Self-Precharge in Single-Leg Flying Capacior Converers Seven Thielemans Elecrical Energy, Sysems and Auomaion Deparmen Ghen Universiy (UGen), EESA Ghen, Belgium Email: Seven.Thielemans@UGen.be Alex uderman Elmo Moion Conrol Ld. Peach-Tikva 493, Israel Email: aruderman@elmomc.com Jan Melkebeek Elecrical Energy, Sysems and Auomaion Deparmen Ghen Universiy (UGen), EESA Ghen, Belgium Email: Jan.Melkebeek@UGen.be Absrac Flying Capacior (FC) mulilevel pulse widh modulaed (PWM) converers are an aracive choice due o he naural volage balance propery. During sar-up of he converer, care has o be aken ha he power swiches are no exposed o volage oversress due o uncharged capaciors. A flying capacior self-precharge echnique is proposed which, by making use of naural balancing and a DC-bus rae conrol, makes he capaciors balance wih a zero average load curren. The DC-bus rae conrol depends on he capacior volage balance dynamics. The regular PWM naural balancing echnique gives good resuls for even-level single-leg converer self-precharge, for odd-level converers a special swiching paern is necessary. I. INTODUCTION Mulilevel converers were developed as a resul of a growing need for higher power converers, [], []. In order o achieve his higher power raing, he volage and curren capabiliies of he devices used in he converer need o be increased. Curren insulaed gae bipolar ransisor (IGBT) echnology exends up o 6.5 k 9 A per swiching device. Converers ha make use of a series connecion of swiches, allow for he use of swiches wih reduced volage raings. These lower volage swiches have lower swiching losses and can swich a a higher frequency. Higher swiching frequencies and a smaller volage sep capabiliy resul in higher qualiy swiching waveforms. Flying capacior mulilevel converers are an aracive choice due o he naural volage balance propery. The naural balancing is achieved by applying a phase shifed carrier PWM (PSCPWM) mehod. The balancing of he capaciors is driven by load curren high order harmonics, [3]-[6], namely, by he capacior volage unbalance excessive energy dissipaion in he converer load by swiching harmonics in he load curren. Though i is acceped o consider a simplified series L-load model, pracically high frequency loss mechanisms like skineffec and PWM eddy curren core losses are expeced o make volage balance rae faser. FC lieraure survey shows ha so far he engineering communiy is convinced ha flying capaciors precharge is a complex ask ha may be considered as a FC converer serious disadvanage. Saemens as Addiional circuis are also required o iniialize he capacior charge, [7] and Precharging all he capaciors o required volage level a sar-up is complex, [8], make one believe i can be a serious drawback for FC converers. Fig.. n C S A a B S Three-level flying capacior mulilevel converer circui opology. I is his paper s goal o show ha he common spread opinion abou FC converer precharge complexiy o a cerain exen is a myh and, given DC power supply volage build-up rae conrol a sar-up, flying capaciors may be precharged o heir required balanced volage levels a virually no cos. This can be done wih no change o he converer s opology and by using as much as possible he normal conrol of he converer and is swiches. II. SELF-PECHAGE FO THEE-LEEL FC CONETE The opology of a hree-level single leg FC converer is depiced in Fig.. In all FC converer opologies, each pair of swiches (as, and S, S ) are swiched complemenary. The pulse widh modulaion (PWM) sraegy used for his opology incorporaing he naural balancing mechanism is depiced in Fig.. When he normalized volage command D is above carrier c (c ), swich (S ) is urned on; when below carrier c (c ), swich (S ) is urned on. Wih he sar-up of he converer, capacior C is expeced o be discharged, so he volage over he capacior equals zero. The capacior can be regarded as a shor circui. Poins A and B in Fig. are a he same volage and a ha poin here is in fac a wo-level converer, wih only swiches S, S. When suddenly a volage is pu on he DC bus, volage oversress can occur on hese swiches. To avoid oversress of he swiches, i is required ha L
D c c L DC 8 6 4 Fig.. D=. Naural balancing PWM sraegy for hree-level FC converer wih...3.4.5.6.7 capacior C has a volage which is consisen wih dc. This can be done by increasing he volage on he DC-bus slowly. A simple approach o achieve his is by placing a resisor (, precharge resisor) beween he power supply and he DC-bus capaciors. This gives following ime consan for he DC-bus volage rise when no exra load is presumed: T P C =. () Afer precharging, swiches are closed, shoring resisances. This way exra losses during normal operaion are avoided. This circui can already be found in normal converers o avoid large charge currens while urning on he DC power supply. During he precharging, he load curren mus be under conrol and as close o zero as possible. To achieve his, a normalized volage command of D= is chosen. As depiced in Fig., D = for a hree-level converer resuls in a zero oupu volage on average on a swiching period for an arbirary capacior volage and pure zero for a perfecly balanced capacior. When he capacior has zero volage, he oupu volage v an swiches beween CDC, he volage over he DC-bus capaciors, and CDC wih a duy raio of /. The swiching of he oupu volage v an resuls in currens which will balance he capaciors. Charging of capacior C wih a volage sep on he DC-bus is depiced in Fig. 3. Parameers used in his simulaion are: =.5Ω, L=mH, C =5µF, T pwm =4µs. For a hree-level FC converer wih zero volage command (D=), volage balance exponenial dynamics ime consan is, [9], T = 48L C. () T P W M Formula () and oher ime consan esimaions in his paper assume inducance dominaed load on swiching frequency: T pwm < T L = L, (3) meaning low ripple curren. Anoher requiremen is a relaively low capacior ripple volage ha allows effecive averaging on a swiching period o calculae average volage balance dynamics. If (3) does no hold, hen he acual volage balance Fig. 3. Self-precharge of capacior C of a hree-level FC converer wih volage sep on DC-bus, T=.96s. 8 6 4...3.4.5.6.7 Fig. 4. Self-precharge of capacior C of a hree-level FC converer wih making use of. ime consan is larger han ha prediced by formula (). On he oher hand, unaccouned addiional high frequency load loss mechanisms, like skin-effec, PWM eddy curren and hyseresis core loss, make volage balance dynamics faser. The ime consan of equaion () can now be used o calculae a ime consan for he volage on he DC-bus capaciors. By aking a ime consan for he DC-bus volage () which is sufficienly larger, e.g. wo imes he balancing ime consan, he volage over capacior C can follow he DC-bus volage, as is depiced in Fig. 4. This way he volage over every swich is never higher han he volage in normal use. There can also be noiced ha he curren ripple says smaller because he DC-bus and he flying capacior volage gradually rise. The capacior volage balancing ime consan depends on he load parameers. If he load of he converer is no primarily known, a special precharge load can be conneced only for he self-precharge balancing, or a balance booser can be used for he self-precharge and during normal operaion of he
D c c c 3 n a S L C C S 6 L 3 3 3 3 3 3 Fig. 5. converer, [6]. Four-level flying capacior mulilevel converer circui opology. III. SELF-PECHAGE FO FOU-LEEL FC CONETE The opology of a four-level single leg FC converer is depiced in Fig. 5. To creae four levels on he oupu, now wo flying capaciors and hree pair of swiches are needed. To conrol hese hree pair of swiches while incorporaing he naural balancing mechanism, hree carrier waves are necessary o define he swiching saes paern for a given normalized volage command D. The hree carrier waves can be ordered using wo differen modulaion sraegies. The firs sraegy can be referred o as he lead sraegy because he carrier wave c leads c and c leads c 3, as depiced in Fig. 6(a). For he alernaive, he lag modulaion sraegy, he carrier wave c 3 leads c and c leads c, as depiced in Fig. 6(b). As may be observed, he lag modulaion sraegy generaes inverse swiching saes sequence wih respec o he lead modulaion sraegy. As follows from he modulaion sraegies, i is impossible o ge a consan zero load volage L for D= and balanced capaciors. Insead, a swiching volage beween dc 3 and dc 3, wih zero mean volage, is applied over he load. This zero mean volage resuls in a zero mean load curren. A. Ideal swiches wihou ani-parallel clamping diodes In he heoreical work regarding sep response ime consans and oscillaion frequencies, ideal swiches and he lack of ani-parallel clamping diodes are assumed, []. Oherwise he clamping diodes would inroduce non-lineariies which are hard o ake ino accoun. For a four-level FC converer, under he assumpion (3), he flying capacior volages show an oscillaing sep response for a sep in he DC-bus volage. For a zero normalized volage command D =, he volage balance angular frequency and damping ime consan amoun o, []: ω = T pwm L C C, (4) D 6 L (a) Lead PWM sraegy. c 3 c c 3 3 3 3 3 3 (b) Lag PWM sraegy. Fig. 6. Naural balancing PWM sraegy for four-level FC converer, lead and lag sraegies. T = 648L C C 5T pwm (C + C ). (5) The capacior volages sep response on a DC-bus volage sep for a four-level FC converer wih ideal swiches, using he same parameers as for he hree-level converer wih equal capacior values (C = C ) and using he lead modulaion sraegy, is depiced in Fig. 7(a). The one for he lag modulaion sraegy is depiced in Fig. 7(b). For he lead modulaion sraegy, he oscillaing volage componen of he firs capacior leads ha of he second capacior. For he lag sraegy, he oscillaing volage componen of he firs capacior lags ha of he second capacior. B. eal swiches wih ani-parallel clamping diodes eal FC converers use swiches wih ani-parallel clamping diodes, like IGBT s wih an ani-parallel clamping diode in he same package. This has some consequences when hese swiches are used for he self-precharging of he capaciors: The capaciors can no have a negaive volage. (due o he clamping diodes, bu also because mosly elecrolyic capaciors are used)
8 4 8 4 8 4...3.4.5 (a) Lead modulaion sraegy 4...3.4.5 (b) Lag modulaion sraegy 6 4 Fig. 7. Self-precharge of he flying capaciors of a four-level FC converer wih volage sep on DC-bus and ideal swiches wihou ani-parallel clamping diodes. 8 6 4...3.4 8 6 4...3.4.5 (a) Lead modulaion sraegy (b) Lag modulaion sraegy Fig. 8. Self-precharge of he flying capaciors of a four-level FC converer wih volage sep on DC-bus and ani-parallel clamping diodes...4.6.8 (a) Lead modulaion sraegy 8 6 4 There exiss an order in capacior volages: C3. Boh properies have an influence on he sep response as nonlineariies are inroduced. The capacior volage sep response for he lead modulaion sraegy is depiced in Fig.8(a), he one for he lag modulaion sraegy in Fig. 8(b). For he lead modulaion sraegy, he oscillaing volage componen of he firs capacior leads ha of he second capacior, bu he clamping diode clamps he volage of he second capacior o ha of he firs capacior. Boh capaciors are hen conneced in parallel. Boh capaciors are now charged a he same ime unil he firs capacior reaches is norminal volage. The oal balancing is now slighly faser and wih a smaller ampliude of he oscillaions, making i accepable o use he ideal equaions. The ime consan T, from equaion (5), can be used o find a DC-bus volage rise ime consan. Similar o he hree-level case, precharge resisors can be used. The resisors can be calculaed so he DC-bus volage rise ime consan is around double he balancing ime consan (5). The balancing ime consan for he given parameers is.9. For DC-bus capaciors of 47µF and a DC-bus ime consan double of he balancing ime consan, is 55Ω. The capacior volage responses, using he calculaed, for he lead and he lag modulaion sraegies are depiced in Fig. 9). The influence of he modulaion sraegy on he capacior volage response is no very significan because he change of he DC-bus volage is small enough...4.6.8 (b) Lag modulaion sraegy Fig. 9. Self-precharge of he flying capaciors of a four-level FC converer wih making use of. I. SELF-PECHAGE FO FIE-LEEL FC CONETE The opology of a five-level single leg FC converer is depiced in Fig.. To creae five levels on he oupu, now hree flying capaciors and four pairs of swiches are needed. This ime four carrier signals are needed o define he swiching saes paern, as depiced in Fig.. Here only he lead modulaion sraegy is depiced, bu also for he five-level case a lag modulaion sraegy can be considered. For he lag modulaion sraegy, he order of he carrier signals is revered, resuling in a swiching saes sequence which is he inverse of he one of he lead modulaion sraegy. As follows from he swiching saes paern, here will be a pure zero oupu volage for D = and perfecly balanced capaciors. Simulaions for a DC-bus volage sep response, for ideal swiches wihou ani-parallel clamping diodes, are depiced in Fig.. For hese simulaions he same parameers as previously were used wih equal capacior values (C = C = C 3 ). The volages of capaciors C and C 3 are opposie o each oher and he volage of capacior C oscillaes o is nominal volage.
S 4 8 8 n a S 6 4 4 C3 6.5..5..5.3 (a) Lead modulaion sraegy 6 4 4 6.5..5..5.3 (b) Lag modulaion sraegy C3 C 3 C C S L Fig.. Self-precharge of he flying capaciors of a five-level FC converer wih volage sep on DC-bus and ideal swiches wihou ani-parallel clamping diodes. 8 C3 8 C3 S 4 6 4 6 4 Fig.. D Five-level flying capacior mulilevel converer circui opology. c c c 3 c 4.5..5..5.3.5..5..5.3 (a) Lead modulaion sraegy (b) Lag modulaion sraegy Fig. 3. Self-precharge of he flying capaciors of a five-level FC converer wih volage sep on DC-bus and ani-parallel clamping diodes. conneced capaciors: 4 L 34 34 34 34 Fig.. Naural balancing PWM sraegy for five-level FC converer, lead modulaion sraegy The flying capacior s volage dynamics are dependen on wo ime consans. One aperiodic ime consan conrolling he common mode volage of capaciors C and C 3, [], (for D <.5): T A (D) = 48L (C + C 3 ) T pwmd (3 4D). (6) For D, his ime consan T A ends o infiniy, which corresponds o he resuls from he simulaion. The second ime consan conrols he balancing of he excessive unbalance energy beween capaciors C and boh C and C 3, [], (for D <.5): T P (D) = wih C 3 384L (C + C 3 ) T pwm [6D 3 3 (F + 6) D + (F + )], (7) he equivalen capaciance of he hree series F = F (C, C, C 3 ) = C + C 3 C + C C 3 + C 3 C. (8) The same simulaions for real swiches wih ani-parallel diodes are depiced in Fig. 3. The non-lineariies, inroduced by he clamping diodes, allow self-precharge in his case. A simulaion wih firs order DC-bus volage rise is depiced in Fig. 4. I can be concluded ha he non-lineariies only allow self-precharge for fas DC-bus build-up raes. This makes his self-precharge mehod unusable in his case as fas DC-bus build-up raes lead o volage oversress on he swiches.. SELF-PECHAGE FO HIGHE LEEL FC CONETES The suggesed approach for he self-precharge (using regular PWM wih D = ) works for FC converers wih even levels as hey have only oscillaing decaying volage balance componens wih a ime consan ha is small enough o ensure a good balancing. An example of he self-precharge of a sixlevel FC converer is depiced in Fig. 5. For an odd number of levels (5-, 7-,... level) here is an aperiodic volage balance dynamics erm wih a ime consan which ends o infiniy for D and creaes poenial selfprecharge problems. A general soluion for his is a special self-precharge swiching paern, preserving he zero mean load curren, bu alering he capacior volage balancing ime consans. This is a opic for fuure research. Fig. 6 shows he example for a seven-level converer.
8 8 6 4, C3 6 4 C3, C4, C5,,,.5..5..5.3..4.6.8 Fig. 4. Self-precharge failure for slow DC bus ramp-up rae for a five-level FC converer wih lead modulaion sraegy. Fig. 6. Self-precharge failure of he flying capaciors wih making use of for a seven-level FC converer wih lead modulaion sraegy. research. 8 6 4 C4 C3..4.6.8 Fig. 5. Self-precharge of he flying capaciors wih making use of for a six-level FC converer wih lead modulaion sraegy. I. CONCLUSION A self-precharge mehod was proposed for FC converers which uses he naural balancing propery of he PSCPWM sraegy wih a normalized volage command of D = and a conrolled DC bus volage ramp-up rae. This mehod is an easy o implemen and o conrol self-precharge mehod. I does no need special adapaions o he sysem. For even level FC converers his mehod works, resuling in a self-precharge of he flying capaciors wihou volage oversress on he swiches. The balancing ime consan depends on he load conneced o he converer. For odd level FC converers, his mehod does no seem o be sufficien o garanee an accurae balancing of he flying capacior volages, excep for a hree-level where is balancing is rivial. This is due o he aperiodic ime consan in he volage balancing which becomes infinie when D ends o zero. This can be solved by using a differen swiching paern and no jus keeping D =. This will be invesigaed in furher ACKNOWLEDGMENT S. Thielemans wishes o hank he Ineruniversiy Aracion Poles programme IUAP P6/ funded by he Belgian governmen for he financial suppor. A. uderman graefully acknowledges Elmo Moion Conrol managemen for on-going suppor o advanced applied power elecronics research. EFEENCES [] J.-S. Lai and F.Z. Peng, Mulilevel Converers - A New Breed of Power Converers, IEEE Trans. on Indusry Applicaions, vol 3, no. 3, pp. 59-57, May/June 996. [] S.S. Fazel, S. Berne, D. Krug, and K. Jalili, Design and Comparison of 4-k Neural-Poin-Clamped, Flying-Capacior, and Series-Conneced H-Bridge Mulilevel Converers, IEEE Trans. on Indusrial Applicaions, vol. 43, no. 4, pp. 3-4, Jul./Aug. 7. [3] B.P. McGrah and D.G. Holmes, Analyical Modelling of olage Balance Dynamics for a Flying Capacior Mulilevel Converer, Proc. IEEE APEC 7, Orlando, Florida, USA, pp. 543-55. [4] T. Meynard, M. Fadel and N. Aouda, Modeling of Mulilevel Converers, IEEE Trans. on Indusrial Elecronics, vol. 44, no. 3, pp. 356-364, June 997. [5] X. Yuan, H. Semmler, and I. Barbi, Self-Balancing of he Clamping- Capacior-olages in he Mulilevel Capacior-Clamping-Inverer under Sub-Harmonic PWM Modulaion, IEEE Trans. on Power Elecronics, vol. 6, no., pp. 56-63, Mar.. [6].H. Wilkinson, T.A. Meynard, and H. du Toi Mouon, Naural Balance of Mulicell Converers: The Two-Cell Case, IEEE Trans. on Power Elecronics, vol., no. 6, pp. 649-657, Nov. 6. [7] S. Daher, J. Schmid and F.L.M. Anunes, Mulilevel Inverer Topologies for Sand-Alone P Sysems, IEEE Trans. on Indusrial Elecronics, vol. 55, no. 7, pp. 73-7, Jul. 8. [8] M. H. ashid, Power Elecronics Handbook: Devices, rcuis, and Applicaions, nd Ediion. Chaper 7. Mulilevel Power Converers. p.456, Academic Press, 7. [9] A. uderman, B. eznikov, and M. Margalio, Simple Analysis of a Flying Capacior Converer olage Balance Dynamics for DC Modulaion, Proc. EPE/PEMC 8, Aachen, Germany, pp. 6-67. [] B. eznikov and A. uderman, Four-Level Single-Leg Flying Capacior Converer olage Balance Dynamics Analysis, 3h European Conf. on Power Elecronics and Applicaions (EPE), Barcelona, Spain. [] A. uderman and B. eznikov, Five-Level Single-Leg Flying Capacior Converer olage Balance Dynamics Analysis, 35h Annual Conf. he IEEE Indusrial Elecronics Sociey (IECON), Poro, Porugal.