Abstract
In this paper it is presented a formulation for the DC Optimal Power Flow problem considering load and generation cost uncertainties and the corresponding solution algorithms. The paper also details the algorithms implemented to allow the integration of losses on the results as well the algorithm developed to compute the nodal marginal price in the presence of such uncertainties. Since loads and generation costs are represented by fuzzy numbers, nodal marginal prices are no longer represented by deterministic values, but instead, by membership functions. To illustrate the application of the proposed algorithms, this paper also includes results based on a small 3 bus system and on the IEEE 24 bus/38 branch test system.

Abstract
One of the challenges that generation companies having hydro stations are facing corresponds to build the most adequate bids to send to day-ahead markets, maximizing their profit and taking into account the expect inflows, market prices and the interdependency between hydro plants in cascades. As a contribution to address this problem, this paper describes a short-term optimization model to build one-week schedules for a set of hydro power plants so that the outputs can be used to bid in the day-ahead market. This model is coordinated with a medium-scale (one year) model that inputs the value of using the water in the short-term problem. The developed model considers the non-linear relationship between the electric power, the net head and the turbine discharge and it takes in consideration pumping as well. The solution approach is based on an under-relaxed iterative procedure based on the algorithm described in [1] and the players are considered as price-takers, so that market prices are input variables. To solve the medium-term problem we propose a similar model that sends information about the final week volumes of each power plant to the short-term problem. On the other hand, we conducted a scenario analysis regarding market prices and inflows to internalize uncertainty. Finally, the model was successfully applied to a real size Portuguese cascade and the paper includes several results to illustrate the application of the developed models.

Abstract
Marginal prices have been recognized as the core approach to the economic evaluation of generation and transmission services in an electricity market environment. In this context, this paper presents the New Fuzzy Optimal Power Flow algorithm as a model to addresses the impact of load and generation cost uncertainties in nodal marginal prices. Since loads and generation costs are represented by fuzzy numbers, nodal marginal prices will no longer be represented by deterministic values, but rather by fuzzy membership functions reflecting the specified uncertainties. The paper also presents the algorithm used for the integration of the transmission losses effect on the results. Since the proposed algorithm uses multiparametric programming techniques, it contributes to characterize in a better way the system behavior. Finally, it includes results based on the IEEE 24 bus/38 branch test system to illustrate the proposed approach.

Abstract
This paper describes an optimization model to be used by System Operators in order to validate the economic schedules obtained by Market Operators together with the injections from Bilateral Contracts. These studies will be performed off-line in the day before operation and the developed model is based on adjustment bids submitted by generators and loads and it is used by System Operators if that is necessary to enforce technical or security constraints. This model corresponds to an enhancement of an approach described in a previous paper and it now includes discrete components as transformer taps and reactor and capacitor banks. The resulting mixed integer formulation is solved using Simulated Annealing, a well known metaheuristic specially suited for combinatorial problems. Once the Simulated Annealing converges and the values of the discrete variables are fixed, the resulting non-linear continuous problem is solved using Sequential Linear Programming to get the final solution. The developed model corresponds to an AC version, it includes constraints related with the capability diagram of synchronous generators and variables allowing the computation of the active power required to balance active losses. Finally, the paper includes a Case Study based on the IEEE 118 bus system to illustrate the results that it is possible to obtain and their interest.

Abstract
This paper describes the formulations and the solution algorithms developed to include uncertainties in the generation cost function and in the demand on DC OPF studies. The uncertainties are modelled by trapezoidal fuzzy numbers and the solution algorithms are based on multiparametric linear programming techniques. These models are a development of an initial formulation detailed in several publications coauthored by the second author of this paper. Now, we developed a more complete model and a more accurate solution algorithm in the sense that it is now possible to capture the widest possible range of values of the output variables reflecting both demand and generation cost uncertainties. On the other hand, when modelling simultaneously demand and generation cost uncertainties, we are representing in a more realistic way the volatility that is currently inherent to power systems. Finally, the paper includes a case study to illustrate the application of these models based on the IEEE 24 bus test system.

Abstract
The continuous growth of wind energy integration on electrical networks has led many utilities to impose fault ride-through capability to wind farms. This means that wind turbines must remain connected to the system during severe fault occurrence. Regarding the existing wind farms equipped with fixed speed induction generators directly connected to the grid, fault ride-through capability is commonly assisted with dynamic compensation devices, such as DSTATCOM units. These power electronic devices are controlled for voltage regulation purposes and behave like a balanced three-phase voltage source converter since commonly used control techniques are based only on the positive sequence of both voltage and current measured at its connection point. These control techniques are suitable only when compensation devices are operated under balanced conditions and therefore its performance when facing unbalanced faults needs to be evaluated. This paper tackles with this subject and the results obtained through numerical simulations demonstrate that over voltages can arise on non faulty phases leading to the wind farm disconnection.