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DEPARTMENT OF TECHNICAL EDUCATION
ANDHRA PRADESH
Name : G.Venkateswara Rao
Designation : Lecturer
Branch : Electrical & Electronic Engg.
Institute : G.P.T,Hyderabad
Year/semester : V Semester
Subject : Power systems-II
( Transmission & Distribution)
Subject code : EE-504
Topic : Transmission lines
Sub topic : Expression for the capacitance of single
phase line and Problems.
Duration : 50 min
Teaching Aids : ppt, diagrams.

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Recap
• Definition of the capacitance
• Derivation of the expression for the capacitance of
single phase line and problems.
In the previous class, we have learnt about

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Objectives
• Capacitance of three phase symmetrical and
asymmetrical and transposed round conductor.
• Use the conductor tables for determining the
resistance, inductance and capacitance of
over head lines at different voltages.
On completion of this period you would be able
to know

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Three phase symmetrical spaced conductors:
(Equally spaced).
• A,B,C are three conductors equally spaced
at distance of ‘D’ meters and radius of the
conductors is ‘r’ meters.
Inductance of three phase transmission line

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Capacitance/conductor/km
=0.0556/loge(D/r) µF

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Three phase unsymmetrical spaced conductors:
(un equal spacing)
• A,B,C are three conductors unequally spaced at
distance of ‘DAB’, ‘DBC’, ‘DCA’, meters and radius of the
conductors is ‘r’ meters.

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Geometrical mean distance
D = 3 DAB DBC DCA
Capacitance / conductor / km
= 0.0556 / loge [( 3 DAB DBC DCA )/ r] µ F

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1) Calculate the capacitance of the each conductor of a 400
km, three phase line with an equilateral configuration. The
spacing between conductors is 3 m and radius of the
conductor is 1 cm.
Solution :
Given data :
Length of the line L = 400 km
Spacing between conductor, D = 3m = 300 cm
Radius of the conductor, r = 1cm
Problem :

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Capacitance / conductor / km = 0.0556 / loge (D/r)
= 0.0556 / lobe (300/1)
= 9.747 x 10-3 µ F / km
Total Capacitance / conductor = 9.747 x 10-3 x 400
= 3.898 µ F

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2) Calculate the capacitance / km of a three phase line
completely transposed with a triangle configuration. The
spacing between conductors are 1 m, 1.25m and 2.125 m.
Diameter of the conductor is 1.25 cm.
Solution :
Given data :
DAB = 1m, DBC = 1.25 m, DCA= 2.125m
Geometric mean distance D = 3 DAB DBC DCA
D = 3 1 x 1.25 x 2.125 = 1.385 m =138.5 cm

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Diameter of the conductor = 1 cm
Radius of the conductor r = ½ = 0.5 cm
Capacitance / conductor / km
= 0.0556/ loge[( 3 DABDBCDCA ) / r ]
=0.0556/loge(138.5/0.5)
=0.0556/5.624=0.0098µF/km

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3) Calculate the capacitance / phase or line to neutral
capacitance of a three phase line completely transposed
with horizontal configuration. The spacing between
conductors are 2 m, 2.5m and 4.5 m. Diameter of the
conductor is 1.25 cm.
Solution :
Given data :
DAB = 2m, DBC = 2.5 m, DCA= 4.5m

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Geometric mean distance D = 3 DAB DBC DCA
= 3 2 x 2.5 x 4.5
= 2.82 m = 282 cm
Radius of the conductor, r = 1.25 /2 = 0.625 cm
Line to neutral capacitance or
Capacitance / conductor / km
= 0.0556/ loge[( 3 DABDBCDCA ) / r ]
= 0.0556/loge(282/0.625)
= 0.0556/6.112=0.00909µF/km

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Resistance, inductance and capacitance of the three
phase over head line conductors at different voltages.
(Values apply to double circuit lines, A.C.S.R conductors).
1.Rated voltage kv 20 30 60
2.Nominal x section 35 150 35 150 95 240
Al ( mm2)
3.Diameter of the 8.1 17.3 8.1 17.3 13.4 21.7
conductor (mm)
4.Resistance at 200C 0.87 0.2 .87 0.2 0.32 0.13
(ohm/km)
5.Reactance (2 fl) at 0.39 0.34 0.4 0.35 0.4 0.37
50 Hz (ohm/km)
6.Mutual cap. (10-9 F/km) 9.7 11.2 9.5 10.9 9.5 10.3
7.cap.To earth(10-9 F/km) 3.4 3.6 3.5 3.7 3.8 4.0

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Resistance, inductance and capacitance of the three
phase over head line conductors at different voltages.
(Values apply to double circuit lines, A.C.S.R conductors).
1.Rated voltage kv 110 220
2.Nominal x section 120 300 340 2x240
Al ( mm2)
3.Diameter of the 15.7 24.2 28.1 2x21.7
conductor (mm)
4.Resistance at 200C 0.25 0.10 0.09 0.062
(ohm/km)
5.Reactance (2 fl) at 0.41 0.38 0.40 0.32
50 Hz (ohm/km)
6.Mutual cap. (10-9 F/km) 9.3 10 9.5 11.5
7.cap.To earth(10-9 F/km) 4.0 4.2 4.8 6.3

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Summary
• Capacitance of three phase symmetrical, asymmetrical
and transposed round conductors and Problems.
• Conductor tables for determining the resistance,
inductance and capacitance of over head lines
at different voltages.
We have discussed about

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1. capacitance/conductor/km for symmetrical spaced three
phase over head line is given by
a) 0.0556 / loge (r / d )
b) 0.02781/ loge (d / r)
c) 0.0556 / loge (D / r)
d) 0.0556 / loge (r / d)
QUIZ

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2. Capacitance/conductor/km for unsymmetrical spaced
and transposed three phase over head line is given by
a) 0.0556 / loge (r / d )
b) 0.0556/ loge( 3 (DABDBCDCA / r))
c) 0.0556 / loge (D / r)
d) 0.0556 / loge (r / d)
QUIZ

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Frequently asked questions.
1) Calculate the capacitance of the each conductor of a 250
km, three phase line with an equilateral configuration. The
spacing between conductors is 2.5 m and radius of the
conductor is 1.2 cm.
2) Calculate the capacitance / km of a three phase line
completely transposed with a triangle configuration. The
spacing between conductors are 1.5 m, 1.75m and 2.125
m. Diameter of the conductor is 1.45 cm.

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3) Calculate the capacitance / phase or line to neutral
capacitance of a three phase line completely transposed
with horizontal configuration. The spacing between
conductors are 2.2 m, 2.55m and 4.75 m. Diameter of the
conductor is 1.65 cm.

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