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.

Abstract
The present paper describes an optimization strategy, to be adopted at the wind park control level, especially for those with large power output, that allow to define the commitment of the wind turbines and their active and reactive set points following requests from the wind park dispatch centers, assuming that individual wind turbines short term wind power forecasts are known and are expressed as power availability. This approach was also developed with a concern on the minimization of the connection / disconnection of the individual wind generators, for a given time horizon, and takes also into account restrictions in the limits for reactive power generated at the wind turbines.

Abstract
The present work investigates the dynamic behaviour of a mixed system consisting of a wind farm and a diesel group supplying a load, under different disturbances. In this regard, dynamic models and control systems that enable the generation part to support the grid are needed. The objective of this work has been also the implementation of the diesel group model and its afferent control system into Matlab-Simulink and to demonstrate their use by evaluating the response in time of the electric parameters.