Extending Equivalent Circuit Models for State of Charge and Lifetime Estimation

Equivalent circuit modelling (ECM) of electrochemical impedance spectroscopy (EIS) data is a common technique to describe the state-dependent response of electrochemical systems such as batteries or fuel cells. To use EIS for predictive assessments of the future behaviour of such a system or its state of health (SOH), a more elaborate digital twin model is needed. Developing a robust and continuous SOH estimation poses a formidable challenge. In this study, a framework is presented where ECM parameters are expanded in a high-dimensional Chebyshev space. It facilitates not only a mapping of the state of charge dependence with robust boundary conditions but also an extension towards a more abstract SOH description is possible. Such methods can bridge the gap between the experiment and purely data-driven techniques that do not rely on fitting of experimental data using a priori defined models. In the absence of long-time impedance measurements of a battery, quasi-Monte Carlo sampling can be employed to generate differently aged synthetic battery models with limited experimental impedance data. As additional data becomes available, the space spanning the possible states of a battery can be gradually refined. The developed framework, therefore, allows for the training of big data models starting with very little experimental information and assuming random fluctuations of the model parameters consistent with available data.