  Users can arbitrage against Time-of-Use (ToU) pricing with storage by
charging in off-peak period and discharge in peak periods. In this paper we
design the optimal control policy and the solve optimal investment for general
ToU scheme. We formulate the problem as dynamic programming for efficient
solution. Our result is feasible facing multi-peaked ToU scheme. Simulation
studies examine how the user's cost varies with respect to the user's demand
randomness; we also demonstrate the performance of our scheme when aggregating
users for extra savings.
