Design Considerations of Coupling Inductance for Active Power Filters

Transcription

1 Deign Conideation of Coupling nductance fo Actie Powe Filte Ning-Yi Dai, Man-Chung Wong Depatent of Electical and Electonic Engineeing Unieity of Macau Macau, P.R. China Abtact A ethod fo calculating the coupling inductance of actie powe filte (APF i popoed in thi pape. The cuent ipple i defined and it elationhip with the coupling inductance alue i deduced baed on eo analye. Hence, the lowe bounday of the inducto alue could be deteined fo the cuent ipple liit. A ethod to etiate the uppe bounday of the inducto alue i alo popoed baed on the capability to tack copenating cuent efeence. t i uggeted to elect the coupling inducto alue cloe to the lowe bounday fo the APF. The uppe bounday i ued to check if any futhe ipoeent i needed fo getting the balance between tacking peed and uppeing cuent ipple. The conete topology and odulation ignal chee ae alo conideed in electing the coupling inducto. iulation and expeiental eult ae poided to how the alidity of the popoed ethod. Copaion with peiou ethod ae alo gien. The popoed ethod ay alo wok fo othe inducto-coupled yte, uch a TATCOM. Keywod-actie powe filte, coupling cicuit, oltage ouce conete. NTRODUCTON Actie powe filte (APF ae widely ued paallel powe quality copenato fo copenating cuent haonic, eactie cuent and neutal cuent in thee-phae fou-wie yte [1]-[3]. The baic tuctue of the APF i hown in Fig.1. A coupling inductance i connected between the point of coon coupling (PCC and the oltage ouce conete (C To elect a pope coupling inductance i ipotant fo the APF, ince it diectly affect the output filteing and haonic tacking capability. The deign of coupling inductance wa baed on the capability of copenating eactie cuent and haonic cuent in [3]-[5]. The application of thi ethod i liited ince load chaacteitic ae needed fo calculating the inductance, which ae uually tie-aying and oetie unaailable. ince only paaete fo the APF ae needed fo calculating the inductance, the capability of uppeing output cuent ipple wa ued oe often [3] [6]-[9]. Diffeent ethod ae poided to etiate the inducto alue fo atifying the cuent ipple liit. Howee, thee i no clealy definition fo the cuent ipple. The elationhip between the The cience and Technology Deelopent Fund, Macao AR Goenent Unieity of Macau cuent ipple and inducto alue i only oughly etiated without eo analye. Hence, the accuacy of the obtained eult could not be guaanteed. n addition, the effect of the conete topology and odulation ignal on cuent ipple ae oelooked in the pat tudie. When both copenation capability and cuent ipple liit ae conideed, a ange of coupling inductance i obtained [10]. Howee, the obtained uppe bounday i fequently alle than the lowe bounday by uing the ethod in [10]. iulation tet ay poide a taightfowad ethod to deteine the coupling inductance in the gien ange, but tyand-tet poce i uually tie-conuing, epecially fo the beginne in thi field. Hence, the ethod fo deteining coupling inducto of the APF need to be ipoed. n thi pape, deign ethod of the coupling inductance of the APF i tudied. n eion, the cuent ipple i defined a the axiu diffeence between the copenating cuent and it efeence in a pule width odulation (PWM peiod. The ethod of calculating the iniu coupling inductance to atify the cuent ipple liit i deduced baed on the eo analye. The conete leel and odulation ignal ae alo conideed when the coupling inductance i elected. The capability to tack copenating cuent i ued to deduce an uppe bounday of the inducto alue. Finally, a ethod fo deteining the pope coupling inducto of the APF i popoed in thi eion. n eion, iulation eult ae poided to how the alidity and copaion with peiou ethod ae poided. Expeiental eult ae poided in eion. PCC Coupling nductance PWM C Figue 1. Baic tuctue of the APF /11/$6.00 c 011 EEE 1370

2 . METHOD FOR CALCULATNG COUPLNG NDUCTANCE A. uppe the cuent ipple The coupling inductance of the APF could uppe the output cuent ipple. When the peiod of the PWM contol i all enough, the cuent paing though the coupling inducto aie linealy, a gien in (1 and illutated in Fig.. L T in Δ * =, (1 whee in i the aeage output of the inete in a witching peiod, i the oltage at the PCC, and T i the peiod of PWM. Figue. Cuent ipple and yetical-aligned odulation ignal When PWM i ued to contol oltage ouce conete, the output oltage of the C alway change dicontinuouly. Fo exaple, the output oltage aie between 0 and _bu fo a two-leel. A hown in Fig., the output oltage of the conete aie between two neighboing leel to yntheize the efeence oltage. The aeage output oltage in each peiod equal to in, a expeed in (. in T = DT ( Eq. ( i fo two-leel and it need to be eied a (3 fo a ulti-leel C [11]. t i aued in i in the ange of offet to offet +. denote oltage of each leel, D i the duty atio and offet i intege ultiple of. in offet * Δ T = ( + DT + (1 D T (3 offet Fo iplicity, ( fo two-leel inete i ued heeinafte. Howee, it can be poed that all the deduced eult alo wok fo ulti-leel inete. The ouce oltage i aued to be a contant in a peiod. The cuent paing though the coupling inducto aie like a awtooth wae. yeticalaligned odulation ignal i elected ince it gie the lowet cuent ipple [1]. The cuent aiation in a peiod i hown in Fig. and i expeed in (4. 1 D 1 D Δ = T + DT + T (4 L L L * Accoding to (, the Δ in (1 and Δ in (4 ae the ae. Pactically, dead-tie duing the witching, delay in the contol yte and eo in the inducto alue geneate eo * between Δ and Δ. They ay not atch exactly a hown in Fig.. All thee facto ae oelooked in thi pape ince they ae not the ain caue of the cuent ipple. The cuent ipple exit ainly due to the output oltage of the inete change dicontinuouly. A hown in Fig., the eo between the copenating cuent and it efeence ae two hadowed aea. Due to the yetical popetie, the aea of the two hadowed eo aea i the ae and total eo aea i calculated by (5, 1 T Δ 1 T DT 1 DT Δ eo = [ + ( + Δ ( + Δ ] 1 1 D = T ( Δ + Δ (5 whee Δ i the change of the APF output cuent fo 0 to 1 D (1-DT/, and Δ = T. Cobined with ( and L (4, (5 could be futhe eied a: T eo = ( D D (6 4L ince D i the duty atio and aie fo 0 to 1, eo d eo inceae a inceae. Accoding to (7, equal dd zeo when D=1/, i.e., the axiu alue of eo occu when D=1/. deo T = ( D = 0 (7 dd 4L Cuent ipple i defined a (8, which i the axiu aiation of the output cuent of the APF fo the efeence cuent in a peiod. Accoding to (5, the elationhip between the eo aea and cuent ipple i gien in (9. ipple = Δ (1 D + Δ 1 eo = T ipple (9 When D=1/ and the eo aea achiee the axiu alue, ipple i ipple (8 T =. (10 8L 011 6th EEE Confeence on ndutial Electonic and Application 1371

3 f the cuent ipple i et to be alle than Δ, (11 i obtained. L (11 8 f Δ n addition, if left-aligned o ight-aligned odulation i ued intead of yetical-aligned odulation, the cuent ipple i hown in Fig.3. The eo aea i calculated by (1 and the coeponding cuent ipple i gien in (13. 1 eo = T ( Δ DΔ (1 = Δ DΔ (13 ipple When D=1/, ipple i T ipple = (14 4L The cuent ipple i doubled. Hence, the yeticalaligned odulation could educe the cuent ipple without inceaing the witching fequency. t i uggeted to be adopted in APF. Fo ulti-leel inete = _bu / (Leel- 1, and (11 i eied a (15. L (15 8( Leel 1 f Δ Finally, (15 i eployed fo handling coupling inducto alue in the following dicuion. B. Cuent tacking peed When only eactie cuent i copenated by the APF, the yte oltage and output cuent of the APF ae expeed a (16 and (17. = in( ωt (16 i = in( ω t 90 (17 ipple DT Δ Δ T in 0 Cuent Refeence Output oltage of DT T Figue 3. Cuent ipple and left-aligned odulation ignal The lope of the copenating cuent i (18. di dt = ω co( ωt 90 = ω inωt (18 The elationhip between the coupling inducto and the lope of the copenating cuent i di in =. (19 dt L f the axiu alue of the cuent lope in (18 could be achieed, the coupling inducto hould atify (0. in L (0 ω Accoding to (16 and (18, the ouce oltage eache it peak when the lope of the copenating cuent eache the axiu alue. The oltage aco the coupling inducto fo tacking the axiu cuent lope of diffeent type of C ae lited in Table. _bu i the oltage of the inete and phae_to_neutal i the oot-ean-quae (RM alue of the phae-to-neutal oltage at PCC. A facto of two i diided fo thee-leg full bidge inete and fou-leg inete, ince two inducto exit in the phae-to-phae cicuit. Fo iplicity, it i aued = and (1 i obtained. L in in = (1 ω ω could be etiated accoding to Table, and the typical alue of i in the ange of 0.1~0.3. When eactie cuent and cuent haonic ae copenated iultaneouly by APF, the cuent lope i expeed a: di di c dich = +, ( dt dt dt d( h t whee di ch in( ω ϕh ch h= = dt dt = h= ch hω co( hωt ϕ (3 TABLE. OLTAGE DROP ACRO THE NDUCTOR FOR DFFERENT C Conete topology ingle-phae C Thee-phae full bidge C Thee-leg cente-plit C Fou-leg C in h phae _ to _ neutal ( _ 6 bu / phae to ( _ 6 bu neutal / phae _ to _ neutal phae to neutal / th EEE Confeence on ndutial Electonic and Application

4 nequality in (4 need to hold fo tacking the axiu cuent lope. L (4 ω + hω co( hωt ϕ h= ch The axiu cuent lope aie with phae hift between the haonic cuent and eactie cuent. t i alo not feaible to include all the haonic in (4. Pactically, the iplified eion (5 could be ued to deteine the uppe bounday of the coupling inductance. L (5 cω c i the cuent ating of the APF and i uggeted to elect the ode of the ot ignificant haonic in the load cuent. The alue of could be etiated without eauing the load cuent. When the load ae ainly hoe o office appliance, which ue ingle-phae witch ode powe upply, hould be thee. f the load i a thee-phae adjutable peed die, uually elect fie. C. Method fo calculating coupling inductance Cobining the eult of the peiou two pat; the ange of the coupling-inductance of an APF i expeed a (6. The detailed explanation fo each paaete ae gien in Table. The lowe bounday i totally deteined by the APF etting. The lat two paaete in Table ay with non-linea load to be copenated and ae ued fo etiating the uppe bounday. L (6 8 f ( Leel 1 Δ ω c When the final alue of the inducto i deteined, it i uggeted to elect a alue cloe to the lowe bounday. The alue cloe to the lowe bounday could poide bette cuent tacking peed with acceptable cuent ipple. A alle inducto alo educe the cot. Howee, it i uggeted to till tet the final alue by etiating the uppe bounday accoding to (6. n oe cae, the obtained uppe liit of the inducto alue i alle than the lowe liit. t indicate conflict exit in the equieent of cuent tacking peed and uppeing cuent ipple. oe appoache, uch a inceaing PWM fequency and adopting ulti-leel, could be conideed to educe the lowe bounday. Anothe altenatie olution i to ue LC o LCL filte in the coupling cicuit [13]. TABLE. PARAMETER FOR CALCULATNG NDUCTOR ALUE Paaete Explanation Exaple _bu DC bu oltage of the inete 00 Leel The leel of the o 3 f PWM fequency 5000 c Cuent ating of the APF (RM 5A ω Fundaental Fequency 314 Δ Maxiu cuent ipple. 0.5A Typical alue: 0.1 ~ The ode of the ot ignificant haonic 3 h. MULATON REULT A. Copae coupling inducto alue of APF uing twoleel C iulation odel ae built by uing PCAD/EMTDC. A two-leel cente-plit oltage ouce conete i fit ued a the ain cicuit of the actie powe filte. The yte configuation i hown in Fig.4. Paaete ae lited in Table and oot ean quae (RM alue of ouce oltage i 55. ingle-phae ectifie ae ued a load. Hence, the ot ignificant haonic ae thid ode haonic. n addition, yetical-aligned chee i ued in PWM ethod. Foula fo calculating the coupling inducto in [6][8][10] ae gien in (7-(9 epectiely _ f Δ 6 f Δ Δ ω c _ ax bu < L L Δ L 4Δ f whee in (9 i the diffeence between the ouce oltage and the inete oltage, which depend on the alue of the DC link oltage and the odulation index, and Δ = 0. i ued in thi pape. The inducto alue calculated by diffeent ethod ae lited in Table. The lowe bounday i lage than uppe bounday when both (6 and (9 ae ued. Howee, the eo in the popoed ethod i uch alle. ince thee i no dicuion about how to elect the inducto alue inide the gien ange in [10]. The popoed ethod i uch eaie fo the ue to find a pope inducto alue. The total haonic ditotion (THD of the load cuent i 30.8% and RM of neutal cuent i 9.A befoe copenation. THD of the ouce cuent and RM alue of neutal cuent afte copenation ae lited in Table. Reult indicate that the copenating pefoance i kept acceptable when the inducto i elected in the popoed ange. Figue 4. APF ue two-leel cente-plit conete 011 6th EEE Confeence on ndutial Electonic and Application 1373

5 TABLE. COUPLNG NDUCTANCE AND COMPENATON REULT FOR THE APF UNG TWO-LEEL NERTER Foula L(H THD Neutal cuent Eq. (17 Lin=15 9.7% 3.A Eq. (8 Lin= %.8A Eq. (9 Lin= % 3.7A Lax= % 1.9A Eq. (6 Lin= %.A Lax=8.4 6.% 1.9A B. Copae coupling inducto alue of APF uing theeleel C n ode to educe the lowe bounday of the inducto alue, thee-leel cente-plit conete i ued intead of the twoleel inete in the APF odel. The yte configuation i hown in Fig.5. The othe etting ae the ae a thoe gien in Table. The lowe bounday i educed to 5H by uing the popoed ethod, a lited in Table. ince conete topology i not conideed in [6][8] and [10], the inducto alue ae the ae fo thee ethod. The iulation eult of the APF uing thee-leel C ae gien in Table. Reult indicate that the popoed ethod could adjut the coupling inducto alue accoding to the inete topology, o that it i oe geneal applicable than peiou ethod. Fig.6 how the pefoance of the APF to tack the copenating cuent efeence fo thee diffeent inducto alue. A lage inducto alue educe the cuent tacking peed, while a alle inducto alue inceae the cuent ipple. When inducto alue i 5H, the ouce cuent ae hown in Fig.7, in which the APF begin copenation at Figue 6. Output cuent and efeence cuent of the APF uing thee-leel inete Figue 7. ouce cuent when L=5H. EXPERMENTAL REULT A thee-phae fou-wie APF pototype i built, in which a thee-leel cente-plit C i ued. The yte configuation i hown in Fig.5. The paaete in Table ae ued and coupling inducto i 5H. The ouce cuent befoe copenation and afte copenation togethe with the ouce oltage ae hown in Fig.8. The coeponding paaete ae lited in Table. Figue 5. APF ue thee-leel cente-plit conete TABLE. COUPLNG NDUCTANCE AND COMPENATON REULT FOR THE APF UNG THREE-LEEL NERTER L(H THD Neutal cuent Eq. (17 Lin=15 9.4% 3.1A Eq. (8 Lin= %.8A Eq. (9 Lin= % 3.6A Lax= % 1.8A Eq. (6 Lin=5 5.43% 1.6A Lax= % 1.9A Figue 8. Expeiental eult th EEE Confeence on ndutial Electonic and Application

6 TABLE. COMPENATON PERFORMANCE THD Powe Facto Diplaceent Powe facto Load Cuent 5.3% ouce Cuent 6.5% CONCLUON A ethod fo calculating the ange of the coupling inductance of actie powe filte i popoed in thi pape. The inducto alue i uggeted to elect nea the lowe bounday, which i calculated accoding to the cuent ipple liit. The uppe bounday i etiated accoding to copenation equieent, which could be ued to decide if any futhe ipoeent i needed fo educing the cuent ipple. iulation and expeiental eult ae poided to how it alidity. Copaion with othe ethod ae alo poided. Reult indicate that the popoed ethod ha bette accuacy and i oe geneal applicable in electing the coupling inducto of the APF. ACKNOWLEDGMENT The autho would like to thank the cience and Technology Deelopent Fund, Macao AR Goenent and Unieity of Macau fo thei financial uppot. REFERENCE [1] H. Akagi, New tend in actie filte fo powe conditioning, EEE tan. nduty Application, ol. 3, no.6, pp , No [] Ning-Yi Dai, Man-Chung Wong, Ying-Duo Han, Application of a Thee-leel NPC nete a a 3-Phae 4-Wie Powe Quality Copenato by Genealized 3DM, EEE Tan. Powe Electo., ol.1,no., pp , Mach 006. [3] A. Chaoui, J.P. Gaubet, et.al., On the deign of hunt actie filte fo ipoing powe quality, in Poc.EEE ndutial Electonic ypoiu ( E 008, pp [4]. J. Chiang, J.M. Chang, Deign and pleentation of the paallelable actie powe filte, in Poc.EEE 30th Powe Electo. pec. Conf. (PEC 99, ol. 1, June/July 1999, pp [5]. K. Jain, P. Agawal, H.O. Gupta, Fuzzy logic contolled hunt actie powe filte fo powe quality ipoeent, EE Poc. Elect. Powe Appl., ol. 149, no. 5, pp ept. 00. [6] A. Caini, F. Ronchi,, A. Tilli, Fou-wie hunt actie filte: optiized deign ethodology, in Poc. 003 EEE nd. Electon. oc. (ECON, ol.3, pp [7]. Ponnalui, A. Bickwedde, yte Deign of Thee phae Actie filte uing Tie doain technique, in Poc EPE. Powe Electonic n Geneation, Taniion And Ditibution Of Electical Enegy. Gaz, Autia.001. [8] F. Ronchi,, A. Tilli, Deign Methodology fo hunt actie filte in Poc. EPEEPMC, 10th ntenational Powe Electonic and Motion Contal Confeence, Coatia, 00. [9] L.A. Moan, J.W. Dixon, R.R. Wallace, A thee-phae actie powe filte opeating with fixed witching fequency fo eactie powe and cuent haonic copenation, EEE Tan. nduty Electonic, ol.4, no.4, pp , Aug [10] H. J. Azeedo, J. M. Feeia, A. P. Matin and A.. Caalho, Diect cuent contol of an actie powe filte fo haonic eliination, powe facto coection and load unbalancing copenation in Poc. EPE, powe electonic in geneation, taniion and ditibution of electical enegy,touloue,003. [11] Ning-Yi Dai, Man-Chung Wong, Ng Fan, Ying-Duo Han, A FPGAbaed Genealized Pule Width Modulato fo Thee-leg Cente-plit and Fou-leg oltage ouce nete, EEE Tan. Powe Electon., ol.3, no.3, pp , May 008. [1] R. Zhang,. Hiahu Paad, D. Booyeich, and F. C. Lee, Thee dienional pace ecto odulation fo fou-leg oltage-ouce conete, EEE Tan Powe Electon., ol. 17, no. 3, pp , May 00. [13] O. odyakho, C. C. Mi, Thee-leel nete-baed hunt actie powe filte in thee-phae thee-wie and fou-wie yte, EEE Tan. Powe Electon., ol.4, no.5, pp , May th EEE Confeence on ndutial Electonic and Application 1375