Effect of earth on transmission line, Bundle conductor & Method of GMD EFFECTS OF EARTH ON THE CAPACITANCE OF THREE PHASE TRANSMISSION LINES Bundle Conductors

1. Topic
Effect of earth on transmission line,
Bundle conductor & Method of GMD

2. EFFECTS OF EARTH ON THE CAPACITANCE OF
THREE PHASE TRANSMISSION LINES
The capacitance of transmission line is affected by the presence of earth.
Because of earth, electric field of a line is reduced. If we assume that the
earth is a perfect conductor in the form of a horizontal plane of infinite
extent, we realize that the electric field of charged conductors above the
earth is not the same as it would be if the equipotential surface of earth were
not present.
The method of images is used while considering this type of problems.
For this consider a single phase line having 2 conductors as shown in the
Fig.

3. A fictitious conductor is placed below
each conductor of the same size and
shape as the overhead conductor lying
directly below the original conductor at a
distance equal to twice the distance of the
conductor above the plane of ground. If
the earth is removed and a charge equal
and opposite to that an overhead
conductor is assumed on the fictitious
conductor, the plane midway between
conductor and its image is an
equipotential surface and occupies the
same position as the equipotential surface
of earth. This fictitious conductor is called
image conductor having the charge
opposite to that of overhead conductor.

5. oComparing above equation with expression for capacitance of
single phase line without considering the effect of earth, we can
see that earth tries to increase the capacitance of line by small
amount.
oBut the effect is negligible if the conductors are high above
ground compared to distances between them.

6. Bundle Conductors
o Bundled Conductors are used in transmission lines where the
voltage exceeds 230 kV.
o At such high voltages, ordinary conductors will result in
excessive corona and noise which may affect communication
lines.
o The increased corona will result in significant power
loss. Bundle conductors consist of three or four conductors
for each phase.
o The conductors are separated from each other by means of
spacers at regular intervals. Thus, they do not touch each
other.

7. How Bundle Conductor Work.
ofor extra high voltage lines corona causes a large problem if the
conductor has only one conductor per phase. Corona occurs when
the surface potential gradient of a conductor exceeds the dielectric
strength of the surrounding air.
oThis causes ionization of the area near the conductor. Corona
produces power loss. It also causes interference with communication
channels. Corona manifests itself with a hissing sound and ozone
discharge. Since most long distance power lines in India are either
220 kV or 400 kV, avoidance of the occurrence of corona is desirable.

8. oThe high voltage surface gradient is reduced considerably by having
two or more conductors per phase in close proximity. This is called
conductor bundling .
oThe conductors are bundled in groups of two, three or four . The
conductors of a bundle are separated at regular intervals with spacer
dampers that prevent clashing of the conductors and prevent them
from swaying in the wind. They also connect the conductors in
parallel.

9. Advantage Of Bundle Conductor
o Bundled conductors are primarily employed to reduce the corona loss and radio interference.
However they have several advantages:
o Bundled conductors per phase reduces the voltage gradient in the vicinity of the line. Thus
reduces the possibility of the corona discharge. (Corona effect will be observed when the air
medium present between the phases charged up and start to ionize and acts as a conducting
medium. This is avoided by employing bundled conductors)
o Improvement in the transmission efficiency as loss due to corona effect is countered.
o Bundled conductor lines will have higher capacitance to neutral in comparison with single lines.
Thus they will have higher charging currents which helps in improving the power factor.

11. Method of GMD
• Concept of Self-GMD and Mutual-GMD The use of self geometrical mean distance and mutual
geometrical mean distance (mutual-GMD) simplifies the inductance calculations, particularly relating to
multi conductor arrangements. The symbols used for these are respectively Ds and Dm.
• Self-GMD (DS) :
• In order to have concept of self-GMD (also sometimes called Geometrical mean radius ; GMR), consider
the expression for inductance per conductor per metre
• = 2 × 10−7 1
4
+ log 𝑒
𝑑
𝑟
• = 2 × 10−7
×
1
4
+ 2 × 10−7
log 𝑒
𝑑
𝑟

12. In this expression, the term 2 × 10-7 × (1/4) is the inductance due to flux within the solid conductor.
For many purposes, it is desirable to eliminate this term by the introduction of a concept called self-
GMD or GMR. If we replace the original solid conductor by an equivalent hollow cylinder with
extremely thin walls, the current is confined to the conductor surface and internal conductor flux
linkage would be almost zero.
Consequently, inductance due to internal flux would be zero and the term 2 × 10-7 × (1/4) shall be
eliminated. The radius of this equivalent hollow cylinder must be sufficiently smaller than the
physical radius of the conductor to allow room for enough additional flux to compensate for the
absence of internal flux linkage.
Self - GMD.

13. The mutual-GMD is the geometrical mean of the distances form one conductor to the other and, therefore, must be
between the largest and smallest such distance. In fact, mutual-GMD simply represents the equivalent geometrical
spacing.
The mutual-GMD between two conductors (assuming that spacing between conductors is large compared to the
diameter of each conductor) is equal to the distance between their centres i.e.
Dm = spacing between conductors = d
For a single circuit 3-φ line, the mutual-GMD is equal to the equivalent equilateral spacing i.e., (d1 d2 d3) 1/3 .
Dm = (d1 d2 d3) 1/3
The principle of geometrical mean distances can be most profitably employed to 3-φ double circuit lines. Consider the
conductor arrangement of the double circuit shown in Fig. below Suppose the radius of each conductor is r.
Fig. Self-GMD of conductor = 0·7788 r
Self-GMD of combination aa´ is Ds1 = (𝐷𝑎𝑎 × 𝐷𝑎𝑎′ × 𝐷𝑎′𝑎′ × 𝐷𝑎′𝑎)
1
4
Self-GMD of combination bb´ is Ds2 = (𝐷𝑏𝑏 × 𝐷𝑏𝑏′ × 𝐷𝑏′𝑏′ × 𝐷𝑏′𝑏)
1
4
Self-GMD of combination cc′ is Ds3 = (𝐷𝑐𝑐 × 𝐷𝑐𝑐′ × 𝐷𝑐′𝑐′ × 𝐷𝑐′𝑐)
1
4
Equivalent self-GMD of one phase Ds =(𝐷𝑠1 × 𝐷𝑠2 × 𝐷𝑠3)
1
3
Mutual-GMD.

14. • The value of Ds is the same for all the phases as each conductor has the same radius Mutual-GMD between phases A
and B is
• DAB = (Dab × Dab′× Da′b × Da′b′) 1/4
• Mutual-GMD between phases B and C is
• DBC = (Dbc × Dbc′× Db′c × Db′c′) 1/4
• Mutual-GMD between phases C and A is
• DCA = (Dca × Dca′× Dc′a × Dc′a′) 1/4
• Equivalent mutual-GMD, Dm = (DAB × DBC × DCA) 1/3
• It is worthwhile to note that mutual GMD depends only upon the spacing and is substantially independent of the
exact size, shape and orientation of the conductor.