Abstract
Electrochemical and equivalent-circuit modeling 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 analyze 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 behavior 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.
Highlights
The popular equivalent-circuit approach to battery modelling [1] is efficient, but has limited physical detail and extrapolates poorly
Newman and Tiedemann [7] recognise that spatial gradients can be ignored at low current; they state a ‘lumped parameter model’ (LPM) that depends only on time, but do not show how it derives from a porous-electrode model
The asymptotic methods developed in this paper allow us to simulate a discharge of a lead-acid battery with the low complexity and high speed of equivalent-circuit models, while retaining the accuracy and physical insights of electrochemical models
Summary
The popular equivalent-circuit approach to battery modelling [1] is efficient, but has limited physical detail and extrapolates poorly. This paper puts forward several reduced-order models of lead-acid battery discharge, each derived from a mechanistic description based on an extension of Newman’s porous-electrode theory [11], which we developed in part I. Several authors have simplified mechanistic lead-acid-battery models to improve their computational efficiency. Newman and Tiedemann [7] recognise that spatial gradients can be ignored at low current; they state a ‘lumped parameter model’ (LPM) that depends only on time, but do not show how it derives from a porous-electrode model. Knauff [13] simplifies a porous-electrode model by assuming, without justification, that current is linear in space, and acid molarity, quadratic
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