## String Efficiency

Table of Contents

what is string efficiency

**String Efficiency of Insulator:**

The voltage applied across the string of suspension insulators is not evenly distributed across different components or discs, as was already mentioned. The potential of the disc closest to the conductor is much higher than that of the other discs. This undesirable uneven potential distribution is typically expressed in terms of the string efficiency of the insulator.

**String efficiency, or the “string efficiency formula,” is the ratio of the voltage across the entire string to the product of the number of discs and the voltage across the disc that is closest to the conductor.**

The string efficiency of the insulation is a crucial factor because it determines how the potential is distributed along the string. The voltage distribution is more consistent the higher the string efficiency. Therefore, a perfect scenario in which the voltage across each disc is the same is a string efficiency of 100%. Although 100% string efficiency is unachievable, efforts should be made to bring it as close to this value as possible.

**Expression in mathematics: Figure 8.11 depicts the equivalent circuit for a string of three discs. Let’s assume that each disc has a C self capacitance. Assume further that shunt capacitance C1 is some fraction K of self capacitance, or that C1 = KC. The voltage across each unit, as measured from the cross-arm or tower, is V1, V2, and V3, respectively, as shown.**

### Applying Kirchhoff’s current law to node A, we get,

### Applying Kirchhoff’s current law to node B, we get,

### Voltage between conductor and earth (i.e., tower) is

From expressions (i), (ii) and (iii), we get,

And Voltage across top unit,

Voltage across second unit from top, V_{2} = V_{1 }(1 + K)

Voltage across third unit from top, V_{3} = V_{1} (1 + 3K + K^{2})

The following points may be noted from h above mathematical analysis :

**If K = 0.2 (Say), then from exp. (iv), 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.**The greater the value of K (= C**_{1}/C), the more non-uniform is the potential across the discs and lesser is the String Efficiency of Insulator.**Shorter strings are more efficient than longer ones because there is an increase in voltage distribution inequality with the number of discs in the string.**

**Methods of Improving String Efficiency**

It has been seen above that potential distribution in a string of suspension insulators is not uniform. The maximum voltage appears across the insulator nearest to the line conductor and decreases progressively as the cross-arm is approached. If the insulation of the highest stressed insulator (i.e. nearest to conductor) breaks down or flash over takes place, the breakdown of other units will take place in succession. This necessitates to equalize the potential across the various units of the string i.e. to improve the string efficiency.

#### The various methods to improve string efficiency

**By using longer cross-arms.**

The value of K, or the ratio of shunt capacitance to mutual capacitance, determines the value of the string efficiency of the insulator. The String Efficiency of Insulator is higher and the voltage distribution is more uniform the lower the value of K. Shunt capacitance can be decreased to lower the value of K. Longer cross-arms should be used in order to increase the distance between the conductor and the tower in order to reduce shunt capacitance. However, using very long cross-arms is not an option due to tower strength and cost restrictions. The upper limit that can be reached by this method in practise is K = 0.1.

**By grading the insulators**

With this technique, insulators of various sizes are selected so that each has a unique capacitance. The insulators are capacitance graded, which means that they are put together in the string so that the top unit has the lowest capacitance,. And the capacitance rises steadily until it reaches the bottom unit (i.e., the one closest to the conductor). This technique has the tendency to equalise the potential distribution among the units in the string because voltage is inversely proportional to capacitance. The drawback of this approach is the necessity of using numerous insulators of various sizes. However, if standard insulators are used for the majority of the string. And larger units are used for the area close to the line conductor, good results can be obtained.

**By using a guard ring.**

A guard ring, which is a metal ring electrically connected to the conductor and encircling the bottom insulator as shown in Fig. 8.13, can be used to equalise the potential across each unit in a string. Capacitance between metal fittings and the line conductor is introduced by the guard ring. Shunt capacitance currents i1, i2, etc. are equal to metal fitting line capacitance currents i′1, i′2, etc. thanks to the guard ring’s contouring. As a result, each string unit experiences the same charging current I. As a result, potential will be distributed equally among the units.