Abstract
Power flow calculations are one of the most important computational tools for planning and operating electric power systems. After the stabilization of the deterministic power flow calculation methods, the need to capture uncertainty in load definition lead first to the development of probabilistic models, and later to fuzzy approaches able to deal with qualitative declarations and other non-probabilistic information about the value of the loads. Present fuzzy power flow (FPF) calculations use typically incremental techniques, in order to obtain a good approximation of the fuzzy state variables. However, these models and procedures are not entirely satisfactory for the evaluation of the adequacy of the electric transmission system, since they are not completely symmetric. In this paper, we show how to perform the detailed calculation of the state variables of the FPF problem in an exact and symmetrical way, by means of solving multiple optimization problems. The procedure is illustrated using the IEEE 118 test system.

Abstract
There are already several power systems coping with large amounts of wind power. Hi h penetration of wind power has impacts that have to be manage through proper plant interconnection, integration, transmission planning, and system and market operations. This report is a summary of case studies addressing concerns about the impact of wind power.s variability and uncertainty on power system reliability and costs. The case studies summarized in this report are not easy to compare due to different methodology and data used, as well as different assumptions on the interconnection capacity available. Integration costs of wind power need to be compared to something, like the production costs or market value of wind power, or integration cost of other production forms. There is also benefit when adding wind power to power systems: it reduces the total operating costs and emissions as wind fossil fuels. Severalissues that impact on the amount of wind power that can be integrated have been identified. Large balancing areas and aggregation benefits of large areas help in reducing the variability and forecast errors of wind power as well as help in pooling more cost effective balancing resources. System operation and working electricity markets at less than day-ahead time scales help reduce forecast errors of wind power. Transmission is the key to aggregation benefits, electricity markets and larger balancing areas. From the investigated studies it follows that at wind penetrations of up to 20 % of gross demand (energy), system operating cost increases arising from wind variability and uncertainty amounted to about 1.4 ./MWh. This is 10 % or less of the wholesale value of the wind energy.

Abstract
Back in 1999, the Power Systems Unit of INESC Porto concluded a consultancy study to estimate the remuneration that could be obtained by the Portuguese transmission provider using Short Term Marginal Prices. By that time the Regulatory Agency decided not to include a marginal based term on the Transmission Network Tariffs. However, that study was updated using information about the operation of the network in 2001 and recently it was concluded a new version of this study using information from 2004. This paper describes the models used in these studies, the assumptions that were adopted and the evolution of the marginal based remuneration that the Portuguese transmission provider could obtain if a marginal based tariff term existed. This evolution is important in order to get insight on the congestion level of the transmission network and on how neutral the transmission network is behaving in being able to physically implement the dispatches prepared by the Market Operator or related with bilateral contracts.

Abstract
This paper addresses the generation expansion-planning problem describing a model that generation companies and regulators can use to get insight to this problem and to more completely study and characterize different investment decisions. The simulation model considers a number of possible generation technologies and aims at characterizing the corresponding investment plans from an economic point of view having in mind that market prices, the demand growth, investment and operation costs, as well as other factors, are affected by uncertainties. With the objective of helping generation companies and regulators to carry out this planning, we adopted an approach based on System Dynamics. This methodology allows simulating the long-term behavior of electricity markets, namely to help getting insight into the way new generation capacity enters in the market in a liberalized framework. Finally, the paper presents results from a case study illustrating the use of this approach.

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.