Improved transmission representations in oligopolistic market models: Quadratic losses, phase shifters, and DC lines

Practical models of competition among power generators who possess market power have generally had to use simplified models of transmission costs and constraints in order to be tractable. In particular, the linearized de load flow model has been popular in complementarity and other types of oligopoly models. In this paper, we show how such models can be generalized to include quadratic losses, controllable DC lines, and phase shifting transformers. These generalizations preserve convexity of the feasible region, a property that facilitates computation and proof of solution uniqueness and existence. Piecewise and successive linearization formulations are also provided that allow consideration of nonlinear losses in models that require linear constraints. A simple six-bus example illustrates the application of these generalizations. In that example, the impact of losses on prices is much greater under strategic behavior than under competition. Large-scale applications of these approaches to markets in western North America and the European Union illustrate how inclusion of nonlinear losses and controllable DC lines can affect estimates of prices, flows, and economic efficiency indices resulting from oligopoly models.