Abstract
Generation expansion planning gained a new dimension with the advent of electricity markets. It is now an activity decoupled from transmission and there are several agents competing to generate electricity and aiming at maximizing their individual profits. In view of this, it becomes more important to develop tools to help generation agents to build their expansion plans, internalizing several uncertainties in the model, an being able to simulate different possible reactions of the other competitors, given their impact in the profits of the agent being modelled. In this paper, we present a long-term decision aid tool that uses System Dynamics to model the long run of electricity markets together with Genetic Algorithms to solve the individual expansion problem of generation agents given their mixed-integer nature. Apart from the detailed description of the developed approach, the paper also includes a Case Study based on a four generation agent system to illustrate its application.

Abstract
This paper describes a formulation to solve the long-term power generation expansion planning assuming a competitive electricity market. In a competitive environment each company aims at maximizing its profit through its individual expansion plan. In this formulation there is an inter connection between the expansion plans proposed by each company in the sense that the decisions taken by each company are influenced by decisions of the other players. In this formulation we assume there a centralized entity in charge of evaluating each plan both technically and economically taking into account a set of pre established constraints. As a result of that assessment, this centralized entity sends new information to the players. Using this scheme it is possible to assess the influence that the decisions of each company have in the decisions of its competitors, leading to the referred interconnection. The adopted solution approach is based in the decomposition of the global problem in a main problem to be solved by the Independent System Operator (ISO), and in several sub problems one per generating company. Finally, the paper includes a Case Study designed to illustrate this approach as well as its interest for several agents acting in the electricity market.

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.