Abstract
In this paper one formulates the coordination problem of a set of directional overcurrent relays installed in meshed networks. After analysing the topology of the network to identify the primary/back up pairs, the coordination problem is organized in terms of a linear programming problem to be solved using the Simplex method. As results, this application gives the instantaneous relay settings, the relay pick up taps and the time dial settings. The methodology is illustrated using a small network mainly conceived for didactic purposes.

Abstract
This paper describes a mathematical model and the developed solution algorithm to solve an integrated active/reactive dispatch while retaining competitive aspects. The main drive for this research was the recognition that the introduction of competitive mechanisms lead to a certain extent to a decoupling between active and reactive power scheduling. Aiming at remarrying them, the developed approach includes an initial bid based uniform price active power auction run by the Market Operator, followed by a technical validity analysis run by the System Operator. If necessary, the System Operator uses adjustment bids to recover the technical feasibility of the dispatch. These bids are presented both by the demand and by generators meaning that demand can play an important role in increasing the liquidity of this specific market. This approach also includes capacitor banks and transformer taps leading to a combinatorial problem solved using Simulated Annealing. Finally, the paper includes results from a case study based on the IEEE 24 Bus Test System to illustrate the interest of this type of approaches.

Abstract
This paper describes a long-term simulation model to help generation companies building expansion plans. Different from the past, the generation activity is now provided under competition, and investments are affected by uncertainties and by the decisions of other players. This paper describes the use of System Dynamics to model the evolution of the demand and of the electricity price along the planning horizon. These evolutions will then be used by individual agents to prepare their own expansion plans. These plans will globally have to comply with general constraints, typically present in Grid Codes, as for instance, a maximum value for an adequacy index as LOLE. This model and the corresponding solution algorithm will be illustrated using a Case Study to illustrate the use of the developed approach to build the expansion plans and to conduct sensitivity studies.

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

Abstract
This paper presents a multicriteria formulation for multiyear dynamic transmission expansion planning problems. This formulation considers three criteria: investment costs, operation costs, and. the expected energy not supplied. The solution algorithm adopts an interactive decision-making approach that starts at a nondominated solution of the problem. This solution is identified transforming two of the three criteria in constraints specifying aspiration levels and using afterwards simulated annealing to deal with the integer nature of investment decisions. After obtaining this first solution, the decision maker can alter the aspiration levels and run the application again to obtain a new solution. Once an expansion plan is accepted, the algorithm computes long-term marginal costs, reflecting both investment and operation costs. These costs are more stable than short-term ones and inherently address the revenue reconciliation problem well known in short-term approaches. The developed algorithm is tested using a case study based on the Portuguese 400/220/150-kV transmission network.