A flow-rate-aware data-driven model of vanadium redox flow battery based on gated recurrent unit neural network

The vanadium redox flow battery (VRB) system involves complex multi-physical and multi-timescale interactions, where the electrolyte flow rate plays a pivotal role in both static and dynamic performance. Traditionally, fixed flow rates have been employed for operational convenience. However, in today's highly dynamic energy market environment, adjusting flow rates based on operating conditions can provide significant advantages for improving VRB energy conversion efficiency and cost-effectiveness. Unfortunately, incorporating the electrolyte flow rate into conventional multi-physical models is overly complex for VRB management and control systems, as real-time operations demand low-computational and low-complexity models for onboard functionalities. This paper introduces a novel data-driven approach that integrates flow rates into VRB modeling, enhancing data processing capabilities and prediction accuracy of VRB behaviors. The proposed model adopts a gated recurrent unit (GRU) neural network as its fundamental framework, exhibiting exceptional proficiency in capturing VRB's nonlinear voltage segments. The GRU network structure is carefully designed to optimize the predictive ability of the model, with flow rate considered as a crucial input parameter to account for its influence on VRB behavior. Model refinement involves analyzing well-designed simulation results obtained during VRB operations under various flow rates. Laboratory experiments were also designed and conducted, covering different conditions of currents and flow rates to validate the proposed data-driven modeling method. Comparative analyses were performed against several state-of-the-art algorithms, including equivalent circuit models and other data-driven models, demonstrating the superiority of the proposed GRU-based VRB model considering flow rates. Thanks to the GRU's outstanding capability in processing time series data, the proposed model delivers impressively accurate terminal voltage predictions with a low error margin of no more than 0.023 V (1.3%) under wide operating ranges. These results indicate the efficacy and robustness of the proposed approach, highlighting the novelty and significance of accounting for flow rates in accurate VRB modeling for management and control system design.