Modeling and optimization of a proton exchange membrane fuel cell using particle swarm algorithm with constriction coeff

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Modeling and optimization of a proton exchange membrane fuel cell using particle swarm algorithm with constriction coefficient Hamid Abdi1 · Noureddine Ait Messaoudene1 · Lioua Kolsi2,3   · Mohamed Wahib Naceur4 Received: 6 April 2020 / Accepted: 15 October 2020 © Akadémiai Kiadó, Budapest, Hungary 2020

Abstract The present study aims at estimating the values of an electrochemical model parameter of a proton exchange membrane fuel cell (PEMFC). A variant of the particle swarm optimization (PSO) algorithm is adopted. This variant introduces a constriction coefficient to better regulate the convergence of the numerical code. Parameters’ identification of the PEMFC stack model is performed by specifying a range for each. Validity of the adopted approach is confirmed by confronting simulation results with experimental data in terms of current–voltage polarization curves. It should be noted that the optimal value of the objective function is largely affected by the lower and upper values of the parameters. Comparison of present results with other optimization methods shows a noticeable improvement in PEMFC stack performance when using particle swarm optimization algorithm with constriction coefficient (PSO-χ). This confirms that this version of PSO algorithm is very suitable for the optimization and parameter estimation of PEMFC stack modeling. Keywords  PEMFC · Parameter identification · Current–voltage · Particle swarm optimization · Constriction coefficient List of symbols A Electrode active area ­(cm2) b Semiempirical coefficient (V) c1, c2 Acceleration coefficients CO2 Dissolved oxygen concentration (mol cm−3) ENernst Thermodynamic potential of the cell (V) * Lioua Kolsi [email protected]; [email protected] Hamid Abdi [email protected] Noureddine Ait Messaoudene [email protected] Mohamed Wahib Naceur [email protected] 1



Laboratoire des Applications Energétique de l’Hydrogène (LApEH), Faculté de Technologie, Université BLIDA1, B.P. 270, Route de Soumaa, Blida, Algeria

2



Department of Mechanical Engineering, College of Engineering, Ha’il University, Ha’il, Saudi Arabia

3

Research Laboratory of Metrology and Energy Systems, National Engineering School of Monastir, University of Monastir, Monastir, Tunisia

4

Laboratoire Eau, Environnement et Développement Durable (2E2D), Faculté de Technologie, Université BLIDA1, B.P. 270, Route de Soumaa, Blida, Algeria





Fobj Objective function j Dimension of particle j ∈ {1, 2, …, D} i Individual particle i ∈ {1, 2, …, Ns} i Cell current (A) I Actual current density (A cm−2) Imax Largest current density (A cm−2) gbest Global best solution l Thickness of the membrane (cm) n Number of cells in the stack N Experimental data points Ns Swarm size Pa Inlet pressure at anode (atm.) pbest Personal best solution Pc Inlet pressure at cathode (atm.) PH2 Hydrogen pressure (atm.) Psat Vapor saturation pressure (atm.) H2 O PN2 Nitrogen Pressure (atm.) PO2 Pressure of oxygen (atm.) r1, r2 Random numbers in the interval [0, 1] RHa Relative humi