Perturbation analysis of market equilibrium in the presence of renewable energy resources and demand response

One of the main challenges in the emerging smart grid is the integration of renewable energy resources (RER). The latter introduces both intermittency and uncertainty into the grid, both of which can affect the underlying energy market. An interesting concept that is being explored for mitigating the integration cost of RERs is Demand Response. Implemented as a time-varying retail electricity price in real-time, Demand Response has a direct impact on the underlying energy market as well. In this paper, beginning with an overall model of the major market participants together with the constraints of transmission and generation, the energy market is analyzed in the presence of both RERs and Demand Response. The effect of uncertainties in the RER on the market equilibrium is quantified, with and without real-time pricing. Standard KKT criteria are used to derive optimality conditions. Perturbation analysis methods are used to compare the equilibria in the nominal and perturbed cases. Sufficient conditions are derived for the existence of a unique equilibrium for the perturbed market. Numerical studies are reported using a 4-node IEEE bus to validate the theoretical results.