A closed-form approximation for ground return impedance of underground cables

Saad, Omar M.; Gaba, Gurjot Singh; Giroux, M.

doi:10.1109/61.517514

Cited by 82 publications

(45 citation statements)

References 4 publications

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“…El modelo propuesto por Saad, Gaba y Giroux [19] es considerado aceptable para cables subterráneos, debido a la buena aproximación en sus resultados con respecto a la integral de Pollaczek. Por tal razón, en este artículo se utilizará este modelo para calcular la impedancia de retorno por tierra, el cual es dado por las ecuaciones (18) …”

Section: Impedancia De Retorno Por Tierraunclassified

Análisis de formulaciones aproximadas de impedancia interna para el estudio de transitorios de alta frecuencia en cables subterráneos de alta tensión

et al. 2014

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En este artículo se presenta un análisis de las formulaciones aproximadas de impedancia interna para el estudio de transitorios de alta frecuencia en cables subterráneos de alta tensión. El análisis se desarrolla en el dominio de la frecuencia y la conversión al dominio del tiempo se realiza utilizando la transformada rápida de Fourier. El cable se modela como una línea de transmisión multiconductora, utilizando análisis modal y la teoría de redes de dos puertos. Las formulaciones aproximadas de impedancia interna que se analizan son las propuestas por Gary y Wedepohl-Wilcox, las cuales son utilizadas en el modelado de líneas de transmisión aérea y subterránea, respectivamente. Para efectuar el análisis se realiza una comparación de las formulaciones aproximadas con el modelo exacto de impedancia interna y se determina el error relativo de cada formulación para los valores reales como para los valores imaginarios. Los resultados muestran que la formulación aproximada propuesta por Gary para el modelado de líneas de transmisión aéreas se puede utilizar en cables subterráneos para analizar fenómenos transitorios electromagnéticos de alta frecuencia con resultados aceptables. Para realizar el estudio comparativo de las formulas aproximadas de impedancia interna se propone una serie de casos de estudios en los cuales se determina la magnitud del voltaje transitorio, el tiempo de viaje y la atenuación de la onda en líneas monofásicas subterráneas utilizando diferentes longitudes.

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Section: Impedancia De Retorno Por Tierraunclassified

Análisis de formulaciones aproximadas de impedancia interna para el estudio de transitorios de alta frecuencia en cables subterráneos de alta tensión

et al. 2014

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“…The accuracy of the results was measured with the criterion of absolute percent error. By comparing absolute errors in Figures 6 and 7, one can say that Saad et al (1996) formula gives significant errors, greater than 1%, at high frequency. Oppositely, the recursive formula and the numerical integration give accurate results, smaller than 0.1 % over the entire frequency range.…”

Section: Typical Case Of a Power System Of Buried Cablesmentioning

confidence: 99%

“…In this section the self and mutual earth return impedances (Z T ) are evaluated with three different methods: a) the recursive formula proposed in this paper, b) the numerical integration method "quadl" (Gander and Gautschi, 2000), and c) the approximated formula published by Saad et al (1996). The validation test consists of comparing the frequency responses obtained with these three methods through the absolute percent error.…”

Section: Case Studiesmentioning

confidence: 99%

“…These expressions are given by a set of improper integrals that do not have an analytic closed form solution. Traditionally, numerical integration methods and approximate formulas have been widely discussed in the specialized literature to solve these improper integrals (Ametani, 1980;Deri et al, 1981;Dubanton et al, 1969;Legrand et al, 2008;Nguyen, 1998;Papagiannis et al, 2005;Saad et al, 1996;Uribe et al, 2004 andZou et al, 2011). It has been demonstrated that both approaches can be implemented successfully for solving Carson's integral, whose integrand behavior is non-oscillatory.…”

Section: Introductionmentioning

confidence: 99%

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A Recursive Formula for the Evaluation of Earth Return Impedance on Buried Cables

Iracheta¹

2015

ing.inv.

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This paper presents an alternative solution based on infinite series for the accurate and efficient evaluation of cable earth return impedances. This method uses Wedepohl and Wilcox's transformation to decompose Pollaczek's integral in a set of Bessel functions and a definite integral. The main feature of Bessel functions is that they are easy to compute in modern mathematical software tools such as Matlab. The main contributions of this paper are the approximation of the definite integral by an infinite series, since it does not have analytical solution; and its numerical solution by means of a recursive formula. The accuracy and efficiency of this recursive formula is compared against the numerical integration method for a broad range of frequencies and cable configurations. Finally, the proposed method is used as a subroutine for cable parameter calculation in the inverse Numerical Laplace Transform (NLT) to obtain accurate transient responses in the time domain.Keywords: Earth-return impedance, Pollaczek's integral, Wedepohl's integral, infinite series expansion, recursive formula, buried cables, Numerical Laplace Transform (NLT). RESUMENEn este artículo se presenta una solución alternativa basada en series infinitas para la evaluación precisa y eficiente de la impedancia de retorno por tierra en cables subterráneos. En este método se utiliza la transformación de Wedepohl y Wilcox para descomponer la integral impropia de Pollaczek en un conjunto de funciones de Bessel más una integral definida. La característica principal de las funciones de Bessel es que son fáciles de calcular con herramientas modernas de software matemático como Matlab. Las principales contribuciones de este artículo son la aproximación de la integral definida por una serie infinita, dado que no tiene solución analítica, y su evaluación numérica por medio de una fórmula recursiva. La precisión y eficiencia de la fórmula recursiva se compara contra el método de integración numérica para un amplio rango de frecuencias y configuraciones de cables subterráneos. Finalmente, se utiliza el método propuesto como una subrutina de cálculo de parámetros de cables en la Transformada Numérica de Laplace (NLT) para obtener respuestas transitorias precisas en el dominio del tiempo.Palabras clave: Impedancia de retorno por tierra, Integral de Pollaczek, Integral de Wedepohl, serie infinita, fórmula recursiva, cables subterráneos, Transformada Numérica de Laplace (NLT).

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“…The phase series impedance matrix describing one minor section is comprised of the cable conductors' self and mutual impedances with earth return. For high frequency studies, the calculations of these impedances involve complex calculations using Bessel's functions -some of the most important contributions are [75,76,77,78,79]. At power frequency, simplification can, however, be made [80].…”

Section: Systemsmentioning

confidence: 99%

Online Location of Faults on AC Cables in Underground Transmission Systems

Jensen

2014

Springer Theses

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University in partial fulfilment of the requirements for the PhD degree in Electrical Engineering. The research has been carried out between the 1.09.2010 and the 15.07.2013 at the Department of Energy Technology for Energinet.dk by which I was hired as a PhD-student for the entire project period.The project has been followed full time by two supervisors: Professor Claus Leth Bak (Department of Energy Technology) and Dr. Unnur Stella Gudmundsdottir (Energinet.dk).Energinet.dk has fully funded the research leading to this thesis "Online Location of Faults on AC Cables in Underground Transmission Systems". This funding has been vital for this research project. Travelling to conferences, two visits at forging research institutions, renting of laboratory equipment and performance of and field measurements was made possible thanks to support from the company. During the projet period I supervised two master projects and thought one semester course in power system transients.The scientific papers written as a part of this PhD are included in the back of both the printed version of the thesis as well as in the PDF-file. The papers should not be considered a part of this monograph, but are enclosed if the reader is interested.This thesis has five parts and appendices. An overall literature reference list is presented at the end of the main report. A list of the authored publications is presented at the end of the thesis. Literature references are shown as [i], where i is the number of the literature in the reference list. Tables, figures and equations are shown as C.F, where C is the chapter number and F is a unique number for the figure or table. AcknowledgementsI owe gratitude to many people who helped me in different ways. I would like to thank:• My supervisors, Claus Leth Bak and Unnur Stella Gudmundsdottir for all their help, comments, and many technical discussions during the last three years.• Carl-Erik Madsen, Henrik Kastberg and Carl Willi Hansen for their help with carrying out the field measurements. In the same regards, a very special thanks is extended to Filipe Faria da Silva and Unnur Stella Gudmundsdottir for participating during all measurements.• Filipe Faria da Silva for numerous technical discussions, for reading large parts of the thesis and for many good times in the office.• Rasmus Schmidt Olsen, Unnur Stella Gudmundsdottir, Joachim Holbøll, Per Balle Holst, Poul Erik Pedersen, Thomas Kvarts, Carsten Rasmussen, Claus Leth Bak and Bjarne Søndergaard Bukh for their contributions and comments during the project period.• Everyone at the transmission department at Energinet.dk for their contributions.• Professor Ali Abur for his hospitality and comments to my work during my three month stay at North Eastern University in Boston 2012.• • A special thanks to Dr. Jeewantha Da Silva for numerous discussions, valuable advice and guidance throughout the entire project period.• To Prof. Athula Rajapakse and PhD-student Kasun Nanayakkara both from University of Manitoba, Winnipeg, Manitoba for valuable discuss...

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A closed-form approximation for ground return impedance of underground cables

Cited by 82 publications

References 4 publications

Análisis de formulaciones aproximadas de impedancia interna para el estudio de transitorios de alta frecuencia en cables subterráneos de alta tensión

Análisis de formulaciones aproximadas de impedancia interna para el estudio de transitorios de alta frecuencia en cables subterráneos de alta tensión

A Recursive Formula for the Evaluation of Earth Return Impedance on Buried Cables

Online Location of Faults on AC Cables in Underground Transmission Systems

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