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High Voltage Techniques - 2010
Prof.Dr.Aydoğan ÖZDEMİR
Department of Electrical Engineering
Istanbul Technical University
34469 Maslak, ISTANBUL
Tel: 212 – 285 6758
High Voltage Laboratory
ITU Gümüşsuyu Campus
Tel 212 – 252 2220
Email : [email protected]
Website : http://www.elk.itu.edu.tr/~ozdemir
Grading Policy
Midterm test: 25 %
2 Homeworks: 5% + 5%
1 group project : 15%
Final test : 50%
References
1. Prof.Dr.Muzaffer ÖZKAYA, Yüksek Gerilim Tekniği : Cilt 1, Birsen Yayınevi, İstanbul
1996.
2. Akpınar S., Yüksek Gerilim Tekniği, Karadeniz Teknik Üniv., Trabzon, 1997.
3. Gönenç İ.., Yüksek Gerilim Tekniği, Cilt 1: Statik Elektrik Alanı ve Basit Elektrot
Sistemleri, İ.T.Ü. Kütüphanesi, Sayı:1085, İstanbul, 1977.
4. E. Kuffel, W. S. Zaengl, J. Kuffel, High Voltage Engineering Fundamentals, Pergamon
Press, Oxford, 2000.
5. E. Kuffel, W. S. Zaengl, J. Kuffel , Yüksek Gerilim Mühendisliği Temelleri, Tercüme
yayın EMO Yayınları, 2008.
6. M. S. Naidu, V. Kamaraju, High Voltage Engineering, Tata McGraw-Hill, New Delhi,
1997.
7. M. Abdel-Salam, H. Anis, A. El Morshedy, R. Radwan, High Voltage Engineering:
Theory and Practice, Marcel Dekker, New York, 2000.
8. Kind, D., Feser, K., High-Voltage Test Techniques, SBA Publ./Vieweg, 2. Ed. 1999.
9. M. Khalifa, High Voltage Engineering, Theory and Practice, Marcel Dekker, New York,
1990.
10. H. M. Ryan, High Voltage Engineering and Testing, Peter Peregrinus Ltd., London,
2001.
11. C. L. Wadhwa, High Voltage Engineering, New Age Int. Ltd., New Delhi, 1995.
12. Subir Ray, An Introduction to High Voltage Engineering, Printice Hall of India, New
Delhi 2004
October 13,2010
Homework I
1. a) Determine the potential and the field strength expressions for concentric spherical electrode
system. Plot field strength versus radial distance and assign the maximum and the minimum
field strengths. Evaluate the geometric characteristics of the system providing the best
conditions from the point of maximum field strength.
b) Outer sphere radius of a concentric spherical electrode system is given to be r2 = 15 cm.
Determine the maximum voltage that can safely be applied to the system if the dielectric
strength of the insulation is Ed = 30 kV/cm.
c) Determine the inner radius of the system in order to apply U=100 kV.
d) Evaluate the system from the point of discharge phenomena (will there be a discharge, if so
the type) for the inner radiuses of r1’= 2 cm , r1’’= 7 cm and r1’’’= 14 cm.
a) Refer the textbook for the expressions and derivations.
12
212min
12
121max21
12
21
2
/)(,
/)(,;)(
rr
rrUrEE
rr
rrUrEErrr
rr
rr
r
UrE
An example is given below
Refer the textbook for the evaluation of the system geometric characteristic providing the
best conditions from the point of maximum field strength,
4/)(,2,2/
2
minmax1
2/1
221
21
r
UErE
r
rprr d
rr
dd
d
b) kVUUrr
rrUEcmkVEcmr
mr
mrd 5.1125.715
5.7/15//30,15 maxmax
12
12maxmax2
5.71
152
c) 15,5solved if15
/15100
/
100
/30
15
2111
1
1
12
12max
2
152
cmrcmrr
r
rr
rrUEE
kVU
cmkVE
cmr
mrdd
d)
/2since discharge partial a be willThere
/7.57/
100,2,15
21
12
12max12
rr
EcmkVrr
rrUEkVUcmrcmr d
discharge a bet won'There
/8.26/
100,7,1512
12max12
dEcmkV
rr
rrUEkVUcmrcmr
/2sincebreakdown totala be willThere
/0.107/
100,14,15
21
12
12max12
rr
EcmkVrr
rrUEkVUcmrcmr d
2. Potential distribution of an electrode system for a voltage of U=100 kV is given as follows,
cmycmxyxkVyx
bayxv ,,41;1.),( 22
22
a) Determine the constants ( a and b) if v(0 , 1 cm)=100 kV and v(2 cm , 0)=0 kV.
b) Determine and sketch the equipotential curves of v1=0 kV and v2=100 kV.
c) Determine the field strength vector E
andminmax
, EE
.
a) cm2bandkV100a solved if
2/12
.)0,2(
11
.)1,0(
aabb
av
aabb
av
b) cm 2 of radius a with Circle212
.1000 222
221
yx
yxkVv
cm 1 of radius a with Circle112
.100100 222
222
yx
yxkVv
c)
jyx
yi
yx
xj
y
vi
x
vvgradE
yxv
2/32/3 222222
2002001
2.100
cmkVEEcmkVEE
yxyxyx
yxyxE
yxyx/100,/200
21200
*200),(
21
3
2222 minmax
22
2222
22
3. a) Determine the potential and the field strength for coaxial cylindrical electrode system. Plot
field strength versus radial distance and assign the maximum and the minimum field
strengths. Evaluate the geometric characteristics of the system providing the best
conditions from the point of maximum field strength.
b) Given that the maximum voltage that can safely be applied to an air-insulated (Ed = 30
kV/cm) coaxial cylindrical system is 300 kV. Determine the inner radius of the system in
order to apply U=250 kV.
c) Evaluate the maximum field strengths for an inner radius of r1 and for an increased outer
radiuses of r2’= 1.5* r2, r2’’= 2.0* r2, r2’’’= 3.0* r2 and r2’’’’= 4.0* r2; where r1 and r2
are the inner and outer radiuses calculated in b). What can you say about the maximum
field strength versus outer radius of the system?
a) Refer the textbook for the expressions and derivations.
)/()(,
)/()(,;
)/()(
122
2min
121
1max21
12 rrLnr
UrEE
rrLnr
UrEErrr
rrLnr
UrE
An example is given below
Refer the textbook for the evaluation of the system geometric characteristic providing the
best conditions from the point of maximum field strength,
2/)(,,/
2
minmax1
/1
221
21
r
UErEe
r
rperr d
err
dd
d
b) cmrercmrrrrLnr
UEcmkVE
errd 18.27*,10
300
)/(/30 121
1121
maxmax
/21
cmrcmrsolvedifrLnr
EEkVUFor d 8.4,3.1630)/18.27(
250250 2111
11
max
c) )/(
,250,8.4121
max1rrLnr
UEkVUcmr
cmkVEcmr
cmkVEcmr
cmkVEcmr
cmkVEcmr
/7.167.10818.27*0.4
/3.185.8118.27*0.3
/4.214.5418.27*0.2
/3.248.4018.27*5.1
4max2
3max2
2max2
1max2
Increasing r2 decreases Emax. However decreasing rate decreases r2 increases and therefore r2
is not an effective means of reducing Emax, especially after a certain value.
Due date : October 20, 2010
Week Date Subject
1 29.9.2010 Introduction. Basic concepts of electrostatic field, Laplace's and Poisson's
equations in different coordinate systems.
2 6.10.2010 Basic equations of electrostatic fields. Planar electrode systems. Concentric
spherical electrode systems.
3 13.10.2010 Concentric spherical electrode systems. Coaxial cylindrical electrode
systems.
4 20.10.2010 Coaxial cylindrical electrode systems (cont).
5 27.10.2010 High Voltage Laboratory Visit
6 3.11.2010 Non-coaxial cylindrical electrode systems: eccentric and parallel cylindrical
electrode systems.
7 10.11.2010 Approximate calculation of maximum electric field strength for different
electrode systems.
8 24.11.2010 Electrode systems with multi-dielectrics: planar electrode systems of two
dielectrics.
9 01.11.2010 Electrode systems with multi-dielectrics: coaxial cylindrical systems with
multi-dielectrics
10 8.12.2010 Numerical methods for electrostatic field calculations.
11 15.12.2010 Conduction and breakdown in gases.
12 22.12.2010 Midterm test
13 29.12.2010 Conduction and breakdown in gases (cont.). Corona discharges, surface
discharges and lightning discharges. Breakdown in liquid and solid dielectrics
14 05.01.2011 Project presentation