The grading of cables

ANALS POWER SYSTEM ANALYSIS MISSAN UNIVERSITY\ COLLEGE OF ENGINEERING / ELECTRICAL DEP.

Chapter Seven

Under Ground Cables

Construction of cables

In the fig (7.1)below, shows the general construction of

(3-condctor) cable

The various part of cable are :

1- Core or conductor

A cable may have one or more than one core (conductor) depending upon the type of service for which it is intended.

For instance, the 3- conductor cable shown in the fig. (7.1) is used for

service.

The conductors are made of tinned copper or aluminum an are usually stranded in order to provide flexibility to the cable.


2- insulation

Each core or conductor is provide with a suitable thickness of insulator, the thickness of layer depending upon the voltage

To be with stood by the cable. The commonly used materials for insulation are impregnated paper, varnished cambric or rubber mineral compound.

3- Metallic sheath.

In order to protect the cable from moisture, gases or other damaging liquids (acids or alkalis) in the soil and atmosphere, a metallic sheath of lead or aluminum is provided over the insulation as shown in the fig.

(7.1)

4- Bedding

Over the metallic sheath is applied a layer of bedding which consists of a fibrous material like jute or hessian tape. The purpose of bedding is to protect the metallic a against corrosion of bedding is to protect the metallic against corrosion and from mechanical in jury due to armoring.

5- Armouring :

Over the bedding armaouring is provide which consists of one or two layers of galvanized steel wire or steel tape. Its purpose is to protect the cable from mechanical injury while laying it and during the course of handling . Armouring may not be done in the case of some cable.

6- Serving :.

In order to protect armouring from atmospheric condition. Layer of fibrous material (like jute) similar to bedding is providing over the armouring. This is known as serving. It may not be out of place to mention here that bedding, armouring and serving are only applied to the cable for protection of conductor insulation and to protect the metallic sheath from mechanical in jury.



Under Ground Cable

The most materials that used for made the insulator of cable is the paper that saturate by oil like manila hemp or wood pulp or Ray. Also there is another impotent materials that used for made the insulator which is P.V.C. ( poly ving chloride) .

R

The fig. (7.2) represent a cross- section

For a single core cable where r is the radius of the conductor

R is the radius of the cable or

( the inside radius of the sheath) r

(q) represent the charge on the

Surface of the conductor for

Each on mater from the length

Of the cable.

Fig . (7-2)

is the electric flux density at aradius X meter from the center of the cable ( for one mater of the length of conductor)

Coulomb/

(1)


The electric field intensity or voltage gradient or electric stress at the same distance X is

Volt / meter

(2)

Where o is the relative permittivity of free space

( o= and is the relative permittivit of insulator.

V is the voltage difference between the conductor and sheath.

Volt

(3)

The capacity for each meter of the length of single core cable is

( one meter of length of conductor )

F/m

(4)

MF/m

(5)


Electric stress in single core cable :.

The direction of the electric field in the insulator will be radial value of its will as follow : and the

Where q is the charge

Of the cable and

Of the cable.

As shown in eq.(2) at a distance x

v/cm at a distance X

(6)

The maximum electric stress will be at the surface of the conductor

(at x=r)

v/cm

(7)


The minimum electric stress will at the inside surface of the sheath of the cable (at X= R )

V/cm

(8)

Also

* In the case of the stranded conductor. The electric stress will be increase by 15 %, 25% from the value of the smooth conductor.

*If the value of the voltage V and the inside radius of the sheath R are constant and r is variable where ( r is the radius of the conductor of the cable )

(

*Most economical conductor size in the cable

The minimum value of the electric stress on the surface of the conductor

will be when is amaximum value.

Now

Assume

The maximum value will be when


The grading of cables :.

The grading of the cable is redistribution the electric stress on the insulator where the value of the electric stress will be increase at the outside layer of insulator and it is value will be remain constant at the surface of the conductor as before the grading. Also by this method we can reduce the thickness of the insulator.

There are two method for grading the cable

1-Capacitive grading :.

By using a different insulator layers have a different relative permittivity.

2-Metallic inter sheath grading :.

By using the same insulator material for the different insulating layers and separate these layers by a metallic inter sheath in order to control the voltage across the insulator.

Capacitive grading

R

Where is the maximum electric stress of the cable of the first layer

is the minimum electric stress of the first layer


is the maximum electric stress of the second lager

is the minimum electric stress of the second lager

is the maximum electric Stress of the third layer

is the minimum electric Stress of the third layer and

for the cable


Ex1) single core cable covered by the lead and design for 66 kv. If the radius of the conductor is 0.5 cm and the insulator consists of three layers have a relative permittivity of 5,4,3 respectively and the electric stresses on these layers are 40,30,20 kv/cm respectively. Find inside of the sheath of the cable.

So1) v r

R

Also



Ex2) 66 kv single core cable covered by the lead the radius of it's conductor is 0.5cm. The insulating materials consists of two layers the thickness of each layers is 1.5cm . The relative permittivity of inside layers is 3 and for the outside layer is 2.5 calculate the electric stress at the surface of the conductor.

So1) r

R


*Inter sheath grading

In this method the insulator of the cable is consists of two layers or more than two layers from the same material and spate each of two next layers by a screen or metallic inter sheath has a cylindrical shape and the inter sheaths are connected to tapping from the supply transform where the voltage across these sheath make the layers of the insulator take each it's voltage from the total voltage.

r

V

O

Supply

Transformer


Ex3) A single core cable covered by the lead and design for 100 kv. The radius of it's conductor is 1 cm the inside radius of the outside sheath is 4 cm. If an metallic inter sheath is placed at a radius 2.5 cm and connected to supply transformer through an switch. The relative permittivity of the insulator is 3.5. Find :.

1-The maximum electric stress of the cable and the voltage of the inter sheath to the surface of the conductor when this inter sheath is not connected to supply transformer ( the switch is open )

2-When the switch is closed, find the electric stress on the surface of the conductor and on the two sides of the inter sheath when the voltage of the inter sheath to the conductor surface is 44 kv. Also find the voltage of the transformer.

3-Compare the cable in (2) which is a grading cable with section (1) which is not grading cable.

So1)

R r

Supply

Transformer


( the voltage between surface of conductor

and the inter sheath )

2) when the switch closed

The electric stress at the inside surface of metallic inter sheath

The electric stress at the outside of the inter sheath

Where

3) Comparing

The using of inter sheath grading cause a reduction in the maximum electric stress by


In the case of not grading cable in section (1) , and order to reduce this max. electric stress to the value of grading cable

without using metallic inter sheath grading with same cable :.

We must increase the radius of cable in other words increase the distance of insulator as follow :.

We must increase the thickness of insulator by 4.03 cm in order to get the same maximum electric stress of grading cable without using metallic inter sheath grading.

Ex4) A single core cable covered by the lead and design for 120 kv and 50

HZ. The radius of it's conductor is 1cm and the inside radius of the outside sheath is 4.2cm. An metallic inter sheath of radius 2 cm is used for grading the cable. The relative permittivity of the insulator is 3.8. the length of the cable is 6.4 km. find :.

1-The capacity of each of the two layers that have the same insulator materials.

2-The overall efficiency

3-The maximum electric stress when the inter sheath is not connected to the supply to the supply transformer.

4-The voltage of the inter sheath to the surface of the conductor in order to keep the electric stress on the surface of the conductor at 55 kv/cm (the inter sheath is connected to supply transformer)

5-The charging current.


So1)

R r

2)

OR


3)

Not grading

4)

grading

5)


-- Optimal or best location of the inter sheath inside the cable

If we have a cable having a two metallic inter sheath as shown in the fig.

below:.

And in order to get the

Optimal or best location

Of the inter sheath, we

Must put

R r

O

V


- The maximum and minimum electric stress of cable with optimal location of metallic inter sheath

In order to make the maximum electric stress at the surface of conductor and the minimum electric stress at the inside surface of the sheath of cable we must put:.


Kv/cm

For 3 layer

2 metallic inter sheath

Also

Kv/cm

For 3 layers

2 metallic inter sheath


As before

For the same distance of grading cable, we have un grading cable has the same distance of grading cable un

Or

..........

We see that if the voltage across the cable is constant and the volume

(distance (r,R)) is constant the grading cable by the inter sheath grading cause a reduction in the value of maximum electric stress by

.........


Also in other sides

For the same value of maximum electric stress and with remain the distance of cable constant (r,R) we can increase the voltage across the cable due to the inter sheath grading of cable.

We see that if the voltage across the cable is constant and the volume

(distance (r,R) ) is constant. The grading cable by the inter sheath grading cause a reduction in the value of maximum electric stress by

-- Also in other side :.

For the same value of maximum electric stress and with remain the distance of cable (r . R) constant, we can increase the voltage across the cable by due to the inter sheath grading of cable.


*Note

When there is one metallic inter sheath

R r

Kv/ cm

Also



Ex5) 33kv single core cable has a conductor diameter of 2.5cm and the diameter of the inside sheath of the cable is 6 cm. It is design to reduce the maximum electric stress by using a two metallic inter sheath.

Determine the best position of the inter sheath and the reduction in electric stress.

So1) Best position of inter sheath means

=

The reduction is


Ex6) single core cable of 66kv has a radius of conductor of 1cm. The radius of the cable is 6 cm. The insulator consists of one layer. If a two metallic inter sheath is placed into the insulator and connected to supply transformers through an switches. If the radius of first metallic inter sheath is 2.5cm, and the radius of second metallic inter sheath is 4 cm.

1-When the switches are open. Find the voltage between the first and second metallic inter sheath.

2- When the switches are closed and the voltage of first transformer is 30kv and the voltage of second transformer is 20 kv. Find the electric stress at the inside surface of second metallic inter sheath, also find the min. electric stress of cable.

So1)

1)

R

V r


The voltage between the firs

And second metallic inter sheath

2)

the voltage of the first transformer

The voltage of the second transformer

In order to find the min. electric stress of cable electric stress of cable is


Or in other way

(1)


Ex7) find the most economical conductor diameter of single core cable to be used on 132 kv, also, find the overall diameter of insulator if the permissible stress is not to exceed.

So1)

For most economical conductor diameter

The value of operating voltage per phase

The diameter of the cable is


Resistance of cable :.

R r

Where is the resistivity of insulator

L is the length of cable

R is the radius of cable

is the radius of conductor

Ex8) single core cable of 33kv, consist of two layers of insulators, each of its have a relative permittivity of 5,3 respectively. If a metallic inter sheath is placed between the layers and connected to supply transformer through an switch.

If the ratio of electric stress at the outside surface of metallic inter sheath to the electric tress at the inside surface of sheath of cable is .

The radius of the conductor is 1.5 cm and the radius of the cable is 7cm.

when the switch is open

1-Find the voltage between metallic inter sheath and the sheath of cable.

2-The electric stress at the inside surface of metallic inter sheath

3-Min electric stress of cable of cable


So1)

R r

1)

2)

3)


EX9) single core cable of 80kv has a radius of conductor of 1cm and the radius of cable is 7cm. his insulator consists of one material.

If a two metallic inter sheath is placed into the insulator and connected to the supply transformer through an switches. The radius of first and second metallic inter sheath are 3,5cm respectively and the voltage of transformers are 4 cm

1-When the switches are open find the voltage between the first metallic inter sheath and sheath of cable

2-When the first switch that connected to first transformer is closed and the second switch remain open.

Find the voltage between second metallic inter sheath and sheath of cable.

So1) r


2)

OR

OR

15.73=


EX10) single core cable of 66kv has a radius of conductor of 1.5cm.

The insulator consists of two layer. The thickness of first layer is 2.5

cm and the thickness of second layer is 4cm. Also the relative permittivity of first and second layers are 5,4 respectively. If an metallic inter sheath is placed at a radius of 6cm and connected to supply transformer through an switch when the switch is open find

-The voltage between metallic inter sheath and the sheath of cable also find. The electric stress at the outside surface of metallic inter sheath.

So1) r


1)

OR


Type of cable fault :.

Cables are generally laid directly in the ground or in ducts in the underground distribution system. For this reason, there are little chances of fault in underground cables. However, if a fault does occur, it is difficult to locate and repair the fault because conductors are not visible. Never the less, the following are the fault most likely to occurs in underground cables

1-Open – circuit fault

2-Short – circuit fault

3-Earth fault.

1-Open –circuit fault :.

When there is a break in the conductor of a cable, it is called opencircuit fault. The opencircuit fault can be cheeked by a mugger. For this purpose, the three conductors of the 3- core cable at the for end are shorted and earthed. Then resistance between each conductor and earth is measured by a mugger. The mugger will indicate zero resistance in the circuit of the conductor that is not broken. However, if the conductor is broken, the mugger will indicate infinite resistance in its circuit.

2-Short- Circuit fault :.

when two conductors of a malt- core cable come in electrical contact with each other due to insulation failure, it is called a short- circuit fault.

A gain, we can seek the help of a megger to check the fault. For this purpose the two terminal of the megger are connected to any two conductors. If the megger gives zero reading. It indicates short circuit fault between these conductor the same step is repeated for other conductors taking two at a time.


3) Earth fault:.

when the conductor of a cable comes in contact with earth it is called

\ earth fault or ground fault. To indentify this fault, one terminal of the mugger is connected to the conductor and the other terminal connected to earth. If the mugger indicates zero reading, it means the conductor is earthed. The same procedure is requited for other conductor of the cable.

Murray loop lest :.

The Murray loop lest is the most common and accurate method of locating earth fault or short- circuit fault in underground cables.

i -) Earth fault:.

In fig. below :

Fig . (7.3)


Fig.(7.3) shows the circuit diagram for locating the earth fault by

Murray loop test. Here AB is the sound cable and CD is the fault cable; the earth fault occurring at point F. The foe and D of the faulty cable is joined to the for end B of the sound cable through a low resistance link.

The variable resistance P and Q are joined to ends A and C respectively and serve as the ratio arms of the Wheatstone bridge. Let R= resistance of the conductor loop up to the fault from the test end

X= resistance of the other length of the loop

Note that P,Q,R and X are the four arms of the Wheatstone bridge. The resistances P and Q are varied till the galvanometer indicates zero deflection. In the balanced position of the bridge, we have

II r is the resistance of each cable, then R+X=2r

II L is the length of each cable in meters, then resistance per meter length of cable =

Distance of fault point from test end is


M

Thus the position of the fault is located. Note that resistance of the fault is in the battery circuit and not in the bridge circuit . therefore, fault resistance does not a fact the balancing of the bridge However. If the fault resistance is height, the sensitivity of the bridge is reduced.

In the fig. (7.4) below: fig. (7.4) loop test. A gain P,Q, R and X are the arms circuit and not in the bridge circuit. The bridge in balanced by adjusting the resistance P and Q .

In the balanced position of the bridge


Thus the position of the fault is located


* Capacitance of 3-core cables

The capacitance of a cable system is much more important than that of over head line because in cables

1- Conductors are nearer to each other and to the earthed

2- They are separated by a dielectric of permittivity much greater than that of air

The fig. (7.5) below shows the system of capacitance in belted cable.

fig (7.5)

Since potential difference exists between pairs of conductors and between each conductor and sheath. The electrostatic fields are setup in the cable and gives arise to core-core capacitance Cc and conductorearth capacitance Ce as shown in the fig (7.5 ii)

The three capacitance Cc are delta connected where's the three capacitance Ce are star connected, the sheath for many the star point as

In order to find the whole equivalent capacitance of cable we must make the following steps.

1-Convert the three delta core capacitance Cc into star connection

Where


2- It can be easily show that the equivalent star capacitance is in parallel with the sheath capacitance as shown in the fig.(7-6) below:

Fig (7.6)

If is the phase voltage then the charging current is

The grading of cables

Chapter Seven

Under Ground Cables

Construction of cables

Under Ground Cable

Electric stress in single core cable :.

*Most economical conductor size in the cable