Comparative Modeling of Vanadium Redox Flow Batteries Using Multiple Linear Regression and Random Forest Algorithms

This paper presents a comparative study of data-driven modeling approaches for vanadium redox flow batteries (VRFBs), utilizing Multiple Linear Regression (MLR) and Random Forest (RF) algorithms. Experimental voltage–capacity datasets from a 1 kW/1 kWh VRFB system were digitized, processed, and used for model training, validation, and testing. The MLR model, built using eight optimized features, achieved a mean error (ME) of 0.0204 V, a residual sum of squares (RSS) of 8.87, and a root mean squared error (RMSE) of 0.1796 V on the test data, demonstrating high predictive performance in stationary operating regions. However, it exhibited limited accuracy during dynamic transitions. Optimized through out-of-bag (OOB) error minimization, the Random Forest model achieved a training RMSE of 0.093 V and a test RMSE of 0.110 V, significantly outperforming MLR in capturing dynamic behavior while maintaining comparable performance in steady-state regions. The accuracy remained high even at lower current densities. Feature importance analysis and partial dependence plots (PDPs) confirmed the dominance of current-related features and SOC dynamics in influencing VRFB terminal voltage. Overall, the Random Forest model offers superior accuracy and robustness, making it highly suitable for real-time VRFB system monitoring, control, and digital twin integration. This study highlights the potential of combining machine learning algorithms with electrochemical domain knowledge to enhance battery system modeling for future energy storage applications.