UBC Theses and Dissertations

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UBC Theses and Dissertations

Photovoltaic array simulators Liu, Guang 1985

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PHOTOVOLTAIC ARRAY SIMULATORS by . GUANG^LIU B. Sc., Guangxi U n i v e r s i t y , 1982, A THESIS SUBMITTED IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF APPLIED SCIENCE i n FACULTY OF GRADUATE STUDIES Department of E l e c t r i c a l E n g i n e e r i n g We a c c e p t t h i s t h e s i s as co n f o r m i n g t o the r e q u i r e d s t a n d a r d THE UNIVERSITY OF BRITISH COLUMBIA June, 1985 © Guang L i u , 1985 In presenting t h i s thesis i n p a r t i a l f u l f i l m e n t of the requirements for an advanced degree at the University of B r i t i s h Columbia, I agree that the Library s h a l l make i t f r e e l y available for reference and study. I further agree that permission for extensive copying of t h i s thesis for scholarly purposes may be granted by the head of my department or by h i s or her representatives. I t i s understood that copying or publication of t h i s thesis for f i n a n c i a l gain s h a l l not be allowed without my written permission. Department of BLtofcr tCeJl. 6K^,VI <?er/> The University of B r i t i s h Columbia 1956 Main Mall Vancouver, Canada V6T 1Y3 Date /si *\ ABSTRACT Two b a s i c t y p e s of p h o t o v o l t a i c (PV) a r r a y s i m u l a t o r have been d e s i g n e d and t e s t e d . The f i r s t i n v o l v e s the use of a p i l o t p a n e l and v a r i a b l e l i g h t s o u r c e . I t i s implemented w i t h a n a l o g u e c i r c u i t s . A s t a b i l i t y a n a l y s i s based on Popov's method i s p r e s e n t e d f o r t h i s s i m u l a t o r w i t h r e s i s t a n c e - i n d u c t a n c e (R-L) l o a d s . I n the second, c h a r a c t e r i s t i c a r r a y c u r v e s a r e s t o r e d i n the memory of a m i c r o p r o c e s s o r - b a s e d s i m u l a t o r . The d e s i g n of both s i m u l a t o r s i s based on the t r a n s f e r f u n c t i o n method. By u s i n g the computing f a c i l i t y a v a i l a b l e , a s t a b i l i t y study f o r the Type I s i m u l a t o r and some dynamic s i m u l a t i o n s a r e c a r r i e d o u t . Both s i m u l a t o r s a r e c a p a b l e of d r i v i n g a s p e c i a l l o a d , namely, an e x p e r i m e n t a l s o l a r pumping system. The e x p e r i m e n t a l r e s u l t s f o r both t y p e s o f ' s i m u l a t o r a r e s a t i s f a c t o r y i n terms of s t e a d y s t a t e p r e c i s i o n and dynamic b e h a v i o u r when used w i t h t h i s l o a d . Compared w i t h p r e v i o u s l y - r e p o r t e d PV a r r a y s i m u l a t o r d e s i g n s [ 6 , 7 , 8 , 9 , 1 8 ] , the two s i m u l a t o r s d e s c r i b e d here have the f o l l o w i n g d i s t i n c t i v e f e a t u r e s : 1. A new method of sample c u r v e g e n e r a t i o n f o r the Type I I s i m u l a t o r r e s u l t s i n r e l a t i v e l y s h o r t s a m p l i n g p e r i o d and s m a l l memory s i z e . 2. The sample c u r v e s of t h e type I I s i m u l a t o r a r e based d i r e c t l y on the r e a l PV a r r a y t o be s i m u l a t e d . They are more a c c u r a t e than the sample c u r v e s i n r e f e r e n c e s [ 6 , 7 , 9 ] . i i 3. D i f f e r e n t l o a d s (R , R - L and an e x p e r i m e n t a l s o l a r pumping system) have been c o n s i d e r e d i n the d e s i g n and have been t e s t e d i n l a b o r a t o r y . 4 . A s t a b i l i t y a n a l y s i s and some dynamic s i m u l a t i o n s a r e p r e s e n t e d f o r the type I s i m u l a t o r . An a n a l y s i s of t h i s type has not been r e p o r t e d i n p r e v i o u s s t u d i e s [ 6,7,8,9,18]. i i i Table of C o n t e n t s 1. INTRODUCTION 1 1.1 PV a r r a y powered systems 1 1.2 PV a r r a y s i m u l a t o r s 4 1.2.1 P r e v i o u s S i m u l a t o r D e s i g n s 5 1.2.2 S i m u l a t o r Requirements 6 2. TYPE I SIMULATOR 9 2.1 D e s ign C o n s i d e r a t i o n s f o r Type I S i m u l a t o r 9 2.1.1 Sample Curve g e n e r a t i o n 9 2.1.2 C o n t r o l Loops 11 2.1.3 Power C o n v e r t e r 12 2.2 D e s ign and Test of Type I S i m u l a t o r 14 2.3 S t a b i l i t y A n a l y s i s w i t h R-L Loads 24 2.4 A p p l i c a t i o n t o a Pumping System 33 3. TYPE I I SIMULATOR 41 3.1 D e s ign C o n s i d e r a t i o n s 42 3.1.1 Sample Curve G e n e r a t i o n 42 3.1.2 C o n t r o l Scheme of the S i m u l a t o r 44 3.1.3 Power C o n v e r t e r : 45 3.2 D e s ign and Test of the Type I I S i m u l a t o r 46 3.2.1 Hardware of the Type I I S i m u l a t o r 46 3.2.2 T r a n s f e r F u n c t i o n A n a l y s i s f o r the Pumping System Load 51 3.2.3 S o f t w a r e of the System 57 4. DISCUSSION 64 5. CONCLUSION 66 REFERENCES 67 APPENDIX A: ALGORITHM FOR STABILITY STUDY 69 i v APPENDIX B: PROGRAM LISTING FOR STABILITY STUDY APPENDIX C: CONTROL PROGRAM LISTING v L i s t of F i g u r e s ; page F i g u r e 1-1. F u n c t i o n a l Elements of A S o l a r C e l l System 1 F i g u r e 1-2. T y p i c a l PV A r r a y C h a r a c t e r i s t i c s 2 F i g u r e 1-3. Power Demand and Power Supply V e r s u s Time of Day 3 F i g u r e 2-1. S o l a r C e l l E q u i v a l e n t C i r c u i t 10 F i g u r e 2-2. One Way t o Generate Sample Curves 10 F i g u r e 2-3. C i r c u i t Diagram of t h e Chopper 13 F i g u r e 2-4. Waveform of Chopper Output and Base S i g n a l 14 F i g u r e 2-5. Schematic Diagram of Type I S i m u l a t o r 15 F i g u r e 2-6. C i r c u i t Diagram of Type I S i m u l a t o r 16 F i g u r e 2-7. C u r r e n t Loop T r a n s f e r F u n c t i o n B l o c k Diagram 17 F i g u r e 2-8. Load L i n e of the T r a n s i s t o r T 18 F i g u r e 2-9. V o l t a g e Loop T r a n s f e r F u n c t i o n B l o c k Diagram 19 F i g u r e 2-10. Output C h a r a c t e r i s t i c w i t h V a r y i n g Load 21 F i g u r e 2-11. S i m u l a t o r Output w i t h Mismatched Parameters 22 F i g u r e 2-12. E x p e r i m e n t a l Output of C o r r e c t l y A d j u s t e d S i m u l a t o r 23 F i g u r e 2-13. Model of the Whole System 24 F i g u r e 2-14. M o d i f i e d Model of t h e Whole System 27 F i g u r e 2-15. The E q u i v a l e n t N o n - l i n e a r Element 29 F i g u r e 2-16. T y p i c a l N y q u i s t P l o t of the S i m u l a t o r 30 F i g u r e 2-17. S t a b l e V a l u e of k w i t h Respect t o R^, L 31 F i g u r e 2-18. Type I S i m u l a t o r Response t o S t e p Change 32 v i F i g u r e 2-19. S c h e m a t i c a l Diagram of the Pumping System 33 F i g u r e 2-20. E q u i v a l e n t C i r c u i t of the Pumping System 34 F i g u r e 2-21. Model of M o d i f i e d V o l t a g e Loop 35 F i g u r e 2-22. S t e p Response of the V o l t a g e Loop 37 F i g u r e 2-23. Ramp Response of the V o l t a g e Loop 38 F i g u r e 2-24. E q u i v a l e n t Load L i n e of the Pumping System 39 F i g u r e 2-25. S i m u l a t e d Load f o r P r e l i m i n a r y Test 40 F i g u r e 3-1. One of t h e I/V Curves t o Be S i m u l a t e d 43 F i g u r e 3-2. A r c h i t e c t u r e of 6809 M i c r o p r o c e s s o r Development System 48 F i g u r e 3-3. Hardware C o n f i g u r a t i o n of the Type I I S i m u l a t o r 49 F i g u r e 3-4. S i g n a l Assignment t o I/O P o r t s 50 F i g u r e 3-5. C i r c u i t Diagram of PV7M S i g n a l G e n e r a t o r 52 F i g u r e 3-6. T r a n s f e r F u n c t i o n B l o c k Diagram f o r Pumping System Load 54 F i g u r e 3-7. C i r c u i t Diagram of Analogue P a r t 55 F i g u r e 3-8. Type I I S i m u l a t o r I/V Curves (PI C o n t r o l ) 58 F i g u r e 3-9. Type I I S i m u l a t o r Output U s i n g P C o n t r o l 59 F i g u r e 3-lOa. F l o w c h a r t of C o n t r o l Program 61 F i g u r e 3-lOb. F l o w c h a r t of S u b r o u t i n e s 62 F i g u r e 3-11. S t e p Response of the Type I I s i m u l a t o r 63 v i i Acknowledgements I w i s h t o thank Dr. W. G. Dunford f o r h i s a d v i c e and h e l p t h r o u g h o u t my work on t h i s p r o j e c t . Thanks a r e a l s o due t o Dr. M. S. D a v i e s who h e l p e d me w i t h t h e s t a b i l i t y a n a l y s i s , and Dr. D. L. P u l f r e y from whom I r e c e i v e d h e l p on m a t t e r s c o n c e r n i n g s o l a r c e l l s . v i i i 1 . INTRODUCTION S o l a r energy i s a p r o m i s i n g energy s o u r c e f o r the f u t u r e . When o t h e r non-renewable energy s o u r c e s , such as g a s , o i l and c o a l , become l i m i t e d and e x p e n s i v e , e l e c t r i c energy from p h o t o v o l t a i c a r r a y s w i l l be e c o n o m i c a l l y c o m p e t i t i v e . Some e x p e r t s i n t h i s f i e l d have g i v e n q u i t e o p t i m i s t i c p r e d i c t i o n s . I t has been p r e d i c t e d [ 1] t h a t i n a r e g i o n w i t h an annual i n s o l a t i o n l e v e l of 1750 kwh/m2 ( t r o p i c s ) , t he e l e c t r i c i t y from PV a r r a y s w i l l be cheaper than t h a t from c o n v e n t i o n a l power g r i d by the year 2000. 1.1 PV ARRAY POWERED SYSTEMS A s k e t c h showing a t y p i c a l PV array- p o w e r e d system i s i l l u s t r a t e d s c h e m a t i c a l l y i n F i g u r e 1-1. When the PV a r r a y i s exposed t o s u n l i g h t , i t becomes a power sou r c e w i t h the c u r r e n t / v o l t a g e (I/V) c h a r a c t e r i s t i c s shown i n F i g u r e 1-2. Sunlight concentrator Tracking Semiconductor ^Charge-separating barrier region Power condition-ing Energy storage Electrical load F i g u r e 1-1. F u n c t i o n a l Elements of A S o l a r C e l l System As can be seen, the I/V c h a r a c t e r i s t i c s of a PV a r r a y v a r y 1 2 w i t h both the l i g h t i n t e n s i t y and t e m p e r a t u r e . F or t h i s r e a s o n , 'power c o n d i t i o n i n g ' and 'power s t o r a g e ' e l e m e n t s a r e n e c e s s a r y i n most systems. T y p i c a l ' e l e c t r i c a l l o a d s ' i n a s t a n d - a l o n e system a r e l i g h t b u l b s , e l e c t r i c a l a p p l i a n c e s i n r e s i d e n c e s , motors i n a pumping system o r , i n i n t e r c o n n e c t e d systems, the PV a r r a y c o u l d f e e d power i n t o t h e g r i d . T a k i n g a r e s i d e n t i a l system as an example [ 4 ] , the power demand of a r e s i d e n c e over a t y p i c a l 24-hour p e r i o d d u r i n g the S p r i n g and the power a PV a r r a y may produce a r e shown i n F i g u r e 1-3. As can be seen, from 6 am t o 6 pm, the PV a r r a y o u t p u t power exceeds the power needed. F i g u r e 1-2 T y p i c a l PV A r r a y C h a r a c t e r i s t i c s 3 3.0 r-2.5 -2.0 £ 1.5 5 1.0 0.5 .JL 1 I p o w e r s u p p l y f r o m t h e a r r a y \ P o w e r d e m a n d _L_± 2 4 6 8 10 12 2 4 6 8 10 12 AM 4- PM-T i m e of day F i g u r e 1-3. Power Demand and Power Supply V e r s u s Time of Day To make good use of t h i s energy, i t i s s t o r e d i n b a t t e r i e s . At o t h e r t i m e s , when t h e power demand of the r e s i d e n c e exceeds t h e power o u t p u t of the PV a r r a y , the demand can be met by r e l e a s i n g the energy s t o r e d i n the b a t t e r i e s . These f u n c t i o n s a r e c o n t r o l l e d by the power c o n d i t i o n e r . A f u r t h e r f u n c t i o n of the power c o n d i t i o n e r i s t o ensure t h a t the t o t a l l o a d i s matched t o the a r r a y so t h a t maximum power i s alw a y s e x t r a c t e d . T h i s c o r r e s p o n d s t o o p e r a t i o n c l o s e t o the 'knee' of the c u r v e s of F i g u r e 1-2. T h i s m a t c h i n g must be done c o n t i n u o u s l y as l o a d and s u n l i g h t c o n d i t i o n s change. In some s i m p l e systems the power c o n d i t i o n e r i s e l i m i n a t e d , w i t h the l o a d b e i n g connected d i r e c t l y t o the a r r a y . The o v e r a l l e f f i c i e n c y of t h e s e systems i s low s i n c e 4 t h e maximum power t r a c k i n g f u n c t i o n i s not p r e s e n t . The purpose of the work d e s c r i b e d i n t h i s t h e s i s i s t o d e s i g n a c i r c u i t which w i l l produce an output c h a r a c t e r i s t i c of the t y p e shown i n F i g u r e 1-2. T h i s w i l l a l l o w f o r r e s e a r c h on many d i f f e r e n t t y p e s of l o a d s t o be p e r f o r m e d i n the absence of a r e a l a r r a y . T h i s w i l l remove any r e l i a n c e on p r e v a i l i n g weather c o n d i t i o n s , and s h o u l d a l s o p r o v i d e some c o s t s a v i n g s . Two approaches t o the d e s i g n of a s i m u l a t o r a r e d e s c r i b e d i n the next s e c t i o n . The emphasis of t h e work d e s c r i b e d here i s on the c i r c u i t d e s i g n . The s t a b i l i t y a n a l y s i s of the system i s complex and i s o n l y p e r f o r m e d f o r c e r t a i n l o a d c o n d i t i o n s . The completed s i m u l a t o r i s t o be used t o s u p p l y a pumping system. I n i t i a l t e s t s w i t h t h i s l o a d have been s a t i s f a c t o r y . 1.2 PV ARRAY SIMULATORS The r e q u i r e m e n t s of a s i m u l a t o r v a r y a c c o r d i n g t o the l o a d t o be t e s t e d . For i n s t a n c e , i n l a b o r a t o r y t e s t i n g of a PV arr a y - p o w e r e d pumping system, one may need the I/V c u r v e of the a r r a y t o be f i x e d f o r a p e r i o d of t i m e so t h a t measurement and comparisons can be done. I t i s not p o s s i b l e t o count on the n a t u r a l environment t o p r o v i d e a f i x e d l i g h t i n t e n s i t y and t e m p e r a t u r e , and i t i s c o s t l y t o b u i l d up an a r t i f i c i a l environment f o r a l a r g e s i z e a r r a y . However, i t i s easy f o r the PV a r r a y s i m u l a t o r t o output a f i x e d I/V c h a r a c t e r i s t i c c u r v e . 5 A PV a r r a y s i m u l a t o r i s a c o n t r o l l e d power s o u r c e t h a t can produce output c h a r a c t e r i s t i c s m i m i c k i n g t h a t of a r e a l PV a r r a y . A power c o n v e r t e r i s u s u a l l y used, and i t can be an ac t o dc b r i d g e c o n v e r t e r or a dc t o dc chopper. Though c o n t r o l schemes may d i f f e r v e r y much from each o t h e r , t h e y b a s i c a l l y c o n s i s t of sample cu r v e g e n e r a t i o n and c o n t r o l l o o p s . 1.2.1 PREVIOUS SIMULATOR DESIGNS In r e f e r e n c e [ 6 ] , sample c u r v e s a r e o b t a i n e d by c a l c u l a t i n g a s e r i e s of fo r m u l a e . The stea d y s t a t e e r r o r i s r e a s o n a b l y s m a l l . However, due t o the r e l a t i v e l y l o n g s a m p l i n g p e r i o d caused by the fo r m u l a c a l c u l a t i o n , t h e dynamic response i s not v e r y f a s t (0.3 s e c o n d ) . I n r e f e r e n c e [ 7 ] , the c o n t r o l f u n c t i o n i s implemented • w i t h a n a l o g u e c i r c u i t r y . A chopper ( s w i t c h i n g r e g u l a t o r ) i s used as the power c o n v e r t e r . The sample cu r v e i s o b t a i n e d by p h y s i c a l s i m u l a t i o n based on the s o l a r c e l l e q u i v a l e n t c i r c u i t . The s t e p response of t h i s s i m u l a t o r i s ve r y f a s t (about 20 ms). However, the e f f e c t of temperature i s not c o n s i d e r e d . A comparison between the I/V c u r v e s of the s i m u l a t o r and t h o s e of the r e a l a r r a y was not r e p o r t e d . R e f e r e n c e [9] d e s c r i b e s a low c o s t s i m u l a t o r . In t h a t r e p o r t , an I/V c u r v e i s d i v i d e d i n t o two l i n e a r s e c t i o n s and one n o n - l i n e a r s e c t i o n (around the maximum power p o i n t ) . The n o n - l i n e r s e c t i o n i s a p p r o x i m a t e d by an e x p o n e n t i a l c u r v e and i s implemented w i t h an analogue e x p o n e n t i a l m u l t i p l i e r . The s t e a d y s t a t e 6 a c c u r a c y i s not as good as t h a t of r e f e r e n c e [ 6 ] , The i n f o r m a t i o n r e g a r d i n g dynamic response i s not p r o v i d e d . A l l the s i m u l a t o r s mentioned above produce f i x e d , r e p e a t a b l e I/V c u r v e s w h i c h a r e not s u b j e c t t o the i n f l u e n c e of the environment. In r e f e r e n c e s [8 & 18], s o l a r c e l l s a r e used t o o b t a i n sample, c u r v e s . As a r e s u l t , the output I/V c u r v e s of thes e s i m u l a t o r s a r e s u b j e c t t o the i n f l u e n c e of the environment. However, t r a n s i e n t response i s not d i s c u s s e d i n e i t h e r r e f e r e n c e . 1.2.2 SIMULATOR REQUIREMENTS The o v e r a l l d e s i g n of a s i m u l a t o r i s governed by the r e q u i r e m e n t s of the a p p l i c a t i o n . I t may be d e s i r a b l e t o reprod u c e a c o n t i n u o u s v a r i a t i o n i n the I/V c h a r a c t e r i s t i c s , as might be e x p e r i e n c e d d u r i n g a t y p i c a l o p e r a t i n g day, f o r example, d u r i n g the f i e l d t e s t of PV array-powered systems. The s i m u l a t o r s r e p o r t e d i n r e f e r e n c e s [8,18] are s u i t a b l e f o r t h i s k i n d of a p p l i c a t i o n . A l t e r n a t i v e l y , i t may be r e q u i r e d t h a t a p a r t i c u l a r , r e p e a t a b l e I/V c h a r a c t e r i s t i c s h o u l d be produced f o r comparison p u r p o s e s . In t h i s t h e s i s , two d i f f e r e n t t y p e s of PV a r r a y s i m u l a t o r s a r e i n t r o d u c e d , w h i c h w i l l be r e f e r r e d t o as type I and type I I . The major d i f f e r e n c e between the s e two t y p e s of s i m u l a t o r s i s the way they g e n e r a t e sample c u r v e s . A s m a l l PV p a n e l i s used as a p i l o t i n the t y p e I s i m u l a t o r . The p i l o t p a n e l can be put o u t d o o r s , b e i n g i n f l u e n c e d by the n a t u r a l e n v i r o n m e n t , or i t can be p l a c e d i n a l i g h t and temp e r a t u r e 7 c o n t r o l l e d e n v i r o n m e n t . The c o n t r o l u n i t of the type I s i m u l a t o r keeps t h e s i m u l a t o r output c u r r e n t p r o p o r t i o n a l t o the p i l o t p a n e l c u r r e n t , and the s i m u l a t o r o utput v o l t a g e p r o p o r t i o n a l t o t h e p i l o t p a n e l v o l t a g e . As a r e s u l t , the I/V c u r v e s of t h e s i m u l a t o r a r e a m p l i f i e d v e r s i o n s of tho s e of the p i l o t p a n e l . The s t e a d y s t a t e e r r o r (compared w i t h the p i l o t p a n e l ) i s w i t h i n 1%. More d e t a i l e d d i s c u s s i o n about the s t e a d y s t a t e e r r o r of t h e type I s i m u l a t o r i s g i v e n i n C h a p t e r 4. The t r a n s i e n t s t a t e caused by a s t e p change of l o a d from open c i r c u i t t o maximum power p o i n t i s about 50 ms. In t h e type I I s i m u l a t o r a p i l o t p a n e l i s not used. I n s t e a d , r e f e r e n c e I/V c u r v e s a r e s t o r e d i n the memory of a m i c r o p r o c e s s o r system. In the system d e s c r i b e d here the sample c u r v e g e n e r a t i o n and c o n t r o l t a s k s a r e implemented u s i n g a M o t o r o l a 6809 M i c r o p r o c e s s o r . The method used f o r sample c u r v e g e n e r a t i o n i s a c o m b i n a t i o n of fo r m u l a c a l c u l a t i o n and d a t a s t o r a g e , which i s a t r a d e - o f f between e x e c u t i o n t ime and memory s i z e . D i f f e r e n t c u r v e s can be s e l e c t e d by s e t t i n g a code. Once a c u r v e i s s e l e c t e d , the type I I s i m u l a t o r can output an I/V c h a r a c t e r i s t i c c o r r e s p o n d i n g t o t h i s c u r v e f o r as l o n g as i s r e q u i r e d . The l o a d c o n n e c t e d t o the s i m u l a t o r i s an e x p e r i m e n t a l pumping system. The r e g u l a t o r i n the pumping system matches the dc motor t o t h e a r r a y so t h a t when the I/V c u r v e of the a r r a y changes w i t h t h e l i g h t i n t e n s i t y and te m p e r a t u r e , the o p e r a t i n g p o i n t i s kept c l o s e t o the maximum power p o i n t . The r e g u l a t o r a d j u s t s the o p e r a t i n g p o i n t a p p r o x i m a t e l y 10 8 times e v e r y second. R e s i s t i v e and r e s i s t i v e - i n d u c t i v e l o a d s a re a l s o c o n s i d e r e d i n t h i s t h e s i s . F o r b o t h t y p e s of s i m u l a t o r s t u d i e d i n t h i s work, the power c o n v e r t e r i s a one quadrant ( p o s i t i v e v o l t a g e , p o s i t i v e c u r r e n t ) power t r a n s i s t o r chopper w i t h h i g h s w i t c h i n g f r e q u e n c y and low s w i t c h i n g l o s s e s . The major c o n t r i b u t i o n s of t h i s t h e s i s a r e : 1. Two new d e s i g n s of PV a r r a y s i m u l a t o r a r e p r e s e n t e d . These s i m u l a t o r s can be used w i t h a p a r t i c u l a r s o l a r pumping system l o a d and some o t h e r l o a d s , such as R , R-L and dc motor l o a d s . 2. A s t a b i l i t y a n a l y s i s f o r the type I s i m u l a t o r and some p a r t i a l dynamic s i m u l a t i o n s have been c a r r i e d o u t . The r e s u l t s of t h i s a n a l y s i s and s i m u l a t i o n s h e l p the d e s i g n e r t o choose system parameters p r o p e r l y so t h a t i n s t a b i l i t y ( o s c i l l a t i o n ) w i l l not o c c u r , have not been r e p o r t e d p r e v i o u s l y . The d e t a i l e d d e s i g n of a type I s i m u l a t o r and p r a c t i c a l problems e n c o u n t e r e d d u r i n g t e s t i n g of the s i m u l a t o r are p r e s e n t e d i n Chapter 2. Chapter 3 p r o v i d e s the d e t a i l s of the d e s i g n and t e s t i n g of a type I I s i m u l a t o r . Some d i s c u s s i o n of the two s i m u l a t o r s i s g i v e n i n Chapter 4. F i n a l l y , c o n c l u s i o n s a r e drawn i n Chapter 5. 2. TYPE I SIMULATOR 2.1 DESIGN CONSIDERATIONS FOR TYPE I SIMULATOR The b a s i c r e q u i r e m e n t s of a type I s i m u l a t o r a r e l i s t e d below: 1. The s t e a d y s t a t e e r r o r must not exceed 5% i n o r d e r t o a s s u r e t h e a c c u r a c y of the experiment u s i n g t h i s s i m u l a t o r . 2. The t r a n s i e n t s t a t e caused by a s t e p change of l o a d from open c i r c u i t t o maximum power p o i n t must not exceed 150 ms. Slower response w i l l a f f e c t the o p e r a t i o n of the pumping system c o n n e c t e d t o i t . 3. The open c i r c u i t v o l t a g e and s h o r t c i r c u i t c u r r e n t must be a d j u s t a b l e . 4. The s i m u l a t o r must be c a p a b l e of d r i v i n g an e x p e r i m e n t a l s o l a r pumping system l o a d as w e l l as R and R-L l o a d s . 5. The o u t p u t I/V c u r v e s h o u l d be c a p a b l e of smooth adjustment between d i f f e r e n t i n s o l a t i o n c o n d i t i o n s . To meet the r e q u i r e m e n t s l i s t e d above, v a r i o u s d e s i g n f e a t u r e s had t o be c o n s i d e r e d . These a r e d e s c r i b e d below. 2.1.1 SAMPLE CURVE GENERATION Sample c u r v e g e n e r a t i o n i s i m p o r t a n t t o the o v e r a l l performance of the s i m u l a t o r because the o u t p u t of the s i m u l a t o r i s c o n t r o l l e d t o f o l l o w the sample c u r v e . In r e f e r e n c e [ 7 ] , p h y s i c a l s i m u l a t i o n i s used. The sample c u r v e i s based on t h e e q u i v a l e n t c i r c u i t shown i n f i g u r e 2-1. T h i s 9 10 e q u i v a l e n t c i r c u i t i s implemented u s i n g t h e analogue c i r c u i t i l l u s t r a t e d i n f i g u r e 2-2. By v a r y i n g the base b i a s of Q1, one can change the v a l u e of the c u r r e n t s o u r c e so t h a t the v a r i a t i o n of l i g h t i n t e n s i t y i s s i m u l a t e d . Rs and Rp can be a d j u s t e d e a s i l y t o s i m u l a t e PV a r r a y s w i t h d i f f e r e n t v a l u e s of Rs and Rp. Is F i g u r e 2-1. S o l a r C e l l E q u i v a l e n t C i r c u i t + 1 5 v F i g u r e 2-2. One Way t o Generate Sample Curves However, the i n f l u e n c e of temperature i s not s i m u l a t e d 11 p r o p e r l y i n t h i s scheme. R e f e r e n c e [6] uses formulae based on t h e o r e t i c a l a n a l y s e s t o produce sample c u r v e s . Once the l i g h t i n t e n s i t y , t e m p e r a t u r e and s p e c i f i c a r r a y type are g i v e n , t h e fo r m u l a e can reproduce the I/V c u r v e w i t h s a t i s f a c t o r y p r e c i s i o n . Moreover, t o s i m u l a t e d i f f e r e n t t y p e s of PV a r r a y , one o n l y need a d j u s t c e r t a i n c o n s t a n t s a c c o r d i n g l y . T h i s method can reproduce a r e p e a t a b l e sample c u r v e q u i t e w e l l . However, both methods mentioned above are u n s u i t a b l e f o r the type I s i m u l a t o r because n e i t h e r can s i m u l a t e the i n f l u e n c e of the environment e a s i l y . As mentioned i n Chapter 1, the p i l o t p a n e l method has been chosen t o form the sample c u r v e s f o r the type I s i m u l a t o r . Because the sample i s t a k e n from the PV p a n e l , which i s a reduced v e r s i o n of the PV a r r a y , t h i s method produces sample c u r v e s c l o s e r t o the r e a l a r r a y c u r v e s than the p r e v i o u s l y r e p o r t e d methods [ 6 , 7 , 9 ] . More i m p o r t a n t l y , the sample c u r v e i s a f f e c t e d by the environment i n the same manner as the cu r v e from a r e a l a r r a y might be. 2.1.2 CONTROL LOOPS A l t h o u g h d i g i t a l c i r c u i t r y can be used, i t i s more c o n v e n i e n t t o use analogue c i r c u i t r y t o form the c o n t r o l l o o p s because the sample c u r v e s g e n e r a t e d w i t h the p i l o t p a n e l method a r e analogue s i g n a l s . A v o l t a g e l o o p and a c u r r e n t l o o p a r e c o n s i d e r e d i n the d e s i g n of type I s i m u l a t o r . The v o l t a g e l o o p keeps the ou t p u t v o l t a g e p r o p o r t i o n a l t o t h a t of the p i l o t p a n e l and the c u r r e n t l o o p 1 2 keeps the c u r r e n t of t h e p i l o t p a n e l f o l l o w i n g t h e l o a d c u r r e n t . P r o p o r t i o n a l - i n t e g r a t i o n a l ( P I ) compensators a r e used i n both c o n t r o l l o o p s . W ith PI compensators, z e r o s t e a d y s t a t e e r r o r can t h e o r e t i c a l l y be a c h i e v e d . The parameters can be a d j u s t e d t o a c h i e v e s a t i s f a c t o r y dynamic b e h a v i o u r . Because t h e sample c u r v e s a r e n o n - l i n e a r and the l o a d parameters may f a l l w i t h i n a wide range of v a l u e s , s t a b i l i t y may be a problem. To i n v e s t i g a t e such p r o b l e m s , a computer program has been d e v e l o p e d t o a s s e s s the s t a b i l i t y f o r a p a r t i c u l a r l o a d c o n d i t i o n . D e t a i l s of the s t a b i l i t y a n a l y s i s a r e d e s c r i b e d i n s e c t i o n 2.3. The a l g o r i t h m of the program i s g i v e n i n Appendix A. The complete program l i s t i n g i s g i v e n i n Appendix B. 2.1.3 POWER CONVERTER The power c o n v e r t e r used here i s a one quadrant power t r a n s i s t o r chopper o p e r a t i n g a t 25 KHz. T h i s i s based on the c o n s i d e r a t i o n of g e t t i n g f a s t response w i t h o u t s u b s t a n t i a l l y i n c r e a s i n g the s w i t c h i n g l o s s e s . The c i r c u i t d i a g r a m of the chopper i s shown i n F i g u r e 2-3. The power t r a n s i s t o r i n F i g u r e 2-3 works as a power s w i t c h c o n t r o l l e d by the base v o l t a g e . I f the base v o l t a g e i s p o s i t i v e 5 v o l t s , t h e s w i t c h i s on; i f the base v o l t a g e i s n e g a t i v e 5 v o l t s , the s w i t c h i s o f f . By c o n t r o l l i n g the l e n g t h s of the on p e r i o d and o f f p e r i o d , the o u t p u t average v o l t a g e of the chopper can be a d j u s t e d . F i g u r e 2-4 shows the base d r i v e s i g n a l and the waveform of the c o r r e s p o n d i n g 13 o u t p u t v o l t a g e of the chopper. 4- o-I>-C. SUPPLY -HO— C E + V, Vk +5' 500MF zv7 P a LOAD — o-F i g u r e 2-3. C i r c u i t Diagram of the Chopper The d o t t e d l i n e s i n F i g u r e 2-4 r e p r e s e n t t h e - a v e r a g e chopper o u t p u t v o l t a g e of each c y c l e . The average o u t p u t v o l t a g e of the chopper i s g i v e n by the f o l l o w i n g r e l a t i o n : Vch=(d.c. source voltage)•§ where, 6 i s the duty r a t i o of the chopper. A l t e r n a t i v e l y , an ac t o dc c o n v e r t e r can be used where a dc s o u r c e i s u n a v a i l a b l e . However, the o p e r a t i n g f r e q u e n c y would be l i m i t e d by the ac source f r e q u e n c y . T h i s may r e s u l t i n a l a r g e r f i l t e r time c o n s t a n t and s l o w e r dynamic r e s p o n s e . A r e s i s t o r , R 1 8 (see F i g u r e 2-6), a c t i n g as a c u r r e n t l i m i t e r i s i n s e r i e s w i t h the chopper o u t p u t so t h a t t h e r e i s no 1 4 danger of o v e r c u r r e n t when the s i m u l a t o r i s s h o r t c i r c u i t e d , •5 -5 base voltage • T A chopper output average value F i g u r e 2-4. Waveforms of Chopper Output and Base s i g n a l 2.2 DESIGN AND TEST OF TYPE I SIMULATOR The type I s i m u l a t o r i s shown s c h e m a t i c a l l y i n the b l o c k diagram of F i g u r e 2-5, i t s e r v e s t o d u p l i c a t e the I/V c h a r a c t e r i s t i c s of a PV p a n e l , but a t a h i g h e r power r a t i n g . I t i s i n t e n d e d t o be used i n a p p l i c a t i o n s where a s i n g l e c o mmercial p a n e l i s a v a i l a b l e , and where i t i s r e q u i r e d t o s i m u l a t e a l a r g e a r r a y of t h e s e p a n e l s . The p a n e l used i n the t e s t s d e s c r i b e d here i s an ARCO G100. I t i s r a t e d a t 5 W (peak power), open c i r c u i t v o l t a g e 20.8 v o l t s and s h o r t 15 c i r c u i t c u r r e n t 435 mA. A t r a n s i s t o r i s conn e c t e d i n L I G H T ~ \ SOURCE DC. SUPPLY CONTROL P W M _ T L T L < U N I T DRIVER PV PANEL LOAD F i g u r e 2-5. Schematic Diagram of the Type I S i m u l a t o r p a r a l l e l (c-e) w i t h the p i l o t p a n e l , as shown i n the c i r c u i t d iagram of F i g u r e 2-6. By c o n t r o l l i n g the base b i a s of the t r a n s i s t o r , the p a n e l c u r r e n t can be v a r i e d from n e a r l y z e r o ( l i m i t e d by I c e o ) , t o n e a r l y s h o r t c i r c u i t c u r r e n t ( l i m i t e d by e m i t t e r r e s i s t o r and s a t u r a t i o n v o l t a g e of the t r a n s i s t o r ) . The v o l t a g e o f - t h e p a n e l w i l l v a r y a c c o r d i n g l y . Thus the sample c u r v e i s o b t a i n e d . The v o l t a g e of the p i l o t p a n e l i s used as a r e f e r e n c e i n p u t f o r the v o l t a g e l o o p . In a d d i t i o n t o the v o l t a g e l o o p t h e r e i s a c u r r e n t l o o p , each w i t h a PI compensator. The l o a d c u r r e n t i s sensed by a H a l l e f f e c t sensor and t h e c u r r e n t s i g n a l goes t h r o u g h a 'T' f i l t e r and o p e r a t i o n a l a m p l i f i e r A l b e f o r e i t i s sent t o the PI compensator. The purpose of the f i l t e r i s t o o b t a i n a r e l a t i v e l y ' r i p p l e f r e e ' c u r r e n t feedback s i g n a l . PILOT PANEL 1560K 1 R10 5 A. Rb 4.7 K 10 Rgh K l R11 2 VOLTAGE ISOLATOR C7_ 150P 2 l Q R C6 Hfl-10uf 100A R14 27K R20 R15 2K | ^200K C10 -4V 10:1 VOLTAGE ISOLATOR 1ft f RT7 10K R_4 2 2 47K C2~ 4.7K R6 4.7 K 0.47uf 4.7K C3 R6 = 2 0.4 7^f PULSE WIDTH MODULATION J L RJ_ 2 -CD-2.2 K RJ_ 2 R2l 10K 2.2K =3 50Aif DRIVER _TL CURRENT SENSOR 115 V D.C. CHOPPER 1.4K LOAD F i g u r e 2-6 . C i r c u i t Diagram of the Type I S i m u l a t o r 17 T h i s i s i m p o r t a n t t o the c u r r e n t l o o p . The o p e r a t i o n a l a m p l i f i e r A1 i s used t o a d j u s t t h e s h o r t c i r c u i t c u r r e n t of the s i m u l a t o r . The s h o r t c i r c u i t c u r r e n t can be a d j u s t e d t o as h i g h as the power c o n v e r t e r can t o l e r a t e by s i m p l y v a r y i n g p o t e n t i o m e t e r R3. The PI compensator i n c l u d e s op amps, A2 and A3, t r a n s i s t o r T, and some c a p a c i t o r s and r e s i s t o r s . F i g u r e 2-7 shows a t r a n s f e r f u n c t i o n b l o c k d i a g r a m of the c u r r e n t l o o p , where: Is • t K , TjS+1 ( K 3 h 2 i / T 3 R b ) ( T 3 S + l ) S(T2S+1) K 8 R 1 0 T8S+1 F i g u r e 2-7. C u r r e n t Loop T r a n s f e r F u n c t i o n B l o c k Diagram T,=R,C,/4 (2-1) T 2=R„C 2/4 (2-2) T 3=R BC 5 (2-3) T 8=R 1 1C 7/4 (2-4) K!=R T / R 3 (2-5) K 3=R 8/R f l (2-6) K 8 = R 1 2 / R 1 1 (2-7) 18 a i s the c o n v e r s i o n r a t i o of the c u r r e n t s e n s o r and h 2 1 i s a h y b r i d parameter of the t r a n s i s t o r T. F i g u r e 2-8 shows how the p i l o t p a n e l i s a d j u s t e d by the shunt t r a n s i s t o r T. The v o l t a g e and c u r r e n t i n F i g u r e 2-8 ar e i n per u n i t v a l u e s . The c u r r e n t base and the v o l t a g e base a r e the s h o r t c i r c u i t c u r r e n t and the open c i r c u i t v o l t a g e r e s p e c t i v e l y . 0 0-5 1.0 VOLTAGE (PU) F i g u r e 2-8. Load L i n e of the T r a n s i s t o r T When the output v o l t a g e of A2 changes, the base c u r r e n t of T w i l l change, and thus the o p e r a t i n g p o i n t w i l l move a l o n g the p i l o t p a n e l c h a r a c t e r i s t i c c u r v e , p r o d u c i n g a r e f e r e n c e i n p u t f o r the v o l t a g e c o n t r o l l o o p . Assuming a change i n the l o a d c u r r e n t , t h e r e w i l l be a d i f f e r e n c e between the r e f e r e n c e i n p u t and feedback c u r r e n t s i g n a l s . The PI compensator then r e g u l a t e s the p i l o t p a n e l c u r r e n t u n t i l the 19 r e f e r e n c e i n p u t and feedback c u r r e n t a r e e q u a l ( r e a c h i n g s t e a d y s t a t e ) . The f o l l o w i n g formulae a r e used t o de t e r m i n e the c u r r e n t l o o p p arameters: R b = 1 2 - h 2 i / I p s c (2-8) R i 2 / R 1 i = 1 0 / ( I p s e • R 1 0 ) (2-9) I s s c = l O - R , / ( R 3 a ) (2-10) where Ipse i s the s h o r t c i r c u i t c u r r e n t of the p i l o t p a n e l , I s s c i s the s h o r t c i r c u i t c u r r e n t of the s i m u l a t o r . F i g u r e 2-9 i s the t r a n s f e r f u n c t i o n b l o c k diagram of the v o l t a g e l o o p , where: T « = R 1 6 C 8 (2-11) T 5 = R 2 , R l f l C 6 / ( R 2 1 + R i a ) * R 2,C 6 (2-12) T 7 = R ! 5 R 2 0 C , 0 / ( R i 5 + R 2 0 ) (2-13) Vp K 5 T5S+I -(g)-[ K C / ( R 1 8 + R L ) T A ] ( T 4 S + 1 ) S ( T C S + 1 ) ( T L | S+l) pK 7RL ( T4S+l) T7S+I F i g u r e 2-9. V o l t a g e Loop T r a n s f e r F u n c t i o n B l o c k Diagram K 5 1 6 / ( ^ 2 1 + R 1 « ) K 7 = ^ 1 6 / ( R 1 S + ^ 2 0 ) Kc=(dc s o u r c e v o l t a g e ) / l 0 (2-(2-( 2 -14) 15) 16) 20 (2-17) T L 1=L/(R L+R, 8) (2-18) Tc i s the chopper p e r i o d . R and L a r e t h e l o a d r e s i s t a n c e and i n d u c t a n c e r e s p e c t i v e l y (assuming R-L l o a d ) . Kc i s t h e chopper v o l t a g e g a i n parameter. The i n p u t t o the v o l t a g e l o o p i s the p i l o t p a n e l v o l t a g e , which i s compared w i t h the feedback v o l t a g e from the s i m u l a t o r o u t p u t , f o r m i n g the e r r o r s i g n a l . The PI compensator r e g u l a t e s the o u t p u t of A4 (Vc) a c c o r d i n g t o the e r r o r s i g n a l . The chopper o u t p u t v o l t a g e Vch i s r e l a t e d t o t h i s by the f o l l o w i n g form: Vch=Kc-Vc (2-19) By a d j u s t i n g R 1 S , the s i m u l a t o r open c i r c u i t v o l t a g e can be s e t : Vsoc=0.1-Vpoc(R, S+R 2 0) / (R,«+R 2 i )0 (2-20) where Vsoc i s s i m u l a t o r open c i r c u i t v o l t a g e , Vpoc i s the p i l o t p a n e l open c i r c u i t v o l t a g e and j3 i s the c o n v e r s i o n r a t i o of the v o l t a g e s e n s o r . W i t h i n the whole v o l t a g e range the chopper s h o u l d not s a t u r a t e . To meet t h i s c o n d i t i o n , I s s c , V s o c , R 1 B and the source v o l t a g e must be chosen p r o p e r l y . F i g u r e 2-10 shows how the I/V c u r v e i s a c h i e v e d at the s i m u l a t o r output t e r m i n a l s (assuming a r e s i s t i v e l o a d f o r s i m p l i c i t y ) . In F i g u r e 2-10, suppose the l o a d c h a r a c t e r i s t i c changes from L1 t o L2. The chopper o u t p u t v o l t a g e w i l l change from Vsm1 t o Vsm2, the o p e r a t i n g p o i n t w i l l move from A t o B. Thus the ou t p u t f o l l o w s the p i l o t p a n e l . On the o t h e r hand, i f the chopper v o l t a g e s a t u r a t e s b e f o r e r e a c h i n g Vsm2, the o p e r a t i n g p o i n t w i l l move t o C 21 i n s t e a d of B. C o n s e q u e n t l y , s u b s t a n t i a l d i s t o r t i o n o c c u r s . To a v o i d t h i s problem, I s s c and Vsoc must be l i m i t e d so t h a t the e n t i r e s i m u l a t o r I/V c u r v e (under the h i g h e s t i l l u m i n a t i o n l e v e l ) Is \ \ / / X V / / ^ \ \ \ \ \ \ \ 0 Vsm, V s m Vs F i g u r e 2-10. Output C h a r a c t e r i s t i c w i t h V a r y i n g Load i s i n s i d e the t r i a n g l e formed by the two axes and l i n e P 2 ( F i g u r e 10, assuming Vsm 2 i s the h i g h e s t chopper o u t p u t v o l t a g e ) . F i g u r e 2-11 shows the r e s u l t s of a s a t u r a t e d chopper caused by mismatched parameters (Vsoc t o o h i g h ) . D u r i n g t h e t e s t of the s i m u l a t o r w i t h R-L l o a d , an a d j u s t a b l e l i g h t s ource i s used t o o b t a i n d i f f e r e n t l i g h t i n t e n s i t y c o n d i t i o n s . The o u t p u t c u r r e n t i s a d j u s t e d by v a r y i n g t h e l o a d r e s i s t o r . When the s i m u l a t o r i s s h o r t 22 c i r c u i t e d , the s h o r t c i r c u i t c u r r e n t of the s i m u l a t o r i s a d j u s t e d t o 10 amperes. The open c i r c u i t v o l t a g e of the s i m u l a t o r i s a d j u s t e d t o 50 v o l t s . T h i s s e t t i n g VOLTAGE (PU) F i g u r e 2-11. S i m u l a t o r Output w i t h Mismatched Parameters i s chosen a r b i t r a r i l y t o t e s t the s t e a d y s t a t e e r r o r of the system. As the s h o r t c i r c u i t c u r r e n t and open c i r c u i t v o l t a g e can be a d j u s t e d w i t h i n a c e r t a i n range, once the a c t u a l s h o r t c i r c u i t c u r r e n t ( I s c ) and open c i r c u i t v o l t a g e (Voc) a r e g i v e n , the s h o r t c i r c u i t c u r r e n t and the open c i r c u i t v o l t a g e of the s i m u l a t o r can be s e t t o I s c and Voc r e s p e c t i v e l y . The s i m u l a t o r output v o l t a g e and c u r r e n t a r e m o n i t o r e d by an o s c i l l o s c o p e ( i n x-y mode) and r e c o r d e d by an x-y p l o t t e r . The I/V c h a r a c t e r i s t i c s of the s i m u l a t o r and 23 the p i l o t p a n e l a r e r e c o r d e d from the x-y p l o t t e r and a r e shown i n f i g u r e 2-12. PER UNIT VOLTAGE 0.2 0.4 0.6 0.8 1.0 F i g u r e 2-12. E x p e r i m e n t a l Output of C o r r e c t l y A d j u s t e d S i m u l a t o r A l l v a l u e s a r e p e r - u n i t , f o r easy com p a r i s o n . The d i f f e r e n c e between the s i m u l a t o r I/V c u r v e s and the p i l o t p a n e l I/V c u r v e s i s w i t h i n 1%. As t h e r e a re d i f f e r e n c e s between'the p i l o t p a n e l I/V c u r v e s and the a r r a y I/V c u r v e s ( r e f e r t o Chapter 4 f o r d e t a i l s ) , the steady s t a t e e r r o r (compared w i t h the a r r a y ) i s l a r g e r than 1%. I t i s assumed t h a t the maximum d i f f e r e n c e between a p i l o t p a n e l I/V c u r v e and the c o r r e s p o n d i n g a r r a y I/V cur v e i s not more than 4%. D i f f e r e n t 24 r e s i s t i v e l o a d , R-L l o a d s and motor l o a d s have been c o n n e c t e d t o the s i m u l a t o r and no s t a b i l i t y problems ( o s c i l l a t i o n s ) were o b s e r v e d . 2.3 STABILITY ANALYSIS WITH R-L LOADS T h i s s e c t i o n p r e s e n t s a s t a b i l i t y a n a l y s i s f o r the type I s i m u l a t o r w i t h R-L l o a d s . The r e s u l t s of t h i s a n a l y s i s p r o v i d e g uidance f o r t h e d e t e r m i n a t i o n of c i r c u i t p a r a m e t e r s t o a s s u r e the s t a b i l i t y of the whole system. The t r a n s f e r f u n c t i o n b l o c k diagram of the whole system can be o b t a i n e d by combining the c u r r e n t and v o l t a g e l o o p t r a n s f e r f u n c t i o n b l o c k diagrams ( F i g . 2-7 and 2-9) as shown i n F i g u r e 2-13. N,S*+N,S 3+N,S 2+N.S+N„ 4 3 2 1 0 D9s'*DBS8+D7S7+D6S6+D5S5+D4S4*D3S3+D2S2+OJS+D0 F i g u r e 2-13. Model of the Whole System In F i g u r e 2-13, N 0 = a K 1 K 5 P , P 3 (2-21) N 1 = N 0 ( T 3 T ( l T 7 T 8 ) (2-22) N 2=N 0 (T3T«+T 7.T 8+T 3T 7+T3T B+T,T 7+T aT 8) (2-23) 25 N 3 = N O [ T 3 T , ( T 7 + T 8 ) + T 7 T B ( T 3 + T , ) ] (2-24) N,=N 0T 3T,T 7T 8 (2-25) D 0=C 0F 0 * (2-26) D ^ C o F ^ C F o (2-27) D 2 = C 0 F 2 + C 1 F 1 + C 2 F 0 (2-28) D 3=CoF 3+C lF 2+C 2F 1+C 3Fo (2-29) D^CoFfl+CFa+CzFz+CsF^CaFo D 5=C 0F 5+C 1F ( t+C 2F 3+C 3F 2+C f tF l D 6=C 1F 5+C 2F,,+C 3F 3+C<,F 2 (2-32) D 7=C 2F 5+C 3F l l+C l tF3 (2-33) D 8=C 3F 5+C,F ( ( (2-34) D 9 = C « F 5 (2-35) C 0 = P3P<. (2-36) C 1 = P 3 P « T « + P 3 P ( 1 T L + 1 (2-37) C 2 = P 3 P « T 1 1 T L + T c + T L 1 + T 7 (2-38) C 3=T T T +T 7 (2-39) C « = T c T L 1 T 7 (2-40) P,=K 3h 2,/T 3Rb (2-41) P 2 = l 0 / I p s c c (2-42) P 3 = K c / T „ • ( R L + R , 8 ) (2-43) P«=K 7R L/3 (2-44) F 0=b 0 (2-45) F ^ a t b o + b, (2-46) F 2=a 2b 0+a,b,+b 2 (2-47) F 3=a 2b 1+a,b 2+b 3 (2-48) F „ = a 2 b 2 + a , b 3 (2-49) F 5 = a 2 b 3 (2-50) 26 a , = T , + T 5 ( 2 -51 ) a 2 = T 1 T 5 ( 2 -52 ) b 0 = P , P 2 ( 2 - 5 3 ) b ^ l + P ^ a T j ( 2 - 5 4 ) b 2 = T 2 + T 8 ( 2 - 5 5 ) b 3 = T 2 T ( 2 - 5 6 ) F r o m F i g u r e 2-11 we c a n w r i t e t h e d i f f e r e n t i a l e q u a t i o n f o r t h e l i n e a r p a r t o f t h e s i m u l a t o r a s b e l o w : D 9 i ( 9 ) + D B i ( 8 ) + • • • + D 0 i = N „ v ( •>+ - - - D o V ( 2 - 5 7 ) P P P P P I f a c e r t a i n l o a d i s g i v e n , s ay R 0 a n d L 0 , t h i s l o a d w i l l c o r r e s p o n d t o one o p e r a t i n g p o i n t on t h e c h a r a c t e r i s t i c I / V c u r v e o f t h e p i l o t p a n e l . L e t us d e n o t e t h i s o p e r a t i n g p o i n t a s I 0 a n d V 0 a n d d e f i n e new v a r i a b l e s : T p = i p - I o ( 2 - 5 8 ) v =v - V 0 ( 2 - 5 9 ) P P S u b s t i t u t i o n o f e q s . ( 2 - 5 8 , 2 - 5 9 ) i n t o e q . ( 2 - 5 7 ) l e a d s t o : D 9 T p < 9 , + D 8 T p « 8 ' + + D 0 T p + D 0 I 0 = N f t v p " " + . . . + N 0 v p + N 0 V 0 ( 2 - 6 0 ) S i n c e ( l 0 r v o ) i s an o p e r a t i n g p o i n t on t h e c u r v e , we h a v e : D 0 I 0 = N 0 V 0 ( 2 - 6 1 ) T h u s , e q . ( 2 - 6 0 ) b e c o m e s : D 9 T ( 9 , + . . . + D 0 T = N , v l 0 ) + • • • +N 0 v ( 2 - 6 2 ) P P P P I t s h o u l d be n o t e d t h a t a l l t h e c o e f f i c i e n t s D 0 - - D 9 , N o ~ ~ N « a r e f u n c t i o n s o f l o a d r e s i s t a n c e a n d i n d u c t a n c e . F o r a g i v e n l o a d ( R 0 , L 0 ) , t h e s y s t e m m o d e l c a n be r e p r e s e n t e d a s 2 7 i n F i g u r e 2 - 1 4 . > 1 VP N.S*+N,S3+N,S2+N,S+Nn 4 3 2 1 0 r D9S9+D8S8+D7S7+D6S6+DjS5+D4S*+D3S3+D2S2'H),S+D0 F i g u r e 2 - 1 4 . M o d i f i e d Model of the Whole System Note that i n F i g u r e 2 - 1 4 , the o r i g i n of the n o n - l i n e a r element has been moved to ( I 0 » V 0 ) and the i feedback i s P n e g a t i v e . The v o l t a g e and c u r r e n t v a r i a b l e s v and T P P represent d e v i a t i o n s from the e q u i l i b r i u m v a l u e s V 0 and I 0 . Let the l i n e a r open loop frequency response be: A+jB G(ju)= ( 2 - 6 3 ) C + ] D where, A = N „ C J ' , - N 2 £ J 2 + N 0 ( 2 - 6 4 ) B = N , O > - N 3 < J 3 ( 2 - 6 5 ) C = D B C J B - D 6 O > 6 + D J i a ) A - D 2 w 2 + D 0 ( 2 - 6 6 ) D = D 9 C J 9 - D 7 £ J 7 + D 5 us-D3u>3+D^u ( 2 - 6 7 ) 28 AC+BD Re[G(j w ) ] = C 2+D 2 (2-68) BC-AD Im[G(jw)3= C 2+D 2 (2-69) Assuming the i l l u m i n a t i o n and temperature l e v e l do not change s u d d e n l y , which i s the case i n p r a c t i c e , s t a b i l i t y of the system r e p r e s e n t e d by the m o d i f i e d model of F i g u r e 2-14 can be c o n s i d e r e d u s i n g the method of Popov f o r a s i n g l e n o n - l i n e a r element. A c c o r d i n g t o Popov's c r i t e r i o n , t h e system i s A s y m p t o t i c a l S t a b l e In the Large i f t h e r e e x i s t s a s c a l a r q such t h a t l/k+Re[ (1+jaxj)G( jw) ]>0 (2-70) f o r a l l co. In our c a s e , w h i c h i s the s l o p e of the c o n s t r a i n t l i n e , as shown i n F i g u r e 2-15. For the system t o be ASIL w i t h a p a r t i c u l a r l o a d , t he PV a r r a y c h a r a c t e r i s t i c must be c o n f i n e d t o the V o-0 (2-71 ) k = I 0 - I p s c 29 s e c t o r bounded by the c o n s t r a i n t l i n e . c o n s t r a i n t 1 i n e V P - 1 P PV ARRAY V P / 0 - 1 p F i g u r e 2-15. The E q u i v a l e n t N o n - l i n e a r Element The w o r s t s i t u a t i o n i s when the s i m u l a t o r i s s h o r t c i r c u i t e d , t h a t i s , I 0 = I p s c , V o=0. In t h i s s i t u a t i o n , the c o n s t r a i n t l i n e has the h i g h e s t s l o p e k. Based on Eqs.(2-20 t o 2-71), a computer program was w r i t t e n t o a s s e s s the s t a b i l i t y of the system under d i f f e r e n t l o a d c o n d i t i o n s . An summary of the program i s g i v e n i n appendix A. The complete program i s g i v e n i n Appendix B. The program c a l c u l a t e s the e i g e n v a l u e s of the l i n e a r t r a n s f e r f u n c t i o n , and d a t a f o r N y q u i s t p l o t s as w e l l as f o r t h e m o d i f i e d N y q u i s t p l o t s used t o t e s t the s t a b i l i t y c r i t e r i o n g r a p h i c a l l y . D i f f e r e n t v a l u e s of R L and L were t e s t e d on the computer. By examining the open l o o p e i g e n v a l u e s and the m o d i f i e d N y q u i s t p l o t , we can e s t a b l i s h s t a b i l i t y f o r a c e r t a i n l o a d c o n d i t i o n by Popov's c r i t e r i o n . A f t e r a s e r i e s of t e s t s on R and R-L l o a d ( the v a l u e s of R and L a r e v a r i e d ) , i t was found t h a t : 30 ( a ) . t y p i c a l N y q u i s t p l o t s resemble the one shown i n F i g u r e 2-16. S i n c e the N y q u i s t p l o t s were found t o be convex, the m o d i f i e d p l o t s a r e not needed. • F i g u r e 2-16. T y p i c a l N y q u i s t P l o t of the S i m u l a t o r The c r i t i c a l p o i n t Pc moves f u r t h e r away from the o r i g i n as R d e c r e a s e s . A c c o r d i n g t o Popov's c r i t e r i o n , t h e s t a b l e v a l u e of k d e c r e a s e s a c c o r d i n g l y . When the c r i t i c a l p o i n t g e t s too f a r away from the o r i g i n the system becomes u n s t a b l e . In p r a c t i c e , h o w e v e r , by a d j u s t i n g the system parameters p r o p e r l y , t h e c r i t i c a l p o i n t can be moved a r b i t r a r i l y c l o s e t o t he o r i g i n . Thus the system i s s t a b l e f o r a l l R-L l o a d c o n d i t i o n s . ( b ) . F o r a f i x e d r e s i s t a n c e and v a r y i n g i n d u c t a n c e , t h e r e i s a v a l u e of i n d u c t a n c e t h a t g i v e s the s m a l l e s t s t a b l e s e c t o r . T h i s can be seen from F i g u r e 2-17. The c r i t i c a l v a l u e of k 31 d e c r e a s e s as l o a d r e s i s t a n c e d e c r e a s e s . o — o 0) 3 (0 > o o — RL = 0. 1 OHM m — eg -o - i — i i 11uni— i i 1 1 1 1 i n — i i i | i n i | — i i 11 1 ' 1 11 — i i 1 1 l i m 10-* 3 5 lO"5 3 5 10" 3 5 10"1 3 5 10"1 3 5 10'' ' 1 ' I'"'I 3 5 10° LOAD INDUCTANCE (Henry) F i g u r e 2-17. S t a b l e V a l u e of k w i t h Respect t o R L f L The h i g h e s t s l o p e of the c o n s t r a i n t l i n e must not exceed the lo w e s t v a l u e of k i n F i g u r e 2-17, which i s about 50. ( c ) . The f i l t e r time c o n s t a n t s T,,T 5 and T 7 p l a y an i m p o r t a n t r o l e i n s t a b i l i t y of the whole system. T 5 and T 7 s h o u l d be a t l e a s t a few tim e s s m a l l e r than T, i n o r d e r t o keep the system s t a b l e over the f u l l v o l t a g e or c u r r e n t range. F u r t h e r m o r e , i n o r d e r t o o b t a i n q u i c k dynamic r e s p o n s e , T,, T 5 and T 7 s h o u l d be r e a s o n a b l y s m a l l (T, i s 55 ms i n the type I s i m u l a t o r ) . U n f o r t u n a t e l y , t h e i r lower bounds a r e l i m i t e d by the system n o i s e or chopper f r e q u e n c y , w h i c h e v e r i s l o w e r . The chopper o u t p u t i s m o d e l l e d by an i d e a l v o l t a g e s o u r c e w i t h a v a l u e e q u a l t o the average o u t p u t v a l u e . S i n c e i t i s i n f a c t composed of a t r a i n of 32 p u l s e s , t h e model i s v a l i d o n l y when the o u t p u t f i l t e r has a c o r n e r f r e q u e n c y s u b s t a n t i a l l y lower than the chopper or n o i s e f r e q u e n c y so t h a t the o u t p u t v o l t a g e r i p p l e i s s m a l l . T h i s means t h a t T 5 and T 7 must be s u b s t a n t i a l l y l a r g e r than t h e chopper p e r i o d , T , which i s 40 us. A s t e p change of l o a d from n o - l o a d t o maximum power p o i n t and back t o n o - l o a d was a p p l i e d t o the system. The response of the type I s i m u l a t o r (R-L l o a d ) i s shown i n F i g u r e 2-18. •0.4 a i 0 oi 1.2 ftJ t csec.) F i g u r e 2-18. Type I S i m u l a t o r Response t o S t e p Change The f a l l and r i s e time i s 50 ms and 38 ms r e s p e c t i v e l y . The speed of response i s f a s t enough t o meet the requirement of 150 ms. 33 2.4 APPLICATION TO A PUMPING SYSTEM The type I s i m u l a t o r has been connected t o an e x p e r i m e n t a l s o l a r pumping system. An i m p o r t a n t r e q u i r e m e n t of t h i s pumping system i s t o keep the system o p e r a t i n g a t the maximum power p o i n t of the p h o t o v o l t a i c a r r a y so t h a t maximum power i s e x t r a c t e d from the g i v e n a r r a y w i t h c h a n g i n g i l l u m i n a t i o n l e v e l and t e m p e r a t u r e . A s c h e m a t i c diagram of the pumping system i s shown i n F i g u r e 2-19. PV ARRAY REGULATOR 3> MOTOR F i g u r e 2-19. Schematic Diagram of the Pumping System The dc motor d r i v e s a pump which can be c o n s i d e r e d as a c o n s t a n t t o r q u e l o a d . As i l l u m i n a t i o n l e v e l and te m p e r a t u r e v a r y d u r i n g the day, so does the a r r a y I/V c h a r a c t e r i s t i c c u r v e . That i s , the motor has a c o n s t a n t t o r q u e l o a d and a v a r y i n g power s o u r c e . The purpose of the r e g u l a t o r i n the pumping system i s t o match the motor t o the PV a r r a y such 34 t h a t the a r r a y operates at i t s peak power p o i n t r e g a r d l e s s of the d e v i a t i o n of the i l l u m i n a t i o n l e v e l and temperature, and the motor operates at constant c u r r e n t and v a r y i n g v o l t a g e or speed depending on the environmental c o n d i t i o n . To accomodate t h i s kind of load,the v o l t a g e loop d e s c r i b e d i n S e c t i o n 2.2 has to be m o d i f i e d . As f a r as the s i m u l a t o r i s concerned, the pumping system can be c o n s i d e r e d as the e q u i v a l e n t c i r c u i t shown in F i g u r e 2-20. F i g u r e 2-20. E q u i v a l e n t C i r c u i t of the Pumping System In f i g u r e 2-20, Em i s a v a r i a b l e v o l t a g e source r e p r e s e n t i n g the emf of the dc motor. During the operation,Em i s c o n t r o l l e d by the r e g u l a t o r in the pumping system. The t r a n s f e r f u n c t i o n block diagram of the m o d i f i e d v o l t a g e loop i s shown in Figure 2-21, where, T^C•R, Ta =Ce * R1 a T 5 ^ 2 i 'C 6 — C 35 « 5 Tsstl -CT4S+l)Kc Vc > K Ts t l F i g u r e 2 - 2 1 . Model of the M o d i f i e d V o l t a g e Loop K=R/(R+R 0) Ke=R 0/(R+R 0) K 5 = 1O/Vpoc K 7 = 1 0 / V S O C Other p a r a m e t e r s remain the same as those i n S e c t i o n 2 . 2 . The t r a n s f e r f u n c t i o n of th e m o d i f i e d v o l t a g e l o o p can be w r i t t e n as below: V g ( s ) B O + B T S V p ( s ) s 3 + A 2 s 2 + A 1 s + A 0 ( 2 - 7 2 ) V s ( s ) Q,s ( 2 - 7 3 ) Em(s) s 2+M,s+M 0 Where, 36 B 0=K-Kc-K 5/(T,T 5T) Bi=B 0Tn A 2 = (T f lT 5+T f lT+T«TsKK 7Kc)/ (T-T„T 5) A,=(T„ + T f lK•K 7Kc + T 5 K - K 7 K c ) / T«T,T 5 A 0=K-K 7Kc/T-T(,T 5 Q,=Ke/T M,=(1+K-Kc-K 7 ) / T M 0=(K-Kc-K 7)/T-T« The s t e p and ramp response of t h e v o l t a g e l o o p have been s i m u l a t e d on the computer ( u s i n g FORSIM) w i t h the parameters l i s t e d below: T=0.02 s e c . T„=5.6X10" 3 sec. T 5=10" 3 s e c . K=0.054 Ke=0.946 K 5 = 0. 5 K 7=0.5 Kc=11.5 The u n i t s t e p response i s shown i n F i g u r e 2-22, from which i t can be seen t h a t the s t e a d y s t a t e e r r o r i s z e r o . A ramp (Vp=t) response of the v o l t a g e l o o p i s g i v e n i n F i g u r e 2-23. There i s a steady s t a t e e r r o r w h i c h can be d e t e r m i n e d from the t r a n s f e r f u n c t i o n b l o c k d i a g r a m of F i g u r e 2-21: 37 RUN 2 PLOT 1 to > 1 .100 0.880 0.660 0.440 0.220 0 000 A = VPIVI V s i i « 1 —1 lUUUi. aOOOflD 1QQOOO£ A A A A A A A A A A A A ? A l . 100 A l .060 A l .020 AO.980 > AO.940 AO.900 0.000 0.625 1.250 1.875 2.500 3.125 3.750 4.375 5.000 TIME ( SEC.) F i g u r e 2-22. Step Response of t h e V o l t a g e Loop s(Ts+1) E ( s ) =  V p ( s ) S(TS+1)+K (T4S+I) (2-74) where, KK 7Kc v — (2-75) 38 RUN 2 PLOT 1 > 5.000 4.000 3.000 2.000 I .000 0.000 A = VP!VI 5.000 A4.000 A3.000 A2.000 A l .000 AO.000 OniOCJ 0.625 1 .250 1 .875 27500 3.125 3.750 4.375 5.000 TIME ( S E C . ) F i g u r e 2-23. Ramp response of the V o l t a g e Loop For a ramp i n p u t of v (t)=K t , p a V p ( s ) = K a / s 2 The s t e a d y s t a t e e r r o r : S(T S+1) Ka Ka e(=°) = l i m s• • — = — s-O s(Ts+1)+K T(T,s+1) s 2 K T (2-76) From eqs. (2-75)&(2-76) i t can be seen t h a t the s t e a d y s t a t e e r r o r w i t h ramp i n p u t i s p r o p o r t i o n a l t o T,. Thus, T«, s h o u l d be r e a s o n a b l y s m a l l . In the f i n a l c i r c u i t , T, i s .0056 second. When K =1 v o l t / s e c . e(»)=1/55.4 (V) 39 T h i s e r r o r i s s m a l l enough t o meet our r e q u i r e m e n t s . The e q u i v a l e n t l o a d l i n e of the pumping system i s shown i n F i g u r e 2-24. Em 3 Em2 Eir 1 0 F i g u r e 2-24. E q u i v a l e n t Load L i n e of the Pumping System From eq.(2-73) i t can be seen t h a t the s t e p response of the s i m u l a t o r o u t p u t v o l t a g e v w i t h r e s p e c t t o the emf of t h e s motor e„ w i l l s e t t l e down t o z e r o . That i s , when t h e r e i s a m ' s t e p change i n e m , the output of the s i m u l a t o r w i l l s e t t l e down t o the v a l u e d e t e r m i n e d by the r e f e r e n c e i n p u t v . The c u r r e n t l o o p remains the same as i n s e c t i o n 2.2. The s i m u l a t o r w i t h the pumping system as the l o a d was t e s t e d f i r s t w i t h a s i m u l a t e d l o a d s e t up as i l l u s t r a t e d i n 40 F i g u r e 2-25. F i g u r e 2-25. S i m u l a t e d Load f o r P r e l i m i n a r y T e s t D u r i n g the t e s t w i t h the s i m u l a t e d l o a d , t h e . v o l t a g e source i s a d j u s t e d so t h a t the l o a d v o l t a g e v a r i e s from z e r o t o V s o c . The v o l t a g e and the c u r r e n t of the s i m u l a t o r are m o n i t o r e d by an o s c i l l o s c o p e and r e c o r d e d by an x-y p l o t t e r . I t has been o b s e r v e d t h a t the s i m u l a t o r ' o u t p u t v o l t a g e and c u r r e n t f o l l o w t h e sample c l o s e l y w h i l e the v o l t a g e source i s b e i n g a d j u s t e d . S i n c e the p i l o t p a n e l i s not changed, the I/V c u r v e s r e c o r d e d by the p l o t t e r are the same as those i n F i g u r e 2-12. 3. TYPE I I SIMULATOR As mentioned i n the INTRODUCTION, i t i s d e s i r a b l e i n some e x p e r i m e n t s of PV a r r a y powered system t o have r e p e a t a b l e a r r a y c u r v e s . The type I I s i m u l a t o r p r o v i d e s f i x e d PV a r r a y c u r v e s under d i f f e r e n t i l l u m i n a t i o n l e v e l s and t e m p e r a t u r e s . The b a s i c r e q u i r e m e n t s of the type I I s i m u l a t o r a r e l i s t e d below: 1. The stea d y s t a t e e r r o r must be s m a l l e r than 5%. S i n c e the o p e r a t i n g p o i n t s of most l o a d s move a l o n g the a r r a y c u r v e d u r i n g o p e r a t i o n , f o r i n s t a n c e , when t r a c k i n g the maximum power p o i n t i n the pumping system, the PV a r r a y s i m u l a t o r s h o u l d have output I/V c h a r a c t e r i s t i c s as c l o s e t o tho s e of the r e a l a r r a y as p o s s i b l e . 2. The t r a n s i e n t s t a t e due t o a s t e p change of l o a d from open c i r c u i t t o maximum power p o i n t must not exceed 150 ms. L i k e any o t h e r dynamic system, the s i m u l a t o r has a t r a n s i e n t s t a t e when a l o a d d i s t u r b a n c e or any o t h e r system d i s t u r b a n c e o c c u r s . For example, i n a s o l a r pumping system, t h e r e i s a r e g u l a t o r t h a t keeps a d j u s t i n g the v o l t a g e and c u r r e n t of the PV a r r a y . I f the PV s i m u l a t o r has slow dynamic response, the experiment w i t h t h i s PV a r r a y s i m u l a t o r may l e a d t o i n c o r r e c t r e s u l t s . 3. The s h o r t c i r c u i t and open c i r c u i t v o l t a g e must be a d j u s t a b l e so t h a t the s i m u l a t o r can r e p r e s e n t a r r a y s of d i f f e r e n t I s c and Voc r a t i n g s . 41 42 The n e x t s e c t i o n d e s c r i b e s how these r e q u i r e m e n t s can be met. 3.1 DESIGN CONSIDERATIONS 3.1.1 SAMPLE CURVE GENERATION Among the p r e v i o u s l y - r e p o r t e d PV a r r a y s i m u l a t o r s , r e f e r e n c e [ 6 ] a c h i e v e s q u i t e p r e c i s e sample c u r v e s . However, the f o r m u l a c a l c u l a t i o n method used i n r e f e r e n c e [ 6 ] causes a l o n g e x e c u t i o n time and sampl i n g p e r i o d . As a r e s u l t , the dynamic r e s p o n s e i s not v e r y f a s t . A new method, which combines f o r m u l a c a l c u l a t i o n and da t a s t o r a g e , i s used i n the type I I s i m u l a t o r . I t i s a compromise between e x e c u t i o n time and memory s i z e . Suppose the I/V c h a r a c t e r i s t i c s of the PV a r r a y t o be s i m u l a t e d a r e g i v e n ( u s u a l l y PV a r r a y c h a r a c t e r i s t i c s a r e a v a i l a b l e from m a n u f a c t u r e r s ) . The I/V c h a r a c t e r i s t i c s can be s t o r e d i n the memory of a m i c r o p r o c e s s o r - b a s e d system. Once a c e r t a i n i l l u m i n a t i o n l e v e l and temperature a r e g i v e n , then f o r eve r y v a l u e of output c u r r e n t t h e r e i s a c o r r e s p o n d i n g v a l u e of v o l t a g e , which i s o b t a i n e d from the l o o k - u p t a b l e s t o r e d i n the memory. As the number of I/V c u r v e s i n c r e a s e s , t h e memory s i z e i n c r e a s e s l i n e a r l y . To save some memory space, a formu l a c a l c u l a t i o n method i s used f o r the low c u r r e n t h a l f of the I/V c u r v e . T h i s i s based on the f a c t t h a t when the a r r a y c u r r e n t i s lower than h a l f the s h o r t c i r c u i t c u r r e n t , the I/V c u r v e i s b a s i c a l l y a s t r a i g h t 43 l i n e as shown i n F i g u r e 3-1. 330 . D - i V0lTflG£ F i g u r e 3-1. One of the I/V c u r v e s t o Be S i m u l a t e d T h e r e f o r e , a s i m p l e s t r a i g h t l i n e f o r m u l a can r e p r e s e n t the lower h a l f of the a r r a y I/V c u r v e w i t h s u f f i c i e n t a c c u r a c y . In t h i s way, h a l f of the memory s i z e can be saved i n comparison t o the f u l l memory s t o r a g e method. A l s o , r e l a t i v e l y s h o r t e x e c u t i o n time (compared w i t h the f u l l f o r m u l a c a l c u l a t i o n method) i s a c h i e v e d , which l e a d s t o a h i g h e r s a m p l i n g r a t e and f a s t e r dynamic r e s p o n s e . In F i g u r e 3-1, the I/V c u r v e i s based on an ASI 16-2300 p a n e l made by ARCO SOLAR INC.. The I/V c u r v e g i v e n by the s p e c i f i c a t i o n i s measured and then p l o t t e d u s i n g the 44 c o m p u t i n g f a c i l i t y a v a i l a b l e . T h e I / V c u r v e i n F i g u r e 3 - 1 i s u s e d a s a p r o t o t y p e t o a s s e s s t h e s t e a d y s t a t e e r r o r . T h e c u r r e n t a n d v o l t a g e a r e n o t r e p r e s e n t e d i n a c t u a l v a l u e s , b u t i n s c a l e d v a r i a b l e s t h a t c a n b e r e p r e s e n t e d b y o n e b y t e i n t h e m i c r o p r o c e s s o r . 3 . 1 . 2 C O N T R O L S C H E M E O F T H E S I M U L A T O R A s t h e s a m p l e c u r v e g e n e r a t i o n i s i m p l e m e n t e d i n a m i c r o p r o c e s s o r s y s t e m , i t i s n a t u r a l t o u s e a d i g i t a l c o n t r o l s c h e m e . S p e c i a l c a r e h a s b e e n t a k e n t o d e s i g n t h e v o l t a g e l o o p i n o r d e r t o a c h i e v e g o o d d y n a m i c r e s p o n s e o f t h e w h o l e s y s t e m . T h e i d e a i s t o h a v e a f a s t r e s p o n s e v o l t a g e l o o p , f a s t e n o u g h t o f o l l o w t h e v a r y i n g v o l t a g e i n p u t c a u s e d b y t h e r e l a t i v e l y s l o w e r c h a n g e o f l o a d c u r r e n t . I n o t h e r w o r d s , t h e s p e e d o f r e s p o n s e o f t h e v o l t a g e l o o p d e t e r m i n e s t h e a l l o w e d m a x i m u m c h a n g i n g r a t e o f l o a d c u r r e n t . I n e a c h c y c l e , l o a d c u r r e n t i s s a m p l e d a n d a c o r r e s p o n d i n g r e f e r e n c e v o l t a g e i s g e n e r a t e d b y t h e c o n t r o l p r o g r a m . A c u r r e n t l o o p i s n o t n e e d e d i n t h e t y p e I I s i m u l a t o r . P r o p o r t i o n a l a n d i n t e g r a t i o n a l ( P I ) c o n t r o l a n d p r o p o r t i o n a l c o n t r o l ( P ) s c h e m e s h a v e b e e n d e s i g n e d a n d i m p l e m e n t e d . B y s e l e c t i n g t h e p a r a m e t e r s Q O a n d Q 1 , t h e P I c o n t r o l l e r h a s t h e s a m e f o r m a s a d e a d b e a t c o n t r o l l e r . H o w e v e r , d u e t o s o m e p r a c t i c a l p r o b l e m s t h a t w i l l b e e x p l a i n e d i n s e c t i o n 3 . 2 . 2 , a d e a d b e a t c o n t r o l i s n o t d e s i r a b l e . A c c o r d i n g t o t r a n s f e r f u n c t i o n a n a l y s i s , a P I c o n t r o l l e r g i v e s z e r o s t e a d y s t a t e e r r o r a n d g o o d d y n a m i c 45 r e s p o n s e , p r o v i d e d the a s s u m p t i o n of l i n e a r i t y i s t r u e . U n f o r t u n a t e l y , the assumption i s not t r u e i n t h i s a p p l i c a t i o n . One problem e n c o u n t e r e d i n the d e s i g n of the v o l t a g e l o o p i s whether t h e c o n t r o l l e r o u t p u t w i l l exceed the l i m i t e d range of the system. I f i t does, t h e expected r e s u l t based on t r a n s f e r f u n c t i o n a n a l y s i s w i l l be wrong. To f i n d out whether the c o n t r o l l e r s a t u r a t e s , a computer s i m u l a t i o n program can be used. A l t e r n a t i v e l y , the s a t u r a t i o n problem can be i g n o r e d i n the e a r l y stage of d e s i g n . For i n s t a n c e , an o s c i l l o s c o p e can be used t o m o n i t o r the c o n t r o l o u t p u t . Any s a t u r a t i o n can be e a s i l y d e t e c t e d w i t h the o s c i l l o s c o p e . The s a m p l i n g f r e q u e n c y i s chosen as the h i g h e s t p o s s i b l e v a l u e , which i s about 2.5 kHz. T h i s c o r r e s p o n d s the e x e c u t i o n time of one c y c l e of the c o n t r o l program. 3.1.3 POWER CONVERTER As i n the type I s i m u l a t o r , a one quadrant t r a n s i s t o r chopper i s used as the power c o n v e r t e r . A c u r r e n t l i m i t e r i s i n s e r t e d i n the chopper o u t p u t f o r the same r e a s o n mentioned i n s e c t i o n 2.1.3. There a r e two ways t o o b t a i n a p u l s e w i d t h modulated s i g n a l f o r the chopper. One i s t o use the m i c r o p r o c e s s o r s o f t w a r e , the o t h e r i s t o use e x t r a hardware. The f i r s t method was used i n the p r e l i m i n a r y d e s i g n and the second was adopted i n the f i n a l d e s i g n of the s i m u l a t o r . The advantages of the second method a r e t h a t the e x e c u t i o n time of the c o n t r o l program and t h u s the s a m p l i n g p e r i o d can be 46 s h o r t e n e d . B e s i d e s , by u s i n g a PWM IC c h i p (NE5561N), the PWM g e n e r a t i n g c i r c u i t i s v e r y s i m p l e and the o p e r a t i n g f r e q u e n c y can be e a s i l y a d j u s t e d . 3.2 DESIGN AND TEST OF THE TYPE I I SIMULATOR T h i s s e c t i o n d e s c r i b e s the d e s i g n and t e s t of the type I I s i m u l a t o r i n f u l l d e t a i l . The I/V c u r v e s t o be s i m u l a t e d are from the s p e c i f i c a t i o n of an ASI 16-2300 p a n e l made by ARCO SOLAR INC.. One of the I/V c u r v e s g i v e n by the m a n u f a c t u r e r i s r e p r o d u c e d and p l o t t e d i n F i g u r e 3-1. The whole c o n t r o l u n i t , i n c l u d i n g sample curve g e n e r a t i o n and c o n t r o l a l g o r i t h m , i s implemented on a 6809 m i c r o p r o c e s s o r development system. A s i m p l i f i e d diagram showing the a r c h i t e c t u r e of the m i c r o p r o c e s s o r development system i s g i v e n i n f i g u r e 3-2. Only the MPU, VIAO, VIA1 and some RAM are used d i r e c t l y by the s i m u l a t o r . That i s , once the d e s i g n i s c omplete and ready t o put i n p r o d u c t i o n , o t h e r elements i n F i g u r e 3-2 (which are n e c e s s a r y d u r i n g d e s i g n and t e s t ) can be d i s p e n s e d w i t h . Other elements r e q u i r e d i n c l u d e A/D, D/A c o n v e r t e r s , a PWM g e n e r a t o r and a chopper w i t h i t s d r i v e c i r c u i t . 3.2.1 HARDWARE OF THE TYPE I I SIMULATOR The hardware c o n f i g u r a t i o n of the type I I s i m u l a t o r i s g i v e n i n F i g u r e 3-3. VIA1 i s a v e r s a t i l e i n t e r f a c e a d a p t o r w hich c o n t a i n s two programable INPUT/OUTPUT p o r t s . Each p o r t can be e i t h e r an i n p u t p o r t or an out p u t p o r t , depending on 47 the c o n t e n t s of the d a t a d i r e c t i o n r e g i s t e r DDRA or DDRB. When a '1' i s put i n b i t O of DDRA, b i t O of p o r t A w i l l become an o u t p u t b i t ; when a '0' i s put i n b i t O of DDRA, b i t O of p o r t A w i l l become an i n p u t b i t . Other b i t s work the same way. Making use of t h i s f l e x i b l e p r o p e r t y , one can use one p o r t t o t a k e i n the feedback s i g n a l ( i n p u t ) as w e l l as t o send out the c o n t r o l s i g n a l ( o u t p u t ) a c t i n g l i k e two p o r t s . I n t h e type I I s i m u l a t o r , p o r t A of VIA1 i s used t o i n p u t t h e c u r r e n t feedback s i g n a l and t o o u t p u t the c o n t r o l s i g n a l V c , as shown i n F i g u r e 3-3. P o r t A of VIAO (PAO) i s used t o s e l e c t c u r v e s c o r r e s p o n d i n g t o d i f f e r e n t i l l u m i n a t i o n l e v e l s and t e m p e r a t u r e s , t o i n p u t the s t a r t s i g n a l and t o p r o v i d e e n a b l e s i g n a l s f o r the A/D and D/A c o n v e r t e r s . The output v o l t a g e s i g n a l i s p i c k e d up by a v o l t a g e s e n s o r and i s then sent t o an A/D c o n v e r t e r which i s c o n n e c t e d t o p o r t B of VIA1, as shown i n F i g u r e 3-3. F i g u r e 3-4 shows the s i g n a l assignment t o the INPUT/OUTPUT p o r t s . B i t O b i t 3 of PAO a r e used t o s e l e c t d i f f e r e n t I/V c u r v e s . Thus, a maximum number of 16 c u r v e s can be s e l e c t e d . The A/D c o n v e r t e r used i s an ANALOG DEVICES AD750, w i t h 8 - b i t d a t a o utput and 0 10 v o l t s a nalogue i n p u t . When the a n a l o g u e i n p u t i s n e g a t i v e , the d i g i t a l o u t p u t i s 0; when a n a l o g u e i n p u t i s h i g h e r than 10 v o l t s , the d i g i t a l o u t p u t w i l l be l o c k e d a t 255. T h e r e f o r e , i f the v o l t a g e or c u r r e n t feedback s i g n a l i s beyond the normal range, the da t a o b t a i n e d from the RESET NMI V1A1(6522) CFEO-CFEF DISPLAY ROM RAM DO0O- 0000-FFFF DFFF i ^ \ VIA 4) (6522) CFFO-CFFF T — T (DLV.16) Q D AC1A 1(6551) CFD8-CFDB * CASSETTE INTERFACE LEVEL SHIFT Q D AUX. AC1A (t> (6551) CFDC-CFDF * LEVEL SHIFT GO CONSOLE F i g u r e 3-2. A r c h i t e c t u r e of 6809 M i c r o p o c e s s e o r Development System CD Control Bus D.C. Source Data Bus 6809 portA V T A 1 V J. H I portB RAM portA VI AO Address Bus D/A PWM Cenerator Chopper A/D F i l t e r Sensor A/D Sensor Curve Select Start S tgnal Ro i i I I I I _ j i LOAD F i g u r e 3 - 3 . Hardware C o n f i g u r a t i o n of the Type I I S i m u l a t o r vo 50 EIT7 6 5 4 3 2 1 0 sta r t curve s e l e c t i o n D/A A/D enable enable PAO 7 6 5 4 3 i 1 1 0 PB1 Y input current s i g n a l r input voltage signal ^ I I I I 1 . 1 1 1 7 6 5 4 3 1 0 T J output c o n t r o l s i g n a l PA1 F i g u r e 3-4. S i g n a l Assignment t o I/O p o r t s A/D c o n v e r t e r i s not the c o r r e c t v a l u e . A 25 t o 40 MS w a i t time i s r e q u i r e d a f t e r an e n a b l e s i g n a l i s a p p l i e d t o the 51 A/D c o n v e r t e r . The D/A c o n v e r t e r i s an AD558 IC c h i p . I t has an 8 - b i t d a t a i n p u t and two l e v e l s of d a t a o u t p u t . One i s 0 t o 2.56V, the o t h e r i s 0 t o 10 v o l t s . The l a t t e r i s used i n the s i m u l a t o r because the PWM c h i p r e q u i r e s an analogue s i g n a l of 2 t o 5 v o l t s . As mentioned i n s e c t i o n 3.1.3, the p u l s e w i d t h modulated s i g n a l can be g e n e r a t e d d i r e c t l y from the m i c r o p r o c e s s o r , u s i n g s o f t w a r e . T h i s was a t t e m p t e d i n the p r e l i m i n a r y d e s i g n s t a g e . The f r e q u e n c y of the PWM s i g n a l was about 4 kHz. The t e s t of the scheme shows a good s t e a d y s t a t e a c c u r a c y f o r most of the v o l t a g e range. However, the dynamic response was slow. The hardware i m p l e m e n t a t i o n of the PWM g e n e r a t o r i s shown i n the c i r c u i t d i agram of F i g u r e 3-5. A 2 t o 5 v o l t s i g n a l i n the i n p u t of the IC c h i p NE5561N w i l l produce a PWM s i g n a l w i t h 5% t o 98% d u t y r a t i o . When t e s t i n g the PWM g e n e r a t o r , one can remove the r e s i s t o r R 3 f i r s t and a d j u s t R 6 so t h a t when Vc i s 10 v o l t s , V i s 3 v o l t s . Then R, i s c o n n e c t e d and a d j u s t e d ' pwm J J u n t i l V r e a c h e s 5 v o l t s (Vc remains 10 v o l t s ) . I t has been pwm o b s e r v e d t h a t the r e l a t i o n s h i p between chopper output v o l t a g e and the c o n t r o l i n p u t i s not s t r i c t l y l i n e a r . 3.2.2 TRANSFER FUNCTION ANALYSIS FOR THE PUMPING SYSTEM LOAD For the pumping system l o a d , the t r a n s f e r f u n c t i o n b l o c k diagram of the whole system i s shown i n F i g u r e 3-6. where, T^400 M S ( s a m p l i n g p e r i o d ) F i g u r e 3 - 5 . C i r c u i t D i a g r a m o f the PWM G e n e r a t o r 53 T,=RaR 0Ca / (Ra+R 0) K,=Ra/(R 0+Ra) K 2=R 0/(Ra+R 0) Kc=DC SOURCE VOLTAGE / 255 K f v=255/Vsoc K f • = 2 5 5 / I S S C Ta=RaCa T i = R i C i / 4 I n s i d e the dashed frame of F i g u r e 3-6 i s t h e d i g i t a l p a r t and o u t s i d e i s the analogue p a r t . The c i r c u i t d iagram of the analogue p a r t i s shown i n F i g u r e 3-7. S i n c e t h e r e i s a l a r g e c a p a c i t o r i n the pumping system l o a d ( i t i s q u i t e common i n p r a c t i c e t h a t a l a r g e c a p a c i t o r i s c o n n e c t e d i n p a r a l l e l w i t h the PV a r r a y ) , the v o l t a g e waveform w i l l be f l a t and a v o l t a g e f i l t e r i s not n e c e s s a r y . A c u r r e n t f i l t e r i s used i n o r d e r t o o b t a i n a smooth c u r r e n t feedback s i g n a l . The open c i r c u i t v o l t a g e and s h o r t c i r c u i t c u r r e n t of the s i m u l a t o r can be a d j u s t e d by v a r y i n g p o t e n t i o m e t e r s R 2 and R 5 r e s p e c t i v e l y . The L a p l a c e t r a n s f e r f u n c t i o n of V^ w i t h r e s p e c t t o Vc i s g i v e n by: V f ( s ) / V c ( s ) = K c k , K f v / ( T , s + 1 ) (3-1 ) The t r a n s f e r f u n c t i o n of V ^ w i t h r e s p e c t t o Em i s g i v e n by: V f ( s ) / E m ( s ) = K 2 K f v / ( T , s + 1 ) (3-2) C o n v e r t i n g eqs(3-1,3-2) i n t o z t r a n s f e r f u n c t i o n s [13] and u s i n g s t e p response e q u i v a l e n c e y i e l d s : K 2 + ) — • £ c 0 0 i D/A I r -* K, T i s + I / r _ l F i g u r e 3 - 6 . T r a n s f e r F u n c t i o n B l o c k Diagram f o r Pumping System Load 55 Figure 3-7. C i r c u i t Diagram of Analogue Part G v c ( z ) = ( 1 - 2 - 1 ) Z [ G v c ( s ) / s ] =V f(z)/Vc(z) = z - V ( a 0 + a , z * 1) (3-3) Gve(z)=V f(z)/Em(z) = z- 1/(b 0+b,z* 1) (3-4) where, a 0 = l / K a ( l - e - T / T 1 ) a i = - e - T / T 1 / K a ( 1 - e - T / T 1 ) b 0 = l / K b ( l - e - T / T 1 ) b 1 - e " T / T l / R b ( 1 - e - T / T l ) Ka=KcK,K Kb=K2K fv fv From F i g u r e 3-6 we can see that the p l a n t i s of f i r s t order, with a r e f e r e n c e input Vp and a d i s t u r b a n c e Em. A PI 56 c o n t r o l l e r i s d e s i g n e d f o r t h e v o l t a g e l o o p . The z t r a n s f e r f u n c t i o n of the c o n t r o l l e r i s shown below: V c ( z ) / E ( z ) = ( Q 0 + Q 1 Z - 1 ) / ( 1 - z - 1 ) (3-5) W i t h PI c o n t r o l , The z t r a n s f e r f u n c t i o n of V^ w i t h r e s p e c t t o Vp becomes: V f ( z ) / V p ( z ) = ( Q O z - ' + Q 1 Z ' 2 ) / [ a 0 + ( a 1 + Q O - a 0 ) z - ' + ( Q 1 - a , ) z " 2 ] (3-6) The z t r a n s f e r f u n c t i o n o f V ^ w i t h r e s p e c t t o Em i s g i v e n by: V f ( z ) / E m ( z ) = z - ' O - z " 1 ) / [ b o + t b ^ b o + Q O z ^ + t Q I - B j z - 2 ] (3-7) From eq(3-6) i t c a n be seen t h a t , i f Q 0 = a o and Q 1 = a , , the s t e p response of V p w i l l have a deadbeat b e h a v i o u r . However, as the deadbeat c o n t r o l depends on the c a n c e l l a t i o n of p o l e s and z e r o s , i t i s s e n s i t i v e t o the d e v i a t i o n of the system parameters. S i n c e t h e c i r c u i t elements a r e not i d e a l , and e s p e c i a l l y t h a t the chopper i s not q u i t e l i n e a r , a deadbeat c o n t r o l scheme i s not used. I n s t e a d , QO and Q1 a r e s e l e c t e d so t h a t the s y s t e m p o l e s a r e a t z = 0 . 2 ± j 0 . 3 . QO an Q 1 can be c a l c u l a t e d from the f o l l o w i n g f o r m u l a e : Q 0 = - 0 . 4 • a 0 + a 0 _ a , Q1 = 0 . 1 3 ' a 0 + a , D u r i n g o p e r a t i o n , t h e r e f e r e n c e i n p u t Vp i s v a r y i n g due t o the change of l o a d o r t h e change of sample c u r v e . Thus, f a s t dynamic response of t h e v o l t a g e l o o p i s e s s e n t i a l t o the o v e r a l l performance of the s i m u l a t o r . The s i m u l a t o r I/V c u r v e s a r e r e c o r d e d by an x-y p l o t t e r and p l o t t e d t o g e t h e r w i t h t h e sample c u r v e , as shown i n 57 F i g u r e 3-8. The s c a l e s i n F i g u r e 3-8 ( a l s o i n F i g u r e 3-9) r e p r e s e n t t h e c u r r e n t and v o l t a g e v a l u e s s t o r e d i n the m i c r o p r o c e s s o r . These v a l u e s c o r r e s p o n d t o the a c t u a l c u r r e n t and v o l t a g e v a l u e s of the s i m u l a t o r . As an a l t e r n a t i v e , a p r o p o r t i o n a l c o n t r o l l e r was a l s o d e s i g n e d and implemented. The advantage of the P c o n t r o l i s t h a t the e x e c u t i o n time of one c y c l e of the c o n t r o l program i s s u b s t a n t i a l l y s h o r t e r than t h a t u s i n g PI c o n t r o l . The s i m u l a t o r o u t p u t w i t h P c o n t r o l i s p l o t t e d t o g e t h e r w i t h the sample c u r v e as shown i n F i g u r e 3-9. A l l the v a l u e s of c u r r e n t and v o l t a g e a r e c o r r e s p o n d i n g v a l u e s r e p r e s e n t e d by the m i c r o p r o c e s s o r . 3.2.3 SOFTWARE OF THE SYSTEM The c o n t r o l program i s w r i t t e n i n assembly language. The b a s i c t a s k s of the c o n t r o l program are l i s t e d below: 1. S e l e c t one I/V c u r v e . 2. Sample s i m u l a t o r o u t p u t v o l t a g e and c u r r e n t . 3. Generate r e f e r e n c e v o l t a g e a c c o r d i n g t o s e l e c t e d I/V c u r v e . 4. C o n t r o l a l g o r i t h m . 5. Output th e c o n t r o l s i g n a l . The f l o w c h a r t s of the c o n t r o l program a r e g i v e n i n F i g u r e 3-lOa and 3-lOb. One can see from F i g u r e 3-lOa t h a t p o r t A of VIA1 i s d e f i n e d t w i c e , f i r s t as an i n p u t p o r t t o read the c u r r e n t s i g n a l and then as an o u t p u t p o r t t o send out the 58 c o n t r o l s i g n a l t o the D/A c o n v e r t e r , 3 0 0 . (H 2 5 0 . O H -a ?00.0 1 5 0 . 0 £ 1 0 0 . 0 ZD 5 0 . 0 - ^ s i m u l a t o r o u t p u t sample c u r v e s i m u l a t o r out w i t h reduced s u n l i g h t i i i i I i i i i I i i i i | i i i i | i i ' ' ' | 11 1 1 1 | 5 0 . 0 1 0 0 . 0 1 5 0 . 0 2 0 0 . 0 2 5 0 . 0 3 0 0 . 0 VOLTAGE F i g u r e 3-8. Type I I S i m u l a t o r I/V Curves (PI c o n t r o l ) ( s c a l e d i n terms of m i c r o p r o c e s s o r b i t s i z e ) 59 300.0-1 0 50.0 100.0 150.0 200.0 250.0 300.0 VOLTAGE F i g u r e 3-9. Type I I S i m u l a t o r Output U s i n g P C o n t r o l ( s c a l e d i n terms of m i c r o p r o c e s s o r b i t s i z e ) The enable s i g n a l f o r the A/D c o n v e r t e r i s i s s u e d 13 i n s t r u c t i o n s e a r l i e r than when the m i c r o p r o c e s s o r a c t u a l l y 60 samples the c u r r e n t and v o l t a g e s i g n a l s from A/D c o n v e r t e r s . Thus a 40 M S w a i t time i s e n s u r e d . From F i g u r e 3-3 one can see t h a t a D/A and an A/D c o n v e r t e r a re c o n n e c t e d t o g e t h e r t o p o r t A of VIA1. Care must be ta k e n t o make s u r e t h a t the A/D c o n v e r t e r and the D/A c o n v e r t e r a r e not e n a b l e d a t the same t i m e . A l l a d d i t i o n s and s u b t r a c t i o n s i n the c o n t r o l a l g o r i t h m a r e c a r r i e d out w i t h two-byte r e p r e s e n t a t i o n . The dynamic range of the c o n t r o l a l g o r i t h m i s l a r g e enough t o a v o i d o v e r f l o w . However, the c o n t r o l output i s r e p r e s e n t e d by o n l y one b y t e . T h e r e f o r e , i n both c o n t r o l a l g o r i t h m s , Vc i s s e t t o z e r o when the c a l c u l a t e d v a l u e i s n e g a t i v e . When the c a l c u l a t e d v a l u e i s l a r g e r than 255, Vc i s s e t t o 255. T h i s s a t u r a t i o n n a t u r e of the c o n t r o l l e r must be t a k e n i n t o account when a n a l y z i n g the performance of the s i m u l a t o r . The f u l l v o l t a g e and c u r r e n t ranges a r e q u a n t i z e d i n t o 256 s t e p s , w i t h one s t e p r e p r e s e n t i n g 0.39% of Vsoc and I s s c . T h i s i s s u f f i c i e n t f o r most a p p l i c a t i o n s . A s t e p change of l o a d from open c i r c u i t t o maximum power p o i n t and back t o open c i r c u i t has been a p p l i e d t o the type I I s i m u l a t o r , the system response ( s i m u l a t e d pumping system l o a d ) i s g i v e n i n F i g u r e 3-11. 61 E N T R Y I N I T I A T E VARIABLES OUTPUT "o" FOR Vc D I S A B L E A / D , I V A NO E N A B L E A/» INPUT CURVE SELECT WORP SET TABLf ADDRESS 6U&P.0UTI N E A D J INPUT 1.1/ S i j u a l D I S A B L E A / D V= Vmo.x-IR.UfJ LOOK TAB UP LE EQUAL SUBROUTINE CONT SET PORT A O U T P U T PORT 5EWP OUT DISABLE VIA SET PORT A INPUT PORT F i g u r e 3-1Oa. F l o w c h a r t of C o n t r o l Program SUBROUTINE C ENTRY") I E R R O R : TWO'S COMPLEMENT T I M E TWOS COMPUMEUT T I M E t G U A U Z E R I SUBROUTINE APJ TIME o-»vc T I M E UPDATE : SUBROUTIUE CONT 1 ^ EM7RY ^  TWO'S C0MPL6MEK1 Vc» P, t p,-V,(«-') T l M j . eat/* (^ FETURAT) F i g u r e 3-1 Ob. F l o w c h a r t of S u b r o u t i n e s 63 The speed of response meets our req u i r e m e n t ( a p p r o x i m a t e l y 120 ms f a l l time and 80 ms r i s e time r e s p e c t i v e l y ) . V« ( P U ; Q6 0-4 Mi 01 M »5 OS e-6 (ij F i g u r e 3-11. Step Response of Type I I S i m u l a t o r 4. DISCUSSION Among the previously-reported PV array simulators, those in references [ 8 , 1 8 ] can be categorized as type I simulators because the output c h a r a c t e r i s t i c s are affected by the natural environment. The simulators reported in references [ 6 , 7 , 9 ] can be categorized as type II simulators since their output c h a r a c t e r i s t i c s are not affe c t e d by the natural environment. The influence of l i g h t i n t e n s i t y and temperature is reproduced by manual adjustment. Actual solar panels are not uniform (even i f they are of the same type). Due to the dispersion of panel parameters, mismatch loss exists when many panels are connected to form a large array. The amplitude of the mismatch loss increases with the degree of dispersion. For instance, when two panels with s l i g h t l y 'different open c i r c u i t voltages are connected in p a r a l l e l , some current w i l l flow from the panel with higher open c i r c u i t voltage to the one with lower open c i r c u i t voltage so that the t o t a l output power is smaller than the sum of the two separate panel output powers. An example given in reference [20] shows that for the p a r a l l e l array being studied, the t o t a l array output power i s 2.25% lower than the sum of the separate c e l l powers. Because of the mismatch problem, the I/V curves of the array do no have the same shape as the p i l o t panel. This i s a l i m i t a t i o n in assessing the steady state error of the type I simulator introduced in t h i s thesis ( t h i s l i m i t a t i o n 6 4 6 5 e x i s t s i n r e f e r e n c e s [8,18] t o o ) . In r e f e r e n c e s [ 7 , 9 ] , the s i m u l a t o r o u t p u t c h a r a c t e r i s t i c s a r e not compared w i t h the r e a l a r r a y I/V c u r v e s so t h a t the a c t u a l s t e a d y s t a t e e r r o r i s d i f f i c u l t t o a s s e s s . The type I I s i m u l a t o r d e s c r i b e d i n t h i s t h e s i s uses the o b j e c t curve ( t h e a c t u a l I/V c u r v e t o be s i m u l a t e d ) as the c r i t e r i o n t o a s s e s s the steady s t a t e e r r o r . T h i s p r o v i d e s a c c u r a t e i n f o r m a t i o n about the s t e a d y s t a t e e r r o r of the s i m u l a t o r . The o b j e c t c u r v e s can be the c h a r a c t e r i s t i c s of a complete a r r a y . The t y p e I I s i m u l a t o r d e s c r i b e d here can t h u s e a s i l y s i m u l a t e a complete a r r a y , which i s not p o s s i b l e w i t h the type I s i m u a t o r s . When an a r r a y i s p a r t i a l l y shaded, the o u t p u t c h a r a c t e r i s t i c w i l l change a c c o r d i n g l y . As the s h a d i n g i s a r b i t r a r y , the s i m u l a t i o n of t h i s e f f e c t w i l l be complex and i s not c o n s i d e r e d i n t h i s t h e s i s . 5. CONCLUSION Two d i f f e r e n t t ypes of PV a r r a y s i m u l a t o r have been d e s i g n e d and t e s t e d . The type I s i m u l a t o r i s s u i t a b l e where a f i e l d t e s t of a p a r t i c u l a r p a n e l type i s r e q u i r e d . The d e s i g n of a type I s i m u l a t o r i n v o l v e s s t a b i l i t y a n a l y s i s and p a r t i a l s i m u l a t i o n of dynamic b e h a v i o u r , which p r o v i d e g u i d a n c e i n c h o o s i n g system parameters t o a s s u r e s t a b i l i t y and good dynamic b e h a v i o u r . The type I I s i m u l a t o r i s s u i t a b l e f o r ex p e r i m e n t s demanding f i x e d i r r a d i a t i o n and te m p e r a t u r e l e v e l s f o r a p e r i o d of t i m e . A new s i m u l a t i o n method, co m b i n i n g f o r m u l a c a l c u l a t i o n and da t a s t o r a g e i s used i n t h e s i m u l a t o r , which l e a d s t o a r e l a t i v e l y s h o r t s a m p l i n g p e r i o d and s m a l l memory s i z e . The e x p e r i m e n t a l r e s u l t s of t h e s e two s i m u l a t o r s meet the r e q u i r e m e n t s l i s t e d a t the b e g i n n i n g of Chapter 2 and Chapter 3.• The s i m u l a t o r s d e s i g n e d i n t h i s t h e s i s p r o v i d e c o n v e n i e n t r e p l a c e m e n t s f o r PV a r r a y s used i n e x p e r i m e n t s s t u d y i n g PV array-powered systems. They were o r i g i n a l l y d e s i g n e d f o r the use i n an e x p e r i m e n t a l s o l a r pumping system w h i c h i s under study a t t h e Department of E l e c t r i c a l E n g i n e e r i n g a t U.B.C. F u r t h e r work t o d e v e l o p commercial v e r s i o n s of such s i m u l a t o r s i s w o r t h w h i l e . 66 REFERENCES 1. M i c h a e l R. S t a r r & W. P a l z , P h o t o v o l t a i c Power f o r  Europe ,D. R e i d e l P u b l i s h i n g Company, Dordrecht, H o l l a n d , 1983. 2. W. P a l z , P h o t o v o l t a i c Power Generation,D. R e i d e l P u b l i s h i n g Company,Dordrecht, H o l l a n d , 1983. 3. Chenming Hu & R i c h a r d M. White,Solar C e l l s from b a s i c to advanced systems, McGraw-Hill Book Company, New York, 1983. 4. Matthew Buresch, P h o t o v o l t a i c Energy Systems, McGraw-Hill Book Company, New York, 1983. 5. Joseph A. M e r r i g a n , S u n l i g h t to E l e c t r i c i t y , the MIT P r e s s , Cambridge, Mass., 1982. 6. M.A. Slonim & E.K. Stanek, " S o l a r C e l l Array Using M i c r o p r o c e s s o r - B a s e d C o n t r o l l e r " , IEEE 1982 IECON Proceedings pp. 24-29. 7. D.R. Smith, George A. O ' S u l l i v a n & Frances K. 0 ' S u l l i v a n , "The Design and performance of an 11 kw S o l a r Array S i m u l a t o r " , IEEE PESC '80 RECORD, pp.220-225. 8. D. B a e r t , " S o l a r C e l l Panel S i m u l a t o r " , E l e c t r o n . L e t t e r s 1979, 15(2) pp. 53-54. 9. G.J. Vachsevanos & E . J . Grimbas, "A P h o t o v o l t a i c Array S i m u l a t o r " , I n t e r n a t i o n a l J o u r n a l of S o l a r Energy,1983, v o l . 1 . pp. 285-292. TO. David L. P u l f r e y , P h o t o v o l t a i c Power Generation, Van Nostrand Reinhold Company, New York, N.Y., 1978. 67 68 11. Adam Osborne & G e r r y Kane,4 and 8 B i t M i c r o p r o c e s s o r  Hand Book,, Osborne/McGraw-Hi 11, B e r k e l e y , C a l i f . , 1980. 12. Lance A. L e v e n t h a l 1981, 6809 Assembly Language  Programming , Osborne/McGraw-Hill, B e r k e l e y , C a l i f . , 1981 . 13. G.F. F r a n k l i n & J.D. P o w e l l , D i g i t a l C o n t r o l of Dynamic  Systems, Addison-Wesley P u b l i s h i n g Company,1980. 14. S.M. S h i n n e r s , Modern C o n t r o l System Theory and  A p p l i c a t i o n , Addison-Wesley P u b l i s h i n g Company, Re a d i n g , Mass., 1978. 15. Kenneth L. S h o r t , M i c r o p r o c e s s o r s and Programmed L o g i c , P r e n t i c e - H a l l , I n c . , Englewood C l i f f s , N J, 1981. 16. J.L. W i l l e m s , S t a b i l i t y Theory of Dynamical Systems, John W i l e y & Sons. I n c . , New York, 1970. 17. B.C. Kuo,Automatic C o n t r o l Systems ( 4 t h e d i t i o n ) , P r e n t i c e - H a l l I n c . , Englewood, C a l i f . , 1982. 18. J . Appelbaum, " S o l a r C e l l S i m u l a t o r " , IEEE 1979 Power E n g i n e e r i n g S o c i e t y Summer M e e t i n g (New York, USA:IEEE 1979) p. A79 464-9/1-3. 19. F. Harashima,"Design Method f o r D i g i t a l Speed C o n t r o l System of Motor D r i v e s " , IEEE PESC '82 Recor d , pp. 289-298. 20. J . Appelbaum, J . Bany & A. B r a u n s t e i n , " A r r a y Power Output of N o n - i d e n t i c a l E l e c t r i c a l c e l l s " , 12th IECEC, pp.1686-92. APPENDIX A: ALGORITHM FOR STABILITY STUDY A l g o r i t h m f o r s t a b i l i t y study program: 1. Set f l a g s : U=FALSE, V=FALSE, WW=POSITIVE 2. Input d a t a ( i n c l u d i n g l o a d d a t a R Land L ) . 3. P r i n t out l o a d d a t a . 4. C a l c u l a t e c o e f f e c i e n t s of denominator D 0 D 9. Formulae a r e g i v e n i n Chapter 2 of t h i s t h e s i s . 5. C a l c u l a t e c o e f f e c i e n t s of numerator N 0 N„. Formulae a r e g i v e n i n Chapter 2. 6. C a l c u l a t e the e i g e n v a l u e s of the open l o o p t r a n s f e r f u n c t i o n . 7. P r i n t out e i g e n v a l u e s . 8. co=0 9. I f co > 1 500, go t o 22. AC+BD 10. Re[G(jw)]= C 2+D 2 BC-AD Im[G(jw)]= C 2+D 2 11. P r i n t out Re[G(jcj)], Im[G(ja>)] and coIm[G (ja>) ]. 12. I f ww=0, go t o 16 13. I f R e [ G ( j u ) ] < 0, s e t V=TRUE. 14. I f Im[G(jaj)] £ 0, s e t U=TRUE. 15. I f V.AND. U=TRUE, go t o 19. 16. I f co > 10, go t o 18. 1 7 . co=co+0.1 , go t o 9. 69 70 18. O = C J + 5 , go t o 9. Comment: p r i n t out the c r i t i c a l s l o p e i n p e r - u n i t v a l u e : 19. K= l / R e [ G ( j w ) ] . 20. K= 0.43-K/20.8., p r i n t K. 21. ww=0, got o 16. 22. s t o p . APPENDIX B: PROGRAM LISTING FOR STABILITY STUDY L i s t i n g o f T H E S I S a t 2 2 : 1 0 : 4 9 o n M A Y 3 0 , 1 9 8 5 f o r C C i d = L I U . P a g e 1 1 C 2 C A P R O G R A M T O S T U D Y T H E S T A B I L I T Y O F T Y P E I P V A R R A Y S I M U L A T O R : 3 C 3 . 5 C L O A D D A T A A N D C O R E S P O N D I N G E I G E N V A L U E S A R E O U T P U T T O L O G I C 3 . 7 C U N I T 6 . N Y O U I S T P L O T D A T A I S O U T P U T T O L O G I C U N I T 7 . 3 . 8 C S Y S T E M P A R A M E T E R S ( I N C L U D I N G L O A D P A R A M E T E R S ) A R E I N P U T F R O M 3 . 9 C L O G I C U N I T 5 . 3 . 9 5 C 4 R E A L N . K 1 A , K 3 . K 5 . K 7 . K 8 , K C . L 5 L O G I C A L V , U 6 V = ( 1 . L T . O ) 7 U = ( 1 . L T . O ) 8 W W = 1 0 . 9 D I M E N S I O N D ( 1 0 ) , N ( 5 ) 1 0 C A L L F R E A D ( 5 , ' 1 7 R M : ' . 11 & T 1 , T 2 , T 3 , T 4 . T 5 , T 7 , T 8 . T C . L . K 1 A . K 3 , K 5 , K 7 , K C , H 2 1 . 1 2 & R L . R O ) 1 3 W R I T E ( 6 . 8 ) T 1 , T 2 , T 3 , T 4 , T 5 . T 7 . T 8 . T C . L . K 1 A , K 3 1 4 W R I T E ( 6 . 1 1 ) K 5 , K 7 . K C 1 5 W R I T E ( 6 . 7 ) H 2 1 , R L , R 0 1 6 7 F 0 R M A T ( / , 2 X , ' H 2 1 = ' . F 8 . 3 . 2 X . ' R L = ' . F 1 5 . 4 . 2 X . ' R 0 = ' , F 8 . 3 ) 1 7 11 F 0 R M A T ( / / , ' K 5 - ' . F 8 . 4 . 5 X , ' K 7 = ' . F 8 . 4 . 5 X , ' K C = ' . F 8 . 4 ) 1 8 8 F O R M A T ( / . ' T 1 = ' . F B . 4 . 7 X . ' T 2 = ' , F 1 0 . 6 , 5 X , ' T 3 = ' . F 8 . 4 , 7 X . ' T 4 = ' . F 8 . 4 . 1 9 S / 7 . ' T 5 = ' , F 1 0 . 6 , 2 X , ' T 7 = ' . F 1 0 . 5 , 3 X , ' T 8 = ' , F 1 3 . 9 . 2 X , ' T C = ' , F 9 . 6 . / / . 2 0 & ' L = / , F 1 0 . 6 . 5 X , ' K 1 * A = ' , F 6 . 3 , 8 X , ' K 3 = ' . F 8 . 4 ) 2 1 T L = L / R L 2 2 T L 1 = L / ( R 0 + R L ) 2 3 W R I T E ( 6 , 9 0 ) T L , T L 1 2 4 9 0 F 0 R M A T ( / / . 2 X , ' T L = ' . F 1 5 . 8 . 5 X . ' T L 1 = ' . F 1 5 . 8 ) 2 5 P 1 = K 3 * H 2 1 / ( T 3 * 6 0 0 0 . ) 2 6 P 2 = 1 0 . / . 4 3 2 7 P 3 = K C / ( ( R 0 + R L ) * T 4 ) 2 8 P 4 = K 7 * R L / 1 0 . 2 9 W R I T E ( 6 , 9 ) P 1 . P 2 . P 3 . P 4 3 0 9 F O R M A T ( / / , 7 X , ' P 1 ' , 1 5 X , ' P 2 ' , 1 5 X , ' P 3 ' , 1 5 X , ' P 4 ' . / / , 4 F 1 5 . 1 0 ) 3 1 C C A L C U L A T E D E N O M I N A T O R P O L Y N O M I A L : 3 2 A 1 = T 1 + T 5 3 3 A 2 = T 1 * T 5 3 4 B 0 = P 1 * P 2 3 5 B 1 = 1 . + P 1 * P 2 * T 3 3 6 B 2 = T 2 + T 8 3 7 B 3 = T 2 * T 8 3 8 C 0 = P 3 * P 4 3 9 • C 1 = 1 + P 3 * P 4 * ( T 4 + T L ) 4 0 C 2 = ( T 7 + T L 1 + T C + P 3 » P 4 * T 4 * T L ) 4 1 C 3 = T C * T L 1 + T C * T 7 + T L 1 * T 7 4 2 C 4 = T C * T L 1 * T 7 4 3 C 4 4 F 0 = B 0 4 5 F 1 = A 1 * B 0 + B 1 4 6 F 2 = A 2 * B 0 + A 1 » B 1 + B 2 4 7 F 3 = A 2 » B 1 + A 1 » B 2 + B 3 4 8 " F 4 = A 2 * B 2 + A 1 * B 3 4 9 F 5 = A 2 * B 3 5 0 C . 5 1 D ( 1 ) = F 0 * C 0 5 2 D ( 2 ) = F 0 * C 1 + F 1 " C 0 5 3 D ( 3 ) = F 0 * C 2 + F 1 * C 1 + F 2 * C 0 71 72 L i s t i n g o f T H E S I S a t 1 6 : 2 9 : 3 2 o n J U N 6 . 1 9 8 5 f o r C C 1 d = L I U . P a g e 2 5 4 D ( 4 ) = F O * C 3 + F 1 * C 2 + F 2 * C 1 + F 3 * C O 5 5 D ( 5 ) = F O * C 4 + F 1 * C 3 + F 2 * C 2 + F 3 * C 1 + F 4 * C O 5 6 D ( 6 ) = F 1 * C 4 + F 2 * C 3 * P 3 * C 2 + F 4 * C 1 + F 5 * C 0 5 7 D ( 7 ) = F 2 * C 4 + F 3 * C 3 + ' F 4 * C 2 + F 5 * C 1 5 8 D ( 8 ) = F 3 * C 4 + F 4 * C 3 + F 5 * C 2 5 9 D ( 9 ) = F 4 * C 4 + F 5 * C 3 6 0 D ( 1 0 ) = F 5 * C 4 6 1 C 6 2 C 6 3 C C A L C U L A T E N U E R A T O R : 6 4 C 6 5 H = K 5 * P 1 * P 3 6 6 N ( 1 ) = H * K 1 A 6 7 N ( 2 ) = H * K 1 A * ( T 3 + T 4 + T 7 + T 8 ) 6 8 N ( 3 ) = H * K 1 A * ( T 3 * T 4 + T 7 * T 8 + ( T 3 + T 4 ) * ( T 7 + T 8 ) ) 6 9 N ( 4 ) = H * K 1 A * ( T 3 * T 4 * ( T 7 + T 8 ) + T 7 * T 8 * ( T 3 + T 4 ) ) 7 0 N ( 5 ) = H * K 1 A * 4 * T 7 * T 8 7 1 C P R I N T O U T D E N O M I N A T O R : 7 2 W R I T E ( 6 , 2 0 ) 7 3 C A L L V E C 0 U T ( D , 1 0 ) 7 4 C P R I N T O U T N U M E R A T O R : 7 5 W R I T E ( 6 , 3 0 ) 7 6 C A L L V E C 0 U T ( N , 5 ) 7 7 1 0 F O R M A T ( E I O . O ) 7 8 2 0 F O R M A T ( / / . ' T H E F O L L O W I N G S A R E C O E F F I C I E N T S O F D E N O M I N A T O R 7 9 & P O L Y N O M I A L : ' ) 8 0 3 0 F O R M A T ( / / , ' T H E F O L L O W I N G S A R E C O E F F I C I E N T S O F N U M E R A T O R 8 1 & P O L Y N O M I A L : ' ) 8 2 C F O R M O P E N - L O O P M A T R I X ( L I N E A R P A R T ) : 8 3 D I M E N S I O N G ( 9 , 9 ) . E ( 9 ) , E R ( 9 ) , E I ( 9 ) . V C R ( 9 , 9 ) 8 4 D A T A G / 9 * 0 . , 1 . . 9 * 0 . . 1 . . 9 * 0 . . 1 . . 9 * 0 . . 1 . . 9 * 0 • . 1 . . 9 * 0 . . 1 . . 8 5 & 9 * 0 . . 1 . , 9 * 0 . . 1 . , 0 . / 8 6 D O 5 0 1 = 1 , 9 8 7 E ( I ) = - D ( I ) / D ( 1 0 ) 8 8 G ( 9 , I ) = E ( I ) 8 9 5 0 C O N T I N U E 9 0 W R I T E ( 6 , 5 3 ) 9 1 C A L L M A T 0 U T ( G . 9 , 9 ) 9 2 5 3 F O R M A T ( / / , ' T H E F O L L O W I N G I S G M A T R I X : ' , / ) 9 3 C F I N D O U T E I G E N V A L U E S O F O P E N L O O P M A T R I X : 9 4 C A L L R E I G N ( G , 9 . 9 . E R , E I , V C R , I E . 0 . 0 ) 9 5 W R I T E ( 6 . 6 0 ) I E 9 6 6 0 F O R M A T ( / , 1 0 X , ' I E R R 0 R = ' , I 2 ) 9 7 W R I T E ( 6 . 7 0 ) 9 8 C A L L V E C 0 U T ( E R , 9 ) 9 9 W R I T E ( 6 , 8 0 ) 1 0 0 C A L L V E C O U T ( E I , 8 ) 1 0 1 7 0 F O R M A T ( / / , 2 0 X , ' R E A L P A R T O F E I G E N V A L U E S : ' ) 1 0 2 8 0 F O R M A T ( / / , 2 0 X , ' I M A G E P A R T O F E I G E N V A L U E S : ' ) 1 0 3 C O B T A I N D A T A F O R N Y Q U I S T P L O T : 1 0 4 W = 0 1 0 5 5 5 I F ( W - 1 5 5 0 0 ) 1 3 , 1 3 , 1 0 5 1 0 6 1 3 X 1 = D ( 9 ) * W * * 8 - D ( 7 ) * W * * 6 + D ( 5 ) * W * * 4 - D ( 3 ) * W * * 2 + D ( 1 ) 1 0 7 X 2 = D ( 1 0 ) * W * * 9 - D ( 8 ) * W * * 7 + D ( 6 ) * W * * 5 - D ( 4 ) * W * * 3 + D ( 2 ) * W 1 0 8 X 3 = N ( 5 ) * W * * 4 - N ( 3 ) * W * * 2 + N ( 1 ) 1 0 9 X 4 = N ( 2 ) * W - N ( 4 ) * W * * 3 1 1 0 X R = ( X 1 * X 3 + X 2 * X 4 ) / ( X 1 * * 2 + X 2 * * 2 ) 11 1 X I = ( X 1 * X 4 - X 2 * X 3 ) / ( X 1 * * 2 + X 2 * * 2 ) 1 1 2 W R I T E ( 7 , 6 6 ) X R , X I 1 1 3 I F ( W W . L T . 0 . 0 ) G O T O 3 2 1 1 4 I F ( X R . L T . O . O ) V = ( 1 . G T . 0 ) 1 1 5 U M X I . G E . 0 . 0 ) 1 1 6 I F ( V . A N D . U ) G O T O 1 4 1 1 7 3 2 I F ( W - 5 0 . ) 3 3 , 3 3 . 3 4 1 1 8 3 3 W = W + . 0 2 1 1 9 G O T O 5 5 73 1 2 0 3 4 W = W + 5 0 0 . 1 2 1 G O T O 5 5 1 2 2 6 6 F 0 R M A T ( 2 X , F 1 5 . 1 0 . 2 X . F 1 5 . 1 0 ) 1 2 3 1 4 R L = 1 . E - 6 1 2 4 1 * 1 2 1 2 5 W R I T E ( 6 , 9 8 ) 1 2 6 9 8 F O R M A T ( / / , 7 X , ' R L ' , 2 0 X , ' V p h / I p h ( P U ) ' , / / ) 1 2 7 9 9 I F ( I ) 1 0 2 , 1 0 3 , 1 0 3 1 2 8 1 0 3 X K = K 7 * R L / ( K 5 * . 1 2 ) 1 2 9 X K 1 = X K / 1 6 . 7 1 3 0 W R I T E ( 6 , 1 0 1 ) R L . X K 1 1 3 1 1 0 1 F 0 R M A T ( F 1 5 . 7 , 7 X , F 1 5 . 7 ) 1 3 2 R L = R L * 1 0 . . 1 3 3 1 = 1 - 1 1 3 4 G O T O 9 9 1 3 5 1 0 2 Z = - 1 . / X R 1 3 6 Z = Z * . 4 3 / 2 0 . 1 3 7 W R I T E ( 6 , 1 0 4 ) Z 1 3 8 W W = - 3 . 1 3 9 G O T O 5 5 1 4 0 1 0 4 F O R M A T ( / / , 5 X , ' d V p h / d I p h ( i n p . u . ) m u s t b e l e s s t h a n ' . F 1 5 . 3 ) 1 4 1 1 0 5 S T O P 1 4 2 E N D APPENDIX C C o n t r o l Program f o r Type I I S i m u l a t o r : • A PROGRAM TO CONTROL THE PV SIMULATOR e •INPUTS 1. START SIGNAL FROM BITS OF PA0-7 « £. CURVE SELECT SIGNAL FROM BITO TO e * BITS OF PAIS 9 • 3. CURRENT SIGNAL FROM PA 10 * 4. VOLTAGE SIGNAL FROM PB 11 * 1£ •OUTPUTS: 1. CONTROL SIGNAL OUTPUT TO PA WHICH CONNECTED TO D/A CONVERTER 13 « dm A/D ENABLE SIGNAL TO BIT4 OF VIAO 14 • 2. D/A ENABLE SIGNAL TO BIT6 OF VIA0 1 u 16 • VIAI DEFINITIONS: 18 CFE0 IRB EQU *CFE0 PORTB OF VIAI 19 CFE0 ORB EQU *CFE0 PORTB DP VIAI £0 CFE1 ORP. EQU *CFE1 £1 CFE1 IRA EQU $CFEl PORTA OF VIAI C C CFE£ DDRB EEL1 *CFE£ DATA DIRECTION REG. B ill •J.' CFE3 DDRA EQU 4CFE3 DATA DIRECTION REG. A * VIG0 DEFINITIONS £ 6 . £3 £ 9 33 3£ 34 CFF1 C F F 3 0014 0014 GRA* EQU IRA? EQU DDRA0 EQU $CFF1 *CFF1 S C F F 3 * OTHER DEFINITIONS • KPL EQU £0 KPH EQU £0 PCRTA OF VIAS DATA DIRECTION REG. VI Ad 36 37 36 39 40 41 4£ 43 44 45 46 47 48 49 50 51 53 53 54 55 56 • PROGRAM STARTS HERE: * INITIATE VIA'S * 0100 10CE 0100 START LDS ttSTART 0104 86 50 ' LDA #?<01010000 0106 B7 CFF3 STA DDRA0 SET PORT A OF VIA® 0109 CC 00FF L0 LDD #»&e>FF 010C FD CFE£ STD DDRB SET PA S PB OF VIAI 010F 86 50 LDA #*01010000 0111 B7 CFF1 STA ORA0 DISABLE A/D,D/A CONVERTERS 0114 86 00 LDA #0 0116 B7 CFE1 STA ORA OUTPUT '0' TO PORT A 0119 86 10 LDA #*00010000 01 IB B7 CFF1 STA ORA0 ENABLE D/A CONVERTER, D/A OUTPU 01 IE 86 00 LDA #0 01£0 B7 0££B STA VC SET CONTROL SIGNAL OUTPUT '0' 01£3 86 50 LDA #X01010000 81 £5 B7 CFF1 STA ORA0 DISABLE D/A CONVERTER 01£8 86 00 LDA #0 01£A B7 CFE3 STA DDRA SET PORT A »UTPL>T PORT 58 59 60 * TO FORM V/I CURVE: 75 6 1 i L E 0 1 £ D B E 0 £ 4 0 L I L D X # T T B L O A D X W I T H B E G I N N I N G O F A D D R E S S 6 £ 0 1 3 0 5 6 C F F 1 L D A I R A 0 6 3 0 1 3 3 8 4 £ 0 A N D A «-/00100000 C H E C K S T A R T S I G N A L 6 4 0 1 3 5 £ 6 D £ B N E L0 I F S T O P , T H E N I D L E 6 5 0 1 3 7 8 6 4 0 L D A #/.0 1000000 6 6 0 1 3 3 B 7 C F F 1 S T A O R f i d E N A B L E A / D C O N V E R T E R 6 7 0 1 3 C B 6 C F F 1 L D P I R R 0 S E L E C T C U R V E 6 8 C M 3 F 6 4 0" A N D A » * F 6 3 0 1 4 1 4 8 A S L A 7i2i ; 3 1 4 £ 1 0 A E 8 6 L D Y A , X Y = B E G I N N I N G O F D A T A T O B L E 7 j 0 1 ' - 5 1 7 L B S R R D J T O S U B R U T I N E T O A D J U S T P A R A M E T E R : * ^ 6 3.4 8 F C C " 9 L D D I R B I N P U T I , V S I G N A L 7 3 •'2»:4S B 7 0 £ £ 6 L S T A V S T O R E V S I G N A L 7 4 ? 1 <VI S B 5 0 L D P •^/•t5 1 0 1 0 0 0 0 7 5 0 1 5 0 B 7 C F F i S T A O R R 0 D I S A B L E A / D C G N V E R T E R 7 6 0 1 5 3 F l i ? £ 3 £ C M P B B O U C H E C K W H E T H E R I > I bound 7 7 0 1 5 6 £ 4 0 F B K S L T J U M P T O L O O K U P T A B L E I F D l b o u n d 7 8 0 1 5 8 3 6 1 4 L D R K P H 7 3 0 1 5 R B 7 0 £ 3 7 S T R KP B i ? 0 1 5 D B 6 0 £ 3 1 L D A S L O 8 1 0 1 6 3 3 D M U L 8 £ 0 1 6 1 4 0 N E G R 8 3 0 1 £ £ B E 0 £ 3 0 A D D f l V M R R = V M A - S L O * I , <I U b o u n d ) 8 4 0 1 6 5 £ 0 1 6 B R R L Y 8 5 0 1 6 7 5 6 0 3 L T L D R « 3 8 6 0 1 & 3 4 A L2 D E C R T I M E E Q U A L I Z E R 8 7 0 1 6 f t £ 6 F D B N E L£ 6 6 0 1 6 C 6 6 1 4 L D R # K P L 6 3 0 1 6 E B 7 0 £ 3 7 S T R K P 9 0 0 1 7 1 F l 0 £ £ F C M P B I M R 3 1 0 1 7 4 ££ 0 £ B H I L X 3 8 0 1 7 6 £ 0 0 3 B R R L W 3 3 0 1 7 6 F 6 0£2F LX L D B I M A 3 4 0 1 7 B R 6 0 5 L W L D R B , Y L O C K U P V O L T A G E I N D A T A T A B L E 9 6 * C O N T R O L L O O P 3 7 • 3 8 0 1 7 D 1 7 0 0 8 5 LY L B S R C 0 N T 1 3 3 0 1 8 0 C 6 F F L D B # * F F 1 0 0 0 i e £ F 7 C F E 3 S T B D D R R S E T P O R T A O U T P U T P O R T 1 0 1 0 1 S 5 B 7 C F E 1 S T R O R R S E N D V C T O P O R T fl 1 0 £ 0 1 8 8 C 6 10 L D B #y.00010000 1 0 3 0 1 8 A F 7 C F F I S T B O R R 0 E N A B L E D / A , V C I S O U T P U T T O D / R 1 0 4 0 1 6 D C 6 5 0 L D B #%01010000 I f . 5 0 1 8 F " F 7 C F F I S T B O R R 0 D I S A B L E D / A - -... 1 0 & 0 1 9 £ C 6 0 L D B #0 'Jj 1 3 4 F 7 C F E 3 S T B D D R R S E T P O R T A I N P U T P O R T : ? a 0 1 3 7 1 6 F F 9 3 L B R R L I 1 0 3 • 1 1 0 * S U B R O U T I N E : R D J A 1 A 1 i £ 0 1 9 R B E 0 £ 3 3 A D J L D X # A D T 1 1 3 0 1 3 D E E 8 6 L D U A , X 1 1 4 0 1 3 F 3 7 0 6 P U L U A , B 1 1 5 0 1 A 1 F D 0 2 £ F S T D I M R 1 1 6 0 1 P 4 3 7 0 6 P U L U A , B 1 1 7 0 1 R 6 F D 0 £ 3 1 S T D S L O 1 1 8 0 I . R 3 3 3 R T S 1 1 3 * 76 i £ 0 * SUBRCUTIN IE: CONT 121 »»«*••***•*****»****«*****•#*****»*************• 1££ * 1 £3 * :NPI. COMMAND VOLTAGE VR <IN REGISTER A> 1£4 * £. SAMPLED VOLTAGE IN MEMORY V i £ 5 * i£6 * OUTPUT: CONTROL OUTPUT (IN REGISTER A) 1£7 * 1£8 * MODIFY: MEMORY VC,El 1£9 * 130 01A3 IF 89 CONT TFR A, B 131 01AC 66 00 LDA #0 13£ 01AE B3 0££5 SUED V0 133 e i B i FD 0 2 £ 9 STD E 134 01B4 4D TSTA 135 01B5 £A 0C BPL EPL 13£ 01B7 43 CDMA 137 01BB 53 COMB 136 01B9 5C INCB 139 01BA B 6 0££3 LDfl A0 140 01BD 3D MUL 141 01BE 43 COMA 14E 01BF 53 COMB 143 01C0 5C INCB 144 a i c i £0 04 BRA Cl 145 01C3 B6 0££3 EPL LDA A0 146 01C6 3D MUL 148 01C7 FD 0££D Cl STD SE0 149 01CA FC 0££B LDD E l 150 01CD4D TSTA 151 01CE £0 09 BPL EPL 1 15£ 01D0 43 COMA 153 01D1 53 COMB 154 01D£ 5C INCB 155 01D3 B 6 0££4 LDA A l 156 01D6 3D MUL 157 01D7 £0 07 BRA C£ 158 01D9 B 6 0££4 EPL1 LDA Al 159 01 DC 3D MUL 1 6 i ? 01DD 43 COMA 161 01DE 53 COMB 16£ 01DF 5C INCB 163 01E0 F3 0££D C£ ADDD SE0 164 01E2 F3 0££7 ADDD VC0 1 6 5 01EE A D TSTA 16S 0 i E 7 £& 159 EMI VCM 1 £ 7 i ? V . E 9 £ 7 0E B E C NORM 166 0 1 E B C 6 FF LDB #t=F REQUIRED CONTROL EXCEEDS E 1 6 9 0 1 E D " 7 i ? £ £ 8 S T B VC 1 7 0 0 1 F i S £ C 0 3 BRA C3 1 7 1 0 1 F £ C 6 0 0 VCM LDB # 0 1 7 £ 8 1 F 4 F 7 0 £ £ S STB VC REQUIRED CONTROL IS V C = 0 173 01F7 £ 0 03 BRA C3 174 01F9 F 7 0 £ £ 8 NORM STB VC RE3UIRED CONTROL IS NORMAL 175 01FC F C 0 £ £ 9 C3 LDD E 176 01FF FD 0 £ £ B STD E l UPDATE E 177 0 £ 0 £ B £ 0 £ £ 8 LDA VC PUT CONTROL OUTPUT TD REG. 179 77 i eu « • • » • * # * » « • « * « * * « * # » * » * » • * * * * * * * # * « « * * * » * » * * * * * * * * * * * * * * » # * * * * 1 8 1 * 18£ * 103 * 184 * SUBROUTINE C0NT1: 185 * 186 • INPUT: 187 * 1.VOLTAGE COMMAND IN REGISTER A 188 • 1B9 • 2. SAMPLED VOLTAGE IN MEMORY V 191 * OUTPUT: 192 • CONTROL VC IN REGISTER A 193 0£05 IF 194 0£07 86 195 0£ 0 3 B3 196 0 2 0 C FD 197 0£ 0 F £A 198 0 2 1 1 86 £ 0 0 0 £ 1 3 £0 £ 0 1 0£ 1 5 B 6 £ 0 £ 0 £ 1 6 3D £ 0 3 0 £ 1 9 4 D £ 0 4 0 £ 1 A £7 £ 0 5 0 £ 1 C 86 £ 0 6 0 £ 1 E £0 £ 0 7 0 £ £ 0 I F £ 0 8 0 £ £ £ 39 £ 0 9 £ 1 0 £ 1 1 £ 1 £ 0£ £ 3 £ 1 3 0 £ £ 4 £ 1 4 0 £ £ 5 £ 1 5 0££6 £ 1 6 0££7 £ 1 7 0£ £ 8 £ 1 8 0 £ £ 9 £ 1 9 0 £ 2 3 £ £ 0 0 £ £ D £ £ 1 0 £ £ F £ £ £ 0£30 ££3 0 £ 3 1 ££4 0 £ 3 £ £ £ 5 0 £ 3 3 ££6 0 £ 3 5 £ £ 7 0 £ 3 7 £ £ 8 0 £ 3 8 ££9 0 £ 3 C £30 0 £ 4 0 £ 3 1 0 £ 4 8 £ 3 £ 0 £ 5 0 £ 3 3 0 £ 5 8 1000 FDB *1000, *1100,*1£00,* 1300 "' ' £ 3 4 * £ 3 5 • PV DATA STORAGE: £ 3 6 * £37 0380 ORG *380 £ 3 8 0 3 S 0 EDED FDB CEDED,CEDED £39 0 3 8 4 ECEC FDB SECEC, *ECEC,*EBEB,*EBEB £ 4 0 0 3 8 C EAEA FDB *EAEA, *EAEA,*E9E9,«E9E9 £ 4 1 0 3 3 4 E8E8 FDB *E8E8, *E7E7,*E6E6 £4£ 0 3 9 A E6E5 FDB *E6E5, *E5E5,*E4E4,*E4E3 89 C0NT1 TFR A, B 00 LDA #0 0££5 SUBD V« 0££9 STD E 04 BPL PI 00 LDA #0 0D BRA RT 0£37 PI LDA KP MUL TSTA 04 BEQ P£ FF LDA #«Fr 0£ BRA RT 98 P£ TFR B, A RT RTS RETURN TO r * RESERVED MEMORY UNITS: 14 A0 FCB £0 1£ Al FCB 18 0 0 V0 FCB 0 0 0 V FCB 0 00 VC0 FCB 0 0 0 VC FCB 0 0 0 0 0 E FDB 0 0 0 0 0 El FDB 0 0000 SE0 FDB 0 00 IMA FCB 0 00 VMA FCB 0 00 SLO FCB 0 00 BOU FCB 0 0£38 ADT FDB TTA 0£3C FDB TTA1 00 KP FCB 0 FFFF TTA FDB *FFFF,*2580 CFF0 TTA1 FDB *CFF0,*3867 0400 TTB FDS »400,*500,4600, *700 0800 FDB *800,*900,»A00,*B00 0C00 FDB *C00, *D00, *E00, *F00 0   *1100,*1£00,Si; 2 4 3 0 3 A £ E 3 E 3 F D B £ 4 4 0 3 « f l DrlF F O B £ 4 5 0 3 B £ D B D B F D B £ 4 6 0 3 B A D 7 D 7 F D B £ 4 7 0 3 C £ D 3 D 3 F D B £ 4 8 0 3 C A C F C F F D B £ 4 9 0 3 D £ C B C B F D B 2 5 0 0 3 D A C 7 C 6 F D B £ 5 1 0 3 E £ B F B E F D B £ 5 2 0 3 E A • B 7 B 6 F D B 2 5 3 0 3 F £ A B A 9 F D B £ 5 4 0 3 F A 7 5 6 5 F D B £ 5 5 0 5 6 7 O R G £ 5 6 0 5 6 7 D 9 D 9 F C B £ 5 7 0 5 6 F D 7 D & F D B £ 5 8 0 5 7 7 D 4 D 4 F D B £ 5 9 0 5 7 F D 0 F C B £ 6 0 0 4 8 0 O R G £ 6 1 0 4 8 0 D 0 F C B £ 6 £ 0 4 8 1 C F C F F D B £ 6 3 0 4 8 7 C D C D F D B £ 6 4 0 4 8 F C O C A F D B £ 6 5 0 4 3 7 C S C 6 F D B 2 6 6 0 4 9 F C 2 C 2 F D B £ 6 7 0 4 A 7 B E B E F D B £ 6 8 0 4 O F B A B 9 F D B £ 6 9 0 4 B 7 B £ B 1 F D B £ 7 0 0 4 E F 0 8 0 6 F D B £ 7 1 0 4 C 7 9 B 8 £ F D B £ 7 2 0 4 C F 0 0 F C B £ 7 3 E N D • E 3 E 3 , * E £ E £ , * E 1 E 1 , 4 E 0 E 0 •DFDF,*D£DE,tDDDD.*DCDC • D B D B , 4 D A D A , * D 9 D 9 , • D B D O ' • D 7 D 7 , * D 6 D 6 , 4 D 5 D 5 , S D 4 D 4 V * D 3 D 3 , * D £ D £ , * D 1 D 1 , * D 0 D 0 . • C F C F , • C E C E , t C D C D , * C C C C • C B C B , • C A C A , *CSC<3, * C 8 C 8 • C 7 C 6 , * C 5 C 4 , * C 3 C £ , * C 1 C 0 • B F B E , • B D B C , • B B B A , • B 9 B 8 -• B 7 B 6 , « B 5 B 4 , * B 2 B 0 , • A F A D • A B A 9 , • A 6 A 2 , 4 9 D 9 8 , • B F S S • 7 5 6 5 , * 5 0 3 8 , * 2 0 0 0 • 5 6 7 • D 9 D 9 , i D 9 D 8 , • D S D S , W 7 D 7 • D 7 D 6 , ^ 0 6 0 6 , • D S D S , * D 5 D 4 • D 4 D 4 , » D 3 D 3 , * D £ D £ , • D I D l • D 0 • 4 8 0 • D 0 • C F C F , • C F C E , • C E C E • C D C D , • C D C C , * C C C C , S C B C B • C A C A , • C S C S , « C 8 C 8 , ^ 0 7 0 7 • C 6 C 6 , • S C S , 4 C 4 C 4 , * C 3 C 3 * C £ C £ , • C I C l , » C 0 C 0 , S B F E F •BEBE,•BDBD,•BCBC, •BBBB • B A B 9 , • B 8 B 7 , • B 6 B 5 , • B 4 B 3 • B £ B 1 , • B 0 A F , • A E A D , • A C A A • A 8 A 6 , • A 4 0 2 , 4 A 0 9 E , 4 9 0 9 4 • 9 B 8 2 , 4 7 9 6 F , • 5 A 4 5 , S 2 F 1 8 • 0 0 

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