Marco A. O. Schroeder

Lightning Response of Grounding Grids: Simulated and Experimental Results

The response of grounding grids subjected to currents with typical waveforms of first and subsequent lightning return strokes is analyzed, based on experimental and simulated results. Parameters, which characterize this response, such as the grounding potential rise, impulse impedance, impulse coefficient, and effective grid area are determined for grids buried in soils of low, moderate, and high resistivity, varying the grid dimension and considering the frequency dependence of soil parameters. Based on such results, expressions to obtain the impulse impedance from the low-frequency resistance are derived.

An Adaptive Deep-Cut Ellipsoidal Algorithm Applied to the Optimization of Transmission Lines

This paper presents a computational tool intended to calculate and minimize the electric fields at ground level of high surge impedance loading transmission lines (TLs). This type of TL achieves higher power transmission rates utilizing optimized configuration for the phase conductors. This method is advantageous over other actions taken by the utility company, such as increasing the maximum operation temperature of the line, increasing the size of the conductors, or the utilization of multiple conductors per phase. In this paper, an enhanced deep-cut ellipsoidal method is applied to find a new optimized configuration for the phase conductors. The new proposed configuration results in reduced profiles of electric fields. Two different TLs are analyzed and optimized.

Periodic Boundary Conditions in the Natural Element Method

The purpose of this paper is to introduce periodic and antiperiodic boundary conditions in the natural element method (NEM). It is shown that as the NEM shape functions verify the Kronecker delta property, the imposition of such boundary conditions can be done in an easy way as in the finite-element method (FEM). These boundary conditions are important because they allow exploitation of the inherent symmetry of the electromagnetic devices. Therefore, with these techniques the NEM can now easily take advantage of the symmetry of electrical machines. The proposed approach is evaluated, and its results are compared with those obtained by the traditional FEM.

Electromagnetic Scattering Analysis of Arbitrary Structures by the Natural Element Method Coupled With Absorbing Boundary Condition

The problem of determining the electromagnetic scattering of arbitrary structures consisting of both dielectric and conducting materials are analyzed in this paper by the natural-element method coupled with the absorbing boundary condition (NEM-ABC). By this method, the target is first enclosed by a fictitious boundary. Maxwells equations are then solved by NEM inside and ABC is applied on the fictitious boundary. The results are compared with analytical and finite-element method-ABC ones which show the robustness, applicability and relevance of the method.

Voltage Distribution Along Earth Grounding Grids Subjected to Lightning Currents

This paper applies a rigorous electromagnetic model to determine the transient distribution of potentials along a substation earth grounding grid subjected to lightning currents. The obtained results show that, in the initial period of the transient, equipment pieces that are earth grounded at distinct points of the grid and are electrically linked (for example, by aerial communication cables) experience impulsive loop currents. Such loop currents can cause equipment malfunctions, failures, and damage. A remarkable conclusion of this paper is that such loop currents can reach substantial values even in the case of soils of low resistivity. Some practical aspects are highlighted in order to reduce the risks due to the nonuniform distribution of potentials along earth grounding.

Analysis of the cumulative probability distribution of the stroke angle in lightning incidence to three-phase overhead transmission lines

Lightning leaders follow a random behavior when approaching ground surface, so the usual assumption of a vertical stroke is not realistic. This paper is aimed at analysing the sensitivity of the shielding failure flashover rate (SFFOR) of three-phase overhead transmission lines to a probability distribution of the stroke angle, i.e. both vertical and non-vertical strokes. A modified Electrogeometric Model (mod-EGM), derived from a probabilistic computation of the exposure area of phase conductors is described. A computational code is developed in MATLAB, along with IEEE Flash algorithm implementation. Sensitivity analyses are carried out for a waist-type transmission tower. Results show that considering particularly vertical leaders may lead to underestimated values for flashover rates.

Influence of frequency-dependent soil electrical parameters on the grounding response to lightning

This paper presents a preliminary analysis of the influence of the frequency-dependent soil electric parameters conductivity and permittivity on the grounding response to lightning currents. The soil electric parameters are calculated at each frequency by means of different formulations based on experimental developments. The results show that the inclusion of frequency-dependent soil parameters leads to a reduction of the grounding impulse impedance. This reduction is more significant in case of subsequent strokes than in case of first stroke currents. Also, the order of such reduction varies depending on the formulation applied to calculate the variation of the soil parameters. Impulse coefficients below the unity are obtained when the frequency dependence of the soil parameters are included, even disregarding the soil ionization effects. These results contradict some presented in the traditional literature.

A Finite-Element Approach for Electric Field Computation at the Surface of Overhead Transmission Line Conductors

The purpose of this paper is to introduce a modified approach for the electric field computation at the surface of overhead transmission line (TL) conductors through the finite-element method (FEM). The proposed strategy is based on a spatial transformation, well-known as Kelvin transformation, resulting in a special way to treat the unbounded domain. Unlike other applications of the FEM in TLs, the suggested procedure aims to reduce the computational domain and the solution time, allowing an efficient numerical evaluation of the electric potential gradients, without the need of geometric simplifications of the conductors. Comparative results show that a more realistic treatment offers a better understanding of how electric fields operate near real conductors and, in addition, that the proposed approach can be used to provide an accurate design for conductor systems in TLs.

The surge impedance loading optimization by an adaptive Deep Cut Ellipsoidal algorithm

This paper presents a computational tool intended to achieves optimal configurations of conductors with capacity of transmission of energy improved. This arrangement is obtained by calculate and minimize of electric fields at ground level of High Surge Impedance Loading transmission lines. This type of transmission line has higher power transmission rates by utilizing optimized configuration for the conductors. In the present work, an enhanced Deep Cut Ellipsoidal Method is applied to find a new optimized configuration for the phase conductors. The Surge Impedance Loading of the suggested configuration is analyzed. The new proposed configuration results in reduced profiles of electric fields and higher power transmission capacity.

A non conventional configuration of transmission lines conductors achieved by an enhanced differential evolution optimization method

This paper presents a computational tool intended to calculate and minimize the electric fields at ground level of High Surge Impedance Loading transmission lines. This type of transmission line achieves higher power transmission rates by utilizing optimized configuration for the phase conductors. This method is advantageous over other actions taken by the utility company such as increasing the maximum operation temperature of the line, increasing the size of the conductors or the utilization of multiple conductor per phase. In the present work, an enhanced Differential Evolution Method is applied to find a non conventional optimized configuration for the phase conductors with reduced electric field profiles at ground level.