# Faster Lead-Acid Battery Simulations from Porous-Electrode Theory: II. Asymptotic Analysis

## TL;DR

This paper develops and analyzes simplified models for lead-acid batteries using asymptotic methods, balancing physical accuracy and computational efficiency for various discharge rates.

## Contribution

It introduces three reduced-order models derived from a detailed porous-electrode theory, enabling faster simulations with physical interpretability.

## Key findings

- Lumped model accurate below 0.1C discharge rate
- Higher-order model retains accuracy up to 5C
- Parameter estimation achieved through experimental data fitting

## Abstract

Electrochemical and equivalent-circuit modelling are the two most popular approaches to battery simulation, but the former is computationally expensive and the latter provides limited physical insight. A theoretical middle ground would be useful to support battery management, on-line diagnostics, and cell design. We analyse a thermodynamically consistent, isothermal porous-electrode model of a discharging lead-acid battery. Asymptotic analysis of this full model produces three reduced-order models, which relate the electrical behaviour to microscopic material properties, but simulate discharge at speeds approaching an equivalent circuit. A lumped-parameter model, which neglects spatial property variations, proves accurate for C-rates below 0.1C, while a spatially resolved higher-order solution retains accuracy up to 5C. The problem of parameter estimation is addressed by fitting experimental data with the reduced-order models.