Question

In a string of three identical suspension insulator units supporting a transmission line conductor. If the self capacitance of each unit is denoted as C farad. The capacitance of each conductor pin to ground can be taken as 0.15 C farads. If the maximum permissible voltage per unit is 20 kV. Then the string efficiency (in percentage) is ____________.

• A. 82

Answer 1

The correct option is A 82
Number of units, n = 3
Ratio of shunt capacitance to mutual capacitance,

$K=\frac{0.15C}{C}=0.15$
Voltage across bottom most unit

$V_3=$ safe working voltage of the unit = 20 kV
So voltage across top most unit,

$V_1=\frac{V_3}{1+3K+K^2}=\frac{20}{1+3\left(0.15\right)+(0.15{)}^2}=\frac{20}{1.4725}$

$V_1=13.58$ kV

Voltage across middle unit $V_2=V_1(1+K)$
= (13.58 kV) (1 + 0.15)
= 15.617 kV

Maximum safe working voltage of the string,

$V=V_1+V_2+V_3$
= 13.58 +15.617 + 20
V = 49.197 kV

String efficiency $=\frac{V}{n{V}_n}\times 100=\frac{49.197}{3\times 20}\times 100=81.955=82\%$