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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 dc 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, controilable 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. Index Terms--Economics, optimization methods, power generation, power transmission economics.

Since deregulated power markets are very often oligopolistic ones, efficient models that are able to describe strategic behavior of firms must be developed. In particular, transmission constraints can easily increase the opportunities of market players to exercise market power. This paper presents a model that describes the firms strategic interaction, based on Nash-Cournot equilibrium, when the power network is taken into account. Specifically, this paper introduces a new iterative algorithm, that explicitly considers how the production at a certain bus affects the whole network, and consequently models the opportunities for the firms of exercising market power, taking into account their ability to influence the composition of the set of constrained lines. The theoretical basis of the method as well as a case study based on the Central European network is included. Index Terms--Game theory, interconnected power systems, oligopoly models, power system economics, transmission.