Alex Trenam

Structure-preserving electrokinetics

Batteries in electric vehicles require managing to maximise vehicle longevity, range, and performance, whilst ensuring safe operation. Battery state estimation involves using real-time data collected from the vehicle to estimate current properties of the battery (for example, remaining charge, internal temperature, etc) and to predict future states, possibly making use of other obtainable data such as driving habits and the environment.

State estimation is performed by the onboard battery management system (BMS), which is also responsible for implementing suitable charging and discharging strategies (including cell-balancing and communication with charging infrastructure) and interfacing with thermal management systems to maintain safe operational conditions. There are various methods for battery state estimation including direct estimation (e.g. lookup tables, which are easy to implement but have relatively low accuracy), data-driven models (which offer increased accuracy but depend on the quality and quantity of available data), and physics-based models (which can be highly accurate but require intensive computational power).

An electrolyte is an electrically neutral medium (most commonly a liquid at present) that facilitates the transport of ions between the two electrodes of a battery cell, and so having an accurate description of behaviour in this region is crucial to understanding the state of a cell.

The aim of this research is to develop efficient novel structure-preserving numerical methods for physics-based mathematical models concerning the electrolyte. By "structure-preserving" we mean that the methods will preserve at the discrete level some important structures possessed by the governing system of differential equations (for example: ionic mass conservation, energy dissipation laws, etc).

The models of interest will feature continuum approximations, where the concentrations of ions are considered (as opposed to molecular dynamics approaches, where the behaviour of individual atoms is modelled). The initial considered model is the Poisson-Nernst-Planck (PNP) system, which has been well studied and can be extended in a variety of ways to describe additional physical processes. For example, the size-modified PNP system takes into account the finite size of ions, and when coupled with the Navier-Stokes equations (yielding the Navier-Stokes-Poisson-Nernst-Planck (NS-PNP) system), the fluid properties of the electrolyte can be described.

The primary numerical methods of interest are discontinuous Galerkin (DG) finite element methods, which are suited to approximating pseudo-discontinuous solutions (boundary layers, known as electric double layers, form close to the electrodes and display steep gradients in the electric potential). There is also motivation to use DG methods in the extension to the compressible NS-PNP system, which allows for non-isothermal modelling (crucial when considering situations such as thermal runaway).

The benefits of this project include increased accuracy in battery state estimation, with a logical model progression (due to the fundamental physics-based nature of the work). This can lead to improved safety for users of the vehicle and longer battery lifetimes and range due to more informed management. These points together could lead to increased uptake of electric vehicles as a result of diminished range anxiety and safety fears, aiding the reduction of fossil-fuel powered vehicles on the road.