Abstract
In deregulated electrical systems, production schedule for power plants is the result of an auction process. In the Spanish case, this schedule includes two main concepts: energy production (to be actually produced) and secondary reserve (to maintain available). The generation company faces the problem of converting energy schedule into a power schedule, respecting the reserve schedule as well as technical constraints, and trying to accomplish different goals: to minimise the production costs, to obtain smooth shapes for the power schedules and to optimise eventual compensation in schedules. A weighted goal mixed integer programming model with a real-size application to deal with this problem is presented.

Abstract
It is known that Cournot game theory has been one of the theoretical approaches used more often to model electricity market behavior. Nevertheless, this approach is highly influenced by the residual demand curves of the market agents, which are usually not precisely known. This imperfect information has normally been studied with probability theory, but possibility theory might sometimes be more helpful in modeling not only uncertainty but also imprecision and vagueness. In this paper, two dual approaches are proposed to compute a robust Cournot equilibrium, when the residual demand uncertainty is modeled with possibility distributions. Additionally, it is shown that these two approaches can be combined into a bicriteria programming model, which can be solved with an iterative algorithm. Some interesting results for a real-size electricity system show the robustness of the proposed methodology. © 2005 Cambridge University Press.

Abstract
Many of the models used for the representation of the generation companies' behavior in oligopolistic electricity markets are based on conjectural variation equilibria, which are a generalization of the classic Cournot approach. However, one of the main drawbacks of these approaches is the complexity of assigning adequate values to the conjectures, which can dramatically affect the results obtained from these models. This paper reviews and analyses the main formulations of conjectural equilibria applied to electricity markets. The paper shows how these different formulations are equivalent, and presents the relationships among the conjectures they use. Finally, it presents a brief overview on the main methods to estimate or compute the conjectures of these types of models.

Abstract
Several types of market equilibria approaches, such as Cournot, Conjectural Variation (CVE). Supply Function (SFE) or Conjectured Supply Function (CSFE) have been used to model electricity markets for the medium and long term. Among them, CSFE has been proposed as a generalization of the classic Cournot. It computes the equilibrium considering the reaction of the competitors against changes in their strategy, combining several characteristics of both CVE and SFE. Unlike linear SFE approaches, strategies are linearized only at the equilibrium point, using their first-order Taylor approximation. But to solve CSFE, the slope or the intercept of the linear approximations must be given, which has been proved to be very restrictive. This paper proposes a new algorithm to compute CSFE. Unlike previous approaches, the main contribution is that the competitors' strategies for each generator are initially unknown (both slope and intercept) and endogenously computed by this new iterative algorithm. To show the applicability of the proposed approach, it has been applied to several case examples where its qualitative behavior has been analyzed in detail.

Abstract
This paper presents a new iterative algorithm to compute a conjectured supply function electricity market equilibrium with DC transmission network constraints. This approach extends, to a network constrained system, a model previously developed by the authors for the single-bus case. At each iteration nodal prices are used to split the market into single prices areas. Since each area can be treated as a single-bus market from the transmission constraints' point of view, the single-bus algorithm is applied to compute the generators supply functions for each area. These new generators strategies are then cleared to determine new nodal prices and areas for the next iteration, and convergence is achieved when the network lines status and strategies of the generators do not change significantly in two consecutive iterations. The current approach has also been extended to deal with nodal elastic demands. Unlike previous approaches, the main contribution of this work is that the parameters of the first order approximation of the conjectured supply functions (intercepts and slopes) are endogenously determined, coherently with the network lines status. The algorithm has been applied to some illustrative case examples, and to a simplified version of the MIBEL market (Spain-Portugal). Results have shown to be very close to real data, and very relevant to analyze the economic impact of the capacity network constraints.

Abstract
Electricity markets based on simple bids provide a very high degree of transparency and simplicity. However, simple bids fail to capture many well-known characteristics of generating units and, therefore, the responsibility for obtaining feasible schedules is transferred to market participants. The purpose of this paper is to help the generating utility to automatically analyze the last energy program cleared in the market and, in case this program is technically unfeasible, to provide an alternative schedule by redispatching the generating units. This is achieved by formulating an optimization problem where the objective is to find the cheapest and feasible instantaneous power trajectory of each generator, trying to minimize the differences between its hourly average values and the last energy program. As the objectives of the utility can vary during the day, three different models are presented. Two of them are formulated as a joint energy and reserve dispatch in order to take into account possible commitments acquired in the ancillary services market of AGC regulation. In this sense, a novel approach for considering discontinuous ancillary regulation curves is proposed. Some numerical examples are included to illustrate the essential features of the models.