Impact of storage competition on energy markets
  We study how storage, operating as a price maker within a market environment, may be optimally operated over an extended period of time. The optimality criterion may be the maximisation of the profit of the storage itself, where this profit results from the exploitation of the differences in market clearing prices at different times. Alternatively it may be the minimisation of the cost of generation, or the maximisation of consumer surplus or social welfare. In all cases there is calculated for each successive time-step the cost function measuring the total impact of whatever action is taken by the storage. The succession of such cost functions provides the information for the storage to determine how to behave over time, forming the basis of the appropriate optimisation problem. Further, optimal decision making, even over a very long or indefinite time period, usually depends on a knowledge of costs over a relatively short running time horizon -- for storage of electrical energy typically of the order of a day or so.   We study particularly competition between multiple stores, where the objective of each store is to maximise its own income given the activities of the remainder. We show that, at the Cournot Nash equilibrium, multiple large stores collectively erode their own abilities to make profits: essentially each store attempts to increase its own profit over time by overcompeting at the expense of the remainder. We quantify this for linear price functions   We give examples throughout based on Great Britain spot-price market data. 
James Cruise, Lisa Flatley, Stan Zachary
math.OC