Capacitance of a Single Core Cable

8/4/2019 Capacitance of a Single Core Cable

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Capacitance of a single core

cable


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Capacitance of a single core cable

Single core cable consists of two long co-axial cylinders.Inner cylinder is conductor and outer cylinder is a lead sheath.

R=D/2

R=d/2

Radius of the cylinder is = x


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Flux density =

Here charge=Q

Surface area =2

Radius=2 x

Flux density , Dx Cm

According to gauss law


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Electric Field intensity at point P is given by,

Since

Potential Difference between Conductor and

sheath is given by

R=D/2r=d/2


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V

Since

or

Capacitance for cable is given by

or

Substitute the values of

F/mor


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Dielectric Stress


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Dielectric Stress:

Here dielectric stress is equal to electric field

intensity at point p

Now voltage is given by

Since


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Substitute Q in

Maximum stress will be at the surface of the conductor, x=r

Since,r=d/2

Minimum stress will be at the Sheath, x=R

Since,R=D/2

So dielectric stress is


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Grading of cables


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Grading of cables

Maximum stress will be at the surface of theconductor and minimum stress will be at thesheath.

To avoid breakdown of insulation it isnecessary to have uniform distribution ofstress all along the insulator

The process of obtaining uniform distributionof stress in the insulation of cables is calledgrading of cables


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Types of Grading

Use of inter sheaths for grading

Capacitance grading


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Use of inter sheaths for grading

In this method of

grading the between

the core and lead

sheaths number ofmetallic sheaths are

placed which are called

as inter sheaths

Radius of the conductor =d/2

Radius of the intersheath1=d1/2

Radius of the intersheath1=d2/2

Radius of the lead sheath=D/2


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Use of intersheaths for grading

Let V1 be the voltage

between core and inter

sheath1

Let V2 be the voltagebetween intersheath1

and inter sheath2

Let V3 be the voltage

between intersheath2

and Lead sheath


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Maximum stress between core and sheath given by

We can write Maximum stress between core and inter sheath1 as

Similarly, Maximum stress between inter sheath1 andinter sheath2 is

Similarly, Maximum stress between inter sheath2 and Lead sheath is

Let V1 be the voltage between core and inter sheath1Let V2 be the voltage between intersheath1 and intersheath2

Let V3 be the voltage between intersheath2 and Lead sheath


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Now

Voltage between conductor and lead sheath is


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Capacitance grading


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Capacitance grading

In this type grading is done by using layers of

dielectrics having different permittivitties between

core and sheath

Let d be the diameter ofconductor

Let d1 be the diameter of

dielectric with permittivity Let d2 be the diameter of

dielectric with permittivity


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As we know, dielectric stress isgiven by

Here the stress at inner dielectric is given by

Here the stress at outer dielectric is given by

(1)

(2)


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We know

From (1) the maximum stress at the surface of conductor is ,i.e x=d/2

From (2) the maximum stress at the surface inner dielectric is , i.e x=d1/2

(3)

(4)

Substitute the value of Q in (3)


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Substitute the value of Q in (3)

Similarly Substitute the value of Q in (4)

Capacitance of a Single Core Cable

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