Nonlinear Frequency Analysis of Lithium-ion Batteries

Description of the context of the research including potential impact
Lithium-ion battery models are used for a variety of purposes including the design of battery systems, the estimation of states such as temperature and state of charge, and the control of (dis)charging currents. Characterisation of models remains an open-ended issue. One common approach is electrochemical impedance spectroscopy (EIS) which assumes batteries behave in their linear regime of operation. However, batteries are inherently non-linear systems, for example having a non-linear relationship between open circuit voltage and state of charge, and non-linear kinetics. Non-linearities become evident in the voltage and temperature response when a battery is exposed to moderate to higher amplitude excitation currents. Therefore, battery model characterization based only on linear assumptions can lead to model degeneracy. It is necessary to include nonlinear operational regimes in model parameterisation in order to provide a better characterization of overall behaviour, to include phenomena not triggered in linear regimes. For example this information is commonly overlooked by traditional EIS experiments used to analyse battery degradation over time, which means that insights are missed into the underlying behaviour.
To analyse battery behaviour in a wider range of regimes, frequency response analysis has to be extended to nonlinear systems. This includes a multivariable Fourier analysis, where the interpretation of the spectrum obtained is much more challenging compared to the usual analysis of linear systems. In addition, parameters of the battery model themselves are often functions of the battery states and cannot be considered time-invariant in the analysis.

Aims & Objectives
This project, in close alignment with the Faraday Institution Multiscale Modelling Fast Start Project, seeks to answer the questions of how to extend frequency analysis to nonlinear systems in the context of batteries, how to preserve the relationship between time domain model structure and nonlinear frequency response, and how to include parameter functional dependence on states in the frequency domain analysis. Breakthroughs in these areas will lead to greatly improved, more efficient and more general characterisation procedures for battery models. This will in turn result in more reliable extrapolation of behaviour at design stage (including performance and degradation modelling), and, from relatively simple lab measurements, new insights into the phenomena that impact degradation in commercially available cells. The latter could be extended to a high-throughput study of performance and degradation in a number of cells if sufficient test channels are available to undertake this.

Novelty of the research methodology
Nonlinear frequency analysis experimentally applied to lithium-ion batteries is a new methodology only explored recently with nonlinear EIS (NLEIS) by Murbach et al (1) in 2018 and nonlinear frequency response analysis (NFRA) by Nina Harting et al (2) in 2017. The nonlinearities within a lithium-ion cell remain an open-ended problem which can be explored with NLEIS and NFRA amongst other techniques.
(1) Murbach, Hu, Schwartz, "Nonlinear Electrochemical Impedance Spectroscopy of Lithium-Ion Batteries: Experimental Approach, Analysis, and Initial Findings", .J Electrochem. Soc. 2018 165(11): A2758-A2765.
(2) Harting, Wolff, Röder, Krewer, "Nonlinear Frequency Response Analysis (NFRA) of Lithium-Ion Batteries", Electrochimica Acta, Volume 248, 2017, Pages 133-139, ISSN 0013-4686.

Alignment to EPSRC's strategies and research areas
This project is funded externally to EPSRC therefore it does not fall within any specific research area. Funded by the Faraday Institution. Faraday Training grant reference (FITG030-B). Faraday Grant reference EP/S514901/1.

Any companies or collaborators involved
Supervised by David Howey