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 two-step algorithm to compute a conjectured supply function electricity market equilibrium with DC transmission network constraints. This approach generalizes a previous authors' model developed for the single-bus case. Unlike other approaches, its main contribution is that the parameters of the first order approximation of the conjectured supply functions (intercept and slope) are endogenously determined, coherently with the network lines status. Nodal prices are used to split the market into single prices areas. Each area is treated as a single-bus market from the transmission constraints point of view, and the authors' 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. Convergence is achieved when the network lines status and strategies of the generators do not change significantly in two consecutive iterations. The algorithm has been tested with some illustrative case examples, and with a simplified version of the MIBEL market (Spain-Portugal). © 2011 IEEE.

Abstract
Long term electricity markets models tend to use simplified representations of both the demand and the generation units, to reduce the amount of input data and decision variables used, and also to decrease their execution times. On the one hand, hourly demand curves are usually simplified into a reduced set of non-chronological demand levels, each one representing hours with similar demand values. On the other hand, individual generation units are condensed into technologies grouping their costs curves by similarity in different appropriated technological cost mappings. This paper proposes several novel Mixed Integer Programming models to solve these two curve-fitting problems when the approximating function is a Piece-Wise Linear Function. By means of two real cases study it shows that the approximation approach has real applicability since it does not significantly compromise the traditional system representation. © 2011 IEEE.

Abstract
The increasing penetration of interruptible sources of energy is making security of supply a key aspect of present and future networks management, and reserves markets are gaining significant relevance. Demand representation used in traditional long term market models normally consists in a set of non chronological demand levels corresponding to hours with similar demand values. However, reserve issues are closely related with short term constraints (such as ramps), and this lack of chronological coupling does not allow for an appropriate representation of these technical constraints. This paper presents a joint energy and reserve conjectural equilibrium model that provides signal prices for both commodities and computes productions accordingly by satisfying system demand and reserve requirements. Generation is represented at a technological level, and water contributes to energy and reserve requirements with daily constraints. To reduce the feasible region, clustering is used to simplify hourly demand series into only a few daily patterns. In addition, keeping the link between hours and demand levels allows the model to combine short term technical constraints with traditional long term strategic planning constraints. © 2011 IEEE.

Abstract
Many studies addressing the effect of wind power integration strategies on the system adequacy assessment have been made, only concerning the generation point of view and usually disregarding the effect of the transmission network. On the other hand, studies considering the transmission network usually have ignored the effect of wind power integration strategies, focusing only on capturing the time dependent nature of this type of renewable energy source. Therefore, this work presents a chronological Monte Carlo simulation approach that assesses the system adequacy of composite systems (generation and transmission) considering non-dispatchable and dispatchable renewable energy production (wind and hydro, respectively). Case studies involving the IEEE-RTS 79 and modified versions of this system are presented and discussed as didactic examples.

Abstract
The paper describes some of the initial results of the CIGRE Working Group C4.605 "Modeling and aggregation of loads in flexible power networks". One of the tasks of the working group is to provide recommendations on developing equivalent static and dynamic models for clusters of diverse loads/generators, i.e., models of distribution network cells and microgrids and recommendations on procedures for data/response gathering and processing. This paper focuses on critical review of existing literature on aggregated models of wind-based generation, active distribution network cells and microgrids for power system studies. © 2011 IEEE.