We develop a game-theoretic electricity market model that allows analyzing strategic electricity storage in an imperfect market setting. We apply the model to Germany and examine different cases of pumped hydro storage operation. We find that introducing storage smoothes market prices and increases consumer rent and overall welfare. Electricity producers generally suffer from storage. The utilization of storage capacities depends on their operator's ability to exert market power both regarding storage and conventional generation. Strategic operators tend to under-utilize their storage capacities. The distribution of storage capacities among players also matters. Accordingly, economic regulation of storage capacities may be necessary.