A modified pseudo-steady-state analytical expression for battery modeling

K. Chayambuka, G. Mulder, D.L. Danilov, P.H.L. Notten (Corresponding author)

Research output: Contribution to journalArticleAcademicpeer-review

5 Citations (Scopus)
174 Downloads (Pure)


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.

Original languageEnglish
Pages (from-to)49-53
Number of pages5
JournalSolid State Communications
Publication statusPublished - 1 Jul 2019


  • Analytical methods
  • Porous electrodes
  • Pseudo-steady state
  • Spherical diffusion


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