**String of Suspension Insulator Disc**

- Figure shows three suspension insulators. Each suspension insulator has two metallic links therefore it has its own capacitance and it is called as mutual capacitance or self capacitance.

**Mutual
capacitance ( Self capacitance )( C )**

- It is defined as the capacitance due to suspension insulator itself.
- Each metallic links acts as conducting plate and porcelain acts as dielectric material.
- The voltage across each insulator becomes same when considering only mutual capacitance of insulator.

Voltage
across string V = V1 + V2 + V3

As
V1 = V2 = V3

V1
= V / 3

V2
= V / 3

V3
= V / 3

*Shunt
capacitance ( C1 )*

- It is a capacitance between each insulator and transmission line tower.

*Explain
: The voltage across line insulator is maximum and top of the insulator is
minimum.*

__Effect
of Shunt capacitance__

- There is a capacitance between each insulator and transmission line tower.
- The charging current flows due to shunt capacitance therefore the voltage across each insulator is different.
- The charging current is maximum through line insulator and decrease towards top of the tower therefore the voltage across line insulator is maximum and its value decreases from bottom of the insulator to top of the insulator.

*String
efficiency*

String
efficiency = Voltage across string / ( n × Voltage across line
insulator )

Where
n = Number of string

= Number of discs

*Importance
of string efficiency*

- The string efficiency indicates voltage across string.
- The string efficiency 100% means that the voltage across all the discs is same. However the string efficiency of 100% achieve is almost impossible.

*Mathematically
explanation*

- Figure shows equivalent circuit of three suspension disc insulator. Let us consider that the voltage across top of the insulator to bottom of the insulator is V1, V2 and V3.
- Let

C = Capacitance across disc

= Self capacitance

C1
= Shunt capacitance

- Let us assume that C1 = mC

m = C1 / C

Where m = Constant

**Applying
Kirchhoff’s current law at point R**

I2
= I1 + i1

ɷCV2 = ɷCV1 + ɷC1V1

ɷCV2 = ɷCV1 + ɷmCV1

ɷCV2 = ɷC ( V1 + m V1 )

V2
= V1 ( 1 + m )……..( 1 )

**Applying
Kirchhoff’s current law at point Q**

I3
= I2 + i2

ɷCV3 = ɷCV2 + ɷC1( V1 + V2 )

ɷCV3 = ɷCV2 + ɷmC ( V1 + V2 )

ɷCV3 = ɷCV2 + ɷmCV1 + ɷmCV2

ɷCV3 = ɷmCV1 + ɷCV2 + ɷmCV2

ɷCV3 = ɷC [ mV1 + V2 + mV2 ]

V3
= mV1 + ( 1 + m )V2 …..( 2 )

From
equation ( 1 )

V3
= mV1 + ( 1 + m ) ( 1 + m )V1

V3
= mV1 + ( 1 + 2m + m^{2}
)V1

V3
= ( 1 + 3m + m^{2} )V1………. ( 3
)

Voltage
across string ( all insulators )

V
= V1 + V2 + V3

= V1 + V1 ( 1 + m ) + ( 1 + 3m + m^{2} )V1

= [ 1 + ( 1 + m ) + ( 1 + 3m + m^{2} ) ]V1

= [ m^{2} + 4m + 3 ]V1

= [ m^{2} + 3m + m + 3 ]V1

= [ m ( m + 3 ) + 1 ( m + 3 ) ]V1

= [ ( m + 1 ) ( m + 3 ) ]V1……….( 4 )

V1
= V / ( m + 1 ) ( m + 3 ) ……….( 5 )

From
equation ( 1 ) , ( 3 ) and ( 5 )

V1
= V / ( m + 1 ) ( m + 3 ) = V3 / ( 1 +
3m + m^{2} ) = V2 / ( 1 + m )

**Voltage
across top insulator **

V1
= V / ( m + 1 ) ( m + 3 )

**Voltage
across middle insulator**

V2
= V / ( m + 3 )

**Voltage
across line or bottom insulator**

V3
= V ( 1 + 3m + m^{2} ) / ( m + 1 ) ( m + 3 )

*String
efficiency for three insulators *

= Voltage across string / ( 3 × Voltage across line
insulator )

=
V / ( 3 × V3 )

=
V / { 3 × [V ( 1 + 3m + m^{2} ) / ( m +
1 ) ( m + 3 ) }

=
( m + 1 ) ( m + 3 ) / { 3 ( 1 + 3m + m^{2} ) }

__Let
us assume that m = 1__

String
efficiency = ( 1 + 1 ) ( 1 + 3 ) / {
3 ( 1 + 3 ( 1 ) + ( 1 )^{2} ) }

= ( 2 ) ( 4 ) / { 3
( 1 + 3 ( 1 ) + ( 1 )^{2}
) }

= ( 8 ) / ( 15
)

= 53.34%

__Let
us assume that m = 0__

String
efficiency = ( 0 + 1 ) ( 0 + 3 ) / {
3 ( 1 + 3 ( 0 ) + ( 0 )^{2} ) }

= ( 1 ) ( 3 ) / { 3
( 1 + 0 + 0 ) }

= 3 / 3

= 1

= 100%

- It means that if the shunt capacitance is equal to zero, the string efficiency is 100%

*Important
point*

- The maximum voltage is across the bottom of the string or say line insulator.
- Voltage across string is phase voltage not line voltage
- Line
voltage = ( √ 3 )
× Phase voltage
- Greater the value of m, more non – uniform distribution of voltage across string and less string efficiency
- As the number of insulators increases, the string efficiency decreases and vice versa.

*The
string efficiency becomes 100% *

(
1 ) DC transmission line or

(
2 ) When the shunt capacitance becomes zero or

(
3 ) Charging current from insulator to transmission line tower is equal to zero

*You
may also like :*

Minimum
clearance of transmission line when they crossing to each other

Minimum
clearance between transmission line and ground

Advantages
and Disadvantages of high transmitted voltage

Right of way in the transmission line

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