Transmission Capacity Expansion in Imperfectly Competitive Power Markets

This paper proposes a mathematical model for transmission planning in an environment where there is imperfect competition in electricity supply industry. The model is developed based on the concept of the leader-followers game in applied mathematics. The leader of the game is the transmission planner and the followers are the strategic electricity producing firms. The reaction of the strategic electricity producing firms to the transmission planning decision is modeled using the introduced concept of the worst-Cournot-Nash equilibrium. The worst-Cournot-Nash equilibrium can handle the multiple Nash equilibria problem. The whole mathematical formulation is a bilevel mixed-integer linear programming problem. This formulation is achieved using the Karush-Kuhn-Tucker optimality conditions and a binary mapping approach. The application of the proposed approach to the three-node example system and the modified six-node Garver´s example system are studied. The transmission planning with perfect competition is formulated and used as the benchmark. The numerical results show that the proposed approach in this paper can efficiently allocate the additional transmission capacity to the transmission grid such that it reduces the market power cost in the electricity supply industry. However, further studies should be carried out to scale up the proposed approach to the larger case studies.