Abstract
This chapter presents some case studies using fuzzy equivalent uniform annual worth analysis. It includes three case studies and each case is studied for both crisp and fuzzy cases. Trapezoidal fuzzy numbers and correlated, uncorrelated, and partially correlated cash flows are handled in the cases. © 2008 Springer-Verlag Berlin Heidelberg.

Abstract
This chapter first presents arithmetic operations over independent fuzzy numbers and economic concepts review. Then, it gives the techniques for comparing and ordering fuzzy numbers of independent numbers and dependent numbers. It examines fuzzy case with partial correlation. The chapter also includes many numerical applications. © 2008 Springer-Verlag Berlin Heidelberg.

Abstract
Even in a liberalized environment, managing the security of supply associated to the generating system continues to be a major task of the System Operators. The increased use of renewable energy, in particular wind power, adds new challenges to the process, namely in countries like Portugal and Spain, where strong investments in wind power have been done and are foreseen for the next years. In order to tackle this issue, REN (the Portuguese TSO), REE (the Spanish TSO) and INESC Porto (a RandD institute) joined together to develop a project where Monte Carlo simulation is used to evaluate the risk associated with specific future configurations of the generating system, until the horizon of 2025, in the framework of medium and long term generation planning of MIBEL (the Iberian electricity market). Probabilistic simulation was chosen because deterministic approaches to this problem, although simple to understand and easy to implement, are unable to tackle the complex relations between different uncertain variables. In this project, simulation is organized chronologically, in order to preserve the relations between load and the different variables associated to generation and produce meaningful risk indices of generation adequacy. A new feature is the analysis of the operational reserve, through a process that estimates, in each simulated state, the unforeseen change in load and wind generation. These unexpected changes are then compared with the total available operational reserve, defined by the secondary reserve plus the tertiary reserve units with lead time up to one hour. It is important to point out that the proposed simulation is a tool that is able to quantify the adequacy of different reserve requirements, solutions for reserve enhancement, etc. , in order to support the decision making process. This paper describes the concepts and assumptions of the simulation model and presents results and conclusions of some of the case studies carried out in the project.

Abstract
This paper describes a mathematical model and the developed solution algorithm to solve an integrated active/reactive dispatch while retaining competitive aspects. The main drive for this research was the recognition that the introduction of competitive mechanisms lead to a certain extent to a decoupling between active and reactive power scheduling. Aiming at remarrying them, the developed approach includes an initial bid based uniform price active power auction run by the Market Operator, followed by a technical validity analysis run by the System Operator. If necessary, the System Operator uses adjustment bids to recover the technical feasibility of the dispatch. These bids are presented both by the demand and by generators meaning that demand can play an important role in increasing the liquidity of this specific market. This approach also includes capacitor banks and transformer taps leading to a combinatorial problem solved using Simulated Annealing. Finally, the paper includes results from a case study based on the IEEE 24 Bus Test System to illustrate the interest of this type of approaches.

Abstract
Modeling uncertainties in power systems has long interested researchers. Nowadays, as in 70's, the volatility associated with generation or fuel prices, for one side, and the uncertainties related with load forecasting and generation capacity, for another, places a new emphasis on this kind of problems. As a result of this renewed interest, in this paper we are enlarging the original Fuzzy Optimal Power Flow, FOPF, model in order to consider not only load uncertainties, but also uncertainties in generation or fuel prices, specified using trapezoidal fuzzy numbers. This new approach is based on multiparametric linear programming techniques that lead to the identification of a number of critical regions covering all the uncertainty space. This contributes to build more accurate membership functions of all variables, namely generations, branch flows and power not supplied.

Abstract
This paper describes two new active/reactive dispatch models to be used by System Operators in order to assign reactive power and to validate the economic schedules prepared by Market Operators together with the injections related with Bilateral Contracts. When talking about electricity markets one usually refers to active power markets paying less attention to ancillary services, namely to reactive power/voltage control. This usually leads to a chronological sequence of activities that may lead to inefficiencies because active and reactive powers are coupled given the capability diagram of synchronous generators, the ac power flow equations and the branch thermal limits. In this paper, we propose new models to remarry active and reactive allocation procedures based on a market approach as a way to ensure operation transparency. The resulting optimization problems are solved by a Sequential Linear Programming, SLP, approach that allows one to compute active and reactive nodal marginal prices at its final iteration. The paper includes a case study based on the IEEE 24 Bus Test System to illustrate the application of the developed models and demonstrate their interest in the scope of restructured power systems.