Faster Lead-Acid Battery Simulations from Porous-Electrode Theory: Part I. Physical Model

Abstract

An isothermal porous-electrode model of a discharging lead-acid battery is presented, which includes an extension of concentrated-solution theory that accounts for excluded-volume effects, local pressure variation, and a detailed microscopic water balance. The approach accounts for three typically neglected physical phenomena: convection, pressure diffusion, and variation of liquid volume with state of charge. Rescaling of the governing equations uncovers a set of fundamental dimensionless parameters that control the battery's response. Total volume change during discharge and nonuniform pressure prove to be higher-order effects in cells where variations occur in just one spatial dimension. A numerical solution is developed and exploited to predict transient cell voltages and internal concentration profiles in response to a range of C-rates. The dependence of discharge capacity on C-rate deviates substantially from Peukert's simple power law: charge capacity is concentration-limited at low C-rates, and voltage-limited at high C-rates. The model is fit to experimental data, showing good agreement.

Python Battery Mathematical Modelling (PyBaMM)

“…PyBaMM is one of the major components of the Faraday Institution's 'Common Modelling Framework', part of the Multi-Scale Modelling Fast Start project, which will act as a central repository for UK battery modelling research. PyBaMM has already been used to develop and compare reduced-order models for lithium-ion [7] and lead-acid [8,9] batteries, parameterize lithium-ion cells [10], model spirally-wound batteries [11], model two-dimensional distributions in the current collectors [12,13], and model SEI growth [14]. Further research outcomes are anticipated from continued collaborations with other members of the modelling community, both within and beyond the Faraday Institution.…”

Accelerated battery lifetime simulations using adaptive inter-cycle extrapolation algorithm

“…where C dl is the double-layer capacitance [36,37]. Furthermore, the simplification from ODE to DAE is only applicable for electrode-averaged models such as the Single Particle Model.…”

Predicting battery end of life from solar off-grid system field data using machine learning

“…The internal resistance of all batteries depends on age, current, temperature and state of charge. In lead-acid cells the reasons for this include non-linear kinetics [18], [19], nucleation and dissolution of lead sulfate [37], hydrolysis during charging [38], [39], and degradation mechanisms such as sulfation, loss of active material and electrode corrosion [40], [41]. Because of this, resistance estimates are not a reliable SoH metric unless they are first calibrated to remove the impacts of current, temperature and state of charge.…”