Thermal parameters fitted from electrical data enable lumped models of heterogeneous battery cells by predicting their effective temperature

Battery design, management, and control uses coupled electrical and thermal models to predict cell performance. Computational constraints mean lumped models are used, where temperature and charge are assumed to be spatially uniform. This can limit model accuracy, as electrochemical systems generate heat, causing temperature heterogeneity. This changes the cell behaviour, but is not described by lumped models. Accuracy is further limited as good thermal-model parameters can be challenging to find. This work presents a simple thermal parameterisation scheme, which builds lumped models that accurately describe the voltage behaviours of heterogeneous cells. We first demonstrate a simple experimental method for obtaining thermal parameters, which works by maximising the voltage accuracy of an electrothermal model. Thermal parameters are found quickly and easily, using only voltage-based cell cycling data. We then use formal analysis to define the correct temperature a lumped model should use, when describing cells with a thermal gradient. This is referred to as effective temperature, and quantifies the temperature a lumped, uniform cell must be at to show the same impedance (and therefore electrical behaviour) as a heterogeneous cell. Our thermal model and parameters are shown to predict effective temperature, meaning our lumped models will match the voltage dynamics of heterogeneous cells. To conduct this analysis, an explicit, closed-form distributed cell model is derived, which captures the coupled temperature and charge gradients within a cell. Our results demonstrate that lumped models can be used with confidence, even on large-scale, heterogeneous systems, provided the thermal parameters are calibrated using voltage data.