Charge Equalization Based-on Three-Level NPC Converter for Series Connected Battery Strings

Transcription

1 WEA TRAACTIO on CIRCUIT nd YTEM Chrge Equliztion Bed-on Three-Leel PC Conerter for erie Connected Bttery tring KUEI-HIAG CHAO 1, CHIA-CHAG HU nd CHU-HI CHEG 1 Deprtment of Electricl Engineering, tionl Chin-Yi Unierity of Technology 5, Lne 15ec. 1, Chung-hn Rod, Tiping City, Tichung County TAIWA, R.O.C. chokh@ncut.edu.tw Intitute of Informtion nd Electricl Energy, tionl Chin-Yi Unierity of Technology Atrt: - The min purpoe of thi pper i to deign chrge equliztion circuit for erie connected led-id tterie. The chrger utilize three-leel neutrl point clmped (PC) AC/DC conerter with oltge lnce control to chrge the erie connected rechrgele ttery tring. Thi pper detil the opertion principle of the chrge equliztion circuit under different opertion mode nd derie the goerned eqution. The propoed chrge equliztion circuit cn not only regulte the power ftor of AC ource ide, ut lo cn lnce the chrge oltge for erie connected rechrgele tterie. Finlly, ome imultion reult re mde to demontrte the effectiene of the chrge equliztion circuit cheme preented in thi pper. Key-Word: Led-Acid Bttery, Chrge Equliztion Circuit, Three-Leel Conerter, Voltge Blnce Control, eutrl Point Clmped (PC) Conerter. 1 Introduction Led-id tterie ply n importnt role in humn life. In recent yer, the demnd for led-id tterie h increed due to energy hortge nd prolem of enironmentl pollution. Howeer, ingle rechrgele tterie cnnot tify the electricl demnd of mny ytem, generlly multiple tterie re erie connected into ttery pk in order to proide ufficient oltge. eerthele, when multiple rechrgele tterie re erie connected for rechrging, imlnce reult in the mount of electricity chrged into the tterie due to difference in internl chrteritic, nd chemicl component etween the tterie inoled. Conequently, the numer of tterie erie connected in ttery pk incree, the lifepn of the tterie will decree exponentilly [1,]. The min purpoe of ttery chrger i to crete n equilent tte-of-chrge (OC) in eh ttery in erie connected ttery pk. When there re unequl chrge etween tterie in ttery pk, high cpity tterie require le energy for rechrging, while lower cpity rechrgele tterie require higher energie for rechrging in order to meet the equilent chrging need of ttery pk. Current reerch on chrge equliztion technologie cn e rodly diided into extended time oerchrging, conumle chrge equliztion cheme, inductor chrge equliztion cheme, witched cpitor chrge equliztion ytem, nd multi-winding trnformer chrge equliztion cheme [-10]. The extended time oerchrging method [] inole extending the chrging time for erie connected ttery pk. Bttery pk tht generlly require only 1 hour for chrging he their chrging time extended in order to enure tht eery ttery within the pk i highly chrged nd to llow the lowet-cpity ttery to meet high-cpity need. Howeer, thi method led to the rik of g eepge in higher-cpity tterie. Conumle chrge equliztion cheme [4] connect chrge equlizer to eh ttery in ttery pk. Thee equlizer re generlly compoed of reitor, zener diode, nd oltge controlled current element. When ny ttery in the pk exceed et oltge, the equlizer re tited nd redirect portion of the chrging current to the equlizer, therey reducing current flow to tterie nd preenting the occurrence of oerchrging. Howeer, thi method wte ignificnt mount of energy on equlizer nd led to unnecery energy lo. Inductor chrge equliztion cheme [5] re diided into forwrd nd kwrd chrge equliztion cheme. The opertion principle of inductor chrge equliztion cheme i to ue witche nd inductor of chrge equliztion u-circuit to trnfer energy of high-cpity tterie, cuing the ttery energie of eery ttery in pk to e equlized. The hortcoming of thi method i tht the energy trnfer i limited y the cpity of the inductor, which my led to oerly long chrging time. Cpitor chrge equliztion cheme [] connect linked ttery pk I: Iue 11, Volume 8, oemer 009

2 WEA TRAACTIO on CIRCUIT nd YTEM to cheme coniting of i-direction witche nd cpitor. Thi cheme witche rpidly etween witche nd cpitor to trnfer unequl energy etween tterie, therey reducing power difference etween tterie nd ttining the gol of equl chrging. The hortcoming of thi method re tht energy trnfer i limited y the energy torge cpitie of the cpitor nd tht exceiely long equl chrging time my e produced. The opertion principle of multi-winding trnformer chrge equliztion cheme [-10] lie in uing DC-DC conerter to chrge erie connected ttery pk t the high-chrging rte when the erie connected ttery pk re in low-power tte t the eginning of the chrging proce; when the et oltge h een rehed, the tterie re witched to chrging under chrge equliztion mode. The chrge equliztion circuit of thi cheme conit of et of multi-winding trnformer nd DC-DC conerter. A the erie connected ttery pk chrge eh ttery t identicl oltge on the econdry ide, the tterie re chrged t identicl oltge; higher-cpity tterie re chrged t lower chrging rte, while reltiely lower-cpity tterie re chrged t higher rte. Conequently, oer period of time, the cpitie in eh ttery in erie connected ttery pk will e lnced, therey rehing the effect of chrge equliztion. Thi type of cheme fe the iue of mutul inductnce nd lekge inductnce etween mutully coupled winding. A reult, een with equl numer of winding turn, identicl chrge oltge cnnot e otined. Thi tudy preent the ue of three-leel neutrl point clmped AC/DC conerter to directly perform contnt oltge chrging in order to oercome the prolem with exiting rechrgele ttery chrge equliztion circuit. ot only cn the conerter nd their control cheme cue the power ftor for the AC input ide to pproh 1, it cn lo rpidly complete equl chrging for erie connected ttery pk. Three-Leel eutrl Point Clmped Conerter Chrge Equliztion cheme Figure 1 depict the propoed neutrl point oltge lnce control three-leel AC/DC conerter chrge equliztion cheme tht poee power ftor correction. o tht the power oltge will otin three-leel oltge we form eery 1 1/ cycle, we ue eight IGBT power emiconductor 1 8 power witche nd the neutrl point clmped rectifier compoed of four clmped diode D1 D4 [11-1]. A ooting inductor L i connected to the AC ide torge inductor for power ftor control; the DC ide of the conerter i connected to the eril ttery tring, o tht through the DC oltge controller, tle DC oltge cn e proided to chrge the erie connected ttery pk. In order for the power ftor of the input end to pproh 1.0, the error of DC feedk oltge V ' dc = K ( K i the ened oltge ftor ) nd commnd oltge produce the pek lue commnd I ˆ of the input current fter eing regulted y the oltge controller. Thi lue multiplied y the unit ine we ( ω t) with the me phe the input oltge produce the input current commnd i. Therefter, hyterei current controller (HCC) i ued to produce the witching control ignl for the power emiconductor, therey cuing the tul input ' current i = Ki ( K i the ened current ftor) cloely following commnd current i, cuing the power ftor of the AC input ide to pproh 1. Opertion Principle of the Chrge Equlizer We firt mke the following four umption to nlyze thi chrge equliztion circuit for rechrgele tterie: (1)ume tht ll component re idel nd do not uffer from oltge drop or witching lo; ()the chrteritic of the two rechrgele tterie re identicl; ()within hort witching period, input AC oltge cn e iewed contnt lue; (4)AC line reitnce R cn e ignored. For thi conerter, there re three poile witching tte1 = = 1 ( 5 = = 1 ) = = 1 ( = = 1 ), nd = 4 = 1 ( = 8 = 1 ). Conequently, there re = 9 poile chnge in witching mode for the three-leel neutrl point clmped conerter witch. Three of thee mode cn produce zero oltge t the input end oltge. To e on witching tte, only = = = = 1 zero oltge witching mode w elected. Thu, een poile witch witching mode remin; thee mode cn produce fie type of oltge ( 0, ±, ± Vdc ) leel t AC ide input oltge. If the three-leel input oltge we form i to e otined, the reltionhip etween electricl input oltge nd DC output oltge mut meet the condition of Vdc <, pek < Vdc. Conequently, we firt deignte < Vdc Are 1 nd deignte > V Are ; we ume tht dc I: Iue 11, Volume 8, oemer 009

3 WEA TRAACTIO on CIRCUIT nd YTEM = = V. dc Fig. 1 The cheme of three-leel PC AC/DC conerter chrge equlizer with power ftor correction If the three-leel AC/DC conerter i operted t forwrd power trnmiion, it cn e diided into een different opertion mode for nlyi. The circuit configurtion for the riou mode re hown in Fig. through 8; the correponding witch tte, input oltge, input current, nd chrging nd dichrging tte of the ttery pk re hown in Tle 1. The circuit opertion of the riou operting mode re decried elow. (1) Mode 1 Power emiconductor witche 1, nd 8 re triggered; the circuit configurtion i hown in Fig.. At thi intnt, line current i flow towrd oot inductor L, trel through the nti-prllel diode of witche nd 1, tterie B 1 nd B, nd the nti-prllel diode of witch 8, then finlly return to the electricl upply terminl through the nti-prllel diode of witch. In thi mode, the input terminl oltge of the conerter i = ( = B 1 ). ince the electricl upply oltge > 0 nd it mplitude i within Are, the line current i decree. At thi intnt, the circuit eqution cn e expreed : di = L (1) i L R 1 4 Fig. Circuit for mode 1 of the three-leel neutrl point clmped chrge conerter 5 8 D i i I: Iue 11, Volume 8, oemer 009

4 WEA TRAACTIO on CIRCUIT nd YTEM () Mode Power emiconductor witche 1, nd re triggered; the circuit configurtion i hown in Fig.. At thi intnt, line current i flow towrd oot inductor L, pe through the nti-prllel diode of witche nd 1, ttery B 1, clmped diode D, nd then finlly return to the power ource terminl through witch. In thi mode, the input terminl oltge of the conerter i = Vdc ( = B 1 ). If the power ource oltge > 0 nd it mplitude i within Are, then the line current i will incree. Howeer, if the power ource oltge > 0 nd the mplitude i within Are 1, then the line current i will decree. In thi interl, the circuit eqution cn e written : di = L () i L R 1 4 Fig. Circuit for mode of the three-leel neutrl point clmped chrge conerter () Mode Power emiconductor witche, nd 8 re triggered. At thi time, the line current i flow towrd oot inductor L, ping through witch, clmped diode, ttery B, nd the nti-prllel diode of witch 8, then finlly return to the power ource terminl through the nti-prllel diode of witch. The circuit configurtion i hown in Fig. 4. In thi mode, the input terminl oltge of conerter i = Vdc ( = B ). If the power ource oltge > 0 nd it mplitude i within Are, then the line current i rie. Howeer, if power ource oltge > 0 nd the mplitude i within Are 1, then the line current i drop. At thi intnt, the circuit eqution cn e expreed : 5 8 D i i di = L () i L R 1 4 Fig. 4 Circuit for mode of the three-leel neutrl point clmped chrge conerter (4) Mode 4 Power emiconductor witche, nd re triggered. At thi intnt, the line current i flow towrd oot inductor L, ping through witch, clmped diode D nd D, nd then finlly returning to the power ource terminl through witch. The circuit configurtion i hown in Fig. 5. In thi mode, the input terminl oltge of the conerter i = 0. When the power ource oltge > 0 nd it mplitude i within Are 1, the line current i will rie. Howeer, when the power ource oltge < 0 nd it mplitude i within Are 1, the line current i will drop. At thi intnt, the circuit eqution cn e expreed : di L i L 5 8 D i i = (4) R 1 4 Fig. 5 Circuit for mode 4 of the three-leel neutrl point clmped chrge conerter (5) Mode 5 Power emiconductor witche 5, nd re triggered. At thi intnt, the line current i flow towrd oot inductor L, ping through witch, clmped diode, ttery B 1 nd witch 5, then finlly return to the power ource terminl through witch. The circuit configurtion i hown in Fig.. In thi mode, the input terminl 5 8 D i i I: Iue 11, Volume 8, oemer 009

5 WEA TRAACTIO on CIRCUIT nd YTEM oltge of the conerter i = Vdc ( = B 1 ). When the power ource oltge < 0 nd it mplitude i within Are 1, the line current i rie; when the power ource oltge < 0 nd it mplitude i within Are, line current i drop. At thi time, the circuit eqution cn e expreed : di L i L = (5) R 1 4 Fig. Circuit for mode 5 of the three-leel neutrl point clmped chrge conerter () Mode Power emiconductor witche 4, nd re triggered. At thi intnt, line current i flow towrd oot inductor L, ping through witche nd 4, ttery B, nd clmped diode D, nd then finlly return to the power ource terminl through witch. The circuit configurtion i hown in Fig.. In thi mode, the input terminl oltge of the conerter i = Vdc ( = B ). When the power ource oltge < 0 nd it mplitude i within Are 1, the line current i rie; when power ource oltge < 0 nd it mplitude i within Are, the line current i drop. At thi intnt, the circuit eqution cn e expreed : di L i L 5 8 D i i = () R 1 4 Fig. Circuit for mode of the three-leel neutrl point clmped chrge conerter 5 8 D i i () Mode Figure 8 depict the circuit configurtion for the conerter under operting mode. Power emiconductor witche 4 5, nd re trigger. At thi intnt, line current i flow towrd oot inductor L, ping through witche nd 4, tterie nd B 1, nd witch 5, nd then finlly return to the power ource terminl through witch. In thi mode, the input terminl oltge of the conerter i = ( =B 1 ). ince the power ource oltge < 0 nd it mplitude i within Are, the line current i rie. At thi intnt, the circuit eqution cn e expreed : di = L ( ) () i L R Bi 1 D Bi Fig. 8 Circuit for mode of the three-leel neutrl point clmped chrge conerter Bed on the oe nlyi of the een opertion mode of the chrge equliztion circuit of the three-leel conerter, the goerned eqution tht cn ultimtely e deried : di L = Ri (8) = (9) The witching function nd re defined : And Δ = ( 1 5) Δ = ( 4 8) i= 1,,...,8 i= 1,,...,8 i=,4,,8 (10) = 1(0), if trigger (non-trigger) (11) = 1 (1) 1,,5, The key rile of eery opertion mode hown in Tle 1 cn e found from goerned eqution (8) to (1). According to Tle 1, if the chnge in the I: Iue 11, Volume 8, oemer 009

6 WEA TRAACTIO on CIRCUIT nd YTEM direction of the line current nd the re occupied y the line oltge mplitude re lredy known, then the pproprite operting mode cn e elected to cue input terminl oltge to produce pproprite oltge leel to eqully chrge the rechrgele ttery pk. The lower prt of Fig. 1 i the control lgorithm employed in the three-leel neutrl point clmped chrge equliztion cheme. The outer loop oltge controller dopt proportionl plu integrl (PI) controller to regulte DC-link oltge, while the inner loop employ hyterei current controller (HCC) to force tul ' i i current to follow commnd current. The oltge of the two tterie re djuted uing ttery oltge lnce controller. The AC-ide of the conerter ue n re detector to determine the re occupied y the power ource oltge to decide the witch trigger ignl nd produce the pproprite oltge leel. The deciion for the four control ignl included in thi control lgorithm re: A= 0, if < 0; 1, if > 0 B = 0, if < V / (Are 1); dc 1, if > V / (Are ) dc (1) (14) D = (i i ) K < x 0, if / ; 1, if (i i )/ K > x (1) The reltionhip etween power witch tte nd control ignl in Tle cn e otined from Tle 1 nd (1)-(1). Bed on the tte produced y four digitl ignl A-D, the correponding witching tte of witche cn e determined, cuing line current i to follow the commnd current i, to e of the me phe power ource oltge, nd to control the equl chrging of the ttery pk t the me time. For exmple, if line oltge i greter thn 0 (A=1) nd fll within Are (B=1), the ttery oltge i greter thn (C=1), nd the line current error ( i i )/ K i greter thn the hyterei nd x (D=1), then power witche,, nd 8 re elected to e triggered (Mode ), chrging ttery B, increing the line current, nd producing oltge leel of =. According to the control trtegie employed in Tle, the line current i cn e cued to follow commnd current i nd e of the me phe power ource oltge, relizing high input power ftor nd low current hrmonic. C = 0, if < ; 1, if > (15) Tle 1 Key rile for eh opertion mode of the three-leel PC conerter chrging circuit Mode Vrile witch trigger condition Line current i tte Bttery in chrging or dichrging tte B 1 B Mode 1 1,,, 8 /< < Decree Chrge Chrge Mode 1,,, 0< < / Decree /< < Incree Chrge Dichrge Mode,,, 8 0< < / Decree /< < Incree Dichrge Chrge Mode 4,,, 0 0< < / Incree - /< <0 Decree Dichrge Dichrge Mode 5,, 5, - - /< <0 Incree - < <- / Decree Chrge Dichrge Mode, 4,, - - /< <0 Incree - /< <- / Decree Dichrge Chrge Mode, 4, 5, < <- / Incree Chrge Chrge I: Iue 11, Volume 8, oemer 009

7 WEA TRAACTIO on CIRCUIT nd YTEM 4 imultion Reult Figure 9() how the imulted circuit of the propoed three-leel neutrl point clmped AC/DC conerter for equliztion chrge two erie connected tterie. The numer of required component for the imulted circuit of the three-leel neutrl point clmped AC/DC conerter chrge equlizer cn e otined through the following formul [11]: the formul ( m 1) ( mi the numer of leel) otin the numer of power emiconductor witche need for eh leg of ridge conerter, while the formul ( m 1) ( m) otin the numer of neutrl point clmped diode needed for eh leg of ridge conerter. For exmple, for three-leel conerter, there will e 8 IGBT power emiconductor witche nd 4 neutrl point clmped diode compoing the circuit cheme. Figure 9() i the u-circuit digrm for the led-id tterie in the imulted circuit digrm of the three-leel neutrl point clmped circuit uing PIM oftwre [14]. Figure 10 () i the imulted circuit for the controller of the three-leel neutrl point clmped chrge equlizer. The prmeter etting for the outer loop oltge controller re K P = nd K I = ; the power ource terminl reitnce i R = 5mΩ, the power ource terminl inductor i L = 0.15mH, the power ource oltge i = 14V, nd the DC link output oltge i Vdc = 8V ; the ttery i 1V-1Ah ttery. The inner loop produce n A-D digitl ignl through comprion, nd then ue the reltionhip etween the witching function of power witche nd control ignl, writing the reltionhip C-code nd uing complier to produce the dynmic link lirry (DLL) needed for the PIM circuit imultion oftwre [15]. Figure 10 () i the witch control deciion etlihed in Tle ued to decide the operting mode of the witche. () () Fig. 9 imulted circuit digrm uing PIM oftwre for the three-leel neutrl point clmped conerter chrger equliztion circuit: ()min circuit cheme; ()u-circuit of led-id tterie I: Iue 11, Volume 8, oemer 009

8 WEA TRAACTIO on CIRCUIT nd YTEM V V () () Fig. 10 Control circuit digrm uing PIM oftwre for the three-leel neutrl point clmped conerter chrge equliztion circuit: ()oltge controller; ()witching controller of digitl ignl Tle Reltion etween control ignl nd witching function of power witche in eh mode A B C D 1 ( ) ( 4 ) 5 ( ) ( 8 ) Opertion Mode Figure 11 how the imulted we form of the input terminl oltge for the three-leel PC conerter equliztion equl chrger, it cn e eem from imultion reult tht h three leel t poitie nd negtie hlf cycle nd cn thu reduce output oltge hrmonic. Figure 1 how the chnge cure for the cpitie of the two tterie during chrging. The initil oltge nd cpitie of the two tterie were et differently t the trt of the imultion. The oltge of Bttery 1 w initilly et t 11.1V, while the oltge of Bttery w initilly et 11.9V. In the chrging period (t minute), the cpity of Bttery w increed to exerte the inequlity in the cpitie of led-id tterie. The imultion reult hown in Fig. 1 indicte tht the chrge equliztion circuit doe indeed he good equl chrging effect. Figure 1 how the oltge chnge in the two tterie during the chrging period, while Fig. 14 how the oltge difference etween the two tterie. Fig. 15 how the imulted we form for input AC oltge nd current i during the chrging period. It cn e een from the imultion reult hown in Fig tht the three-leel conerter chrger equliztion circuit poee excellent performnce in proiding ttery pk with equl chrging nd cn improe the power qulity of the chrging power ource. I: Iue 11, Volume 8, oemer 009

9 WEA TRAACTIO on CIRCUIT nd YTEM Output oltge(v) AC input (V/A) i Fig. 11 imulted we form for input oltge of the three-leel neutrl point clmped conerter chrge equliztion circuit Fig. 1 Cpitie nd chrge time reltionhip grph for the tterie in the three-leel neutrl point clmped conerter chrge equliztion circuit Bttery oltge(v) Initil oltge:11.9v Bttery Initil oltge:11.1v Bttery Chrging time(minute) Fig. 1 Reltionhip grph for the oltge nd chrging time of the two tterie in the three-leel neutrl point clmped conerter chrge equliztion circuit 0.5 Voltge difference of two tterie Chrging time(minute) Fig. 14 Reltionhip grph of the ttery oltge difference nd chrging time of the three-leel neutrl point clmped conerter chrge equliztion circuit Fig. 15 imulted we form for the AC input terminl oltge nd current i for the three-leel neutrl point clmped conerter chrge equliztion circuit 5 Concluion Thi pper preented ttery chrge equliztion circuit uing three-leel neutrl point clmped conerter cheme nd ued PIM imultion oftwre to etlih imulted circuit model. imultion reult demontrted tht the ttery chrge equliztion circuit cn not only ttin the purpoe of eqully chrging rechrgele tterie, ut cn lo cue the power ftor for the AC input terminl to pproh 1, therey riing the power qulity for the AC-ide power upply. Acknowledgement Thi work w upported y the tionl cience Council, Tiwn, R.O.C., under the Grnt of # C 9-1-E-1-0. Reference [1]. H. Kutkut, D. M. Din, nd D. W. ootny, Chrge Equliztion for erie Connected Bttery tring, " IEEE Trntion on Indutry Appliction, Vol. 1, 1995, pp []. Wet nd P. T. Krein, Equliztion of Vle-Regulted Led-Acid Btterie: Life Tet Reult, in Proceeding of IEEE Telecommuniction Energy Conference, 000, pp [] P. T. Krein nd R.. Blog, Life Extenion through Chrge Equliztion of Led-Acid Btterie, " in Proceeding of Interntionl Telecommuniction Energy Conference, 00, pp [4] B. Lindemrk, Indiidul Cell Voltge Equlizer (ICE) for Relile Bttery Performnce,"in Proceeding of Interntionl I: Iue 11, Volume 8, oemer 009

10 WEA TRAACTIO on CIRCUIT nd YTEM Telecommuniction Energy Conference, 1991, pp [5] Y. C. Hieh, et l., Blnce Chrging Circuit for Chrge Equliztion, in Proceeding of IEEE Power Conerion Conference, 00, pp [] P. T. Krein nd C. Pcul, witched Cpitor ytem for Automtic erie Bttery Equliztion,"in Proceeding of IEEE Applied Power Electronic Conference, 199, pp. -. []. H. Kutkut, D. M. Din nd D. W. ootny, Chrge Equliztion for n Electronic Vehicle Bttery ytem, " IEEE Trntion on Aerope nd Electronic ytem, Vol. 4, 1998, pp [8]. H. Kutkut, H. L.. Wiegmn, D. M. Din nd D. W. ootny, Deign Conidertion for Chrge Equliztion of n Electric Vehicle Bttery ytem, IEEE Trntion on Indutry Appliction, Vol. 5, 1999, pp [9]. H. Kutkut, D. M. Din nd D. W. ootny, Chrge Equliztion for erie Connected Bttery tring, in Conference Record IEEE on Indutry Appliction ociety Annul Meeting, 1994, pp [10]. H. Kutkut, ondiiptie Current Dierter Uing Centrlized Multiwinding Trnformer, in Proceeding of IEEE Power Electronic pecilit Conference, 199, pp [11] J.. Li nd F. Z. Peng, Multileel Conerter - A ew Breed of Power Conerter, IEEE Trntion on Indutry Appliction, Vol., 199, pp [1] B.. uh, G. inh, M. D. Mnjrekr nd T. A. Lipo, Multileel Power Conerion - An Oeriew of Topologie nd Modultion trtegie, in Proceeding of the th Interntionl Conference on Optimiztion of Electricl nd Electronic Equipment, Vol., 1998, pp. AD-11 -AD-4. [1] B. R. Lin nd D. J. Chen, Power Ftor Correction Bed on Diode Clmped Rectifier, Interntionl Journl of Electronic, Vol. 88, 001, pp [14] Z. M. lmeh, M. A. Cc nd W. A. Lynch, A Mthemticl Model for Led-Acid Btterie, IEEE Trntion on Energy Conerion, Vol., 199, pp [15] PIM Uer Guide, Powerim Inc., I: Iue 11, Volume 8, oemer 009