This document discusses capacitance in power transmission lines. It begins by defining potential difference between two points due to a charge and the concept of capacitance as the work done to move a unit charge through an electric field. It then examines the capacitance of two-wire and three-phase power lines with both equilateral and unsymmetrical spacing between conductors. Specifically, it provides equations for calculating capacitance between conductors in different configurations and discusses the effects of bundling multiple conductors.

1. EE313
Power Transmission
Lecture 3: Capacitance
Dr. Ammar Arshad
Assistant Professor
Dept. of Electrical Engineering
Ghulam Ishaq Khan Institute of Engineering
Sciences and Technology
ammar.arshad@giki.edu.pk

2. Electric field intensity of along
straight line
Gaussian Law
E is constant
– Moving outward radially
– Surface is equidistant from the conductor
1

3. Potential Difference b/w Two Points
Due to a Charge
• Conductor carrying +ve charge
• Positive charge movement
– P2 P1 (work done)
– P1 P2 (Energy released)
– Potential of P2 in comparison to P1???
• Potential difference between 2-points
– Work done in moving unit charge through the electric field
produced by the charge on the conductor
2

4. Capacitance of 2-wire line
Conductor 1  q1
Conductor 2  q2
Assumption:
– Conductor 1 alone has a charge q1
– Voltage between conductor 1 and 2 is:
– Conductor 2 alone has a charge q2
– Voltage between conductor 2 and 1 is:
3

5. Capacitance of 2-wire line
Principle of superposition
For a single phase line:
Capacitance between conductors:
4

6. Capacitance of 2-wire line
Line to neutral capacitance
– Voltage between the conductor and neutral is half
5

7. Capacitance of 2-wire line
6

8. Capacitance of 3-phase line
Equilateral spacing
To calculate
– Voltage 𝑉𝑎𝑏 of the 3-phase line only due to the charges
on conductors 𝑎 and 𝑏:
– To add the effect of 𝑞𝑐
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9. Capacitance of 3-phase line
Equilateral spacing
– Similarly for 𝑉
𝑎𝑐:
– Adding 2 equations
– For the balanced system
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10. Capacitance of 3-phase line
Equilateral spacing
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11. Capacitance of 3-phase line
Equilateral spacing
Per phase capacitance
Charging current
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12. Capacitance of 3-phase line
Equilateral spacing
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13. Capacitance of 3-phase line
Unsymmetrical spacing
Non transposed line
– Phase to neutral capacitances are different
Transposed line
– Average capacitances of phase to neutral are
equal
12

14. Capacitance of 3-phase line
Unsymmetrical spacing
Position 1
Position 2
Positioin 3
13

15. Capacitance of 3-phase line
Unsymmetrical spacing
Average voltage
14
Average

16. Capacitance of 3-phase line
Unsymmetrical spacing
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18. 17

19. 18
Effect of Bundling
The Capacitance per phase:

20. 19
Capacitance of Bundled Conductor
Calculate 𝑉
𝑎𝑐
and the find the
𝑉
𝑎𝑛 ………

21. 20