"Applied Science, Faculty of"@en . "Electrical and Computer Engineering, Department of"@en . "DSpace"@en . "UBCV"@en . "Sawada, Jack Hisao"@en . "2010-01-22T03:28:44Z"@en . "1974"@en . "Master of Applied Science - MASc"@en . "University of British Columbia"@en . "This thesis provides some guidelines of fast control application for transient power system stability, including the braking resistor, the forced excitation, the fast-valving, and combinations of them. Multiple applications of single and combined fast controls of various resistor capacities, various ceiling voltages, full or partial valve closures are also examined.\r\nChapter 2 gives the power system model for the thesis investigation.\r\nComputer simulation results of individual braking resistor, forced excitation, and fast-valving fast controls are presented in Chapter 3,and also in Chapter 4, but of combined fast controls. Included in Chapter 5 are the experimental results in comparison with computer simulation results, and also instrumentations of transducers and circuits for implementing the fast controls. Finally, the main conclusions of the thesis study and suggestions\r\nfor future investigation are summarized in Chapter 6."@en . "https://circle.library.ubc.ca/rest/handle/2429/18902?expand=metadata"@en . "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, \u00E2\u0080\u00A2;.. 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 \u00E2\u0080\u00A2 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\u00C2\u00BB4 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\u00C2\u00AB2 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 . < , . . . < > . . . . \u00E2\u0080\u00A2 . . 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\u00E2\u0080\u009E2 - 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 . . . . . . . . . . . \u00C2\u00BB . . . \u00C2\u00BB .>. . 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\u00C2\u00BB 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 \u00C2\u00A3, 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\u00C2\u00AB0 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 \u00E2\u0080\u00A2 x - - . \u00E2\u0080\u0094 - 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\u00E2\u0080\u00A2! 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\u00C2\u00BB 1 , 5 > ! \u00E2\u0080\u00A2 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\u00C2\u00AB10\u00C2\u00BB1\u00C2\u00AB11,1.12 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 (*\u00C2\u00A3) 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 \u00E2\u0080\u00A2 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\u00C2\u00ABulic 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 ' \u00C2\u00B0 w a t t s \"e base = 3 7 7 ' \u00C2\u00B0 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 * \u00C2\u00B0 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 = \u00C2\u00B0* 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 \u00C2\u00BB* = 0.456 x . = 0.0253 q q a l T, \u00C2\u00BB = 5.0 sec. T, \u00C2\u00BB\u00C2\u00BB = 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) \u00E2\u0080\u00A2 I, ,-.,l.|>L (1 + sTE) '\u00E2\u0080\u00A2Fd 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 >\u00C2\u00ABf 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 .\u00E2\u0080\u0094 \u00E2\u0080\u0094 A ' l r t ' - m l ; \u00E2\u0080\u00A2-\u00E2\u0080\u00A2 ' - J \u00E2\u0080\u009E .V-f __\u00E2\u0080\u00A2 - i x. - . - J ' . - . l . . - ' i . - i . \u00C2\u00BB- -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 (Intermediate X ^ - v ^ pressure) (High pressure) 0.05 -i o \u00E2\u0080\u00A2 ' 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 =\u00E2\u0080\u00A2 500 watt o 3. P = 400 watt o 4. P = 300 watt 0 . 5 \u00E2\u0080\u00A2 '\u00E2\u0080\u00A2\u00E2\u0080\u00A2 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 - \u00C2\u00AB Pm - \u00E2\u0080\u0094 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 \u00C2\u00A9 \u00C2\u00AE % 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 ~\u00C2\u00A3\u00C2\u00A3i~ 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-\u00E2\u0080\u00A2angle 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 \u00E2\u0080\u00A2 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 \u00E2\u0080\u00A2 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 \u00C2\u00A3 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\u00E2\u0080\u0094will- 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 \u00E2\u0080\u0094 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 \u00E2\u0080\u00A2 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 \u00E2\u0080\u009E and w > 0 . 0 e \u00E2\u0080\u0094 e r e f e Small Di\u00C2\u00A3 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 - \u00E2\u0080\u0094 f i e l d c u r r e n t s \u00E2\u0080\u0094 r u m s tr> the* nnrma-l- 'ira or-\u00E2\u0080\u0094 > 1 . 0 rad./sec. and w > 0 . 0 r r e \u00E2\u0080\u0094 e A P > P . and u > 0 . 0 e \u00E2\u0080\u0094 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 \u00C2\u00A3 ) 12. 10 8 6. UJ 4 in CC \u00C2\u00A3 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 \u00E2\u0080\u009E 3 .00 ^ 2 .00 Cl. \" 1 0 n \u00C2\u00A7-1.00 \u00C2\u00A7-2.00 \u00E2\u0080\u00A2* ^ - 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 -*\u00E2\u0080\u00A2>\u00E2\u0080\u00A2 \" 1 H ! /! / 1 < 1 > 1 ' 1-ii \u00E2\u0080\u00A2 I ' I J / I 1 ii ni l IPs \u00E2\u0080\u00A2 \u00E2\u0080\u00A2/ 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 / \u00E2\u0080\u00A2 \"i= / 11 / i 1 !\u00E2\u0080\u00A2\u00E2\u0080\u00A2 I \u00E2\u0080\u00A2 \u00E2\u0080\u00A2 /\u00E2\u0080\u00A2 i i ; T ! ! M 1 i / i V . i I I I v# I ' M / 1 l! / i ' \u00E2\u0080\u00A2 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 \u00E2\u0080\u00A2 ' 1 r 1 1 1 \l 1 \l VI (^ i i i i i 0 . 5 1.0 1.5 2 .0 TIME (SECONDS) \u00E2\u0080\u00A2 \u00E2\u0080\u00A2 i i 2 . 5 3 . F i g . 3.10(c) FE c o n t r o l (E \u00E2\u0080\u00A2) 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 \u00E2\u0080\u00A211 \u00E2\u0080\u00A2 \u00E2\u0080\u00A2 0.5 \u00E2\u0080\u00A2 \u00E2\u0080\u00A2 i i i \u00E2\u0080\u00A2' 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 \u00E2\u0080\u00A2 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 - - - - \u00E2\u0080\u0094r= -. h\u00E2\u0080\u0094F-R-removed\u00E2\u0080\u0094 - \u00E2\u0080\u0094 - 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 \u00E2\u0080\u00A2(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\u00C2\u00AB11 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 \u00E2\u0080\u0094 5 -40.0 UJ \u00C2\u00A3 -60.0 \u00C2\u00B0 -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 \u00E2\u0080\u009450% 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 \u00E2\u0080\u00A2 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 \u00C2\u00A7 \u00C2\u00B0 0 . 4 0 -i 0.30 0.20-3 0.10-3 \u00E2\u0080\u00A2Tup -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\u00C2\u00AB 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 '\u00E2\u0080\u00A2\u00E2\u0080\u00A2\u00E2\u0080\u00A21 1 ' 1 1 1 1 1 \" ) \u00E2\u0080\u00A2 ' \" \u00E2\u0080\u00A2 -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 \u00E2\u0080\u009E0.60 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 \u00C2\u00B1 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. \u00C2\u00B16.0 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 \" \u00E2\u0080\u00A2 \u00E2\u0080\u00A2 1 1 11 1 1 1 1 1 1 1 1 11 1 \u00E2\u0080\u00A2 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) \u00C2\u00B16.0 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 ) \u00C2\u00B16.0 p.u. FE ( l ) F u l l IV ( l ) 2. Same as 1. except -8.0 p.u. FE 3 . 25$ BR ( l ) / ^ \u00C2\u00B18.0 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 ) \u00E2\u0080\u00A2 ^6.0 p.u. FE ( l ) 50$ IV ( l ) 2. 50$ BR ( l ) \u00C2\u00B16.0 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, \u00C2\u00B16.0 p.u. FE and FV combination w i t h LOC 66 60.0 Curves 1. 25$ BR ( l ) \u00C2\u00B16.0 p.u. FE (3) F u l l IV (2) 2. 25$ BR ( l ) \u00C2\u00B16.0 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 \u00E2\u0080\u00A2 0 0.5 1.0 1.5 2.0 2.5 3.0 TIME (SECONDS) F i g . 4.6(b) 25% BR. \u00C2\u00B16.0 p.u. FE and FV combination w i t h LOC Curves 1. 25$ BR ( l ) \u00C2\u00B16.0 p.u. FE (3) 50$ IV (2) 2. 25$ BR (2) \u00C2\u00B16.0 p.u. FE (3) 50$ IV ( l ) 3. 25$ BR ( l ) \u00C2\u00B16.0 p.u. FE (3) 50$ IV (2) 50$ CV (2) 4. 25$ BR (2) \u00C2\u00B16.0 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\u00E2\u0080\u0094T-T-T \u00E2\u0080\u00A2 \u00E2\u0080\u0094 T . r r i i i-to \u00E2\u0080\u009E \u00E2\u0080\u0094 \u00E2\u0080\u009E\u00E2\u0080\u0094_~ J T.ii-fVio-nrmiTtTrfQ^\u00E2\u0080\u0094 r ^ s w l t s ~ r e c a r d e d ~as~'C'_irT.Te\"s~\u00E2\u0080\u0094 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 \u00C2\u00A3-40 \u00C2\u00B0 - 5 0 -60 -70 -80 -90 -100 -110 -120 0 ? o -: o-j o ] o o -: o \u00E2\u0080\u00A2; 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 \u00C2\u00B1 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 \u00E2\u0080\u00A210 -20 \u00C2\u00A3 -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 \u00E2\u0080\u00A2: .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: \u00C2\u00B18.0 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: \u00C2\u00A3 -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,\u00E2\u0080\u0094i,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 . | \u00E2\u0080\u00A2 . I . . I i t r p n i . i n ,\ I \u00E2\u0080\u00A2 I I I I I I i ! \u00E2\u0080\u00A2 \u00E2\u0080\u00A2 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 \u00E2\u0080\u009480.0 \"} 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*\u00E2\u0080\u0094 LOC IA I! \ / M \ \ ./\u00E2\u0080\u00A2' ^ Curves 1,1: 25$ BR (l) \u00C2\u00B16.0 p.u. FE (l) Full IV (l) \.\u00C2\u00BB 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) \u00C2\u00B16.0 p.u. FE {3, Full IV (2) < 1\" 1111 \u00E2\u0080\u00A2 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 \u00C2\u00B1 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 - ^ \u00E2\u0080\u0094 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\u00E2\u0080\u0094 \u00E2\u0080\u00A2 - - f, \u00E2\u0080\u0094 \ \ 1 -f?. H T--\V \u00E2\u0080\u00A2 T \u00E2\u0080\u00A2 F i g . 5.7 A schematic diagram of the speed transducer Time Time OUTPUT DC VOLTS r 4. 1 Aid RAD./SEC. SLOPE \u00E2\u0080\u00A2 V 0 L T , S L 0 F E \u00E2\u0080\u00A2* 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 \u00E2\u0080\u00A2 l & h i . 4>i INTO. Aw L e v e l \u00E2\u0080\u00A2 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/? \u00E2\u0080\u00A2o R E S E T COUNTER i PULSE \u00E2\u0080\u00A2 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 < 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 \u00C2\u00A3 ^ 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 \u00E2\u0080\u0094 3 _ ^d\"xa\u00C2\u00A3> ( xd\" xd> < x> x\"> 0 0 < x d - x a \u00C2\u00A3 ) ( x d - x a i ) ( x d - x a 4 ) w e T f ( A.2 ) . \u00E2\u0080\u009E \u00E2\u0080\u009E, \u00E2\u0080\u009Erd A.2 The 3 Order Model P J = ( to - to ) v e o J P u>e to 0 ( T - OL - T ) \u00E2\u0080\u0094 m D e 2H P * f = \"7- t < ^ f + 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 \u00C2\u00BB 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 ) \u00C2\u00A9 \"C \u00C2\u00A9 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\u00C2\u00BB96 -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. 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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. "@en . "Thesis/Dissertation"@en . "10.14288/1.0099927"@en . "eng"@en . "Electrical and Computer Engineering"@en . "Vancouver : University of British Columbia Library"@en . "University of British Columbia"@en . "For non-commercial purposes only, such as research, private study and education. Additional conditions apply, see Terms of Use https://open.library.ubc.ca/terms_of_use."@en . "Graduate"@en . "Fast control of power system transient stability"@en . "Text"@en . "http://hdl.handle.net/2429/18902"@en .