CONSTANT INPUT POWER CONTROL OF THREE-PHASE ISOLATED BUCK+BOOST RECTIFIER * A. MOHAMMADPOUR AND M. R. ZOLGHADRI **

Iranan Journal of Scence & Technology, Transacton B: Engneerng, Vol. 34, No. B6, 637-648 Prnted n The Islamc Reublc of Iran, 2010 Shraz Unersty CONSTANT INPUT POWER CONTROL OF THREE-PHASE ISOLATED BUCK+BOOST RECTIFIER * A. MOHAMMADPOUR AND M. R. ZOLGHADRI ** Det. of Electrcal Engneerng, Sharf Unersty of Technology, Tehran, I. R. of Iran Emal: zolghadr@sharf.edu Abstract A noel control method s roosed for sngle-stage three-hase solated buck+boost rectfer. The control method s based on the conentonal cascade two-loo control structure and s modfed to achee constant nstantaneous nut ower. Inut oltages, outut oltage, and DClnk nductor current are measured to control the ower swtches to achee outut oltage regulaton as well as nut ower factor correcton. In the roosed method, nut currents are controlled such that nut ower s constant, een for unbalanced mans. Thus, for the balanced mans conerter t behaes lke an deal rectfer, and for unbalanced mans, low-frequency harmoncs of the outut oltage are suressed. The erformance of the roosed control structure s erfed by the numercal smulaton of a 6kW, 380V/48Vdc desgned rototye. Keywords Three-hase sngle-stage ower suly, buck+boost rectfer, unbalanced mans, ower factor correcton 1. INTRODUCTION A tycal telecom ower suly should rode regulated dc oltage to the load wth the followng features: Low (Total Harmonc Dstorton) THD of nut currents to meet nternatonal standard requrements such as IEC 61000-3-2 Unty nut ower factor Inut-outut electrcal solaton Hgh effcency (more than 90% at full load) Hgh ower densty Accetable outut for unbalanced mans Low cost These requrements motate the desgn of three-hase sngle-stage (Power factor Correcton) PFC rectfers comared to conentonal two-stage structures. A boost-tye AC-DC conerter s resented n [1] for both sngle-hase and three-hase structures. Unty ower factor three-swtch solated buck rectfer s roosed n [2] for three-hase AC-DC conerson. Ths structure s dered from three-hase three-swtch buck rectfer [3], where hgh frequency solaton s acheed by ntroducng a forward conerter. A three-hase sngle-stage solated buck+boost rectfer for telecommuncaton ower suly modules s roosed n [4]. The schematc of the roosed crcut and system secfcatons are shown n Fg. 1 and Table 1. Ths structure s toologcally equalent to the conerter descrbed n [2], and s controlled wth the control method of [5], [6] to hae a unty ower factor, een for unbalanced nut oltages. The roblem wth ths control concet s the outut oltage low-frequency harmoncs for the Receed by the edtors February 4, 2010; Acceted Noember 3, 2010. Corresondng author

638 A. Mohammadour and M. R. Zolghadr unbalanced mans condton. In lterature some works are carred out for harmonc elmnaton n boostbased rectfers [7-9]. One method for outut oltage harmonc suresson s resented n [10] for a sx swtch buck rectfer whch elmnates a lmted number of harmonc frequences. Fg. 1. Three-hase solated buck+boost rectfer Table 1. Oeratng ont for desgn and smulaton Parameter Inut flter nductor Value L 240 μ H Inut flter caactor C f 6.8 μ F Outut caactor C o 40 mf Outut nductor L 200 μ H o N : Ns : N 10:3:1 d f Magnetzng nductance L m 4 mh In ths aer a new control structure s roosed to elmnate the aforementoned low-frequency harmoncs n the case of the unbalanced mans wthout the erformance degradaton for the balanced mans condton. The roosed control method utlzes the DC-lnk current sensor nstead of AC current sensors. Ths control technque s adantageous to the load snce the outut flter caactance can be mnmzed wth a mnmal outut DC oltage rle. In secton 2, the oeraton of a conerter wth resste nut control method s reewed. The rncle of constant nut ower control s dscussed brefly n secton 3. The roosed control structure for constant nut ower s resented n secton 4. The numercal smulaton results are roded n secton 5 to erfy the aldty of the theoretcal concets. Secton 6 summarzes the results of the roosed control method. 2. THREE-PHASE ISOLATED BUCK+BOOST RECTIFIER WITH RESISTIVE INPUT CURRENT METHOD The schematc crcut of the three-hase solated buck+boost rectfer s shown n Fg. 1. The conerter can be dded nto three functonal blocks. The three-hase three-swtch buck s used at the nut to control the nut currents of the conerter. The hgh frequency solaton s roded by the forward/flyback conerter wth transformer demagnetzaton through the load. The outut boost stage s ntegrated nto the conerter structure to ensure the roer oeraton of the conerter durng healy unbalanced mans condton. The detaled oeraton of the nut and outut arts of the conerter s exlaned n references [4] and [6]. Iranan Journal of Scence & Technology, Volume 34, Number B6 December 2010

Constant nut ower control of three-hase 639 An otmzed sace ector modulaton method was deeloed n [11] for non-solated buck conerter consderng swtchng loss, rle alues, and mans current qualty. The modulaton method of [11] s not drectly alcable to the solated buck rectfer and s modfed n [4] to reent transformer core saturaton. One mans erod s dded nto 12 sectors based on the nut hase oltages relaton. The swtchng state sequence for the frst sector of the mans s shown n Fg. 2, where j = ( srssst) ndcates a combnaton of the three nut buck swtches, s = 1 shows on-state, and s = 0 off state of the accordng swtch. The swtchng states wth only one conductng brdge leg cannot be aled n the freewheelng state, and (000) s aled n ths case to ensure comlete demagnetzaton of the transformer. For balanced mans, the buck stage modulaton ndex M s defned as 2 N Vo M =, M (0;1) (1) 3 N V s N where V N s the eak alue of the hase-to-neutral oltage and V o s the dc-lnk oltage. Maxmum modulaton ndex, M max, s lmted such that the transformer s comletely demagnetzed durng the freewheelng state 1 M max = (2) N 1.5V d N,mn 1+ N V The outut boost stage has to be actated only for a combnaton of nut and outut oltages whch results n M > Mmax n ths case 3 N s V0 = M maxvn (3) 2 N Ths s smaller than the desred outut oltage. Therefore, the duty cycle of the boost swtch s determned by Vref Vo δ = (4) V ref o,max Fg. 2. Swtchng state sequence for the frst mans sector For unbalanced mans the maxmum aerage alue of buck stage outut oltage wthn a swtchng cycle s defned as 3 Ns $ o,max = Mmax N (5) 2 N $ 2 ( 2 2 2 = + + ) (6) N CFR, CFS, CFT, 3 December 2010 Iranan Journal of Scence & Technology, Volume 34, Number B6

640 A. Mohammadour and M. R. Zolghadr For Vo < o,max, $ N > V the buck nut stage oerates at a modulaton ndex smaller than the maxmum N,mn modulaton ndex, and the boost outut stage duty cycle s zero. For M > Mmax the boost stage has to be actated wth ref o,max δ = (7) Calculaton of the relate on-tmes of the ower transstors for the resste nut ower method s dscussed n [4]. For examle, the relate on-tmes for the frst mans sector are gen n Eqs. (3) and (4), ref N δ = o, ref 101 2 2 2 CF, T Ns C + FR, C + FS, CFT, (8) N δ = o, ref 110 2 2 2 CF, S Ns C + FR, C + FS, CFT, (9) The relate on-tme of the freewheelng state s ealuated based on the fact that the sum of the relate on-tmes durng a swtchng erod has to be equal to one. Wth the resste nut currents method, the conerter s smlar to the deal three-hase rectfer as dected n Fg. 3. Total nstantaneous nut ower s Fg. 3. Ideal three-hase rectfer model 1 t = + + (10) 2 2 2 n() ( R S T ) Re For balanced mans, the second harmonc of the nut ower s added to zero and the rectfer can suly constant nstantaneous nut ower to a DC load. For unbalanced mans the nut ower has a second harmonc term whch results n outut oltage rle. 3. CONSTANT INPUT POWER METHOD PRINCIPLES It s shown that wth resste nut method the nut ower s not constant for unbalanced nut oltages, and the outut oltage contans a 100 Hz rle [4]. In fact hang an nut hase current roortonal to the nut hase oltage wll lead to a tme aryng nut ower for an unbalanced nut oltage. Tme aryng nut ower s the orgn of the outut oltage rle. It s clear that the outut oltage rle can be elmnated f the nut ower s constant. Poste and negate sequence currents and oltages wll be used to analyze the nut ower and to synthesze the method that wll be used to fx the nut ower. As known, nut oltages and conerter currents can be exressed n terms of oste and negate sequences comonents, Iranan Journal of Scence & Technology, Volume 34, Number B6 December 2010

Constant nut ower control of three-hase uur uuur uuur + + + j( ωt+ θ ) j( ωt+ θ ) n V = V + V = V e + V e ur uur uur + + + j( ωt+ θ ) j( ωt+ θ ) In = I + I = I e + I e (12) uur uur uur uur + + + + where V, V, I, I are nut oste and negate sequence oltage and current ectors. V, V, I, I + + are the magntude of the oste and negate sequence oltage and current ectors. θ, θ, θ, θ are the hase angle of the oste and negate sequence oltage and current ectors. Thus the nut aarent ower s ur uur ur * + + + + + + j( θ θ ) j( θ θ ) + j(2 ωt+ θ θ ) + j( 2 ωt+ θ θ ) Sn = Pn + jqn = V n In = V I e + V I e + V I e + V I e In order to make nut ower constant and elmnate the low-frequency rles of the outut oltage, Eqs. (14) and (15) must be satsfed [8], [9]: V V 641 (11) (13) I = (14) I + + θ θ = θ θ π (15) + + An addtonal condton s mosed to hae a unty ower factor for balanced mans [8], θ = θ (16) + + If Eqs. (13), (14) and (15) are satsfed, the acte and reacte nut owers are + + P = V I V I (17) n + + + Q = ( V I + V I )sn(2 ωt+ θ θ ) (18) n It can be seen that the nstantaneous nut ower s constant and low-frequency harmoncs are elmnated for unbalanced mans. Furthermore, for balanced mans, constant nut ower s equalent to the unty ower factor oeraton [7]. 4. CONSTANT INPUT POWER CONTROL METHOD FOR THREE-PHASE ISOLATED BUCK+BOOST RECTIFIER The roosed control structure s dected n Fg. 4. Ths control structure s smlar to the resste nut control structure [4], [5]. The man dfference s n the dc-lnk current reference calculaton. In [5] a dccurrent shang block was used to control the dc-lnk nductor current to achee the snusodal mans currents n-hase wth the nut oltages for unbalanced mans. For the constant nut ower method, the dc-current shang block s relaced wth the harmonc elmnaton block. Detals of the harmonc elmnaton block for reference dc-lnk current ealuaton n constant nut ower method s dected n Fg. 5. Outut oltage controller s a sngle-nut mult-outut system wth two oututs. These oututs are used to regulate the magntude and hase of nut current sequence comonents. The magntudes of the oste and negate sequence comonents of the nut currents are gen by I =,1 V ( V V) (19) + * + C * C ref I =,1 V ( V V) (20) where * C,1 s the frst outut of the oltage controller. Phase of the nut currents s ealuated by ref December 2010 Iranan Journal of Scence & Technology, Volume 34, Number B6

642 A. Mohammadour and M. R. Zolghadr θ = θ ( ),2 V V (21) + + * C ref θ = θ + π + ( ),2 V V (22) * C ref where * C,2 s the second outut of the oltage controller. Usng the reference alues of magntude and the hase of oste and negate sequence nut currents, the reference alues of three hase nut currents are calculated. Fg. 4. Control structure of three-hase solated buck+boost rectfer for constant nut ower Fg. 5. DC-lnk current reference calculaton * + + () t = I sn( ωt+ θ ) + I sn( ωt+ θ ) (23) R * + + 2π 2π S () t = I sn( ωt+ θ ) + I sn( ωt+ θ + ) 3 3 (24) * + + 2π 2π T () t = I sn( ωt+ θ + ) + I sn( ωt+ θ ) 3 3 (25) If ower dssaton s neglected the nut and outut owers are equal. n RR S S TT out o Then the reference dc-lnk nductor current s ealuated = + + = = (26) * o,lm * * * R R + S S+ T T = (27) o,lm s the reference sgnal of the outut oltage where ts uer bound s lmted by o,max 3 N 2 = M ( + + ) (28) s 2 2 2 o,max max CFR, CFS, CFT, 2 N 3 The controller desgn s based on the gudelnes resented n [4] and [5] wthout the load current feedforward. A roortonal current controller k () s = 2.5s used. The outut oltage controller wth a sngle nut and two oututs s desgned as Iranan Journal of Scence & Technology, Volume 34, Number B6 December 2010

Constant nut ower control of three-hase 643 For the frst sector the nut currents are 2 1 k( s) = 0.2+ 0.1+ s s (29) R = Ns ( 101 110) N δ + δ (30) S N = (31) s 110 N δ T N = (32) s 101 N δ Relate on-tmes of buck swtches n a swtchng erod s obtaned by the followng equatons N N δ = = * * s o 110 * * * * Ns Ns RR + SS + TT N N δ = = * * T o 101 * * * * Ns Ns RR + SS + TT * S * T (33) (34) 5. SIMULATION RESULTS In ths secton the smulaton results of a conerter are resented to erfy the aldty of the roosed control method. For balanced mans condton the conerter behaor s smlar to an deal three hase rectfer. DC-lnk nductor current and the outut oltage of the conerter for load change from a half-load to a full-load condton are dslayed n Fgs. 6a and 6b. It can be seen that the current loo shows a fast dynamc resonse, but the oltage loo s slower. Howeer, the oltage decrease for ths load change s smaller than 1 V and resonse tme s 0.04 seconds. From Fg. 6c the nut currents are n-hase and roortonal to the nut oltage n both cases. In order to nestgate the erformance of the control structure for the unbalanced mans condton, the smulaton results are resented for 5% and 50% oltage reducton n one hase oltage. If the ower loss of the conerter s neglected, the nut ower s roortonal to the square of the outut oltage for a resste load. So the outut oltage rle s used as an ndcator of outut and nut ower oscllatons. The outut oltage of the conerter for 5% decrease n the oltage of hase R (equalent to 1.7% oltage unbalance factor accordng to IEC defnton [12]) s shown n Fg. 7a. The eak-to-eak rle alue s 0.02V and aerage THD of the nut currents s 4.5%. Inut currents are snusodal and n-hase wth corresondng nut oltages as dected n Fg. 7b. The erformance of the system for healy unbalanced mans condton s analyzed wth 50% oltage reducton n hase R oltage (equalent to 17% oltage unbalance factor accordng to IEC defnton). The smulaton results for ths case are dslayed n Fg. 8. The eak-to-eak outut oltage rle s 0.2V and the aerage THD of the nut the currents s 15%. Snce the nut currents must hae the same olarty as the corresondng nut oltages, they do not track the nut oltages n the roxmty of ther zero crossngs (Fg. 9). Ths results n waeform dstorton n the nut and outut of the conerter. Table 2 comares the outut oltage rle for dfferent alues of oltage decrease n one hase for the roosed constant nut ower control method and resste nut control method n [5]. For a 5% decrease n one hase oltage the outut rle for buck resste nut buck+boost conerter s 0.28V, whereas for the same condton outut rle s only 0.01V. Smulaton result for 25% and 50% decrease December 2010 Iranan Journal of Scence & Technology, Volume 34, Number B6

644 A. Mohammadour and M. R. Zolghadr n one hase oltage also shows that outut oltage rle s consderably lower for constant nut ower method. For unbalanced mans condton, nut current THD s hgh for constant nut ower method comared to resste nut method. Ths s not mortant because the unbalanced condton s temorary. It s noteworthy that the roosed method cannot elmnate low-frequency rle of the outut oltage for two-hase oeraton (loss of one hase). In ths case nstantaneous nut ower s ulsatng, whch wll result n the outut oltage second harmonc rle. (a) (b) (c) Fg. 6. Smulaton result for load change from half-load to full-load, a) dc-lnk nductor current, b) outut oltage, c) nut oltage and current Iranan Journal of Scence & Technology, Volume 34, Number B6 December 2010

Constant nut ower control of three-hase 645 (a) (b) Fg. 7. Smulaton result for 5% decrease n the oltage of hase R, (a) outut oltage, (b) nut oltage and current (a) (b) Fg. 8. Smulaton result for 50% decrease n the oltage of hase R, (a) outut oltage, (b) nut oltage and current December 2010 Iranan Journal of Scence & Technology, Volume 34, Number B6

646 A. Mohammadour and M. R. Zolghadr Fg. 9. Inut oltages, nut currents, nut currents references and sector number for an nut lne erod for 50% decrease n the oltage of hase Table 2. Comarson of outut oltage rle alue n the roosed control method wth 2 other methods Voltage decrease n Phase R (%) 5 25 50 Constant nut ower 0.01 0.05 0.2 Resste Inut characterstc 0.28 1.7 3.8 Based on the equatons for small-sgnal modelng of the system, the dynamc behaor of the system deends on the ower stage comonent alues, nut and outut oltages, and load alue [5]. Fnally, n order to erfy the robustness of the control system aganst these uncertantes, the dynamc resonse for dfferent oeratng onts s nestgated by smulaton. Fg 10a shows the outut oltage for load change from half-load to full-load for three alues of the nut oltage. It can be seen that the dynamc resonse of the outut oltage does not deend on the nut oltage alue excet for a small dfference n the outut oltage decrease. Outut oltage of the conerter, when reference oltage changes from 42 V to 48 V s shown n Fg. 10(b) for three load alues (1kW, 3kW, 6kW). The results of smulaton demonstrate the neglgble effect of these uncertantes on system stablty and transent resonse. (a) Fgure 10. Contnued. Iranan Journal of Scence & Technology, Volume 34, Number B6 December 2010

Constant nut ower control of three-hase 647 (b) Fg. 10. Robustness of control system aganst (a), nut oltage aratons, (b) load aratons 6. CONCLUSION A new control structure s roosed for three-hase solated buck+boost rectfer. Ths control method offers good dynamc resonse and shows a resste characterstc n the nut for balanced nut oltages. In ths case the nut currents are n-hase and roortonal to the corresondng nut oltages. Furthermore, wth ths control strategy low-frequency harmoncs from the nut and outut of the conerter are elmnated for unbalanced mans. Only DC-lnk nductor current s measured nstead of AC nut currents. It s aarent that due to the sngle-stage structure of the conerter, constant nut ower method s not realzable for two-hase oeraton. REFERENCES 1. Khoe, A. & Yuarajan, S. (2000). Alcaton of rectfed-oltage PWM for ower factor correcton. Iranan Journal of Scence and Technology, Transacton B: Engnnerng, Vol. 24, No. B1. 2. Greff, D. & Barb, I. (2006). A sngle-stage hgh-frequency solated three-hase AC/DC conerter. IEEE IECON 06, The 32nd Annual Conference of the IEEE Industral Electroncs Socety. 3. Malesan, L. & Tent, P. (1987). Three-hase AC/DC conerter wth snusodal ac currents and mnmum flter requrements. IEEE Trans. Ind. Al., Vol. IA-23, No.1,. 71-77. 4. Mohammadour, A. & Zolghadr, M. R. (2009). Control of three-hase sngle-stage solated buck+boost unty ower factor rectfer for unbalanced nut oltages. Proceedngs of the 4 th IEEE Internatonal Conference on Electrc Power and Energy Conerson Systems (EPECS), Sharjah, UAE. 5. Nussbaumer, T., Guangha, G., Heldwen, M. L. & Kolar, J. W. (2008). Modelng and robust control of a threehase Buck+Boost PWM rectfer (VRX-4). IEEE Trans. Ind. Al., Vol. 44, No. 2,. 650 662. 6. Baumann, M. & Kolar, J. W. (2007). A noel control concet for relable oeraton of a three-hase threeswtch buck-tye unty-ower-factor rectfer wth ntegrated boost outut stage under healy unbalanced mans condton. IEEE Trans. Ind. Electron., Vol. 52, No. 2,. 399 409. 7. Jn, A., L, H. & L, S. (2006). A flexble nut currents control strategy for three-hase PFC rectfer under unbalanced system. Proc. 1 st IEEE Industral Electroncs and Alcatons,. 1-6. 8. Stankoc, A.V. & Lo, T. A. (2001). A noel control method for nut outut harmonc elmnaton of the PWM boost tye rectfer under unbalanced oeratng condtons. IEEE Trans. Power Electron, Vol. 16, No. 5,. 603 611. 9. Jn, A., L, H. & L, S. (2006). A smle dgtal controller for constant nstantaneous nut ower tye threehase boost rectfer under unbalanced system. Proc. CES/IEEE 5 th IPEMC, Vol. 2,. 1-5. December 2010 Iranan Journal of Scence & Technology, Volume 34, Number B6

648 A. Mohammadour and M. R. Zolghadr 10. Enjet, P. N. & Choudhury, S. A. (1993). New control strategy to mroe the erformance of a PWM AC to DC conerter under unbalanced oeratng condtons. IEEE Trans. Power Electron, Vol. 8, No. 4,. 493 500. 11. Nussbaumer, T., Baumann, M. & Kolar, J. W. (2007). Comrehense desgn of a three-hase three-swtch buck-tye PWM rectfer. IEEE Trans. Power Electron, Vol. 22, No. 2,. 551-562. 12. IEC Internatonal Electrotechncal Commssons, Electromagnetc Comatblty (EMC) - Part 2-1: Descrton of the Enronment Electromagnetc Enronment for low-frequency Conducted Dsturbances and Sgnalng n ublc ower suly systems, Ed. 1.0, 1990, Genea, Swtzerland. Iranan Journal of Scence & Technology, Volume 34, Number B6 December 2010