  This paper presents a novel algorithm to optimize energy capacity restoration
of vanadium redox flow batteries (VRFBs). VRFB technologies can have their
lives prolonged through a partially restoration of the lost capacity by
electrolyte rebalancing. Our algorithm finds the optimal number and time of
these rebalancing services to minimize the service cost, while maximizing the
revenues from energy arbitrage. We show that the linearized form of this
problem can be analytically solved, and that the objective function is convex.
To solve the complete problem, we develop a two-step mixed integer linear
programming (MILP) algorithm, which first finds the bounds for optimal number
of services and then optimizes the number, and time of the services. We then
present a theoretical analysis and optimization results for a case study of
energy arbitrage in New York ISO.
