Dynamic modeling of a hybrid electric system based on an anion exchange membrane fuel cell

Figures & data

Figure 1. Hybrid system configuration.

Figure 2. DC-DC converter model.

Table 1. Converter circuit parameters

RL	0.0003	Ω
L	0.00041	H
Rc	0.005	Ω
C	0.03	F
Ron FET	0.038	Ω
Rd	0.01	Ω
Rs FET	0.00001	Ω
Cs FET	inf	F
Ron diode	0.001	Ω
Rs diode	500	Ω
Cs diode	2.5 E-7	F

Figure 3. Output voltage and comparison.

Figure 4. Battery stack model.

Figure 5. Equivalent circuit of the generic battery model (Shepherd, 1965; Tremblay et al., 2007).

Table 2. Battery parameters

Nominal voltage	3.2	V
Rated capacity	40	Ah
Maximum capacity	43	Ah
Fully charged voltage	3.33	V
Nominal discharge current	12	A
Internal resistance	0.001	Ω
Capacity at nominal voltage	36.17	Ah
Voltage exp zone	3.25	V
Capacity exp zone	19.652	Ah

Figure 6. Model and experimental battery discharging characteristic.

Figure 7. Load subsystem.

Table 3. Modulating signals for batteries SOC < 60% (a) and for batteries SOC ≥ 60% (b) according to equivalent load resistance R

(a) SOC < 60%			(b) SOC ≥ 60%
if		mod Signal	if		mod Signal
R ≤ 0.6	→	0.9	R ≤ 0.4	→	0.9
0.6 < R ≤ 0.7	→	0.7	0.4 < R ≤ 0.5	→	0.8
0.7 < R ≤ 0.8	→	0.6	0.5 < R ≤ 0.6	→	0.6
0.8 < R ≤ 1.5	→	0.5	0.6 < R ≤ 0.8	→	0.5
1.5 < R ≤ 5	→	0.4	0.8 < R ≤ 1	→	0.4
5 < R	→	0.3	1 < R	→	0.3

Figure 8. Fuel cell power (a), battery power (b) and SOC (c).

Table 4. Simulations results for R values in electric load equal to 12 Ω (a) and to 0.8 Ω (b)

Rload (Ω)	Pload (W)	Vbatt (V)	Pbatt (W)	PAEMFC (W)	${\overline{\mathit{\eta }}}_{\text{DC,conv}}$	ηAEMFC	ηT
(a) Initial SOC: 19%
12	32	19.53	−460	510	0.852	0.348	0.335
6	63	19.51	−430	518	0.852	0.353	0.337
3	127	19.58	−605	770	0.852	0.525	0.500
1.5	255	19.54	−475	782	0.852	0.533	0.498
(a) Initial SOC: 70%
12	32	19.54	32	0	–	0.000	0.437
6	63	19.52	63	0	–	0.000	0.444
3	127	19.51	127	0	–	0.000	0.440
1.5	252	19.47	252	0	–	0.000	0.441
(b) Initial SOC: 19%
0.8	477	19.53	−460	1,050	0.887	0.257	0.229
0.4	952	19.52	−442	1,560	0.887	0.382	0.341
0.2	1,850	19.24	447	1,590	0.887	0.389	0.337
0.1	3,488	18.71	2,075	1,618	0.887	0.396	0.331
(b) Initial SOC: 70%
0.8	470	19.41	472	0	–	0.000	0.319
0.4	926	19.25	926	0	–	0.000	0.320
0.2	1,877	19.39	477	1,578	0.884	0.386	0.337
0.1	3,545	18.86	2,130	1,610	0.884	0.394	0.331

Shepherd, C. M. (1965). Design of primary and secondary cells-Part 2. An equation describing battery discharge. Journal of The Electrochemical Society, 112, 657–664.10.1149/1.2423659

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Tremblay, O., Dessaint, L.A., & Dekkiche, A.I. (2007, September, 9–12). A generic battery model for the dynamic simulation of hybrid electric vehicles. In Proceedings of Vehicle Power and Propulsion Conference (VPPC) 2007 (pp. 284–289). Arlington, TX: IEEE.10.1109/VPPC.2007.4544139

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