Low-rank value function approximation for co-optimization of battery storage

We develop a near-optimal solution to the problem of co-optimizing frequency regulation and energy arbitrage with battery storage using backward approximate dynamic programming, which is shown to handle the different time scales of each revenue stream. Solution of the problem using classical backward exact dynamic programming is computationally intractable for this problem due to the large state space and long horizon. Instead, we use state sampling and low-rank approximations to estimate the entire value function, producing a high quality solution that can be computed in real time. The new algorithm is shown to reduce the computational time by one order of magnitude, and the storage requirements by two orders of magnitude, while producing near optimal policies that consistently outperform pure frequency regulation.