A three-port bi-directional converter for hybrid fuel cell systems

Transcription

1 A three-port bi-directional converter for hybrid fuel cell systems Jorge Duarte Marcel Hendrix Group of Electromechanics and Power Electronics Technische Universiteit Eindhoven The Netherlands & Marcelo Godoy Simões Engineering Division Colorado School of Mines USA Abstract The implementation of a hybrid fuel cell/battery system is proposed to improve the slow transient response of a fuel cell stack. This system can be used for an autonomous device with quick load variations. A suitable three-port galvanic isolated bi-directional power converter is proposed to control the power flow. An energy management method for the proposed three-port circuit is analyzed and implemented. Measurements from a 500W laboratory prototype are presented to demonstrate the validity of the approach. Paper presented at IEEE PESC2004 Corresponding author: dr. J.L. Duarte TU Eindhoven Electro Dept. Room Elaag 1.07 P.O.Box MB Eindhoven The Netherlands voice: fax: j.l.duarte@tue.nl 1

2 1 Introduction Fuel cells have very slow response due to the natural electrochemical reactions required for the balance of enthalpy [1-4]. Therefore electrical output load power is not matched during transients and the deficiency or surplus must be managed by an external levelling system. A fuel cell generator will shutdown or collapse when more current is taken than it can supply; so current demand should never exceed the available current. Current demand may be less than available current but this results in unused fuel and decrease of efficiency from the fuel cell. For these two reasons bi-directional energy storage is required to sink/source the power difference. Lead acid batteries provide a suitable choice for storage because they show fast response time to load changes being therefore capable of handling the power difference between the load demand and the available fuel cell generation. Moreover lead acid batteries are not expensive and widely available. The subject of this paper is the design and the implementation of a suitable interface circuit for a hybrid fuel cell/battery system aiming at feeding a small autonomous load. An overview of the complete system is shown in Fig. 1 where a converter controls the power flow between a 25-39V 500W PEM fuel cell stack and 48V lead acid batteries. As soon as power deficiency or excess occurs because of load variations the converter regulates this extra power flow from or to the energy storage element. Furthermore since the possibility to supply AC loads through a 400Vdc inverter output should also be available a three-port bi-directional topology has to be chosen in view of the characteristic behavior of the fuel cells batteries and load. Of course there should be no compromising in reliability and battery lifetime. Multiple-port bi-directional converter topologies that may be suitable for the system requirements in Fig. 1 can be found in literature [56]. The main drawback of the existing 2

3 concepts is that they cannot handle a wide variety of voltage range inputs. A resonant converter topology is presented in [7] but it is very hard to implement. Since the system under consideration combines a 25-39V fuel cell stack and 48V batteries with a 400V inverter output the use of magnetic transformers may facilitate matching the different voltage levels. The dual active bridge described in [8] proposed to control the power flow between two ports can be expanded to three ports in order to satisfy the needs of the complete system in Fig. 1. The advantages of a magnetically-coupled multiple-port topology aiming at UPS applications have also been recognized in [9]. This paper is a reviewed version of our previous work [10]. A three-port concept for the converter which employs a single high-frequency isolation transformer is introduced in Section 2. Then a control-oriented modelling approach is presented in Section 3. Shortterm and long-term power management strategies are discussed in Section 4. Theoretical considerations are verified by simulation results in Section 5 and by measurement results in Section 6. Finally concluding remarks are placed in Section 7. 2 Transformer-coupled converter Fig. 2(a) shows a three-port converter as an extension of the ideas in [8] which may support the bi-directional energy flow requirements in Fig. 1. The full-bridge modules are coupled by means of a three-winding transformer eventually with the addition of external inductors. Each full-bridge operates at fixed switching frequency (100kHz in the current application) and fixed 50% duty cycle. The power flow between sources and sinks can be controlled by shifting the switching patterns with respect to the master module i.e. the fuel cell bridge. 3

4 3 System modelling Conceptually the circuit in Fig. 2(a) can be viewed as a grid of inductors (the transformer magnetizing inductance leakages and external inductors) driven by controlled square-wave voltage sources. The voltage sources are phase shifted from each other by controlled angles and these displacements impose the power flow between the sources. Fig. 2(b) illustrates this fundamental modelling approach based on the π-equivalent transformer representation with the magnetizing inductance and the leakages referred to the fuel cell side. The transformer π-model in Fig. 2(b) facilitates the system analysis in addition simple formulas allow to convert the parameters from a conventional T-model to the π-description (see Appendix). According to the definitions in Fig. 2 the relationship between the bridge phase shift angles and the power flow in the system is found to be ( P 10 = S 10 ϕ 10 1 ϕ ) 10 (1) π ( P 20 = S 20 ϕ 20 1 ϕ ) 20 (2) π ( P 21 = S 21 ϕ 21 1 ϕ ) 21 (3) π P 0 = P 10 + P 20 (4) P 1 = P 10 P 21 (5) P 2 = P 20 + P 21 (6) S 10 = V 0 ˇV 1 ωl 10 S 20 = V 0 ˇV 2 ωl 20 S 21 = ˇV 1 ˇV2 ωl 21 (7) where ω = 2πf s and f s is the switching frequency; 4

5 ˇV 1 = V 1 /n 1 and ˇV 2 = V 2 /n 2 are the load and battery voltages respectively referred to the fuel cell side; ϕ 10 and ϕ 20 denote the phase shifts (in radians) of the load bridge and battery bridge with reference to the fuel cell bridge respectively; ϕ 21 = ϕ 20 ϕ 10 ; P 0 is the power delivered by the fuel cell generator; P 1 is the power consumed by the load (a negative P 1 means energy injection into the grid of inductors from the dc buffer capacitor at the load side); P 2 is the power stored into the battery (negative sign means that energy is drawn from the battery). Fig. 3 illustrates some simulation results of the triple active bridge system under openloop control of the bridge phase shift angles. The simulation parameters are given in the next section. 4 Power flow control On the basis of (1)-(7) different control strategies can be realized. For instance if ϕ 10 = ϕ 10 is imposed by a classic analog (PID) compensator the voltage V 1 is kept constant. If V 1 increases due to some load variation ϕ 10 will be decreased accordingly such that less power will be delivered to the dc buffer capacitor at the load side. As a consequence of (1) phase shift ϕ 10 will impose the power flow through L 10 in Fig. 2(b) that is P 10 = S 10 ϕ 10 ( 1 ϕ 10 ). (8) π In order to avoid multiple solutions in (8) the absolute value of the load bridge phase shift must be bounded to ϕ 10 π/2. 5

6 Let now P0 denote the desired electric power to be delivered by the fuel-cell generator (normally P0 = P fc nom the nominal power of the fuel cells.) Then in view of (2) (4) and (8) the phase shift to be adjusted in the battery bridge should obey ϕ 20 ( 1 ϕ 20 ) = (9) π where = 1 S 20 (P 0 P 10). (10) After some algebraic manipulations the solution of (9) is found to be ϕ 20 = sign( ) [ ( )] π 1 1. (11) 2 π/4 Another possible energy flow situation would be to charge the battery when the power delivered to the load denoted as P 1 is less than P nom fc. Again ϕ 10 = ϕ 10 is imposed by a compensator and now P 1 is known (for instance by measuring the dc load current). By choosing P0 in the range P 1 P 0 P fc nom and by adjusting ϕ 20 battery will be charged with an average current level I 2 where as given by (11) the I 2 = (P 0 P 1 )/ ˇV 2. Eventually by making P 0 = P 1 the charging process will be stopped. In the power management policies described above it should be clear that ϕ 10 is obtained by means of closed-loop control as implemented by an analog compensator that compares continually the error between V1 and a desired reference value. However the value of ϕ 20 is obtained by means of feed-forward control according to (11) on the basis of measured values of a few circuit variables (ϕ 10 V 0 V 1 and V 2 ). The calculations in (11) can be easily performed by a digital signal processor. 6

7 5 Simulation results A Spice-based model was developed to investigate the performance of the system. Parameters for the simulations are as follows: Fuel-cell generator: modelled according to [1]. Fig. 4 shows the equivalent circuit where ( ) IF C + I n E F C = E rev A ln I 0 with E rev = 57V A = 0.3V I n = 30mA I 0 = 4.6µA R P = 0.23Ω R S = 0.55Ω C D = 270mF ; and I F C is the current drawn from the terminals. Battery: modelled as a constant voltage source (V 2 = 48V ). Load: modelled as simple resistances in parallel with a bus capacitance (C 1 = 4.7µF ); desired voltage level : V 1 = 400V. ; Transformer: n 1 = 7.66 n 2 = 0.96 L 00 = 350µH L 10 = 26µH L 20 = 230µH L 21 = 230µH. Switching frequency: 100kHz. In all situations the same PI-compensator was applied to control the output voltage implemented as ϕ 10 (s) ɛ(s) = K 1 s/s z s/s z (12) with ɛ = V 1 V 1 and K = 6.2rad/V s z = 50krad/s. A variety of operating conditions were studied to verify the effectiveness of the power control algorithm. Fig. 5(a) shows the response of the system to step changes in the load assumed in this case to be resistors suddenly switched in parallel with the output DC capacitor. The results in Fig. 5(a) illustrate the output voltage is regulated to a constant 7

8 value while the power delivered by the fuel cells remains unchanged at its nominal value. Fig. 5(b) also shows a charging cycle for the battery while keeping constant the power delivered to the load. Simulation results have also shown that if the circuit parameters are adequately designed it is possible to assure soft-switching for all bridges over the whole phase shift range. 6 Experimental results An experimental set-up was assembled using MOSFETs as switching devices the test circuit being rated at 500W for 100kHz switching frequency. A PEM 500W fuel cell set from Avista Labs [1] was used as generator in combination with 48V-12A lead-acid batteries. A dspace DS1104 controller board has been chosen to implement the energy management strategies. The experimental circuit parameters are shown in Table 1 together with the ones used for numerical simulations in the previous section. Fig. 6 gives an overview of the laboratory set-up. The overall system control is based on prescribed phase-shift of a three-port magnetic coupled structure. This control strategy works really well during steady-state conditions. However during transient there is always a dc-offset that may build up in one of the ports which can lead the transformer towards saturation. Although a programmable slewrate on the phase-shift control helps to mitigate the dc-current build-up with an eventual decay based on the constant time of the equivalent Thvenin of the magnetic structure the transformer needs to incorporate an airgap to store any remaining energy. The worstcase scenario was simulated in order to determine the required magnetizing inductance of the transformer. In addition to the phase-shift transients under rated power conditions the effects of harmonics were also considered. For this particular structure the value of 8

9 Table 1: Circuit quantities Parameter* Simulated Experimental value value L µh L µh L µh L µh n ratio n ratio V V V V V V *Parameter definitions are given in Fig. 2 9

10 h! Table 2: Transformer design parameters L mag I mag max I 0 rms I 1 rms I 2 rms N turns 0 N turns 1 N turns 2 Core 350µH 0.3A 4.3A 1.9A 1.7A ETD µh was determined that would lead a maximum of 10% of dc-current flow (based on rated power). The software Magtool and Conv (Philips proprietary program) were used to design and optimized the transformer core windings interleaving and half-winding effects. A combination of Litz wire (for primary) and solid wire (for secondary) was determined. The transformer parameters are given on Table 2 and the experimental setup corroborated the successful operation of this transformer under practical conditions. Fig. 7 shows measurement results illustrating characteristic voltage and current waveforms. Operating conditions are chosen to be equivalent to the the ones as for the simulation results in Fig. 3. A comparison between both figures reveals that the simulated and measured results are consistent. Also it is possible to recognize the soft-switching operation of the topology from the voltage and current waveforms in Fig. 7. Fig. 8 illustrates the response for a pulsating load demand while keeping the power drawn from the fuel cells constant and the ability to charge the battery according to an arbitrary profile. In Fig. 8(a) a step reduction of about 50W in the load takes place; it can be seen that after a transient the power delivered by the fuel cells returns to its nominal value while the deficit is covered by the battery. In Fig. 8(b) the output load is kept constant and an increase of around 50W is injected into the system by the fuel cells. Therefore the power delivered by the battery decreases. In Fig. 8(c) the fuel cell generator feeds the load (step increase of 50W) while the energy from the battery is kept constant. 10

11 In Fig. 8 the current variations are directly related to energy changes because during the time period shown the voltage changes are not significant. 7 Conclusions A power electronic system capable to interface battery energy storage to a fuel cell generator and a generic load was described. A three-port galvanically isolated topology was developed based on full bridge converters that allow bidirectional power flow in each port. configuration facilitates matching of different voltage levels in the overall system. Such The transformer design was optimally performed in order to incorporate the leakage inductances as required by the topology. The power flow control has a closed-loop strategy to keep output voltage constant during transients with a feedforward strategy to distribute the energy. The fundamental behaviour of the proposed converter system was verified on a 500W AVista fuel cell system. 11

12 Appendix Considering the three-port transformer in Fig. 2 parameter conversion from the T-model to the π-model representation is as follows: n 1 = L 10 = L 20 = L 21 = l 3 N 1 n 2 = l 3 N 2 l 0 + l 3 l 0 + l [ 3 ( 1 l 0 + l l ) ] 1 ( 1 [l 1 + l 3 l ) ] 1 l 3 ( 1 l ) l0 + l 3 l 3 l 3 [ ( 1 l 0 + l l ) ] 1 ( 1 [l 2 + l 3 l ) ] 1 l 3 ( 1 l ) l0 + l 3 l 3 l 3 [ ( 1 l l 0 l ) ] 1 ( 1 [l ) ] 1 l 3 l 0 l 3 ( ) ( ) l0 + l 2 3 l 0 l 3 l 3 L 00 = l 0 + l 3 l 1 = (1/N 2 1 ) l 1 l 2 = (1/N 2 2 ) l 2. and conversely from π- to T-model: M 0 = L 00 ( 1 M 01 = + 1 ) L 00 L 10 L 20 + L 21 ( 1 M 02 = + 1 ) L 00 L 20 L 10 + L 21 [ ( ) ] 1 M 1 = n L L 10 L 20 + L 21 ( ) 1 M 10 = n L 10 L 20 + L 21 12

13 M 12 = n ( L 21 1 L ) 1 L 00 L 20 [ ( ) ] 1 M 2 = n L L 20 L 10 + L 21 ( ) 1 M 20 = n L 20 L 10 + L 21 M 21 = n L 21 1 ( 1 L L 00 L 10 ) M 01 = M 0 M 01 M 02 = M 0 M 02 /[ l 3 = M 01 M ( M21 + M )] 12 2 M 2 M 1 l 0 = M 0 l 3 ( l 1 = M 1 1 M ) 01 l 3 ( l 2 = M 2 1 M ) 02 l 3 N 1 = M 01 M 1 /l 3 N 2 = M 02 M 2 /l 3 l 1 = N 2 1 l 1 l 2 = N 2 2 l 2. Acknowledgment The authors wish to thank Ms. M. Michon and Mr. H. Tao for their help in the experimental work. 13

14 References [1] P. Wingelaar J.L. Duarte M.A.M. Hendrix; Computer controlled linear regulator for characterization of PEM fuel cells IEEE International Symposium on Industrial Electronics ISIE 2004; June 2004; Ajaccio (France). [2] J.M. Corrêa F.A. Farret L.N. Canha and M. Godoy Simões An electrochemicalbased fuel cell model suitable for electrical engineering automation approach IEEE Transactions on Industrial Electronics - accepted for publication. [3] J.M. Corrêa F.A. Farret M. Godoy Simões V.A. Popov Sensitivity analysis of the modeling parameters used in simulation of proton exchange membrane fuel cells IEEE Transactions on Energy Conversion - accepted for publication. [4] J.M. Corrêa F.A. Farret J.R. Gomes and M. Godoy Simões Simulation of fuel cell stacks using a computer-controlled power rectifier with the purposes of actual high power injection applications IEEE Transactions on Industry Applications July/August 2003 vol. 39 no. 4 pp [5] K. Wang C.Y. Lin L. Zhu D. Qu F.C. Lee J.S. Lai; Bi-directional DC to DC converters for fuel cell systems Power Electronics in Transportation Oct 1998 pp [6] A. Di Napoli F. Crescimbini S. Rodo L. Solero; Multiple input DC-DC power converter for fuel-cell powered hybrid vehicles th Annual IEEE Power Electronics Specialists Conference; vol. 4 pp [7] H. Pinheiro P.K. Jain; Series-parallel resonant UPS with capacitive output DC bus filter for powering HFC networks IEEE Trans. on Power Electronics Vol. 17 nr. 6 Nov 2002 pp

15 [8] R.W.A.A. De Doncker D.M. Divan M.H. Kheraluwala; A three-phase soft-switched high-power-density DC/DC converter for high-power applications IEEE Trans. on Industry Appl.; vol. 27 nr. 1 Jan.-Feb pp [9] C. Zhao J.W. Kolar; A novel three-phase three-port UPS employing a single highfrequency isolation transformer th Annual IEEE Power Electronics Specialists Conference; Aachen Germany; pp [10] M. Michon J.L. Duarte M.A.M. Hendrix M. Godoy Simes; A three-port bidirectional converter for hybrid fuel cell systems th Annual IEEE Power Electronics Specialists Conference; Aachen Germany; pp

16 Load Fuel cell generator Bi-directional converter Battery storage Figure 1: System overview : a power electronic converter regulates the energy flow between the fuel cell generator an energy storage device and the load. 16

17 Figure 2: (a) Proposed DC/AC/DC converter topology that matches sources and sinks of energy in Fig. 1 through a three-winding transformer and bi-directional high-frequency switching bridges. Full H-bridges are shown at each port; however it would be also possible to implement this converter by using half bridges. (b) Fundamental system model: three square-wave voltage sources that exchange energy through a grid of inductors as a consequence of the phase shift angle between the switching patterns. The network of inductors is derived from the transformer in (a) based on a π-model representation. 17

18 M 2.487M 2.491M 2.495M 2.499M time in secs M 2.487M 2.491M 2.495M 2.499M time in secs ϕ 10 = 34 o ϕ 20 = 34 o ; Figure 3: Simulation results of the three-port converter in Fig. 2: square wave voltages across the transformer terminals and corresponding current waveforms at a time base of 2µs/div. Left frame : fuel-cell (Trace 1 : 50V/div Trace 3: 10A/div) and load terminals (Trace 2: 500V/div Trace 4: 1A/div.); right frame: battery terminals (Trace 1: 50V/div Trace 2: 2A/div.) Figure 4: Equivalent dynamic circuit model of a PEM fuel-cell generator [1]. 18

19 (a) (b) Figure 5: Simulation results showing (a) step change in the load while the energy delivered by the fuel cells remains constant (load variation from 370W to 320W ) and (b) battery charging (step of 40W ) under constant output load (300W ). Traces from top to button: power delivered by the fuel cells battery and load; lower picture frames are zoomed views of the upper ones. 19

20 (a) (b) Figure 6: Experimental set-up showing (a) the fuel-cell generator (right) together with the DSpace system (left) and (b) details of the three-port converter. 20

21 (a) ϕ 10 = 34 o ϕ 20 = 34 o ; (b) ϕ 10 = 28 o ϕ 20 = 40 o ; Figure 7: Measurement results: square wave voltages across the transformer terminals and corresponding current waveforms at a time base of 2µs/div. Left frames : fuel-cell (Ch.1 : 50V/div Ch. 2: 10A/div) and load terminals (Ch. 3: 500V/div Ch. 4: 1A/div.); right frames: battery terminals (Ch. 1: 50V/div Ch. 2: 2A/div.) 21

22 (a) (b) (c) Figure 8: Measurement results; in all pictures the traces from top to bottom correspond to: (i) trigger event (Ch. 2) (ii) current drawn from the fuel cell generator (ground reference at Ch.1 1A/div) (iii) dc load current (ground ref at Ch.3 0.2A/div) (iv) battery current (ground ref at Ch.4 0.5A/div; note that to fit the screen this current is shown as a negative value). (a) Step reduction of 50W in the load; (b) injection of 50W by the fuel cells; (c) step increase of 50W in the fuel cells and no power is stored in the battery. All traces are shown at a time scale of 20µs/div. 22