A Model-Based Direct Power Control for Three-Phase Power Converters

Abs ac — Di ec Powe Con ol (DPC) echnique has been widely used as con ol s a egy o h ee-phase powe ec i ie s due o i s simplici y and good pe o mance. The DPC uses he ins an aneous ac i e and eac i e powe o con ol he powe con e e , he con olle design has been p oposed as a di ec con ol wi h a look up able (LUT), and in ecen wo ks, as an indi ec con ol wi h an inne con ol loop wi h p opo ional plus in eg al con olle s o he ins an aneous ac i e and eac i e powe e o s. In his pape a model-based DPC o h ee-phase powe con e e s is designed, ob aining exp essions o he inpu con ol signal which allow o design an adap i e con ol law minimizing he e o s in oduced by he pa ame e s unce ain ies as he smoo hing induc o alue o he g id equency. Con olle design p ocess, s abili y s udy o he sys em and expe imen al esul s o a synch onous h ee-phase powe ec i ie p o o ype a e p esen ed o alida e he p oposed con olle . Index Te ms— Adap i e con ol, di ec powe con ol, powe ac o co ec ion, powe quali y, h ee-phase powe con e e s. I. INTRODUCTION owe ec i ie s a e well-known powe sys ems o indus ial applica ions as DC-bus supply o h ee-phase ec o -con olled PWM in e e s and DC-Loads and o he in eg a ion o enewable ene gy applica ions. No con olled h ee-phase ec i ie s ha e been widely used due o i s eliabili y, obus ness and low cos , a he expense o in oducing ene gy losses in he ansmission line and ha monic cu en s in o he g id ha no ul il he new s anda ds o he elec ic g id, IEEE-519 o USA and IEC 61000-3-2 and 61000-3-4 o Eu ope [1]-[4]. Due o hese ac s new powe con e e opologies and hei con ol s a egies ul illing wi h hese s anda ds ha e been de eloped and s udied in ecen yea s [5]-[18]. Among hese opologies, PWM egene a i e ec i ie s (Fig. 1) ha e some ex a ad an ages as: bidi ec ional powe low, almos sinusoidal Manusc ip ecei ed Ap il 23, 2007. Accep ed o publica ion No embe 21, 2007. This wo k was suppo ed in pa by he Andalusian Go e nmen unde g an TIC-1172. Copy igh (c) 2007 IEEE. Pe sonal use o his ma e ial is pe mi ed. Howe e , pe mission o use his ma e ial o any o he pu poses mus be ob ained om he IEEE by sending a eques o pubs-pe [email protected] g. S.Vazquez, J. A. Sanchez, J. M. Ca asco, J. I. Leon, E. Gal an a e wi h he Depa men o Elec onic Enginee ing, Uni e si y o Se ille, 41092 Se ille, Spain (e-mail: s azquez@g e.esi.us.es). cu en s, nea uni y powe ac o and egula ion o dc-link ol age. Due o hese ac s he con ol o hese powe sys ems is cu en ly one objec i e o he esea che s. One o he mos e icien con ol s a egies o his sys em is Di ec Powe Con ol (DPC). DPC con ol s a egy lies on he ins an aneous eac i e powe heo y in oduced by Akagi e al. [19] and is based on he e alua ion o he ac i e and eac i e ins an aneous powe e o s alues and he ol age ec o posi ion [20] o he Vi ual-Flux ec o posi ion [21] wi hou any in e nal con ol loop o he cu en s. The basic idea o DPC is o choose he bes s a e o he powe swi ches among he eigh possible s a es in o de o main ain he DC-Link ol age cons an , and o keep he uni y powe ac o . The ec o selec ion is made h ough a Look Up Table (LUT), whe e he inpu a iables a e he ol age g id ec o posi ion and he ins an aneous ac i e and eac i e powe e o s. This con olle has he beha iou o a bang-bang con olle , so he au ho s usually include a hys e esis band in o de o educe he con olle gain. One d awback o his DPC con olle is ha i has no a cons an swi ching equency and in o de o o e come his ac Pulse Wid h Modula ion (PWM) and Space Vec o Modula ion (SVM) wi h cons an swi ching equency ha e been in oduced [22]-[27]. Howe e he main d awback o DPC is he high gain o he con olle , and as consequence, he alues o he inpu induc o s ha e o be e y la ge o a enua e he cu en ipple, inc easing he cos , size and weigh o he sys em. In o de o educe he inpu induc o s alues, LCL il e s ha e been p oposed o connec he powe con e e o he g id [28]-[30]. Tha solu ion has he d awback o he il e esonance so i has o be well s udied. Besides, ecen ly wo ks ha e in oduced p edic i e con ol s a egies o he DPC [31]-[32]. Applica ions based on DPC ha e demons a ed ha i is a simple and e icien con ol s a egy achie ing good dynamic pe o mance and nea uni y powe ac o . Howe e he smoo hing induc ances used o connec he powe con e e o he g id a e s ill oo la ge, inc easing he cos , size and weigh o he o al sys em and educing dynamics and ope a ion ange o PWM ec i ie [33]. A con olle design based on he sys em model can o e come his d awback op imizing he powe sys em beha iou . Fu he mo e adap i e con ol s a egies can be applied o minimize he e o s in oduced by he pa ame e s unce ain ies as he induc o alue o he g id equency. A model-based Di ec Powe Con ol o Th ee- Phase Powe Con e e s Se gio Vazquez. S uden Membe , IEEE, Juan An onio Sanchez, Juan Manuel Ca asco, Membe , IEEE, Jose Ignacio Leon, Membe , IEEE, Edua do Gal an, Membe , IEEE P > REPLACE THIS LINE WITH YOUR PAPER IDENTIFICATION NUMBER (DOUBLE-CLICK HERE TO EDIT) < 2 This pape is o ganized as ollows: Fi s ly he disc e e model o a h ee-phase wo-le el ec i ie is p esen ed. Secondly, based on he sys em model he di ec powe con ol law is de i ed, and an adap i e con ol law and he s abili y s udy o he sys em a e p esen ed. In he las sec ion o he pape expe imen al esul s a e included and analyzed in o de o e i y he heo e ical s udy ha has been p esen ed in he p e ious sec ions. 2 dc V a i c i b i an cn con i Load i cap i 2 dc V bn Fig. 1 Th ee-phase wo le el powe con e e . II. MODEL OF THE SYSTEM A h ee-phase wo le el powe con e e is depic ed in Fig. 1, whe e he neu al poin is deno ed by n. The sys em is connec ed o he g id h ough smoo hing induc o s L, and i is assumed ha a pu e esis i e load RL is connec ed a DC-Link capaci o C. The sys em pa ame e s and a iables a e desc ibed in Table 1. TABLE 1 SYSTEM VARIABLES AND PARAMETERS Va iable Desc ip ion ={ a b c}T Phase o neu al inpu ol age ec o i ={ia ib ic}T Phase inpu cu en ec o d ={ d a d b d c}T Con ol inpu ec o w G id equency L Smoo hing induc o C Ou pu capaci o RL Load esis ance Vdc Ou pu capaci o ol age The equa ions ha desc ibe he inpu cu en s dynamics and he ou pu DC ol age dynamic can be de i ed om he sys em model. Following he echnique p esen ed in [34], he sys em model can be ob ained in he s a iona y αβ ame [23]. 2 dc di V L d ab abab d =×+ (1) 22 22 T dcdcdc L VVV d Ci d R abab d æö ×=- ç÷ èø (2) T Auu abab dd éù == ëû (3) 11 1 2 22 3 33 0 22 A éù -- êú êú =× êú - êú ëû (4) Equa ions (1) and (2) a e he disc e e model o he powe con e e in ab coo dina es, he ab a iables can be calcula ed as {·} ab =A{·}abc, whe e he ma ix A is de ined by (4). In hese equa ions δαβ has been de ined as (3) and i is assumed ha Vdc is always posi i e. Fig. 2 shows he eigh possible s a es o he swi ches in he ab ame, and Table 2 summa izes he possible swi ch posi ions in ab coo dina es. TABLE 2 AVAILABLE SWITCH POSITIONS IN THE CONVERTER DISCRETE MODEL S a e u a u b U0 0 0 U1 2 2 3 0 U2 2 3 2 U3 2 3 - 2 U4 2 2 3 - 0 U5 2 3 - 2 - U6 2 3 2 - U7 0 0 a b Fig. 2 Swi ch posi ions in ab ame. The con ol objec i es o he h ee-phase powe con e e a e he ollowing: (i) The ins an aneous ac i e powe p and he ins an aneous eac i e powe q should ack hei e e ence, p* and q* espec i ely, which a e calcula ed in such way ha he capaci o ou pu ol age is egula ed owa ds i s e e ence and om he sou ce e minals only ins an aneous ac i e powe is supplied [19]. * * 0 pp qq ® ®® (5) Thus, DPC con ols indi ec ly he cu en s p o ided by he sou ce h ough he alues o he ins an aneous ac i e and eac i e powe . (ii) The capaci o ou pu ol age should be egula ed owa ds i s e e ence. * dcdc VV ® (6) > REPLACE THIS LINE WITH YOUR PAPER IDENTIFICATION NUMBER (DOUBLE-CLICK HERE TO EDIT) < 3 III. CONTROL DESIGN The p oposed con olle o he sys em (1)-(2) is composed o an ins an aneous powe acking (inne ) loop and a ol age egula ion (ou e ) loop. In wha ollows is desc ibed he design o he wo con ol s ages. A. Ins an aneous powe acking loop The objec i e o he inne con ol loop is o gua an ee acking o p and q owa ds hei e e ences. The ins an aneous ac i e powe e e ence, p*, is he ou pu o he ou e con ol loop, and is calcula ed in o de o achie e DC- Link ol age egula ion. The ins an aneous eac i e powe e e ence, q*, is made ze o in o de o achie e uni y powe ac o . In [23], i is shown ha in he known pa ame e s case, and assuming ha inpu ol ages a e balanced and wi hou ha monic con en , he ins an aneous ac i e powe i s de i a e o e he ime, . p, and he ins an aneous eac i e powe i s de i a e o e he ime, . q, a e exp essed espec i ely as 2 12 Tdc V Lq Lp ababab ab wd æö æö ç÷ ç÷ =+- ç÷ ç÷ ç÷ èø èø & (7) 2 2 TT dc J V Lq JLp ab abab ab dw æö ç÷ =-- ç÷ èø & (8) Now he locus o dab poin s whe e (7) and (8) a e made equal o he cons an s k1 and k2 espec i ely can be calcula ed. ( ) 12 11 2 2 pk dc Lq kcJ V ab ababab ab dw = =+-+ & (9) ( ) 2 22 2 2 qk dc J Lpkc V ab abab ab dw = =-++ & (10) Equa ion (9) is he ec o ial ep esen a ion o a s aigh line in he ab ame, whe e c1J ab desc ibes he di ec ion o he line, and c1 is an a bi a y cons an . This line is he se o alues o δαβ ha makes . p equal o he cons an k1, and spli s he alpha-be a plane in wo egions, alues o δαβ abo e (9) make . p smalle han k1, while alues o δαβ below (9) make . p la ge han k1. Equa ion (10) ep esen s he same idea o he eac i e powe i s ime de i a e, whe e c2 ab desc ibes he di ec ion o he line, and c2 is an a bi a y cons an . 2 qk ab d = & also spli s he alpha-be a plane in wo egions, alues o δαβ abo e (10) make . q la ge han k2, while alues o δαβ below (10) make . q smalle han k2. Fig. 3 shows he alpha-be a ame egions whe e . p and . q a e enclosed o ce ain alues. When cons an s k1 and k2 a e made equal o ze o equa ions (9) and (10) a e espec i ely ans o med in he ollowing exp essions [23] ( ) 2 0 1 2 2 p dc Lq cJ V ab ababab ab dw = =++ & (11) ( ) 0 2 2 2 q dc J Lpc V ab abab ab dw = =-+ & (12) These wo s aigh lines spli he alpha-be a ame in ou quad an s as i is shown in Fig. 4. Each zone is cha ac e ized by he sign o he ins an aneous ac i e and eac i e powe i s de i a e o e he ime, so when he sys em is wo king inside one o hem he ins an aneous ac i e and/o he eac i e powe can inc ease o diminish acco ding which wo k a ea is. The in e sec ion poin be ween hese wo s aigh lines can be calcula ed as 22 22 1 eq cc LqLp J VV ababab abab ww d æöæö ç÷ç÷ =+- ç÷ç÷ èøèø (13) a b ab Fig. 3 Bounda y limi s o he ins an aneous ac i e and eac i e powe i s ime de i a e. ab eq ab d 0 0 p q < < & & 0 p ab d = & 0 q ab d = & 0 0 p q > < & & 0 0 p q < > & & 0 0 p q > > & & a b Fig. 4 Equilib ium poin in s eady s a e d eq ab ep esen s he equilib ium poin o he sys em in s eady s a e due o in his poin he ins an aneous ac i e and eac i e powe demanded by he powe con e e o he powe supply do no inc ease o diminish, and he e o e, a his poin , he ins an aneous ac i e and eac i e powe demanded by he powe con e e emain cons an s. > REPLACE THIS LINE WITH YOUR PAPER IDENTIFICATION NUMBER (DOUBLE-CLICK HERE TO EDIT) < 4 The ollowing equa ions de ine he alues o ins an aneous ac i e powe e o , ~ p, and ins an aneous eac i e powe e o , ~ q, espec i ely. * * ppp qqq =- =- % % (14) The powe swi ches s a e should be chosen among he disc e e possible s a es inside a selec ion a ea de ined by he sign o he ins an aneous ac i e and eac i e powe e o . Table 3 shows he selec ion a ea as a unc ion o he sign o ins an aneous powe e o s. This basic selec ion algo i hm has he ollowing d awbacks: 1) The possible powe swi ches s a e is no always unique, i.e. he e is mo e han one possible s a e o he powe swi ches inside he selec ion a ea. Fig. 5 shows a possible si ua ion whe e in a ea A2 he e a e i e possible s a e ec o s. 2) The powe swi ches s a e is no always de ined inside he selec ion a ea. Fig. 5 shows a possible si ua ion whe e in a ea A4 he e is no any s a e ec o . TABLE 3 SELECTION AREA AS FUNTION OF THE INSTANTANEOUS POWER ERRORS ~ p ~ q A ea >0 >0 A1 >0 <0 A4 <0 >0 A2 <0 <0 A3 U0U7 U1 U2U3 U5 U6 U4 A2 A3 A4 A1 0 0 p q < < & & A1 0 0 p q > < & & A2 0 0 p q < > & & A4 0 0 p q > > & & A3 0 p ab d = & 0 q ab d = & a b ab Fig. 5 Powe swi ches s a es a iable in each selec ion a ea. To o e come hese d awbacks in he basic selec ion algo i hm is necessa y o de ine a ec o e e ence ha is always in he app op ia e selec ion a ea, and o gene a e his e e ence ec o wi h a modula ion echnique wi h a cons an swi ching equency as PWM o SVM. I is possible o de ine such a ec o e e ence aking in o accoun he equilib ium poin d eq ab ec o alue and he in ol ed selec ion a ea. The e e ence ec o can be calcula ed as a composi ion o he d eq ab ec o , a p opo ional ec o o ab and a p opo ional ec o o J ab . As a unc ion o he selec ion a ea, hese wo las ec o s a e added o sub ac ed o he d eq ab ec o o gene a e he e e ence ec o . In wha ollows i is p esen ed how he e e ence ec o is composed o each selec ion a ea. Besides, a ec o diag am including he e e ence ec o and i s componen s is shown in o de o demons a e ha he p oposed e e ence ec o de ini ion is co ec and ha he de ined e e ence ec o is loca ed inside he app op ia e selec ion a ea. Fo ins ance, he e e ence ec o in he selec ion a ea A1 is de ined as ollows, whe e k1 and k2 a e de ined as posi i e alues, ensu ing ha he e e ence ec o is loca ed inside he selec ion a ea A1. 12 eq k kJ abababab dd D =+×+ (15) Fig. 6 shows how e e ence ec o d ab is composed, and shows ha a e e ence ec o de ined as (15) is always inside he selec ion a ea A1. Due o his ac he p oposed e e ence ec o p o ides he necessa y con ol ac ion o achie e he con ol objec i es, i.e., o educe he ins an aneous ac i e powe and o educe he ins an aneous eac i e powe d awn om he g id. ab d eq ab d ab k 1 ab J k 2 0 0 p q < < & & 0 0 p q > < & & 0 0 p q < > & & 0 0 p q > > & & 0 p ab d = & 0 q ab d = & a b ab Fig. 6 Re e ence ec o o selec ion a ea A1. Using he same concep s i is possible o de ine he e e ence ec o d ab o each a ea. The p oposed algo i hm o calcula e he e e ence ec o has he ollowing s eps: 1) Calcula e ~ p, and ~ q. 2) Se he selec ion a ea. 3) Calcula e he e e ence ec o Table 4 summa izes he p oposed algo i hm o calcula e he e e ence ec o . TABLE 4 REFERENCE VECTOR DEFINITION AS A FUNCTION OF THE SELECTION AREA. 1s S ep 2º S ep 3º S ep ~ p ~ q Selec ion A ea Re e ence Vec o >0 >0 A1 12 eq k kJ abababab dd =+×+ >0 <0 A2 12 eq k kJ abababab dd =+×- <0 >0 A3 12 eq k kJ abababab dd =-×+ <0 <0 A4 12 eq k kJ abababab dd =-×- Re e ence Vec o de ini ion in Table 4 can be w i en in a single equa ion, educing he algo i hm compu a ional cos , i k1 and k2 alues a e espec i ely de ined as > REPLACE THIS LINE WITH YOUR PAPER IDENTIFICATION NUMBER (DOUBLE-CLICK HERE TO EDIT) < 5 1 2 p q kkp kkq D D =× =× % % (16) kp and kq a e de ined as a nonze o posi i e cons an s, and he p oposed e e ence ec o can be calcula ed independen ly o he selec ion a ea. eq pq kp kqJ abababab dd D =+××+×× %% (17) Con olle (17) in closed-loop wi h he sys em dynamics (7)- (8) p o ides he ollowing equa ions 2 2 2 2 dc p dc q V Lp kp V Lq kq ab ab =-××× =-××× &% &% (18) Taking in o accoun ha in s eady s a e he ins an aneous ac i e and eac i e e e ence powe a e cons an s hen * * 0 0 dp Ld dq Ld = = (19) 2 2 0 2 0 2 dc p dc q V Lp kp V Lq kq ab ab +×××= +×××= & %% & %% (20) Equa ions (20) demons a e ha using he p oposed e e ence ec o , he ins an aneous ac i e and eac i e powe e o s end exponen ially o ze o and he sys em is s able. Now an adap i e law wi h he aim o elimina e he e ec s o he sys em pa ame e s unce ain ies, he smoo hing induc o and he g id equency alue, is de i ed. In he h ee-phase powe con e e he eac ance pa ame e , X, is he p oduc o he smoo hing induc o alue and he g id equency. XL w D = (21) ˆ XXX =- % (22) ˆ XX = & & % (23) Equa ion (22) de ines he e o be ween he ac ual alue o he eac ance and i s es ima ed alue ^ X. Taking in o accoun ha pa ame e X is assumed o be cons an o slowly a ian , equa ion (23) de ines he e o ime de i a e. 22 ˆˆ 22 ˆ 1 eq dcdc XqXp J VV ababab abab d æöæö ×× ç÷ç÷ =+- ç÷ç÷ èøèø (24) ˆeq pq kp kqJ abababab dd =+××+×× %% (25) Equa ion (24) is he exp ession o d eq ab as a unc ion o he es ima ed pa ame e alue, and he p oposed con olle o he h ee-phase powe con e e is ans o med in (25), in oducing he new p oposed con olle in (7) and (8), he exp essions o he powe e o s dynamics a e de i ed. ( ) 2 ˆ 2 dc p V Lp kpqXX ab =-×××+×- & %% (26) ( ) 2 ˆ 2 dc q V Lq kqpXX ab =-×××-×- & %% (27) To de i e an adap i e law o econs uc pa ame e ^ X a Lyapuno app oach is ollowed. Fo his pu pose a posi i e- de ini e unc ion is p oposed, whe e pa ame e g is a posi i e cons an ha ep esen s he adap a ion gain. 222 111 222 HLpLqX g =++ × % %% (28) 22 22 1 22 dcdc pq VV H kp kqXpqqpX abab g æö =--+-+ ç÷ èø & &%% %%%% (29) ( ) ˆ Xqppq g =×-× & %% (30) 22 22 22 dcdc pq VV H kp kq abab =-×××-××× & %% (31) The ime de i a e o (28) along he ajec o ies o (26) and (27) is (29) which is made nega i e semide ini e by p oposing (30) o econs uc he pa ame e ^ X. Finally he ime de i a e is gi en by (31). Following Lasalle´s heo em a gumen s i can be s a ed ha ~ p → 0 and ~ q → 0 as → ∞ asymp o ically. Mo eo e , om (30) ~ p ≡ 0 and ~ q ≡ 0 imply ha ~ X is cons an . Acco ding o (26) and (27) his cons an should be ze o. This gua an ees con e gence o he es ima ed alue owa ds i s ac ual alue. Now aking in o accoun ~ p and ~ q de ini ions and ha q* is ze o wi h he aim o achie e uni y powe ac o , he pa ame e ^ X can be econs uc ed using exp ession * ˆ Xqp g =-×× & (32) B. Vol age egula ion loop The ou e con ol loop is designed o egula e he ou pu capaci o ol age, his ol age should be main ained equal o he DC-Vol age e e ence alue * dc V . The ol age capaci o dynamic is de ined by (2), and assuming ha ins an aneous powe dynamics a e much as e han DC-Vol age dynamic hen i is possible o a i m ha * pp @ and 0 q @ , and he e o e (2) can be educed o 22 2 T dcdc L VV d C i d R abab æö ×=- ç÷ èø (33) F om Akagi´s powe heo y he ins an aneous ac i e powe is de ined as T p i abab = so he DC-Vol age dynamic equa ion can be w i en as 22 2 æö ×=- ç÷ èø dcdc L VV d Cp d R (34) Now, in o de o educe no a ion, wo new a iables a e de ined as ollows 2 2 D = dc V z (35) * D =- % zzz (36) whe e z % ep esen s he e o and * z is he new e e ence de ined as ( ) 2 * * 2 =dc V z (37) > REPLACE THIS LINE WITH YOUR PAPER IDENTIFICATION NUMBER (DOUBLE-CLICK HERE TO EDIT) < 6 ( ) 2 2 * dc V * p * 0 q = p ˆ eq ab d ab d s K b s aK i p+ + q kJ ab p k ab 2 2 dc V q 22 ˆˆ 22 1 dcdc XqXp J VV abab abab æöæö ×× ç÷ç÷ +- ç÷ç÷ èøèø * qpd g -× ò X ˆ p Fig. 7 Block diag am o he p oposed DPC con olle . and in oducing hese news a iables in (34) () ( ) 2 * 2dc LL V dz Czp d RR -×=+- % % (38) No ice ha (38) is a simple i s -o de s able sys em, so a p opo ional plus in eg al con olle would sol e he p oblem since he pe u ba ion is an unknown cons an . Finally he p oposed PI con olle o he ou e con ol loop is *p i s K K pzz ss =+ + %% (39) whe e Kp, Ki and s a e design pa ame e s and p*is he e e ence alue o he ins an aneous ac i e powe . This con olle includes a low pass il e in he p opo ional e m o educe he high equency noise. Summa izing, he inal exp essions o he p oposed con olle a e gi en by he ollowing equa ions. (i) Powe acking loop. * 22 * * * ˆ ˆˆ 22 ˆ 1 ˆ 0 eq dcdc eq pq Xqp XqXp J VV kp kqJ ppp qqq q ababab abab abababab g d dd =-×× æöæö ×× ç÷ç÷ =+- ç÷ç÷ èøèø =+××+×× =- =- = & %% % % (40) (ii) Vol age egula ion loop. * * p i s K K pzz ss zzz D =+ + =- %% % (41) Fig. 7 shows he block diag am o he p oposed DPC con olle including he adap i e law. I. EXPERIMENTAL RESULTS In his sec ion expe imen al esul s a e shown in o de o es he p oposed con olle using a p o o ype. Fo his pu pose he h ee-phase wo-le el powe con e e o Fig. 8a has been de eloped, wi h a digi al implemen a ion o he con ol algo i hm ha has been execu ed in a TMS320VC33 loa ing poin DSP homemade boa d. The expe imen consis s o a load s ep a DC-Link om no-load o ull load o 9.375kW. Fo his pu pose capaci o ol age e e ence has been es ablished o 750V and a 60 Ohm esis i e load (Fig. 8b) has been suddenly connec ed o he DC-Link. To assess he DPC con olle wi h he adap i e law app oach, a compa a i e wi h he DPC con olle wi hou he adap i e law has been ca ied ou . Measu emen s o DC-Link ol age, phase ol ages and cu en s, ha monic con en s o cu en s, ac i e powe , eac i e powe and powe ac o , ha e been aken wi h a Fluke 434 powe quali y analyze . Table 5 shows he elec ical pa ame e s o he powe con e e , DC-Link ol age e e ence, swi ching and sampling equencies ha ha e been used in he expe imen al se up. Fig. 8 Labo a o y p o o ype, om le o igh : a) Th ee-phase wo le el powe con e e . b) Resis i e load o 60 W > REPLACE THIS LINE WITH YOUR PAPER IDENTIFICATION NUMBER (DOUBLE-CLICK HERE TO EDIT) < 7 TABLE 5 ELECTRICAL AND CONTROL PARAMENTERS FOR THE EXPERIMENTAL SYSTEM. Pa ame e Desc ip ion Phase- o-neu al Vol age 230 V Smoo hing induc ance 0.8 mH DC-Link capaci o 7050 µF Resis i e load 60Ω DC-Link Re e ence Vol age 750 V Swi ching equency 11.2 KHz Sampling equency m 22.4 kHz All he cons an s used in he p oposed con olle ha e been adjus ed expe imen ally. This includes, Kp and Ki o he ol age egula ion loop, kp and kq ha p o ide he necessa y damping o he con olle , and he adap a ion gain g. A. T ansien beha io Fig. 9 shows DC-Link ol age ansien alue when load s ep om ze o o ull load (9.375kW) is applied o DC-Link. Fig. 9a shows ansien esponse when he p oposed non- adap i e DPC con olle is applied and Fig. 9b when he p oposed adap i e DPC con olle is used. I can be no iced ha in bo h cases he ansien esponse is simila . DC-Link ol age only dec eases 15 V a e he load is connec ed, and i s e e ence is achie ed again only in 0.6s a e he load change, so a good ol age egula ion is ensu ed. Fig. 9 DC-Link ansien ol age du ing load s ep om ze o o ull load. a) o he p oposed non-adap i e DPC con olle . b) o he p oposed adap i e DPC con olle Fig. 10 Ins an aneous ac i e powe ansien esponses when load s ep occu s, om 50 % o ull load, o g = 1e-6. F om op o bo om: a) Ins an aneous ac i e powe e e ence. b) Ins an aneous ac i e powe e o . Fig. 10 shows he ins an aneous ac i e powe ansien esponse when a load s ep om 50% o ull load occu s. F om expe imen s i is obse ed ha he adap a ion gain pa ame e does no ha e in luence in he dynamic and he beha io o he ins an aneous ac i e powe , o his eason only he ansien esponse when g = 1e-6 is shown. Fig. 10a shows he ins an aneous ac i e powe e e ence alue and Fig. 10b he ins an aneous ac i e powe e o when he p oposed adap i e DPC con olle is used. Compa ed wi h classic DPC, he ansien beha io is qui e simila , due o when a load s ep akes place he alues o ~ p and ~ q become high and he ou pu o he con olle (40) is e y close o he ec o chosen by he classic DPC. In Fig. 11 a possible case, when p* and q* suddenly dec ease, is shown. ab d eq ab d p kp ab % q kqJ ab % 0 p ab d = & 0 q ab d = & a b ab Fig. 11 Compa ison be ween he e e ence ec o s ob ained wi h he Classic DPC (□) and he p oposed DPC (○) when he ac i e and eac i e ins an aneous powe e e ences dec ease suddenly. Fig. 12 Ins an aneous eac i e powe ansien esponses when load s ep occu s, om 50 % o ull load, o di e en alues o g. F om op o bo om: a) g = 0. b) g = 1e-8. c) g = 1e-6. Fig. 13 Es ima ed alue ansien esponses when load s ep occu s, om 50 % o ull load, o di e en alues o g. F om op o bo om: a) g = 1e-8. b) g = 1e-6. Fig. 12 shows he ins an aneous eac i e powe ansien esponse when a load s ep om 50% o ull load occu s. I can be no iced ha he p oposed adap i e DPC con olle pe mi s > REPLACE THIS LINE WITH YOUR PAPER IDENTIFICATION NUMBER (DOUBLE-CLICK HERE TO EDIT) < 8 o educe he eac i e powe consump ion. Fig. 12a shows he ins an aneous eac i e powe when he p oposed non-adap i e DPC is used, Fig. 12b and Fig. 12c show ins an aneous eac i e powe when he p oposed adap i e DPC is used o di e en alues o he adap a ion gain. Fig. 13 shows he es ima ed alue ansien esponse when a load s ep om 50% o ull load occu s. I can be no iced ha ^ X ipple inc eases when he adap a ion gain is high. In he expe imen s i is obse ed ha highe alues o g lead o highe ipples ha make sys em uns able. Howe e , he eac i e powe consump ion is lowe as g inc eases. The e o e, due o his ac he adap a ion gain has o be chosen as high as possible bu aking in o accoun he possible sys em ins abili y. B. S eady s a e beha io Fig. 14(a,b) shows he phase cu en s achie ed wi h he p oposed non-adap i e DPC con olle , i can be no iced ha low cu en s dis o ion is achie ed, in ac i s o al ha monic dis o ion alue (THD) is 3.0% (Fig. 15a). Howe e he cu en is leading he ol age and he powe ac o alue is 0.99 capaci i e as can be seen in Fig. 15b. Fig. 14 Phase ol ages and cu en s o he p oposed non-adap i e DPC con olle . Le o Righ : a) Phase c ol age and cu en . b) a, b and c phase cu en . Fig. 15 F om op o bo om: a) Cu en s ha monic con en o he p oposed non-adap i e DPC con olle . b) Ac i e and eac i e powe and powe ac o o he p oposed non-adap i e DPC con olle . Fig. 16(a,b) shows he phase cu en s deli e ed by he powe con e e when he p oposed adap i e DPC con olle is used. I can be no iced ha in spi e o he limi ed smoo hing induc ance alue (0.8mH) he cu en ipple is small and he cu en THD is only 3.2% (Fig. 17a). Mo eo e compa ed wi h he phase cu en s achie ed wi h he non-adap i e DPC con olle he ha monic con en o cu en s is o he same o de . Besides uni y powe ac o alue is achie ed as can be seen in Fig. 17b. Due o his ac less eac i e powe is d awn om he g id, eac i e powe is d as ically educed in 75% ( om 1.14 kVA in Fig. 15b o 0.3 kVA in Fig. 17b) and be e pe o mance is achie ed wi h he same powe con e e . Fig. 18a shows he ec o diag am wi h he p oposed non- adap i e DPC con olle and Fig. 18b shows he ec o diag am wi h p oposed adap i e DPC con olle . I can be seen ha due o pa ame e s unce ain ies when he non-adap i e con ol law is used ol ages and cu en s a e shi ed (Fig. 18a). Howe e , when he adap i e solu ion is adop ed, hese pa ame e s unce ain ies a e a oided and ol age and cu en s a e in phase almos pe ec ly (Fig. 18b), showing he g ea ad an age o using adap i e con ol echniques. Fig. 19 shows he ins an aneous eac i e powe alue in s eady s a e o di e en alues o g. As i was p esen ed in Fig. 12 o ansien ope a ion, he eac i e powe consump ion dec eases when g inc eases. Fig. 16 Phase ol ages and cu en s o he p oposed adap i e DPC con olle (g = 1e-6). F om op o bo om: a) Phase c ol age and cu en . b) a, b and c phase cu en . Fig. 17 F om op o bo om: a) Cu en s ha monic con en o he p oposed adap i e DPC con olle (g = 1e-6). b) Ac i e and eac i e powe and powe ac o o he p oposed adap i e DPC con olle (g = 1e-6). > REPLACE THIS LINE WITH YOUR PAPER IDENTIFICATION NUMBER (DOUBLE-CLICK HERE TO EDIT) < 9 Fig. 18 Vec o diag am. F om le o igh : a) Vec o diag am o he p oposed non-adap i e DPC con olle . b) Vec o diag am o he adap i e DPC con olle (g = 1e-6). Fig. 19 Ins an aneous eac i e powe s eady s a e alues o ull load and di e en alues o g. F om op o bo om: a) g = 0. b) g = 1e-8. c) g = 1e-6. II. CONCLUSIONS DPC s a egies a e simple and e icien con ol s a egies ha can be applied o powe sys ems as powe ec i ie s allowing he use o low cos mic op ocesso s o hei implemen a ion. Howe e , some d awbacks associa ed o he high g id connec ion induc ance alue a e p esen in his ype o con ol echniques. The p oposed DPC s a egy based on he sys em model pe mi s o make smoo h he high gain o p e ious DPC echniques and consequen ly, pe mi s o dec ease he smoo hing connec ion induc ance alue educing he cos , size and weigh o he o al sys em and inc easing he ope a ion ange o he powe con e e and imp o ing he dynamics o he sys em. Expe imen s wi h a h ee-phase wo- le el labo a o y p o o ype ha e been ca ied ou o illus a e he good pe o mance o he p oposed con ol echnique. Besides, adap i e echniques ha e been applied o o e come p oblems associa e wi h sys em pa ame e s unce ain ies, which leads he p oposed con olle o achie e uni y powe ac o , p o iding a be e pe o mance o he o e all sys em. 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