  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.
