String efficiency Methods of improving string efficiency

String efficiency in this article we are going to analyse more about what is string efficiency and what are the different types of methods used to improve the string efficiency of suspension insulator.

Distribution of potential over the string of suspension insulator:-

In suspension type string insulator the number of porcelain disc is connected and those are in series through the metallic link which dorms a string. Generally, each of the discs is designed for 11 kV.those number of discs in series depends on the line operating voltage. In below fig  we can see the spring of suspension and capacitance 'C' of each insulator disc.

If there were self-capacitance 'C' or we can also call as mutual capacitance the charging through the each disc is the same so that the voltage across each disc has the same that is V/3.but in actual the capacitance is also formed between the metal links fitting and the tower through the air a dielectric medium. This capacitance is called shunt capacitance and denoted as C₁.

As we can see the charging current in the nearest disc is more the voltage across this disc is also more than the other discs. So the disc nearest to the conductor is under high electrical stress and it is likely to be a break.

Equivalent circuit for 3 disc insulator

From the above circuit diagram which shows an equivalent circuit of the string consist of  3 insulator disc 

Let

C=self capacitance of each disc insulator.

C₁=shunt capacitance between metal link and tower.

V=Phase voltage.

V₁=voltage across disc near to cross arm.

V₂=voltage across middle disc.

V₃=voltage across disc near to conductor.

I₁, I₂, I₃=self capacitance charging current.

i₁, i₂, i₃=shunt capacitance charging current.

Applying Kirchoff's current low to the node P.

I₂=I₁+i₁

V₂.ωC=V₁.ωC+V₁.ωC₁

V₂.ωC=V₁.ωC+V₁.KC

V₂.ωC=V₁.ωC(1+K)

V₂=V₁(1+K)..................equ (1)

Applying Kirchoff's current low to the node Q.

I₂=I₁+i₁

V₃ωC=V₂ωC+(V₁+V₂)ωC₁

V₃=V₂+(V₁+V₂)K=V₂+V₁K+V₂K

V₃=V₁K+V₂(1+K)

V₃=V₁K+V₁.(1+K)(1+K)

V₃=V₁K+V₁(1+K)²

V₃=V₁[K+(1+K)²]

V₃=V₁[K+1+2K+K²]

V₃=V₁(1+3K+K²)..................equ (2)

The voltage between conductor and tower is:-

V=V₁+V₂+V₃

V=V₁+V₁(1+K)+V₁(1+3K+K²)

V=V₁(3+4K+K²)

V=V₁(1+K)(3+K)..................equ (3)

from equation (1) (2) and (3) we can say that top disc voltage is minimum and voltage is disc near to the conductor is maximum

Also read about synchronous generator

String efficiency 

Definition:- It is the ratio of the voltage across the whole string to the product of number of discs and voltage across the disc which is near to the conductor is known as String efficiency.

String efficiency formula:-

String efficiency =Voltage across the string / n x Voltage across the disc near to the conductor

where     n = no. of disc in the string from above mathematical expression

               η = V/3 x V₃

The voltage across the string of suspension insulators is not equally distributed across the dirrerent discs. The nearest disc of the line conductor subjected to a higher potential than any other disc. This unequal potential difference is not good and is usually expressed in terms of string efficiency.

 Why string efficiency in dc is 100%:-

If the voltage across the each disc is exactly the same the string efficiency becomes 100%. If the string efficiency is good then the voltage distribution is more uniform. but this is the ideal condition and this is impossible. in the DC the insulator capacitance is ineffective so the voltage across each unit is the same.

Methods of improving string Efficiency:-

1) Longer cross arm:-

From the above equation, we can say that the less the value of  'K'  then the string efficiency is high. This is gained by reducing the value of C1 means the shunt capacitance. If  we increase the distance of the insulator from the tower then the value of the shunt capacitor is reduced this can be done by increasing the length of the cross arm. For a longer cross arm the supporting structure should be taller hence it is not a cost-effective method beyond a certain length of the cross arm. Practically k=0.1 it is the limit of this method.

2)Grading of insulator:-

If there is any leakage current from the insulator pin to the tower structure then the unequal distribution of voltage is formed. If we use the different capacities disc then the product of their capacitive reactance and the current flowing through the respective unit is the same. The unit near the cross arm should have few capacitances. From this grading complete equal voltage can be obtained. This method is not normally used because this requires large stocks of differently sized units 

3)By using guard ring:-

If we use a guard ring that is a metal ring that is electrically connected to a line the potential across each disc can be equalized. Because of this ring, the capacitance exists between the metal fitting of each disc and guard ring. The guard ring is placed in such a way that I, and i that is shunt capacitance current is equal to the guard ring capacitance current i', i' and i respectively. From this the same charging current I flows from each disc of the string so that there is an equal potential distribution across the units.

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