The battery as an electrochemical system can be considered a Blackbox with no way of observing processes occurring within it in a nondestructive manner¹. However, most physical, and chemical processes in electrochemical systems are shown to be distinguishable by their distinct characteristic time constant. Electrochemical impedance spectroscopy (EIS) can therefore be a valuable tool to distinguish between internal processes within batteries based on their frequency response^2–4.

Numerical approaches for understanding battery systems have long been explored by researchers in academia and industry alike^2,4,5. Generally, it is computationally expensive to develop a high fidelity multiscale and multiphysics model with high predictive capability that can estimate critical transport parameters and material decay. Thus, model development traditionally starts with simplistic models where more physics is added as per requirements. Many approaches to mathematical modelling of the battery at different length scales and complexity are available today⁶.

The impedance response of the battery can also be simulated coupled with various other parameters using the battery models⁷. Basic equivalent circuit models of the battery are commonly used for this but they suffer from lack of physical interpretability and model degeneracy⁸. The impedance response based on models are obtained in a physics-based model by linearizing the non-linear models and transforming equations in the time-domain into the frequency domain^5,9. This generally is achieved by applying a Laplace transform to the system of linearized equations. Now, based on the complexity of the model, these equations can be solved analytically or after separating the real and imaginary parts for numerical simulation.

Therefore, there are varied solution strategies appropriate for individual battery models that depend on underlying scale and physics involved. Through this work we aim to comprehensively compile these solution strategies and present the best approach for the individual electrochemical model based on criteria such as faster convergence times and error minimization.

References:

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9. M. Pathak et al., J. Electrochem. Soc., 165, A1324–A1337 (2018).