Duration-differentiated energy services with a continuum of loads

The problem of balancing supply and demand in the power grid becomes more challenging with the integration of uncertain and intermittent renewable supply. The usual scheme of supply following load may not be appropriate for large penetration levels of renewable supply. The reason is the increased level of reserves required to maintain a reliable grid, which affects both operational costs (reserves are expensive) and the environmental benefits of renewables (on-line reserves might increase CO2 emissions). An alternative paradigm is to use demand side flexibility for power balance. In this paper, we focus on one particular way of exploiting the demand side flexibility. We consider a group of loads with each load requiring a constant power level for a specified duration within an operational period. The loads are differentiated in terms of the duration of service they require. The flexibility of a load resides in the fact that the power delivery may occur at any subset of the total operational period. We consider the problems of scheduling, control and market implementation for a continuum of these loads. If the loads and the available power are known in advance, we find conditions under which the available power can service all 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. In addition, we investigate the implementation of a forward market in which consumers can purchase duration differentiated services. We first characterize the social welfare maximization problem and then show the existence of an efficient competitive equilibrium in this forward market.