Download Electric and magnetic fields produced by 400kv double circuit

Electric and magnetic fields produced
by 400kv double circuit overhead lines –
Measurements and calculations
in real lines and line models
Evangelos I. Mimos*, Dimitrios K. Tsanakas, Antonios E. Tzinevrakis
Department of Electrical and Computer Engineering, University of Patras, Greece
Abstract:
1. Introduction
In this paper, the results of systematic measurements and
comparative calculations of the electric and magnetic
fields in the vicinity of two parallel running 400kV double
circuit power lines of the Greek transmission system are
presented. The measurements were conducted during the
operation of the lines with the usual symmetrical phase
conductor arrangement as well as after the application
of the optimum phase conductor arrangement for the
electric and magnetic field minimization.
Overhead high and extremely high voltage lines are
often a cause of public concern about possible effects
of the produced electric and magnetic fields on health.
Until recently, the limit values of the field intensities
(reference values) for public exposure for the 50Hz
frequency were common in ICNIRP guidelines [1] and
in the European Union Council Recommendation [2].
These limit values were 5kV/m for the intensity of the
electric field and 100μT for the magnetic flux density.
For occupational exposure the corresponding values in
guidelines [1] and the Directive of European Parliament
and Council [3] were 10kV/m and 500μT. In December
2010, ICNIRP published its new guidelines [4]. The
new reference values for the magnetic flux density
are for public exposure 200μΤ and for occupational
exposure 1000μT. The reference values for the intensity
of the electric field remain the same. ICNIRP has also
published a fact sheet which explains the reasons why
reference values of the magnetic flux density have been
increased. In 2013 the new reference values of ICNIRP
[4] for the occupational exposure were adopted by the
new Directive of European Parliament and Council [5].
Measurements were also conducted in the vicinity of a
model of the power lines. The design and construction of
the power line model was an interesting technical task.
The model dimensions must be large enough so that,
given the size of the instruments, measurement of the
fields in the vicinity of the model depictures the situation
in the vicinity of real lines. The electrical supply system
has been designed so that the line currents are large
enough to create equal levels of the magnetic field as
in the vicinity of real power lines. Special equipment
is needed for power supply and current control for the
application of different phase arrangements.
The measurements in the vicinity of real lines confirmed
the drastic reduction of the electric and magnetic field
levels after the application of the optimum phase
conductor arrangement. The measurements in the
vicinity of models and the computational investigations
led to the same result.
The phase conductor arrangement of double circuit lines is
an important factor on the produced electric and magnetic
field. Until few years ago, 400kV double circuit power
lines of the Greek transmission system were constructed
with the symmetrical phase arrangement. A series of
*[email protected]
KEYWORDS
Calculations, double circuit lines, electric and magnetic fields, measurements, overhead, power line models.
Cigre Science & Engineering • N°5 June 2016
28
Figure 1: Arrangements of the 400 kV double circuit parallel running lines.
a) Symmetrical phase arrangements on line (1) and line (2)
b) Optimum phase arrangements on line (1) and line (2)
c) Towers of line (1) and (2)
theoretical studies, such as [6]–[10], showed that this
arrangement was not optimum as far as the reduction of
electric and magnetic fields is concerned and proposed
another phase arrangement as the optimum one. New
400kV double circuit power lines in Greece are now
being constructed with the optimum phase arrangement
for the minimization of electric and magnetic fields.
The optimum phase arrangement is also being applied
to existing 400kV double circuit power lines (with the
symmetrical phase arrangement). The application of the
optimum phase arrangement to an existing double circuit
line is an easy process, which is achieved by proper
interchanging of the phase conductors at both ends of
the line. In the current paper, measurements of electric
and magnetic fields are presented before and after the
application of the optimum arrangement in real 400kV
double circuit transmission lines. Electric and magnetic
field measurements in the vicinity of power lines are
also presented in [11]–[17]. In [18], the minimization of
electric and magnetic fields in the planning and design
of transmission lines is examined.
BAC|B’A’C’ BAC|C’A’B’ BAC|B’A’C’
BAC|C’A’’B
double circuit lines has been developed and constructed
at the Power Systems Laboratory of the University of
Patras in order to investigate experimentally the effect
of the many possible phase conductor arrangements on
the produced electric and magnetic fields. Power line
models have also been developed in [19]–[21].
The measurements and calculations in the vicinity of real
lines and line models confirm the drastic reduction of
electric and magnetic field levels due to the application
of the optimum phase conductor arrangement.
2. Measurements in the vicinity
of real 400kV double circuit
power lines
In order to confirm the ability of the optimum phase
arrangement of conductors to reduce electric and
magnetic fields produced by 400kV double circuit
power lines, measurements were performed before and
after the application of the optimum arrangement in the
vicinity of two parallel running 400kV double circuit
power lines. Figure 1a shows the symmetrical phase
arrangement before the application and Figure 1b shows
the new optimum phase arrangement which was applied
to the power lines. Figure 1c shows the dimensions of
the towers in both power lines.
The various phase arrangements for the reduction of
electric and magnetic fields cannot be tried on real
operating lines. Power line models offer the ability
to confirm experimentally the results of theoretical
investigations of the electric and magnetic field. A
model of one line and two parallel running 400kV
Cigre Science & Engineering • N°5 June 2016
29
Figure 2: Changes required for the application of the optimum phase arrangement
on a double circuit transmission line
a) Symmetrical phase arrangement (before)
b) Optimum phase arrangement (after). Changes are marked with dashed lines.
shown in Figure 1c. The lines are equipped with twin
phase conductors of 2x954 MCM (2x483mm2) cross
section. The separation between the two sub-conductors
is 40cm. The ground wires are equipped with steal
conductors of 190 MCM (96,47mm2).
Figure 2 shows the changes required for the application
of the optimum phase arrangement to an existing double
circuit power line. Figure 2 shows one double circuit line
and the portals of the line at the substations SΙ and SII. In
Figure 2a the symmetrical phase arrangement is applied
and in Figure 2b the optimum phase arrangement. Only
the conductors of one circuit are shown in Figure 2 but
the locations of both circuits’ conductors are shown.
The measurements were performed with the Standard
EMDEX II meter of ENERTECH Consultants [22]
complying with IEC Standard 61786 [23] and the IEEE
Standard 644-1994 [24]. The typical measurement
accuracy of the EMDEX II meter is ±1% for the
magnetic flux density and ±5% for the intensity of the
electric field.
In order to switch from the symmetrical arrangement to
the optimum one, only simple changes and only for one of
the two circuits of the lines are necessary. The optimum
arrangement is obtained by interchanging the conductors
of phases B’ and C’ at the parts of the line between the
fist tower T1 and the substation SI and between the last
tower Tn of the line and the corresponding substation
SII. The application of the same optimum arrangement
on each double circuit line leads to an overall optimum
arrangement for parallel running lines, [6]–[8].
At the measurement area the distance of the lower
conductors of line (1) from the ground is h(1)=21,8m and
the corresponding distance for line (2) is h(2)=23,8m.
The currents were I(1)=I(2)=99A per phase and circuit
for the measurements during the symmetrical phase
arrangement and I(1)=I(2)=114A during the optimum
phase arrangement. The measured values have been
also verified computationally. The computer software
that was used is based on the numerical calculation of
the field intensities as the vectorial sum of the field
intensities produced by each conductor separately. This
Figure 3 shows the measured values of the intensity of
the electric field and the magnetic flux density for the
two parallel running lines (1) and (2) with their phases
arranged according to Figure 1a and Figure 1b. The
tower type and the distances between the conductors are
Cigre Science & Engineering • N°5 June 2016
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Figure 3: Measured and calculated values of the electric strength E and the magnetic flux density B as a
function of the distance x (indicated in Figure1)
measuredcalculated
Before, symmetrical arrangement BAC|B’A’C’
BAC|B’A’C’
X X X X
______
After, optimum arrangement
BAC|C’A’B’
BAC|C’A’B’ ∙ ∙ ∙ ∙
-----
is a typical method for the calculation of field intensities
produced by power lines [25], [26]. The same software
has been used for the calculation of the magnetic flux
density in [27], [28] and the intensity of the electric
field in [29], [30]. The deviation of the maximum values
between measurements and calculations for the intensity
of the electric field comes up to about 6,66-15,5%
taking into consideration the typical accuracy of the
measurement meter and is mainly due to the distortion
of the electric field by nearby objects (vehicles, houses,
trees). The deviation of the magnetic flux density values
is much smaller and is due to the change of the line
current during measurements.
theoretical investigations a model of two parallel running
400kV double circuit lines has been constructed.
3.1. Operating principle of the model
Figure 4a shows the magnetic flux density at a point
of interest P produced by a conductor of a real power
line, either phase conductor or ground conductor, and
Figure 4b the magnetic flux density produced by a
corresponding conductor of the power line model.
Figure 3 confirms the effective reduction of the
field intensities by the application of the optimum
arrangement. For example, the maximum measured
value of the intensity of the electric field is limited from
3,04kV/m to 1,35kV/m and the magnetic flux density
from 0,65μΤ to 0,38μΤ (reduction to its 40,2-49,1% and
57,3-59,6% respectively).
Figure 4: Magnetic flux density
at a point of interest P
a) Produced by a real conductor with current Ii
The relatively low values of the magnetic flux density
are due to the relatively low load of the lines during
measurements (about 100A per circuit and phase).
Loading with the tenfold current will increase by ten the
magnetic flux density.
b) Produced by a model conductor with current Imi
at the point of interest P
The magnetic flux density
produced by the real power line is given by the general
relation [25], [26]:
3. Measurements in the vicinity
of a model of 400kV double
circuit power lines
where μ0=4π·10-7 H/m is the magnetic permeability of
free space, Ii is the current of the conductor i and
is the vector distance of point P to the conductor i. The
magnetic flux density
at point P produced by the
power line model is given by:
The various phase arrangements for the reduction of
electric and magnetic fields cannot be tried on actual
operating lines. A model of the power line is an alternative
for these trials. In order to confirm experimentally the
Cigre Science & Engineering • N°5 June 2016
31
The intensity of the electric field at point P produced by
the real power line is given by the general relation [25],
[26]:
where Imi is the current of the model conductor i and
is the vector distance of point P to the model
conductor i. If the distance of the model conductor is
Kl times smaller than the distance of the real conductor
(geometric scale model 1: Kl) and the current of model
conductor is KI times smaller than the current of the real
conductor (current scale model 1: KI) then
where ε0=(1/36π).10-9 F/m is the electric permittivity of
free space, Qi is the electric charge of the conductor i and
is the vector distance from point P to the conductor i.
The charge Qi of the conductor i is given by
and
where
The magnetic flux density from the real power line,
given in (1) can be rewritten as:
V1, V2,… Vn are conductors’ voltages and the terms sii and
sij are given by
If the constant Kl is equal to the constant KI, then the
magnetic flux density of the power line model is equal to
.
the magnetic flux density of the real power line,
where hi , ri , dij, d'ij are:
Figure 5 shows the intensity of the electric field at the
point of interest P produced by the conductor of a real
power line, either phase conductor or ground conductor,
(Figure 5a), and the intensity of the electric field produced
by the conductor of the power line model (Figure 5b).
hi , the height of the conductor i above ground
ri , the radius of the conductor i
dij, distance between the conductors i and j
d'ij, distance between the conductor i and conductor’s j
image.
The intensity of the electric field
at point P produced
by the power line model is given by:
where Qmi is the electric charge of the model conductor i
and
is the vector distance from point P to the model
conductor i.
Figure 5: Intensity of the electric field
The charge Qmi of the model conductor i is given by
at a point of interest P
a) Produced by a real conductor with charge Qi
b) Produced by a model conductor with charge Qmi
Cigre Science & Engineering • N°5 June 2016
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where
Vm1, Vm2,… Vmn are the model conductors’ voltages and
the terms smii and smij are given by
Therefore, replacing (18) and (19) in (7) the charge Qi
results
where hmi , rmi , dmij, d'mij are
hmi , the height of the model conductor i above ground
Using (14) and (20) the intensity of the electric field
from the real power line can be rewritten as:
rmi , the radius of the model conductor i
dmij , distance between the model conductors i and j
d'mij , distance between the model conductor i and model
conductor’s j image.
If every distance (radius, height above ground, distance
between conductors) of the model conductor is Kl times
smaller than the distance of the real conductor (geometric
scale model 1: Kl) and the voltage of the model conductor
is Kv times smaller than the voltage of the real conductor
(voltage scale model 1: Kv) then
If the constant KV is equal to the constant Kl, then the
intensity of the electric field of the power line model
is equal to the intensity of the electric field of the real
.
power line,
3.2. Construction of the model
The dimensions of the model must be enough so that,
given the size of the instruments, measurement of the
fields in the vicinity of the model depictures the situation
in the vicinity of real lines. Models with small dimensions
lead to a relatively large measurement error due to the
size of the sensors of EMF meters. Models with large
dimensions have economical and spatial constraints.
The 1:16 scale emerged as the best scale for the model
of lines taking into account the space available and the
requirements of accurate measurements. The dimensions
of the tower of a real line are given in Figure 1c. The
dimensions of the model are 12m (length), 3.2m (width)
and 3.6m (height). The distance between the model lines
is 2,19m. Figure 6 shows a photograph of the model. In
the power line model the ground conductors have been
placed above the phase conductors in correspondence
with the real line. The model towers are wooden in order
to avoid distortions of the field intensities.
and
Taking into consideration (16) and (17) the following
relations arise
Cigre Science & Engineering • N°5 June 2016
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Figure 7: Diagram with equipment for the electrical supply of the model lines.
* Connections for applying different phase arrangements
may be chosen between 6 steps of 10,2V, from 10,2V to
6x10,2V = 61,2V. The current on the secondary circuit
may come up to 500A. There is also the ability to divide
the winding of each phase of the secondary circuit
and connect the halves in parallel, in order to achieve
currents up to 1000A.
For the adjustment of the desired currents on the lines,
beside the choice of the secondary circuit voltage,
reactance coils without iron core are used. These coils
had to be carefully winded so that the line currents are
balanced. Also two special switchboards were needed in
order to control the operation and to be able to change the
phase arrangements on the two lines. The switchboards
are also equipped with current and voltage measurement
instruments as well as short circuit and ground fault
protecting equipment. The main switchboard and the
two special switchboards are presented in Figure 7. The
electric equivalent circuit of the model lines with the
supply equipment is given in Figure 8.
3.3. Measurement results
Figure 9 shows characteristic measurement results in
the vicinity of the model lines and relevant comparative
calculations.
Figure 6: The model of the two parallel 400kV lines under 1:16 scale
The electrical supply system must be designed so that
the line conductors carry current large enough to create
equal levels of the magnetic field as in the vicinity of
real power lines. The model lines are equipped, as real
400kV power lines, with twin phase conductors, with
loading capability up to 200A per phase and circuit.
This current corresponds to a load of real lines 200Α x
16=3200Α.
The distance between the lower conductors of the model
lines and the measurement and calculation level is 1,25m,
which corresponds to 1,25mx16=20m in the vicinity of
a real line. The axis x is not the distance from the model
line but the corresponding distance in the vicinity of a
real line, which is 16 times higher.
The current during measurements was 185A per circuit
and phase, which corresponds to 185Ax16 = 2960A
current of the real line. The measurement values given in
Figure 9 are normalized to 1000A per circuit and phase
actual line current, so that the magnetic flux density
values correspond to actual values under 1000A loading.
The lines are supplied through two transformers (one
for each line) which were designed especially for this
purpose. These high current transformers have a nominal
power of 50kVA each and are connected to the 220/380V
main supply. The polar voltage of the secondary circuit
Cigre Science & Engineering • N°5 June 2016
34
Figure 8: Electric equivalent circuit of the model lines with the supply equipment. Values in mΩ. Outside brackets the values are
given at 20oC, within brackets in operating temperatures.
For this normalization, the measured values have been
multiplied by the factor 1000Α / 2960Α =0,338. Thus,
it is possible to reach conclusions about the field levels
appearing in the vicinity of real lines, based on the model
measurements.
accuracy. The measured values are not symmetrical to
the axis of the arrangement because the field at the right
of line (1) is affected by the fields produced by nearby
equipment (reactance coils, switchboards).
Using the power line model it is possible to try various
scenarios of arrangements and loadings that would be
difficult to try on real lines. For example, comparing
Figure 9a and Figure 9b, it is concluded that the parallel
running of two or more equally loaded double circuit
lines does not practically affect the maximum values
of the field intensities in comparison with one double
circuit line alone.
Figure 9a shows the magnetic flux density in the case
that only the one line is loaded, that is line (1). Using
the optimum phase arrangement an overall reduction
of the magnetic field levels is achieved. The maximum
measured value is reduced from 6,4μΤ to 3,9μΤ
(reduction from 59,7% to 62,2% according to meter
accuracy). The corresponding reduction at the right of
way limit is significantly higher, reduction from 4,3μΤ
to 1,7μΤ (reduction from 38,8% to 40,3% according to
meter accuracy).
4. Conclusions
The phase arrangement of double circuit lines is an
important factor on the produced electric and magnetic
fields. New 400kV power lines in Greece are being
constructed with the optimum phase arrangement for the
minimization of the field intensities. The optimum phase
Figure 9b shows the magnetic flux density in the case
where both lines are loaded. The overall reduction of
the magnetic field levels, caused by the optimum phase
arrangement, is observed. The maximum measured value
is reduced from 46,6% to 48,5% according to meter
Figure 9: Measured and calculated values of the magnetic flux density B in the vicinity of the model
Cigre Science & Engineering • N°5 June 2016
35
arrangement is also being applied to existing 400kV
double circuit power lines with the symmetrical phase
arrangement. The application of the optimum phase
arrangement to an existing double circuit line is an easy
process, achieved by proper interchanging of the phase
conductors at both ends of the line.
agents (electromagnetic fields) (18th individual Directive within
the meaning of Article 16(1) of Directive 89/391/EEC),” pp.
L184/1-L184/9, May 2004.
[4] International Commission on Non-Ionizing Radiation Protection,
“Guidelines for limiting exposure to time-varying electric, magnetic
and electromagnetic fields (up to 300GHz),” Health Physics, vol. 99,
issue 6, pp. 818 -836, Apr. 2010.
[5] European Parliament and Council, “Directive 2013/35/EC of 26
June 2013, on the minimum health and safety requirements
regarding the exposure of workers to the risks arising from
physical agents (electromagnetic fields) (20th individual Directive
within the meaning of Article 16(1) of Directive 89/391/EEC)
and repealing Directive 2004/40/EC,” pp. L179/1-L179/21, Sep.
2013.
Measurements of electric and magnetic fields before and
after the application of the optimum arrangement in real
lines verified the drastic reduction of the field intensities.
Also, the application of the same optimum arrangement
on each double circuit line leads to an overall optimum
arrangement for the parallel running lines.
[6] D.Tsanakas, D. Tsalemis, D. Agoris and J. Vojazakis, “Optimum
arrangements of the phase conductors of overhead transmission lines
for the magnetic field minimization,” CIGRE Rep. 36-101, Paris,
France, 1994.
Power line models offer the ability to confirm
experimentally the results of theoretical investigations
for the electric and magnetic field. The model dimensions
must be large enough so that, given the size of the
instruments, measurements of the fields in the vicinity
of the model depictures the situation in the vicinity of
real lines. The electrical supply system must be designed
so that the line conductors’ currents are large enough to
create equal levels of the magnetic field as in the vicinity
of real power lines. Special equipment is needed for
power supply and current control for the application of
different phase arrangements. The chosen scale for the
two parallel 400kV double circuit model lines occurred
1:16.
[7]Cigre Working Group 22.14, “High voltage overhead lines
Environmental concerns, procedures, impacts and mitigations,”
Technical Brochure No. 147, Oct. 1999.
[8] D. Tsanakas, G. Filippopoulos, J. Voyazakis, and G. Kouvarakis,
“Compact and optimum phase conductor arrangement for the
reduction of electric and magnetic fields,” CIGRE Rep. 36-103, Paris,
France, 2000.
[9] CIGRE WG B2.06, “The Influence of Line Configuration on
Environment Impacts of
Electrical Origin,” CIGRE Technical Brochure 278, Aug. 2005.
[10]CIGRE WG C4.204, “Mitigation Techniques of Power Frequency
Magnetic Fields originated from Electric Power Systems,” CIGRE
Technical Brochure 373, Feb. 2009.
Using the power line model it is possible to try various
scenarios of arrangements and loadings that would be
practically impossible to try on real lines. For example,
it is concluded that the parallel running of two or more
equally loaded double circuit lines does not practically
affect the maximum values of the field intensities in
comparison with one double circuit line alone.
[11]CIGRE TF C4.205, “Characterisation of ELF Magnetic Fields,”
CIGRE Technical Brochure 320, Apr. 2007.
[12]K .M. Srinivasa, R. Maruti, Rajesh Kumar O. et al “Field
measurements of electric and magnetic fields on HV and EHV
transmission lines and substations,” IEEE Int. Symp. on Electrical
Insulation: pp.347-350, Virginia, USA, 1998.
[13]C.Garrido, A.F. Otero, J. Cidrás, “Low-frequency magnetic fields
from electrical appliances and power lines,” IEEE Trans Power
Delivery, vol.18, issue 4, pp. 1310-1319, Oct. 2003.
5. References
[14]J. M. Bakhashwain, M. H. Shwehdi, U. M. Johar, A. A. AL-Naim,
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lines in Saudi Arabia,” Proc. Int. Conf. on Non-Ionizing Radiation
at UNITEN (ICNIRP 2003) Electromagnetic fields and our health,
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[2] European Union Council, “Recommendation of 12 July 1999 on
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emf_rec519_en.pdf
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Cigre Science & Engineering • N°5 June 2016
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6. Biography
[17] C.P. Nicolaou, A.P. Papadakis, P.A. Razis, G.A. Kyriacou, J.N. Sahalos,
“Measurements and predictions of electric and magnetic fields from
power lines,” Electric Power Systems Research vol. 81, issue 5, pp. 11071116, May 2011.
E. I. Mimos was born in Athens, Greece,
in 1978. He received the Electrical
Engineering degree and the Ph.D.
degree in electrical engineering from the
University of Patras, Patras, Greece, in
2001, and 2009 respectively. He worked
in Hellenic Electricity Distribution
Network Operator (HEDNO) from 2010 to 2014. Since
2010 he has been working in the Technological Education
Institute of Western Greece.
[18]A.S. Farag, A. Al-Shehri, J. Bakhashwain, T.C. Cheng, D. Penn,
“Impact of electromagnetic field management on the design of 500kV
transmission lines,” Electric Power Systems Research vol.40, issue 3, pp.
203-238, Mar. 1997.
[19]M. Shimizu, T. Nagae, N. Hayakawa, M. Hikita, H. Okubo,
“Measurement of magnetic field distribution around power
transmission line using reduced scale model,” 10th ISH 6, pp. 69 – 72,
Montreal, 1997.
[20]N.A. Rahman, H. Hussain, I. Said, T.S. Jalal, A.S. Farag, “Magnetic
fields from a scaled down model transmission line – Simulation and
comparison to measurements,” Proc. Asia-Pacific Conf. on Applied
Electromagnetics, pp.147-151, DOI:10.1109/APACE.2005.1607795,
Malaysia, Dec. 2005.
His research interests include analysis and measurements
of low frequency electric and magnetic fields produced by
electric power systems.
[21]J. Estacio, A. Escobar, G. Aponte, H. Cadavid, “A transmission line
scale model for characterizing electric and magnetic fields,” In
Electromagnetic Field, Health and Environment – Proc. of EHE’07,
Studies in Applied Electromagnetics and Mechanics, IOS Press, 2008,
pp. 162-167.
D. K. Tsanakas received the Electrical
Engineering degree and the Ph.D.
degree in electrical engineering from
the Technical University of Darmstadt,
Darmstadt, Germany, in 1970 and 1976,
respectively.
[22]ENERTECH Consultants, “EMDEX II Specifications,” [Online].
Available: http://www.enertech.net/html/EMDEXIISpecs.html
[23]IEC 61786, “Measurement of low-frequency magnetic and electric
fields with regard to exposure of human beings –Special requirements
for instruments and guidance for measurements,” Aug. 1998.
He is Emeritus Professor of the Department of Electrical
and Computer Engineering of University of Patras, Patras,
Greece. From 1970 to 1973 and from 1977 to 1979, he
was with the Public Power Corporation, Athens, Greece.
From 1979 to 1990, he was a Professor of Electric Energy
Systems, Demokritos University, Thrace, Greece and from
1990 to 2008 he was Professor and Director of the Power
Systems Laboratory at the University of Patras, Patras,
Greece. His research interests include short-circuit currents
and their dynamic effects, analysis of electric and magnetic
fields produced by power systems, and power system
planning.
[24]
IEEE Standard 644-1994, “IEEE standard procedures for
measurements of powerfrequency electric and magnetic fields from ac
power lines,” Jan. 2002.
[25]CIGRE WG 36.01, “Electric and Magnetic Fields Produced by
Transmission Systems. Description of Phenomena - Practical Guide
for Calculation,” CIGRE Tech. Brochure 21, 1980.
[26] D. W. Deno and L. E. Zaffanela, “Field effects of overhead transmission
lines and stations,” in Transmission Line Reference Book – 345 kV and
Above, 2nd ed., California: Electric Power Research Institute, 1982,
ch.8.
[27]G. Filippopoulos and D. Tsanakas, “Analytical calculation of the
magnetic field produced by electric power lines”, IEEE Transactions
on Power Delivery, vol. 20, no. 2, pp. 1474-1482, April 2005.
A. E. Tzinevrakis was born in Chania,
Greece, in 1981. He received the
Electrical Engineering degree and the
Ph.D. degree in electrical engineering
from the University of Patras, Patras,
Greece, in 2004, and 2009 respectively.
[28]Evangelos I. Mimos, Dimitrios K. Tsanakas and Antonios E.
Tzinevrakis, “Optimum phase configurations for the minimization of
the magnetic fields of underground cables”, Springer Berlin, Electrical
Engineering, vol. 91, pp. 327–335, Jan. 2010.
[29]A. E. Tzinevrakis, D. K. Tsanakas and E. I. Mimos, “Analytical
calculation of the electric field produced by single-circuit power lines,”
IEEE Transactions on Power Delivery, vol. 23, no. 3, pp. 1495-1505,
July 2008.
His research interests include analysis and calculations of
low frequency electric and magnetic fields produced by
electric power systems.
[30]A. E. Tzinevrakis, D. K. Tsanakas and E. I. Mimos, “Electric field
analytical formulas for single-circuit power lines with a horizontal
arrangement of conductors,” IET Generation, Transmission &
Distribution, vol. 3, no. 6, pp. 509-520, 2009.
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