Voltage Balancing Method Using Phase-Shifted PWM for Stacked Multicell Converters

Transcription

1 oltage Balancng Method Ung haeshfted WM for Stacked Multcell onverter Amer M. Y. M. Gha () Joep ou ()() alo G. Ageld () Mha obotaru () () Autralan Energy Reearch Inttute & School of Electrcal Engneerng and Telecommuncaton, The Unverty of New South Wale, UNSW Sydney, NSW 5, Autrala. () Terraa Indutral Electronc Group & Department of Electronc Engneerng, Techncal Unverty of atalona, atalona, Span. Emal: Abtract Th paper propoe an actve voltage balancng method for tacked multcell converter (SM) ung phaehfted pulewdth modulaton, whch eay to mplement and extend to hgh number of level. The propoed method balance the voltage of the capactor by modfyng the duty cycle of each wtch of the SM ung a proportonal controller. The croed effect between capactor current and duty cycle condered and ued for optmal capactor voltage balance. The performance of the propoed voltage balancng method verfed by mulaton for dfferent operatng condton, uch a unbalanced lnear load, nonlnear load and load tranent. Index Term Multlevel converter; Stacked multcell converter; apactor voltage balancng; ulewdth modulaton. I. INTRODUTION Multlevel converter allow hgher voltage/power ratng, lower total harmonc dtorton (THD), and lower loe, when compared wth the conventonal twolevel converter [], []. The mot popular multlevel toploge are the cacaded multmodular converter [3], the modular multlevel converter (MM) [4], the neutralpontclamped (N) converter [5], and the flyng capactor (F) converter [6]. Mot of thee topologe are well etablhed by ndutry. Multlevel topologe wth more than fve level, requre to tore large amount of energy, whch trongly mpact on the converter ze and prce. Recently, hybrd multlevel converter ha been ntroduced and are condered a compettve oluton, nce they requre le energy torage when compared wth the popular multlevel topologe [7]. One of the hybrd multlevel topology the tacked multcell converter (SM) whch cont of two multlevel F converter that are tacked together to generate multlevel voltage waveform, a hown n Fg.. Th Y (cell) Z(tage) SM allow hgher voltage, wth reduced F n the converter, when compared wth the conventonal multlevel F converter. Lke the other multlevel topologe, the SM alo requre capactor voltage balancng for the acceptable performance of the converter. In [9] [5], phaehfted pulewdth modulaton (SWM) wa propoed, whch provde natural voltage balance. However, natural voltage balance depend on the load condton. The dynamc of the converter low down wth dfferent type of load condton. Some reference n [9], [], [], [4] propoed a balance booter to acheve fat voltage balance dynamc. Th balance booter cont of a pave RL flter, whch ntroduce addtonal power loe. There are a few actve voltage balancng method found n the techncal lterature [6] [8]. In [6], a drect torque control method wa propoed. Th method regulate the F voltage; however, no lnetolne voltage hown and analyzed n the paper. Another actve balancng method wa propoed n [7], whch make ue of a ldng mode oberver. Th method perform well a t doe not requre any voltage enor. However, the method complcated and requre a lot of computaton. Fnally, an actve voltage balancng method whch wa propoed n [6], cont on evaluatng a cot functon for the redundant tate ung pace vector modulaton (SM) n a fourlevel hybrd SM. However, ome lmtaton have been reported when operatng wth hgh modulaton ndce. The author ugget ncreang the number of voltage level to extend the operatng range of the converter, whch obvouly not an optmal oluton. The majorty of the oluton dcued above are complex from the mplementaton pont of vew and not eay to extend to hgher number of level. The man objectve of th paper to preent a novel actve voltage balancng method for the SM that effcent and can be ealy extended to any number of level. It mplemented ung SWM and baed on a proportonal ( ) controller. The effect between the F current and the duty cycle of the wtche are condered and ued to optmze the voltage balancng proce. Furthermore, the voltage balancng dynamc performance very good. Although the propoed method ha been appled to the evenlevel (3 ) SM, t can be ealy extended to any number of level. The ret of the paper organzed a follow. Secton II decrbe the operatng prncple of the SM. Secton III explan the propoed F voltage balancng method. Secton I preent mulaton reult from a evenlevel SM to verfy the effectvene of the propoed method. Fnally, the concluon are ummarzed n Secton. II. OERATING RINILE OF THE SM ONERTER Fg. how a crcut dagram of a threephae evenlevel SM. It cont of three cell (Y = 3) of F unt,

2 Reference Sgnal, v xref arrer 4 arrer5 arrer 6 a 3 a a a a Stage a 3 a 3 a a a a a a v a arrer Tme arrer arrer3 Stage a3 b3 b3 b3 a b b b b a b b b b v b Output oltage, v x Tme b b Fg.. SWM technque for 3 SM: reference nuodal gnal wth x carrer and output voltage. c3 b3 c3 c3 c3 ell3( Y ) c c c b c c c ell c c c b c c c ell Fg.. rcut dagram of a threephae 3 SM. whch are ntegrated to form two tage/tack (Z =).It called a 3 SM. The converter nclude four F, the upper F,.e, x and x, are n the Stage, whle the lower F x, x are n the Stage, where the ubcrpt x ued for phae dentfcaton x={a, b, c}. The bu cont of two capactor, and, each of them regulated to have a half of the lnk voltage ( /). Durng normal operaton, the mean voltage of the F x and x have to be mantaned at /6, wherea for F x and x have to be mantaned at /3. The output voltage v x can produce even voltage level (3 ),.e., /6, /3, /, /3, 5 /6, and. The wtch control functon are defned a xyz, where y denote the wtch number correpondng to a partcular cell n the phaeleg x of the SM converter y = {,.., Y } (Y =3), and z defne a partcular wtch aocated wth the tage Stage Stage ( Z ) v b z = {,.., Z} (Z =). The wtch control functon can take two value xyz = {, }, meanng and that the wtch off and on, repectvely. The wtch par n each phaeleg ( xyz and xyz ) operate n a complementary manner. Fg. how a nuodal reference gnal and the carrer gnal ung SWM appled to a 3 SM. In th converter, SWM requre x carrer. The upper three carrer n Stage are phaehfted between conecutve carrer. The ame charactertc apply to the three lower carrer n Stage. A nuodal reference gnal (v xref ) ha been normalzed to range n the nterval [, ] under lnear modulaton mode. It compared wth all x trangular carrer to defne the voltage level that ha to be generated at the output. Ung th method, natural voltage balancng can be acheved. However, the voltage balancng proce uually low and depend on the loadng condton. Therefore, an actve balancng method requred to regulate the F voltage at ther dered level wth mproved dynamc, epecally under tranent condton and unbalanced lnear/nonlnear load. III. ROOSED OLTAGE BALANING METHOD Fg. 3 how a general Y Z SM phaeleg chan. The propoed voltage balancng method developed baed on the analy of a generc cell ecton of the SM a hown n Fg. 3. In th analy Z = condered for mplcty. Aumng v xref >, where the wtche xy and x (y) are turned on. Therefore, the current through capactor xy repreented by [9]: x y =( x (y) xy ) x. () It can be oberved that durng v xref >, the current through a capactor affected by the control gnal aocated

3 xy xy ( ) x3 x x Y x( Y ) xy ( ) x x x x Stage( Z ) xy xy xy ( ) xy ( ) x3 x3 x x x x x( Y ) x x Y xy ( ) x x x Stage xy xy ( ) x3 x x elly ell ell x( y) x y y x( y) x( y ) y x y xy y x( y) x( y ) y x( y) x( y) x y x y x( y) x y x( y ) y xy y x( y) x( y ) x( y) x y Fg. 3. One phaeleg of an SM: General Y cell chan repreentaton and a ecton of the chan. x y v x y x y ( ) Sgn x d x( y ) d x y v xref Stage arrer Stage arrer WM x( y) Fg. 4. Development of the propoed voltage balancng method baed on (). x y to the two adjacent wtche. The locallyaveraged repreentaton of the capactor current calculated over a wtchng perod : x y =(d x (y) d xy ) x, () where x y and x are the locallyaveraged current of the capactor xy and the output current, repectvely, and d x (y) and d xy are the duty cycle of the wtche x (y) and xy for Stage, repectvely. Aumng a potve output current ( x > ), () how that by ncreang the duty cycle d x (y) the locallyaveraged current through the capactor wll ncreae, whle the oppote effect wll be produced f d xy ncreaed. If the voltage of the capactor xy greater than t reference value, a negatve current hould be mpoed to th capactor. Therefore,

4 x( Y ) x v xy ( ) x( Y ) v x x ( ) Sgn x d xy d d x v x ref xy ( ) xy xy ( ) x TABLE I SM ONERTER ARAMETERS rcut arameter alue D Lnk oltage ( ) Flyng apactor ( x, x ) 4 μf Load Retance (R) 44 Ω Load Inductance (L) 6mH arrer Frequency (f ) khz Fundamental Frequency (f) 5 Hz ontrol arameter ( ).4 x x( Y ) x v x v x xy ( ) x( Y ) v x x d x Stage x d xy d xy ( ) d x arrer Stage arrer xy xy ( ) x where, d x (y) = v xref Δd x (y), (5) d xy = v xref Δd xy. (6) Aumng mall varaton around the operatng pont, ung (5) and (6) n (4), one can obtan: Δv x y Δt = x (Δd x (y) Δd xy ) xy. (7) The varaton of the duty cycle are gven by a proportonal controller, a follow: Δd x (y) = gn( x )(ε xy ε x (y) ), (8) x x v x d x WM x Fg. 5. ropoed voltage balancng method for a general Y SM. the duty cycle d xy and d x (y) hould be ncreaed and decreaed, repectvely. On the other hand, f the output current negatve ( x <), the duty cycle hould be manpulated n the oppote drecton to help for voltage balance. Baed on th analy, the control method for voltage balancng developed for the upper cell located n the Stage. A mlar analy can be performed for the bottom capactor xy to acheve voltage balance, whch n the Stage. In th cae v xref <, and the wtche x (y) and xy are turned on. Fg. 4 how the propoed voltage balance method for a general cae, where Δd xy and Δd x (y) are control magntude added to the reference gnal v xref to compenate for voltage balance. Fg. 5 how the complete voltage balancng method for a Y SM. Aumng v xref >, the wtche xy and x (y) are turned on, the voltage balancng dynamc of capactor xy can be analyzed baed on: x y = xy dv x y dt From () and (3), one can obtan: dv x y dt dv x y dt = x y xy. (3) = x (d x (y) d xy ) xy, (4) Δd xy = gn( x )(ε x (y ) ε xy ), (9) where ε x (y ), ε xy, and ε x (y) are the voltage error of the capactor x (y ), xy, and x (y) at Stage, repectvely, and the proportonal control parameter. gn( x ) the gn of the output current defned a and when x potve and negatve, repectvely. Subttutng (8) and (9) nto (7): Δv x y Δt = x (ε xy ε x (y) ε x (y ) ) xy. () Equaton () defne the balancng dynamc of the propoed voltage control for Y SM when v xref > and can be ued to tune the controller gan parameter to acheve a atfactory converter performance. A mlar knd of analy can be performed for v xref <, when wtche x (y) and xy are turned on, for the voltage balance of the bottom capactor xy n Stage. I. ERFORMANE EALUATION Smulaton tet are performed on a threephae 3 SM converter a hown n Fg.. The converter ha been mulated ung the MATLAB/Smulnk [] and LES Toolbox []. The parameter of the converter are hown n Table I. The dynamc behavor of the propoed voltage balancng method hown n Fg. 6. In th tet, the SM operatng over a lnear unbalanced RL load (R a = 7.4Ω,R b = 7.6Ω,R c = 44Ω). The lnetolne voltage v ab and the capactor voltage (v a, v a, v a, and v a ) are hown n Fg. 6. In th mulaton, the ntal capactor voltage are et to v a =6, v a =4, v a =8,

5 oltage () 5 5 v ab v a v a v a v a urrent (A) Tme () Tme () Fg. 6. 3x SM operatng over an unbalanced lnear load. A tep change n the modulaton ndex from m =.6 to m =.9 occur at 8 m, and at 6 m a threephae Yconnected retve load added n parallel (R x = 88Ω): lnetolne voltage (v ab ) and F voltage (v a,v a,v a, and v a ), and output current ( a, b, and c). a b c oltage () 5 5 v ab v a v a v a v a Tme () urrent (A) 3 3 a b c Tme () Fg. 7. 3x SM operatng over an unbalanced lnear load and at m an nonlnear load added: lnetolne voltage (v ab ) and F voltage (v a,v a,v a, and v a ), and output current ( a, b, and c).

6 v a =6 and regulated to the dered voltage,.e. 6.67, 6.67, 33.33, and 33.33, repectvely, n about 3 m. It can be oberved that the propoed voltage balancng method capable of mantanng the capactor voltage at the reference value under th unbalanced condton. There a tep change n the modulaton ndex from m =.6 to m =.9 at 8 m, and later at 6 m, a threephae Yconnected retve load added n parallel (R x = 88Ω). Oberve that durng the tranent the voltage n the F reman unaffected. In Fg. 6, the load current ncreae a expected durng thee tranent. The propoed voltage balancng method prove to be robut under unbalanced load and tranent. Furthermore, although the propoed voltage balancng method baed on a proportonal controller, the capactor voltage are properly regulated at the reference value wth no zeroorder error n the teadytate. Th becaue no control acton requred (Δd xy =and Δd xy =for y = {,, 3}) when the capactor voltage are at the reference value. In Fg. 7, the converter teted agant a nonlnear load. Intaly, the converter operate over a lnear unbalanced RL load (R a = 44Ω,R b = 35.Ω,R c = 5.8Ω) wth a modulaton ndex of m =.9. At m, a nonlnear load contng of a threephae dode rectfer wth a flter capactor of 3μF and a load retor of 88Ω added. It can be oberved n Fg. 7, that the capactor voltage are mantaned to the dered reference. The load current hown n Fg. 7, are hghly dtorted a expected, but no effect on the F een. Hence, the propoed voltage balancng method qute robut, a the capactor voltage are mantaned at ther reference value under uch a nonlnear load and unbalanced condton.. ONLUSION A new voltage balancng method for SM operatng wth SWM ha preented whch enure the acceptable performance of the converter by mantanng the capactor voltage level. The method ha been formulated for a Y SM and teted on 3 SM whch produce even level. The propoed method baed on a proportonal controller whch able to remove the teadytate error. Th becaue when the capactor voltage are at ther reference value,.e. the voltage error are zero, no control acton requred. It can regulate the capactor voltage to ther reference value, even under unbalanced load, nonlnear load and tranent. Moreover, t mple and eay to mplement n any Y Z SM confguraton. AKNOWLEDGMENT Th work ha been upported by the Unverty of New South Wale, Autrala Energy Reearch Inttute and the School of Electrcal engneerng and Telecommuncaton. It ha alo been upported by the Mntero de Economa y ompettvdad of Span under project ENE3687. REFERENES [] J. S. La and F. Z. eng, Multlevel converter A new breed of power converter, IEEE Tran. Ind. Appl., vol. 3, no. 3, pp. 5957, May/Jun [] S. Kouro, M. Malnowk, K. Gopakumar, J. ou, L. G. Franquelo, B. Wu, J. Rodrguez, M. A. erez, and J. I. Leon, Recent advance and ndutral applcaton of multlevel converter, IEEE Tran. Ind. Electron., vol. 57, no. 8, pp , Aug.. [3] F. Z. eng, J. S. La, J. W. 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