Controller design for a single-phase two-cell multilevel cascade H-bridge converter

Con olle Design o a Single-Phase Two-Cell Mul ile el Cascade H-B idge Con e e S. Vazquez; J.I. Leon; J.M. Ca asco; L.G. F anquelo; E. Gal an; J.A. Sanchez; E. Domínguez A da. De los descub imien os s/n; Escuela Supe io de Ingenie os; Uni e si y o Se ille; Se ille 41092; SPAIN Email: s azquez@g e.esi.us.es; gal an@g e.esi.us.es; ca asco@g e.esi.us.es; lg [email protected] g; egal [email protected]; shanshe@g e.esi.us.es; buge@g e.esi.us.es Abs ac - In his pape is s udied he single-phase wo-cell mul ile el cascade H-b idge powe con e e connec ed o he g id, ac ing as a synch onous ec i ie . The powe exchange p ocess be ween he cells o he con e e and he g id is analyzed. Based on his analysis and on he powe con e e model he s ages o he con olle design p ocess a e shown. A new con olle o he cascade powe con e e is p oposed, achie ing he egula ion o each DC-Link capaci o ol age owa ds i s e e ence. The p oposed con olle includes a epe i i e scheme in he cu en acking loop, p o iding low cu en ha monic con en and almos uni y powe ac o . Simula ion esul s ha e been ca ied ou in a 10 kVA single-phase wo-cell mul ile el cascade H-b idge powe con e e model o illus a e he good pe o mance o he p oposed con olle . Index Te ms— Mul ile el con e e , powe quali y, non-linea con ol. I. INTRODUCTION Mul ile el cascade con e e s, also named cascaded H- b idge con e e s, we e i s p esen ed in 1988 [1]. Since hen hey ha e been a ocus o esea che s because hey p esen se e al ad an ages compa ed wi h o he mul ile el con e e opologies in e ms o modula i y, simplici y and numbe o le els wi h minimum numbe o powe semiconduc o s [2]-[4]. Di e en applica ions ha e been de eloped using he mul ile el cascade con e e : Synch onous ec i ie s [5], enewable ene gy in eg a ion sys ems [6], in e e s [7], S a coms [8] and ac i e il e s [9]. Fo each applica ion, speci ic con ol s a egies ha e been designed, being he DC- Link ol ages con ol he mos impo an challenge in his powe con e e opology. The DC-Link ol ages con ol p oblem is no a i ial issue in he cascaded mul ile el opology. As in o he mul ile el con e e s, he ol ages con ol ask can be app oached h ough modula ion o as a pa o he sys em con olle . When he modula ion is used o con ol he ou pu ol ages, he edundan ou pu s a es o he con e e a e used. In [10] his ac is used o egula e he ou pu s ol ages o he same e e ence alue. When he con ol app oach is used, a speci ic con ol has o be designed o ca y ou he ol ages con ol ask. Due o his mul iple signals a e needed, one o each H- b idge, making he con olle design mo e complex. Howe e he ad an age is ha he ou pu ol age e e ences can be se independen ly. Se e al s a egies o achie e he ol age balance can be ound in he li e a u e such as a passi i y con ol s a egy [11], non-linea con ol s a egy [12], and s a egies based on PI con olle s [13]. In his pape he con olle app oach will be conside ed. To de elop he con olle design he powe exchange p ocess be ween he cells o he cascade con e e and he g id is analyzed. F om his analysis, he powe low limi s as a unc ion o he ou pu ol age alues will be poin ed ou , and inally he con olle exp ession is de i ed. II. SYSTEM DESCRIPTION A single-phase wo-cell mul ile el cascade H-b idge powe con e e (CHB) is depic ed in Fig. 1. The sys em is connec ed o he g id h ough a smoo hing induc o L, and i is assumed ha pu e esis i e loads R1 and R2 a e connec ed o each DC- Link capaci o C1 and C2 espec i ely. The sys em pa ame e s and a iables a e desc ibed in TABLE I, whe e he con inuous con ol signals d1 and d2, which ep esen he swi ching unc ions ha e been de ined. 1 S 1 S 2 S 2 S 4 S 4 S 3 S 3 S Fig. 1 Single-phase wo cell mul ile el cascade H-B idge con e e TABLE I SYSTEM PARAMETERS Pa ame e Desc ip ion L Induc ance C1; C2 Capaci ances R1; R2 Resis i e loads is( ) G id cu en s( ) G id ol age iR1; iR2 Load cu en s Vdc1; Vdc2 Capaci o ol ages d1;d2 ò [−1, 1] Con ol signals The equa ions ha desc ibe he CHB beha io a e well known and hey ha e been epo ed in se e al p e ious wo ks [14], hese equa ions a e m11dc1 V =d (1) m22dc2 V =d (2) s sm1m2 di L d =++ (3) 22 dc1dc1 m1s1 1 2 VV d iC d R æö =+ ç÷ èø (4) 22 dc2dc2 m2s1 2 2 VV d iC d R æö =+ ç÷ èø (5) In hese equa ions he con ol signals m1 and m2 de ined in (1) and (2) ha e been in oduced. These signals ep esen he ol ages ha a e modula ed in each cell. The equa ion ha ep esen s he inpu cu en dynamic is (3) and he ou pu capaci o DC ol ages dynamics a e (4) and (5). To analyze he con olle design s ages, he powe exchange be ween he cells o a cascade con e e and he g id has o be s udied. Fo his pu pose he powe con e e ep esen a ion o Fig. 2 is used. In his ep esen a ion he cells ha e been eplaced by ol age sou ces wi h alues equal o he ins an aneous ol ages modula ed by he cells, m1 and m2 espec i ely. The ac i e and eac i e powe consumed o injec ed by each cell depend on he shi angle be ween he cu en is, and he modula ed ol age in he cell ( mi). This can be analyzed using he phaso ial diag am o he cascade powe con e e ep esen ed in Fig. 3. Now he ollowing assump ions a e made: (i) The ol ages dc1 and dc2 a e lowe han he peak alue o s (ii) Cell 1 and cell 2 consume ac i e powe , and no eac i e powe is d awn om he g id. Fig. 2 CHB ep esen a ion h ough ol age sou ces Fig. 3 CHB phaso ial diag am o ol ages and cu en Fo a gi en powe consump ion p1 and p2 in each DC-Link, he heo e ical e e ence ol ages o each H-b idge can be de e mined. The o al amoun o ac i e powe ha has o be d awn om he g id is T1212 ;0;0 ppppp =+>> (6) The necessa y g id cu en and he associa ed induc o d op ( L) can be hen calcula ed and he e o e he ol age ha should be modula ed be ween he poin s ab o he con e e can be de e mined. T ss 2 sRMS p i = (7) s L d di L= (8) absL =- (9) The ol age ab is composed by he sum o he ou pu ol age o he cells, m1 and m2. Fo his eason, he DC-Link capaci o ol age alues a e cons ain s ha should be conside ed when he load is applied, because only ce ain phaso s composi ions a e allowed. Fig. 4 shows he phaso s o all ol ages in ol ed. The se o poin s ha can be eached o a gi en DC-Link capaci o ol age alues is ep esen ed using a ma ke egion. An example o alid poin is shown in Fig. 4a. Any poin ou side o his egion would make he sys em uns able because he e e ence ol age o one cell o bo h can no be modula ed wi h he ac ual alues o he DC-Link capaci o ol ages as is shown in Fig. 4b. 1 > 0 ; 2>0 s s ab dc1 dc2 m1 m2 ds d s s ab dc1 dc2 m1 m2 ds d a b Fig. 4 Re e ence ol age be ween poin s ab. a) Solu ion inside he eachable egion b) Solu ion ou side he eachable egion Fo a gi en o al amoun o powe pT, he alues o powe ha can be consumed in each cell can no be chosen eely. Fig. 5a and Fig. 5b show he minimum alue o ac i e powe ha should be consumed in cell 1 and cell 2 espec i ely, o main ain he sys em s abili y. Among he possible solu ions, only hose poin s whe e he ac i e powe consumed by each cell co esponds wi h p1 and p2 espec i ely a e alid solu ions o he sys em. Fo ins ance, om p1 i is possible o calcula e he p ojec ion o m1 o e is as 1 m1p s RMS p i = (10) 1 > 0 ; 2>0 s s ab dc1 dc2 m1p m2p ds d s s ab dc1 dc2 m1p m2p ds d a b Fig. 5 Minimum alues o ac i e powe mus be consumed by he cells o a consumed o al amoun o ac i e powe pT. a) Minimum alue o p1. b) Minimum alue o p2 This ac leads o calcula e he alue o he p ojec ion o m2 o e is, and o de e mine he possible poin s o ob ain a alid solu ion. These poin s a e loca ed o e he line o hogonal o s placed a dis ance m1p om he o igin. The alid solu ions a e he poin s which simul aneously belong o ha line and a e inside he se o poin s ha can be eached wi h he DC ol age alues in cell 1 and 2. Fig. 6 shows he se o possible solu ions o powe consump ion p1 and p2, which a e loca ed be ween he poin s MN. m1p m2p M N 1>0 ; 2>0 ds d ab s s dc1 dc2 Fig. 6 Se o possible solu ions o p1 and p2 I is wo h poin ing ou ha he e is no a single solu ion o he sys em. The only es ic ion is ha he solu ion has o be loca ed be ween poin s MN, and he e o e he e is one deg ee o eedom which can be used o op imize he con e e beha io and design. Fig. 7 shows wo possible solu ions o he sys em. Bo h solu ions lead o he same esul d awing ac i e powe p1 and p2. The only di e ence is he eac i e powe alue deli e ed o consumed by each cell. III. CONTROLLER DESIGN To design he con olle wo ac s mus be conside ed, he o al ol age egula ion and he ol ages a io. The o al ol age egula ion is ela ed wi h he sum o he DC-link capaci o ol ages, and he ol ages a io is de ined as he a io be ween he DC-link capaci o ol ages o he cells o he con e e , meaning o ins ance ha i DC ol age a io is k:1 in a wo- cell CHB, hen dc1=k· dc2. 1 > 0 ; 2>0 s s ab dc1 dc2 m1p m2p m1 m2 ds d s s ab dc1 dc2 m1p m2p m1 m2 ds d a b Fig. 7 Two possible solu ions o achie e he same ac i e powe consump ion p1 and p2 in each cell espec i ely. Fo he con ol law design, i is assumed ha he swi ching equency is high enough o conside he con ol signal as a con inuous signal. Due o his ac he a e aged model o he sys em can be used o de elop he con olle . Also i is assumed ha he cu en dynamic is as e han he ol age egula ion and a io dynamics o a CHB con e e . Finally he con ol design is spli in h ee s ages: (i) Vol age egula ion con ol loop, which ensu es capaci o ol age egula ion owa ds i s e e ence. The ou pu o his loop is he cu en e e ence. (ii) Cu en con ol loop, which ensu es induc o cu en acking owa ds i s e e ence. The ou pu o his con olle is he con ol signal u= m1+ m2. (iii) Vol age a io con ol loop, which ensu es capaci o ol age a io owa ds i s e e ence. The ou pu o his con olle a e he con ol signals m1 and m2. The con ol objec i es a e: (i) Regula e he capaci o ol ages o he desi e alues V* dc1 and V* dc2 (ii) Achie e induc o cu en wi h high quali y ha monic con en and main ain he powe ac o as close o uni y as possible. A. Vol age egula ion con ol loop The a e aged pa o equa ions (4) and (5) can be used o ob ain he necessa y inpu ac i e powe o egula e he DC- Link ol ages. 2 dc1 1 2 dc2 2 2 2 V z V z = = (11) In oducing he a iables z1 and z2, equa ions (4) and (5) a e ans o med in 11 11 1 2 dzz pC d R =+ (12) 22 22 2 2 dzz pC d R =+ (13) Equa ions (12) and (13) a e well-known LTI sys ems, hus he alues o p1 and p2 can be calcula ed h ough a PI con olle as in [15], yielding o he ollowing exp essions p1 i1 111 s1 kk pzz ss =+ + %% (14) p2 i2 222 s2 kk pzz ss =+ + %% (15) Con olle s (14) and (15) include a low pass il e in he p opo ional e m o educe he high equency noise, he pa ame e s kp1, 1, ki1, kp2, 2 and ki2 a e design posi i e non- ze o cons an s and he e o and he e e ences alues a e calcula ed as ( ) ( ) 1 2 * 111 * 222 2 * dc1 * 2 * dc2 * 2 2 zzz zzz V z V z =- =- = = % % (16) The o al amoun o ac i e powe ha he ol age sou ce should p o ide is he sum o p1 and p2, and hen he cu en e e ence can be calcula ed as ( ) 12 * RMS RMS ** s RMS RMS pp i ii + = = (17) B. Cu en con ol loop Equa ion (3) ep esen s he induc o cu en dynamic, o simpli y he con ol design p ocess he con ol signal u is de ined as m1m2 u =+ (18) Thus he induc o cu en dynamic is ans o med in s s di Lu d =+ (19) Equa ion (19) is equal han he cu en dynamic equa ion o he single-phase H-B idge con e e and he h ee-phase wo- le el powe con e e . Se e al linea and non-linea con olle s ha e been p oposed o achie e he cu en acking in hose powe con e e s, in [16]-[17] a epe i i e con ol scheme is p oposed o he cu en acking p ocess, and in his wo k he same solu ion is adop ed. spcs s 1 1 s s Ke u kiki Ke p - w p - w æö -× ç÷ =+×+ ç÷ ç÷ +× èø %% (20) * sss iii =- % (21) The pa ame e s kpc, k and K a e posi i e non-ze o design cons an s. Equa ion (20) is he exp ession o he con ol signal u and (21) is he cu en e o de ini ion. In (20) he p opo ional e m adds damping o he con olle o ensu e s abili y and he epe i i e e m ep esen s an es ima ion o * L. * * L s di L d = (22) C. Vol age a io con ol loop As i is shown in sec ion II, he ol age modula ed by each cell ( mi) oge he wi h he g id cu en mus p o ide he ac i e powe and he eac i e powe demanded by he cell. The ac i e powe demand is sa is ied when he p ojec ion o m1 and m2 o e is a e de ined espec i ely as s 1 m1p * RMS RMS p i =× (23) s 2 m2p * RMS RMS p i =× (24) Besides, o achie e uni y powe ac o he eac i e powe deli e ed by he cells mus be equal o he eac i e powe demanded by he smoo hing induc o . In addi ion, o ensu e cu en acking (20) mus be sa is ied. To ca y ou all hese cons ain s he e e ence ol ages in each cell a e de ined as m1m1ppc1s1 s 1 1 s s Ke kikki Ke p - w p - w æö -× ç÷ =+×+ ç÷ ç÷ +× èø %% (25) m2m2ppc2s2 s 1 1 s s Ke kikki Ke p - w p - w æö -× ç÷ =+×+ ç÷ ç÷ +× èø %% (26) whe e he ollowing es ic ion mus be sa is ied 12 1 kk += (27) pc1pc2pc kkk += (28) whe e he pa ame e s kpc1, k pc2, k1 and k2 a e posi i e non- ze o design cons an s. The cons ans k1 and k2 ep esen how he eac i e powe is sha ed be ween he cells. IV. SIMULATION RESULTS In his sec ion simula ion 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 single-phase wo-cell mul ile el cascade H-b idge powe con e e has been conside ed. The expe imen consis s o a load s ep om no-load o ull load, including di e en capaci o ol ages e e ence. To modula e he e e ence ol age a phase-shi ed PWM s a egy has been used. To assess he con olle pe o mance, measu emen s o DC-Link capaci o ol ages, g id ol age and cu en s a e ep esen ed. TABLE II shows he elec ical pa ame e s o he powe con e e , swi ching and sampling equencies ha ha e been used in he model. Fig. 8 shows he ob ained esul s o he comple e expe imen pe iod. The expe imen has h ee s eps. In he i s s ep, he DC-Link capaci o ol age e e ences a e se o 200V in bo h cells. Once he e e ence is achie ed, a load s ep is in oduced connec ing a 20W esis o in each DC-Link. TABLE II ELECTRICAL PARAMETERS OF THE SYSTEM G id Vol age 230 V G id equency 50 Hz Smoo hing induc ance 1 mH DC-Link capaci o C1 4700 µF DC-Link capaci o C2 4700 µF Swi ching equency 10 KHz Sampling equency m 10 kHz The second s ep is ca ied ou when he s eady s a e is eached, and hen he DC-Link capaci o ol age e e ence o he cell 1 is se o 300V. Finally, he hi d s ep is in oduced when cell 1 achie es i s e e ence, in his momen he DC-Link capaci o ol age e e ence o cell 2 is se o 100V. As i can be seen in Fig. 8 he p oposed con ol s a egy is capable o egula e each DC-Link capaci o ol ages o he desi ed alues, and o con ol he g id cu en . F om Fig. 9 and Fig. 10 i is demons a ed ha he p oposed con olle has good pe o mance in ansien and s eady s a e condi ions when a load s ep is applied. When a e e ence DC ol age s ep is applied in any cell he same good beha io is ob ained as is shown in Fig. 11 and Fig. 12. Fig. 9a shows he DC-Link capaci o ol ages ansien esponse when he loads a e connec ed and he ol age e e ences a e 200V. Fig. 9b shows he co esponding g id cu en and ol age. Fig. 10a shows he DC-Link capaci o ol ages in s eady s a e. I can be no iced ha he e e ences a e achie ed, he 100 Hz ipple in he ol ages is due o he ac i e powe consump ion. Fig. 10b shows he g id ol age and cu en in s eady s a e. I can be obse ed ha he g id cu en has high quali y and is almos in phase wi h he g id ol age. Fig. 11a shows he DC-Link capaci o ol ages ansien esponse when he e e ence o cell 1 is changed om 200V o 300V and he e e ence o cell 2 is main ained in 200V. I can be no iced ha in a ew g id cycles he e e ence is achie ed, and he ol age in cell 2 is almos no a ec ed by he e e ence change in cell 1. In Fig. 11b i can be obse ed ha he g id cu en inc eases un il he DC-Link capaci o ol age is s abilized in he new e e ence alue. Fig. 12 shows simila esul compa ed wi h Fig. 11 when he e e ence o he cell 2 is changed om 200V o 100V and he e e ence o he cell 1 is main ained in 300V. V. CONCLUSIONS In his pape a single-phase wo-cell mul ile el cascade H- b idge powe con e e connec ed o he g id, ac ing as a synch onous ec i ie is s udied. F om he analysis o he powe exchange p ocess be ween he cells o he con e e and he g id, i is demons a ed ha o a gi en o al ac i e powe consump ion he ac i e powe sha ing be ween he cells can no be chosen eely. The con olle design s ages a e shown, and ollowing hese s ages a con olle is p oposed, using in he cu en acking loop a epe i i e con ol scheme. Simula ion esul s ha e been de eloped and i has been e i ied ha he p oposed con olle p o ides DC-Link capaci o ol ages egula ion and a io con ol. Besides he p oposed epe i i e scheme p o ides cu en wi h low ha monic con en and also i is capable o achie e almos uni y powe ac o , p o iding a e y good pe o mance o he o e all sys em. Fig. 8 Cu es o he comple e expe imen pe iod. a) dc1 and dc2 b) is Fig. 9 Capaci o ol ages and g id cu en ansien s wi h DC ol age e e ences equal o 200V o bo h cells. a) dc1 and dc2 b) s, and is Fig. 10 Capaci o ol ages and g id cu en de ails in s eady s a e, wi h DC ol age e e ences equal o 200 V o bo h cells. a) dc1 and dc2 b) s, and is Fig. 11 Capaci o ol ages and g id cu en ansien s wi h DC ol age e e ences equal o 300V o cell 1 and 200 V o cell 2. a) dc1 and dc2 b) s, and is Fig. 12 Capaci o ol ages and g id cu en ansien s wi h DC ol age e e ences equal o 300V o cell 1 and 100 V o cell 2. a) dc1 and dc2 b) s, and is ACKNOWLEDGMENT This wo k has been de eloped hanks o he inancial suppo o Spanish Go e nmen wi hin he esea ching p ojec TEC2006-03863. REFERENCES [1] M. Ma chesoni, M. Mazzucchelli and S. Tenconi, “A non Con en ional Powe Con e e o Plasma S abiliza ion,” in Powe Elec onics Specialis Con e ence 1988 (PESC’88), pp. 122–129, 11-14 Ap il 1988. [2] J. Rod iguez, Jih-Sheng Lai and Fang Zheng Peng, “Mul ile el in e e s: a su ey o opologies, con ols, and applica ions”, IEEE T ansac ions on Indus ial Elec onics, Volume 49, Issue 4, pp. 724 – 738, Augus 2002. [3] Y. Cheng, C. Qian, M.L. C ow, S. Peka ek and S. A ci y, "A Compa ison o Diode-Clamped and Cascaded Mul ile el Con e e s o a STATCOM Wi h Ene gy S o age," IEEE T ansac ions on Indus ial Elec onics, ol. 53, no. 5, pp. 1512-1521, Oc obe 2006. [4] M.E. O uza , R.E. Ca mi, J.W. Dixon and L. Mo an, "Vol age-sou ce ac i e powe il e based on mul ile el con e e and ul acapaci o DC link," IEEE T ansac ions on Indus ial Elec onics, ol. 53, no. 2, pp. 477- 485, Ap il 2006. [5] Lin, B.-R.; Lu, H.-H.; “New mul ile el ec i ie based on se ies connec ion o H-b idge cell” Elec ic Powe Applica ions, IEE P oceedings- ol 147, no 4, pp 304 – 312 July 2000 [6] Alonso, O.; Sanchis, P.; Gubia, E.; Ma oyo, L.; “Cascaded H-b idge mul ile el con e e o g id connec ed pho o ol aic gene a o s wi h independen maximum powe poin acking o each sola a ay” in Powe Elec onics Specialis Con e ence 2003 (PESC’03), ol 2, pp 731 – 735, 15-19 June 2003 [7] Lezana, P.; Sil a, C.A.; Rod iguez, J.; Pe ez, M.A.; “Ze o-S eady-S a e- E o Inpu -Cu en Con olle o Regene a i e Mul ile el Con e e s Based on Single-Phase Cells” IEEE T ansac ions on Indus ial Elec onics, ol 54,no 2, pp 733 – 740,Ap il 2007 [8] Ba ena, Jon Andoni; Ma oyo, Luis; Rod iguez, Miguel Angel; Alonso, Osca ; To ealday, Jose Ramon; “DC Vol age Balancing o PWM Cascaded H-B idge Con e e Based STATCOM”; in IEEE Indus ial Elec onics Con e ence(IECON06), pp 1840 – 1845, No embe . 2006 [9] Escoba , G.; Ma inez-Mon ejano, M.F.; Ma inez-Rod iguez, P.R.; He nandez-Gomez, M.; “A model-based con olle o he cascade h- b idge mul ile el con e e used as a shun ac i e il e ”; in Powe Elec onics Specialis Con e ence 2006 (PESC’06), pp 1-5, 18-22 June 2006 [10] Ceca i, C.; Dell'Aquila, A.; Lise e, M.; Monopoli, V.G.; “Design o H- b idge mul ile el ac i e ec i ie o ac ion sys ems” IEEE T ansac ions on Indus y Applica ions, Vol 39,no 5,, pp 1541-1550, Sep embe .-Oc 2003 [11] Dell'Aquila, A.; Lise e, M.; Monopoli, V.G.; Ro ondo, P.; “Two passi i y-based app oaches o he con ol o he H-b idge-based mul ile el ec i ie ”; in IEEE Indus ial Elec onics Con e ence 2003 (IECON03) Vol 2, pp 1191 – 1196, 2-6 No embe . 2003 [12] So o, D.; Pena, R.; “Nonlinea con ol s a egies o cascaded mul ile el STATCOMs”; IEEE T ansac ions on Powe Deli e y, Vol 19, no 4, pp 1919 – 1927, Oc obe . 2004 [13] Dell'Aquila, A.; Lise e, M.; Monopoli, V.G.; Ro ondo, P.; “O e iew o PI-based solu ions o he con ol o he dc-buses o a single-phase H- b idge mul ile el ac i e ec i ie ”; Applied Powe Elec onics Con e ence and Exposi ion, 2004 (APEC04). Vol 2, pp 836 – 842, 22-26 Feb ua y 2004 [14] Dell'Aquila, A.; Lise e, M.; Monopoli, V.G.; Ro ondo, P.; “An Ene gy- Based Con ol o an n-H-B idges Mul ile el Ac i e Rec i ie ”, IEEE T ansac ions on Indus ial Elec onics, Volume 52, 3, pp. 670 – 678, June 2005. [15] G. Escoba , A.M. S anko ic, J.M. Ca asco, E. Gal an and R. O ega, “Analysis and design o di ec powe con ol (DPC) o a h ee phase synch onous ec i ie ia ou pu egula ion subspaces”, IEEE T ansac ions on Powe Elec onics, Vol. 18, Issue 3, pp. 823-830, May 2003 [16] Escoba , G.; O ega, R.; As ol i, A.; Ma inez, M.F.; Ley a-Ramos, J, “A epe i i e based con olle o a shun ac i e il e o compensa e o eac i e powe and ha monic dis o ion”, Con e ence on Decision and Con ol, 2005 and 2005 Eu opean Con ol Con e ence. (CDC-ECC '05), pp. 6480 – 6485, 12-15 Decembe . 2005 [17] J.A. Sanchez, S. Vazquez, G. Escoba , J.M. Ca asco, E. Gal an, E. Dominguez, M. Reyes, “Digi al Implemen a ion Issues o a Th ee- Phase Powe Con e e De elopmen Using a Repe i i e Con ol Scheme”, in In e na ional Symposium on Indus ial Elec onics 2007 (ISIE07), pp 1-6, 4-7 June 2007