Journal article Open Access

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

Kudakwashe Chayambuka; Grietus Mulder; Dmitri L. Danilov; Prof. Peter H. L. Notten

### Citation Style Language JSON Export

{
"DOI": "10.1016/j.ssc.2019.04.011",
"author": [
{
"family": "Kudakwashe Chayambuka"
},
{
"family": "Grietus Mulder"
},
{
"family": "Dmitri L. Danilov"
},
{
"family": "Prof. Peter H. L. Notten"
}
],
"issued": {
"date-parts": [
[
2019,
4,
24
]
]
},
"abstract": "<p>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.</p>",
"title": "A modified pseudo-steady-state analytical expression for battery modeling",
"type": "article-journal",
"id": "3253470"
}
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