Abstract
Over the past two decades, the fact that many games have been formulated as variational inequalities problems has led to relevant developments related with the existence and uniqueness of equilibriums, and with their calculation methodologies. Based on this approach, this study applies sufficient conditions for Cournot equilibriums existence and uniqueness, proving that while existence holds, uniqueness cannot be proved in general. To find one of the existent equilibriums, this study also proposes a novel variational inequalities algorithm which is globally convergent and easy to implement. It iteratively computes searching directions of the equilibrium by generating hyper-planes that separate the equilibrium from the intermediate solutions obtained relaxing the original Cournot game. Unlike other related algorithms, the proposed algorithm does not require Jacobian matrixes evaluation, and the iterative relaxed games can easily be solved using convex and quadratic optimisation models. Numerical results show the operation and convergence of the algorithm.

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
This paper proposes a methodology for determining the optimal bidding strategy of a retailer who supplies electricity to end-users in the short-term electricity market. The aim is to minimize the cost of purchasing energy in the sequence of trading opportunities that provide the day-ahead and intraday markets. Agenetic algorithm has been designed to optimize the parameters that define the best purchasing strategy. The proposed methodology has been tested using real data from the Spanish day-ahead and intraday markets over a period of two years with a significant cost reduction with respect to trading solely in the day-ahead market.

Abstract
This paper proposes an optimization model based on a centralized dispatch to analyze the impact of plug-in electric vehicles (PEV) penetration on the Spanish electricity demand and price. Different charging strategies, from the plug-and-charge strategy to the smartest vehicle-to-grid (V2G) capabilities, have been simulated and compared with the non PEV scenario, under different penetration values. Traditional generation resources have been represented with technical aspects such as ramps and minimum loads. Hydraulic resources management is also partially supported but limited to weekly management. Distribution network constraints and how they could limit the contribution of PEV to the grid services have been neglected. The model considers both load and reserve requirements to evaluate the PEV contribution to energy production or consumption, but also to secondary reserve regulation. Interesting results comparing the different simulation scenarios are discussed in the case examples. © 2012 IEEE.

Abstract
Modeling competition in the future European Electricity Market (EEM) suggests considering new perspectives of leadership between the participant generators. EEM models should then be able to represent the possible existence of leaders and followers, and Conjectural Stackelberg equilibriums could be a powerful approach to do so. These asymmetric equilibriums can represent several types of competitive advantages among the market participants, though existing literature approaches generally assume single-leader-follower games. In addition, the complexity of the resolution methodologies sometimes compromises their applicability, especially if large-scale problems have to be solved. In this paper, a multi-leader-follower conjectural Stackelberg equilibrium model is presented. A simple convex quadratic optimization problem is proposed for its resolution, and the conditions for the equilibrium existence are discussed. A case study is presented to validate the model, and to analyze how market competition changes with the number of leaders or followers. The main conclusion is that if leadership spreads and Stackelberg models are used for its representation, regulatory policies should be oriented to increase the number of followers. However, there exists a maximum number of followers for which Stackelberg equilibriums does not exist, suggesting a deeper analysis for these cases to understand that matter and to decide the possible use of other market models. © 2012 IEEE.