electric field effects of bundle and stranded conductors in overhead power lines

Electric Field Effects of Bundleand Stranded Conductors inOverhead Power LinesJORDI-ROGER RIBA RUIZ, ANTONIO GARCIA ESPINOSA, XAVIER ALABERN MORERA

Electrical Engineering Department, Universitat Politecnica de Catalunya, Barcelona, Spain

Received 18 July 2008; accepted 27 October 2008

ABSTRACT: High-voltage overhead power lines are a source of quasi-static electric and magnetic fields and

also of audible noise and electromagnetic interferences due to corona activity. Electrical engineers have the

responsibility to design and to maintain such lines, so it is very important that they acquire sufficient knowledge

about these subjects while they are studying. Bundle and stranded conductors modify the spatial distribution of

the electric field generated by the power line and also affect the corona onset conditions. This article describes the

implementation of a method that models the behavior of electric fields generated by any three-phase power line.

Different configurations of overhead power lines are analyzed. The proposed methodology has been contrasted

with results from other authors and with available experimental data. �2009 Wiley Periodicals, Inc. Comput Appl

Eng Educ 19: 107�114, 2011; View this article online at wileyonlinelibrary.com; DOI 10.1002/cae.20296

Keywords: electric field; corona effect; bundle conductors; stranded conductors; simulation

INTRODUCTION

The study of power lines is a fundamental topic in electrical

engineering undergraduate curriculum [1�3]. This topic

includes generation, transmission, and distribution of electrical

energy. Any powered electric wire produces an electric field in

the area that surrounds it. Electric fields are invisible vectorial

magnitudes. This invisibility and its vectorial nature mean that

its effects, strengths, and spatial distribution are difficult to

understand for most students. The objective of the practical

session proposed in this work is to improve students’ knowledge

of these subjects, to study the effects of bundle and stranded

conductors as well as to be an introduction to the study of the

corona effect.

The corona effect is a very complex phenomenon and is

characteristic of conductors carrying very high voltage. It

consists of an electrical discharge due to the ionization of the

air surrounding a conductor. Corona effect occurs when the

strength of the electric field exceeds a certain value but

conditions are insufficient to cause complete electrical break-

down of air. This phenomenon is of particular interest in high-

voltage engineering where non-uniform fields are unavoidable

[4]. Corona effect takes place in the region with higher

electrical stress. Thus, air surrounding the conductor can

become ionized—partially conductive—while regions more

distant do not become so. It has the effect of increasing the

apparent size of the conductor. Since the new conductive region

has a greater radius—is less sharp—the ionization may not

progress past this limited region. The principal negative effects

of corona phenomenon are energy losses and radio frequency

interferences (RFI), but it also causes deterioration of the

insulators and audible noise [5]. Meteorological conditions such

as fog, relative humidity, and frost can, notoriously, influence

the corona activity. High-voltage power lines are designed in

order to minimize the losses and electromagnetic emissions

associated with corona activity.

In this article, a method that permits the calculation of the

electric field distribution generated by high-voltage power lines

will be deduced and subsequently the electric fields generated by

different overhead power lines will be simulated. The program

also allows students to simulate the electric field strength in

points very close to the conductors’ surface in order to study the

corona effect. The effect of bundle and stranded conductors in

the electric field distribution in the vicinities of the power lines is

also studied.

In order to validate the proposed model, results obtained

from simulations are compared with experimental data reported

by other authors [6], resulting in strong agreement between

simulations and experimental data, as shown in Experimental

Validation of the Methodology Section.

The aim of teaching is to make student learning possible,

where retention rate is a key point. Retention rate is a measure

of the effectiveness in promoting student retention of the

material taught. It is well known that retention rate effectiveness

depends on the learning experiences and the media that was

used during instruction, that is, to say, the learning methodology

Correspondence to J.-R. Riba Ruiz ([email protected]).

� 2009 Wiley Periodicals Inc.

107

[7�8]. The retention rate for students who practice by doing is

higher than in other learning systems (lecture, reading, demons-

tration, or discussion group) [9]. The goal of the proposed

system is not only to focus students in the interpretation of a

standard executable program’s output results, but also encour-

age them to understand the physical and electrical laws involved

in the computation of electric field. To meet these objectives it

is very useful that students are able to write the source code of

the program, because in this task their effort is oriented towards

analyzing and thoroughly understanding the steps involved in

the computation of the electric field generated by overhead

power lines.

The Matlab package has been used for implementing the

programs necessary to compute the electric field. The choice of

this package is due to the fact that our students have previous

knowledge of Matlab and furthermore it is widely used in

university communities [10�13]. The software presented in this

work allows students to simulate the electric fields created by

any geometry of three-phase power lines.

COURSE STRUCTURE AND DETAILS

The method proposed in this article has been applied in a

practical session on the undergraduate Electrotecnia course at

the School of Industrial and Aeronautic Engineering of Terrassa

(ETSEIAT). It is part of the Electric Engineering Department at

the Universitat Politecnica de Catalunya (UPC, Spain). This

practical consists of a 2-h session. It was taught during

the second semester of the 2006�2007 academic year and

was well accepted by the students. It has been very successful,

and the majority of students have expressed their satisfaction

with the proposed learning methodology and content. In

the practical session realized in the laboratory of the school,

students write the source code—using the Matlab environ-

ment—under the guidance and supervision of their instructors.

In ETSEIAT, the courses are being offered in a 15-week

semester. The classes of Electrotecnia are four 1-h sessions in

each of the 15 weeks. Moreover, every 2 weeks the students are

grouped in teams of three to attend a practical session that lasts

a minimum of 2 h, depending on how students do their

assignments. On average, students dedicate four extra hours of

work in order to finish the calculations, simulations, and reports

related to each practical session. The laboratory reports are

submitted 2 weeks after each laboratory session.

DEDUCTION OF THE ELECTRIC FIELDGENERATED BY OVERHEAD POWER LINES

Electric field generated by power lines depends strongly on the

voltage between the conductors and the ground, and it is largely

independent of the current intensity that these conductors carry.

As the voltage of the conductors is a sinusoidal magnitude, it is

characterized by its root mean square (RMS) value. A balanced

three-phase system of voltages is assumed.

Calculation of the Electric Field Generated by anInfinite and Isolated Rectilinear Conductor

In order to deduce an expression for the electric field generated

by an infinite and isolated rectilinear conductor (conductor i),

the method of images [14] will be useful because the electrical

potential at ground level must be zero. This method supposes

that each real conductor has an image conductor with the same

electrical potential but with an opposite sign than the electrical

potential of the original conductor, as shown in Figure 1.

Figure 1 shows a very long rectilinear conductor and its

image conductor placed symmetrically with respect to the

ground plane.

From now on, the electric field components (Ex, Ey, and Ez)

and the electrical potentials (U) dealt with are complex magni-

tudes with real and imaginary parts, due to their sinusoidal

nature.

WhereasUs,i is the electrical potential on the surface of the

real conductor i with respect to ground potential (arbitrarily set

to zero), �Us,i is the electrical potential of the image conductor

i. This set-up generates an electric field at any point (x, y) in the

surrounding space.

We know that the electric field generated by any very long

rectilinear conductor is radial, which is to say that the com-

ponent Ez¼ 0.

Since this is a problem with a high degree of symmetry,

Gauss’s theorem can be appliedZ~E d~S ¼ Qint

eoð1Þ

where Qint is the total charge existing inside the integration

enclosure and eo the permittivity of air.

Figure 2 shows the Gaussian surface used to calculate the

electric field.

By applying Gauss’s theorem to the real conductor, the

result is

E1i2pr1L¼2pRiLsi

eo!E1i¼siRi

eo

1ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiðx�xiÞ2þðy�yiÞ2

q ð2Þ

where si is the conductor surface charge density.

The electric field generated by the image conductor at any

point (x, y) in space gives the result

Figure 1 Real conductor and conductor image.

108 RIBA RUIZ, ESPINOSA, AND MORERA

E2i ¼ �siRi

eo

1ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiðx� xiÞ2 þ ðyþ yiÞ2

q ð3Þ

Then, the electrical potential at any point in space can be

computed from the electric field as

Ui ¼ Ui1 þ Ui2 ¼ �Z

~E1i d~r1 �Z

~E2i d~r2 þ C ð4Þ

where C is an integration constant whose value depends on the

boundary conditions. By replacing expressions (2) and (3) in

expression (4), this leads to

Ui¼siRi

eolnr2

r1þC¼siRi

eoln

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiðx�xiÞ2þðyþyiÞ2ðx�xiÞ2þðy�yiÞ2

sþC ð5Þ

Boundary condition 1: The electrical potential at ground

level is set to zero, resulting in

Uið0; 0Þ ¼ siRi

eoln

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffix2i þ y2ix2i þ y2i

sþ C ! C ¼ 0 ð6Þ

Boundary condition 2: The electrical potential on the

surface of the conductor must be Us,i, leading to

Us;i ¼ Uiðxi; yi � RiÞ ¼ siRi

eoln

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffið2yi � RiÞ2

R2i

sð7Þ

From the approximation yi >> Ri, the result is

Us;i ¼ siRi

eoln2yi

Ri

! siRi

eo¼ Us;i

lnð2yi=RiÞ ð8Þ

resulting in

Ui ¼ Us;i

lnð2yi=RiÞ lnffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiðx� xiÞ2 þ ðyþ yiÞ2ðx� xiÞ2 þ ðy� yiÞ2

s¼ Us;i

ni

Ai

ð9Þ

where ni and Ai are, respectively,

ni ¼ ln

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiðx� xiÞ2 þ ðyþ yiÞ2ðx� xiÞ2 þ ðy� yiÞ2

s; Ai ¼ ln

2yi

Ri

ð10Þ

From Equation (9) the electric field at any point (x, y) in

the surroundings of conductor i can be obtained as

~Ei ¼ � @Ui

@x;@Ui

@y; 0

� �ð11Þ

Deduction of the Electric Field Generated by anInfinite and Isolated Rectilinear Conductors

From the electric field generated by a very long rectilinear

conductor, it is not possible to apply directly the superposition

principle in order to compute the total electric field generated by

n real conductors and their respective images. This is due to the

fact that the field of a conductor induces a superficial charge

density on the other conductors. For similitude to the case of a

unique conductor we suppose that each conductor generates an

electrical potential given by

Ui ¼ U0s;i

ni

Ai

ð12Þ

where Ui is the electrical potential due to conductor i at the

point (x, y) and U0s;i is an unknown electrical potential whose

value must be computed. Parameters Ai and ni should be

computed as explained in Equation (10).

The electrical potential generated by the n real conductors

and their images can be computed as

U ¼Xni¼1

Ui ¼Xni¼1

U0s;i

ni

Ai

ð13Þ

Now, the boundary conditions can be applied. Electrical

potential Us,j on the surface of any conductor must be equal

to the sum of the electrical potentials generated by all the real

and image conductors at this point, resulting in

Us;j ¼ Uðxj; yj � RjÞ ¼Xni¼1

U0s;i

niðxj; yj � RjÞAi

ð14ÞThe former expression can be expressed by means of a

matrix as follows:

Us;1

..

.

Us;n

0B@

1CA ¼

n1ðx1 ;y1�R1ÞA1

� � � nnðx1 ;y1�R1ÞAn

..

. � � � ...

n1ðxn ;yn�RnÞA1

� � � nnðxn ;yn�RnÞAn

0BB@

1CCA

U0s;1

..

.

U0s;n

0B@

1CA ð15Þ

Equation (15) can be expressed as

Us;ðn;1Þ ¼ Nðn;nÞU0s;ðn;1Þ ð16Þ

From Equation (16) the coefficients of the unknown

electrical potentials matrix U0s can be calculated as shown in

Equation (17).

U 0s;ðn;1Þ ¼ N�1

ðn;nÞUs;ðn;1Þ ð17Þwhereas matrixes Us and U 0

s have complex coefficients, matrix

N is squared and real, being easily invertible.

Then, the electrical potential at any point (x, y) of the

space can be calculated as

Uðx; yÞ ¼Xni¼1

Uiðx; yÞ ¼Xni¼1

U0s;i

niðx; yÞAi

ð18Þ

As the potentials U0s;i and the parameters Ai are constants,

the total electric field at any point (x, y) can be computed by

means of Equation (19)

~E¼� @U

@x;@U

@y;0

� �¼�

Xni¼1

U0s;i

Ai

@ni@x

;Xni¼1

U0s;i

Ai

@ni@y

;0

!ð19Þ

where

@ni@x

¼ �4yyiðx�xiÞððx�xiÞ2þðyþyiÞ2Þððx�xiÞ2þðy�yiÞ2Þ

;

@ni@y

¼ 2yiððx�xiÞ2þy2i �y2Þððx�xiÞ2þðyþyiÞ2Þððx�xiÞ2þðy�yiÞ2Þ

ð20Þ

Figure 2 Electric field vector generated by a very long

rectilinear conductor (named conductor i).

EFFECTS OF BUNDLE AND STRANDED CONDUCTORS 109

In the deduction of the previous expressions, the following

approximations have been supposed:

The effect of the support structures of the conductors

has been ignored.

The effect of trees, vegetation, and other conductor

elements placed nearby the conductors has been

ignored.

It is supposed that the horizontal conductors are very

thin and infinitely long.

A flat, horizontal, and uniform terrain has been

supposed.

EXPERIMENTAL VALIDATION OF THEMETHODOLOGY

The results of the method explained in this work have been

validated with experimental data and also have been compared

with simulated results from other authors.

Using the program explained in Deduction of the Electric

Field Generated by Overhead Power Lines Section, we proceed

to study the distribution of the electric field strength in the

proximity of two types of 525 kV overhead power lines.

Geometric data of the simulated high-voltage power lines

shown in Figures 3 and 5 have been collected from Ref. [6].

Figures 3 and 5 show the geometrical dispositions of two

525 kV lines, whereas Figures 4 and 6 show the simulated

profile of the electric field strength and results of measurements

reported in Ref. [6].

The results of Figures 4 and 6 clearly indicate that the

proposed system of simulation gives nearly the same results as

were found in Ref. [6]. Therefore, the results of simulations are

very similar to measurements.

EFFECTS OF BUNDLE CONDUCTORS

Bundle conductors consist of several conductor cables con-

nected by non-conducting spacers. Each phase of the line is

built with two, three, or four conductors connected in parallel

and separated by about 1.5 feet (0.46 m).

Bundle conductors are used to increase the amount of

current that may be carried in a line. Bundle conductors are

generally applied for line voltages over 200 kV.

The use of several conductors—a bundle—for each phase,

influences the distribution of the electric field in the vicinities of

the line. The larger the bundle, the larger the electric field

strength near the ground. The effect of the bundle is to increase

the effective radius of an equivalent conductor. As a

consequence, the electric field strength near the conductor is

reduced and, contrarily, it is increased near the ground plane.

Thus, bundle conductors increase corona critical voltage

because of the reduction of the electric field strength near the

conductor. Therefore, negative effects due to corona activity

such as power loss, audible noise, and radio interference are

reduced.

The disadvantages of bundled conductors are increased by

ice and wind loading, more complicated inspection, increased

clearance requirements for structures, among others.

Figure 7 shows the effect of bundle size on the electric

field distribution.

Figure 7 clearly corroborates that bundle size has an

important effect on the electric field strength at a height of 1 m

above the ground. Concretely, larger bundles generate larger

electric field strengths near the ground plane.

Figure 8 plots the electric field strength generated by line

1. It has been simulated in a close circular perimeter with a

distance gap r2 [1, 10] mm from conductor surface, for both a

bundle of four conductors and a smooth round conductor.

Figure 3 Geometric arrangement of 525 kV, line 1.

Figure 4 Measured and simulated electric field strength at a

height of 1 m under a span of 13.4 m (V¼ 525 kV, line 1).

Figure 5 Geometric arrangement of 525 kV, line 2.


Bundle conductors generate an electric field strength

distribution in close proximity to the conductor surface weaker

than that generated by an equivalent smooth conductor, as

shown in Figure 8. Thus, the effect of bundle conductors is

making the corona onset difficult. Consequently, the effect of

the bundle is to increase the effective radius of the equivalent

conductor.

EFFECTS OF STRANDED CONDUCTORS

High-voltage transmission lines use stranded conductors such

as aluminum cable steel reinforced (ACSR). In an ACSR

conductor, a stranded steel core supports the mechanical load,

and layers of aluminum strands surrounding the core carry the

current.

Figure 9 shows a two-layer stranded conductor, with an

outer layer formed of six strands and an external radius r.

Figure 10 shows the effect of stranded conductors on the

electric field distribution at 1 m above the ground level.

As displayed in Figure 10, the effect of stranded con-

ductors is a slight reduction in the electric field strength at 1 m

above the ground level. As a consequence, the electric field

strength near the conductor surface should be slightly increased.

When dealing with single conductors, the corona onset

voltage is a function of both surface electric field and the

conductor radius. The influence of stranding on the corona onset

voltage of single round conductor has been investigated experi-

mentally and the results show that this case is more complex

[15].

Corona onset is still a matter for study and is not a closed

question [15,16]. As pointed out by Yamazaki and Olsen [15],

the surface field does not completely characterize the corona

onset for stranded conductors. There are diverse factors

involved in the corona onset, such as the properties of the gas

(pressure, humidity, etc.) in which the conductor is located, the

rate at which the electric field decays away from the surface, the

radius of the conductors, the network frequency (50�60 Hz),

etc.

Figure 11 plots the electric field strength generated by line

1. It has been simulated in a close circular perimeter with a

distance gap r2 [1, 10] mm from conductor surface, for both a

Figure 6 Measured and simulated electric field strength at 1 m

height under span 10.2 m at center line (V¼ 525 kV, line 2).

Figure 7 Simulated electric field strength at 1 m height under

span 13.4 m for different bundle sizes (525 kV, line 1).

Figure 9 Stranded conductor used in the simulations, with six

strands in the outer layer.

Figure 8 Electric field strength simulated in a close circular

perimeter with a distance gap r2 [1, 10] mm from conductor

surface (525 kV, line 1).


six-strand conductor in the outer layer and a smooth round

conductor with the same external diameter.

From the results in Figure 11, it is shown that stranded

conductors create at some points in the surroundings of the

conductor surface, electric field strengths higher to those

created by a smooth round conductor with the same outer

diameter. Thus, the effect of stranded conductors is un-

homogenizing the electric field distribution around the

conductor’s surface, thus generating favorable conditions for

corona onset.

Note that as pointed out previously, corona onset is still

object of investigation. This study does not claim to be an

accurate revision of corona onset, but rather to introduce

students to a thorough understanding of the topic.

STUDENTS EVALUATION

In this section, we describe how the methodology explained in

this article has been integrated into the Electrotecnia course at

the UPC. The proposed practical was for 75 undergraduate

students, in the second semester of the 2006�2007 academic

year.

Students’ reactions to this practical were very positive.

Some of them expressed that this practical helped them to

understand the behavior of electric fields generated by overhead

power lines given that before the practical they were concerned

about their possible effects. Other students commented that they

were surprised by the important effects that bundle and stranded

conductors have on electric field distribution.

The method presented here consists of a practical session

where the concepts related to transmission of energy are dealt

with. In this session, the students write the code program and

simulate the profile of the electric field generated by different

configurations of overhead power lines. Results from simu-

lations are compared with experimental data available in the

technical literature. It is also suggested that students simulate

different configurations of bundle and stranded conductors. The

results obtained allow the students to find out which config-

uration generates favorable conditions for corona onset and

which do not.

The students were asked to fill out a questionnaire about

the practical session. It provided an important source of

feedback, allowing the instructors to identify possible errors

and possible improvements. In this questionnaire, students were

able to assess different aspects related to their satisfaction with

the proposed practical and its usefulness for consolidating their

knowledge about the contents studied. The questionnaire

consisted of the six questions shown in Table 1. The students

Figure 10 Simulated electric field strength at a height of 1 m

under a span of 13.4 m for a smooth round conductor and a six-

strands conductor (525 kV, line 1).

Figure 11 Electric field strength simulated in a close circular

perimeter distant a gap r2 [1, 10] mm from conductor surface

(525 kV, line 1).

Figure 12 Answers of the questionnaire.

Table 1 Questionnaire Answered for the Students

Questions Score

1. I had previous knowledge of Matlab

2. The instructor’s help was valuable

3. The level of the practical is appropriate

4. Teamwork has helped me in this

practical

5. This practical has helped me to

understand the theory better

6. The content of this practical is valuable

for an engineer


graded them from 1 (very poor) to 5 (excellent). Figure 12

shows the global results obtained from the students’ question-

naire.

Table 2 shows the average scores for each question.

Question 1 asks for the students’ previous knowledge of

Matlab. Answers to question 1 indicate that students have an

intermediate previous knowledge of Matlab�Simulink.

Answers to this question clearly indicate that the guidance of

the instructor is very important in order to meet the expected

objectives. As indicated by the scores for question 3, most

students consider the level of the practical suitable for their

initial knowledge. Question 4 asks about the role of teamwork

in meeting the objectives of the practical. The results for this

question show that the majority of the students think that

teamwork is advantageous. Answers to question 5 clearly

indicate that the methodology applied has a positive contribu-

tion in consolidating the theoretical concepts. Finally, question

6 expresses that students believe that the proposed methodology

is useful for an engineer.

The average response for all the questions was 3.90. This

overall mark indicates a satisfactory degree of student approval

for the methodology presented in this work.

The final conclusion is that the practical session was well

accepted by the students. This result means that this system

motivates students and it has also helped towards a better

understanding of the theoretical concepts involved in the

proposed practical session.

CONCLUSION

The methodology proposed in this work has been applied to the

Electrotecnia course at the UPC (Spain). Students are grouped

in teams of three in order to realize the practical.

In this article, an accurate mathematical method to

simulate the electric field generated by any power line

configuration has been shown. An important objective of the

presented practical is that students are able to study the

important influence that bundle and stranded conductors have

on the spatial distribution of the electric field generated by the

power line.

The aim of the proposed system is to encourage students to

understand the physical and electrical laws involved in the

computation of electric field as well as interpreting the

program’s output results which calculate the electric field

generated by overhead power lines. To meet these objectives, it

is very useful that students are able to write the source code of

the Matlab program, because in this task their effort is oriented

towards analyzing and understanding thoroughly the steps

involved in the computation of electric field.

Results from simulations through applying the method

explained in this work have been compared with experimental

data available in the technical literature, showing a close

correlation between the two.

The results obtained allow students to find out that for an

equivalent power line bundle conductors hinder corona onset,

whereas stranded conductors generate favorable conditions for

corona onset.

On the other hand, instructors explain to the students that

while the burial of high-voltage power lines is not a good

solution to reduce the strength of magnetic fields, electric fields

can be totally canceled out by burying the power lines. This is

due to the fact that underground cables have a metallic shield

that acts as a Faraday cage, totally canceling the electric field in

the exterior of the cable.

By means of a questionnaire answered by the students on

the Electrotecnia course, a successful degree of satisfaction was

expressed with the methodology proposed in this work.

APPENDIX

The most significant international regulations regarding the

exposure of workers and the general public to low-frequency

electric fields can be found in Refs. [17�20].

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Question 6 4.12

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BIOGRAPHIES

Jordi-Roger Riba Ruiz received the MS

in Physics and PhD degrees from the

Universitat de Barcelona (UB) in 1990 and

2000, respectively. In 1992, he joined the

College of Industrial Engineering of Igua-

lada (Universitat Politecnica de Catalunya,

UPC) as a full-time lecturer and in 2001 he

joined the Electric Engineering Department

of the UPC. His research interests include

signal processing, electromagnetic devices, electric machines,

variable-speed drive systems, and fault detection algorithms. He

belongs to the Motion and Industrial Control Group (MCIA). The

Group’s major research activities concern induction and permanent

magnet motor drives, enhanced efficiency drives, fault detection and

diagnosis of electrical motor drives, and improvement of educa-

tional tools.

Antonio Garcia Espinosa (M’05) received

his electrical engineering degree and the

PhD degree from the Universitat Politecnica

de Catalunya (UPC) in 2000 and 2005,

respectively. In 2000, he joined the Electric

Engineering Department of the UPC, where

he is currently a lecturer. His research

interests include electromagnetic devices,

electric machines, variable-speed drive sys-

tems, and fault detection algorithms. He belongs to the Motion and

Industrial Control Group (MCIA). The Group’s major research

activities concern induction and permanent magnet motor drives,

enhanced efficiency drives, fault detection and diagnosis of

electrical motor drives, and improvement of educational tools.

Xavier Alabern Morera received the MS in

Electrical Engineering and PhD degrees from

the Universitat Politecnica de Catalunya

(UPC) in 1975 and 1989, respectively. In

1986, he joined the UPC Department of

Electric Engineering as a full-time associate.

His research interests include electromag-

netic actuators, electrical machines, and

electrical drives. He belongs to the research

group of Aeronautic and Industrial Research and Studies Laboratory

of the UPC, working in the area of electromagnetic devices and

electrical machines.


electric field effects of bundle and stranded conductors in overhead power lines

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