Low-Order Mathematical Modelling of Electric Double Layer Supercapacitors Using Spectral Methods

TL;DR

This paper develops and compares spectral element models for electric double layer supercapacitors, demonstrating improved accuracy and efficiency over finite difference methods, with potential applications in control and state estimation.

Contribution

It introduces spectral element discretization for supercapacitor models, showing faster convergence and reduced computation time compared to finite difference methods.

Findings

Spectral element method achieves faster error convergence.

Model simulations closely match experimental data.

Spectral approach reduces computation time by about 50%.

Abstract

This work investigates two physics-based models that simulate the non-linear partial differential algebraic equations describing an electric double layer supercapacitor. In one model the linear dependence between electrolyte concentration and conductivity is accounted for, while in the other model it is not. A spectral element method is used to discretise the model equations and it is found that the error convergence rate with respect to the number of elements is faster compared to a finite difference method. The increased accuracy of the spectral element approach means that, for a similar level of solution accuracy, the model simulation computing time is approximately 50% of that of the finite difference method. This suggests that the spectral element model could be used for control and state estimation purposes. For a typical supercapacitor charging profile, the numerical solutions from both models closely match experimental voltage and current data. However, when the electrolyte is dilute or where there is a long charging time, a noticeable difference between the numerical solutions of the two models is observed. Electrical impedance spectroscopy simulations show that the capacitance of the two models rapidly decreases when the frequency of the perturbation current exceeds an upper threshold.