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Name:
Number:
14/11/2012
EENG 451 High Voltage Techniques
Eastern Mediterranean UniversityDepartment of Electrical and
Electronic Engineering
Midterm Exam 1, 2012
Q1.The outer radius of a concentric spherical electrode system
is r2= 25 cm = constant. The system is
dimensioned with regard to the optimum breakdown case. There is
an insulator gas in between spheres
with a breakdown strength of Eb= 75 kV/cm (the relative
dielectric constant of gases is r = 1).
a. Determine the capacitance and maximum voltage that can be
applied for this system.b. Determine maximum and minimum electric
field strength if the applied voltage is U = 100 kV.c. Determine
the actual electrode separation, d; effective electrode separation,
and utilization
factor,
for this electrode system (0= 8,854 10
-12F/m).
Solution:
Optimum case with regard to breakdown:
a.Capacitance and Maximum voltage
[]
[
]
b. Electric Field calculations
c. Actual electrode separation Effective electrode
separation
Utilization factor
Q1 Q2 Q3 Q4 Total
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Q2.In a three layered, uniformly stressed bushing, radii of
cylinders in this system are: r1= 0.5 cm, r2= 2
cm, r2= 4 cm, r4= 8 cm and relative dielectric constants of
layers are r1 = 1, r2 = 3, r3 = 6, the length of
the first layer is l1= 100 cm and the applied voltage is 100
kV.
a. Determine lengths of 2ndand 3rdlayer.b. Calculate voltages
across each layer.c. Calculate maximum field strengths across each
layer.d. Calculate the capacitance of the system.
Solution:
a. Uniformly stressed condition:
b.capacitances are connected in series:
[
]
[
]
[
]
Voltage across the 1stlayer:
Voltage across the 2nd
layer:
Voltage across the 3rd
layer:
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c.Maximum electric fields across each layer:
Uniformly stressed:
d.Equivalent capacitance of the system:
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Q3.An insulation environment consists of polyethylene (r1 = 1)
and air (r2 = 2.3). Electric field vector
comes to the interface with an angle of 55through
polyethylene.
a. Determine the refraction angles of electric field lines and
equipotential lines.b. If electric field strength in polyethylene
is E1= 90 kV/cm, determine electric field strength in air,
E2; normal and tangential components of E1 and E2.
c. Does air have a breakdown considering breakdown strength of
air is 30 kV/cm?Solution:
a.
b.
c.
1
2
Et1
Et2
En1
En2
E1
E2
Interface
Equipotential lines
1
2
E1= 90 kV/cm
1= 90 55 = 35
1= 90 1= 55
2= 16.932
2= 90 2= 73.068
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Q4.
a. In a sphere-sphere (identical spheres) electrode system,
using approximated field calculationdetermine the breakdown
voltage. Radii of the spheres are 2.5 cm, electrode separation is
0.2
cm and breakdown strength of air is 30 kV/cm (k = 0.9).
b. In the region given as Figure 1, V3= V4= 0 V (grounded); V5=
22 kV; V6= V7= 88 kV; V8= 44 kV.Determine the potentials at point 1
and point 2 by Finite Element Method.
Figure 1
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[
]
1 25
67
8
43
d = 0.2 cmr r = 2.5 cm
U
