We develop a model for the storage dynamics in the electricity market. We consider that the storage facilities behave as price takers in this market. Given an exogenous price process, a single storage player solves a maximisation problem representing the best earning strategy for the asset owner. Using a stochastic optimal control approach, we find an explicit expression for the optimal strategy of a Pumped Hydroelectric Energy Storage (PHES). With this knowledge, the focus shifts to viewing the electricity market as a platform for interaction between energy demand, price taker storage players, renewable energy producers bidding always their full, stochastic, capacity, and conventional producers who have a supply function supposedly known. We prove the existence and uniqueness of the price process resulting from a market equilibrium between energy supply and demand under Lipschitz conditions. We then illustrate through multiple numerical examples the concrete influence of storage in terms of the variation of the short-term electricity price and we observe that it reduces its volatility.