Retailer-consumers model in electricity market under demand response

Demand response (DR) programs have gained much attention during the last three decades to optimize the decisions of the electricity market participants considering the demand-side management (DSM). It can potentially enhance system reliability and manages price volatility by modifying the amount or time of electricity consumption. This paper proposes a novel game-theoretical model accounting for the relationship between retailers (leaders) and consumers (followers) in a dynamic price environment where both players optimize their respective economic goals under uncertainty. The model is solved under two frameworks. First by considering retailer's market power and second by accounting for an equilibrium setting based on a Cournot game. These are formulated in terms of a mathematical program with equilibrium constraints (MPEC) and with a mixed-integer linear program (MILP), respectively. In particular, the retailers' market power model is first formulated as a bi-level optimization problem, and the MPEC is subsequently derived by replacing the consumers' problem (lower level) with its Karush-Kuhn-Tucker (KKT) optimality conditions. In contrast, the Cournot equilibrium model is solved as a MILP by concatenating the retailer's and consumers' KKT optimality conditions. The solution sets, the practical approaches for solutions, the required techniques to test and compare the performance of the model are undertaken with realistic data. Numerical simulations confirm the applicability and effectiveness of the proposed model to explore the interactions of markets power and DR programs. The results confirm that consumers are better off in an equilibrium framework while the retailer increases its expected profit when the market power is considered. However, we show how these results are highly affected by the levels of of consumers' flexibility.