Perturbation Analysis of the Wholesale Energy Market Equilibrium in the Presence of Renewables

Abstract—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 electricity price in real-time, Demand Response has a direct impact on the underlying energy market as well. Beginning with an overall model of the major market participants together with the constraints of transmission and generation, we analyze the energy market in this paper and derive conditions for global maximum using standard KKT criteria. The effect of uncertainties in the RER on the market equilibrium is then quantified, with and without real-time pricing. Perturbation analysis methods are used to compare the equilibria in the nominal and perturbed markets. These markets are also analyzed using a game-theoretic point of view. Sufficient conditions are derived for the existence of a unique Pure Nash Equilibrium in the nominal market. The perturbed market is analyzed using the concept of closeness of two strategic games and the equilibria of close games. This analysis is used to quantify the effect of uncertainty of RERs and its possible mitigation using Demand Response. Finally numerical studies are reported using an IEEE 30-bus to validate the theoretical results. NOMENCLATURE θn Set of indices of generating units at node n ϑn Set of indices of demands at node n Ωn Set of indices of nodes connected to node