Dynamic tariff-based demand response in retail electricity market under uncertainty

Demand response (DR) programs play a crucial role in improving system reliability and mitigating price volatility by altering the core profile of electricity consumption. This paper proposes a game-theoretical model that captures the dynamic interplay between retailers (leaders) and consumers (followers) in a tariffs-based electricity market under uncertainty. The proposed procedure offers theoretical and economic insights by analyzing demand flexibility within a hierarchical decision-making framework. In particular, two main market configurations are examined under uncertainty: i) there exists a retailer that exercises market power over consumers, and ii) the retailer and the consumers participate in a perfect competitive game. The former case is formulated as a mathematical program with equilibrium constraints (MPEC), whereas the latter case is recast as a mixed-integer linear program (MILP). These problems are solved by deriving equivalent tractable reformulations based on the Karush-Kuhn-Tucker (KKT) optimality conditions of each agent's problem. Numerical simulations based on real data from the European Energy Exchange platform are used to illustrate the performance of the proposed methodology. The results indicate that the proposed model effectively characterizes the interactions between retailers and flexible consumers in both perfect and imperfect market structures. Under perfect competition, the economic benefits extend not only to consumers but also to overall social welfare. Conversely, in an imperfect market, retailers leverage consumer flexibility to enhance their expected profits, transferring the risk of uncertainty to end-users. Additionally, the degree of consumer flexibility and their valuation of electricity consumption play significant roles in shaping market outcomes.