Optimal control of storage for arbitrage, with applications to energy systems

We study the optimal control of storage which is used for arbitrage, i.e. for buying a commodity when it is cheap and selling it when it is expensive. Our particular concern is with the management of energy systems, although the results are generally applicable. We consider a model which may account for nonlinear cost functions, market impact, input and output rate constraints and inefficiencies or losses in the storage process. We develop an algorithm which is maximally efficient in then sense that it incorporates the result that, at each point in time, the optimal management decision depends only a finite, and typically short, time horizon. We give examples related to the management of a real-world system.Comment: 7 pages, 6 figure

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. 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 stores which between them have market impact 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 electricity storage and Great Britain electricity spot-price market data