Mathematical modelling of lead-acid batteries

Thesis

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, online diagnostics, and cell design.

In this thesis, we present a porous-electrode model of a lead-acid battery, which includes an extension of concentrated-solution theory that accounts for excluded-volume effects, local pressure variation, and a detailed microscopic water balance.

Asymptotic analysis of the one-dimensional model in the limit of small discharge rate 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 small discharge rates (below 0.1C), while a spatially resolved higher-order solution retains accuracy at higher discharge rates (up to 5C). The reduced-order models provide improved insight into the battery's behaviour. The models are fit to experimental data, showing good agreement.

We then consider the three-dimensional model and exploit the limit of small aspect ratio to decompose the through-cell and transverse dimensions. Further asymptotic analyses in the limit of high conductivity and/or small discharge rate give new simplified models that capture transverse non-uniformities at reduced computational cost. In the simplest case, the current collectors act as series resistors.

In order to explore the behaviour of a lead-acid battery during recharge, we return to a one-dimensional model and add an oxygen reaction to the model. We find that the oxygen recombination must be diffusion limited in the negative electrode, leading to non-monotonic voltage increase during constant-current recharge. Reduced-order models in the limit of slow recharge provide good approximations to the full charging model.

Authors: Sulzer, V

• Type of award: DPhil
• Level of award: Doctoral
• Awarding institution: University of Oxford
• Language: English
• Keywords: lead-acid batteries; asymptotics
• Subjects: Electrochemistry; Applied mathematics