Reliable exponential distribution optimizer-based methodology for modeling proton exchange membrane fuel cells at different conditions

Establishing a precise model for proton exchange membrane fuel cell (PEMFC) is vital to simulate, manage, control, and estimate the optimal parameters accurately. However, the process has some challenges due to the nonlinear nature of fuel cells (FCs) and the missing parameters in datasheet. Also, the reported approaches have some restrictions in their behaviors. This paper proposes a new methodology incorporated exponential distribution optimizer (EDO) to construct PEMFC's equivalent circuit through estimating their parameters with the aid of experimental data. The algorithm is characterized by exploration/exploitation balance that avoids falling in local solutions. Sum square error (SSE) between the measured and estimated terminal voltages is selected as the target to be mitigated. The analysis is performed on four different FCs which are Ballard Mark V 5 kW, BCS-500 W, SR-12 500 W, and NedStack PS6. The proposed EDO is compared to reported approaches of mayfly optimization algorithm (MOA), chaotic mayfly optimization algorithm (CMOA), modified Harris hawks optimizer (MHHO), fractional order modified HHO (FMHHO), hybrid vortex search algorithm and differential evolution (VSDE), and other programmed approaches of sine cosine algorithm (SCA), seagull optimization algorithm (SOA), tunicate swarm algorithm (TSA), and gold rush optimizer (GRO). The best scores are 0.852056, 1.16978E-02, 1.056628, and 2.079166 obtained through the proposed EDO for Ballard Mark V 5 kW, BCS-500 W, SR-12 500 W, and NedStack PS6 cells, respectively. The absolute error ratios of CMOA, MOA, FMHHO, MHHO, VSDE, SOA, SCA, GRO, and TSA attributed to the error obtained by the proposed EDO in case of BSC-500W are 0.17%, 3.49%, 0.62%, 15.50%, 3.78%, 29.12%, 86.30%, 0.90%, and 10.33%, respectively. Despite the nine approaches considered in comparative analysis having some issues with convergence speed, they converged the best solution. Moreover, the dynamic model of PEMFC is established in Simulink and its performance is assessed through applying step load disturbance. The fetched results demonstrated the superiority of the proposed EDO in establishing reliable models of various PEMFCs.