Mixed Integer Linear Program model for optimized scheduling of a vanadium redox flow battery with variable efficiencies, capacity fade, and electrolyte maintenance

Redox Flow Batteries are a versatile and durable type of electrochemical storage and a promising option for large-scale stationary energy storage. The vanadium redox flow battery represents the most mature chemistry for the technology, and it is the most widely commercialized system thanks to its high chemical stability and performance. This work aims to optimize the scheduling of a vanadium redox flow battery that stores energy produced by a renewable power plant, keeping into account a thorough characterization of the battery performance, with variable efficiencies and capacity fade effects. A detailed characterization of the battery performance improves the calculation of the optimal number of cycles and revenue associated with the battery use if compared to the results obtained using simpler models, which take into account constant efficiencies and no capacity fade effects. The presented problem is nonlinear due to the functions of the battery efficiency, which depend upon charging and discharging powers and state of charge with nonlinear, non-convex correlations. Therefore, as per the state of the art of operation research, the problem is linearized using convex hulls in three dimensions. The optimization program also calculates the progressive battery capacity fade due to undesired secondary electrochemical reactions and the economic impact of capacity restoration through periodic maintenance. The final problem is solved as a Mixed-Integer Linear Program (MILP) to guarantee the global optimality of the linearized problem. The proposed optimization model has been applied to two different case studies. The first is a case of energy arbitrage, where the electric energy produced by a renewable plant is stored when the energy price is low and sold to the grid when the energy price is high to maximize the profit. The second is a case of load-shifting, balancing electric energy generation and demand from a grid-connected renewable energy community, where storage minimizes the expenses for the energy purchased from the grid. The optimization results have been compared to those obtained with constant battery efficiency models, which do not consider the capacity fade effects. Results show that simpler models overestimate the optimal number of cycles of the battery and the revenue by up to 15% if they do not take into account the degradation model of the battery, and respectively up to 32% and 42% if they also assume constant efficiency for the battery.

Automated summary

Redox Flow Batteries, particularly the vanadium redox flow battery, are a promising option for large-scale stationary energy storage due to their versatility and durability. This research aims to optimize the scheduling of a vanadium redox flow battery used to store energy from renewable sources, taking into account the battery's performance characteristics and degradation effects. By considering a detailed battery characterization, the optimization model provides more accurate predictions on the optimal number of cycles and revenue, compared to simpler models that assume constant efficiency and neglect capacity fade effects. The proposed model uses convex hulls and is solved as a Mixed-Integer Linear Program (MILP) to ensure global optimality.