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Power system (14) - NOTES
Power Electronics (203122357)
Parul University
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string efficiency is an ideal case for which the voltage across each disc will be exactly the same.
Although it is impossible to achieve 100% string efficiency, yet efforts should be made
to improve it as close to this value as possible.
Mathematical expression. Fig. 2(iii) shows the equivalent circuit for a 3-disc string. Let us
suppose that self capacitance of each disc is C. Let us further assume that shunt capacitance C1 is
some fraction K of self capacitance i., C1 = KC. Starting from the cross-arm or tower, the
voltage across each unit is V1,V2 and V3 respectively as shown.
Applying kirchoff’s current law to node A
I 2 I 1 i 1
V 2 C V 1 CV 1 C 1
V 2 C V 1 CV 1 KC
V 2 V 1 ( 1 K )
Applying kirchoff’s current law to node B
I 3 I 2 i 2
V 3 C V 2 C( V 1 V 2 ) C 1
V 3 C V 2 C(V 1 V 2 ) KC
V 3 KV 1 V 2 ( 1 K )
( 1 3 )
2 V 3 V 1 KK
100
3
%
3
V
V
stringefficiency
The following points may be noted from the above mathematical analysis:
(i) If K = 0·2 (Say), then we get, V 2 = 1·2 V 1 and V 3 = 1·64 V 1. This clearly shows that disc
nearest to the conductor has maximum voltage across it; the voltage across other discs decreasing
progressively as the cross-arm in approached.
(ii) The greater the value of K (= C1/C), the more non-uniform is the potential across the discs
and lesser is the string efficiency.
(iii) The inequality in voltage distribution increases with the increase of number of discs in
the string. Therefore, shorter string has more efficiency than the larger one
String Efficiency and methods to improve String Efficiency
The ratio of voltage across the whole string to the product of number of discs and the voltage
across the disc nearest to the conductor is known as string efficiency i.,
n Voltageacrossdiscnear to conductor
Voltageacrossthestring String Efficiency
where n = number of discs in the string.
String efficiency is an important consideration since it decides the potential distribution along the
string. The greater the string efficiency, the more uniform is the voltage distribution. Thus 100%
string efficiency is an ideal case for which the voltage across each disc will be exactly the same.
Although it is impossible to achieve 100% string efficiency, yet efforts should be made to
improve it
as close to this value as possible.
Methods of Improving String Efficiency
The maximum voltage appears across the insulator nearest to the line conductor and decreases
equalise the potential across the various units of the string i. to improve the string efficiency
progressively as the cross arm is approached. If the insulation of the highest stressed insulator
(i. nearest to conductor) breaks down or flash over takes place, the breakdown of other units
will take place in succession.
The various methods for improving the string efficiency are:
- By using longer cross-arms. The value of string efficiency depends upon the value of K i.,
ratio of shunt capacitance to mutual capacitance. The lesser the value of K, the greater is the
string efficiency and more uniform is the voltage distribution. The value of K
can be decreased by reducing the shunt capacitance. In order to reduce shunt capacitance, the
distance of conductor from tower must be increased i., longer cross-arms should be used.
However, limitations of cost and strength of tower do not allow the use of very long cross-
arms. In practice, K = 0·1 is the limit that can be achieved by this method.
- By grading the insulators. In this method, insulators of different dimensions are so chosen
that each has a different capacitance. The insulators are capacitance graded i. they are
Power system (14) - NOTES
Course: Power Electronics (203122357)
University: Parul University
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