A novel mixed-integer linear programming formulation of vanadium redox flow battery for energy management system applications considering dynamic nonlinearities

Accurate battery storage system modelling considering its nonlinear operational dynamics is crucial for achieving more economic benefits and higher flexibility. In this paper, a novel mixed-integer linear programming (MILP) formulation of vanadium redox flow batteries (VRFBs) is presented considering the dynamic nonlinear performance of charge losses and voltaic losses, as well as the actual battery management scheme. This research utilises a newly introduced multi-physics VRFB model, which incorporates all ion crossover and electrolyte transfer mechanisms to validate the model's effectiveness in precisely estimating the remaining energy. Rigorous simulation studies are conducted to validate the proposed model deployed in a residential energy management system (EMS) using 5-minute resolution data from residential consumers in Australia. The results show that the proposed MILP model achieves highly accurate remaining energy and economic benefit estimations, with power mismatch errors of less than 1%. Most importantly, the simulation results demonstrate that the proposed model results in up to 57.1% increase in economic benefits and 8.5% improvement in round-trip efficiency compared to traditional models that are widely used to estimate remaining energy.