Abstract
The main purpose of this paper is the development of an optimization model to design grounding grids in electrical substations. The design of a grounding grid in a substation is formulated as a mixed-integer linear programming problem. The developed optimization model incorporates the constructive Characteristics, as well as the technical and security requirements inherent to the construction, installation and operation of these grids. The model includes variables defining the grid characteristics according to the configurations admitted by the designer, which are selected amongst a set of pie-selected grounding designs. The definition of these configurations includes the geometry of the grid, the depth at Which the conductors will be installed and the radius of the conductor. A finite number of configurations can be generated before running the optimization process by considering all the variables in accordance with the IEEE Std 80-2000. The optimization problem also includes safety constraints related with the maximum allowed touching and step voltages, which are defined according to the fibrillation discharge limits. These fibrillation discharge limits are defined by IEEE Std 80-2000 for low frequencies for high frequencies. the limits are not the same as in 50 Hz). The model also includes the equivalent impedance of the transmission line supplying the substation where it will be located the grounding grid to be designed. As a result, the problem outputs define the most adequate grounding grid among the possible pre-selected configurations. This selection is driven by the total investment and installation costs, corresponding to the objective of the optimization model. To illustrate the interest of this research, the paper includes a case study based oil a real Situation, as all example of a potential application of this approach for engineering grounding design. Finally, it should also be referred that the scope of application of this methodology is potentially very wide given that it is in accordance with the specifications defined by the IEEE Std 80-2000.

Abstract
This paper presents an enhanced version of an AC Fuzzy Power Flow model designed to integrate correlation data between nodal injections. The model gives the user the possibility to specify fuzzy numbers to represent the possible behavior of loads and generations and outputs fuzzy membership functions for voltage magnitudes and phases, active and reactive flows, losses and generations. The algorithm is organized in two basic steps. The first one corresponds to a linearized procedure while the second aims at introducing correlated data leading to a reduction of the width of the membership output functions. In a final section, we present results obtained with a case study based on a didactic power system to illustrate and highlight details of the proposed models.

Abstract
In this paper we describe two approaches developed by two research teams to address the topology identification problem in the scope of state estimation. Both approaches aim at enlarging the traditional concept of strict state estimation, assuming that the network topology is pre-determined and is fixed. In fact, we are generalizing state estimation, enlarging its domain and aiming at obtaining topology information from a state estimation run. Apart from the description of those two techniques, the paper includes a'set of tests performed over the same test system in order to illustrate the interest of the approaches and to evaluate their performances. © 2001 IEEE.

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
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.

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.