chapter seven under ground cables

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

Chapter Seven

Under Ground Cables

Construction of cablesIn the fig (7.1)below, shows the general construction of(3-condctor) cable

The various part of cable are :

1- Core or conductorA cable may have one or more than one core (conductor) dependingupon 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 usuallystranded in order to provide flexibility to the cable.


2- insulationEach 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 forinsulation are impregnated paper, varnished cambric or rubber mineralcompound.

3- Metallic sheath.In order to protect the cable from moisture, gases or other damagingliquids (acids or alkalis) in the soil and atmosphere, a metallic sheath oflead or aluminum is provided over the insulation as shown in the fig.(7.1)

4- BeddingOver the metallic sheath is applied a layer of bedding which consists ofa fibrous material like jute or hessian tape. The purpose of bedding is toprotect the metallic a against corrosion of bedding is to protect themetallic against corrosion and from mechanical in jury due toarmoring.

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

6- Serving :.In order to protect armouring from atmospheric condition. Layer offibrous material (like jute) similar to bedding is providing over thearmouring. This is known as serving. It may not be out of place tomention here that bedding, armouring and serving are only applied tothe cable for protection of conductor insulation and to protect themetallic sheath from mechanical in jury.


Under Ground Cable

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

The fig. (7.2) represent a cross- sectionFor a single core cable wherer is the radius of the conductorR is the radius of the cable or( the inside radius of the sheath)

(q) represent the charge on theSurface of the conductor forEach on mater from the lengthOf the cable.

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

Coulomb/(1)

r

R

Fig . (7-2)


The electric field intensity or voltage gradient or electric stress at the samedistance 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 and thevalue of its will as follow :

Where q is the chargeOf the cable andOf 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 thecable (at X= R )

V/cm (8)

Also

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

*If the value of the voltage V and the inside radius of the sheath R areconstant and r is variable where ( r is the radius of the conductor of thecable )

*Most economical conductor size in the cableThe minimum value of the electric stress on the surface of the conductor( will be when is amaximum value.NowAssume

The maximum value will be when


The grading of cables :.The grading of the cable is redistribution the electric stress on theinsulator where the value of the electric stress will be increase at theoutside layer of insulator and it is value will be remain constant at thesurface of the conductor as before the grading. Also by this method wecan 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 andseparate these layers by a metallic inter sheath in order to control thevoltage across the insulator.

Capacitive grading

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

R


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 theradius of the conductor is 0.5 cm and the insulator consists of three layershave a relative permittivity of 5,4,3 respectively and the electric stresseson these layers are 40,30,20 kv/cm respectively. Find inside of the sheathof the cable.

So1)

Also

R

v

r


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

So1)

R

r


*Inter sheath gradingIn this method the insulator of the cable is consists of two layers or morethan two layers from the same material and spate each of two next layersby a screen or metallic inter sheath has a cylindrical shape and the intersheaths are connected to tapping from the supply transform where thevoltage across these sheath make the layers of the insulator take each it'svoltage from the total voltage.

O

V

r

SupplyTransformer


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

1-The maximum electric stress of the cable and the voltage of theinter sheath to the surface of the conductor when this inter sheath isnot connected to supply transformer ( the switch is open )2-When the switch is closed, find the electric stress on the surface ofthe conductor and on the two sides of the inter sheath when thevoltage of the inter sheath to the conductor surface is 44 kv. Alsofind 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

SupplyTransformer

r


( 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) ComparingThe using of inter sheath grading cause a reduction in the maximumelectric stress by


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

without using metallic intersheath grading with same cable :.We must increase the radius of cable in other words increase the distanceof insulator as follow :.

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

Ex4) A single core cable covered by the lead and design for 120 kv and 50HZ. The radius of it's conductor is 1cm and the inside radius of the outsidesheath is 4.2cm. An metallic inter sheath of radius 2 cm is used forgrading the cable. The relative permittivity of the insulator is 3.8. thelength of the cable is 6.4 km. find :.

1-The capacity of each of the two layers that have the same insulatormaterials.2-The overall efficiency3-The maximum electric stress when the inter sheath is not connectedto the supply to the supply transformer.4-The voltage of the inter sheath to the surface of the conductor inorder to keep the electric stress on the surface of the conductor at 55kv/cm (the inter sheath is connected to supply transformer)5-The charging current.


So1)

2)OR

rR


3)

4)

5)

Not grading

grading


-- 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 theOptimal or best locationOf the inter sheath, weMust put

R

O V

r


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

In order to make the maximum electric stress at the surface of conductorand the minimum electric stress at the inside surface of the sheath of cablewe must put:.


Kv/cm For 3 layer 2 metallic inter sheathAlso

Kv/cm For 3 layers 2 metallic inter sheath


As before

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

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 gradingcause a reduction in the value of maximum electric stress by

.........

un


Also in other sidesFor the same value of maximum electric stress and with remain thedistance of cable constant (r,R) we can increase the voltage across thecable 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 gradingcause 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 thedistance of cable (r . R) constant, we can increase the voltage across thecable by due to the inter sheath grading of cable.


*NoteWhen there is one metallic inter sheath

Kv/ cm

Also

R r


Ex5) 33kv single core cable has a conductor diameter of 2.5cm and thediameter of the inside sheath of the cable is 6 cm. It is design to reducethe maximum electric stress by using a two metallic inter sheath.Determine the best position of the inter sheath and the reduction in electricstress.

So1) Best position of inter sheath means

=

The reduction is


Ex6) single core cable of 66kv has a radius of conductor of 1cm. Theradius of the cable is 6 cm. The insulator consists of one layer. If a twometallic inter sheath is placed into the insulator and connected to supplytransformers through an switches. If the radius of first metallic intersheath 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 andsecond metallic inter sheath.2- When the switches are closed and the voltage of first transformeris 30kv and the voltage of second transformer is 20 kv. Find theelectric 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 sheath2)

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 tobe used on 132 kv, also, find the overall diameter of insulator if thepermissible 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 :.

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 ofits have a relative permittivity of 5,3 respectively. If a metallic inter sheathis placed between the layers and connected to supply transformer throughan switch.If the ratio of electric stress at the outside surface of metallic inter sheathto 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 ofcable. 2-The electric stress at the inside surface of metallic inter sheath 3-Min electric stress of cable of cable

r

R


So1)

1)2)

3)

rR


EX9) single core cable of 80kv has a radius of conductor of 1cm and theradius of cable is 7cm. his insulator consists of one material.If a two metallic inter sheath is placed into the insulator and connected tothe supply transformer through an switches. The radius of first and secondmetallic inter sheath are 3,5cm respectively and the voltage oftransformers are 4 cm

1-When the switches are open find the voltage between the firstmetallic inter sheath and sheath of cable2-When the first switch that connected to first transformer is closedand the second switch remain open.

Find the voltage between second metallic inter sheath and sheath ofcable.

So1)

RRr


2)

OR

15.73=

OR


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 2.5cm and the thickness of second layer is 4cm. Also the relativepermittivity of first and second layers are 5,4 respectively. If anmetallic inter sheath is placed at a radius of 6cm and connected tosupply transformer through an switch when the switch is open find

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

So1)

r


1)

OR


Type of cable fault :.

Cables are generally laid directly in the ground or in ducts in theunderground distribution system. For this reason, there are littlechances of fault in underground cables. However, if a fault does occur,it is difficult to locate and repair the fault because conductors are notvisible. Never the less, the following are the fault most likely to occursin underground cables

1-Open – circuit fault2-Short – circuit fault3-Earth fault.

1-Open –circuit fault :.

When there is a break in the conductor of a cable, it is called open-circuit fault. The open- circuit fault can be cheeked by a mugger. Forthis purpose, the three conductors of the 3- core cable at the for end areshorted and earthed. Then resistance between each conductor and earthis measured by a mugger. The mugger will indicate zero resistance inthe circuit of the conductor that is not broken. However, if the conductoris 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 contactwith 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 thispurpose the two terminal of the megger are connected to any twoconductors. If the megger gives zero reading. It indicates short circuitfault between these conductor the same step is repeated for otherconductors taking two at a time.


3) Earth fault:.when the conductor of a cable comes in contact with earth it is calledearth fault or ground fault. To indentify this fault, one terminal of themugger is connected to the conductor and the other terminal connectedto earth. If the mugger indicates zero reading, it means the conductor isearthed. 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 oflocating 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 byMurray 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 isjoined 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 respectivelyand serve as the ratio arms of the Wheatstone bridge. Let R= resistanceof the conductor loop up to the fault from the test end X= resistance of the other length of the loopNote that P,Q,R and X are the four arms of the Wheatstone bridge. Theresistances P and Q are varied till the galvanometer indicates zerodeflection. 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 meterlength 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 isin the battery circuit and not in the bridge circuit . therefore, faultresistance does not a fact the balancing of the bridge However. If the faultresistance is height, the sensitivity of the bridge is reduced.

In the fig. (7.4) below:

fig. (7.4)

Shows the circuit diagram for locating the short circuit fault by Murrayloop test. A gain P,Q, R and X are the arms circuit and not in the bridgecircuit. The bridge in balanced by adjusting the resistance P and Q .In the balanced position of the bridge

P


Thus the position of the fault is located


* Capacitance of 3-core cablesThe capacitance of a cable system is much more important than that ofover head line because in cables

1- Conductors are nearer to each other and to the earthed2- They are separated by a dielectric of permittivity much greater than

that of airThe fig. (7.5) below shows the system of capacitance in beltedcable.

fig (7.5)

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

The three capacitance Cc are delta connected where's the threecapacitance Ce are star connected, the sheath for many the star point asin the fig.( 7 .5 iii)In order to find the whole equivalent capacitance of cable we must makethe following steps.

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


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

If is the phase voltage then the charging current is

Fig (7.6)

chapter seven under ground cables

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