A Suspension type string insulation It is made up of several porcelain discs linked in series by links of metallic. String insulators, also known as suspension insulators are extensively used in electric overhead transmission system for electrical overhead transmission . However, there’s an important aspect to consider in the this case that are also commonly referred to as **String performance **.

## The potential distribution over a Suspension Insulator String

The picture below shows three discs of suspension and insulator. Since each disc of porcelain is the middle of two links made from metal, it creates an electrical capacitor. The capacitance that it creates is known as *self-capacitance *or *mutual capacitance *. Furthermore, air capacitance is in the links between the metal and the tower with an earthed base. This is referred to as *Capacity of shunt *. The image below illustrates the **equivalent circuit for an insulator with 3 discs **(assuming that the shunt capacitance is a proportion of self-capacitance i.e the shunt capacitance is self-capacitance * k).In the event that there was only mutual capacitance then the current of charging would be the same across all discs. In this situation it would be evenly dispersed across the entire string, i.e. the voltage across every disc would have been identical. Butdue to closed capacitances, the charging currents are not equal across all discs.

From the equivalent circuit using this law of Kirchoff to the node.

I_{2} = I_{1} + i_{1}

V_{2}oC = V_{1}oC + V_{1}okC

V_{2} = V_{1} + V_{1}k

V_{2} = (1 + k)V_{1} …… eq. (i)

applying Kirchoff’s current law for node B.

I_{3} = I_{2} + i_{2}

V_{3}oC = V_{2}oC + (V_{2} + V_{1})okC

V_{3} = V_{2} + (V_{1} + V_{2})k

V_{3} = kV_{1} + (1 + k) V_{2}

3 = kV 1 + (1+ k) 2 V _{3.} equals KV _{1} + (1 + k) ^{2} V _{1} …… from equation. (i)

V_{3} = V_{1} [k + (1 + k)^{2}]

V_{3} = V_{1} [k + 1 + 2k + k^{2}]

V_{3} = V_{1} (1 + 3k + k^{2}) …… eq. (ii)

Now, the voltage that exists between conductors and earthers towers will be,

V = V = _{1.} + V _{2} + V _{3}

V = V = _{1.} + (1 + k)V _{1} + V _{1} (1 + 3k + k ^{2})

V = V = _{1.} (3 + 4k+ ^{2.}) …… eq. (iii)

From using the formulas (i), (ii) from the above equations (i), (ii) and (iii) from the above equations (i), (ii) and (iii) it obvious from the above equations that voltage on the disc at the highest is minimal as the it is clear that the voltage across the disc closest to the conductor will be the highest, i.e. V _{3 }= V _{1 }(1 plus 3k) + 1 + 3k + ^{2 }). When we get closer to the cross-arm, the voltage across the disc is decreasing. Because of this uneven voltage distribution across the string the closest unit to the conductor is subject to most stress electrically and could be punctured.

## String Efficiency

As mentioned above it is not evenly distributed across a suspension insulation string. The disc closest to the conductor will have the highest voltage across it , and consequently, is under the greatest tension. This means that the disc closest to the conductor will be more likely to be punctured. Afterwards the other discs could be punctured repeatedly. Thus, this uneven voltage distribution is unaffordable and is typically described as string efficiency.

The ratio of the voltage across the entire string to the product of the number of discs as well as the voltage across the disc that is closest to the conductor is referred to as **string efficiency.**

String efficiency = voltage across the string (number of discs X the voltage across the disc closest to conductor).

The higher the efficiency of the string More uniform is the voltage distribution. String efficiency is 100% when the voltage across every disc is identical but this isn’t the ideal scenario and is not feasible in a real-world scenario. For DC voltages, the insulator capacitances aren’t effective, and the voltage across every unit will be exactly the same. This is **the reason why string efficiency for DC system is 100%.**.

Inequality in voltage distribution grows as you increase the amount of discs within strings. So shorter strings perform better than insulators with longer strings.

### Strategies to Improve String Efficiency

#### (I) Using Longer Cross Arms

It is evident from the mathematical expression on string efficiency the amount of string efficiency is contingent upon the amount of *K *. Lower the value *K *The higher the string’s effectiveness. The more string efficiency, the higher *K *is close to zero, and the string efficiency increases to 100%.. The value is *K *It is possible to reduce the capacitance of the shunt. To reduce the capacitance of the shunt it is recommended that it is recommended that the distance of the string to the tower must be increased, i.e. longer cross-arms must be employed. However there is a limit in the lengthening of cross-arms based on economic reasons.

#### (Ii) Grading of Insulator (II) Grading Of Insulator

This method allows it is possible for the voltage on each disc to be balanced by using discs that have different capacitances. To equalize the distribution of voltage in the string, the upper part of the string has to be the lowest capacitance, and the disc closest to the conductor should possess the greatest capacitance. The insulator discs that have different sizes are selected so that each disc is equipped with an individual capacitance. They are placed so that the capacitance grows gradually towards the lower. Because voltage is ininverse proportion the capacitance of an object, this approach can help equalize the voltage distribution across the disc.

#### (Iii) With the help of a Guard or Grading Ring

A grading the ring is essentially a rings that is electrically connected to the conductor that surrounds the lower part of the string insulation. The guard ring increases the capacitance between the links of metal as well as the conductor for line, which can be used to reduce capacitances of the shunt. In the end, almost identical charging currents flow through all discs increasing the efficiency of the string. Grading rings can be similar to corona rings However, they surround conductors rather than insulators.