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We consider a liberalized electricity market, divided in zones interconnected by capacitated transmission links, where a large dimensional power producer operates. We introduce a model for determining the optimal bidding strategies of the large dimensional producer, so as to maximize his own market share, while guaranteeing an annual profit target and satisfying technical constraints. The model determines the optimal medium-term resource scheduling and yields the hourly zonal electricity prices, as it includes constraints representing the Market Clearing process. In order to compute the global solution, the complementarity conditions are formulated as mixed integer linear constraints and the revenue terms are expressed by piece-wise linear functions. The model can be used for analyzing the behavior of market prices in electricity markets where a large dimensional producer can exert market power. It can also be used by investors as a simulation tool for evaluating both the impact on the market and the profitability of investment decisions in the zonal electricity market. A case study related to the Italian electricity market is discussed.

In some countries the structure of the electric power industry, resulting from the privatization and liberalization process, is such that the former monopolist enjoys significant market power. Regulatory constraints to the incumbent's offer strategy are usually introduced, like an average price-cap, or an absolute price-cap, or a cap on the geographic price-differentiation. Many models of strategic interaction on networks have been developed, see the reviews in Ventosa et al. (2005), Ramos et al. (1998) and Smeers (1997); see also Barquin et al. (2008), Day et al. (2002), Hobbs (2001), Hobbs et al. (2000), Schuler (2001), Li and Tesfatsion (2009) and Somani and Tesfatsion (2008). In this paper we consider an electricity market divided in zones, interconnected by capacitated transmission links, and characterized by the presence of a dominant producer, who may exert market power to achieve a predetermined annual gross-margin target, whereas the other firms behave like a competitive fringe. Indeed, it is often recognized that incumbents do not take full advantage of their capability to control prices in order to maximize profits. The representation of this assumption on the dominant producer's behavior has the advantage of being easily implementable, since in most markets the dominant company statements to the financial markets report the revenue targets and information about the generating capacity is generally available. Moreover, it is assumed that, among all solutions that guarantee the annual profit target, the dominant producer prefers one that maximizes the annual market share. In order to solve the dominant producer problem, we propose a two-stage procedure. The first stage is based on a linear programming model that computes, while assuming perfect competition among producers, the hourly zonal prices and the accepted bids determined by the Market Operator, given the hourly zonal demands and the power producers' hourly bids for every generation plant. The second stage is based on the dominant producer's annual resource scheduling model, in which the interdependencies between the hourly zonal prices and the dominant producer's hourly production decisions are expressed by the optimality conditions of the Market Clearing problem. The optimal solution of this model determines the hours in which the dominant producer can increase his profits by modifying the perfect competition solution. The nonlinearities in the Market Clearing optimality conditions are eliminated by using a binary variable formulation of the complementarity conditions; the nonlinear revenue terms in the profit constraint are substituted by piece-wise linear functions. In this way a Mixed Integer Linear Programming formulation of the dominant producer model is obtained, whose solution yields a global optimum. The optimal solution can be efficiently computed by commercial codes, when the problem dimension is not too big. For the cases in which the model dimension becomes a substantial issue, we developed an iterative algorithm, based on a model for the single hour t, that exploits the quasi-separability of the problem with respect to the hours. The dominant producer model solution yields the hourly zonal electricity prices and therefore can be used by investors as a simulation tool for analyzing both the impact on the market and the profitability of investment decisions in the zonal electricity market. Spot market price forecasts are crucial to assessing profitability of investments in electricity generation capacity. Since electricity is not storable and demand is highly inelastic, electricity prices are highly variable in time and the presence of very large incumbents adds considerably to the complexity of price-forecasting. Profitability of marginal generators might depend crucially on high spot prices resulting in a limited number of hours. Further, in some markets, locational price differentiation is implemented in case of transmission congestion, so that profitability of a generator depends on where it is located. The paper is organized as follows. In Section 2 the model used in the first stage of the procedure is presented, namely the Market Clearing model used by the Market Operator for determining the equilibrium hourly zonal prices and productions. In Section 3 the Mixed Integer Linear Programming model of the dominant producer problem is introduced, on which the second stage of the procedure is based. In Section 4 some tests related to the Italian electricity market are discussed. Future work planned is described in Section 5 and in the Appendix the algorithm is presented for computing the optimal solution of large dimensional problems.

In this paper a decision support model has been introduced for a dominant producer who wants to exert market power in order to achieve a yearly profit target. The model of the dominant producer's behavior is of Mixed Integer Linear Programming type, since the revenue terms are linearized and the complementarity conditions are represented by linear constraints depending on binary variables. This representation of the complementary constraints guarantees that the global optimum is obtained. Future work is planned to deal with the evaluation of the model performance in forecasting electricity prices, using historical scenarios in the Italian market. Also, the following issues, related to two empirically verifiable implications of our behavioral assumptions, will be addressed. First, when entry occurs in the industry, i.e. the fringe's capacity increases, market prices increase, the loss of market share by the dominant firm, at any price level, gets larger. As a consequence the dominant firm must increase the exercise of market power to achieve the same level of profits and market prices will increase. This will take place until the size of the fringe is such that the dominant company can no longer achieve the predefined profit target. Second, if the dominant firm owns a significant quantity of inframarginal capacity, like hydro or nuclear, an increase in the price of the marginal fuel, typically natural gas or oil, will have a smaller impact on prices than under the standard profit maximization assumptions. That happens because the price increase, caused by the marginal cost increase, generates a higher inframarginal rent for the dominant firm and therefore relaxes the profit-target constraint. Symmetrically, a marginal cost reduction should, under our assumptions, translate on market prices less than it would under the standard profit maximization assumptions. Those observable implications of our assumptions should provide hints as to the empirical relevance of our model for the market that is being analyzed.