Capacitance of High Voltage Capacitance of High Voltage

Overhead Power LinesOverhead Power Lines

1. Line Capacitance1. Line Capacitance

V

qC

d

AC 0

• Transmission line conductors exhibit capacitance with respect to each other due to the potential difference between them.• The amount of capacitance C, between conductors is a function of conductor size, spacing and height above ground.

• Where A is the surface area of the conductor, d is the distance between conductors and 0 = 8.85 x 10-12F/m is the permittivity of free space.• By definition capacitance is also the ratio of charge q to voltage V.

• Consider a round conductor of length l .• The charge on the conductor gives rise to the Electric field with radial flux lines.• The electric field intensity at any point is defined as the force per unit charge E.

• The concentric cylinders surrounding the conductor are equipotential surfaces and have the same electrical flux density D.• From Gauss’ law the electrical flux density at radius x is:

0D

E

lx

q

A

qD

2

d1

d2

qx

E - Field

• For a 1 meter length of conductor this results in:

• The work done in moving a unit charge of 1 coulomb from d2 to d1 through the E-field is the potential difference V12. This is given as:

x

qE

02

1

2

0012 ln

2.

2.

2

1

2

1 d

dqdxx

qdxEV

d

d

d

d

2. Capacitance of single phase lines2. Capacitance of single phase lines

• Consider the two round conductors of radius r. Separated by distance d and carrying charges of q1 and q2 respectively.

q1

rq2

r

d

• Voltage between conductor 1 and 2 due to charge q1 is:

r

dqV q ln

2 0

1)(12 1

• Voltage between conductor 2 and 1 due to charge q2 is:

r

dqV q ln

2 0

2)(21 2

• Since vectors give, )(21)(12 22 qq VV

• Thus:d

rq

r

dqVVV qq ln

2ln

2 0

2

0

1)(12)(1212 21

you have:

d

rqV q ln

2 0

2)(12 2

• For a single phase line you have that qqq 12

• Thus:r

dqV ln

012

• Thus the capacitance between two conductors is:

rd

Cln

012

F/m

3. Capacitance and Neutral Planes3. Capacitance and Neutral Planes

• As previously defined for capacitance between two conductors you have C12.

• The voltage to neutral is half V12 because of half the distance between conductor 1 and 2. • Hence the capacitance to neutral C = 2C12

1 2

C12

1 2

C C

n

• For the purpose of modelling transmission lines it is convenient to define a capacitance C between each conductor and a neutral.

rd

CCln

22 0

12

F/m

• Recalling e0 = 8.85 x 10-12 F/m and converting to F/km:

• For a three phase bundled conductor line you have that:

• Where GMD is the Geometric Mean Distance and GMR is the Geometric Mean Radius of bundled conductors.

rd

Cln

0556.0 F/km

GMRGMD

Cln

0556.0 F/km

4. Capacitance of a double circuit line4. Capacitance of a double circuit line

• The per phase capacitance to neutral is:

CGMRGMD

Cln

0556.0 F/km, where

• GMRC is the GMR for calculating the per phase capacitance to neutral and calculated by considering the following circuit.

a1

a2

b1 b2

c1

c2

d1

d2

d3

3CBAC rrrGMR

1dGMRr bundleA

3dGMRr bundleC

2dGMRr bundleB

5. Effect of Earth Proximity5. Effect of Earth Proximity

• Assume the earth surface to be at same potential as neutral point of three phase system (abc). The earth can then be represented by three equivalent phase conductors (a’b’c’). Each at a depth equal to the height of the corresponding conductor.• This is known as Lord Kelvin’s Method of Images.

• For a three phase bundled conductor line you then have:

3'''''' )/(lnln

0556.0

ccbbaacabcab ddddddGMRGMD

C

F/km

• The effect of earth is to increase the Capacitance, but due to the height being large compared to the distance between conductors it is normally negligible.

6. The Ferranti Effect6. The Ferranti Effect

• A long transmission line draws a substantial quantity of charging current – Leading Mvars. • If such a line is open circuited or very lightly loaded at the receiving end, the voltage at receiving end may become greaterthan voltage at sending end.• This is known as Ferranti Effect and is due to the voltage drop across the line inductance (due to charging current) being in phase with the sending end voltages. • Therefore both capacitance and inductance is responsible for producing this phenomenon.• To counter this effect, connect shunt reactors in parallel to the end of the line – Adds lagging Mvars

7. Effect of Capacitance on pipe lines7. Effect of Capacitance on pipe lines

• Voltage from overhead power lines can be induced in pipe lines by a capacitance effect (electrostatic voltage). • This is a form of capacitive coupling operating across the capacitance between the AC transmission lines and the pipeline, in series with the capacitance between the pipeline and adjacent earth.

• These potentials are normally not induced on a buried pipeline since the capacitance between the pipeline and earth is negligible.

• However, during installation, a voltage can be produced by the influence of a strong electrical field on an insulated pipe when located above and insulated from the ground. • The electric field tends to move electrons from the earth to the pipe and also from the pipe to the overhead power line.

• In some cases, the voltage can be above maximum safe voltage limitations for a pipe; however, in normal situations, contacting the pipe will only result in a slight electrical shock and the pipe voltage is immediately reduced to zero.

• During construction, safety precautions can be established during pipe installation to protect construction personnel from the hazard of electric shock. These include grounding straps, chains attached to vehicles with rubber tires to provide a ground etc