EE356: Power Transmission,
Distribution and Utilization
Farhan Mahmood, PhD
Department of Electrical Engineering
UET, Lahore
May 23, 2016
Outline
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Capacitance of transmission lines
•
Transmission line parameters
•
Potential at a charged single conductor
•
Capacitance of single-phase transmission line
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Capacitance of three-phase transmission line
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Method of images
Page 2
Field Lines Produced by Transmission Lines
Page 3
Capacitance of Transmission Lines
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The two parallel wires act as plates of a capacitor and that the air between them acts
as a dielectric.
•
Capacitance also exists between the transmission line wires, as illustrated in figure.
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The capacitance between the wires is usually expressed in picofarads per unit
length.
•
This electric field between the wires is similar to the field that exists between the two
plates of a capacitor.
Page 4
Capacitance of Transmission Lines
•
Advantages of shunt capacitance of transmission lines:
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Reduction in line losses due to decrease in the magnitude of current
˗
Improved efficiency of transmission lines
˗
Reduction in voltage drop, and hence voltage regulation
Page 5
Transmission Line Parameters
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Since any dielectric, even air, is not a perfect insulator, a small current known as
leakage current flows between the two wires.
•
In effect, the insulator acts as a resistor, permitting current to pass between the
two wires.
•
Figure shows this leakage path as capacitors-resistors in parallel connected
between the two lines. This property is called conductance (G) and is the opposite
of resistance.
Page 6
Potential at a Charged Single Conductor
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We first compute the electric field of a uniformly charged, solid cylindrical conductor
and the voltage between two points outside the conductor.
•
We also compute the voltage between two conductors in an array of charged
conductors.
•
Gauss’s law states that the total electric flux leaving a closed surface equals the total
charge within the volume enclosed by the surface, that is, the normal component of
electric flux density integrated over a closed surface equals the charge enclosed:
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where D ┴ denotes the normal component of electric flux density, E ┴ denotes the
normal component of electric field strength, and ds denotes the differential surface
area.
Page 7
Potential at a Charged Single Conductor
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From Gauss’s law,
where ε = ε0 is the permittivity of free space
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Electric field intensity at any point is the
gradient of voltage,
Page 8
Capacitance of Single-Phase Transmission Line
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The Inductance of a single-phase lines can be expressed as below,
Page 9
Capacitance of 3-Phase Transmission Line
Symmetrical Spacing
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Inductance per phase of three-phase line with symmetrical spacing (equilateral
spaced soild conductor) is given by,
Page 10
Exercise
Problem 1:
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A 3-phase, 132 kV, 50 Hz, transmission line has an equilateral spacing of 1.5 m,
diameter of each conductor is 1.5 cm. Calculate the capacitive reactance of the line if
the length of the line is 100 km. Also, calculate the charging current in amp per km
length of the line.
Page 11
Capacitance of 3-phase Transmission Line
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The average capacitance per phase is given by,
Page 12
Capacitance of 3-Phase, Double Circuit Line
Double Circuit Transmission Line
r’
Page 13
Capacitance of 3-Phase, Double Circuit Line
Page 14
Capacitance of 3-Phase, Bundled Conductor Line
Page 15
Conductor Tables
Inductive reactance at
1 feet spacing (Xa)
Inductive reactance
spacing factor (Xd)
Page 17
Method of Images (or Mirror Charges)
Page 18
Method of Images (or Mirror Charges)
Page 19
Capacitance of 1-phase Transmission Line Considering the
Effect of Ground
Page 20
Exercise
Problem 2:
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A single-phase transmission line consists of two conductors spaced at a distance of
1.2 m, the diameter of each conductor is 1.5 cm. Assuming that the height of the line
from the ground is 8 m, calculate capacitance between conductors and capacitance
from conductor to ground for the following cases:
(a) ignoring the effect of ground
(b) considering the effect of ground.
Page 21
CLO-1
• Apply the concept of flux linkages and voltage drop
in the calculation of inductance and capacitance of
transmission lines.
Page 22
THANK YOU FOR YOUR ATTENTION