Improved approximation for the Butler-Volmer equation in fuel cell modelling

•Proposes an improved explicit form approximation for the Butler-Volmer equation.•Convergence properties of proposed forms studied using the fixed point theorem.•Useful for devising efficient iterative algorithms based on the fixed point method.

This work presents an improved approximation for the explicit form of the Butler-Volmer (BV) equation, which is used in modelling the activation phenomena in fuel cells. Three representations of the BV-equation in the form x = f(x) are presented in this paper, out of which, two forms are reducible to the high field approximation and one is reducible to the hyperbolic sine approximation under certain conditions. It is found that one of the forms offer an excellent approximation for the BV-equation throughout the applicable range. The detailed analysis of the convergence properties, the applicability ranges and comparative studies offer insights into the ranges of relevance. The proposed approximation will be accurate and applicable for a wide range of operation enabling its adaptation into model based algorithms for fuel cell operation and control. The proposed fixed point based iterative method can offer an alternative to the traditional methods that require the Jacobian information.