Nonlinear Analysis: Real World Applications 12 (2011) 2077–2090
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Nonlinear Analysis: Real World Applications
journal homepage: www.elsevier.com/locate/nonrwa
Approximate analytic solutions to Radulet equations for the analysis of
electromagnetic transients in single-phase power transmission lines
J. Arturo Mendez Navarro
a,∗
, Elena I. Kaikina
b
, Héctor F. Ruiz
a
, Leonardo Guardado Z.
a
,
Alejandro Castellanos
a
a
Programa de Graduados e Investigación en Ingeniería Eléctrica, Instituto Tecnológico de Morelia, C.P. 58120, Morelia, Michoacán, Mexico
b
Instituto de Matemáticas UNAM, Campus Morelia, C.P. 58180, Morelia, Michoacán, Mexico
article info
Article history:
Received 17 June 2010
Accepted 24 December 2010
Keywords:
Radulet
Transmission lines
abstract
In this work, an analytic development for a transmission line with a corona effect for
simulating an electromagnetic transient is presented. The asymptotic solution for the
Radulet equations in which a nonlinear term is presented is obtained. The study is carried
out for a single-phase transmission line. The electrical parameters for an overhead line
are defined and several formulations for their calculation are presented. The frequency
dependence of the electrical parameters is considered. In the first part, the linear problem
solution is found; the Fourier and Laplace transforms are applied with respect to distance
and time respectively. After finding the solution in the Fourier–Laplace domain, which
is expressed in terms of a Green’s function integral, an approximate analytical solution
is obtained in the distance–time domain by means of asymptotic methods. Finally, the
nonlinear solution is found using as a first approach the linear solution. The results obtained
show an attenuation in the voltage wave due to the corona effect.
© 2010 Elsevier Ltd. All rights reserved.
1. Introduction
In 1970 Radulet et al. [1] proposed
v
x
+ L
0
i
t
+ ∂
t
∫
t
0
r (t − τ)i(τ)dτ = 0,
i
x
+ C
0
v
t
+ ∂
t
∫
t
0
g (t − τ)v(τ)dτ = 0
(1.1)
for a single-phase transmission line. These equations take into account the skin effect in the conductor and the relaxation
effect in the dielectric. They are expressed in terms of transient parameters and the telegrapher’s equations are a particular
case of them.
The terms r (t ) and g (t ) are called the transient line resistance and transient line conductance, respectively. The function
r (t ) is defined as the time variation of the line voltage per unit length after the application of a unit-step current (i = u(t )).
In the same way g (t ) is defined as the time variation of the line current, per unit length, after the application of a unit-step
∗
Corresponding author.
E-mail addresses: jam_arturo@hotmail.com (J.A. Mendez Navarro), ekaikina@matmor.unam.mx (E.I. Kaikina), hruiz@itmorelia.edu.mx (H.F. Ruiz),
lguarda@elec.itmorelia.edu.mx (L. Guardado Z.).
1468-1218/$ – see front matter © 2010 Elsevier Ltd. All rights reserved.
doi:10.1016/j.nonrwa.2010.12.023