Abstract
This paper presents a new Fuzzy Dynamic Programming model that calculates the optimum solution of problems with uncertainties in data defined by fuzzy sets. The result includes the determination of an Intrinsic Risk Threshold of the solution. Extrinsic Risk Thresholds may also be set by a Decision Maker, in order to obtain more robust solutions. The technique is applied to the calculation of Distribution System expansion costs to serve the objectives of a Regulatory Authority (Regulator) in fixing levels of efficiency, targets and penalties to a regulated market.

Abstract
This paper presents a new and efficient methodology for network reconfiguration with optimal power flow based on Benders Decomposition approach. The objective minimizes the power losses, balancing load among the feeders and subject to the constraints: capacity limit of the branches, minimal and maximal limits of the substation or generator, minimum deviation of the nodes voltages and radial operation of the networks. A variant of the generalized Benders decomposition algorithm is applied for solving the problem, since the formulation can be embedded under two stages. The first one is the Master problem and Is formulated as Mixed Integer non-Linear Programming. This stage determines the radial topology of the distribution network. The second stage is the Slave problem and is formulated as a non-Linear Programming problem. This stage is used to determine the feasibility of the Master problem solution by means of an Optimal Power Flow and provides information to formulate the linear Benders cuts. The model is programmed in GAMS mathematical modeling language. The effectiveness of the proposal is demonstrated through an example extracted from the specialized literature.

Abstract
In this paper a tool for the evaluation of transmission system adequacy is presented. Although similar in the basic assumptions to the classic versions of the Fuzzy Power Flow (FPF), the approach has significant differences in the formulation. First, it is symmetrical (no influence of the slack bus in the results), so all the fuzzy power injections are in the same situation. Second, by including line constraints, only feasible deterministic power flows are accepted in the fuzzy variables calculations, leading to a more correct representation of the possible impact of uncertainty. Third, recalculation of the estimated node fuzzy injections leads to a clear picture of the repressed power flows and thus of the adequacy of the grid. On the other hand, the Constrained Fuzzy Power Flow (CFPF) separates completely the analysis of the network from the generation influence and costs, which is indispensable in a unbundled organization of the power system.

Abstract
The concept of microgrid (mu grid) has been emerging as a way to integrate microgeneration (mu G) in LV networks and simultaneously improve its potential benefits. Technical requirements to connect mu grids to LV networks have been studied in order to make this concept technologically feasible and safe to operate. However, the regulatory framework for economic integration of mu G and mu grids on distribution systems, despite being crucial, is still an open issue. The main purpose of this paper is to contribute for the development of an appropriate economic regulation framework that removes the barriers to mu G and mu grid development To do so, the relevant costs and benefits resulting from the establishment of mu G and mu grid are identified and a methodology for sharing those costs and benefits among the involved economic agents is presented. The only pre-requisite of such a methodology is that a net benefit to all economic agents exists, which is the case most of the times. An illustrative example is included

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.