A trilevel model for best response in energy demand-side management

Demand-side management (DSM) is a powerful tool to efficiently manage the consumption of energy. DSM relies on various techniques and means. In this work, we propose a trilevel energy market model for load shifting induced by time-of-use pricing. Four kinds of actors are involved: electricity suppliers (sell energy), local agents (buy, sell and consume), aggregators (buy and sell) and end users (consume). The interactions among these actors lead to a trilevel multi-leader–multi-follower game. Solving such games is known to be hard, thus we assume that the decision variables of all electricity suppliers but one are known and optimize the decisions of the remaining supplier. This leads to a single-leader–multi-follower game, which aims to compute the leader’s best response to the decisions of his competitors. The trilevel model is first formulated as a bilevel problem using an explicit formula for the lowest optimization level. Solution algorithms are developed in the optimistic case and in a variant named “semi-optimistic” approach leading to more robust solutions. Finally, numerical results highlight the efficiency of the methods and the sensitivity of the solutions with respect to the model parameters.