Fermín Navarrina

A Numerical Formulation for Grounding Analysis in Stratified Soils

The design of safe grounding systems in electrical installations is essential to assure the security of the persons, the protection of the equipment, and the continuity of the power supply. To achieve these goals, it is necessary to compute the equivalent electrical resistance of the system and the potential distribution on the earth surface when a fault condition occurs. This paper presents a formulation for the analysis of grounding systems embedded in stratified soils, on the basis of the boundary element method (BEM). Suitable arrangements of the final discretized equations allow the use of highly efficient analytical integration techniques derived by the authors for grounding systems buried in uniform soils. Feasibility of this approach is demonstrated by applying the HEM formulation to the analysis of a real grounding system with a two-layer soil model.

High order sensitivity analysis in shape optimization problems

Abstract A formulation for high order directional differentiation of functions defined through integration is presented. The formulation has been developed initially for sensitivity analysis in optimal shape design problems by the finite elements method. However, its application range is much wider. Explicit analytical expressions are given for sequential directional derivatives. Special emphasis has been made in holding recurrence and simplicity of intermediate operations. The proposed scheme does not depend strongly on any particular form of the state equations, and its numerical implementation in finite elements method programs can be considered easy and efficient. As an example, up to second order sensitivity techniques are applied to the optimization of a concrete roof. Structural analysis has been performed in linear elastic conditions, with quadratic three-dimensional elements for the discretization of the roof.

Grounding Analysis in Heterogeneous Soil Models: Application to Underground Substations

Most of the research and development work done until now in earthing analysis is devoted to cases where the soil can be modelled in terms of an homogeneous and isotropic semi-infinite continuous medium, being the soil resistivity an order of magnitude higher than the resistivity of the electrode itself. Furthermore, all formulations of this classical (single-layer) type can be quite easily extended for solving more complex cases in which the soil is stratified in two or more layers of different resistivities. Assuming that the soil is regularized before installing the earthing grid and that the surface is leveled right after (prior to the equipment being assembled and brought into service) this approach is suitable for computing the equivalent resistance and the step and touch voltage in most large electrical over ground facilities. This important category includes all step up and step-down transmission substations, as well as a number of distribution substations indeed. Nevertheless, the current trend in electric power Engineering moves in another direction, due to the growing preference for smaller underground substations as a general rule. This pushes the need for developing new earthing analysis techniques that could be applied to facilities of this kind. In an attempt to do so, we present a mathematical model for earthing analysis in soils with enbedded finite regions of different resistivities. We also present the Boundary Element formulation that we propose for the numerical solution of the resulting equations, which implemention is being considered at present. Finally, we present some preliminary results of the earthing analysis of an underground substation. These results have been obtained by means of an approximated technique which details will be given in forthcoming publications.

Numerical Simulation of Multilayer Grounding Grids in a User-friendly Open-source CAD Interface

In this paper we present TOTBEM: a freeware application for the in-house computer aided design and analysis of grounding grids. The actual version of the software is available for testing purposes (and also use) at no cost and can be run on any basic personal computer (as of 2011) with no special requirements. The distribution kit consists in a single ISO bootable image file that can be freely downloaded from the Internet and copied into a DVD or a USB flash memory drive. The application runs on the Ubuntu 10.04 (Lucid Lynx) LTS release of Linux and can be easily started by just booting the system from the live DVD/USB that contains the downloaded file. This operation does not modify the native operative system nor installs any software in the computer, but the application is still fully operational while the live DVD/USB is taking control. The pre- and post-processing engines of the application have been built on top of the open source SALOME platform toolkit. On the other hand, the analysis part of the code is based on the Boundary Element Method (BEM). The implemented BEM formulation (that has been presented by the authors in previous publications) is suitable for computing the equivalent resistance and the step and touch voltage in most large electrical over ground substations with a grounding grid embedded in a single- or multi-layer stratified soil.

Comprehensive Model for Fatigue Analysis of Flexible Pavements Considering Effects of Dynamic Axle Loads

A comprehensive model for the fatigue analysis of flexible pavements that considers the effects of dynamic axle loads is presented in this paper. The main objective of this work is to quantify the reduction in the structural service life of the pavement resulting from the rise of the dynamic axle loads exerted by traffic as the progressive deterioration of the road profile occurs. First, the procedure for the fatigue analysis of flexible pavements, as defined in the Spanish Standard 6.1-IC, is explained in detail. The implementation presented here is specific for this standard, but the underlying concepts are not restrictive and the model can be easily adapted to fit the distinctive features of other regulations. Second, the concepts of accumulated damage and structural service life are formalized in mathematical terms. Next, the introduction of dynamic axle loads leads to the definition of a suitable accumulated fatigue damage indicator that takes into account these effects. Dynamic axle loads are introduced in this formulation by means of the dynamic load amplification factor. For the quantification of this factor, the quarter-car model is extended to allow for computing the time evolution of the dynamic axle load exerted by a heavy vehicle on the pavement. The model is completed by adding a simple procedure for simulating how the road profile deteriorates over time. Finally, an application example is presented.

Numerical Modeling of Grounding Systems for Aboveground and Underground Substations

In this paper, we present a numerical model based on the boundary element method that allows to analyze the grounding systems (GSs) of aboveground and underground substations under different locations and considerations. The proposed formulation allows to consider most of the specific properties and conditions of this kind of substations, i.e., complex geometry, different material properties, and different grounding grid configurations, and to study phenomena like transferred potentials by earthing electrodes. Finally, GSs of real substations have been analyzed as application examples.