Physics-Constrained Deep Neural Network Method for Estimation and Simulation of Vanadium Redox Flow Battery

Modeling and simulation have been indispensable to advance the analysis and design of flow batteries. The calibration of model parameters is critical to accurately predict battery responses under different operating conditions. In this study, we propose a physics-constrained machine learning approach that allows to perform multiple parameter estimation along with numerical simulation of vanadium redox flow batteries (VRFBs). With representing model parameters by separate neural networks, a reduced VRFB electrochemical model is encoded as the physical constraints during training processes, leading to enhanced parameter estimation and voltage prediction. To improve the predictive capability at extreme ranges, an auxiliary network is further introduced as a high-fidelity correction to capture the mismatch against the measurements. We test the proposed approach on both simulation and experimental datasets. The numerical results show that the developed method can provide optimal subsets of model parameters under different operating conditions and give more accurate voltage prediction compared to a purely data-driven machine learning approach.