ACTIVE RESISTANCE EMULATION IN THREE-PHASE RECTIFIER WITH SUBOPTIMAL CURRENT INJECTION

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1 6 th INTNTIONL SYMPOSIUM on POW ELECTRONICS - Ee NOVI SD, REPULIC O SI, October 6 th - 8 th, CTIVE RESISTNCE EMULTION IN THREE-PHSE RECTII WITH SUOPTIML CURRENT INJECTION Mlan Darjeć, Predrag Pejoć, Yasuyuk Nshda Johann W Kolar 3 aculty of Electrcal Engneerng, Unersty of elgrade, Serba Chba Insttute of Technology, Japan 3 Swss ederal Insttute of Technology, ürch, Swtzerl bstract: In ths paper, suboptmal current njecton n three-phase dode brdge rectfers that apply swtchng resstance emulators s analyzed Two rectfers are focused, one that apples flterng of the resstance emulator output current, the other one that does not Models that coer both the contnuous the dscontnuous conducton mode of the rectfers are deeloped Optmzaton s performed, showng that both of the rectfers prode about the same performance when the emulated resstance takes the optmal alue The results are expermentally erfed Key Words: C DC power conerson, conerters, harmonc dstorton, power conerson harmoncs, power qualty, rectfers INTRODUCTION In order to reduce total harmonc dstorton (THD) of the nput currents of three-phase dode brdge rectfers, current njecton methods [] may be appled s t s shown n [], current njecton networks requre some power to be taken from the rectfer output to prode reducton of the nput current THD There are seeral methods how the current njecton may be mplemented, but n all cases the power taken by the current njecton network s less than % of the rectfer nput power Recoery of ths power, e transfer of the power taken by the current njecton network to the load, s the topc addressed n ths paper In order to recoer the power taken by the current njecton network, concept of the loss-free resstor [] s appled The current njecton method focused n ths paper s suboptmal current njecton The method s dscussed n [], from the optmal current njecton, proposed n [3], dffers n the subsystem that prodes njecton of the harmoncs at een trples of the lne frequency Ths subsystem neglgbly mproes the nput current THD, but ncreases the system complexty; thus, the rectfers that apply suboptmal current njecton hae ths subsystem omtted Typcal rectfer of ths class s g Three-phase rectfer wth suboptmal current njecton a resstance emulator

2 presented n g The rectfer of g conssts of a dode brdge (D to D6), a current njecton system, a resstance emulator, encrcled wth the dotted lne, modeled as a loss-free resstor [] The resstance emulator mght be followed by a flter consstng of L C Smlar approach n the thrd harmonc current njecton based rectfers s appled n [4], where a passe resstance emulatng crcut has been appled result of [4] s that flterng of the resstance emulator output current, contrary to ntal expectatons, does not contrbute to the reducton of the nput current THD Instead, the flterng ncreases the nput current THD, thus the flter s omtted from the rectfer proposed n [4] The reason for ths effect s that the output current rpple of the resstance emulator contans a harmonc at sxth multple of the lne frequency wth the ampltude close to the ampltude requred by the optmal current njecton [3] Effects caused by flterng of the resstance emulator output current n the rectfers that apply suboptmal current njecton are analyzed n ths paper In [5], the same topc s addressed, feasblty of the concept s expermentally erfed lso, t s obsered that the rectfers wth suboptmal current njecton that apply the resstance emulator tend to operate ery close to the dscontnuous conducton mode, snce the operatng pont wth the mnmum of THD s close to the boundary between the contnuous the dscontnuous conducton mode Ths paper extends the results of [5] n theoretcal drecton The rectfers are modeled to coer both the contnuous the dscontnuous conducton mode, applyng technques of [6] [7] Next, an optmzaton s performed, to determne optmal resstance at the resstance emulator nput port It wll be shown that n the case the flterng s appled the optmal operatng pont s n the contnuous conducton mode, whle n the case the flterng s not appled the optmal operatng pont s n the dscontnuous conducton mode nally, the analytcal results are expermentally erfed MODELS To analayze the rectfer of g n two cases, when complete flterng of the resstance emulator output current s appled, assumng L C, n the case when the flterng s omtted, when L C, approprate models should be dered In the analyss, both the contnuous the dscontnuous conducton mode are of nterest, the model should coer both of them The model s dered applyng technques deeloped n [6] [7] Capactors C of the current njecton network are assumed to hae neglgble oltage rpple, ther oltages are for symmetry reasons assumed as beng the same, equal to V C [7] To determne the nput current waeforms, t s suffcent to determne the waeforms of (g ), snce Y =, X = Y 3, the conducton of dodes s controlled by the nput oltages It s conenent to determne the waeforms of from the equalent crcuts of gs 3, deeloped applyng g Equalent crcut of the rectfer wth flter g 3 Equalent crcut of the rectfer wthout flter technques ntroduced n [6] [7] for the analyss of rectfers n the dscontnuous conducton mode In the analyss of the equalent crcuts, as well as to determne the output oltage, waeforms of are also of nterest Let us assume that the supply oltages are π k = Vm cos ωt ( k ) () 3 for k {,,3} Waeforms of the equalent crcuts of gs 3 are defned as ([6], [7]) = max(,, 3 ) () = mn(,, 3 ) (3) Let us also defne a oltage waeform + V = (4) Ths waeform plays an mportant role snce under mposed assumptons + V = (5) regardless conducton of D D In the contnuous conducton mode, dodes D D of the equalent crcuts of gs 3 conduct durng the whole perod, resultng n = = In ths case > > durng the whole perod, resultng n V = V Y = V R Ths apples for both of the analyzed equalent crcuts In dscontnuous conducton modes, there are nterals of tme n whch or are equal to zero

3 These nterals correspond to dodes D or D beng reerse based Out of four possble combnatons of dode states only three are of nterest, characterzed by at least one dode n conductng state Model of the rectfer wth flter The rectfer wth flter s analyzed assumng alue of a current defned as I I Solng the crcut of g, a model that conssts of three lnear segments s obtaned The frst segment coers the contnuous conducton nteral, where both D D conduct, resultng n = =, Y = V R, +, Ths apples for Y V > RI < V RI In the case > V RI, D s off, =, = + 4RI, Y,, = or V < RI, D s off, = 4RI, =, Y = I, =, fter the waeforms are computed, actual output current s computed from I + I, where I s obtaned as RY I = (6) where oerlne represents aeragng oer the lne perod When the waeforms of the rectfer oltages currents are determned, parameters lke the nput current THD the power factor are computed applyng stard procedures Model of the rectfer wthout flter In the same manner as for the rectfer wth flter, n the case the flter s omtted waeforms of the rectfer oltages currents are obtaned solng the equalent crcut of g 3 or the contnuous conducton nteral, when both D D conduct, =, =, = R In that case Y V Y V (7) R V (8) R Ths apples for > > In the case D s off, =, RI = + RI (9) = Y () + RI = Ths apples for < Smlarly, when D s off + RI = () RI =, =, = Y () RI g 4 Dependence of the nput current THD on G Ths apples for > 3 OPTIMITION fter the conerter models are dered, numercal computaton s appled to determne optmal alues for the emulated resstance n both of the consdered cases In order to generalze the results, normalzaton s performed, the nput current THD s expressed n terms of normalzed conductance of the resstance emulator nput port, defned as Vm G = (3) RI Numercal computaton s performed applyng GNU Octae, obtaned dependence of the nput current THD on G s presented n g 4, where the full lne corresponds to the contnuous conducton mode, whle the dashed lne corresponds to the dscontnuous conducton mode ccordng to the dagrams of g 4, the result of optmzaton n the case the flter s appled s that the mnmum of the nput current THD of THD = 4 mn % s obtaned for G = 6 6 n the contnuous conducton mode, requrng the resstance emulator to process 866% of the nput power In the case the flterng s omtted, mnmum of the nput current THD of THD = 4 mn % s obtaned for G = 6 5 n the dscontnuous conducton mode, the resstance emulator processes 84% of the nput power Comparson of the smulaton results ndcate that both of the rectfers prode about the same performance dantage proded by applyng flterng of the resstance emulator output current s slghtly better THD, whle omttng the flter prodes slght reducton of the power processed by the resstance emulator ccordng to the results, for applcatons n practce the soluton wthout flterng would be adsed, regardless slghtly hgher THD alues 3

4 g 5 Resstance emulator 4 EXPIMENTL RESULTS To prode expermental erfcaton of the theoretcally obtaned results, a rectfer wth the rated power of kw s bult The rectfer s ntended to operate wth the phase oltage ampltude of V m = 4 V, at the lne frequency of 5 Hz The resstance emulator s bult usng a transformer wth the turns rato : 3, sngle-phase dode brdge, a boost conerter wth current mode control, as depcted n g 5 flter consstng of L EMI = 4µH C EMI = 3 n s appled n front of the boost conerter to reduce the electromagnetc nterference Smlarly, the output capactor of the boost conerter, C = µ, s appled to absorb spectral components of the dode current at hgh frequences, n the order of magntude of the swtchng frequency Inductor of L = 5µH s appled If low frequency flterng, at seeral multples of the lne frequency s needed, the addtonal flter consstng of L =5 mh C = µ, shown n g, could be appled The resstance emulator of g 5 s appled to emulate resstance slghtly lower than optmal, snce a part of the current njecton network optmal resstance s obtaned from the current njecton network losses These losses are prmarly located n the g 6 Expermental results, THD ( G), wth flter g 7 Waeforms of at, wth flter THD mn I = 5 g 8 Expermental results, THD ( G), wthout flter current njecton dece, beng modeled by a seres resstance of R CID = 35 Ω Expermentally obtaned dependence of the nput current THD on normalzed conductance n the current njecton network n the case flterng of the resstance emulator output current s appled s presented n g 6 The dagram s obtaned for the rectfer operatng at I = 5 In the dagram of g 6, the thn lne presents theoretcally obtaned dependence, already shown n g 4, whle the crosses correspond to the expermental data ponts The expermental results are n good agreement wth the theoretcal expectatons In g 7 waeforms of the nput oltage the nput current at the frst phase of the rectfer,, are presented n the case the rectfer s tuned to operate at the mnmum of the nput current THD In the case flterng of the resstance emulator output current s not appled, expermentally obtaned dependence of the nput current THD on normalzed conductance n the current njecton network s presented n g 8 gan, the dagram s obtaned for the rectfer 4

5 operatng at I = 5, the expermental results are n good agreement wth the theoretcal predctons Waeforms of the nput oltage the nput current at the frst phase of the rectfer for the rectfer operatng wth the mnmum of the nput current THD are presented n g 9 The dagrams of gs 7 9 are recorded at the output power of about 5 W, correspondng to the output current V g 9 Waeforms of at, wthout flter THD mn I 5 the output oltage 3 V In both cases, effcency of the rectfers s measured to be about 95% Comparson of the waeforms of gs 7 9 yeld concluson that the waeforms are almost the same ccordng to the analyss performed, as well as the expermental experence, t can be concluded that slght mproement n the performance does not justfy applcaton of the resstance emulator output current flter, although the reasons to aod the flter are not that clear as n [4] 5 CONCLUSIONS I = 5 Resstance emulaton n three-phase dode brdge rectfers that apply suboptmal current njecton s analyzed n ths paper In comparson to the thrd harmonc current njecton, where passe resstance emulaton mght be appled [4], suboptmal current njecton requres applcaton of swtchng resstance emulators Optmal emulated resstance of the resstance emulator flterng of the resstance emulator output current are dscussed Snce the rectfers wth suboptmal current njecton tend to operate close to the dscontnuous conducton mode, rectfer models that coer both the contnuous the dscontnuous conducton modes are deeloped The method of equalent crcuts ntroduced n [6] s appled The rectfers wth suboptmal current njecton are treated as resste crcuts, assumng constant oltages across the capactors of the current njecton network, as well as assumng deal flterng f the resstance emulator output flter was appled Ths sgnfcantly smplfes the analyss, makng t comparable n complexty to the analyss of multpulse rectfers presented n [7] Equalent crcuts are presented for both of the consdered rectfers, the one that apples deal flterng of the resstance emulator output current, the one that does not apply flterng Man equatons that descrbe the models are gen Obtaned rectfer models are appled to perform numercal optmzaton of the emulated resstance n order to mnmze total harmonc dstortons of the nput currents or the rectfer that apples flterng, the mnmum of THD = 4 mn % s obtaned n the contnuous conducton mode, whle for the rectfer that does not apply flterng the mnmum of THD = 4% mn s obtaned n the dscontnuous conducton mode The rectfer wthout flterng requres slghtly lower power to be processed by the resstance emulator, equal to 84% of the nput power, n comparson to the rectfer wth flter that requres 866% lthough applcaton of the flter prodes somewhat lower nput current THD, smulaton results the expermental experence do not justfy applcaton of the resstance emulator output flter nalytcal results are erfed on a rectfer laboratory model wth the rated power of kw The expermental results are n good agreement wth the theoretcal predctons 6 REENCES [] P Pejoć, Three-Phase Dode Rectfers wth Low Harmoncs Current Injecton Methods, Sprnger, 7, ISN [] S Snger, The applcaton of loss-free resstors n power processng crcuts, IEEE Transactons on Power Electroncs, ol 6, no 4, pp 595 6, Oct 99 [3] P Pejoć, Ž Ja, Three phase rectfers that apply optmal current njecton, IEEE Transactons on erospace Electronc Systems, ol 38, no, pp 63 73, Jan [4] P Pejoć, P ožoć, D Shmlotz, Low harmonc, three-phase rectfer that apples current njecton a passe resstance emulator, IEEE Power Electroncs Letters, ol 3, no 3, pp 96, Sept 5 [5] L Karbunar, P Pejoć, Current programmng n three-phase dode brdge rectfers that apply suboptmal current njecton, 4th Internatonal Symposum on Power Electroncs, Ee 7, No Sad, No 7 [6] P ožoć, P Pejoć, Current njecton based low harmonc three-phase dode brdge rectfer operatng n dscontnuous conducton mode, IEE Proceedngs Electrc Power pplcatons, ol 5, no, pp 99 8, Mar 5 [7] P ožoć, P Pejoć, Current njecton based -pulse rectfer usng a sngle three-phase dode brdge, IET Electrc Power pplcatons, ol, no, pp 9 6, Mar 7 5

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