test and computed r e s u l t s of BR c o n t r o l 71 experimental r e s u l t s . Although the l a b t e s t r e s u l t s of the BR are not as good as the s i m u l a t i o n r e s u l t s , s t i l l i t does i n d i c a t e that t h i s f a s t c o n t r o l can e f f e c t i v e l y reduce f i r s t and subsequent swings. With the i n c r e a s e i n BR c a p a c i t y from 25% to 50%, s i g n i f i c a n t improvement i n the o v e r a l l system i s accomplished as i n d i c a t e d by curve I I I of the t e s t r e s u l t . In F i g . 5.3, r e s u l t s of both computer s i m u l a t i o n and l a b t e s t w i t h three a p p l i c a t i o n s of FE c o n t r o l s are shown. Curves 1 and. 2 r e s p e c t i v e l y are computed r e s u l t s of - 8.0 p.u. FE c o n t r o l w i t h and without LOC w h i l e curves I and I I are t h e i r experimental c o u n t e r p a r t s . The l a b t e s t r e s u l t s i n d i c a t e again that FE i s very e f f e c t i v e i n reducing the f i r s t n e gative swing but not n e a r l y as e f f e c t i v e i n the f i r s t p o s i t i v e swing. The system s t a b i l i t y i s c o n s i d e r a b l y improved a l s o w i t h m u l t i p l e a p p l i c a t i o n s . Curve I I I of F i g . 5.4 corresponds to ± 6.0 p.u. c e i l i n g v o l t a g e l i m i t s of FE c o n t o l . I t i s not as e f f e c t i v e as the - 8.0 p.u. l i m i t s of curve I . F i g . 5.4 shows swing curves of the system w i t h two a p p l i c a t i o n s of FV c o n t r o l s , a l l w i t h LOC. Curves 1 and I correspond to a f u l l IV c l o s u r e t w i c e , curves 2 and I I , a f u l l IV c l o s u r e i n the f i r s t a p p l i c a t i o n and a 50% IV c l o s u r e i n the second a p p l i c a t i o n , and curves 3 and I I I , a f u l l IV and a 50% CV c l o s u r e s t w i c e . Although the l a b t e s t r e s u l t s of the FV are not as good as t h a t computed, they s t i l l i n d i c a t e that the FV c o n t r o l i s e f f e c t i v e i n reducing the f i r s t swing. A l s o appreciable system s t a b i l i t y improvements are observed. When FV i s a p p l i e d again i n the second swing f u r t h e r improvement i n the secondary swings can be seen. R e s u l t s of combined two k i n d s of f a s t c o n t r o l s are shown i n F i g . 5.5, a l l w i t h - 6.0 p.u. FE a p p l i e d three times and w i t h the LOC. Curves 1 and I , correspond to two a p p l i c a t i o n s of 25% BR, curves 2 and I I correspond to two f u l l IV c l o s u r e s , and curves 3 and I I I , correspond to f u l l IV c l o s u r e i n the f i r s t a p p l i c a t i o n and only 50% IV c l o s u r e i n the second. The computer s i m u l a t i o n s and lab t e s t s c o n f i r m t h a t the 25% BR p l u s FE c o n t r o l i s more e f f e c t i v e than the FV and FE combination i n improving the f i r s t and the second swings. R e s u l t s of combined three k i n d s of f a s t c o n t r o l s are shown i n F i g . 5.6. F i g . 5.6 (a) shows the r e s u l t of one a p p l i c a t i o n of a - 6.0 p.u. FE p l u s a 25% BR p l u s a f u l l IV c l o s u r e . The t e s t r e s u l t s of LOC alone i s a l s o i n c l u d e d f o r comparison. The l a b t e s t r e s u l t , , curve I i s not as 72 cr. o IPO. 110. 100. 90. 60 70 CO 50 10 30 20 10 •10 -20 £ -40 <~> -GO -70 -80 -SO -100 -110 -120 0 0-5 0 0 0 0 -. 0 i o -: o o o -: o o 0 .0 .0-5 ,0 ,0 •: .0 -I ,0 -: ,o .0 -. .o -i .o i .0 III SK-V Curves 1,1: -8.0 p.u. FE (j) with LOC 2,11: ±8.0 p.u. FE (3) without LOC III: -6.0 p.u. FE (3) with LOC 0 0.5 1.0 1.5 2.0 2.5 3.0 TIKE (SECONDS) Fig. 5.3 Test and computed results of FE control 120. no 100 90 80 70 60 _ 5 0 U J 40 Q *~ 30 U J 20 zz. tt 10, LU n o a: £ -10 5 -20 g 4-60 -70 -80 -90 -100 -110 -120 0 0^ 0 o 4 0 0 0^ 0 0 -i o-i 0 0 04 0 0 i o -i ,o -o .0-i .o-i .o -i .0 .0 .0 C,—i,n Curves 1,1: Full IV (2) with LOC 2,11: Full IV firsi and 50$ IV second with LOC 3,111: Full IV (2) 50$ CV (2) with LOC " i 1 1 0.5 i . | • . I . . I i t r p n i . i n ,\ I • I I I I I I i ! • • I I I i I I i | 1.0 1.5 2.0 2.5 3.0 TIME (SECONDS) Fig. 5.4 Test and computed results of FV control 73 80.0 -3 70.0 -j -40.0--50.0 -i -60.0 -j -70.0 -j —80.0 "} 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0.5 I.D 1.5 2.0 2.5 3.0 TIME ISECONDS] F i g . 5.5 Test and computed r e s u l t s of combined two f a s t c o n t r o l s 1,1 : 25% BR (2) p l u s - 6.0 p.u. FE (3) w i t h LOC 2,11 : - 6.0 p.u. FE (3) p l u s f u l l IV (2) w i t h LOC 3,111: -6.0 p.u. FE (3) p l u s f u l l IV f i r s t and 50% IV second w i t h LOC 74 U J a cn o e o . o 70 .0 60.0 50.0 4 o . o -: 3 o . o 20 .0 10.0 0 - 1 0 . 0 - 2 0 . 0 - 3 0 . 0 - 4 0 . 0 -50.0-3 -60 .0 - 7 0 . - 8 0 . F i g . 0 0 -f~X*— LOC IA I! \ / M \ \ ./•' ^ Curves 1,1: 25$ BR (l) ±6.0 p.u. FE (l) Full IV (l) \.» r>l, / V T T T n T t ' n ] T I 'f1 r i i r t r p r i T i 0 . 5 1.0 1.5 2.0 TIME (SECONDS! 2 . 5 3 . 0 5.6(a) Combined three f a s t c o n t r o l s , one" a p p l i c a t i o n (1) Curves 1,1: 25$ BR (2) -6.0 p.u. FE (3) Full IV (l) -2,11: 25$ BR (l) ±6.0 p.u. FE {3, Full IV (2) < 1" 1111 • 1.0 1.5 2 . 0 TIME (SECONDS) 3.0 Fig. 5.6(b) Combined three f a s t c o n t r o l s , m u l t i p l e a p p l i c a t i o n s 75 e f f e c t i v e as the computed, curve 1, but when they are compared w i t h the LOC alone, curve I I , there i s a s i g n i f i c a n t improvement i n the f i r s t n egative swing. F i g . 5.6 (b) a l s o shows the r e s u l t s of three k i n d s of combina-t i o n a l f a s t c o n t r o l . Curves I and 1 show t h a t of a p p l y i n g 25% BR t w i c e , p l u s ± 6.0 p.u. FE three times, p l u s one f u l l IV c l o s u r e . Curves I I and 2 show one a p p l i c a t i o n of 25% BR, p l u s three a p p l i c a t i o n s of - 6.0 p.u. FE, p l u s f u l l IV c l o s u r e twice. The r e s u l t s show that two a p p l i c a t i o n s of the BR (curves I and 1) i s b e t t e r than two a p p l i c a t i o n s of FV (curves I I and 2 ) . Furthermore, w i t h a second a p p l i c a t i o n of e i t h e r BR or FV c o n t r o l (curves I or I I of F i g . 5.6 (b) ) the second swing i s f u r t h e r improved as compared w i t h t h a t w i t h only one a p p l i c a t i o n ( curve I of F i g . 5.6 (a) ). In summary, the lab t e s t r e s u l t s of t h i s chapter confirm t h a t the f i r s t and the second swings can be e f f e c t i v e l y reduced by one or combina-t i o n s of f a s t c o n t r o l s and the the LOC provides s u f f i c i e n t damping of s m a l l o s c i l l a t i o n s . A l s o , i t i s safe to conclude that among the three f a s t con-t r o l s t e s t e d , the BR c o n t r o l i s more u s e f u l than the other two i n terms of reducing the p o s i t i v e swing and i t ' s s i m p l i c i t y i n a p p l i c a t i o n . However, the usefulness of the FE c o n t r o l i n damping the system o s c i l l a t i o n , espe-c i a l l y the f i r s t negative swing and a l s o the FV c o n t r o l i n reducing the f i r s t or the second p o s i t i v e swing are recognized and a p p r e c i a t e d . 5.3 Speed, Torque-angle and other Transducers Accurate measurements of system v a r i a b l e s are necessary f o r proper c o n t r o l of power system. In p a r t i c u l a r , the speed, the torque-angle, and the power s i g n a l s are important f o r the f a s t c o n t r o l s . In F i g . 5.7, a schematic diagram of the speed transducer i s shown. I t has a s h a f t d r i v e n pulse generator which w i l l produce a 45 KHZ pulse t r a i n at the 1800 rpm mechanical speed. These pulses are fed i n t o a monostable which squares and f i x e s the time d u r a t i o n of each p u l s e . The squared pulses are then averaged by a low-pass f i l t e r and compared w i t h a re f e r e n c e s i g n a l of the synchronous speed to o b t a i n the speed d e v i a t i o n . The p u l s e generator used i s a o p t i c a l s h a f t - a n g l e encoder which produces 1500 square pulses per s h a f t r e v o l u t i o n and the f i l t e r designed i s a f i v e - p o l e Chebyshev low-pass f i l t e r w i t h a c u t o f f near, 20 HZ. The l i n e a r i t y of the speed transducer was c a l i b r a t e d by t i m i n g the torque angle s l i p p i n g one p o l e - p a i r . ' The r e s u l t i s shown in F i g . 5.8 76 |0OK p - ^ — I v2 > M0NO5TABI.E ) '1 SQUARE WAVE GENERATOR 45 KHZ. YL -A. LOW PASS F 1 L T 13 R f c " IS l i t . | O K 1. V0LT= I. RAD./SEC. * r e f . ZERO SET 1 ' _* di— • - - f, — \ \ 1 -f?. H T--\V • T • F i g . 5.7 A schematic diagram of the speed transducer Time Time OUTPUT DC VOLTS r 4. 1 Aid RAD./SEC. SLOPE • V 0 L T , S L 0 F E •* 1.00 RAD./SEC. - * 4 F i g . 5.8 Speed transducer t r a n s f e r c h a r a c t e r i s t i c 77 For the torque-angle measurement, the transducer developed i n a previous t h e s i s f o r a d u a l - a x i s e x c i t e d synchronous machine i s i n c o r p o r -ated i n t o the Dynamic Test Model w i t h minor improvements.^*^ The f i l t e r was changed from a two-pole low-pass f i l t e r w i t h a c u t o f f at 60 HZ to a f i v e - p o l e low-pass f i l t e r w i t h a c u t o f f at 15 HZ. This m o d i f i c a t i o n im-proved the q u a l i t y of the torque-angle s i g n a l s i n c e some of the high f r e -quency n o i s e present i n the o r i g i n a l design were e l i m i n a t e d without s e r i o u s l y decreasing the s i g n a l bandwidth. The power and other s i g n a l s such as t e r m i n a l v o l t a g e and c u r r e n t are converted to analogue vol t a g e s p r o p o r t i o n a l to t h e i r instantaneous v a l u e s . These transducers of e a r l i e r design have adequate response time f o r the t r a n s i e n t s t a b i l i t y s t u d i e s . 5.4 Speed and Power S i g n a l L e v e l and Speed Slope D e t e c t i o n C i r c u i t s A schematic diagram of a s i g n a l l e v e l d e t e c t o r used t o produce the speed or the power s i g n a l i s shown i n F i g . 5.9. I t i s a comparator which w i l l produce a high l e v e l d i g i t a l output when the input i s g r e a t e r than a r e f e r e n c e , a low l e v e l output when the input i s lower than the r e f e r e n c e . The speed slope detector i s e s s e n t i a l l y a d i f f e r e n t i a t i o n c i r c u i t w i t h the comparator as shown i n F i g . 5.10. The speed s i g n a l i s d i f f e r e n -t i a t e d and the output i s compared w i t h the zero r e f e r e n c e . I f the slope i s p o s i t i v e , a h i g h l e v e l output w i l l be produced and i f the slope i s n e g a t i v e , a low output w i l l r e s u l t . To e l i m i n a t e the o s c i l l a t i o n t h a t can occur when the speed i s n e a r l y s t a b l e , a h y s t e r e s i s loop i s b u i l t i n t o the comparator so t h a t t r a n s i t i o n occurs only when the magnitude of the d i f f e r e n t i a t e d speed s i g n a l i s above or below the two h y s t e r e s i s r e f e r e n c e s e t t i n g s . The deadban'd created by the h y s t e r e s i s loop i s kept at a minimum so that accur-acy of the slope s i g n a l i s adequate f o r the f a s t c o n t r o l s t u d i e s . 5.5 Counting and I n h i b i t C i r c u i t f o r A p p l i c a t i o n Number of Fast C o n t r o l The counting and i n h i b i t c i r c u i t to l i m i t the number of each f a s t c o n t r o l i s shown i n F i g . 5.11. I t c o n s i s t s of a r i p p l e counter w i t h a decoder to produce a h i g h l o g i c output when f a s t c o n t r o l s may be continued, and a low l o g i c output when the l i m i t has been reached. To i n h i b i t f u r t h e r counting, the l o g i c s i g n a l i s fed back t o prevent the counting s i g n a l from e n t e r i n g the counter. With the present scheme, one, two, or three f a s t c o n t r o l a p p l i c a t i o n s can be preset by choosing,one of the feedback switches., 78 A 0) COMPARATORS L6W P A S , * F I L T E R f i • l & h i . 4>i INTO. Aw L e v e l • e +1 Aco L e v e l 6 + 2 Am L e v e l e +3 ,Aw L e v e l e -1 Aco e L e v e l -2 Leve l +1' Lev e l 42' L e v e l +3 Le v e l -1 . Le v e l -2 ' er-J l Time Time Time Time Time Time F i g . 5.9 A schematic diagram of speed l e v e l d e t e c t o r F i g . 5.10 A schematic diagram of speed slope d e t e c t o r 79 FLIP-FLOP COUNTER COUNTER N A N [ ) I N INPUT X r-COUN TER INHIBIT FEE DBACK 5w. *Jf WO/? Svv*3 A/0/? •o R E S E T COUNTER i PULSE • TWPTTT1 A -#1 ft 0-#1 < #2 4 #2 f 0-#3 'f *-Time Time -*- Time Time Time Time F i g . 5.11 A schematic diagram of the counting and i n h i b i t c i r c u i t 80 5.6 The Braking R e s i s t o r C o n t r o l C i r c u i t The schematic diagram of the BR c o n t r o l s i m i l a r t o t h a t o u t l i n e d i n s e c t i o n 3.3 i s shorn i n F i g . 5.12. The only d i f f e r e n c e i s t h a t i n the hardware design, there e x i s t s a p o s s i b i l i t y of r e s i s t o r i n s e r t i o n before the f a u l t i s c l e a r e d because the r e s i s t o r i s supposed to be a p p l i e d when the power or speed d e v i a t i o n i s g r e a t e r than the s p e c i f i e d l e v e l . However, sinc e a f a u l t may l a s t f o r only 0.05 second, the e x t r a BR a p p l i c a t i o n time i s n e g l i g i b l e as compared to the o v e r a l l d u r a t i o n of about 0.2 to 0.5 second. The BR i s i n s e r t e d by the r e l a y which i s a c t i v a t e d by the s w i t c h i n g t r a n s i s t o r as shown. The o p t i o n of choosing one, two, or three r e s i s t o r banks i s made by the corresponding switches which a c t i v a t e the s w i t c h i n g t r a n s i s t o r s . A l s o i n s t a l l e d are the l i g h t e m i t t i n g diodes (LED) i n d i c a t i n g the corresponding BR bank i n s e r t i o n . For the BR c o n t r o l , the a p p l i c a t i o n number i s counted a f t e r each removal of BR, l e v e l 1, which i s a p p r o p r i a t e s i n c e t h i s BR bank i s removed only when one complete BR a p p l i c a t i o n i s made. When the a p p l i c a t i o n l i m i t i s reached, f u r t h e r a p p l i c a t i o n s i g n a l w i l l be blocked by the BR i n h i b i t l o g i c c i r c u i t . 5.7 The Forced E x c i t a t i o n C o n t r o l C i r c u i t The schematic diagram of the FE c o n t r o l c i r c u i t s i m i l a r to that o u t l i n e d i n s e c t i o n 3.4 i s shown i n F i g . 5.13. As i n the BR c i r c u i t , the p o s s i b i l i t y of a FE a p p l i c a t i o n before the f a u l t removal e x i s t s but again t h i s time p e r i o d i s very s m a l l as compared to the whole a p p l i c a t i o n d u r a t i o n . The FE i s a p p l i e d according to the system c o n d i t i o n , the speed d e v i a t i o n and i t ' s s l o p e , the torque angle and the f i e l d c urrent s i g n a l s . The s i g n of the FE a p p l i e d i s i n d i c a t e d by the corresponding LED i n d i c a t o r l i g h t . In the c i r c u i t , a p p l i c a t i o n number i s counted e i t h e r a f t e r comple-t i o n of the FE a p p l i c a t i o n c y c l e which i s detected by f i e l d c u r r e n t (*f) r e t u r n i n g to i t s normal l e v e l or a f t e r the f i r s t p o s i t i v e FE a p p l i c a t i o n of the next c y c l e f o r severe cases which r e q u i r e s advanced r e - i n i t i a t i o n . POWER CHANGE SIGNAL SPEED CHANGE SIGNA L "LEVEL 1 DE7ECT0RS\BRAI</NG RES/STER APPLICATION SIGNAL SETR1 COUNT AN0 INK 18 IT I BRAKING RES I STEP. BANK CIRCUIT BREAKER RELAYS 3 5vJtrc.f1/rVG TRANSISTORS F i g . 5.12 A schematic diagram of the BR c o n t r o l c i r c u i t MAXIMUM SPEED O E l S C T O P SPEED ASLOPE SIGNAL TIM £H RE-INtJlA TE NEXT CYCLE • tCH A(-^< O.O &Lf Z o.o O R Rssej, SET •SET RESET M A X I M U M D E T E C T O R A 4" r M I N I M U M SffT 2SJET - F £ J COUNT AND INHIBIT CIRCUIT POSITIVE FE NEGATIVE f=E F i g . 5.13 A schematic diagram of the FE c o n t r o l c i r c u i t •FV CONTROL -SIGNAL NAND INVT. COUNTER AND INHIBIT CIRCUIT F E T l •K6-Vt) C. « T0 C/ MULTIPLIER © TO MULTIPLIER F i g . 5.14 A schematic diagram of the FV c o n t r o l c i r c u i t 84 When the a p p l i c a t i o n number l i m i t i s reached, f u r t h e r a p p l i c a t i o n i s prevented by the FE i n h i b i t l o g i c c i r c u i t . 5.8 The F a s t - V a l v i n g C o n t r o l C i r c u i t The schematic diagram of the FV c o n t r o l c i r c u i t s i m i l a r to that o u t l i n e d i n s e c t i o n 3.5 i s shown i n F i g . 5.14. The only d i f f e r e n c e i s that i n the hardware design, FV i s i n i t i a t e d when power d e v i a t i o n exceeds a given l e v e l wheras i n the computer s i m u l a t i o n , FV i s i n i t i a t e d by the t e r m i n a l c u r r e n t . However, the time d i f f e r e n c e between the two i s very s m a l l ( 0.005 sec.) and considered t o be n e g l i g i b l e . The IV and CV s i g n a l outputs of the FV c o n t r o l l o g i c c i r c u i t s are a p p l i e d to two analogue m u l t i p l i e r s which s i m u l a t e the v a l v e s . Under normal operating c o n d i t i o n s , the m u l t i p l i e r f a c t o r i s set equal to 1.0 but equal to 0.0 and 0.5 under f u l l and 50% va l v e c l o s u r e s , r e s p e c t i v e l y . The v a l v e c l o s u r e or opening i s simulated by FET 1 s w i t c h which set s the c l o s i n g and opening time. The v a l v e c l o s i n g time constant i s near 0.15 second. The v a r i o u s v a l v e opening times are r e a l i z e d w i t h the com-b i n a t i o n of one-capacitor and one r e s i s t o r - i n t h e feedback loop of- the o n e r — a t i o n a l a m p l i f i e r . The p a r t i a l v a l v i n g i s simulated by c l o s i n g FET 2 sw i t c h which s e t s the m u l t i p l i e r f a c t o r to 0.5. Although not shown i n the p a r t i c u l a r diagram of F i g . 5.14, the network which allows f u l l IV c l o s u r e f o r the f i r s t FV ap-p l i c a t i o n and 50% IV c l o s u r e s f o r the successive a p p l i c a t i o n s has a l s o been b u i l t . The CV ope r a t i o n i s by means of the CV s w i t c h . Only 50% c l o s u r e i s permitted f o r t h i s v a l v e . The f a s t - v a l v i n g number i s counted at the beginning of each v a l v e re-opening. When the l i m i t i s reached, f u r t h e r a p p l i c a t i o n of t h i s c o n t r o l i s prevented by the FV i n h i b i t l o g i c c i r c u i t . 85 6. CONCLUSIONS From the computer s i m u l a t i o n and a l s o the l a b o r a t o r y t e s t r e s u l t s , the f o l l o w i n g c onclusions may be drawn. 1, The b r a k i n g r e s i s t o r c o n t r o l i s very e f f e c t i v e i n h a r n e s s i n g the p o s i t i v e t r a n s i e n t swings because i t has an immediate e f f e c t on the system and i t can be a p p l i e d or removed very q u i c k l y . The BR should be a p p l i e d when the speed or the power d e v i a t i o n exceeds a p r e s c r i b e d reference l e v e l s (e.g., 20% of generated power or 1.0 rdd/sec.) and the BR c a p a c i t y should be chosen according to the power d e v i a t i o n at l e a s t and to the speed d e v i a t i o n throughout the a p p l i c a t i o n p e r i o d . Of course, the l a r g e r the c a p a c i t y and the g r e a t e r the number of p a r a l l e l r e s i s t o r banks, the smoother w i l l be the c o n t r o l and g r e a t e r i s the s t a b i l i t y margin. The BR a p p l i c a t i o n should be terminated at the peak torque-angle i n order to prevent an e x c e s s i v e reverse swing. I f the second and subsequent swings are severe, m u l t i p l e a p p l i c a t i o n s of BR c o n t r o l i s necessary and proved very h e l p f u l i n reducing the magnitude of swings. i_ud l u i c t t u c A C j . L a L j . u i i C u i i t i r o i J-3 mCot e f f e c t i v e in. .rcd*ucz.n£; the f i r s t negative swing but i s a l s o v a l u a b l e i n reducing the p o s i t i v e swings. The p o s i t i v e FE should be a p p l i e d when the speed or the power d e v i a t i o n exceeds p r e s c r i b e d reference l e v e l s , (e.g., 20% of generated power or 1.0 r a d / s e c ) . To a l l o w f o r the generator f i e l d d e l a y , p o s i -t i v e FE should be removed s h o r t l y a f t e r the peak speed and not at the peak torque angle. At peak torque angle, the n e g a t i v e FE should be ap-p l i e d and continued u n t i l the minimum speed i s reached. At the minimum speed, a d e c i s i o n must be made whether to r e - i n i t i a t e a f u l l FE c o n t r o l c y c l e f o r severe d i s t u r b a n c e , or i n t e r m e d i a t e FE c o n t r o l f o r a moderate di s t u r b a n c e , or j u s t r e t u r n the f i e l d c u r r e n t to the normal value f o r the l e s s severe disturbance. This d e c i s i o n may be based on the magni-tude of speed d e v i a t i o n as d e s c r i b e d i n t h i s t h e s i s . 3. The f a s t - v a l v i n g c o n t r o l i s very u s e f u l s i n c e i t c o n t r o l s the mechanical power i n p u t , which has no d i r e c t i n t e r a c t i o n w i t h the r e s t of the interconnected power system. With t h i s c o n t r o l , e x c e s s i v e ac-c e l e r a t i o n or d e c e l e r a t i o n of the generator can be prevented. The FV c o n t r o l i s most e f f e c t i v e i n reducing the f i r s t p o s i t i v e swing and a l s o successive p o s i t i v e swings w i t h m u l t i p l e a p p l i c a t i o n s . 86 Fast v a l v i n g of the i n t e r c e p t o r v a l v e i s i n i t i a t e d at the d e t e c t i o n of power or speed d e v i a t i o n beyond the p r e s c r i b e d l i m i t s and continued u n t i l s h o r t l y a f t e r the peak speed i s reached, making allowance f o r the steam t u r b i n e time delays. The opening of the v a l v e should be accom-p l i s h e d as f a s t as p o s s i b l e i n order to prevent e x c e s s i v e generator r e -verse swing. Further improvements i n the t r a n s i e n t s t a b i l i t y can be achieved by f a s t - v a l v i n g the c o n t r o l v a l v e at the same time. M u l t i p l e a p p l i c a t i o n s of f u l l or p a r t i a l IV or IV and CV c o n t r o l should be decided -according to the s e v e r i t y of the d i s t u r b a n c e . 4. The combination of f a s t c o n t r o l s i s f a r s u p e r i o r t o i n d i v i d u a l f a s t c o n t r o l s i f p r o p e r l y coordinated s i n c e b e n e f i t s of i n d i v i d u a l c o n t r o l s can be obtained simultaneously. With the a d d i t i o n of l i n e a r o p t i m a l e x c i t a t i o n c o n t r o l , to improve the system damping i n the s u c c e s s i v e swings, r e - a p p l i c a t i o n s of f a s t c o n t r o l s a f t e r the second swing may not be necessary. Furthermore, gr e a t e r economy can be gained w i t h the com-- Vi jnorl r n n t r o l S . - . In t h i s t h e s i s , guide l i n e s of s i n g l e and combined b r a k i n g r e s i s t o r , f o r c e d e x c i t a t i o n and f a s t - v a l v i n g c o n t r o l s w i t h s i n g l e and m u l t i p l e a p p l i c a t i o n s have been e s t a b l i s h e d . F u r t h e r i n v e s t i g a t i o n can be done reg a r d i n g : (a) f a s t t r a n s i e n t s t a b i l i t y c o n t r o l of multi-machine systems and the dynamic i n t e r a c t i o n among them. (b) t r a d e o f f s of e l a b o r a t e but e f f e c t i v e f a s t c o n t r o l schemes w i t h s i m p l i -c i t y , economy and r e l i a b i l i t y . (c) c o n t i n u i n g the development of o n - l i n e computer c o n t r o l . 87 APPEJNDLX A THE 5 t h AND THE 3 r d ORDER SYNCHRONOUS MACHINE MODELS I N PARK'S PARAMETERS 2 , 1 A . l The 5 t h Order Model * 6 = ( w e ~ W o } p to = W o ( T - T_ - T ) r e — m D e 2H p ^ f - f = -T—j { 1 + d d d d J y^. + ( d a l y v d d J - y ^ d 0 (x *-x ) 2 T * (x *-x ) 2 V Z d a l ; ^do ^ x d x a l ; < V « a l > < V ' - ~ a l > *d + W o V f P > d ' - ^ 3 L L _ y , f - > D _ - ( f d ^ f a l l i d _ ( X a " Z a l ^ i m i l rjl 1.1 qo q.0 T e = ( ^ " - ' . l ^ V ' d ^ f f + (fd^V2. ^ D ) i £ ^ a l ^ d ' " ^ ^ d ' " ^ (x - X " ) ( V X a l } T D = D ( V ~ W q ) 88 The d and q curr e n t and vo l t a g e components a t the machine t e r m i n a l can be expressed i n terms of the s t a t e v a r i a b l e s " ^ ' s , & , and to as f o l l o w s : 6 v d + R a -x" q *d v q x" X d R a i q -(x -x") 0 0 0 0 2 — 3 _ ^d"xa£> ( xd" xd> < x> x"> 0 0 < x d - x a £ ) ( x d - x a i ) ( x d - x a 4 ) w e T f ( A.2 ) . „ „, „rd A.2 The 3 Order Model P J = ( to - to ) v e o J P u>e to 0 ( T - OL - T ) — m D e 2H P * f = "7- t < ^ f + <V X al> h> + W o V f do ( A.3. ) T = e - ( V X a l } T = D D ( to e - a>o ) S i m i l a r i l y , the d and q c u r r e n t and vo l t a g e components a t the machine t e r m i n a l i n ( A.2 ) are reduced as i n ( A.4 ). R -x a q x » R d a x, - x. ( x . - x a l ) Y f ( A.4 ) 89 APPENDIX B LINEAR OPTIMAL EXCITATION CONTROL DESIGN t h For the t h e s i s study, the system was modelled as a 6 order system i n c l u d i n g one v o l t a g e - r e g u l a t o r - e x c i t e r b l o c k time constant and the s t a t e v a r i a b l e s are: Y = (A 6 A coe A > f A ^ A > Q A E f d ) T ( B - l ) Since the f l u x l i n k a g e s are not d i r e c t l y measurable, the s t a t e v a r i a b l e s are transformed by the f o l l o w i n g . r e l a t i o n : X = T Y ( B-2 ) r e s u l t i n g s t a t e v a r i a b l e s a r e : X = (A 6 A w A V A P i i , A E..) T ( B-3 ) © "C © X I u The f i n a l system s t a t e equation becomes; X = A X + B U_ ( B-4 ) hi where A = T A1 T """"" B = T B* A* i s the o r i g i n a l system m a t r i x w i t h f l u x l i n k a g e as the s t a t e v a r i a b l e s and B' = ( 0 0 0 0 0 ( -Br-5 ) TA 90 Next for the LOC design, the cost index is chosen as J = i 1 ( X T Q X + U T R U ) d t 2 ( B-6 ) where Q = q66 R ( B-7 ) The Riccati matrix K was computed from the eigenvectors of M = -1 T - E R B -Q - A T ( B-8 ) and Q and K are determined simultaneously with an eigenvalue shift technique -1 T U = - R B K X E ( B-9 ) The eigenvalues of the system without the LOC were: ( +0.11 - 5.98 -9.89 - 7»96 -66.86 -38.57 ) and system eigenvalues with the LOC become: ( -3.27 -5.73 -10.16 i 9.1 -66.86 -38.59 ) where Q = ( 416724 4590 0 277695 0 0 ) diagonal REFERENCES 1.1 F. P. DeMello, "The E f f e c t s of C o n t r o l " , IEEE T u t o r i a l course t e x t 70 M62-FWR on "Modern Concepts of Power System Dynamics". 1.2 F. P. DeMello and C. Concordia, "Concept of Synchronous Machine A f f e c t e d by E x c i t a t i o n C o n t r o l " , IEEE Trans. Power Apparatus and System (PAS), V o l . 88, pp. 316-319, A p r i l 1969. 1.3 H. Moussa and Y. N. Yu, "Optimal Power System S t a b i l i z a t i o n Through E x c i t a t i o n and/or Governor C o n t r o l " , IEEE Trans. PAS V o l . 91, pp. 1166-1174, May/June 1972. 1.4 R. H. Park, "Improved R e l i a b i l i t y o f Bulk Power Supply by Fas t Load C o n t r o l " , presented at the American Power Conference, Chicago, 111., A p r i l 24, 1968. 1.5 R. H. Park, "The Design and Use of Br a k i n g R e s i s t o r s " , Proceedings IEEE Resources Roundup pp. 52-61, A p r i l 1969. 1.6 ' H. M. E l l i s , J . E. Hardy, A. L. Bly t h e and J . W. Skooglund, "Dynamic S t a b i l i t y of the Peace R i v e r .Transmission System", IEEE Trans. PAS, Vol.-85, pp. 586-600, June 1966. 1.7 M. L. Shel t o n , W. A. M i t t e l s t a d t , P. F. Winkelman and ¥. J . B e l l e r b y , " B o n n e v i l l e Power A d m i n i s t r a t i o n 1400-MW Bra k i n g R e s i s t o r " , IEEE Trans, paper T74 433-9. 1.8 S. M. Minesy and E. V. Bonn, "Optimum Network S w i t c h i n g i n Power System", IEEE Trans. PAS-90, pp. 2118-2123, Sept. 1971. 1.9 E. V. Bohn, "Improving Power System T r a n s i e n t S t a b i l i t y by' Pre-programmed Optimum Network Sw i t c h i n g " , J o i n t Automatic C o n t r o l Conference paper 6-3, pp. 143 and 144, 1973 1.10 0. J . Smith, "Optimal Tra n s i e n t Removal i n a Power System", IEEE Trans. PAS Vol.-84, pp. 361-374, May 1965. 1.11 G. A. Jones, "Tran s i e n t S t a b i l i t y o f a Synchronous Generator under c o n d i t i o n s of Bang-bang E x c i t a t i o n Scheduling", IEEE PAS-84, pp. 114-121, Feb. 1965. 92 1.12 D. H. K e l l y and A. H. M. A. Rahim, "Closed-Loop Optimal E z c i t a t i o n C o n t r o l f o r Power System S t a b i l i t y " , IEEE Trans, paper" 71 TP103-PWR 1.13 G. A. Doroshenko, J . N. L u g i n s k i , V. A. Semenov and S. A. Sovalov, " A n t i - d i s t u r b a n c e Automation Devices f o r Improving Power System S t a b i l i t y " , USSR CIGRE I n t . Conference on Large High Tension E l e c t r i c system, Aug. 1972. 1.14 E. ¥. Cushing, J r . , G. E. D r e c h s l e r , ¥. P. K i l l g o a r , H. G. M a r s h a l l and H. R. Stewart, "Past V a l v i n g as an A i d to Power System T r a n s i e n t S t a b i l i t y and Prompt Resynchroniz a t i o n and Rapid Reload a f t e r P u l l Load R e j e c t i o n " , J o i n t IEEE-ASME Power Generation Conference, St. L o u i s , Mo., July. 1971. 1.15 A. C. S u l l i v a n and P. J . Evans, "Some Model Experiments to Improve T r a n s i e n t S t a b i l i t y " , IEEE Conference paper C72 742-1. 1.16 M. E. M a r t i n , D. M. Triezenberg and P. C. Krause, "A Study of Past Turbine V a l v i n g " , IEEE Conference paper C73 080-9. 1.17 R. H. Park, "Past Turbine V a l v i n g " , IEEE Trans. PAS. Vol-92, pp. 1065-1073, May/June 1973. 1.18 E. ¥. Kimbark, "Improvements of Power System S t a b i l i t y by changes i n the network", IEEE Trans. PAS Vol-88 No. 5, pp. 773-781, May 1969. 1.19 0. J . Smith, "Power System C o n t r o l by C a p a c i t o r S w i t c h i n g " , IEEE Trans. PAS Vol-88 No. 1, pp. 28-35, Jan. 1969. 1.20 P. C. Krause and ¥. C. Mauger, "On-line T r a n s i e n t C o n t r o l o f C a p a c i t o r Switching to Improve System S t a b i l i t y " , IEEE Trans. PAS Vol-92 No. 1, pp. 321-329, Jan. 1973. 1.21 E. ¥. Kimbark, "Improvement of System S t a b i l i t y by Switched S e r i e s C a p a c i t o r s " , IEEE Trans. PAS Vol-85, pp. 180-188, Peb. 1966. 1.22 T. Machida, "Improving Tra n s i e n t S t a b i l i t y o f AC System by J o i n t Usage of DC System", IEEE Trans. PAS Vol-85 No. 3, pp. 226-232, March 1966. 1.23 N. G. H i n g o r a n i , N. Sato, and J . J . V i t h a y a t h i l , "Use of Power C o n t r o l on P a c i f i c Northwest-Southwest DC I n t e r t i e Operating i n P a r a l l e l w i t h Two AC I n t e r t i e s " , B o n n e v i l l e Power A d m i n i s t r a t i o n , P o r t l a n d , Oregon, U.S.A. ' 93 1.24 H. A. Peterson and P. 0. Krause J r . , "Damping of Power Swing i n a P a r a l l e l AC and DC Systems", IEEE Trans. PAS Vol-85 No. 12, pp. 1231-1239, Dec. 1966. 2.1 B. S. H a b i b u l l a h , "Dynamic Power System M o d e l l i n g and L i n e a r Optimal S t a b i l i z a t i o n Design Using a Canonical Form", PHD Thesis Dept. o f E l e c t r i c a l E n g i n e e r i n g , UBC, Oct. 1973. 2.2 G. E. Dawson, "A Dynamic Test Model f o r Power System S t a b i l i t y and C o n t r o l S t u d i e s " , PHD Thesis Dept. o f E l e c t r i c a l E n g i n e e r i n g , UBC, Dec. 1969. 2„3 Y. N. Yu and H. A. M. Moussa, "Experimental Determination o f Exact E q u i v a l e n t C i r c u i t Parameters of Synchronous Machines", IEEE Trans, PAS Vol-90 No. 6, pp. 2555-2560, Nov./Dec. 1971. 2.4 D. J . Aanstad, "Dynamic Response and Data Constants f o r Large Steam Turbines", IEEE T u t o r i a l Course, Course Text 70M 29-PWR, pp. 27-33 and 40-56, 1970 IEEE Summer Power Meeting. 3.1 Same as reference 1.6 3.2 Stunt! txa i'ofei'tsnctj 1.7 3.3. Same as reference 1.5 3.4 Same as re f e r e n c e 1.6 3.5 Same as refe r e n c e 1.10 3.6 Same as reference 1.13 3.7 Same as reference 1.17 3.8 Same as refe r e n c e 1.15 5.1 E. P. Dick, "Design o f a D u a l - E x c i t e d Machine and Development of S t a b i l i z a t i o n Techniques", MASc. T h e s i s , Dept. o f E l e c t r i c a l E n g i n e e r i n g , UBC, Aug. 1973. 5.2 J . A. Bond, "A S o l i d - s t a t e Voltage Regulator and E x c i t e r f o r a Large Power System Test Model",. MASc. T h e s i s , Dept. o f E l e c t r i c a l F ^ g i n e e r i n g , UBC, J u l y 1967. 

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