Numerical and semi-numerical solutions of a modified Thévenin model for calculating terminal voltage of battery cells

Abstract

A new Thévenin-type model for evaluating the terminal voltage of rechargeable batteries is developed by adding a nonlinear capacitor element in the circuit. Furthermore, a powerful variant of the improved differential transform method and the nonstandard finite difference schemes are proposed to properly treat the mathematical model. Two separate case studies including a constant and a variable current consumer, with latter representing an inductive electric motor, are carried out. The efficacies of the multistage improved differential transform method, the nonstandard finite difference schemes, and the classical Euler method are compared using a set of appropriate CPU-time and error analyses.