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 strategic and non-strategic pumped hydro storage operation. We find that introducing storage generally smoothes conventional generation patterns and market prices and increases consumer rent and overall welfare. In contrast, electricity producers generally suffer from storage. We also find that the utilization of storage capacities depends on their operator's ability to exert market power both regarding storage and conventional generation. In particular, strategic operators tend to under-utilize their storage capacities, which in turn has welfare implications. The distribution of storage among players also matters. Accordingly, economic regulation of existing and future storage capacities may be necessary.