Abstract
This paper describes a set of mathematical formulations designed to include uncertainties modeled by fuzzy numbers in DC OPF studies. These approaches enhance and generalize an initial formulation and solution algorithm described in several papers co-authored by the second author. The approaches described in this paper adopt multiparametric optimization techniques in order to translate to the results the uncertainties affecting loads, for one side, the generation costs, for another, and also both of them in a simultaneous way. These approaches can be very useful nowadays given the uncertainties and volatility affecting data required to run several studies. They can also be the basis for the computation of nodal short time marginal prices reflecting these uncertainties. This paper also includes results obtained from a Case Study based on the IEEE 24 bus test system.

Abstract
This paper describes a set of mathematical formulations designed to include uncertainties modeled by fuzzy numbers in DC OPF studies. These approaches enhance and generalize an initial formulation and solution algorithm described in several papers co-authored by the second author. The approaches described in this paper adopt multiparametric optimization techniques in order to translate to the results the uncertainties affecting loads, for one side, the generation costs, for another, and also both of them in a simultaneous way. These approaches can be very useful nowadays given the uncertainties and volatility affecting data required to run several studies. They can also be the basis for the computation of nodal short time marginal prices reflecting these uncertainties. This paper also includes results obtained from a Case Study based on the IEEE 24 bus test system.

Abstract
This paper describes the models that were used and the results obtained to estimate the Congestion Cost of the Portuguese National Transmission Network. This network is established at 400 / 220 and 150 kV and the Tariff Code in force is Portugal determines the use of a postage stamp based approach discriminated by voltage level to set the tariffs for the use of the transmission system. However, the value of the congestion cost and its percentage regarding the regulated revenue of the transmission activity set by the Regulatory Agency are good indicators of the quality of the network since they directly reflect problems in the network in terms of congested branches or larger transmission losses. In this sense, we have been computing this indicator since 1998 and this paper reports the conclusions that were recently obtained using data from 2006 and 2008.

Abstract
With the advent of power system restructuring, there is now competition on the generation activity and the generation mix changed in many countries with the incentives to induce investments in renewables, in many cases, using volatile primary resources. Given this increase of the installed capacity in wind parks and PV stations as well as in hydro stations (as a way to address the mentioned volatility), investments in large thermal stations became more risky. In this scope, this paper describes a long term generation expansion planning model that can be used by generation companies to investigate the profitability of new thermal generation investments considering the increasing presence of renewables. This long term simulation tool uses System Dynamics, a framework particularly suited to mode the long term dependencies between different variables while incorporating delays on some decisions. At a final section this paper includes a Case Study based on a generation system that corresponds to a scaled version of the Portuguese system.

Abstract
This paper presents a multiyear dynamic transmission expansion planning, TEP, model aiming at minimizing operation and investment costs along the entire planning horizon while ensuring an adequate quality of service and enforcing constraints modeling the operation of the network along the planning horizon. The developed model profits from the experience of planners when preparing a list of possible branch (lines and transformers) additions each of them associated to the corresponding investment cost. The objective of solving a TEP problem is to select a number of elements of this list and provide its scheduling along the planning horizon such that one is facing a mixed integer optimization problem. In this case, this problem was solved using a discrete evolutionary particle swarm optimization algorithm, DEPSO. based on already reported EPSO approaches but particularly suited to treat discrete problems. Apart from detailing the developed DEPSO, this paper describes the mathematical formulation of the TEP problem and the adopted solution algorithm. It also includes results of the application of the DEPSO to the TEP problem using two test networks widely used by other researchers on this area.

Abstract
This paper presents an integrated model to deal with complex bids and network security constraints in electricity markets. Apart from purely economic aspects, power systems operation is also driven by technical issues that quite often turn unfeasible purely economic schedules. This is the case of up and down ramps and minimum technical limits of generators, nodal voltage ranges and branch flow limits. The activities of the Market and System Operators are quite often organized in terms of a sequential set of actions that may not guarantee identifying the best global solution. This suggests addressing the problem in a more integrated way and adopting a well known optimization technique, as Simulated Annealing. This paper describes the mathematical formulation of the problem, the adopted solution algorithm and details a case study based on the IEEE 24 bus/38 branch system.