Modelización numérica de problemas de potenciales transferidos por redes de tierra mediante el método de los elementos de contorno

Congresso de Métodos Computacionais em Engenharia, Lisboa, 31 de Maio - 2 de Junho, 2004[Resumen] El análisis y diseño de tomas de tierra en subestaciones eléctricas requiere el cálculo de la distribución de los niveles de potencial sobre la superficie del terreno y la resistencia equivalente de la red de tierras, cuando tiene lugar una derivación de corriente eléctrica al terreno. En este artículo se presenta una formulación numérica basada en el método de elementos de contorno para el análisis de un problema común en la ingeniería eléctrica, como es la existencia de potenciales transferidos en una instalación de puesta a tierra. La transferencia de potenciales entre la zona puesta a tierra y puntos exteriores de la misma a través de conductores enterrados (por ejemplo, circuitos de comunicación, neutros, tuberías, raíles o cierres periféricos metálicos) puede producir serios problemas de seguridad. Dado que se dispone de una herramienta de cálculo efectiva y fiable para el análisis de redes de tierra, se propone su empleo para el análisis de estos potenciales inducidos. Para ello, en este artículo se resume brevemente la formulación numérica empleada y se presenta el análisis del problema de transferencia de potenciales. Finalmente, se muestran algunos ejemplos haciendo uso de la geometría de tomas de tierra de subestaciones eléctricas reales.Ministerio de Ciencia y Tecnología; DPI2001-055

A numerical approach based on the BEM for computing transferred earth potentials in grounding analysis

Second MIT Conference on Computational Fluid and Solid Mechanics, Cambridge, USA[Abstract] In this paper we present a numerical approach based on the Boundary Element Method for the analysis of a very common problem in electrical engineering practice: the existence of transferred earth potentials in a grounding installation [1]. We propose a numerical approach to analyze this phenomenum. We demonstrate its feasibility by means of an application example with the geometry of a real grounding system.Ministerio de Ciencia y Tecnología; DPI2001-055

Formulaciones numéricas para el cálculo, diseño y evaluación de la seguridad de las redes de tierra de instalaciones eléctricas

Congreso de Métodos Numéricos en Ingeniería 2005, Granada, SpainLa determinación de los niveles de potencial en la superficie del terreno cuando tiene lugar una derivación de corriente es fundamental en el cálculo y diseño de redes de tierras de subestaciones eléctricas. En el presente trabajo se presenta una formulación numérica del método de elementos de contorno para el análisis de un problema común en la ingeniería eléctrica, como es la existencia de potenciales transferidos en una instalación de puesta a tierra. La transferencia de potenciales entre la zona puesta a tierra y puntos exteriores de la misma a través de conductores enterrados tales como circuitos de comunicación, neutros, tuberías, raíles o cierres periféricos metálicos, puede producir serios problemas de seguridad. En este artículo se analizan y calculan problemas de potenciales inducidos por tomas de tierras de subestaciones considerando modelos de terreno no uniformes y concretamente estratificados en dos capas. Así, en primer lugar se resume brevemente la formulación numérica empleada y el modelo bicapa considerado y se presenta el análisis del problema de transferencia de potenciales. Finalmente, se muestran algunos ejemplos haciendo uso de la geometría real de una red de tierras de una subestación eléctrica considerando diversos tipos de modelo de terreno

Why do computer methods for grounding analysis produce anomalous results?

Aceptado en "IEEE transactions on power delivery"[Abstract] Grounding systems are designed to guarantee personal security, protection of equipments and continuity of power supply. Hence, engineers must compute the equivalent resistance of the system and the potential distribution on the earth surface when a fault condition occurs [1], [2], [3]. While very crude approximations were available until the 70’s, several computer methods have been more recently proposed on the basis of practice, semi-empirical works and intuitive ideas such as superposition of punctual current sources and error averaging [1], [3], [4], [5], [6]. Although these techniques are widely used, several problems have been reported. Namely: large computational requirements, unrealistic results when segmentation of conductors is increased, and uncertainty in the margin of error [2], [5]. A Boundary Element formulation for grounding analysis is presented in this paper. Existing computer methods such as APM are identified as particular cases within this theoretical framework. While linear and quadratic leakage current elements allow to increase accuracy, computing time is reduced by means of new analytical integration techniques. Former intuitive ideas can now be explained as suitable assumptions introduced in the BEM formulation to reduce computational cost. Thus, the anomalous asymptotic behaviour of this kind of methods is mathematically explained, and sources of error are rigorously identified

Numerical computation of grounding grids

[Abstract] Grounding systems are designed to preserve human safety and grant the integrity of equipments under fault conditions. To achieve these goals, the equivalent electrical resistance of the system must be low enough to ensure that fault currents dissipate (mainly) through the grounding electrode into the earth, while maximum potential gradients between close points on the earth surface must be kept under certain tolerances (step and touch voltages) [1,2]. In this paper we present a Boundary Element approach for the numerical computation of grounding systems. In this general framework, former intuitive widespread techniques (such as the Average Potential Method) can be identified as the result of specific choices for the test and trial functions, as well as suitable assumptions introduced in the BEM formulation to reduce computational cost. Linear and higher order elements can be used in order to increase accuracy avoiding excessive segmen- tation. On the other hand, computing time is kept under acceptable levels by means of analytical integration techniques and semi-iterative methods for solving linear equations systems. Finally, an application to a real problem is presented

Fórmulas analíticas de integración para el cálculo de tomas de tierra mediante el método de elementos de contorno

2º Congreso de Métodos Numéricos en Ingeniería, 1993, A Coruña[Resumen] La resolución de problemas en Teoría del Potencial, y en particular, el cálculo de tomas de tierra en instalaciones eléctricas, ha adquirido nuevas perspectivas mediante la aplicación del Método de Elementos de Contorno [4,5]. Éste ha permitido la obtención de formulaciones generalistas que incluyen a los distintos procedimientos intuitivos de cálculo empleados hasta el momento [2,3]. El desarrollo de la formulación completa basada en el Método de Elementos de Contorno, y su discusión, pueden encontrarse en trabajos recientes [4,5,6], en tanto que en este artículo se presentan las técnicas de integración analítica desarrolladas para el tratamiento de sus ecuaciones discretizadas. En primer lugar se deriva el cálculo del potencial generado por un electrodo en un punto del espacio, que es la base para los cálculos de las contribuciones elementales (integrales) del sistema de ecuaciones lineales obtenido de la discretización del problema en elementos de contorno [6]. Estas contribuciones, que pueden interpretarse como medidas ponderadas de los potenciales generados por un electrodo sobre otro en el espacio, se analizan para distintas posiciones relativas características de los electrodos

On the anomalous asymptotic performance of the regular computer methods for grounding analysis

15th International Conference on Boundary Element Technology, Detroit, USA[Abstract] Grounding systems are designed to guarantee personal security, protection of equipments and continuity of power supply. Hence, engineers must compute the equivalent resistance of the system and the potential distribution on the earth surface when a fault condition occurs [1, 2, 3]. While very crude approximations were available until the 70’s, several computer methods have been more recently proposed on the basis of practice, semi-empirical works and intuitive ideas such as superposition of punctual current sources and error averaging [1, 3, 4, 5, 6]. Although these techniques are widely used, several problems have been reported. Namely: large computational requirements, unrealistic results when segmentation of conductors is increased, and uncertainty in the margin of error [2, 5]. A Boundary Element formulation for grounding analysis is presented in this paper. Existing computer methods such as APM are identified as particular cases within this theoretical framework. While linear and quadratic leakage current elements allow to increase accuracy, computing time is reduced by means of new analytical integration techniques. Former intuitive ideas can now be explained as suitable assumptions introduced in the BEM formulation to reduce computational cost. Thus, the anomalous asymptotic behaviour of this kind of methods is mathematically explained, and sources of error are rigorously identified.Ministerio de Educación y Cultura; 1FD97-0108Ministerio de Educación y Cultura; DPI2001-055

A numerical formulation for grounding analysis in stratified soils

Enviado a "IEEE Transactions on Power Delivery"[Abstract] 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. In order 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. In this paper we present a formulation for the analysis of grounding systems embedded in stratified soils, on the basis of Boundary Element Method (BEM). Suitable arrangements of the final discretized equations allow to use the highly efficient analytical integration techniques derived by the authors for grounding systems buried in uniform soils. The feasibility of this approach is demostrated by applying the BEM formulation to the analysis of a real grounding system with a two-layer soil model.Ministerio de Educación y Cultura; 1FD97-010

Analytical integration techniques for earthing grid computation by boundary element methods

[Abstract] Analysis and design of substation earthing involves computing the equivalent resistance of grounding systems, but also distribution of potentials on the earth surface due to fault currents [1]. While very crude approximations were available in the sixties, several methods have been proposed in the last two decades, must of them on the basis of intuitive ideas such as superposition of punctual current sources and error averaging [2,3]. Although these techniques represented a significant improvement in the area of earthing analysis, a number of problems have been reported. Namely: large computational requirements, unrealistic results when segmentation of conductors is increased, and uncertainty in the margin of error [3]. In this paper, a 1D Boundary Element formulation is presented. Several widespread intuitive methods (such as APM) are identified as particular cases of this general approach. Thus, former intuitive ideas can now be explained as suitable assumptions introduced in the BEM formulation to reduce computational cost. The anomalous asymptotic behaviour of this kind of methods is mathematically explained, and sources of error are pointed out. While linear and parabolic leakage current elements allow to increase accuracy, computing time is drastically reduced by means of new analytical integration techniques. Finally, an application example to a real problem is presented