Abstract
Most of the approaches to decision problems under uncertainty are based on decision paradigms, generally associated to an optimization process that leads to a final solution. For the Decision Maker, the basic decision is thus what paradigm to choose, the rest of the procedure being mainly technical. In this paper, a different approach is advocated for this kind of problems. The main idea is to leave prescriptive models in favor of a more flexible approach, where risk related criteria are explicitly considered, conducting to an '' equivalent '' multicriteria (deterministic) model where decision-aid procedures can be used, with a greater involvement of the Decision Maker. The paper discusses first the uncertainty model and then reviews existing paradigms for the single criterion problem under uncertainty. Proposed risk and opportunity attributes come mainly from the analysis of those methodologies and from risk perception studies reports. Some hints about multicriteria aid methods and an illustrative example complete the paper.

Abstract
This paper describes a formulation to solve the long-term power generation expansion planning assuming a competitive electricity market. In a competitive environment each company aims at maximizing its profit through its individual expansion plan. In this formulation there is an inter connection between the expansion plans proposed by each company in the sense that the decisions taken by each company are influenced by decisions of the other players. In this formulation we assume there a centralized entity in charge of evaluating each plan both technically and economically taking into account a set of pre established constraints. As a result of that assessment, this centralized entity sends new information to the players. Using this scheme it is possible to assess the influence that the decisions of each company have in the decisions of its competitors, leading to the referred interconnection. The adopted solution approach is based in the decomposition of the global problem in a main problem to be solved by the Independent System Operator (ISO), and in several sub problems one per generating company. Finally, the paper includes a Case Study designed to illustrate this approach as well as its interest for several agents acting in the electricity market.

Abstract
This paper presents the mathematical models and the solution algorithms of DC optimal power flow problems: considering uncertainties represented by fuzzy numbers affecting loads as well as the elements of the cost function. The main purpose of this work corresponds to transfer the uncertainties affecting both the loads and the cost vector to the results that one usually obtain with such a DC optimal power flow model, that is, to characterize the uncertainties that affect the generations, the voltage phases, the branch flows. Apart from that, this paper also describes the algorithm to be used to calculate the uncertainties affecting the nodal marginal prices, since these prices are related with the dual variables of several constraints in the optimization problem. The developed algorithms are based in the solution of multiparametric problems in which one considers parameters both in the right hand side vector of the constraints (in order to represent load uncertainties) and in the cost function (to consider uncertainties in fuel costs, for instance). Finally, the paper includes a results of a Case Study designed to illustrate the application of the developed algorithms as well as results obtained for the IEEE 24 bus test system.

Abstract
A new methodology is presented for decision making in long-term expansion planning. Power system expansion planning involves an intrinsic uncertainty on data and parameters, a fact often worsened by the new rules of deregulated electrical markets. The proposed procedure models both the uncertainty in load forecasting and the experience of the planning expert who uses fuzzy sets theory and fuzzy dynamic programming in the model algorithm to find an optimal expansion alternative. This procedure was tested in a realistic model system and the results obtained were arranged in an expansion planning ranking list according to their membership in the decision set.

Abstract
The restructuring of power systems has often originated the organization of power system operation planning in a set of chronological sequence of activities that are reasonably decoupled. This means that the Market Operator purely economic schedule together with bilateral contracts is conveyed to the System Operator to be validated from a technical point of view. The System Operator also has to schedule reactive power but some of its reactive power requirements may be unfeasible given the previous active power schedules and the alternator capability diagram. Apart from this aspect, active and reactive powers are coupled in determining the eventual violation of branch thermal limits and reactive power has a well-known local nature. While recognizing the coupling between active and reactive powers, the models presented in this paper admit that the Market Operator schedule may have to be altered either because there are branch limit or nodal voltage violations or because the System Operator requires a reactive output that can not be provided due to the previous active schedule. The changes on the initial schedule are determined by solving an optimization problem that uses adjustment generator or demand bids. Apart from that, we adopted a symmetric fuzzy programming approach recognizing that some constraints have a soft nature, namely the ones related with voltage and branch flow limits. To solve the resulting non-linear problem we used Sequential Linear Programming, SLP. At its final iteration this problem also outputs active and reactive nodal marginal prices useful to build more effective tariff systems. The paper includes a case study based on the IEEE 24 bus test system.

Abstract
Under normal operating conditions, a MicroGrid is interconnected with the medium voltage network; however, in order to deal with black start and islanded operation following a general blackout, an emergency operation mode must be envisaged. A sequence of actions and conditions to be checked during the restoration stage are identified and tested through numerical simulation. Voltage and frequency control approaches, inverter control modes, and the need of storage devices are addressed in this paper in order to ensure system stability, achieve robustness of operation, and not jeopardize power quality during service restoration in the low voltage area.