Abstract
In this paper, system component reinforcements are analyzed from the perspective of their impact in increasing flexibility in system design. The proposed framework integrates a fuzzy optimal power flow model through which one can derive, as a function of load uncertainties, possibility distributions for generation, power flows and power not supplied. Exposure and robustness indices, based on risk analysis concepts, are defined. These indices can be used to rank the expansion alternatives, giving the planner insight to system behavior in face of adverse futures. Their use in conjunction with investment assessments is proposed as a necessary step in a decision making methodology.

Abstract
A fuzzy model for power system operation is presented. Uncertainties in loads and generations are modeled as fuzzy numbers. System behavior under known (while uncertain) injections is dealt with by a DC fuzzy power flow model. System optimal (while uncertain) operation is calculated with linear programming procedures in which the problem nature and structure allow some efficient techniques such as Dantzig-Wolfe decomposition and dual simplex to be used. Among the results, one obtains a fuzzy cost value for system operation and possibility distributions for branch power flows and power generations. Some risk analysis is possible, as system robustness and exposure indices can be derived and hedging policies can be investigated.

Abstract
In this paper, a fuzzy model for power system operation is presented. Uncertainties in loads and generations are modelled as fuzzy numbers. System behavior under known (while uncertain) injections is dealt with by a DC fuzzy power flow model. System optimal (while uncertain) operation is calculated with linear programming procedures where the problem nature and structure allows some efficient techniques such as Dantzig Wolfe decomposition and dual simplex to be used. Among the results, one obtains a fuzzy cost value for system operation and possibility distributions for branch power flows and power generations. Some risk analysis is possible, as system robustness and exposure indices can be derived and hedging policies can be investigated.

Abstract
The power flow is the fundamental tool for the study of power systems. The data for this problem are subject to uncertainty. This paper uses interval arithmetic to solve the power flow problem. Interval arithmetic takes into consideration the uncertainty of the nodal information, and is able to provide strict bounds for the solutions to the problem: all possible solutions are included within the bounds given by interval arithmetic. Results are compared with those obtainable by Monte Carlo simulations and by the use of stochastic power flows. Object oriented programming techniques make it possible to use interval arithmetic with minimal modifications to existing software. However, to reduce the conservatism inherent in all interval curtest computations, the paper describes an iterative method used to obtain the "hull" of the solution set.

Abstract
A new type of bus for load flow analysis is proposed in this paper; this type of bus, named PX, is particularly suited for modelling elements like static compensators or asynchronous generators. The inclusion of this PX bus in the Fast Decoupled Load Flow method is presented and discussed. Numerical results are reported when applying this approach to solve load flow problems in two standard systems.

Abstract
A fuzzy AC load flow model is presented in which fuzzy data are used to obtain possibility distributions of voltages, active and reactive flows and losses, currents, and generated powers. These distributions are compared with the ones obtained through a Monte Carlo based simulation in order to evaluate the errors inherent to the fuzzy AC load flow.