String Efficiency & Improving Methods

String Efficiency:

The total voltage applied across the string of suspension type insulators is not equally distributed across all discs.In this distribution of voltage, disc nearest to the conductor will be at higher potential than the other discs. This unequal potential distribution is undesirable and is usually expressed in terms of string efficiency

What Is 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.e.,String efficiency =Voltage across the string/(n ×Voltage across disc nearest to conductor)

Where n = number of discs in the string.

String efficiency is an important factor is transmission line designing.since it decides the potential distribution along the string.to get uniform distribution string efficiency should be high.Thus 100% string efficiency is an ideal case for which the volatge across each disc will be exactly the same.that gives easy calculations to no.of discs to be added.but 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 for String Efficiency:-

Above Fig. 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 selfcapacitance i.e., C1 = KC. Starting from the cross arm or tower, the voltage across each unit is V1,V2 and V3 respectively as shown. 
Applying Kirchhoff’s current law to node A, we get,

I2 = I1 + i1
or V2ω C* = V1ω C + V1ω C1
or V2ω C = V1ω C + V1ω K C
∴ V2 = V1 (1 + K) ...(i)

Applying Kirchhoff’s current law to node B, we get
I3 = I2 + i2
or V3 ω C = V2ω C + (V1 + V2) ω C1 
or V3 ω C = V2ω C + (V1 + V2) ω K C
or V3 = V2 + (V1 + V2)K
= KV1 + V2 (1 + K)
= KV1 + V1 (1 + K)2   since [ V2 = V1 (1 + K)]
= V1 [K + (1 + K)²]
∴ V3 = V1[1 + 3K + K²] ...(ii)
Voltage between conductor and earth (i.e., tower) is
V = V1 + V2 + V3
= V1 + V1(1 + K) + V1 (1 + 3K + K²)
= V1 (3 + 4K + K²)
∴ V = V1(1 + K) (3 + K) ...(iii)
From expressions (i), (ii) and (iii), we get,
 V1/1=V2/(1+K)=V3/(1 + 3K + K²)=V/(1+K)(3=K)

∴Voltage across top unit, V1 = V/(1 + K)(3 + K)
Voltage across second unit from top, V2 = V1 (1 + K)

Voltage across third unit from top, V3 = V1 (1 + 3K + K²)
%age String efficiency =Voltage across the string*100/(n ×Voltage across disc nearest to conductor)
=V*100/3V3

Methods of Improving String Efficiency:

By using longer cross-arms:-

From above observation we can say The value of string efficiency depends upon the value of K i.e., ratio of shunt capacitance to mutual capacitance.For the low the value of K, the string efficiency will be high and we get uniform voltage distribution.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.e., longer cross-arms should be used.

By grading the insulators:-

In this method, different dimensions of  insulators are chosen which have different capacitance. The insulators are capacitance graded i.e. they are assembled in the string in such a way that the top unit has the minimum capacitance, increasing progressively as the bottom unit (i.e., nearest to conductor) is reached. Since voltage is inversely proportional to capacitance, this method tends to equalize the potential distribution across the units in the string. This method has the disadvantage that a large number of different-sized insulators are required.

By using a guard ring:-

The potential across each unit in a string can be equalized by using a guard ring which is a metal ring electrically connected to the conductor and surrounding the bottom insulator. The guard ring is contoured in such a way that shunt capacitance currents i1, i2 etc. are equal to metal fitting line capacitance currents i′1, i′2 etc. The result is that same charging current I flows through each unit of string. Consequently, there will be uniform potential distribution across the units.

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