The need for improvement of string efficiency arises as the voltage distribution among different insulator discs in a string insulator is not uniform. The voltage across the insulator disc nearest to the line conductor is high compared to the voltage across the insulator disc farthest from the line conductor. In case the voltage across the nearest insulator reaches beyond its safe value, breakdown may occur and successive breakdown of neighboring insulator discs will take place.

Also, if the voltage across the insulator disc farthest from the line is too low, the effective capacity of that disc will not be utilized resulting in decreased efficiency of the insulator string. Therefore, there are methods adopted for equal distribution of voltage across different insulators to improve string efficiency. The following methods used to improve string efficiency are,

## By using Longer Crossarms :

Voltage can be more uniformly distributed across different insulators by reducing the value of k which is the ratio of shunt capacitance to mutual capacitance. This can be done by increasing the distance between the tower and line by using longer cross arms as shown below.

The use of longer cross arms reduces shunt capacitance. This method has limitations of increase in cost and decrease in mechanical strength and the practical value of k obtained by this method cannot be reduced below 0.1.

## By Grading the Insulators or Capacitors :

In order to make the uniform voltage distribution across all the discs, the insulator discs of different capacitances are used such that the insulator disc nearer to the cross-arm is having maximum capacitive reactance (i.e., minimum capacitance) and the disc nearer to the line conductor is having minimum capacitive reactance (i.e., maximum capacitance). Hence, to carry out capacitance grading, it is necessary to stock the insulator discs of different values, which is against the standardization. Thus, this method is used for voltages above 200 kV.

Moreover, the capacitance values of individual insulator discs can be calculated. Consider, a string consisting of four insulator discs whose equivalent circuit is shown in the figure below. Let the capacitance of the insulator discs be C_{1}, C_{2}, C_{3}, and C_{4} respectively and C' be the shunt capacitance. Assume the ratio of shunt capacitance the mutual capacitance be k.

#### Now, applying KCL at node P, we get,
*I*_{2} = I_{1} + i_{P}
*Ï‰ C*_{2} V = Ï‰ C_{1} V + Ï‰ C' V
*C*_{2} = C_{1} + kC_{1} (since C' = kC_{1})
*C*_{2} = C_{1} (1 + k) ...(1)
Applying KCL at node Q, we get,
I_{3} = I_{2} + i_{4}
*Ï‰ C*_{3} V = Ï‰ C_{2} V + Ï‰ C' (2 V)
*C*_{3} = C_{2} + kC_{1} × 2 (since C' = kC_{1})
*C*_{3} = C_{1} (1 + k) + 2kC_{1} (from equation 1)
*C*_{3} = C_{1} (1 + 3k) ...(2)
Similarlly, applying KCL at node R, we get,
*I*_{4} = I_{3} + i_{r}
*Ï‰ C*_{4} V = Ï‰ C_{3} V + Ï‰ C' (3 V)
*C*_{4} = C_{3} + 3kC_{1}
*C*_{4} = C_{1} (1 + 3k) + 3kC_{1} (from equation 2)
*C*_{4} = C_{1} (1 + 6k) ...(3)

*I*

_{2}= I_{1}+ i_{P}*Ï‰ C*

_{2}V = Ï‰ C_{1}V + Ï‰ C' V*C*

_{2}= C_{1}+ kC_{1}(since C' = kC_{1})*C*

_{2}= C_{1}(1 + k) ...(1)_{3}= I

_{2}+ i

_{4}

*Ï‰ C*

_{3}V = Ï‰ C_{2}V + Ï‰ C' (2 V)*C*

_{3}= C_{2}+ kC_{1}× 2 (since C' = kC_{1})*C*

_{3}= C_{1}(1 + k) + 2kC_{1}(from equation 1)*C*

_{3}= C_{1}(1 + 3k) ...(2)*I*

_{4}= I_{3}+ i_{r}*Ï‰ C*

_{4}V = Ï‰ C_{3}V + Ï‰ C' (3 V)*C*

_{4}= C_{3}+ 3kC_{1}*C*

_{4}= C_{1}(1 + 3k) + 3kC_{1}(from equation 2)*C*

_{4}= C_{1}(1 + 6k) ...(3)The capacitance can be calculated for n number of insulator discs in a similar way. From the above calculations, it can be concluded that the distribution of voltage across the individual insulator disc can be made uniform if and only if the capacitance is in the ratio 1:(1+k):(1+3k):(1+6k) and so on.

The drawback of capacitance grading is that the unavailability of insulator discs with the capacitance values as mentioned above. However, nearby values can be achieved by employing standard insulator discs.

## By Using Guard Ring or Static Shielding :

Due to the non-uniform distribution of voltage, the string efficiency is very less, the insulators are not utilized properly. Also, the insulator near the conductor is under more stress and is likely to be punctured. In order to avoid these drawbacks, a guard ring is used.

A guard ring is a metallic ring connected to the conductor and surrounds the bottom disc. It is countered in such a way that the voltage distribution across the string is uniform. The basic idea behind using a guard ring is to create the effect of another capacitance such that the charging current of the earth capacitance and the ring capacitance are almost equal and opposite in direction. Hence, these two currents almost cancel out and the distribution of voltage is uniform across the string. The above figure shows the suspension insulator with a guard ring.

#### Let,- mC = Self capacitance of each disc
- C = Earth capacitance
- C' = capacitance due to guard ring
- I
_{1}, I_{2},....I_{n}, I_{n+1} = Current through each disc - i
_{1}, i_{2},...., i_{n} = Charging current in the earth capacitance - i
_{1}', i_{2}',...., i_{n}' = Charging current in the ring capacitance.

Applying KCL at node n, we get,
*I*_{n+1} + i_{n}' = i_{n} + I_{n}
Since, all the discs are assumed to be ideal,
*I*_{n} = I_{n+1}
*∴ i*_{n}' = i_{n}
Let the voltage across the string be PV, where V is the voltage across each disc and P is the number of discs.

_{1}, I_{2},....I_{n}, I_{n+1}= Current through each disc_{1}, i_{2},...., i_{n}= Charging current in the earth capacitance_{1}', i_{2}',...., i_{n}' = Charging current in the ring capacitance.*I*

_{n+1}+ i_{n}' = i_{n}+ I_{n}*I*

_{n}= I_{n+1}*∴ i*

_{n}' = i_{n}