Duration-Differentiated Services in Electricity

The integration of renewable sources poses challenges at the operational and economic levels of the power grid. In terms of keeping the balance between supply and demand, the usual scheme of supply following load may not be appropriate for large penetration levels of uncertain and intermittent renewable supply. In this paper, we focus on an alternative scheme in which the load follows the supply, exploiting the flexibility associated with the demand side. We consider a model of flexible loads that are to be serviced by zero-marginal cost renewable power together with conventional generation if necessary. Each load demands 1 kW for a specified number of time slots within an operational period. The flexibility of a load resides in the fact that the service may be delivered over any slots within the operational period. Loads therefore require flexible energy services that are differentiated by the demanded duration. We focus on two problems associated with durations-differentiated loads. The first problem deals with the operational decisions that a supplier has to make to serve a given set of duration differentiated loads. The second problem focuses on a market implementation for duration differentiated services. We give necessary and sufficient conditions under which the available power can service the loads, and we describe an algorithm that constructs an appropriate allocation. In the event the available supply is inadequate, we characterize the minimum amount of power that must be purchased to service the loads. Next we consider a forward market where consumers can purchase duration differentiated energy services. We first characterize social welfare maximizing allocations in this forward market and then show the existence of an efficient competitive equilibrium. We also investigate the competitive equilibrium in a sequence of real-time spot markets with flexible loads. We show by an example that the sequence of real-time markets may not be efficient. The first author is with Ming Hsieh Department of Electrical Engineering at University of Southern California. The second, third and fourth authors are with the Department of Electrical Engineering and Computer Sciences, University of California, Berkeley. The second author is also with the Department of Electrical Engineering of Pontificia Universidad Catolica de Chile. This work was supported in part by EPRI and CERTS under sub-award 09-206; PSERC S-52; NSF under Grants 1135872, EECS-1129061, CPS-1239178, and CNS-1239274; the Republic of Singapore’s National Research Foundation through a grant to the Berkeley Education Alliance for Research in Singapore for the SinBerBEST Program; Robert Bosch LLC through its Bosch Energy Research Network funding program. ar X iv :1 40 4. 11 12 v1 [ cs .S Y ] 3 A pr 2 01 4