A quick and efficient method for consistent initialization of battery models

Secondary batteries are usually modeled as a system of coupled nonlinear partial differential equations. These models are typically solved by applying finite differences or other discretization techniques in the spatial directions and solving the resulting system of differential algebraic equations (DAEs) numerically in time. These DAEs are very difficult to solve even using popular DAE solvers. The complications arise partly due to the difficulty in obtaining consistent, or closely consistent, initial conditions for the DAEs. In this paper, a shooting method is proposed as an effective and rapid technique for the initialization of battery models. This method is built on a regionwise shooting approach with initial guess at one end of the electrode and physics based shooting criterion on the other end that can ultimately satisfy all the required conditions in a battery unit. Notably, the computation time required for the proposed method is only milliseconds in a FORTRAN environment for the case of initializing a standard physics based lithium-ion battery model. Also the initial values obtained are exact and can readily be fed into any DAE solver for achieving accurate solutions without solver failure. This rapid method will help in simulating batteries in hybrid environments in real-time (milliseconds).