Published

2015-09-01

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

Una fórmula recursiva para la evaluación de la impedancia de retorno por tierra en cables subterráneos

DOI:

https://doi.org/10.15446/ing.investig.v35n3.49391

Keywords:

Earth-return impedance, Pollaczek’s integral, Wedepohl’s integral, infinite series expansion, recursive formula, buried cables, Numerical Laplace Transform (NLT). (en)
Impedancia de retorno por tierra, Integral de Pollaczek, Integral de Wedepohl, serie infinita, fórmula recursiva, cables subterráneos, Transformada Numérica de Laplace (NLT). (es)

Downloads

Authors

  • Reynaldo Iracheta CENTRO DE INVESTIGACIÓN EN MATEMÁTICAS

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.

En 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 ana-lítica, 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. Finalmen-te, 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.

Dimensions

PlumX

Article abstract page views

1124

Downloads

Download data is not yet available.

How to Cite

A Recursive Formula for the Evaluation of Earth Return Impedance on Buried Cables. (2015). Ingeniería E Investigación, 35(3), 34-43. https://doi.org/10.15446/ing.investig.v35n3.49391
Crossref
Scopus
Google Scholar
Europe PMC

License

Copyright (c) 2015 Reynaldo Iracheta

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 International License.

The authors or holders of the copyright for each article hereby confer exclusive, limited and free authorization on the Universidad Nacional de Colombia's journal Ingeniería e Investigación concerning the aforementioned article which, once it has been evaluated and approved, will be submitted for publication, in line with the following items:

1.    The version which has been corrected according to the evaluators' suggestions will be remitted and it will be made clear whether the aforementioned article is an unedited document regarding which the rights to be authorized are held and total responsibility will be assumed by the authors for the content of the work being submitted to Ingeniería e Investigación, the Universidad Nacional de Colombia and third-parties;

2.    The authorization conferred on the journal will come into force from the date on which it is included in the respective volume and issue of Ingeniería e Investigación in the Open Journal Systems and on the journal's main page (https://revistas.unal.edu.co/index.php/ingeinv), as well as in different databases and indices in which the publication is indexed;

3.    The authors authorize the Universidad Nacional de Colombia's journal Ingeniería e Investigación to publish the document in whatever required format (printed, digital, electronic or whatsoever known or yet to be discovered form) and authorize Ingeniería e Investigación to include the work in any indices and/or search engines deemed necessary for promoting its diffusion;

4.    The authors accept that such authorization is given free of charge and they, therefore, waive any right to receive remuneration from the publication, distribution, public communication and any use whatsoever referred to in the terms of this authorization.