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ABSTRACT
Proton exchange membrane fuel cell (PEMFC) has been gradually applied in new energy vehicles, aviation and other industries, attracting widespread attention. Accurately identifying unknown parameters in the mathematical model of PEMFC is beneficial to the simulation, control and prediction of its output Current-Voltage curve. In order to identify the optimal unknown parameters, based on basic Chicken Swarm Optimization, this paper introduces positive/negative learning strategies for roosters and positive learning strategies for hens and chicks. An Improved Chicken Swarm Optimization algorithm is proposed. Compared with Particle Swarm Optimization, Salp Swarm Algorithm, Whale Optimization Algorithm and basic CSO algorithm, the proposed algorithm shows better convergence and accuracy. The five algorithms are applied to three common stacks (250W PEMFC, NedStack PS6 PEMFC, Ballard Mark V) and PEMFC monomer for model unknown parameter identification and optimization. The results show that, the ICSO algorithm obtains the minimum integral of absolute error of the actual stack voltage and the simulated stack voltage in the three test stacks and a PEMFC monomer, which are 2.288, 5.857, 2.407 and 0.408, the ICSO algorithm has a maximum increase of 8.63%, 4.52%, 6.20% and 64.83% in accuracy, respectively. The simulation data agrees well with the experimental data. These indicating that the mathematical model of PEMFC based on ICSO algorithm can accurately simulate the polarization curve at different temperatures and partial pressures, and it can be obtained that with the increase of temperature and partial pressure, the output performance of the PEMFC is also getting better.
Disclosure statement
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
Nomenclature
| PEMFC | = | proton exchange membrane fuel cell |
| Eact | = | activation loss voltage |
| Eω | = | Ohmic loss voltage |
| Econ | = | concentration loss voltage |
| n | = | number of monomers connected in series in the reactor |
| EN | = | Nernst (reversible) potential |
| TPEM | = | operating temperature of the fuel cell |
| Pa | = | inlet pressure (atm) of the anode |
| Pc | = | inlet pressure (atm) of the cathode |
| Rha | = | relative humidity of the gas in the anode |
| Rhc | = | relative humidity of the gas in the cathode |
| PH2 | = | effective partial pressures (atm) of the hydrogen |
| PO2 | = | effective partial pressures (atm) of the oxygen |
| PH2O | = | effective partial pressures (atm) of the water |
| IPEM | = | current value of the PEMFC |
| βis | = | empirical coefficients |
| CO2 | = | cathode oxygen concentration |
| CH2 | = | anode hydrogen concentration |
| Rm | = | resistance of the membrane |
| Rc | = | resistance of the connection |
| A | = | surface area of the membrane |
| ρm | = | membrane resistivity |
| l | = | thickness of the membrane |
| λ | = | water content of the membrane |
| Jmax | = | maximum current density |
| J | = | actual current density |
| ICSO | = | improved chicken swarm optimization |
| CSO | = | chicken swarm optimization |
| PSO | = | particle swarm optimization |
| SSA | = | salp swarm algorithm |
| WOA | = | estimated voltage for the PEMFC |
| = | experimentally measured voltage for the PEMFC | |
| = | j-th dimension coordinate of the position of the i-th individual in the t-th iteration | |
| = | fitness value of the rooster | |
| f | = | fitness value of the i-th rooster |
| fi | = | estimated voltage for the PEMFC |
| k | = | index of a rooster randomly selected from the rooster group |
| ε | = | extremely small parameter to avoid division by zero |
| r1 | = | the rooster followed by the hen |
| r2 | = | a rooster or hen selected at random from the whole chicken swarm |
| = | position of the mother hen of the i-th chicken | |
| FL | = | influence factor of the position of the mother hen on the position of the chick |
Subscripts
| H2 | = | Hydrogen |
| O2 | = | Oxygen |
| H2O | = | Water |
CRediT authorship contribution statement
Tongying Wang: Writing-Original draft preparation, Formal analysis, Investigation.
Haozhong Huang: Conceptualization, Methodology, Supervision, Resources.
Xuan Li: Data curation.
Xiaoyu Guo: Investigation.
Mingxin Liu: Investigation.
Han Lei: Validation