A modified pseudo-steady-state analytical expression for battery modeling. (July 2019) - Chayambuka, K.; Mulder, G.; Danilov, D.L.; Notten, P.H.L.
Abstract: The solid-state spherical diffusion equation with flux boundary conditions is a standard problem in lithium-ion battery simulations. If finite difference schemes are applied, many nodes across a discretized battery electrode become necessary, in order to reach a good approximation of solution. Such a grid-based approach can be appropriately avoided by implementing analytical methods which reduce the computational load. The pseudo-steady-state (PSS) method is an exact analytical solution method, which provides accurate solid-state concentrations at all current densities. The popularization of the PSS method, in the existing form of expression, is however constrained by a solution convergence problem. In this short communication, a modified PSS (MPSS) expression is presented which provides uniformly convergent solutions at all times. To minimize computational runtime, a fast MPPS (FMPPS) expression is further developed, which is shown to be faster by approximately three orders of magnitude and has a constant time complexity. Using the FMPSS method, uniformly convergent exact solutions are obtained for the solid-state diffusion problem in spherical active particles. Highlights: The pseudo-steady-state (PSS) method is an exact analytical solution method for the solid state diffusion problem. Extensive use of the PSS method in battery modeling is hindered by a solution convergence problem, due to large exponentials. A modified PSS expression (MPSS) is developed to address the solution convergence problem. The MPSS is illustrated to provide uniformly convergent solutions at all times while the PSS is shown to have a blow up of solutions. A fast MPSS (FMPSS) is further presented which is stable and faster than the MPSS by approximately three orders of magnitude.