Integrated Control and Modulation for Three-Level NPC Rectifiers

ene gies A icle In eg a ed Con ol and Modula ion o Th ee-Le el NPC Rec i ie s An onio Ven osa-Cu illas 1,* , Pablo Mon e o-Robina 1, F ancisco Umb ía 2, Fede ico Cues a 1and F ancisco Go dillo 1 1Depa amen o de Sis emas y Au omá ica, Escuela Técnica Supe io de Ingenie ía, Uni e sidad de Se illa, 41092 Se illa, Spain; [email p o ec ed] (P.M.-R.); [email p o ec ed] (F.C.); [email p o ec ed] (F.G.) 2ASM Assembly Sys ems GmbH & Co. KG, 81379 Munich, Ge many; [email p o ec ed] *Co espondence: [email p o ec ed]; Tel.: +34-95-448-2292 Recei ed: 8 Ap il 2019; Accep ed: 26 Ap il 2019; Published: 30 Ap il 2019   Abs ac : This pape uses a no el app oach o he con ol o h ee-le el neu al-poin -clamped (NPC) ec i ie s in o de o ackle he capaci o ol age balance p oblem. A dis inc i e ea u e o he new con ol app oach is ha i is based on a model which is w i en in e ms o he du y a ios o each phase a each le el. Hence, he sys em model p esen s nine du y cycle a iables. Despi e he ac ha his o mula ion is di e en om he usual ones, i is shown ha he con ol p oblem o cu en s and dc-link ol age can be o mula ed in a simila way o con en ional me hods. Fu he mo e, he con ol o he capaci o ol age balance can be exp essed by means o equa ions ha a e decoupled om he cu en s and dc-link ol age dynamics, which esul s in a speci ic con olle o he ol age balancing ha does no a ec he p e ious dynamics. A key poin o he p oposed app oach is ha pa o he modula ion s age is implici in he o mula ion. Two pa icula con olle s a e compa ed in his pape . The i s one ul ills he di e en con ol objec i es a he expense o a la ge numbe o commu a ions. This p oblem is o e come in a new p oposed con olle , which p esen s simila pe o mance and a sa is ac o y numbe o commu a ions. Expe imen al esul s a e pe o med showing he e ec i eness compa ed wi h a modi ied i ual space ec o modula ion wi h capaci o ol age balance capabili ies. Keywo ds: synch onous ec i ie applica ion; neu al-poin -clamped (NPC) con e e ; ol age balancing; in eg a ed con ol and modula ion (ICM); G id-connec ed powe con e e ; mul ile el con e e s 1. In oduc ion In he ield o ene gy con e sion sys ems, he ad an ages ha mul ile el powe elec onic con e e s o e a e well known. Bidi ec ional powe low, inc ease o he ou pu ol age magni ude, obus ness, e c. a e only some o he ad an ages ha ha e made mul ile el con e e s popula in medium and high powe applica ions in he indus y [ 1 – 3 ]. Some o he di e en ypes o opologies o hese con e e s a e neu al-poin -clamped, cascaded H-b idge o lying-capaci o [ 1 , 2 , 4 ]. A Neu al-poin -clamped (NPC) con e e , which was p oposed o he i s ime in [ 5 ], is one o he mos used mul ile el con e e opologies. Du ing no mal ope a ion, he ol age ha d ops ac oss each capaci o mus be balanced o he wise, i can esul in poo ou pu ol age quali y, a ec ing he pe o mance o he con ol o e en damaging he semiconduc o de ices. The e o e, NPC con e e s p esen an addi ional objec i e apa om he usual con ol objec i es in powe con e e s [ 6 ] ha is he ol age balance be ween capaci o s, which is he main ocus in his pape . O e he las ew yea s, nume ous echniques ha e been de eloped o co ec he ol age unbalance. Some o hem use addi ional ci cui y [ 7 – 9 ], bu his would lead o an inc ease in cos , losses and complexi y in ha dwa e. O he au ho s use di e en con ol echniques wi h algo i hms o a ying di icul y [ 10 – 15 ]. One o hese con ol echniques [ 13 ] uses a modi ica ion o i ual space Ene gies 2019,12, 1641; doi:10.3390/en12091641 www.mdpi.com/jou nal/ene gies Ene gies 2019,12, 1641 2 o 15 ec o [ 16 ] (deno ed as mVSVPWM in his pape ). In [ 13 ], he ol age e e ence ec o is ob ained by c ea ing i ual ec o s whe e he possible swi ching s a es a e weigh ed o gene a e cu en s ha bene i he ol age balance. Rega ding he modelling, i is usual o wo k wi h a e aged models whe e he disc e e alues o he ga ing elemen s a e conside ed as con inuous signals [ 1 , 17 ]. In o de o implemen he con ol laws ob ained wi h such models, a disc e iza ion s age, usually called modula ion, needs o be accomplished [ 18 ]. Modula ion plays an impo an ole in he o e all sys em pe o mance since p ope ies such as numbe o commu a ions and ha monic dis o ion o cu en s and ol ages a e a ec ed by he way modula ion is ca ied ou . Modula ion me hods can be classi ied in o h ee main g oups [ 19 ]: pulse wid h modula ion (PWM) [ 20 , 21 ], pseudo-modula ion [ 22 ] and closed-loop con ol me hods wi h implici modula o [23–25]. This pape p esen s a new app oach o deal wi h he con ol o h ee-le el NPC con e e s, which is based on [ 26 ]. In his pape , he ci cui model is o mula ed in e ms o he du y a ios o each phase a each le el. In his way, he e a e nine du y cycle a iables ( h ee du y cycles pe phase) ins ead o jus h ee (one du y cycle pe phase). This o mula ion is no new, e.g., a simila model, based on d–q ans o ma ion, was p esen ed in [ 27 ] o design an LQR con olle o an NPC in e e by linea iza ion using a small-signal model. In [ 26 ], i is shown ha his o mula ion allows o explici ly conside , in he con ol design s age, he ex a deg ee o eedom associa ed wi h he injec ion o homopola componen . The inc ease in he numbe o a iables does no make he design signi ican ly mo e di icul since, wi h an app op ia e change o a iables, he dc-link ol age and ac i e and eac i e powe con ol p oblems can be o mula ed in a simila way o o he usual app oaches. As a esul , he ol age balance con olle can be easily designed a he same ime ha an impo an pa o modula ion is no needed. Fo his, he p oposed app oach can be conside ed as a con ol me hod wi h pa o he modula ion s age included in he con ol o mula ion, he e o e, in wha ollows i would be called “In eg a ed Con ol and Modula ion” (ICM). The main ad an age o he p oposed con ol law is i s simplici y in implemen a ion compa ed o modi ied e sions o space ec o modula ion (SVM) [ 16 ] ha also ackle he capaci o ol age unbalance bu i s ill p esen s some ad an ages wi h espec o CB-PWM app oaches. This is due o he ac ha he modula ion s age is simpli ied wi hou losing pa o he lexibili y o SVM [ 28 , 29 ]. Once he nine du ies a e compu ed, he way hey a e sequenced can be chosen eely, spli ing hem up o shi ing hem among he di e en phases. This eedom allows he use o achie e seconda y con ol objec i es simila ly o SVM such as common-mode ol age educ ion o a oidance o ex a swi ching losses. Fo he sake o a ai compa ison, his a icle will use a simple iangula -shaped sequence simila o ha o CB-PWM app oaches. Fu he mo e, he p oblem o mula ion o powe , cu en and dc-link ol age con ol is he same as when using o he con en ional app oaches, such as model-based di ec powe con ol (DPC) [30–33] o p opo ional- esonan con olle (PR) o cu en s [34,35]. The d awback o he p oposed app oach in [ 26 ] is ha i may lead o an unnecessa y inc ease in he numbe o commu a ions. This is due o he ac ha , unless some o he du y cycle a iables u n ou o be ze o, he esul an swi ching signals will commu e among all he le els o he h ee phases e e y sampling pe iod. This is he case o he i s con ol law conside ed in his pape (ICM1), whe eas wi h he dc-link ol age, cu en o powe con ol can be accomplished by swi ching each phase be ween wo le els [ 36 ] when he ol age balance p oblem is no conside ed. In his pape , by using a emaining deg ee o eedom associa ed wi h he injec ion o homopola componen , some commu a ions a e a oided compa ed o ICM1 p esen ing a second con olle (ICM2) who explodes his capabili y. The ou pu wa e o m o ICM2, as i will be shown la e on in expe imen s, is simila o hose app oaches which injec a hi d ha monic signal in o he ou pu ol age o inc ease he undamen al signal ange wi hou o e modula ing [ 37 ]. The e o e, ICM2 also has his p ope y inhe en wi hou he need o ex a compu a ions. Bo h con ol laws a e alida ed by means o expe imen s and compa ed wi h a con ol echnique based on a modi ied i ual space ec o modula ion (mVSVPWM) [ 13 ], which includes capaci o Ene gies 2019,12, 1641 3 o 15 ol age balance capabili ies. The e o e, he main con ibu ions o his pape in compa ison wi h [ 26 ] a e he inclusion o a new app oach (ICM2) along wi h expe imen al e i ica ion o bo h app oaches. The nex sec ion is de o ed o p esen ing he con e e conside ed in his pape , as well as i s dynamic model. Sec ion 3p esen s he con olle design o ul illing he h ee con ol objec i es: egula ion o he cu en s and he dc-link ol age and capaci o ol age balance. Sec ion 4p oposes wo a ian s o he selec ion o he emaining deg ees o eedom esul ing in wo di e en con olle s, ICM1 and ICM2. Sec ion 5p esen s expe imen al esul s. The pape closes wi h a sec ion o conclusions. 2. Dynamic Model o he Sys em The con igu a ion o he con e e used in his pape is a h ee-phase h ee-le el NPC con e e in ec i ie mode wi h a esis i e load, as shown in he scheme o Figu e 1. Figu e 1. Schema ic diag am o he h ee-phase h ee-le el neu al-poin -clamped (NPC) ec i ie . The elec ical powe g id is conside ed as a h ee-phase ol age sou ce, whe e he phase ol ages a e ep esen ed by sa , sb and sc . The con e e is connec ed o he g id h ough an induc i e il e whe e induc ances ha e he same alue L. On he dc-link side, capaci o s ha e he same alue C and hei ol ages a e deno ed by c1 and c2 . Connec ed o he con e e e minals he e is a esis i e load R . The o al dc-link ol age is de ined as dc = c1+ c2. Conside ed Sys em Model The model conside ed in his pape is desc ibed in [ 26 ], which is based on a model p esen ed in [ 27 ]. This model uses he equa ions in αβγ coo dina es by in oducing he powe -in a ian o m o he Cla ke T ans o m. Fu he mo e, he swi ching signals ha e been eplaced by hei espec i e du y a ios in each le el [ 27 , 38 ], dij wi h i=α , β , γ and j=p , o , n , whe e p is he posi i e le el when swi ches Si 1 and Si 2 a e closed, o is he ze o le el when swi ches Si 1 and Si 2 a e closed and n is he nega i e le el when swi ches Si 1and Si 2a e closed. This o mulism yields Ldiα d = sα−(dαp−dαn) dc 2−(dαp+dαn) d 2(1) Ldiβ d = sβ−(dβp−dβn) dc 2−(dβp+dβn) d 2(2) Cd dc d = (dαp−dαn)iα+ (dβp−dβn)iβ−2 dc R(3) Cd d d = (dαp+dαn)iα+ (dβp+dβn)iβ, (4) Ene gies 2019,12, 1641 4 o 15 whe e d is he dc-link capaci o ol age di e ence de ined by d= c1− c2 . The con ol inpu s dαp , dαn , dβp and dβn a e he du y a ios in αβγ coo dina es. Con ol inpu s dγp and dγn do no appea in he model, as men ioned in [ 26 ], because hey a e mul iplied by iγ , whose alue is ze o o a balanced sys em. Simila ly, a iables dio do no appea in his model bu hei alues can be e ie ed a he inal s age o he con olle using he ollowing cons ain s: dap +dao +dan =1 (5) dbp +dbo +dbn =1 (6) dcp +dco +dcn =1 (7) dij ∈[0, 1], o i=a,b,cand j=p,o,n. Phase cu en s iαand iβcan be exp essed in e ms o powe s as iα=1 2 sα+ 2 sβ sαp− sβq(8) iβ=1 2 sα+ 2 sβ sβp+ sαq, (9) whe e p and q a e he ins an aneous ac i e and eac i e powe s o he sys em, espec i ely. In his way, (3) and (4) could be exp essed as Cd dc d =1 2 sα+ 2 sβdαp−dαn sαp− sβq+1 2 sα+ 2 sβdβp−dβn sβp+ sαq−2 dc R(10) Cd d d =1 2 sα+ 2 sβdαp+dαn sαp− sβq+1 2 sα+ 2 sβdβp+dβn sβp+ sαq, (11) whe e a iables dc and da e exp essed in e ms o he ins an aneous powe pand q. 3. Con olle Design Wi h he pu pose o dealing wi h he h ee con ol objec i es (cu en s, dc-link ol age and capaci o ol age balance con ol), he sys em dynamic model (1) – (4) p esen ed p e iously is conside ed o design he con olle s in his sec ion. I can be seen ha he p oposed modeling allows o cope wi h he capaci o ol age balance p oblem while i does no a ec he cu en and dc-link ol age con olle s. 3.1. To al DC-Link Vol age Con olle In o de o main ain cons an he dc-link ol age and close o i s e e ence ( dc ), as usual, a PI con olle is used [26,30,39], p =kdc p dc 2− 2 dc+kdc iZ 0 dc 2− 2 dcdτ, (12) whe e cons an s kdc pand kdc ia e con olle uning pa ame e s. Ene gies 2019,12, 1641 5 o 15 3.2. Cu en Con olle Obse ing Equa ions (1) and (2), wo i ual con ol a iables can be de ined as u1˙=dαp−dαn(13) u2˙=dβp−dβn. (14) In oducing hese a iables in o he cu en s dynamic model and assuming ha he alue o a iable dis small enough o be neglec ed, Ldiα d = sα−u1 dc 2(15) Ldiβ d = sβ−u2 dc 2. (16) These exp essions a e equi alen o hose cu en dynamics o he con en ional wo-le el con e e [ 26 ]. The e o e, by he use o he change o a iables (13) and (14), he added di icul y inhe en o he adop ed o mula ion disappea s, a leas a his s age. Addi ionally, in oducing he e e ences o he ac i e ( p ) and eac i e powe ( q ) in o (8) and (9) , he cu en e e ences can be e ie ed ( i α , i β ). Once hese alues a e known, a non-ideal p opo ional- esonan con olle [ 35 ], uned a he g id equency, is used o make he phase cu en s o ack hei e e ences. In his way, he acking e o (i α−iα , i β−iβ) inpu s he esonan con olle , p o iding he alue o con ol a iables (u1,u2). GPRω(s) = kp+2k ωcs s2+2ωcs+ω2 u1=2 dc (−GPRωg(i α−iα) + sα)(17) u2=2 dc (−GPRωg(i β−iβ) + sβ)(18) whe e kp and k a e he p opo ional and esonan con ol pa ame e s; ωc is he cu -o equency o he low-pass il e implemen ed in o he esonan pa ; and ω is he esonan equency— uned a he g id equency ωg. 3.3. Vol age Balance Con olle The objec i e o he ol age balance con olle is o keep he s a e a iable d close o ze o, a oiding he unbalance o he dc-link capaci o ol ages, and i is based on he de ini ion o wo new i ual con ol a iables u3˙=dαp+dαn(19) u4˙=dβp+dβn. (20) In oduc ion o (19) and (20) in o (11) yields Cd d d = sαp− sβq 2 sα+ 2 sβ u3+ sβp+ sαq 2 sα+ 2 sβ u4. (21) I is impo an o highligh ha he de ini ion o u3 and u4 causes a decoupling o he i ual con ol a iables o con ol pu poses. No e ha u1 and u2 a e designed o egula e he s a e a iables p and q , whe eas u3 and u4 can be used o egula e d(21) . This is an impo an bene i o he p oposed con ol app oach. Ene gies 2019,12, 1641 6 o 15 Taking in o accoun (21), he p oposed con ol laws [26] a e de ined as ollows u3=kd sαp− sβq p2+q2( d− d)+kdi sαp− sβq p2+q2Z 0 ( d− d)dτ(22) u4=kd sβp+ sαq p2+q2( d− d)+kdi sβp+ sαq p2+q2Z 0 ( d− d)dτ, (23) whe e posi i e cons an s kd and kdi a e cus oma y uning pa ame e s. The e e ence o d is deno ed by d , which is se o ze o o ensu e a balanced dis ibu ion o he dc-link ol age ac oss capaci o s C1 and C2. By in oducing (22) and (23) in o (21), he ol age balance dynamics become linea : Cd2( d− d) d 2+kd d( d− d) d +kdi( d− d) = 0, (24) whose s abili y is assu ed p o ided ha pa ame e s kd and kdi a e posi i e. A comple e schema ic block diag am o all con olle s is illus a ed in Figu e 2. Figu e 2. Comple e schema ic block diag am o he con olle s. Ene gies 2019,12, 1641 7 o 15 4. Modula ion S a egy The con olle p esen ed in he p e ious sec ion p o ides, a each sampling ime, he alues o u1 , u2 , u3 and u4 . The co esponding alues o dαp , dαn , dβp and dβn can be ob ained sol ing he sys em o Equa ions (13), (14), (19) and (20) yielding dαp=1 2(u1+u3)(25) dαn=1 2(−u1+u3)(26) dβp=1 2(u2+u4)(27) dβn=1 2(−u2+u4)(28) In o de o compu e he ac ual du y a ios dij , i=a , b , c ; j=p , n , he Cla ke ans o ma ion can be used    daj dbj dcj   = 2 3         1 0 1 √2 −1 2 √3 2 1 √2 −1 2−√3 2 1 √2            dαj dβj dγj   ,j=p,n. (29) whe e dγp and dγn a e emaining deg ees o eedom. Ob iously, he emaining du y a ios, dao , dbo and dco can be compu ed using (5)–(7). 4.1. Fi s P oposal, ICM1 The i s a ian , ICM1, was p oposed in [ 26 ]. In his a ian , dγp and dγn a e chosen o be cons an and can be conside ed as uning pa ame e s. In [ 26 ], guidelines a e gi en in o de o a oid sa u a ion p oblems. This app oach is a simple way o accomplish he modula ion bu i p esen s an impo an d awback: excep by chance, none o he dij will esul in ze o. This implies ha , in each sampling ime, each phase commu es among he h ee le els, which can be conside ed oo many commu a ions compa ed wi h o he con olle s, e en hose including ol age balancing. This ac could yield la ge swi ching losses. 4.2. Second P oposal, ICM2 In o de o a oid he la ge numbe o commu a ions, a new a ian is p oposed. This a ian akes ad an age o he wo deg ees o eedom associa ed wi h dγp and dγn by imposing, a each sampling pe iod, one dip and one din o be ze o. The wo phases o which one o he du y a ios has o be ze o need o be chosen ca e ully, as i is explained below, aking in o accoun ha he du y cycles in abc coo dina es ha e o be in he in e al [ 0, 1 ] . The esul is ha hese wo phases only swi ch be ween wo le els while he emaining phase commu es among he h ee le els. In o de o selec hese phases, he p ocedu e checks i se ing one o he dij,i=a,b,c;j=p,n o ze o yields o he ul illmen o he cons ain s 0 ≤dij ≤ 1 o he es o du y cycle a iables. S a ing wi h he case dap = 0, Equa ion (29) o j=p can be conside ed as a se o equa ions, whe e dαp , dβp a e known, dap = 0 and dbp , dcp and dγp a e he unknowns. The esul an sys em o equa ions can be sol ed in o de o check i his case is easible, ha is, i dbp and dcp a e in he in e al [ 0, 1 ] . Repea ing o he o he phases, h ee di e en cases ha e o be analyzed o j=p and o he h ee cases o j=n . The associa ed equa ions a e Ene gies 2019,12, 1641 8 o 15 Case 1: daj =0 dbj =−√6 2dαj+√2 2dβj(30) dcj =−√6 2dαj−√2 2dβj(31) Case 2: dbj =0 daj =√6 2dαj−√2 2dβj(32) dcj =−√2dβj(33) Case 3: dcj =0 daj =√6 2dαj+√2 2dβj(34) dbj =√2dβj, (35) whe e j = p , n . The esul an du y a ios o he conside ed sampling ins an a e he co esponding ones o he easible cases, ha is, cases whe e all he du y cycles a e in he in e al [ 0, 1 ] . I will be shown below ha , a e e y ins an , he e exis s a leas one (and apa om some bo de cases, only one) easible case. Rega ding he compu a ion bu den o his app oach, a e e ie ing (25)–(28), he calcula ion o he du y a ios dij can be achie ed by checking he cons ain s dij ∈[ 0, 1 ] o he 3 × 2 = 6 cases. Fo his, (30)–(35) ha e o be used wice ( o le els p and n ). This las s age implies he compu a ion o 20 mul iplica ions and 8 sums as well as 24 compa isons. Al e na i ely, a di e en app oach can be used o choose he co ec case a e e y sampling ins an wi h he help o Figu e 3. This igu e depic s he s aigh lines ha a e he bounda ies o cons ain s 0 ≤dij ≤ 1 using exp essions (30) – (35) . Consequen ly, he shaded egions ep esen he ul illmen o hese cons ain s o each one o he h ee cases abo e. As o each le el j=p , n he e is one dij ha i is equal o ze o, he e a e ou o such lines o each case, ins ead o six. I can be seen ha he h ee shadowed a eas do no o e lap (excep a hei bo de s) and ha hey co e a whole hexagon. An in e es ing ac is ha his hexagon is ela ed o he well-known hexagon o Space Vec o Modula ion (SVM), bu in his case, he e a e wo such hexagons (one o j=p and one o j=n ). The in e es o Figu e 3is wo old: (1) i shows ha , p o ided he con e e does no wo k in o e modula ion egion, one o he h ee cases is always easible, and (2) Figu e 3can be used as an al e na i e me hod o choose he co ec case: he wo king sec o can be compu ed as usual in SVM and once he app op ia e case is selec ed, he co esponding o mulae can be applied. In summa y, he ICM2 algo i hm, whose da a inpu and ou pu a e depic ed in Figu e 4, can be implemen ed in wo al e na i e and equi alen ways ha only di e in he compu a ional bu den, which in al e na i e B depends on he me hod used o he compu a ion o he sex an : Al e na i e A: •Compu a ion o u3and u4using (22) and (23). •Compu a ion o dαp,dαn,dβp,dβnusing (25)–(28). •Fo le els pand n: – Compu a ion o Equa ions (30)–(35) and selec ion o he case ha ul ills he cons ain s 0≤dij ≤1. This p ocedu e gi es di ec ly he esul an du y cycles. Ene gies 2019,12, 1641 9 o 15 Al e na i e B: •Compu a ion o u3and u4using (22) and (23). •Compu a ion o dαp,dαn,dβp,dβn(25)–(28). •Fo le els pand n: – Compu a ion o he sex an inside he hexagon o Figu e 3. This s ep is simila o he co esponding one in SVM (bu i mus be compu ed wice, one o le el p and one o le el n). The sex an gi es he co esponding case. –Compu a ion o he du ies using he co esponding Equa ions o (30)–(35). I can be no ed ha he compu a ional complexi y is lowe in bo h ICM1 and ICM2 wi h espec o SVM s a egies ha include con ol o he ol age balance, such as [13]. Figu e 3. G aphical ep esen a ion o he limi s o each case. Figu e 4. Da a inpu and ou pu o ICM1 and ICM2. 5. Expe imen al Ve i ica ion This sec ion p esen s he expe imen al esul s ob ained in he labo a o y o he wo app oaches p esen ed in his pape and he one used as a compa a i e (mVSVPWM) [ 13 ]. To his end, he h ee-le el NPC con e e shown in Figu e 5has been used. I has been con igu ed as ec i ie and i has he ci cui and con ol pa ame e s p o ided in Table 1. A i s -o de low-pass il e has also been added o he p opo ional pa o he o al dc-link ol age con olle , as i is ecommended in [ 33 ], uned a 5 KHz in o de o educe he ha monics p esence.