Space Vector Modulation Applied to Three-Phase Three-Switch Two-Level Unidirectional PWM Rectifier

Transcription

1 pace Vecor Modulaion pplied o Three-hase Three-wich Two-Level Unidirecional WM Recifier Flabio lbero ardemaker aisa and Ivo arbi, IEEE enior Member ower Elecronics Insiue IE Deparmen of Elecrical Engineering Federal Universiy of ana aarina UF.. ox 5119 Fax Florianópolis, RZIL flabio@inep.ufsc.br, ivobarbi@inep.ufsc.br bsrac This work presens a mehodology o apply space vecor modulaion o hree-phase hree-swich wo-level Y- conneced unidirecional WM recifier. onverer swiching sages are analyzed o deermine swiches conrol signals for space vecor modulaion. swiching sequence is proposed o minimize he number of swiches commuaions. Recifier models and vecor conrol sruce are also described. In order o validae he proposed modulaion, experimenal resuls are presened for a 0 kw prooype. I. ITRDUTI When bidirecional power flux is no necessary, high power facor unidirecional recifiers presen some advanages as he decrease of he number of power swiches, naal proecion of shor-hrough and smaller processing of energy for he acive swiches [1][]. If oupu volage is no so large, wo-level opologies become aracive because hey do no need o conrol middle poin volage of dc bus, reducing he number of sensors and conrollers [3]. In his work space vecor modulaion will be applied o hree-phase hree-swich wo-level Y-conneced unidirecional WM recifier [4] o minimize he number of swiches commuaions and o reduce converer losses. The proposed mehodology o apply his modulaion echnique is based on sub-secors definiion, on recifier operaion sages analysis and on duy cycles deerminaion. Therefore, i is no necessary o idenify he acual vecor secor, jus impose adequae cren secor in phase wih line volages [5]. ecion II presens main characerisics of wo-level unidirecional WM recifier and in secion III are described he basic seps o apply space vecor modulaion o his converer. Recifier models and vecor conrol conceps are showed in secion IV, in secion V experimenal resuls are presened and in secion VI conclusions and resuls analysis are discussed. II. THREE-HE THREE-WITH TW-LEVEL UIDIRETIL WM RETIFIER Three-phase hree-swich wo-level Y-conneced unidirecional WM recifier, showed in Fig. 1, presens high power facor and oupu volage regulaion. This sruce presens six symmerical operaion inervals [3], where six cren secors are defined in one line period:,,,, e. Each secor has an inerval of 60º. secor is defined by he cren ha has he greaer module and is respecive signal. pecific secor analysis may be adaped for oher secors considering he adapaion of crens direcion. Eigh swiching sages may be realized from swiches saes, according o Table I. D 3 D 5 D 3 D 5 L D 4 D 1 D D 6 L L i i i v v () v D 4 D 1 D D 6 D 3 D 4 D 1 D D 5 D 6 i Fig. 1. Three-phase hree-swich wo-level unidirecional WM recifier. TLE I WITHIG TGE. wich wich wich age 1 losed losed losed age losed losed pen age 3 losed pen losed age 4 losed pen pen age 5 pen pen losed age 6 pen losed losed age 7 pen losed pen age 8 pen pen pen M R /06/$ IEEE. 944

2 In secor (where phase cren is posiive wih larger module) fo equivalen saes are verified in sages 1,, 3 and 6 and wo equivalen saes are verified in sages 7 and 8. When cren is flowing from one phase o anoher, wihou circulae in he load, wo swiches may be closed and for obaining of null line volages all hree swiches should be closed. V3 (0 1 0) 3 u (1 1 0) V 1 III. E VETR MDULTI For unidirecional recifiers, he definiion of he vecors is a lile differen o he radiional way [6][7]. In his case, available vecors implemenaion considers phase crens direcion. upposing ha he crens are in phase wih he respecive volages, his sysem presens an equivalen circui wih he relaionship beween inpu volages and recifier fundamenal volage componen showed in Fig.. From vecor secors and cren secors inersecion, subsecors are defined as shown in Fig. 3. pace vecor represenaion is made in one diagram divided in hese sub-secors as shown in Fig. 4. Each cren secor presens fo available vecors. In sub-secor 1, he larger cren is in phase and his cren is posiive and vecors, V 1 and V are used. For hese cren signals, space vecor V 1 is performed in he operaion sage of Fig. 5. pace vecor V is performed in he operaion sage of Fig. 6. vf ir L vr IF δ VF X I L F L (0 1 1) D 1 V4 3 4 V5 (0 0 1) (1 0 1) δ V6 Fig. 4. pace vecor represenaion. D 3 D 5 D 3 D 5 D 4 D D 6 L L i i i v v () v D 4 D 1 D D 6 D 3 D 4 (1 0 0) u α D 1 D D 5 D 6 i Fig. 5. peraion sage for vecor V 1 in sub-secor 1. R V R Fig.. Relaionship beween inpu volages and recifier fundamenal volage componen. Vecor ecors ecor ecor 1 ecor 6 ecor 5 ecor 4 ecor 3 ecor D 3 D 5 D 3 D 5 D 4 D 1 D 6 D 4 D 1 D 6 D 3 D 4 D 1 D 5 D 6 i R vr i i i () R () v vr L D L L i i i D D v v () v () ren ecors δ ecor - ecor ecor - ecor ecor - ecor Fig. 3. ub-secors definiion. π ω Fig. 6. peraion sage for vecor V in sub-secor 1. However, in sub-secor 1, he larger cren is in phase and his cren is negaive and uilized vecors are he same of he previous case:, V 1 and V. Therefore, space vecor is performed in he operaion sage of Fig. 7 and space vecor V is performed in he operaion sage of Fig

3 In boh secors, o implemen null vecor, i is necessary ha he hree swiches are closed. The logic for command signals considers ha he swich in he arm which processes he larges cren is closed in respecive cren secor inerval. roposed conrol signals for implemening hese vecors are shown in Table II. The general rule for formaion of vecors is: o ge he one value in he desired vecor, he swich in corresponden phase is closed (on) when he cren wih greaer module is posiive and he swich is open (off) when his cren is negaive. To ge he zero value in he vecor, his logic is invered. These rules may no be applied o null vecor. Vecor sequences were chosen so ha, in hree phases, he level of conrol signal is he same a he beginning and a he ending of his period (on). The logic main objecive is he minimizaion of he number of commuaions of he swiches and reducion of he converer losses. D 1 D 1 D 1 i For sub-secor 1, he proposed vecors sequence VVVVV, resuling in command signals of Fig. 9. The inervals for he commands of swiches are given in (1). T = T T = T0 T (1) T = T is Using he projecions of he vecors in he axes α and for he respecive secors, hree-phase duy-cycles are deermined in funcion of D α and D duy cycles as showed in (). D = D = 1 Dα D 3 1 D = 1 Dα D For sub-secor 1, he proposed vecor sequence is VVVVV , resuling in command signals of Fig. 10. () D 3 D 5 D 3 D 5 D 6 D 4 D 4 D 6 D 3 D 4 D 5 D 6 R cmd T T 1 T D D D L L L cmd i i i v v () v cmd Fig. 7. peraion sage for vecor V 1 in sub-secor 1. V ( 1 1 0) ( 1 0 0) V ( 1 1 0) D 1 D 1 D 1 i T D 3 D 5 D 3 D 5 D D 6 D 4 4 D 6 D 3 D 4 D 5 D 6 R Fig. 9. ommand signals for sub-secor 1. D D D T 1 T T 1 L L L cmd i i i v v () v () cmd Fig. 8. peraion sage for vecor V in sub-secor 1. TLE II TRL IGL FR U-ETR 1 D 1. U-ETR 1 U-ETR 1 Vecor (1 0 0) n ff ff ff n n V (1 1 0) n n ff ff ff n (0 0 0) n n n n n n cmd ( 1 0 0) V ( 1 1 0) T ( 1 0 0) Fig. 10. ommand signals for sub-secor

4 In his case, he inervals for he commands of swiches are given in (3). T = T0 T = T0 T1 (3) T = T Three-phase duy cycles are showed in (4). 3 1 D = 1 Dα D D = 1 D D = 1 Exending his analysis o he oher secors, he duy-cycle funcions for each swich, are defined as showed in Fig 11, were duy-cycle for swich is presened. In he analysis of duy-cycle equaions, one can verify ha he expressions for neighboring sub-secors are he same in he same cren secor. Therefore, i is no necessary idenify he secors of vecors; only impose desired cren secors from inpu volages. IV. MDELIG D TRL Using lark and ark ransformaion marices, presened in (5) and in (6), he dynamic equaions for describing sysem behavior are obained when he hree-phase WM recifier is modeled (7) [4] u M α = u M dq = 0 cos( ) sin( ) ω ω 0 sin( ω ) cos( ω ) (4) (5) (6) did 3 L = V L ω Iq RE Id V Dd() d diq L = L ω Id RE Iq V Dq() d Direc axis cren and square axis cren decoupling [8] is applied o deermine cren loop ransfer funcions (8). ω L D = D I ω L D = D I d d q V q q d V Transfer funcions for I q and I d compensaors design are shown in (9). i% d() s V = d% d '( s) L s R i% q V = d% q '( s) L s R In he design of cren conrollers i is adoped one mehodology similar o he mehodology applied for singlephase boos recifier. nly direc cren loop is considered in volage loop design, as showed in Fig. 1. s he cren loop is faser han he volage loop, jus is saic gain is considered in volage loop compensaor design. Transfer funcion for v % (s) % i dref(s) is shown in (10). E v% 1 3 Vp R 3 η V 3 η V = i% dref Kh V R 1 s E E 4 R L 1 s (7) (8) (9) (10) Vecor conrol sruce is showed in Fig. 13. In he conrol sysem, inpu crens are sampled, lark and ark ransformaions are applied o hese variables and dq0 crens are obained. For a sysem wih high power facor, he q-axis cren mus be zero. Therefore, he reference for he conroller of his cren is also zero. The reference for d-axis cren comes from volage conroller Da 0.4 REF i I d REF V d d % id d% d id v % v i% d K h 0.1 K a w(rad) Fig. 11. Duy-cycle for swich. Fig. 1. Volage loop block diagram. 947

5 (0 1 1) V 4 V 3 (0 1 0) (0 0 0) V 0 V 7 (1 1 0) (1 1 1) V V (1 0 1) V6 5 (0 0 1) (1 0 0) V 1 α M D 1 D 1 D 1 i D 3 D 5 D 3 D 5 D 3 D 5 D 4 D 6 D 4 D 6 D 4 D 6 R D D D L L L i i i cmd D α v v v cmd D cmd i i i Iq M α, M dq Id I qref Iq Id D q D d Dq Dd 1 M dq I dref V Fig. 14. Laboraory seup. REF Fig. 13. Vecor conrol sruce. The oupus of cren conrollers are he duy-cycles for d- axis and for q-axis. These duy-cycles are decoupled and inverse ark ransformaion is applied o hese variables. Duy cycles for α-axis and for -axis are he resuls of his ransformaion, and hese signals are used in space vecor modulaion. In digial conrol of he WM recifier, he TM30LF407 D is used. For cren loops, he sample rae is in swiching frequency and for volage loop, he sample rae is in line frequency. V. EXERIMETL REULT ower parameers used in experimenal verificaion are showed in Table III. n example of design procede is presened in [4]. In Fig. 14 is presened he laboraory seup for a 0 kw WM recifier. WM signals for sub-secor 1 are in Fig. 15 and WM signals for sub-secor 1 are in Fig. 16. These signals are in accord wih proposed signals showed in Fig. 9 and Fig. 10. In Fig. 17 are presened duy-cycles for hree phases, wih forma similar o heoreical duy-cycle. The inpu crens in he unidirecional WM recifier are presened in Fig. 18, where i should be observed ha hey presen a low cren disorion (THD 40 = 3.16%). TLE III EIFITI UED I IMULTI Variable Descripion Value V eak line volage 311 V p V in RM inpu volage 0 V V o upu volage 700 V f Line frequency 60 Hz r upu power 0 kw o L,L,L 1 3 Recifier inpu inducors.4 mh upu capacior 4400 µf o f s wiching frequency 10k Hz Fig. 15. WM signals for sub-secor 1 Fig. 16. WM signals for sub-secor 1. In Fig. 19 are presened simulaneously he inpu cren in phase and volage reference for phase. In his case, he sysem presens a high power facor (0.998). 948

6 The recifier power facor as funcion of oupu power is in Fig. 1. In his case, he meased inpu volage oal harmonic disorion is.83%. In Fig. is presened he recifier efficiency as funcion of oupu power. The recifier efficiency is greaer han 95% when i is operaing above one half of nominal load Fig. 17. Duy-cycles for phases, and Fig. 0. THD of inpu crens as funcion of oupu power (* experimenal measemens) Fig. 18. Inpu line crens (0 /div) Fig. 1. ower facor as funcion of oupu power (* experimenal measemens) Efficiency (%) 90 Fig. 19. Inpu volage reference and cren in phase. Fig. 0 shows he THD of recifier inpu crens as funcion of oupu power Fig.. Recifier efficiency as funcion of oupu power (* experimenal measemens). 949

7 VI. LUI mehodology o apply space vecor modulaion echnique was proposed o hree-phase hree-swich wo-level unidirecional WM recifier. This mehodology is summarized as: - Idenificaion of cren secors and vecor secors and definiion of sub-secors; - nalysis of opological sages of converer and verificaion of available vecors in each sub-secor; - Definiion of more adequae logic for dispose he command signals and vecors sequence; - Deerminaion of inervals for applicaion of vecors and calculus of duy-cycles funcions in sub-secors; - Implemenaion of command signals from WM modulaor. Wih his mehodology, i is no necessary deermine he secors of vecors, only impose desired cren secors from inpu volages references. The proposed mehodology may be applied o oher wo-level unidirecional WM recifiers [9][10]. roposed modulaion reduces he number of commuaions of swiches and i improves recifier efficiency. Recifier models for cren loops and for volage loop are presened and vecor conrol sruce was described for an implemenaion wih D conroller. Experimenal resuls validae he implemened modulaion and applied conrol sraegy. Unidirecional wo-level WM recifier presens regulaed oupu volage, high efficiency, high power facor and low inpu cren THD. REFEREE [1] J. W. Kolar and H. Erl, aus of he echniques of hree-phase recifier sysems wih low effecs on he mains, The 1s Inernaional Telecommunicaions Energy onference, ITELE '99, June 6-9, [] J. W. Kolar and F.. Zach, novel hree-phase uiliy inerface minimizing line cren harmonics of high-power elecommunicaions recifier modules, IEEE Transacions on Indusrial Elecronics, Volume 44, Issue 4, ug. 1997, pp [3] J. W. Kolar, U. Drofenik and F.. Zach, pace vecor based analysis of he variaion and conrol of he neural poin poenial of hyseresis cren conrolled hree-phase/swich/level WM recifier sysems, roceedings of Inernaional onference on ower Elecronics and Drive ysems, vol. 1, Feb. 1-4, [4] D. orgonovo, Y. R. ovaes and I. arbi, hree-phase hree-swich wo-level WM recifier, roc. of he 34 h nnual IEEE ower Elecronics pecialiss onference, capulco-mexico, 003, pp [5] T. Viianen and H. Tuusa, Experimenal resuls of vecor conrolled and vecor modulaed VIE I recifier, Record of he 35h IEEE ower Elecronics pecialiss onference, vol. 6, June 5-6, 004, pp [6] H. W. Van Der roeck, H. kudelny and G. V. anke, nalysis and realizaion of a pulse widh modulaor based on volage space vecors, IEEE Trans. n Indusry pplicaions, vol. 4, 1988, pp [7] J. W. Kolar and J. W. Droferuk, new swiching loss reduced disconinuous WM scheme for a unidirecional hree-phase/swich/level boos-ype WM (VIE) recifier, The 1s Inernaional Telecommunicaions Energy onference, ITELE '99, June 6-9, [8] M. ichowlas and M.. Kamierkowski, omparison of cren conrol echniques for WM recifiers, roceedings of he 00 IEEE Inernaional ymposium on Indusrial Elecronics, IIE 00, vol. 4, July 8-11, 00, pp [9] Rong-Jie Tu and hern-lin hen, new space-vecor-modulaed conrol for a unidirecional hree-phase swich-mode recifier, IEEE Transacions on Indusrial Elecronics, vol. 45, no., 1998, pp [10] W. Koczara and. ialoskorki, Uniy power facor hree-phase recifiers, 4h nnual IEEE ower Elecronics pecialiss onference, E '93, Record. 0-4, June 1993, pp