Surrogate model-based parameter estimation framework of physics-based model for vanadium redox flow batteries

A physics-based model evaluates the electrochemical kinetics of cells and characterizes the material properties comprising vanadium redox flow batteries (VRFBs). This study proposes a parameter estimation framework for a physics-based model using a surrogate modeling approach. The surrogate model is constructed by establishing a statistical relationship between the sampled parameter sets to be estimated and the voltage obtained from a partial differential equation (PDE)-based model using polynomial chaos expansion (PCE). The electrode-related parameters – specific surface area and reaction rate constant at the negative and positive electrodes – are selected to compare two VRFBs with different electrode materials. The distributions of the estimated parameters are obtained by repeatedly applying a genetic algorithm that optimizes the candidate parameter set to fit the surrogate model outputs to the experimental results. The specific surface area, reaction rate constants for the negative and positive electrode for the mesoporous graphite felt (mp-GF) electrode, which demonstrates superior performance, are estimated to be higher than those of the thermal-treated graphite felt (TGF) electrode. In addition, variance-based global sensitivities are analyzed for the voltage output for each parameter and operating condition using the constructed surrogate model. The specific surface area shows the highest sensitivity in all cases, indicating that it has the highest impact on the voltage magnitude and identifiability. Moreover, internal states, such as the vanadium ion concentration and volumetric current density, of VRFBs with different materials are compared using the PDE-based model with the estimated parameter set with the minimum fitness values. Although the VRFBs assembled with the mp-GF electrode exhibit more uneven state distributions, they can be charged to higher SOCs and discharged to lower SOCs compared with those assembled with the TGF electrode. Consequently, higher electrode-related parameters lead to lower overpotential and wider operating SOC range. The proposed framework helps quantify properties with restricted data and analyze the behavior of cells assembled with newly developed materials.