A Two-stage DC-DC Converter for the Fuel Cell-Supercapacitor Hybrid System

Transcription

1 Downloaded from orbit.dtu.dk on: Apr 05, 09 A Two-tage DC-DC Converter for the Fuel Cell-Supercapacitor Hybrid Sytem hang, he; Thomen, Ole Corneliu; Anderen, Michael A. E. Publihed in: IEEE Energy Converion Congre and Expoition 009 Link to article, DOI: 0.09/ECCE Publication date: 009 Document Verion Publiher' PDF, alo known a Verion of record Link back to DTU Orbit Citation (APA): hang,., Thomen, O. C., & Anderen, M. A. E. (009). A Two-tage DC-DC Converter for the Fuel Cell- Supercapacitor Hybrid Sytem. In IEEE Energy Converion Congre and Expoition 009 (pp ). IEEE. DOI: 0.09/ECCE General right Copyright and moral right for the publication made acceible in the public portal are retained by the author and/or other copyright owner and it i a condition of acceing publication that uer recognie and abide by the legal requirement aociated with thee right. Uer may download and print one copy of any publication from the public portal for the purpoe of private tudy or reearch. You may not further ditribute the material or ue it for any profit-making activity or commercial gain You may freely ditribute the URL identifying the publication in the public portal If you believe that thi document breache copyright pleae contact u providing detail, and we will remove acce to the work immediately and invetigate your claim.

2 A Two-tage DC-DC Converter for the Fuel Cell-Supercapacitor Hybrid Sytem he hang Student Member, IEEE Technical Univerity of Denmark Elektrovej, building 35 Kg. Lyngby, DK 800, Denmark Ole C. Thomen Member, IEEE Technical Univerity of Denmark Elektrovej, building 35 Kg. Lyngby, DK 800, Denmark Michael A. E. Anderen Member, IEEE Technical Univerity of Denmark Elektrovej, building 35 Kg. Lyngby, DK 800, Denmark Abtract -- A wide input range multi-tage converter i propoed with the fuel cell and upercapacitor a a hybrid ytem. The front-end two-phae boot converter i ued to optimize the output power and to reduce the current ripple of fuel cell. The upercapacitor power module i connected by puh-pull-forward half bridge (PPFHB) converter with coupled inductor in the econd tage to handle the low tranient repone of the fuel cell and realize the bidirectional power flow control. Moreover, thi cacaded tructure implifie the power management. The control trategy for the whole ytem i analyzed and deigned. A kw prototype controlled by TMS30F808 DSP i built in the lab. Simulation and experimental reult confirm the feaibility of the propoed twotage dc-dc converter ytem. Index Term DC-DC Converter, oft-witching, control I. NOMENCLATURE V FC : Voltage of fuel cell. V : Voltage of uper-capacitor. V DC : Voltage of high voltage DC bu. L, L : Inductance in the boot converter. L P, L P : Self-inductance of the coupled inductor. L P : Equivalent inductance of the coupled inductor. M: Mutual inductance of the coupled inductor. i L, i L : Intantaneou current through inductor L and L, repectively. i LP, i LP : Intantaneou current through inductor L P and L P, repectively. i : Intantaneou current through econdary winding. i load : Intantaneou load current. i FC : Intantaneou output current of fuel cell. i : Intantaneou output current of upercapacitor. v AB : Intantaneou voltage acro the auxiliary inductor L P and primary winding of tranformer. v CN : Intantaneou voltage acro the econdary winding of tranformer. d: Duty cycle of the witche in boot converter. φ: Phae-hift angle between v AB and v CN. f B : Switching frequency of Boot converter. f P : Switching frequency of PPFHB converter. ω P : Angular frequency of PPFHB converter. P O : Output power. η B : Converion efficiency of the boot converter. N, N, N 3 : Number of turn of two primary winding and econdary winding, repectively. Fig.. Block diagram of the multi-tage energy converion hybrid ytem. II. INTRODUCTION In recent year, development of the clean power ource and electricity ha become an important topic to protect the environment and overcome the energy crii of the whole world. Fuel cell (FC) are electrochemical device which convert the chemical potential of the hydrogen into electric power directly, with conequent high converion efficiency and poibility to obtain the extended range with the combutible feed from the outide []. Baed on thee advantage, fuel cell i a promiing ubtitute to the conventional foil energy. But one of the main weak point of the fuel cell i it low dynamic that i limited by the hydrogen and air delivery ytem. Thu, energy torage unit, uch a batterie or upercapacitor (), are required a the auxiliary power ource for moothing output power in the warming-up tage of the fuel cell or load tranient period. So hybrid power converion ytem with fuel cell and other energy ource, like the ytem hown in Fig., are ued in the many indutrial ytem uch a uninterruptible power upply (UPS), hybrid electrical vehicle (HEV) and o on. Many hybrid ytem tructure have been propoed. In general, they can be divided into three categorie depending on different coupling method of the different power ource: DC-bu-coupled ytem [], [3], [4], tranformer-coupled tructure [5], [6], [7], and multi-tage ytem [8], [9], [0]. For the DC-bu-coupled ytem, each power ource i connected by a eparate converter to the common voltage DC bu. In thi architecture, every ubytem can be deigned a an individual module, but the energy management and control i complicated. In high frequency tranformer coupled ytem, the performance of ytem i mainly affected /09/$ IEEE 45

3 Fig.. The main circuit. by the tranformer deign and power flow control. A to the multi-tage converion ytem, efficiency of the whole ytem i limited by the number of cacaded converter. In thi paper, a high tep-up multi-tage bidirectional iolated DC-DC converion ytem with fuel cell and upercapacitor a energy ource i invetigated, hown in Fig., where the interleaved two-phae boot converter and puh-pull-forward half bridge converter with coupled inductor are ued a the interface topologie. Thi paper i organized into five ection. Following the introduction, the circuit ued in the ytem are preented in Section III. In Section IV, the control method and the tability analyi are decribed. Then the experimental reult for a low-voltage high current power ource and a upercapacitor module are provided to validate the effectivene of the propoed converion tructure in Section V. Finally the concluion are drawn in Section VI. III. SYSTEM CONFIGURATION A the configuration hown in Fig. and Fig., the interleaved two-phae boot converter i ued to reduce the fuel cell output current ripple and boot the fuel cell output voltage which depend on load condition, to the variable low voltage DC bu connected with upercapacitor module. Puh-pull-forward half bridge (PPFHB) converter with coupled inductor [] i ued to implement the high tep-up ratio, electrical iolation between the clean energie and high voltage DC bu, and the bidirectional power flow control to charge or dicharge the upercapacitor module. Becaue of the upercapacitor decoupling the low voltage ide and the high voltage ide, the two-phae boot converter and PPFHB converter can be deigned independently. A. Two-phae interleaved boot converter To reduce the input current ripple and reach high efficiency, the two-phae boot converter operate under CCM (Continuou Current Mode) in the normal load condition. The boot converter ue the MOSFET a rectifier intead of diode to realize ynchronou conduction mode (M) [] operation in light load condition, and the upper and lower witche are gated on-off complementarily. Fig. 3 Key waveform of PPFHB converter With the M operation, all witche can realize VS (ero-voltage-switching) to make the converter achieve high efficiency in whole load range. The deign of the inductor play a crucial role in the overall converter operation, becaue if it i maller, in light load condition, the current through the inductor will have bigger negative peak value (becaue of M operation, there i no DCM (Dicontinuou Current Mode) operation in the converter) that will caue higher reactive power. The relationhip of critical inductance (the value decide the boundary that there i negative part in the inductor current waveform or not), input voltage, output power and witching frequency can be decribed a: ( v v ) vfc FC η L B crit ( vfc, fb ) () fb Po v B. PPFHB converter The propoed topology employ the puh-pull-forward tructure to reduce the number of the power witche; utilie the half-bridge voltage doubler circuit in the econdary ide of the high frequency tranformer to get high voltage tranfer ratio. The auxiliary inductor, L P and L P, and the leakage inductor of the tranformer, L lk, are utilized a the interface and energy tranfer element between the two high frequency voltage-ource inverter on the two ide of the tranformer. The converter i controlled by the phae-hift technique to 46

4 realize table output voltage and bidirectional power flow between the low voltage (LV) ide and high voltage (HV) ide. Becaue the voltage cro the witche i alway leading to the current in the correponding witche, all the witche are turned on under VS. Fig. 3 demontrate the complete cycle of ideal circuit operation, where gate ignal are quare waveform with dead time. The gated and conducting device in every interval are lited in Table I. The detailed decription of the operation principle can be found in the paper [] and [3]. A the concluion drawn in [], coupling coefficient between the two coupled inductor hould not be et very near to, becaue in that condition, the very mall difference in the elf inductance will caue too large unbalance between each equivalent inductance to be acceptable. The phae hift angle φ ( 0.5π ϕ 0. 5π ) between v AB and v CN, which i defined to be poitive when v AB i leading to v CN in phae, i ued to control the power flow. When φ i poitive, the power i delivered from upercapacitor to the high voltage DC bu (boot mode). If φ i negative, the converter will work under buck mode. According to the waveform hown in Fig. 3, the magnitude of delivered active power by thi converter can be calculated a: N V VDC ϕ ( π ϕ ) PO () N 3 ωp ( LP M Llk ) π So from () we alo can get the voltage converion ratio a: M ( ϕ) V V DC N N ω 3 P ( L M L ) P L lk ϕ ( π ϕ) It i clear that the ytem i nonlinear and the output voltage i load-dependent. Interval TABLE I GATED AND CONDUCTED SWITCHES SEQUENCE LV ide HV ide Gated Conduction Gated Conduction t 0<t<t S 4 S 4 Q D Q t <t<t 0 D S3 Q D Q t <t<t 3 S 3 D S3 Q D Q t 3<t<t 4 S 3 S 3 Q Q t 4<t<t 5 S 3 S 3 0 D Q t 5<t<t 6 S 3 S 3 Q D Q π (3) Fig. 4. Small ignal model of boot converter with fuel cell and upercapacitor equivalent impedance. Magnitude (db) D() Bode Diagram N() Frequency (rad/ec) Fig. 5. Impedance analyi. IV. STABILITY AND CONTROLLER DESIGN In general, to guarantee the teady tate tability of a fuel cell powered DC-DC converter ytem, the V-I characteritic of the fuel cell and the locu of the DC-DC converter load power required have to interect at one point and thi et the operating condition of the ytem. In the tranient tability analyi, it i more complex becaue the dynamic of the DC-DC converter i affected by the characteritic of the internal impedance of the fuel cell and the equivalent impedance of the upercapacitor when the cloed-loop controller i deigned for the primary boot converter. In term of the equivalent circuit model of fuel cell in [4], Middlebrook extra element theorem [5] can be ued to analyze the effect caued by fuel cell to the dynamic of the converter. The mall ignal circuit model of boot converter with fuel cell and upercapacitor i hown in Fig. 4, where OFC i the output impedance of the fuel cell, C in i the input capacitor of the boot converter, i the impedance of upercapacitor bank, and i the equivalent load impedance. If the effect caued by O and could be neglected in controller deign, a that hown in [4], the following impedance inequalitie have to be met: o << N and o << D O() According to the calculation procedure in Appendix, we can plot the magnitude of O, N and D, repectively, in Fig. 5. It i clear that by connecting the fuel cell and upercapacitor to the DC-DC converter all the tranfer function are modified including the control to output and the line to output. So to deign the controller of the DC-DC converter, the tranfer function are re-deduced conidering the fuel cell output impedance and upercapacitor equivalent 47

5 v cref - H pv limition lope v fc T fc i Lref d H pi PWM - i L v o /Nv i G vd eq() v c φ f Mode i G L φ id H v G if (M) Anti-wind-up G t - i load G c / v o v oref - Fig. 6. Block diagram of the control trategy. ß impedance. The equation for the boot input current and output voltage tranfer function are preented by (4) and (5). 500 Load diturbance repone G G id vd iˆ L ( ) ( ) dˆ( ) V V D' O ( ) D' ( )L vˆ ( ) ( ) dˆ( ) O D' D' L ( ) D' ( )L For the two-phae boot converter, the dual loop control cheme i deigned. The outer loop i voltage loop, whoe output i et to be the current reference for the inner average current loop, hown in Fig. 6. According to the method in [6], we can get the open loop gain, T i () and T v (), for the current loop and voltage loop, a: O T Ti ( ) Hi ( ) Gid ( ) e T H ( ) H ( ) e G ( ) T ( ) v i vd v Ti ( ) where H i () and H v () are the tranfer function of the PI controller for the current loop and voltage loop, repectively, and e -T i the delay caued by the ampling, computation and control parameter updating in DSP. With the open loop tranfer function, we can deign the PI compenator uing Matlab control toolbox, and get the parameter a: K Pv 0, K Iv.5, K Pi 3.5, K Ii 0.6. To guarantee the large ignal tability during the tartup period, a limiter on the input current i calculated baed on the output power limitation of the fuel cell. (4) (5) (6) Vo Vc Iload Time [] Fig. 7. Simulation of load diturbance repone. Becaue the PPFHB converter can be een a a firt-order ytem [] with the time contant decided by the capacitance of output filter and load impedance, the output voltage controller with the upercapacitor voltage feed-forward i deign to keep the output voltage table. When the converter operate under buck mode, the contant power charge method i ued to charge the upercapacitor. So when the upercapacitor bank i charging, the operating mode i changed from voltage mode to power mode with the voltage limitation that depend on the pecification of the upercapacitor. The control cheme require ampling five variable: V FC, V, V DC, I L and I L, which are obtained through the voltage and current tranducer. The block diagram for the dc converter ytem control i hown in Fig. 6. With the compenator parameter deign above, the load diturbance repone i imulated in the normal operation mode, where energy i delivered from fuel cell and upercapacitor to the high voltage dc bu, hown in Fig. 7, by Matlab/Simulink. Then, the controller deigned in continuou time domain are converted to dicrete time domain by the Euler tranformation and implemented in DSP to control the practical ytem. 48

6 V. EXPERIMENTAL RESULTS In order to verify the effectivene of the propoed twotage high tep-up converter with fuel cell and upercapacitor, a hown in Fig., the correponding experimental reult are provided in thi ection. A programmable DC power upply i ued to imulate the fuel cell for the primary input power ource. Moreover, 4 upercapacitor (BCAP0350,.5 V/350 F) in erie connection are taken a the power torage unit connected in the variable DC bu. In the experimentation, the bidirectional PPFBH converter i deign to operate from a variable dc input, V 40 V-5 V, to deliver a contant output V DC 00 V. The energy torage in upercapacitor can be calculated a: E C ( V V ) (40 5 ) 73 J So the during the warm-up tage of fuel cell, the energy tored in upercapacitor can be delivered to the load to keep the high voltage dc bu table. The digital ignal proceor (DSP) TMS30F808 i adopted to implement the cloe-loop control cheme. The duty cycle and phae-hift ignal i generated by DSP and the peripheral logic circuit ditribute the driving ignal to the correponding witche in the main circuit. Baed on the analyi in Section III, we can chooe the inductance for the two-phae boot converter and make it work in CCM according to (). For the PPFHB converter, the turn ratio of the tranformer and auxiliary inductance hould be deigned to atify the following criteria: ) at heaviet load condition, to keep the DC bu voltage contant, φ i limited under the maximum phae hift angle; ) Trade-off between the turn ratio and auxiliary inductance i to lower RMS current and extend VS operation range. Moreover, the two winding of the coupled inductor are wound on the two outer leg of the EE core with the coupling coefficient k0.34 TABLE II CONVERTER COMPONENTS AND PARAMETERS Switche in boot converter, S, S, S r, S r SUP90N5P (50V/00A) Switche in PPFHB converter: S 3, S 4 Q, Q SUP90N5P (50V/00A) IRFP450LC (500V/4A) Inductor L, L 46uH Core material and ize of L, L Ferrite N87, ETD49 Tranformer core material and ize Ferrite PC40, EE55 Tranformer turn 5:5:5 Tranformer leakage inductance uh Inductor L l, L l and coupling factor 9uH, 0.34 Core material and ize of L l, L l Ferrite N7, E40 Output DC capacitor (C, C ) 470uF/350V Input capacitor, C f, and clamp capacitor 000uF/00V C c Switching frequency f B, f P Digital controller 0 khz, 40 khz TI TMS30F808 DSP The one diadvantage of the puh-pull-forward circuit i that the voltage tre on the MOSFET i doubled comparing with that in full bridge circuit. The high voltage MOSFET will be with higher on tate reitance, R DS(on), which i key to condition lo. But becaue of oft-witching the witching peed which affect the witching lo i not very critical factor, o we can ue the high-current MOSFET with lower R DS(on) to reduce the conduction lo. The prototype with the pecification given in Table II i deigned to illutrate the effectivene of the propoed two-tage bidirectional converter. Fig. 8 how that waveform of the boot converter under CCM condition with 500 W output power. We can ee that the two-phae tructure can reduce the input current ripple comparing with the current ripple through the ingle leg. Fig. 9 how the waveform of the boot converter under light load condition with the output power 00 W. It i clear that i L ha the negative part already becaue of the M operation, but the i FC i till poitive. If i FC ha the negative peak current, the reactive power required will be bigger to caue more power lo in the input capacitor. Fig. 0 and Fig. how the experimental waveform of the PPFHB converter working in boot mode and buck mode, repectively, under the condition: V 30 V and V DC 00 V. v AB i leading to the v CN in Fig. 0 but they are change the leading-lagging relation in phae in Fig., when the energy i delivered from the DC bu to the upercapacitor ide. Fig., Fig. 3 and Fig. 4 how the dynamic experimental waveform of two-tage converter ytem. During the fuel cell warm-up period, the output power i provided by the upercapictor, o the voltage of the upercapacitor reduce from 40 V. But the DC bu voltage, v DC, can keep table at 00 V. Before V reache to 30 V, the warm-up tage of the fuel cell i finihed, o fuel cell output current, i FC, tart to increae and at the ame time the output current of upercapacitor, i, reduce. The power converion from fuel cell and upercapacitor can be realized oftly and moothly, a hown in Fig.. But if the warm-up tage i too long or the load i too heavy, that mean the V reduce rapidly below 30 V, the fuel cell will provide the output power and charge the upercapacitor a well. Becaue of the inner current loop of the two-phae boot converter, i FC i limited to 0 A, and then when the V i charged to 30 V, voltage loop of the controller i functional, and the upercapacitor are in tandby condition, hown in Fig. 3. The load diturbance repone i hown in Fig. 4. So the control cheme deigned in Section IV i validated. The efficiency of the whole ytem i above 87% in the entire load range, and the peak efficiency i 9%. VI. CONCLUSION Thi paper propoed the multi-tage converter tructure with fuel cell and upercapacitor a a hybrid ytem. Converter deign, control cheme analyi and deign are implemented. The topology i baed on the interleaved twophae boot converter and a novel PPFHB converter to provide contant DC bu voltage and can realize bidirectional 49

7 Fig. 8. Waveform of the two-phae boot converter under CCM. CH: VgS (yellow), 0 V/div; CH: VgS (red), 0 V/div; CH3: ifc (blue), 0 A/div; CH4: il (green), 0 A/div. (Time bae: 0 u/div) Fig. 9. Waveform of the two-phae boot converter under light load condition. CH: VgS (yellow), 0 V/div; CH: VgS (red), 0 V/div; CH3: ifc (blue), 5 A/div; CH4: il (green), 5 A/div. (Time bae: 0 u/div) Fig. 0. Waveform of the PPFHB converter working in boot mode. CH: VAB (yellow), 00 V/div; CH: VCN (red), 00 V/div; CH3: ilp (blue), 0 A/div; CH4: ilp (green), 00 V/div. (Time bae: 5 u/div) Fig.. Dynamic tate waveform under normal condition. CH: V (yellow), 0 V/div; CH: ifc (red), 0 A/div; CH3: i (blue), 0 A/div; CH4: VDC (green), 00 V/div. (Time bae: 5 /div) Fig. 3. Dynamic tate waveform under heavy load condition. CH: V (yellow), 0 V/div; CH: ifc (red), 0 A/div; CH3: i (blue), 0 A/div; CH4: VDC (green), 00 V/div. (Time bae: 5 /div) Fig. 4. The load diturbance repone: load current tep up from A to A and tep down. CH: V (yellow), 0 V/div; CH: load current (red), A/div; CH3: i (blue), 5 A/div; CH4: VDC (green), 00 V/div. (Time bae: 5 /div) power flow control. The controller i a fully digital DSP baed ytem. The effect of the fuel cell output impedance and the impedance of upercapacitor to the ytem tability are conidered during the controller deign. The topology and control trategy for the hybrid ytem are verified by the imulation and experimental reult. Fig.. Waveform of the PPFHB converter working in buck mode. CH: VAB (yellow), 50 V/div; CH: VCN (red), 00 V/div; CH3: is (blue), 5 A/div. (Time bae: 5 u/div) APPENDIX According to the model of fuel cell drawn in [4], we can get the FCO, O and a: 430

8 FCO ( RmRpR pcc ) ( RpR pcc ) ( RpC RpC ) ( Rm ( RpC RpC ) RpR p( C C )) ( R R C C ) ( R C R C ) p ( R R C C ) ( R C R C ) p p p Rm Rp Rp p p O FCO Cin RCin C R where R m i the reitance of the membrane, R p -C and R p - C are the time contant of each electrode of the fuel cell. Baed on the Middlebrook extra element theorem [5], N () and D () of the two-phae boot converter are given by: L N ( ) D' D' L LC D' D' D ( ) D' C where the duty cycle of teady tate i D and D equal to D'. The equivalent circuit parameter of the fuel cell, upercapacitor and boot converter are lited in Table III. So we can plot the Fig. 5 in Matlab. TABLE III p p Tranaction on Indutrial Electronic, vol. 56, no. 6, pp , 007. [4] O.C. Onara, M. Uzunoglu and M.S. Alam, Modeling, control and imulation of an autonomou wind turbine/photovoltaic/fuel cell/ultracapacitor hybrid power ytem, Journal of Power Source, vol.85, no., pp , 008. [5] D. Liu and H. Li, A VS bi-directional DC-DC converter for multiple energy torage element, IEEE Tran. Power Electron., vol., no. 5, pp , Sep [6] H. Tao, A. Kotopoulo, J. L. Duarte and M. A. M. Hendrix, Tranformer-coupled multi-port VS bidirectional DC DC converter with wide input range, IEEE Tranaction on Power Electronic, vol. 3, no., pp , 008. [7] C. hao, S. D. Round, J. W. Kolar, An iolated three-port bidirectional DC-DC converter with decoupled power flow management, IEEE Tranaction on Power Electronic, vol. 3, no. 5, pp , 008. [8] J. Wang, F.. 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, 004. [9] M. H. Todorovic, L. Palma and P. N. Enjeti, Deign of a wide input range DC DC converter with a robut power control cheme uitable for fuel cell power converion, IEEE Tranaction on Indutrial Electronic, vol. 55, no. 3, pp , 008. [0] Jineok Hong, Sungyoon Jung, Pham Dai Thang and Kwanghee Nam Hybridization fuel cell with upercapacitor for FCEV, Annual IEEE Applied Power Electronic Conference and Expoition, pp , 008. []. hang, O. C. Thomen, M. A. E. Anderen, Analyi and deign of PPFHB bidirectional DC-DC converter with coupled inductor, in the 3 th European Conference on Power Electronic and Application (EPE 009), Spain, 009 [] W. Yu and J. Lai, Ultra high efficiency bidirectional dc-dc converter with multi-frequency pule width modulation, Annual IEEE Applied Power Electronic Conference and Expoition, pp , 008. [3]. hang, O. C. Thomen, M. A. E. Anderen, A novel PPFHB bidirectional DC-DC converter for uper-capacitor application, in the International Conference on Clean Electrical Power (ICCEP 009), Italy, 009. [4] S. C. Page, A. H. Anbuky, S. P. Krumdieck, and J. Brouwer, Tet method and equivalent circuit modeling of a PEM fuel cell in a paive tate, IEEE Tranaction on Energy Converion, vol., no.3, pp , 007. [5] R. Erickon, D Makimovic, Fundamental of Power Electronic (econdary edition), Springer, pp , 00. [6] X. Huang, X. Wang, T. Nergaard, J. Lai, X. Xu and L. hu, Paraitic ringing and deign iue of digitally controlled high power interleaved boot converter, IEEE Tranaction on Power Electronic, vol. 9, no. 5, pp , 004. R m R p C R p C 6.8 mω 78.6 mω 58.9 mf 8.75 mω mf L C P O V O D 00 uh 5 F 000 W 40 V 0.5 REFERENCES [] X. Yu, M. R. Starke, L. M. Tolbert, and B. Ozpineci, Fuel cell power conditioning for electric power application: a ummary, IET Electric Power Application, vol., pp , 007. [] M. Becherif, M.Y. Ayad and A. Miraoui, Modeling and paivitybaed control of hybrid ource: fuel cell and upercapacitor, Conference Record of the 006 IEEE Indutry Application Conference Forty-Firt IAS Annual Meeting, vol.3, pp , 006. [3] P. Thounthong, S. Rael, and B. Davat, Control trategy of fuel cell and upercapacitor aociation for a ditributed generation ytem, IEEE 43