Lithium-ion batteries are used in complex fields of application, such as electromobility, more often. With the increasing usage of lithium-ion batteries, the demand for battery models is growing as well. However, the parameterization of the models is often time-demanding and requires expert knowledge. Grey-box modelling can simplify the modelling approach. It combines physical and data-driven models to benefit from their respective advantages. Our focus is on using neural networks, especially neural ordinary differential equations (NODEs), for grey-box modelling of lithium-ion batteries. NODEs offer new possibilities for grey-box modelling. Differential equations governed by physical principles and NODEs can be modelled together in one framework.
We use NODEs in combination with a simple equivalent circuit model to build a grey-box model of a lithium-ion battery. The chosen equivalent circuit model is a serial connection of an ideal voltage source, a serial resistor, and an RC circuit (charge-transfer resistance and double-layer capacitance). Additionally, we include a hysteresis voltage. Unknown parameters and dependencies are replaced by learnable parameters and neural networks. The parameterization follows two steps. In the first step, we use experimental data of constant current constant voltage discharge and charge to train a simplified version of the grey-box model (without double-layer capacitance). The charge transfer resistance is assumed state-of-charge dependent. In a second step, we include the double-layer capacitance in the pre-trained model and use data from tests with current pulses to approximate the dynamics of the battery. The resulting grey-box model can reproduce the battery voltage during both constant and dynamic current operation.