Design and Performance of a Digitally Based Voltage Controller for Correcting Phase Unbalance In | Force | Computer Engineering

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IEEE TRANSACTIONS ON INDUSTRY APPLICATIONS, VOL. 26. NO. 3, MAYIJUNE 1990 425 Design and Performance of a Digitally Based Voltage Controller for Correcting Phase Unbalance in Induction Machines be seriously affected with only a few percent voltage unbalance. Conventional remedies for phase unbalance often involve costly modification of the incoming substation equipment, redesign of the feeder line layout to the various loads, or perhaps, retrofit with an oversized machine. In many situations,
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IE E ET R A N S A C T IO N S O N IN D U S T R YA P P L IC A T IO N S ,V O L .2 6 . N O .3 , M A Y IJU N E 1 9 9 0 4 2 5 D esign and Perform ance ofa D igitally Based V o lta g e C o n tro lle r fo r C o rre c tin g P h a s e U n b a la n c ei nIn d u c tio n M a c h in e s A b stract-T h e c a s e o f u n b a la n c e d s u p p ly p r e s e n ts a u n iq u e ly d iffic u lt p r o b le m in m otor application since its causes are varied. In m any situ- ation s a static starter utilizing back-to-back thyristors in series w ith the m otor lines is already installed fo r th e p u rp o se of soft starting or for pow er fa c to r im provem ent. A n a ttr a c tiv e low-cost solution fo r p h a se unbalance is sim ply to m odify the control strategyo f the static starter b ya d ju stin g th e fir in g a n g le s o f th e th r e e th y r isto r p a ir s in d e p e n d e n tly . In this m anner the series connected thyristors serve the functiono fu n - sym m etrical, variable supply im pedances which can be used t o b a la n c e the voltage across the m otor phases. A n ew d ig ita l c o n tr o lle r u tiliz in g a static starter for balancing the phase currents of an induction m otor op- erating w ith unbalanced supply is presented. Experim ental results show a m arked reduction in the current unbalance from a p p r o x im a te ly 4 0 % to a few percent and clearly dem onstrate the attractiveness of the new phase balancer. IN T R O D U C T IO N H E C A SE of unbalanced supply presents a uniquely dif- T fic u lt p ro b le m in m o to r a p p lic a tio n s in c e th e c a u s e s o f such unbalances arise from num erous unsym m etrical condi- tio n s . U n s y m m e tric a l tra n s fo rm e r w in d in g so r transm ission line im pedance, unbalanced three phase loads or a large sin- gle phase load, are som e typical exam ples. C auses existi na ll stages of the electrical energy transform ation from the gener- a tio n to u tiliz a tio n . H o w e v e r, re g a rd le s s o f th e c a u s e , e v e n a sm all phase voltage unbalance can induce large negative se- q u e n c e c u rre n ts d u e to th e re la tiv e ly lo w n e g a tiv e s e q u e n c e im p e d a n c e o f th e c o n n e c te d a c m a c h in e . In d u c tio n m o to rs a re p a rtic u la rly s e n s itiv e to u n b a la n c e d o p e ra tio n s in c e lo c a liz e d h e a tin g c a n o c c u ri nth e s ta to r a n d th e life o f th e m a c h in e c a n Paper IPCSD 8 9 -2 6 , a p p ro v e d by th e In d u s tria l D riv e s C o m m itte e o f th e I E E E In d u s try A p p lic a tio n s S o c ie tyfo r p re s e n ta tio n a t th e1 9 8 8 In d u s try A p - p lic a tio n s S o c ie ty A n n u a l M e e tin g , P itts b u rg h , P A , O c to b e r 2 -7 . M anuscript re le a s e d f o r p u b lic a tio n J u ly2 5 ,1 9 8 9 .This w ork w as supported in part by the W isconsin E lectric M achines and Pow er E lectronics C onsortium . J. Oyam a w a s w ith th e U n iv ersity of W isconsin, M adison, W I. H e i s n o w w ith the D epartm ento fE le c tric a l E n g in e e rin g a n d C o m p u te r S c ie n c e , Faculty of Engineering, N agasaki U niversity 1-1 4 Bunkyo M achi, N agasaki, 8 5 2J a p a n . F. Profum o w as w ith the U niversity o f W isconsin, M adison, W I. H e is n o w w ith th e D ip artim en to d i E le ttro te c n ic a , P o lite c n ic o d i T o rin o , C o r s o Duca degli Abruzzi,24, 10129 T o rin o , Ita ly . E . M u lja d i w a s w ith th e U n iv e rs ity o f W is c o n s in , M a d is o n , W I .H eis n o w w ith th e D e p a rtm e n t o f E le c tric a l E n g in e e rin g , C a lifo rn ia S ta te U n iv e rs ity - Fresno, M ail Stop9 4 ,Fresno, C A 9 3 7 4 0 . T . A . L ip 0 is w ith th e D e p a rtm e n to f E le c tric a l a n d C o m p u te r E n g in e e rin g , U n iv e rs ity o f W is c o n s in ,1 4 1 5 Johnson D rive, M adison, W 1 5 3 7 0 6 - 1 6 9 1 . IEEE Log Num ber9 0 3 4 2 8 7 . be seriously affected w ith only a few p e r c e n t v o lta g e u n b a l- a n c e . Conventional rem edies for phase unbalance often involve c o s tly m o d ific a tio n o f th e in c o m in g s u b s ta tio n e q u ip m e n t, re - d e s ig n o f th e f e e d e r lin e la y o u t to th e v a r io u s lo a d s ,o r p e r - h a p s , re tro fit w ith a n o v e rs iz e d m a c h in e . In m a n y s itu a tio n s , h o w e v e r, a s ta tic s ta r te r u tiliz in g b a c k -to -b a c k th y ris to rsi n s e rie s w ith th e m o to r lin e s is a lre a d y in s ta lle d fo r th e p u rp o s e o fs o f t startingo r for pow er factor im provem ent. H ence an a ttra c tiv e lo w -c o st s o lu tio n fo r c o rre c tin g th e p h a se u n b a la n c e p ro b le m w o u ld b e s im p ly to m o d ify th e c o n tro l s tra te g y o f th e static starter by ad ju stin g firin g th e an g les of th e th ree th y risto r p a irs in d e p e n d e n tly [ l ] . In th is m a n n e r th e s e rie s c o n n e c te d th y ris to rs s e rv e th e fu n c tio n o f u n s y m m e tric a l v a ria b le su p p ly im pedances which can be used to balance the voltage across th e m o to r p h a s e s [2 ]. A n e w d ig ita l c o n tro lle r u tiliz in g a s ta tic s ta rte r fo r b a la n c - in g th e p h a s e c u rre n ts o f a n in d u c tio n m o to r o p e ra tin g w ith an unbalanced supply isth e to p ic o f th is p a p e r. T h e b e n e - fits o b ta in a b le b y th is s o lu tio n a r e n o t o n ly re d u c tio n in h o t s p o ts in s id e th e m a c h in e b u t a ls o , w ith d ra s tic re d u c tio n o f th e n e g a tiv e s e q u e n c e o f c u r r e n t a n d v o lta g e , it is p o s s ib le to im p ro v e a ls o th e m o to r e ffic ie n c y , to lim it th e le v e l o f th e flu x s a tu ra tio n in s id e th e m a c h in e a n d a ls o to e lim in a te a c o u s tic n o ise a n d v ib ra tio n d u e to to rq u e p u ls a tio n s . A P P R O A C H T O A N A L Y S IS T o a v o id th e u n b a la n c e d v o lta g e p r o b le m , a s y s te m c o n s is t- in g o f th re e b a c k -to -b a c k th y ris to rs p a irsi n series w ith the in d u c tio n m a c h in e p h a s e s to g e th e r w ith a n e w control strat- egy that provides different firing angles for each phase has been proposed [2]. T he block diagram of the overall system is show ni n Fig. 1. The three phases constituting an unbalanced s u p p lyV ,;,V b i, V ,; are assum ed to feed the converter. The in d u c tio n m a c h in e , o n th e o th e r s id e o f th e c o n v e r te r s h o u ld b e supplied by the balanced three-phase voltages V ao,V bo,V ,,. T h e u n b a la n c e d c o n d itio n s a re c o u n te ra c te d by th e c o n tro lle r to p r o d u c e b a la n c e d v o lta g e s a c r o s s th e in d u c tio n m a c h in e te r- m in a ls . T h u s th e u n b a la n c e d p a rts o f th e in p u t v o lta g e s d ro p across the silicon-controlled rectifiers (SC R \u2019s) can be repre- sented by a variable series reactance that can be established by m eans of a fundam entalcom ponent analysis [3]. T he voltage drops in each phase areX a Z a ,X bzb,andX J,. To illustrate th is c o n d itio n th e re la te d p h a s o r d ia g ra m is sh o w n in F ig .2 . 0 0 9 3 -9 9 9 4 /9 0 /0 5 O O -0 4 2 5 $ 0 1.O O O 1 9 9 0 IE E E4 2 6 IE E E T R A N S A C T IO N S O N IN D U S T R Y A P P L IC A T IO N S ,VOL. 26, N O .3 , M A Y IJU N E1 9 9 0 C O N T R O L L E R U F ig .1 . Block diagramo f overall system . F ig .2 . Phasor diagramo f back-to-back thyristor converter. F ig .3 . T ria n g le p la n e s h o w in g c o n tr o l s tra te g y g e o m e tric a l a n a lo g y . T h e m a in o b je c tiv e o f th e c o n tro lle r is th e n to e q u a liz e th e line current and the losses in each phase. Since losses are p ro p o rtio n a l to th e lin e c u rre n t s q u a re d , th e c o n tro l v a ria b le s used are the currents. In the plane of a triangleA B C ,as shown in Fig.3 , the c o n tro l a lg o rith m c a n b e d e p ic te d b y a g e o m e tric a l a n a lo g y . T h e tria n g le a n g le s a re d e fin e d a s a!, 0,y a n dS ,, S p ,S , are the corresponding opposite sides. The relations am ong th e a n g le s a n d s id e s fo r th e tria n g le c a n b e w ritte n a s fo llo w s : w hereR is th e ra d iu s o f c irc u m s c rib e d c irc le . can be w ritten for the triangle: F o ra n y o p e ra tin g c o n d itio n th e fo llo w in g v e c to r e q u a tio n (2 ) If it is p o s s ib le to a d ju s t th e a m p litu d e o fS ,, S p ,S , in d e - p e n d e n tly a n d to m a k e th e m e q u a l, th e tr ia n g le w ill th e nfo rm a n e q u ila te ra l tria n g le w ith th e fo llo w in g c h a ra c te ris tic s : s a+ sp+ s,=0 . IS , I= 1 % I= IS , I (3 ) \u2018 b F ig .4 . A s y m m e tric a l c u r r e n ts in tria n g le p la n e R =(IS a 1 h )/3 . (5 ) T h e s e e q u a tio n s fo r th e tria n g le c a n b e c o rre la te d w ith a three-phase balanced w y e c o n n e c te d in d u c tio n m a c h in e , a s show n in Fig.4 .T he three-phase line currents fo r any condi- tion can be w ritten as follow s: r ,+ f b + f c = o . (6 ) F o r b a la n c e d c o n d itio n s , th e lin e c u rre n ts (in th e tim e d o m a in ) are m utually displaced from each other by 1 2 0 \u201d .B y a n a lo g y w ith th e tria n g le , if th e a m p litu d e o f th e th re e lin e c u rre n ts c a n b e m a in ta in e d e q u a l, th e lin e c u rre n ts a re b a la n c e d . T h u s , in p ra c tic e , if th e c o n tro lle r m a in ta in s th e a m p litu d e s o f th e three line currents equal then, consequently, the phase angles o f th e th re e p h a s e s a re a u to m a tic a lly a d ju s te d to th e ir p ro p e r v a lu e sfo rp h a s e b a la n c e a s w e ll. T h is is a c c o m p lis h e d th ro u g h c o n tro l o f th e c o n v e rte r by a d ju s tin g th e firin g a n g le s in d e p e n - dently on each phase. T he \u201ccurrent balancing loops\u201d of Fig. 5p e rfo rm th is c o n tro lle r fu n c tio n . In a d d itio n , to k e e p th e in d u c tio n m a c h in e o p e ra tin g a t th e sam e condition as before the unbalanced condition occurred, the voltage across the phases m ust be kept constant at the rated c o n d itio n . In e ffe c t, th e m a c h in e e x c ita tio n le v e l m u st b e k e p t c o n s ta n t, a n d th e a m p litu d e s o f th e b a la n c e d currents m ust re tu rn to th e ir o rig in a l v a lu e s. T h is is a fu rth e r c o n s tra in t fo r the system , and it defines the necessary steady-state operating p o in t. It is u se fu l to c o n s id e r a g a in th e c irc u m s c rib e d c irc le o f F ig .3 . T h re e c o n d itio n s m ig h t o c c u r d u rin g th e a d ju s tm e n t o f th e c u rre n t a m p litu d e s I,,z b, I C . a) The radius of the circle is kept constant and equal to R o. T h e s u m m a tio n o f th e lin e c u rre n ts a m p litu d e s is the sam e as before the unbalanced condition occurred. b ) T h e ra d iu s o f th e c irc le is la rg e r th a n th e o rig in a l a n d equal toR 2. T h e a m p litu d e o f o n eo r m o re lin e c u rre n ts is la rg e r th a n th e o rig in a l o n e s . c ) T h e ra d iu s o f th e c irc le is s m a lle r th a n th e o rig in a l a n d e q u a l toR I.T h e a m p litu d e o f o n eo r m o re lin e c u rre n ts is s m a lle r th a n th e o rig in a l o n e s . F o r a ll th re e c o n d itio n s to a p p ly , th e c o n tro lle r m u st b e c a - p a b le o f a d ju s tin g th e th re e lin e c u rre n ts b a c k to its o rig in a l a m p litu d e . H e n c e th e c o n tro lle r m u st b e a b le to in c re a s eo rt o d e c r e a s e th e a p p lie d v o lta g e to th e in d u c tio n m a c h in e te r m i- n a ls .Abalanced condition is reached w hen the circum scribed c irc le o f th e lin e c u rre n ts re tu rn to th e o rig in a l c o n d itio n ( r a - d iu s e q u a l to R o ).T h is fe a tu re is c o rre s p o n d st o th e \u201c v o lta g e lo o p \u201d in F ig .5 .O Y A M Ae t a l.: D IG IT A L L Y B A S E DV O L T A G EC O N T R O L L E R 4 2 7 I \u2018c - F ig .5 . C ontrollo o p sb lo c kd ia g r a m . F in a lly , s in c e th e n a tu re o f th e S C R \u2019s c o n tro lle r is to a d ju s t th e v o lta g e a p p lie d to th e p h a s e s w in d in g by m o d ify in g th e firin g a n g le s , th e v o lta g e a p p lie d a t th e in d u c tio n m a c h in e te r m in a ls is a lw a y s s m a lle r th a n th e in p u t v o lta g e o f th e S C R \u2019 s converter for any value of firing angle exceptzero. T herefore, to k e e p th e ra te d v o lta g e a t th e te rm in a l in p u t o f th e in d u c tio n m a c h in e , th e in c o m in g v o lta g e to th e S C R \u2019sconverter m ust be la r g e r th a n th e r a te d v o lta g e o f th e in d u c tio n m a c h in e . T h u s , u n d e r th e n o rm a l b a la n c e d c o n d itio n , th e firin g a n g le s m u st b e s lig h tly g r e a te r th a n z e r o to r e d u c e th e in c o m in g v o lta g e ( i .e ., to m a tc h th e in d u c tio n m a c h in e v o lta g e ). T h is c o n d itio n e n a b le s th e c o n tro lle r n o t o n ly to re d u c e b u t a ls o in c re a s e th e v o lta g e a c ro s s th e in d u c tio n m a c h in e te rm in a ls[1 1 . C O N T R O L S T R A T E G Y The system proposedi nth is p a p e r c o n s is ts o f th re e p a irs o f id e n tic a l th y r is to r s , c o n n e c te d b a c k -to -b a c k in s e r ie s w ith a three-phase wye(o r d e lta ) c o n n e c te d in d u c tio n m a c h in e . In g e n e ra l, th e s ta to r v o lta g e c o n tro l is a c c o m p lis h e d by a d ju s tin g th e h o ld o ff a n g leyw h ic h c o rre s p o n d s to th e tim e th e th y ris to r rem ains open after the current reaches zero in a given phase. The aim o f th e c o n tro lle r is to c o m p e n s a te th e u n b a la n c e d v o lta g e s u p p ly b y c o n tro llin g e a c h p a ir o f th y ris to r d is tin c tly w ith a n u n s y m m e tric a l firin g a n g le su c h th a t d iffe re n t v a lu e s o fyo c c u r in e a c h p h a s e . S o m e o f th e c e n tra l fu n c tio n s im p le m e n te d w ith th e d ig ita l c o n tro lle r a re sh o w ni nth e b lo c k d ia g ra m o f F ig .5 . T h e c o m - p le te c o n tro l c o n s is ts o f th re e m a in lo o p s : a \u201c c u rre n t lim ite r lo o p ,\u201d a \u201c v o lta g e lo o p ,\u201d a n d fin a lly , a \u201cbalancing current lo o p .\u201d E a c h lo o p c o n trib u te s to th e c a lc u la tio n o f th e p h a se a n g le CY; separately for each phase w ithi=a ,6 ,c . T h e c u rre n t-lim ite r lo o p is a p ro te c tio n c o n tro l lo o p a n d m a in ly o p e ra te s d u rin g th e s ta rtin g o f th e m a c h in e a s w e ll a s d u rin g o v e rlo a d c o n d itio n s (tra n s ie n t o p e ra tio n s ). S u c h a lo o p lim its th e a v e ra g e c u rre n t in th e th re e p h a se s to th e v a lu e im posed by the reference valueI,,,. T h e c u rre n t lim it v a lu e c a n e a s ily s e t, c o n s is te n t w ith th e lo a d d e m a n d s a n d th e c o n - n e c te d n e tw o rk c h a ra c te ris tic s . T h e v o lta g e lo o p , o n th e o th e r h a n d , is th e c o n tr o l lo o p f o r th e n o rm a l b a la n c e d c o n d itio n (s te a d y -s ta te o p e ra tio n ). T h e v o lta g e lo o p k e e p s th e v o lta g e a t th e m o to r te rm in a ls a t th e ra te d v a lu e . T he tw op re v io u s lo o p s o p e ra te a lte rn a te ly ra th e r th a n s i- m u lta n e o u s ly . T h e o u tp u t o f e ith e r lo o p c o n trib u te s to th e a v - erage phase angle com m anda 0 w h ic h is n o m in a lly e q u a l f o r th e th re e p h a s e s . In a d d itio n to th e v o lta g e a n d c u rre n t lim ite r loops, the balancing current loops, one for each phase, op- e ra te b o th in s te a d y s ta te a n d d u rin g tra n s ie n t c o n d itio n s a n d control each phase current to m aintain each of them e q u a l to th e a v e r a g e v a lu e o f th e th r e e p h a s e s . T h e o u tp u ts o f th e th r e e loops can be different for each phase, related to th e u n b a l- anced voltage of each phase and are expressed by the angles: A c Y ,,A ab, A c Y ,.A p ic to ria l re p re s e n ta tio n o f th e o v e ra ll p h a se b a la n c in g s tra te g y is sh o w n in F ig .6 .F ro m th is fig u re , th e firin g a n g le s fo r th ea ,b ,cphases can be w ritten: C Y ,= C Y O+A C Y ~ C Yb = C Y0 +A ab C Y ,= (Y O +A C Y , (7 ) w here A cY ,,A ab, A C Y , c a n b e p o s itiv e o r n e g a tiv e . F o r s te a d y -s ta te b a la n c e d c o n d itio n s , th e th re e b a la n c in g c u rre n t lo o p o u tp u ts a re e q u a l to z e ro . T h is m o d e o f o p e ra tio n c a n b e term ed the \u201cvoltage m ode\u201d because the phase angles are con- tro lle d . In a d d itio n , a s e c o n d m o d e o f o p e ra tio n , a s o -c a lle d \u201ccurrent m ode,\u201d is possiblei nw h ic h th e h o ld o ff a n g ley is controlled. Both control schem es have been te s te d , b u t th e best results have been obtained by the first m ode. H ence the r e s u l t si nth is p a p e r a r e a lw a y s re la te d to th e v o lta g e m o d e . S Y S T E MD E S IG N T o o b ta in th e p e rfo rm a n c e s d e s c rib e d , th e a n a lo g c o n tro lle r o f a c o m m e rc ia l s ta tic s ta rte r d riv e h a s b e e n s u b s titu te d w ith4 28 IE E ET R A N S A C T IO N S O N IN D U S T R Y A P P L L C A T IO N S .V O L .2 6 ,N O .3 , M A Y IJU N E 1 9 9 0 F ig .6 . C urrent balancing control strategy. D IG IT A L CONTPOLLEl F ig .7 . O v e r a ll s y s te m w ith d ig ita l c o n tr o lle r . a n e w d ig ita l c o n tro lle r. F ig .7 s h o w s a s im p lifie d b lo c k d ia - g r a m o f th e o v e ra ll im p le m e n ta tio n w ith th e in d e p e n d e n t fir- T h e 8 -k b it E P R O M is prepared with a basic softw are that is c a lle d a “ m in i m o n ito r” a n d m a in ly c o n s is ts o f a d e b u g - g e r , w h ic h is c o m p a tib le w ith M S -D O S d e b u g g e r e x c e p t fo r assem bly and disassem bly com m ands. In addition, som e gen- eral use subroutines,particularly beneficiali nth e s ta g e o f th e s o ftw a re d e v e lo p m e n t, a re re s id e n t in th e E P R O M . T h e 8 -k b it R A M is th e m e m o ry fo r th e a p p lic a tiv e s o ftw a re . T h eso ft- w are has been w ritten in A ssem bler language and consists of a m a in lo o p a n d fiv e le v e ls o f in te rru p tio n lo o p s . The m ain loop analyzes the keyboard com m ands and sets a n d u p d a te s th e c o n tro l p a ra m e te rs a s th e p ro p o rtio n a l, th e d e riv a tiv e a n d th e in te g ra l g a in s fo r e a c h lo o p a n d th e re fe r- e n c e s fo r th e v o lta g e lo o p a n d fo r th e c u rre n t lim ite r lo o p . In a d d itio n , th e m a in lo o p ta k e s c a re to s to re im p o rta n t in te rn a l variables: such as currents, voltages, and balancing angles. Fi- n a lly , th e p r e v io u s v a r ia b le s c a n b e d is p la y e d o n th e s c r e e n , s e le c ta b le b y k e y b o a rd . F ig .9show s a sim ple flow charto f th e m a in lo o p . O n th e o th e r h a n d , th e in te rru p tio n lo o p s c a lc u la te th e rm s values for each current and the outputof proportional-integral- d e riv a tiv e (P ID ) c o n tro l lo o p . T h e first le v e l o f th e in te rru p - tio n lo o p (IN T O ) o c c u rs3 2 tim e si n e a c h p e rio d a n d c a lc u la te s I:, 126,a n dI f . It d e te c ts th e z e ro p o in ts fo r th e th re e v o lta g e s a n d in th e v o lta g e m o d e s e ts th e th r e e c o u n te r s a n d c a lc u la te s th e P ID o u tp u ts . F ig .1 0show s a sim plified flow chart of the lo o p IN T O a n d s o m e d e ta ils a b o u t th e in te g ra tio n p ro c e d u re . T h e fifth le v e l o f in te rru p tio n (IN T 4 ) o c c u rs o n c e in a c y c le a n d re s e ts th e a n g le c o u n te r fo r th e v o lta g ei nIN T O . F in a lly IN T 1 -3 occurs once in each sem iperiod fo r each phase, and these signals com e from the zero current detectors. In th e current m ode, they set the three counters, one for each phase a n d c a lc u la te th e P ID o u tp u ts . E X P E R IM E N T A L R E S U L T S 1 4 1 . In addition, two interface boards have been designed. The first b o a rd h a s a p h a se -lo c k e d lo o p (P L L ) fo r d e te c tin g th e system frequency and synchronizingthe control functions and a D /A c o n v e rte r fo r d e te c tin g c u rre n ts o r v o lta g e s a s s e le c te d by software.The second board is theI / Ob o a rd w ith fo u r A /D converters for the three currents and the voltage feedback and a c o u n te r fo r th e g a te p u ls e g e n e ra to r. T h e s e ria l in te rfa c e is th e c o m m u n ic a tio n lin k b e tw e e n th e single-board com puter and the IB M /A T used as a developm ent s y s te m . T h e IB M /A T is a ls o u tiliz e d a s a n in p u t/o u tp u t te r- m inal for updating the control param eters and checking som e c o n tro l in te rn a l v a ria b le s a s th e firin g a n g le s fo r e a c h p h a s e . The serial interface w as chosen because it is m uch m orero - b u st th a n o th e r c o m m u n ic a tio n in te rfa c e s fro m th e n o ise p o in t o f v ie w since it uses the f15 V /-15 V as signal level and th e p a rity b it to d e te c t s ig n a l e r r o r s . firs t te s t th re e v o lta g e s w ith d iffe re n t a m p litu d e s su p p ly th e b a c k -to -b a c k th y ris to r c o n v e rte r. F ig .1 1 sh o w s th e sim p lified schem atic em ploying one three-phase autotransform er w ith an a d d itio n a l s in g le -p h a s e tra n s fo rm e r fo r o b ta in in g th e u n b a l- anced voltage. T he percentage of unbalanced voltage can be d e fin e d by th e fo llo w in g e x p re s s io n : w h e re th e sym bols are illu s tra te d i n F ig . 1 1 . T he s e c o n d s im u la tio n o f u n b a la n c e h a s b e e n s e t by u s in g d iffe re n t lin e im p e d a n c e in s e rie s w ith th e th re e p h a s e s . S in c e th e re s u lts o b ta in e d by th e tw o e x p e rim e n ts a r e c o m p a ra b le , th e re s u lts reported in this paper are related to the first set of experi- m ents. To evaluate the perform ance of the prototype, the sam e m o-
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