We study the optimal control for the maximization of profit in a grid-connected energy storage system. The changing price of electricity is assumed to be known in advance over the optimization horizon. The system has a storage device (such as a battery) which we model as a capacitor-type device, with natural constraints on its voltage and current. We prove the existence of an optimal control and the fact that a bang-off-bang type policy is optimal. The proof uses Filippov's theorem and the Pontryagin minimum principle.