Abstract
Short-term risk management is highly dependent on long-term contractual decisions previously established; risk aversion factor of the agent and short-term price forecast accuracy. Trying to give answers to that problem, this paper provides a different approach for short-term risk management on electricity markets. Based on long-term contractual decisions and making use of a price range forecast method developed by the authors, the short-term risk management tool presented here has as main concern to find the optimal spot market strategies that a producer should have for a specific day in function of his risk aversion factor, with the objective to maximize the profits and simultaneously to practice the hedge against price market volatility. Due to the complexity of the optimization problem, the authors make use of Particle Swarm Optimization (PSO) to find the optimal solution. Results from realistic data, namely from OMEL electricity market, are presented and discussed in detail.

Abstract
Game theory has traditionally used real-valued utility functions in decision-making problems. However, the real information available to assess these utility functions is normally uncertain, suggesting the use of uncertainty distributions for a more realistic modelling. In this sense, utilities results or pay-offs have been normally modelled with probability distributions, assuming random uncertainty. However, when statistical information is unavailable, probability may not be the most adequate paradigm, and can lead to very large execution times when some real complex problems are addressed. In this article possibility distributions are used to model the uncertainty of utility functions when the strategies are probability distributions (mixed strategies) over a set of original and discrete strategies (pure strategies). Two dual approaches to solve the resulting non-cooperative fuzzy games are proposed: modelling players' risk aversion, and thus providing realistic conservative strategies. Two examples show the robustness of the strategies obtained with the proposed approaches.

Abstract
It is widely known and accepted that Nash equilibrium suitably models agents' behavior in electricity markets, since it is coherent with the common sense of their simultaneous profits maximisation. In the literature, these approaches are usually addressed using deterministic representations, despite the fact that electricity markets are highly conditioned by the uncertainty in demand or in agents' bidding strategies. Only some equilibrium-modelling approaches under uncertainty can be found in the literature, most of them using probability distributions. However, probability approaches may lead to very complex formulations and generally require restrictive assumptions (such as normality or independence) that can hardly be verified in real complex problems. A conjectured-price-response equilibrium model that uses LR-possibility distributions to represent the uncertainty of the residual demand curves faced by the participant agents is proposed. Modelling the risk-aversion attitudes of the agents, the resulting possibilistic equilibrium is transformed into a simplified deterministic one, which is solved with a new globally convergent algorithm for variational inequalities problems. Some interesting results for a real-size electricity system show the robustness of this new approach when compared with other risk-neutral approaches.

Abstract
Evolutionary Particle Swarm Optimization (EPSO) is a robust optimization algorithm belonging to evolutionary methods. EPSO borrows the movement rules from Particle Swarm Optimization (PSO) and uses it as a recombination operator that evolves under selection. This paper presents a reactive power planning approach taking advantage of EPSO robustness, in a model that considers simultaneously multiple contingencies and multiple load levels. Results for selected problems are summarized including a trade-off analysis of results.

Abstract
Evolutionary Particle Swarm Optimization (EPSO) is a robust optimization algorithm belonging to evolutionary methods. EPSO borrows the movement rules from Particle Swarm Optimization (PSO) and uses it as a recombination operator that evolves under selection. This paper presents a reactive power planning approach taking advantage of EPSO robustness, in a model that considers simultaneously multiple contingencies and multiple load levels. Results for selected problems are summarized including a trade-off analysis of results.

Abstract
This paper describes the concept of a voltage/NAR controller based on an interaction of fuzzy Mamdani controllers, with the main objective of keeping voltages at all busbars inside an admissible band while avoiding line flows to exceed admissible limits. Estimation of sensitivities via fuzzy clustering of load profiles is proposed. A complex rule base interacts with a Newton-Raphson power flow routine in iterative steps until a terminating criterion is met, following a basic min-max approach. Tests to the method reveal it as one order of magnitude faster than a competing simulated annealing routine.