Abstract
This paper describes an optimization model to be used by System Operators in order to validate the economic schedules obtained by Market Operators together with the injections from Bilateral Contracts. These studies will be performed off-line in the day before operation and the developed model is based on adjustment bids submitted by generators and loads and it is used by System Operators if that is necessary to enforce technical or security constraints. This model corresponds to an enhancement of an approach described in a previous paper and it now includes discrete components as transformer taps and reactor and capacitor banks. The resulting mixed integer formulation is solved using Simulated Annealing, a well known metaheuristic specially suited for combinatorial problems. Once the Simulated Annealing converges and the values of the discrete variables are fixed, the resulting non-linear continuous problem is solved using Sequential Linear Programming to get the final solution. The developed model corresponds to an AC version, it includes constraints related with the capability diagram of synchronous generators and variables allowing the computation of the active power required to balance active losses. Finally, the paper includes a Case Study based on the IEEE 118 bus system to illustrate the results that it is possible to obtain and their interest.

Abstract
This paper describes the formulations and the solution algorithms developed to include uncertainties in the generation cost function and in the demand on DC OPF studies. The uncertainties are modelled by trapezoidal fuzzy numbers and the solution algorithms are based on multiparametric linear programming techniques. These models are a development of an initial formulation detailed in several publications coauthored by the second author of this paper. Now, we developed a more complete model and a more accurate solution algorithm in the sense that it is now possible to capture the widest possible range of values of the output variables reflecting both demand and generation cost uncertainties. On the other hand, when modelling simultaneously demand and generation cost uncertainties, we are representing in a more realistic way the volatility that is currently inherent to power systems. Finally, the paper includes a case study to illustrate the application of these models based on the IEEE 24 bus test system.

Abstract
This paper describes two new active/reactive dispatch models to be used by System Operators in order to assign reactive power and to validate the economic schedules prepared by Market Operators together with the injections related with Bilateral Contracts. When talking about electricity markets one usually refers to active power markets paying less attention to ancillary services, namely to reactive power/voltage control. This usually leads to a chronological sequence of activities that may lead to inefficiencies because active and reactive powers are coupled given the capability diagram of synchronous generators, the ac power flow equations and the branch thermal limits. In this paper, we propose new models to remarry active and reactive allocation procedures based on a market approach as a way to ensure operation transparency. The resulting optimization problems are solved by a Sequential Linear Programming, SLP, approach that allows one to compute active and reactive nodal marginal prices at its final iteration. The paper includes a case study based on the IEEE 24 Bus Test System to illustrate the application of the developed models and demonstrate their interest in the scope of restructured power systems.

Abstract
This paper presents a model to solve the Generation Expansion Planning (GEP), problem in competitive electricity markets. The developed approach recognizes the presence of several generation agents aiming at maximizing their profits and that the planning environment is influenced by uncertainties affecting the demand, fuel prices, investment and maintenance costs and the electricity price. Several of these variables have interrelations between them turning it important to develop an approach that adequately captures the long-run behavior of electricity markets. In the developed approach we used System Dynamics to capture this behavior and to characterize the evolution of electricity prices and of the demand. Using this information, generation agents can then prepare their individual expansion plans. The resulting individual optimization problems have a mixed integer nature, justifying the use of Genetic Algorithms (GAs). Once individual plans are obtained, they are input once again on the System Dynamics model to update the evolution of the price, of the demand and of the capacity factors. This defines a feedback mechanism between the individual expansion planning problems and the long-term System Dynamics model. This approach can be used by a generation agent to build a robust expansion plan in the sense it can simulate different reactions of the other competitors and also by regulatory or state agencies to investigate the impact of regulatory decisions on the evolution of the generation system. Finally, the paper includes a Case Study to illustrate the use and the results of this approach.

Abstract
A new methodology is presented for decision making in long-term expansion planning. Power system expansion planning involves an intrinsic uncertainty on data and parameters, a fact often worsened by the new rules of deregulated electrical markets. The proposed procedure models both the uncertainty in load forecasting and the experience of the planning expert who uses fuzzy sets theory and fuzzy dynamic programming in the model algorithm to find an optimal expansion alternative. This procedure was tested in a realistic model system and the results obtained were arranged in an expansion planning ranking list according to their membership in the decision set.

Abstract
The restructuring of power systems has often originated the organization of power system operation planning in a set of chronological sequence of activities that are reasonably decoupled. This means that the Market Operator purely economic schedule together with bilateral contracts is conveyed to the System Operator to be validated from a technical point of view. The System Operator also has to schedule reactive power but some of its reactive power requirements may be unfeasible given the previous active power schedules and the alternator capability diagram. Apart from this aspect, active and reactive powers are coupled in determining the eventual violation of branch thermal limits and reactive power has a well-known local nature. While recognizing the coupling between active and reactive powers, the models presented in this paper admit that the Market Operator schedule may have to be altered either because there are branch limit or nodal voltage violations or because the System Operator requires a reactive output that can not be provided due to the previous active schedule. The changes on the initial schedule are determined by solving an optimization problem that uses adjustment generator or demand bids. Apart from that, we adopted a symmetric fuzzy programming approach recognizing that some constraints have a soft nature, namely the ones related with voltage and branch flow limits. To solve the resulting non-linear problem we used Sequential Linear Programming, SLP. At its final iteration this problem also outputs active and reactive nodal marginal prices useful to build more effective tariff systems. The paper includes a case study based on the IEEE 24 bus test system.