Abstract
One of the important decision problems for a power system operator is to choose the appropriate operation point when possible contingencies must be considered. The operator may decide to do nothing or to take some actions that change the operating point and decrease the negative impact (cost) of some or all the contingencies. The purpose of this paper is to investigate the applicability of utility and value functions to this decision problem, since the large range of consequences raises some doubts about the fulfillment of the theoretical conditions imposed by Decision Theory. Although not essential to this discussion, some alternatives to prescriptive methodologies are presented and discussed, mostly regarding the definition of risk attributes and other determinist equivalents, suitable for multicriteria analysis.

Abstract
This paper addresses the allocation of electrical losses in distribution networks with embedded generation, in a liberalized environment. The nonlinear nature of the issue, the loss changes due to voltage variation and, specially, the contribution of embedded generation to loss variation are considered. The proposed method is based on tracing the real and imaginary parts of the currents and has two steps. First, the losses in the distribution network, in the absence of embedded generation, are allocated to the consumers (or their providers). Second, the variations in the losses that result from the influence of embedded generation are allocated to the generatorsi These variations are a measure of the avoided or added costs related to losses. In the allocation process, made in a branch basis, both real and reactive powers are considered. The methodology presented in this paper can be used to evaluate embedded generation incentives or to design tariffs for the use of the distribution network.

Abstract
This paper demonstrates the application of Markov chain models to valuate generation assets within deregulated electricity markets. A new framework for modeling electricity markets with Markov chain model is proposed. The advantage of the Markov chain model is that it deploys fundamental approaches to identify the key economic forces underlying the electricity markets such as demand on electricity and supplied online generation capacity. Based on this new model, real option calculations are used to valuate generation assets. Markov chain model is combined with binomial tree to approximate the stochastic movement of prices on both electric energy and ancillary services, which are driven by the market forces. A detailed example is presented. This method is shown to provide optimal operation policies and market values of generation assets. This method also provides capability to analyze the impacts of demand growth patterns, competition strategies of competitors and other key economic forces.

Abstract
This paper presents an enhanced version of an AC Fuzzy Power Flow model designed to integrate correlation data between nodal injections. The model gives the user the possibility to specify fuzzy numbers to represent the possible behavior of loads and generations and outputs fuzzy membership functions for voltage magnitudes and phases, active and reactive flows, losses and generations. The algorithm is organized in two basic steps. The first one corresponds to a linearized procedure while the second aims at introducing correlated data leading to a reduction of the width of the membership output functions. In a final section, we present results obtained with a case study based on a didactic power system to illustrate and highlight details of the proposed models.

Abstract
Unbundling and liberalization of the electric sector has led in many countries, including Portugal, to the settlement definition of quality standards for the power distribution systems that give rise to penalties when those standards are not met. Also, penalties and rewards related to global reliability indices exist in some countries. Distribution companies must take this into account when planning there systems because the minimization of the net reliability cost is a main criteria when making investment decisions performing reliability studies to support investment decisions, and penalties (or rewards) become direct reliability costs (or benefits), regardless of any other consideration concerning the impact of the frequency and duration of the interruptions. Most of the time, standards are defined in terms of the sum of the interruption durations during a year. In this paper, the details of this discussion are addressed, in the framework of the investment decision-making process. A formal model for the problem is proposed, along with methodologies able to tackle it. The inadequacy of a markovian approach is discussed and illustrated, showing how bad investment decisions can be made due to incorrect evaluation of the reliability costs. The discussion will be illustrated with small numerical examples.

Abstract
Defining the needs of operating reserve in a power system has been always a subject of interest, leading to the development of deterministic rules (e.g. the percentage rule defined by UCTE in Europe or the well-known "largest unit" rule) and probabilistic methods like PJM (Pennsylvania-New Jersey-Maryland) and its enhancements, based on the concept of risk. However, the recent increase in the penetration of wind power generation changed the framework of this evaluation, due to the volatile nature of this kind of energy. In this paper, a detailed model of the unavailability of wind parks that accounts both for machine failures and different wind levels is combined with the modified PJM method, in order to build a consistent framework for the evaluation of the operational risk. The paper also shows how the proposed model can be used as a decision-aid tool for planning the operational reserve, either by performing multicriteria analysis on cost and risk or by stipulating an acceptable risk level.