A novel transient zero-dimensional physics-based model of vanadium redox flow batteries with electrolyte crossover-induced capacity fade

Conventional lumped models of vanadium redox flow batteries (VRBs) typically neglect bulk electrolyte transfer because its effects are often insignificant over short time scales. This simplification, however, prevents accurate representation of electrolyte crossover-induced volume imbalance and the associated capacity fade, limiting their applicability to performance prediction and control. This paper presents a novel transient zero-dimensional (0-D) physics-based VRB model that explicitly considers electrolyte migration mechanisms derived from first principles. The model corrects the convection term in the vanadium ion concentration equations and the pressure difference term in the electrolyte volume equations as incremental improvements, while its novel enhancement lies in capturing the dynamic behavior of proton migration during VRB operation. Osmotically driven water transport across the membrane is modeled using Schlögl's equation, and the combined effects of vanadium ion crossover, osmotic pressure, and shunt currents are integrated to quantify electrolyte volume imbalance. Experimental validation over 300 charge-discharge cycles demonstrates significantly improved prediction accuracy compared with the conventional model, achieving an average capacity prediction error of less than 2.58% and an electrolyte volume prediction error of less than 5.33%. Results indicate that osmotic pressure-driven transport is the dominant contributor to electrolyte imbalance. The model's applicability is further demonstrated under different current densities and cell sizes, providing a theoretical basis for future degradation analysis and operational guidance of VRB systems.