Lumped battery models predict cell heterogeneity and effective temperature when thermal parameters are identified from electrical data

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. Accuracy is not guaranteed, as electrochemical systems generate heat which drives temperature gradients. These change the cell behaviour, but are not described by lumped models. Accuracy is further limited by the difficulties in finding good thermal parameters. To address these challenges, we first demonstrate a simple experimental method for obtaining thermal parameters. Our thermal parameterisation method works by maximising the voltage accuracy of an electrothermal model. This allows thermal parameters to be found quickly and easily, using only voltage-based cell cycling data. We then show that lumped models can perform accurately on cells with temperature gradients. We first define the correct lumped-model temperature for a cell with a thermal gradient, then show that our thermal parameters lead to this temperature. To do so, an explicit distributed cell model is derived and analysed, which consists of parallel connected Thevenin circuits. This is used to construct a formula for effective temperature — the temperature a uniform cell must be at, to show the same impedance, and hence, electrical behaviours, as a heterogeneous cell. Our thermal parameters are shown to produce effective temperature predictions, meaning the lumped model will match the impedance of a heterogeneous 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.