We study the e ect of energy-storage systems in dynamic real-time electricity markets. We consider that demand and renewable generation are stochastic, that real-time produc- tion is a ected by ramping constraints, and that market players seek to sel shly maximize their pro t. We distin- guish three scenarios, depending on the owner of the stor- age system: (A) the supplier, (B) the consumer, or (C) a stand-alone player. In all cases, we show the existence of a competitive equilibrium when players are price-takers (they do not a ect market prices). We further establish that under the equilibrium price process, players' sel sh responses coin- cide with the social welfare-maximizing policy computed by a (hypothetical) social planner. We show that with storage the resulting price process is smoother than without. We determine empirically the storage parameters that max- imize the players' revenue in the market. In the case of consumer-owned storage, or a stand-alone storage operator (scenarios B and C), we nd that they do not match so- cially optimal parameters. We conclude that consumers and the stand-alone storage operator (but not suppliers) have an incentive to under-dimension their storage system. In addition, we determine the scaling laws of optimal storage parameters as a function of the volatility of demand and re- newables. We show, in particular, that the optimal storage energy capacity scales as the volatility to the fourth power.