A suspension type string insulator consists of a number of porcelain discs connected in series through metallic links. Suspension insulators or string insulators are very widely used in electrical overhead transmission system. However, there is a significant thing to be considered in case of these string insulators, known as string efficiency.
Potential distribution over a suspension insulator stringThe figure below shows a 3-disc string of suspension insulator. As each porcelain disc lies in between two metal links, it forms a capacitor. This capacitance is known as self-capacitance or mutual capacitance. Moreover, air capacitance is also present between metal links and the earthed tower. This is known as shunt capacitance. The figure below illustrates the equivalent circuit of a 3-disc suspension insulator (assuming that shunt capacitance is some fraction of self-capacitance i.e shunt capacitance = k * self-capacitance).
If there were only mutual capacitances, then the charging current would have been the same through all the discs. In this case, the voltage would have been uniformly distributed across the string, i.e. voltage across each disc would have been the same. But, due to the shut capacitances, charging current is not the same through all the discs.
From the above equivalent circuit, applying Kirchoff's current law to node A,
V2ωC = V1ωC + V1ωkC
V2 = V1 + V1k
V2 = (1 + k)V1 ...... eq.(i)
applying Kirchoff's current law to node B,
V3ωC = V2ωC + (V2 + V1)ωkC
V3 = V2 + (V1 + V2)k
V3 = kV1 + (1 + k) V2
V3 = kV1 + (1 + k)2 V1 ...... from eq.(i)
V3 = V1 [k + (1 + k)2]
V3 = V1 [k + 1 + 2k + k2]
V3 = V1 (1 + 3k + k2) ...... eq.(ii)
Now, voltage between the conductor and the earther tower is,
V = V1 + (1 + k)V1 + V1 (1 + 3k + k2)
V = V1 (3 + 4k + k2) ...... eq.(iii)
from the above equations (i), (ii) & (iii), it is clear that the voltage across the top disc is minimum while voltage across the disc nearest to the conductor is maximum, i.e. V3 = V1 (1 + 3k + k2). As we move towards the cross arm, voltage across the disc goes on decreasing. Due to this non-uniform voltage distribution across the string, the unit nearest to the conductor is under maximum electrical stress and is likely to be punctured.