Incentives for demand-response programs with nonlinear, piece-wise continuous electricity cost functions

In this paper we identify some of the limitations with previous electricity cost functions used for demand-response (DR) programs in the retail market of the smart grid. In particular, we prove that while previous models lower the demand, they do not guarantee that they will try to flatten the demand. We then introduce a new nonlinear piece-wise continuous electricity cost function to model the way several consumers (from small utilities to retail consumers) are billed for electricity consumption. We show that the new cost function lowers the peaks in DR programs and design new incentive mechanisms to ensure that distributed agents converge to the Pareto-efficient solution of the system. However, we prove that any incentives mechanism either imposes additional taxes or requires external subsidies to operate. The paper finalizes with two examples of such mechanisms.