Generation games with coupled transmission and emission constraints

Competitive thermal generators' emissions constitute an externality, on which the regulator might impose constraints. On the other hand, transmission capacities for sending energy may naturally be restricted by the grid facilities. Both pollution standards and transmission capacities impose several constraints upon the joint strategy space of the agents. Seeking to constrain the competitive electricity generators' behaviour the regulator can solve a generalised Nash equilibrium problem, which is a Nash equilibrium at which the joint strategy-space constraints are satisfied. Using the coupled constraints' Lagrange multipliers, which arise from that equilibrium, as taxation coefficients, the regulator can modify the players' payoffs and thus control them toward an equilibrium where both congestion and excessive pollution are avoided. A three-node network example with a dc model of the transmission line constraints possesses these properties and will be used in this paper to discuss and explain the behaviour of the agents subjected to coupled constraints.