Duration-differentiated Energy Services with a Continuum of Loads

Abstract

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.