Analysis of Nash Equilibrium Considering Multi-commodity Trade in Coupled Constraint Electricity Markets

This paper adopts a Nash-Cournot game theoretic framework and uses a linear DC network to represent transmission constraints. The multi-dimensional Cournot game is presented and, the bilateral model of spatial market is built. Because of capacity constraints and Kirchhoff´s laws, in this equilibrium model, the participants´ strategy space is coupled. The market equilibrium is defined as a set of prices, generator outputs, transmission flows, and consumption that simultaneously satisfy each market participant´s first order conditions for maximization of its profit while clearing the market. The multi-commodity trade in electricity markets is simulated by multi-dimensional Cournot model. A numerical method based on the Nikaido-Isoda function and a relaxation algorithm (NIRA) is presented for a calculation of coupled constraint Nash equilibrium in coupled constraint electricity markets. The interactions between energy and ancillary services markets and the transmission capacity limits effect are discussed. A three-bus bilateral market example with a DC model of the transmission line constraints is used to test the feasibility of the proposed algorithm. Simulation results show that the proposed model can be used to analyze market power in electricity market and to guide the companies in making decisions.