تعادل نش در بازارهای رقابتی انرژی الکتریکی

Several countries have modified the structure of their Electric Energy Markets (EEM) by the introduction of various levels of competence in the generation, transmission and distribution areas, which allows the generators to sell their production at a short-term market price (or spot price). The fundamental premise of the regulation is that the global efficiency can be improved through a strong competence in a market structure governed by explicit rules. The Game Theory is the study of mathematical models of conflict and cooperation between intelligent rational decision-makers. In this paper, the Game Theory is proposed to analyze the economic behavior of the generators to make their offers to the short-term EEM. The IEEE 9-bus system is used to illustrate the main features of the proposed method.

In the last decade, the Electric Industry in Argentine, has changed from a vertically integrated structure of EEM, to a vertically and horizontally segmented one. The introduction of competence by means of the vertical and horizontal disintegration of the Electric Industry requires different forms of regulation compared with the ones traditionally applied in the sector. This approach puts emphasis both in the design of the EEM structure, and the set of rules that regulates, it where their ‘kindness’ is measured by the way in which they establish incentives for those behaviors that would contribute to the global efficiency [1]. The general spirit of the regulation in Argentine incorporates these innovative elements in orders to control the regulated companies through the verification of the fulfillment of obligations, subject to penalties and incentives. This EEM, includes different commercial and financial agreements, by means of contracts of different type and duration, shared risks, short-term transactions, among others. The nucleus of these agreements is the spot market in which the electric energy is valued and commercialized. This task is carried out by CAMMESA, the Argentine Independent System Operator (ISO) [2]. The programming of the economic dispatch (ED) is carried out using models of optimization and simulation of the operation, where the objective is to minimize the cost of operation plus failure of the generating units. The prize of the energy reflects the cost of the next MW of load to be supplied subject to the restrictions associated to the transport and maintenance of the level of quality of the service and security established. From the results obtained in the daily unit commitment, CAMMESA determines the prevision of prices of the energy for each hour. In this paper, a methodology based on the noncooperative Game Theory [3], [4] and [5] is used to analyze the economic behavior of the generating companies. The paper is organized as follows: First the application of the game theory on EEMs is reviewed, then the wholesale competitive spot market is described. Finally, the proposed method is presented.

The current structure of the Argentine EEM considers the possibility of the generators offering their production of the spot market from the definition of a price curve. In this paper, the economic behavior of the generators is modeled by the ISO as a Static Game with Complete and Perfect Information. The participants’ bids are modeled as pure strategies and the Nash equilibrium concept is used. From the results, it is concluded that the number of Nash equilibrium that takes place in the unit commitment diminishes as the load of the system increases. Multiple restrictions such as: spinning reserve, thermal unit (minimum up time, minimum down time, crew constraints), hydro-constraints, fuel constraints, that the unit commitment has in real systems, will affect the value of the point of transition. Nevertheless, it will persist the fact that in the cases in which the multiple Nash equilibria exist, the ISO defines a mechanism that solves the game by programming the ED of the generating units. The design of this EEM induces the competence between generators in scenes of a low load, but not for a high one. In competitive EEM with a high number of generating companies, the possibility of establishing coalitions to increase their benefits is remote, however, it could happen in the case of EEM structures with a reduced number of agents. In this context, the Game Theory provides a methodology to study the way the rules affect the incentives and consequently, the strategies. In some cases, it could be used by individual agents of the EEM to devise strategies that would benefit them, but the most important function of the Game theory is to identify the way the rules must be modified to improve the global efficiency of the EEM.