Neural equivalent circuit models: Universal differential equations for battery modelling

Abstract

Current battery modelling methodologies including equivalent circuital modelling and electrochemical modelling do not maintain accuracy over diverse operating conditions of current rates, depth-of-discharge and temperatures. To address this limitation, this article proposes the Universal Differential Equations (UDE) framework from scientific machine learning (SciML) as a methodology to generate battery models with improved generalisability. The effectiveness of UDE in enhancing generalisability is demonstrated through a specific battery modelling example. The approach starts with the Thermal Equivalent Circuital Model with Diffusion (TECMD), a state-of-the-art battery model, which is then enhanced through the integration of neural networks into its state equations, resulting in the Neural-TECMD; a UDE model. Additionally, a two-stage UDE parameterisation method is introduced, combining collocation-based pretraining with mini-batch training. The parameterisation method enables the neural networks in the Neural-TECMD to efficiently learn battery dynamics from multiple time series data sets, covering a wide operating spectrum. Consequently, the Neural-TECMD model offers accurate predictions over broader operating conditions, thus enhancing model generalisability. The Neural-TECMD model was validated using 20 data sets covering current rates of 0 to 2C and temperatures from 0 to 45 °C. This validation revealed substantial improvements in accuracy, with an average of 34.51% decrease in RMSE for voltage and a 24.94% decrease for temperature predictions compared to the standard TECMD model.