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The electric utility deregulation process and the introduction of competition among its participants introduced the notion of equilibria models adapted to the energy market. Among them, the Stackelberg equilibrium represents a monopolist approach, defined by a hierarchical structure, with a dominant firm acting in a privileged position and a group of subordinated ones acting as followers. Its application to AC power systems can be modeled as a bilevel mathematical problem, and represented by its Karush Kuhn Tucker (KKT) formulation. This paper presents a noninterior point algorithm to solve this Stackelberg equilibrium, considering the electrical power system as an interconnected network through its transmission system. Numerical examples with a 24 bus and the IEEE-118 bus systems illustrated the leader participant behavior and showed the market power exercised by them, which is increased in the presence of tighter transmission capacity constraints. The numerical examples also showed the robustness and efficiency of the proposed algorithm.
Latorre et al. (2003) studied this question.