Analysis and design of PPFHB bidirectional DC-DC converter with coupled

Transcription

1 Analyi and deign of PPFHB bidirectional DC-DC converter with coupled ductor Keyword Zhe Zhang, Ole C. Thomen and Michael A. E. Anderen Technical Univerity of Denmark Elektrovej, Buildg 35 Kg. Lyngby, Denmark Tel.: 45 / Fax: 45 / zz@elektro.dtu.dk «DC-DC converter», «Coupled-ductor», «Zero-voltage-witchg». Abtract In thi paper, a novel puh-pull-forward half-bridge (PPFHB) bi-directional DC-DC converter with coupled ductor i propoed. All witche can operate under zero-voltage-witchg (ZVS). The operation prciple with phae-hift modulation cheme, characteritic of coupled ductor, the teady tate relationhip and mall-ignal model are analyzed. The voltage controller baed on the mall-ignal model z-doma i deigned. A 5W prototype controlled by TMS3F88 DSP i implemented and teted. Experimental reult how the validity of the analyi and deign. Introduction The bi-directional dc-dc converter i generally needed a the terface circuit between the energy torage ytem and load or dc-bu, to control the power flow the ytem, uch a unterruptible power upply (UPS) ytem and hybrid electrical vehicle (HEV) ytem. Without iolation, buck-boot converter ha been implemented the application without high voltage ratio requirement. For high voltage ratio application, tranformer coupled and iolated bi-directional DC converter have been propoed uch a dual active bridge (DAB) converter [], [], dual active half bridge converter [3-5], full bridge current fed converter [6], [7] and their derivative [8-]. To improve the ytem efficiency a well a creae the range of operation for the wide-range put voltage, ome modulation cheme uch a triangular modulation, trapezoidal modulation and PWM plu phae-hift modulation are vetigated [], [3], and [4], with addg the duty ratio a a modulated parameter. In thi paper, a novel PPFHB bi-directional dc-dc converter with coupled ductor, hown Fig., with phae-hift modulation i vetigated. Operation prciple, parameter deign, and cloed-loop digital control baed on DSP are analyzed. Fally, experimental reult verify the effectivene of the analyi and deign. Propoed PPFHB Bi-directional Converter Operation Prciple The propoed topology employ the puh-pull-forward tructure to reduce the number of the power witche; utilie the half-bridge voltage doubler circuit the econdary ide of the high frequency tranformer to get high voltage tranition ratio. The auxiliary ductor, L and L, and the leakage ductor of the tranformer, L lk, are utilized a the terface and energy tranfer element between the two high frequency voltage-ource verter the two ide of the tranformer, repectively. The converter i controlled by the phae-hift technique to realize table output voltage and bidirectional power flow between the low voltage (LV) ide and high voltage (HV) ide. Becaue the EPE 9 - Barcelona ISBN: P.

2 L f R f C L b C f S C c A D S C S - L v v N * i T * L i v - - * N 3 Q i C D Q C N Zload N C D S S S Q B LV ide Power flow Fig. : The PPFHB converter with coupled ductor. D Q C HV ide Table I: Gated and conducted equence Interval LV ide HV ide Gated Conduction Gated Conduction t <t<t S S Q D Q t <t<t D S Q D Q t <t<t 3 S D S Q D Q t 3 <t<t 4 S S Q Q t 4 <t<t 5 S S D Q t 5 <t<t 6 S S Q D Q Fig. : Drivg ignal and theoretical waveform voltage cro the witche are alway leadg to the current the correpondg witche, all the witche are turned on under ZVS. Fig. demontrate the complete cycle of ideal circuit operation, where gate ignal are quare waveform with dead time. The angle between S and Q i the phae hift angle to be ued to control the output voltage and power flow direction. The gated and conductg device every mode are lited Table I. (t <t<t ): i ha the current path: VCc S N L VCc and i : V N L S V. The power i tranferred the forward direction; (t <t<t ): In the dead time between S and S, the energy tored the L and L charge C S and dicharge C S at the ame time. (t <t<t 3 ): The voltage cro dra-ource of S i zero with the conducg D S. (t 3 <t<t 4 ): i i bigger than that of i and the current i diverted from D S to S. In the econdary ide, the current i diverted from D Q to Q a well. (t 4 <t<t 5 ): In the dead time between Q and Q, the current path are not changed. (t 5 <t<t 6 ): At t 5, Q i turned on under ZVS. The detailed decription of the operation prciple every terval can be found the paper [5] that we have publihed before. EPE 9 - Barcelona ISBN: P.

3 Leq/L Leq/L DeltaL/L.5 ΔL eq L k k Δ L ( -7 H) (a) When L=5 uh, ΔL=.4uH Fig. 3: The relationhip curve: L eq, L eq, ΔL and k. Coupled Inductor (b) When L=5 uh, ΔL change from to.uh Baed on the operation prciple of the converter, at any time, we alway can get the relationhip between the voltage cro the ductor L, v, and the voltage cro the ductor L, v, a: v = v. So we could couple the L and L together. The vere couplg i ued thi paper, hown Fig.. It tranformer model can be expreed by the followg equation accordg to the well-known baic circuit theory: di di v = L M dt dt di di v = L M dt dt v = v M = k L L di v = ( L M ) dt di v = ( L M ) dt Leq = L M > L where L =L =L i the elf ductance of each wdg; L eq i the equivalent ductance; M i the mutual ductance and k i the couplg coefficient with k. From equation (), the coupled equivalent ductance i creaed comparg with the non-coupled ductor. The AC flux i cancelled the center leg of the vere-couplg tructure and the core lo can be reduced [6]. If the two ductor coupled together are unbalanced, we have: () L = L ΔL L = L ΔL M = k L L = k L ΔL From equation () and (), we can get: L M ΔL di v = L ΔL M ' L M ΔL dt L M ΔL di v = L ΔL M ' L M ΔL dt The equivalent ductance of the two ductor and the difference between them are expreed a: < M () (3) EPE 9 - Barcelona ISBN: P.3

4 L M ΔL Leq = L ΔL M ' L M ΔL L M ΔL Leq = L ΔL M ' L M ΔL 4 M ' ( L M ') ΔL ΔL = L L = ΔL eq eq eq ( L M ) ΔL Baed on equation (4), we can plot the curve to how the relationhip accordg to the couplg coefficient and equivalent ductance with the parameter: L=5 uh and ΔL=.4 uh, hown Fig. 3(a). In Fig. 3(b), we can ee that when ΔL change the range: ~. uh, the unbalanced equivalent ductance i very enitive to the variation of ΔL the range with bigger k factor. It i clear that good couplg that mean k i near to between the two ductor i not appropriate thi power converion application a the unbalance of the equivalent ductance will be too large to be acceptable. Self ductance and couplg efficient have to be properly elected to limit the unbalance and meet the ductor current ripple requirement. Deign conideration Output Power The delivered active power by thi converter can be calculated, baed on the waveform hown Fig., by: ( π δ ) V δ π π P O = δ (5) ω( L M Llk ) π where ω i the witchg frequency and L lk i leakage ductance of the tranformer. Accordg to (8), when the put voltage and witchg frequency are fixed, the output power i regulated by the phae hift angle and ductance L = L M Llk. It will be found later that different phae hift angle will caue different current tree on the device. Therefore, the L can be deigned accordg to the expected phaed hift angle at the required power ratg to reduce current tree. At the ame time, there i a limitation hown below to guarantee the output power i controlled the whole range of.5π δ. 5π : P O ωl V π We can fd that the phae hift angle i the gle control variable the ytem, but when deep regulation tage, that mean the phae hift angle i near to ±.5π, a large amount of reactive power will be the high frequency tranformer. Power Device Baed on the waveform hown Fig., the peak current occur at the pot t 4 or t 6 accordg to the different put and output voltage. So the device ratg of LV ide can be calculated a: I I V peak peak peak 4nVδ π O = i ( t ) i ( t ) = 4 4 4ωnL V Oδ π = i ( t ) i ( t6) = 6 4ωnL = V ( V nv ) ( nv V ) Equation (6) how the current tre of the ma witche the primary ide agat the output power becaue of the δ relative to the power a hown (5); and at the ame output power condition, the bigger difference between V O and nv, caue the higher current tre. The diadvantage of the PPF circuit i that the voltage tre on the MOSFET i doubled comparg with that full bridge circuit, o the high voltage MOSFET with higher on tate reitance, R DS (on), O, or, and (4) (6) EPE 9 - Barcelona ISBN: P.4

5 ha to be ued and it lead to higher conduction lo. But becaue of the oft-witchg operation of the converter, the witchg peed can be lower. We can chooe ome higher current ratg MOSFET with lower R DS (on) a the witche to reduce the conduction lo. ZVS condition In Fig., the nubber capacitor i connected parallel with each witch both to reduce witchg lo and to damp out over-voltage. A decribed above, the converion for primary ide witche and econdary ide witche occur durg terval t ~t and t 4 ~t 5, repectively. A analyzed [5], when I P plu I P i poitive, where the I P and I P are the peak current value of i and i, repectively, every witch can turn on under ZVS, dependg on the output power P o, the phae hift angle, the put and output voltage, and the dead time. The oft witchg condition will be hown a: I I I P ( t ) I P ( t ) I 4 m( I P, I P ) P ( t ) > P ( t ) > = 4 V VO C nl (7) where C i the capacitance of the C S C S, and I m(ip, IP) i the mimum magnitude of the um of i and i to guarantee the complete reonant between the L and C to realize ZVS. Sytem model and control Baed on (5), the voltage converion ratio can be a: ( π δ ) VO Z L δ M ( δ ) = = V ω( L M Llk ) π (8) where Z L i the impedance of the load. It i clear that output voltage i load-dependent and the ytem i nonlear. To deign the controller, mall-ignal analyi by learization around the operatg pot i required. In the given laboratory etup, the PPFHB converter i controlled by the digital ignal proceor (DSP TMS3F88). Fig. 4 how the mall ignal block diagram of the ytem z-doma. The ytem T amplg time, T, equal to 5 u, o we can get z = e, and cut-off frequency of PI controller i ωc = T i Fig. 4. ADC amplg delay, which i the ub-micro econd range, i ignored here. The delay caued by computation time and PWM modulator amplg delay DSP affect the ytem frequency repone and hould be conidered the deign. The tranfer function of total delay effect i expreed: G delay ( z) = GdelayCom GdelayPWM = z (9) The ymmetric optimum deign method [7] i ued to deign the voltage controller. The imulation baed on MatLab confirm the control method. The proportional ga K p and tegral ga K I were et a: o o K =. /V and K = 6. 5 /V P I * vˆ O ( z) K ( T / T ) z z i (z) p δˆ ( z ) ( π δ ) G delay VV πωl o ˆ ( z) p L T z z C O V O ˆ ( z) v O K AD Fig. 4: Small ignal z-region block diagram of the output voltage control EPE 9 - Barcelona ISBN: P.5

6 Vo (V) Vo (V) Io (A) Io (A) Phae hift (deg) t () Phae hift (deg) t () (b) Load change at.5 from 5 W to 5 W (a) Load change at.5 from 5 W to 5 W Fig. 5: Simulation waveform of tep repone and load diturbance repone. From Fig. 5, the overhoot occur tep repone with light load. The controller effectively adjuted the phae hift angle o that the dc/dc converter regulated the output voltage V o back to V about m. Experimental Reult In order to verify the feaibility and performance of the propoed converter, a laboratory prototype controlled by TMS3F88 DSP, wa implemented and evaluated. The pecification and ma parameter ued the converter are lited Table II. The experimental reult conit of relevant voltage and current waveform, and efficiency curve. Table II: Specification, parameter and component table Input voltage 3-5 V Tranformer 5:5:5, N87 Switche S and S SUP9N5 Output voltage V Inductor L =L =6 uh Switche Q and Q IRF45LC Output Power 5 W Couplg factor.35 Switchg frequency 4 kh Fig. 6 how the voltage cro the primary ide (from pot A to pot B, denoted Fig. ) and econdary ide (voltage on the wdg N 3 ) to how the phae hift modulation cheme with phae hift angle δ=4 o. The waveform of the converter with two dividual ductor and that with coupled ductor are hown Fig. 6 (a) and Fig. 6 (b), repectively. We can fd that the rgg voltage on the primary ide i reduced the condition that the coupled ductor are ued. The current waveform primary ide, depicted Fig., are alo confirmed by the experimental reult. The oft witchg operation i validated Fig. 7. When S i gated off, the um of i and i charge and dicharge body capacitor C S and C S, repectively. Although S i given an on ignal after the dead time when S i gated off, D S i conductg the current at that moment until i creae to i. When i i bigger than i, the current i diverted from D S to S and S i turned on at zero voltage. The oft-witchg proce can be derived imilarly for other witche. Fig. 8 how the output voltage waveform with tep load change, and the load current tepped from A to.5 A. EPE 9 - Barcelona ISBN: P.6

7 Analyi and deign of PPFHB bidirectional DC-DC converter with coupled ductor (a) The waveform of the converter with two (b) The waveform of the converter with coupled dividual ductor ductor Fig. 6: the waveform of teady tate operation. Ch: tranformer primary voltage ( V/div); Ch: tranformer econdary voltage ( V/div); Ch3: i ( A/div); Ch4: i ( A/div). (Time: 5 u/div) (a) Ch: gate-ource voltage of S ( V/div); Ch: dra-ource voltage of S ( V/div); Ch3: i ( A/div). (b) Ch: gate-ource voltage of Q ( V/div); Ch: dra-ource voltage of Q ( V/div); Ch3: i ( A/div). Fig. 7: The ZVS operation of the witche S and Q. (Time: 5 u/div) (a) The load tep from A to.5 A. Ch: Output voltage (5 V/div); Ch: load current ( A/div). (b) The load tep from.5 A to A. Ch: Output voltage (5 V/div); Ch: load current (.5 A/div). Fig. 8: The load diturbance repone. (Time: m/div) (a) Open loop condition. Ch: output voltage (5 (b) Cloe loop condition. Ch: output voltage (5 V/div); Ch: i ( A/div). V/div); Ch: i ( A/div). Fig. 9: The output voltage and current i repone with put voltage tep from to 3 V. (Time: m/div) EPE 9 - Barcelona ISBN: P.7

8 95% 9% Uncoupled Coupled 85% 8% 75% 7% Fig. : Efficiency chart (V =3 V). W W 3 W 4 W 5 W 6 W Fig. 9 (a) and Fig. 9 (b) how the output voltage and i tep repone with opened loop and cloed loop, repectively. We can ee that the cloe loop ytem can limit the overhoot of output voltage. Fig. plot the efficiency curve. The yellow one i the efficiency curve the condition with the coupled ductor and green curve how the efficiency of converter with two dividual ductor (the put voltage equal to 3 V). So the uage of couplg ductor thi converter can improve the ytem efficiency becaue of the reduced core lo of ductor and the clearer waveform. In thi kd of low put voltage converter, the conduction lo i the major power lo and the witchg lo i mimized due to oft witchg. Concluion A ZVS bidirectional dc-dc converter with coupled ductor i propoed and analyi thi paper. Ug the coupled ductor thi converter can reduce the core lo and optimize the waveform to improve the efficiency. But to limit the unbalance of the equivalent ductance, the couplg factor can not be et near to. Baed on the waveform analyi, the parameter are deigned and the ZVS range i dicued. Accordg to the mall ignal model of the ytem z-doma, the parameter of the voltage controller i decided by imulation. Fally, the prototype wa etup and the experimental reult how validity of the theoretical analyi and the performance of converter with coupled ductor i improved comparg with that with two dividual ductor. So the converter propoed thi paper i a promig candidate a the bidirectional terface converter EV ytem or UPS ytem for battery or uper-capacitor application. Reference [] R. W. De Doncker, D. M. Divan, and M. H. Kheraluwala, A three- phae oft-witched high-power deity dc/dc converter for high power application, IEEE Tranaction on Indutry Application, vol. 7, no., pp.63-67, 99. [] S. Inoue and H. Akagi, A Bidirectional DC DC Converter for an Energy Storage Sytem With Galvanic Iolation, IEEE Tranaction on Power Electronic, vol., no. 6, pp , 7. [3] F. Z. Peng, H. Li, G. J. Su, and J. S. Lawler, A new ZVS bi-directional dc-dc converter for fuel cell and battery application, IEEE Tranaction on Power Electronic, vol. 9, no., pp , 4. [4] H. Li and F. Z. Peng, Modelg of a new zv bi-directional dc-dc converter, IEEE Tranaction on Aeropace and Electronic Sytem, vol. 4, pp. 7 83, January 4. [5] D. Liu and H. Li, Deign and implementation of a DSP baed digital controller for a dual half bridge iolated bi-directional dc-dc converter, the th Annual IEEE Applied Power Electronic Conference and Expoition (APEC6), USA, 6. [6] K. Wang, C. Y. L, L. Zhu, D. Qu, F. C. Lee, and J. S. Lai, Bidirectional dc-dc converter for fuel cell ytem, IEEE Tranaction On Tranportation, pp. 47 5, Oct [7] L. Zhu, A novel oft-commutatg iolated boot full-bridge ZVS-PWM dc-dc converter for bidirectional high power application, IEEE Tranaction on Power Electronic, vol., no., pp. 4-49, Mar. 6. EPE 9 - Barcelona ISBN: P.8

9 [8] J. Wnag, F. Z. Peng, J. Anderon, A. Joeph and R. Buffenbarger, Low cot fuel cell converter ytem for reidential power generation, IEEE Tranaction on Power Electronic, vol. 9, no. 5, pp. 35-3, 4. [9] H. Tao, Kotopoulo A., Duarte J.L., Hendrix M.A.M., Tranformer- coupled multiport ZVS bidirectional DC DC converter with wide put range, IEEE Tranaction on Power Electronic, vol. 3, no., pp , 8. [] H. Xiao and S. Xie, A ZVS bidirectional dc-dc converter with phaed-hift plu PWM control cheme, IEEE Tranaction on Power Electronic, vol. 3, no., pp , Mar. 8. [] Z. Zhang, O. C. Thomen, M. A. E. Anderen, Analyi and deign of bi-directional DC-DC converter extended run time DC UPS ytem baed on fuel cell and upercapacitor, the 4th Annual IEEE Applied Power Electronic Conference and Expoition (APEC9), USA, 9. [] N. Schibli, Symmetrical multilevel converter with two quadrant DC-DC feedg. EPFL, PhD Thei, no.,. [3] F. Krimer, S. Round, and J. W. Kolar, Performance optimization of a high current dual active bridge with a wide operatg voltage range, the 37th IEEE Power Electronic Specialit Conference (PESC6), pp. 7, June 6. [4] D. Xu, C. Zhao and H. Fan, A PWM plu phae-hift control bidirectional DC-DC converter, IEEE Tranaction on Power Electronic, vol. 9, no. 3, pp , Mar. 4. [5] Z. Zhang, O. C. Thomen, M. A. E. Anderen, A novel PPFHB bidirectional DC-DC converter for upercapacitor application, the International Conference on Clean Electrical Power (ICCEP9), Italy, 9. [6] P. Wong, P. Xu, B. Yang, and Fred C. Lee, Performance improvement of terleavg VRM with couplg ductor, IEEE Tranaction on Power Electronic, Vol. 6, no. 4, pp , July. [7] F. Krimer and J.W. Kolar, Accurate mall-ignal model for an automotive bidirectional dual active bridge converter, the th Workhop on Control and Modelg for Power Electronic (COMPEL), 8. EPE 9 - Barcelona ISBN: P.9