Abstract
In this paper, we describe an integrated methodology to compute long-term marginal prices in distribution networks. Long-term marginal prices are considered the most interesting and economically sound way of allocating network costs to users. Additionally, they inherently deal with the revenue reconciliation problem, as they generally do not require other large supplementary tariff terms. The proposed methodology uses fuzzy sets to model uncertainties in load forecasts and considers several criteria to guide the identification of solutions. At the end, there is a final decision-making step to select the most adequate expansion plan according to the preferences of the decision maker.

Abstract
This paper describes a mathematical formulation for the active/reactive dispatch in electricity markets, including a number of issues present in market models used in several countries. Traditional market approaches are implemented considering a sequence of activities namely in terms of active power dispatch and ancillary services. However, these two problems are coupled in the sense that dispatching reactive power is not independent from the active power scheduling of generators. The proposed model admits that it is known the purely economic pool dispatch together with bilateral contracts and then it aims at dispatching reactive resources considering voltage and branch limit constraints and constraints reflecting the alternator capability curve. As a sub-result, this formulation also outputs nodal active and reactive marginal prices that can be useful to build tariff schemes. Finally, the paper includes a case study based on the IEEE 30 bus/41 branch system to illustrate the obtained results and their interest for electricity markets.

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.

Abstract
Transmission expansion planning corresponds to a very relevant issue that should not be forgotten in the scope of the implementation of market mechanisms in the electricity sector. This paper describes a multicriteria model to perform transmission expansion planning exercises that combines probabilistic models to represent the reliability of system components with fuzzy models to incorporate the uncertainty on load evolution along the planning horizon. This formulation also outputs long-term marginal prices that can be used to compute the Marginal Based Remuneration. The paper includes a case study based on the Portuguese 400/220/150 kV transmission network.