Research Studentship in Nonlinear Frequency Analysis of Lithium-ion Batteries, Faraday Institution within the Department of Engineering Science

Project: Nonlinear Frequency Analysis of Lithium-ion Batteries, Faraday Institution

4-year D.Phil. studentship
Supervisor: Professor David Howey

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.

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.


This studentship is funded through the Faraday Institution and the UK Engineering and Physical Sciences Research Council (EPSRC) Doctoral Training Partnership and is open to both UK students (full award – fees plus stipend) and EU students (partial award – fees only). Full details of the EPSRC eligibility requirements.

The University of Oxford is committed to fostering an inclusive culture which promotes equality, values diversity and maintains a working, learning and social environment in which the rights and dignity of all its staff and students are respected.

Award Value

University tuition fees are covered at the Home rate (£4327 for the 2019-2020 academic year). (College fees are not included).
The Faraday Institution Cluster PhD students receive an enhanced stipend over and above the standard EPSRC offer. The total annual stipend is approximately £20,000 plus access to an additional £7,000 annually to cover training and travel costs. Recipients will have access to multiple networking opportunities, industry visits, mentorship, internships, as well as quality experiences that will further develop knowledge, skills, and aspirations. 

Candidate Requirements

Prospective candidates will be judged according to how well they meet the following criteria:

  • A first class honours degree in Engineering, Physics or Materials Science
  • Excellent English written and spoken communication skills

The following skills are desirable but not essential:

  • Ability to program in Matlab

Application Procedure

Informal enquiries are encouraged and should be addressed to Professor David Howey.

Candidates must submit a graduate application form and are expected to meet the graduate admissions criteria. Details are available on the course page of the University website.

Please quote 19ENGIN_DH in all correspondence and in your graduate application.

Application deadline

Noon on 1 March 2019

Start date

1 October 2019