Dynamic relaxation: a new optimization method for PEM fuel cell analysis

Sustainability of the membrane conductance in PEM fuel cells is an important issue and determines the performance of the cell. Herein, the relevant numerical analysis is replaced with an optimization procedure. The objective function is energy balance equation and the equality constraints are governing equations of the physical model. In this paper a dynamic relaxation method is proposed which provides a fictitious nonlinear dynamic system model for the fuel cell. Thereafter, by assuming appropriate initial conditions, the steady state solution can be obtained. For any current density, the corresponding temperature in cathode and anode, output voltage of the cell and stack temperature are determined. It is shown that by changing the initial conditions and also the integration method, the convergence into the same steady state values can be guaranteed. It is concluded that dynamic relaxation method which is well known technique in solid mechanics can also be a powerful optimization method for studying the equilibrium in fuel cells. The advantages of this method compared with other techniques are discussed and commented upon.