Power Transmission SystemCalculation of Sag and tension-Insulators

–string efficiency_x0002_grading–corona-Characteristics of
transmission lines-Surge Impedance Loading- Series and shunt
compensation.

Underground cables-ratings- classification- Capacitance –grading-

testing Introduction to EHVAC, HVDC and FACTS: Principle,
classification and advantages/disadvantages

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  While erecting an overhead line, it is very important that conductors are
under safe tension.

 If the conductors are too much stretched between supports in a bid to save
conductor material, the stress in the conductor may reach unsafe value and
in certain cases the conductor may break due to excessive tension.

 In order to permit safe tension in the conductors, they are not fully
stretched but are allowed to have a dip or sag.

 The difference in level between points of supports and the lowest

point on the conductor is called sag

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 (i) supports are at equal levels and
(ii) supports are at unequal levels.

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 1. A 132 kV transmission line has the following data :Wt. of conductor
= 680 kg/km; Length of span = 260 m Ultimate strength = 3100 kg; Safety
factor = 2 Calculate the height above ground at which the conductor should
be supported. Ground clearance required is 10 metres.

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 2. A transmission line has a span of 150 m between level supports. The
conductor has a cross-sectional area of 2 cm2. The tension in the conductor
is 2000 kg. If the specific gravity of the conductor material is 9·9 gm/cm3 and
wind pressure is 1·5 kg/m length, calculate the sag. What is the vertical sag?

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  The overhead line conductors should be
supported on the poles or towers so that
currents from conductors do not flow to earth
through supports i.e., line conductors must be
properly insulated from supports.

 This is achieved by securing line conductors

to supports with the help of insulators.

 The insulators provide necessary insulation

between line conductors and supports and
thus prevent any leakage current from
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 (i) High mechanical strength in order to withstand conductor
load, wind load etc.

(ii) High electrical resistance of insulator material in order to

avoid leakage currents to earth.

(iii) High relative permittivity of insulator material in order that

dielectric strength is high.

(iv) The insulator material should be non-porous, free from

impurities and cracks otherwise the permittivity will be lowered.

(v) High ratio of puncture strength to flashover.

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  The most commonly used material for insulators of overhead line
is porcelain but glass, steatite and special composition materials
are also used to a limited extent.

 Porcelain is produced by firing at a high temperature a mixture of

kaolin, feldspar and quartz.

 There are several types of insulators but the most commonly used
are
1. pin type,
2. suspension type,
3. strain insulator and
4. shackle insulator.

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  The part section of a pin type
insulator is shown in Fig.
 As the name suggests, the pin
type insulator is secured to the
cross-arm on the pole.

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  There is a groove on the upper end of the
insulator for housing the conductor.

 The conductor passes through this groove and

is bound by the annealed wire of the same
material as the conductor.

 Pin type insulators are used for transmission

and distribution of electric power at voltages
upto 33 kV.

 Beyond operating voltage of 33 kV, the pin

type insulators become too bulky and hence
uneconomical.
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 Causes of insulation failure
 Insulators are required to withstand both mechanical and electrical
stresses.

 The latter type is primarly due to line voltage and may cause the
breakdown of the insulator.

 The electrical break-down of the insulator can occur either by flash-

over or puncture.

 In flash-over, an arc occurs between the line conductor and

insulator pin (i.e., earth) and the discharge jumps across the air gaps,
following shortest distance.

 Fig. shows the arcing distance (i.e. a + b + c) for the insulator. In

case of flash-over, the insulator will continue to act in its proper
capacity unless extreme heat produced by the arc destroys the
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  In case of puncture, the discharge occurs from
conductor to pin through the body of the insulator.

 When such breakdown is involved, the insulator is
permanently destroyed due to excessive heat.

 In practice, sufficient thickness of porcelain is

provided in the insulator to avoid puncture by the line
voltage.

 The ratio of puncture strength to flash- over voltage is

known as safety factor i.e.,

 It is desirable that the value of safety factor is high so

that flash-over takes place before the insulator gets
punctured. For pin type insulators, the value of safety
factor is about 10.

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 Suspension type insulators
• The cost of pin type insulator increases rapidly as the
working voltage is increased.

• Therefore, this type of insulator is not economical

beyond 33 kV.
• For high voltages (>33 kV), it is a usual practice to
use suspension type insulators shown in Fig.

 They consist of a number of porcelain discs connected in series by

metal links in the form of a string.
 The conductor is suspended at the bottom end of this string while
the other end of the string is secured to the cross-arm of the tower.
 Each unit or disc is designed for low voltage, say 11 kV. The
number of discs in series would obviously depend upon the
working voltage.
 For instance, if the working voltage is 66 kV, then six discs in
series will be provided on the string.
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 Advantages
 Suspension type insulators are cheaper than pin
type insulators for voltages beyond 33 kV.
 Each unit or disc of suspension type insulator
is designed for low voltage, usually 11 kV.
 Depending upon the working voltage, the
desired number of discs can be connected in
series.
 If any one disc is damaged, the whole string
does not become useless because the damaged
disc can be replaced by the sound one.
 The suspension type insulators are generally
used with steel towers.
 As the conductors run below the earthed cross-
arm of the tower, therefore, this arrangement
provides partial protection from lightning.

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  When there is a dead end of the line or there is
corner or sharp curve, the line is subjected to
greater tension. In order to relieve the line of
excessive tension, strain insulators are used.
 For low voltage lines (< 11 kV), shackle
insulators are used as strain insulators.
 However, for high voltage transmission lines,
strain insulator consists of an assembly of
suspension insulators as shown in Fig.
 The discs of strain insulators are used in the
vertical plane.
 When the tension in lines is exceedingly high,
as at long river spans, two or more strings are
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  In early days, the shackle insulators were
used as strain insulators.

 But now a days, they are frequently used

for low voltage distribution lines.

 Such insulators can be used either in a

horizontal position or in a vertical position.

 They can be directly fixed to the pole with

a bolt or to the cross arm.

 Fig. shows a shackle insulator fixed to the

pole.
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
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 Potential Distribution over
Suspension Insulator String
 A string of suspension insulators consists of a number of
porcelain discs connected in series through metallic links.

 Fig. (i) shows 3-disc string of suspension insulators. The

porcelain portion of each disc is in between two metal links.
Therefore, each disc forms a capacitor C as shown in Fig.(ii).

 This is known as mutual capacitance or self-capacitance. If

there were mutual capacitance alone, then charging current
would have been the same through all the discs and
consequently voltage across each unit would have been the
same i.e., V/3 as shown in Fig.(ii).

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  However, in actual practice, capacitance also exists between
metal fitting of each disc and tower or earth. This is known as
shunt capacitance ��
 Due to shunt capacitance, charging current is not the same
through all the discs of the string (iii). Therefore, voltage across
each disc will be different.
 Obviously, the disc nearest to the line conductor will have the
maximum voltage.
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  The following points may be noted regarding the potential distribution over
a string of suspension insulators :

 The voltage impressed on a string of suspension insulators does not

distribute itself uniformly across the individual discs due to the presence of
shunt capacitance.

 The disc nearest to the conductor has maximum voltage across it. As we
move towards the cross-arm, the voltage across each disc goes on
decreasing.

 The unit nearest to the conductor is under maximum electrical stress and is
likely to be punctured. Therefore, means must be provided to equalise the
potential across each unit.

 If the voltage impressed across the string were d.c., then voltage across
each unit would be the same. It is because insulator capacitances are
ineffective for d.c.
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  As stated above, the voltage applied across the string of suspension
insulators is not uniformly distributed across various units or discs.

 The disc nearest to the conductor has much higher potential than the other
discs.

 This unequal potential distribution is undesirable and is usually expressed

in terms of string efficiency.

 The ratio of voltage across the whole string to the product of number of
discs and the voltage across the disc nearest to the conductor is known as
string efficiency i.e.,

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  String efficiency is an important consideration since it decides the potential
distribution along the string.

 The greater the string efficiency, the more uniform is the voltage
distribution.

 Thus 100% string efficiency is an ideal case for which the voltage across
each disc will be exactly the same.

 Although it is impossible to achieve 100% string efficiency, yet efforts

should be made to improve it as close to this value as possible

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  Fig shows the equivalent circuit for a 3-disc string.
 Let us suppose that self capacitance of each disc is C.
 Let us further assume that shunt capacitance C1 is some fraction K
of self- capacitance i.e.,
 C1 = KC.
 Starting from the cross-arm or tower, the voltage across each unit is
V1,V2 and V3 respectively as shown.

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  The following points may be noted from the above mathematical
analysis :
 If K = 0·2 (Say), then from exp. (iv),
 we get, V2 = 1·2 V1 and V3 = 1·64 V1.
 This clearly shows that disc nearest to the conductor has maximum
voltage across it; the voltage across other discs decreasing
progressively as the cross-arm is approached.
 The greater the value of K (= C1/C), the more non-uniform is the
potential across the discs and lesser is the string efficiency.
 The inequality in voltage distribution increases with the increase of
number of discs in the string. Therefore, shorter string has more
efficiency than the larger one.
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  It has been seen above that potential distribution in a string of suspension
insulators is not uniform.

 The maximum voltage appears across the insulator nearest to the line
conductor and decreases progressively as the cross- arm is approached.

 If the insulation of the highest stressed insulator (i.e. nearest to conductor)

breaks down or flash over takes place, the breakdown of other units will
take place in succession.

 This necessitates to equalise the potential across the various units of the
string i.e. to improve the string efficiency.

 The various methods for this purpose are :

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  The value of string efficiency depends upon the
value of K i.e., ratio of shunt capacitance to mutual
capacitance.
 The lesser the value of K, the greater is the string
efficiency and more uniform is the voltage
distribution.
 The value of K can be decreased by reducing the
shunt capacitance.
 In order to reduce shunt capacitance, the distance of
conductor from tower must be increased i.e., longer
cross-arms should be used.
 However, limitations of cost and strength of tower
do not allow the use of very long cross-arms.
 In practice, K = 0·1 is the limit that can be achieved
by this method.
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  In this method, insulators of different dimensions are so chosen
that each has a different capacitance.
 The insulators are capacitance graded i.e. they are assembled in
the string in such a way that the top unit has the minimum
capacitance, increasing progressively as the bottom unit (i.e.,
nearest to conductor) is reached.
 Since voltage is inversely proportional to capacitance, this
method tends to equalise the potential distribution across the
units in the string.
 This method has the disadvantage that a large number of
different-sized insulators are required.
 However, good results can be obtained by using standard
insulators for most of the string and larger units for that near to
the line conductor.
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  The potential across each unit in a string can be equalised by
using a guard ring which is a metal ring electrically connected
to the conductor and surrounding the bottom insulator as
shown in the Fig.
 The guard ring introduces capacitance between metal fittings
and the line conductor.
 The guard ring is contoured in such a way that shunt
capacitance currents i1, i2 etc. are equal to metal fitting line
capacitance currents i’1, i’2 etc.
 The result is that same charging current I flows through each
unit of string.
 Consequently, there will be uniform potential distribution
across the units

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  While solving problems relating to string efficiency, the following
points must be kept in mind:
 The maximum voltage appears across the disc nearest to the
conductror (i.e., line conductor).
 The voltage across the string is equal to phase voltage i.e.,
 Voltage across string = Voltage between line and earth = Phase
Voltage
 Line Voltage = 3xVoltage across string
Tutorial2
 Example In a 33 kV overhead line, there are three units in the
string of insulators. If the capacitance between each insulator pin
and earth is 11% of self-capacitance of each insulator, find (i) the
distribution of voltage over 3 insulators and (ii) string efficiency.

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  When an alternating potential difference is applied
across two conductors whose spacing is large, as
compared to their diameters, there is no apparent
change in the condition of atmospheric air
surrounding the wires if the applied voltage is low.

 However, when the applied voltage exceeds a

certain value, called critical disruptive voltage, the
conductors are surrounded by a faint violet glow
called corona.
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  The phenomenon of corona is accompanied by a
hissing sound, production of ozone, power loss
and radio interference.
 The higher the voltage is raised, the larger and
higher the luminous envelope becomes, and
greater are the sound, the power loss and the radio
noise.
 If the applied voltage is increased to breakdown
value, a flash-over will occur between the
conductors due to the breakdown of air insulation.
 The phenomenon of violet glow, hissing noise and
p ro d u c t i o n o f o z o n e g a s i n a n o v e rh e a d
transmission line is known as corona.
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  If the conductors are polished and smooth,
the corona glow will be uniform throughout
the length of the conductors, otherwise the
rough points will appear brighter.

 With d.c. voltage, there is difference in the

appearance of the two wires.

 The positive wire has uniform glow about it,

while the negative conductor has spotty glow

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  Some ionisation is always present in air due to cosmic rays, ultra
violet radiations and radioactivity.

 Therefore, under normal conditions, the air around the

conductors contains some ionised particles (i.e., free electrons
and +ve ions) and neutral molecules.

 When p.d. is applied between the conductors, potential gradient

is set up in the air which will have maximum value at the
conductor surfaces. Under the influence of potential gradient, the
existing free electrons acquire greater velocities.

 The greater the applied voltage, the greater the potential gradient
and more is the velocity of free electrons.
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  When the potential gradient at the conductor
surface reaches about 30 kV per cm (max. value),
the velocity acquired by the free electrons is
sufficient to strike a neutral molecule with enough
force to dislodge one or more electrons from it.
 This produces another ion and one or more free
electrons, which in turn are accelerated until they
collide with other neutral molecules, thus
producing other ions.
 Thus, the process of ionisation is cummulative.
 The result of this ionisation is that either corona is
formed or spark takes place between the
conductors.

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  The phenomenon of corona is affected by the physical state
of the atmosphere as well as by the conditions of the line.
The following are the factors upon which corona depends :

 Atmosphere. As corona is formed due to ionsiation of air

surrounding the conductors, therefore, it is affected by the
physical state of atmosphere. In the stormy weather, the
number of ions is more than normal. Corona occurs at much
less voltage as compared with fair weather.

 Conductor size. The corona effect depends upon the shape

and conditions of the conductors. The rough and irregular
surface will give rise to more corona because unevenness of
the surface decreases the value of breakdown voltage. Thus
a stranded conductor has irregular surface and hence gives
rise to more corona that a solid conductor.
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  Spacing between conductors. If the spacing
between the conductors is made very large as
compared to their diameters, there may not be any
corona effect. It is because larger distance
between conductors reduces the electro-static
stresses at the conductor surface, thus avoiding
corona formation.

 Line voltage. The line voltage greatly affects

corona. If it is low, there is no change in the
condition of air surrounding the conductors and
hence no corona is formed. However, if the line
voltage has such a value that electrostatic stresses
developed at the conductor surface make the air
around the conductor conducting, then corona is
formed.
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  The phenomenon of corona plays an important role in the design of
an overhead transmission line. Therefore, it is profitable to consider
the following terms much used in the analysis of corona effects:

 Critical disruptive voltage.

 It is the minimum phase-neutral voltage at which corona occurs.

 Consider two conductors of radii r cm and spaced d cm apart. If V is

the phase-neutral potential, then potential gradient at the conductor
surface is given by

 In order that corona is formed, the value of g must be made equal to

the breakdown strength of air. The breakdown strength of air at 76
cm pressure and temperature of 25ºC is 30 kV/cm (max) or
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 21·2 kV/cm (r.m.s.) and is denoted by go. If Vc is the phase-neutral potential required under
these conditions, then,

 The above expression for disruptive voltage is under standard conditions i.e., at 76 cm of Hg and 25ºC.
However, if these conditions vary, the air density also changes, thus altering the value of go. The value of go is
directly proportional to air density. Thus the breakdown strength of air at a baro- metric pressure of b cm of
mercury and temperature of tºC becomes d go where

Correction must also be made for the surface condition of the conductor. This is accounted
for by multiplying the above expression by irregularity factor mo.

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 2. Visual critical voltage. It is the minimum phase-neutral voltage at which
corona glow appears all along the line conductors.
• It has been seen that in case of parallel conductors, the corona glow does not begin at
the disrup- tive voltage V but at a higher voltage V , called visual critical voltage. The
c v

phase-neutral effective value of visual critical voltage is given by the following

empirical formula :

 where mv is another irregularity factor having a value of 1·0 for

polished conductors and 0·72 to 0·82 for rough conductors.

3. Power loss due to corona. Formation of corona is always accompanied by energy

loss which is dissipated in the form of light, heat, sound and chemical action. When
disruptive voltage is exceeded, the power loss due to corona is given by :

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 Advantages
 Due to corona formation, the air surrounding the conductor
becomes conducting and hence virtual diameter of the
conductor is increased. The increased diameter reduces the
electro- static stresses between the conductors.
 Corona reduces the effects of transients produced by surges.

Disadvantages
 Corona is accompanied by a loss of energy. This affects the
transmission efficiency of the line.
 Ozone is produced by corona and may cause corrosion of
the conductor due to chemical action.
 The current drawn by the line due to corona is non-
sinusoidal and hence non-sinusoidal voltage drop occurs in
the line. This may cause inductive interference with
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neighbouring communication lines.
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  It has been seen that intense corona effects are observed at a working
voltage of 33 kV or above. The corona effects can be reduced by the
following methods :

 By increasing conductor size. By increasing conductor size, the voltage at

which corona occurs is raised and hence corona effects are considerably
reduced. This is one of the reasons that ACSR conductors which have a
larger cross-sectional area are used in transmission lines.

 By increasing conductor spacing. By increasing the spacing between

conductors, the voltage at which corona occurs is raised and hence corona
effects can be eliminated. However, spacing cannot be increased too much
otherwise the cost of supporting structure (e.g., bigger cross arms and
supports) may increase to a considerable extent.

 Example 8.13. A 3-phase line has conductors 2 cm in diameter spaced equilaterally

1 m apart. If the dielectric strength of air is 30 kV (max) per cm, find the disruptive
critical voltage for the line. Take air density factor d = 0·952 and irregularity factor
m = 0·9.
o

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An underground cable essentially consists of one or more conductors covered with
suitable insulation and surrounded by a protecting cover. The conductor used in cables
should be tinned stranded copper or aluminium of high conductivity. Stranding is done so that
conductor may become flexible and carry more current.
 In general, a cable must fulfill the following necessary requirements :
◦ The conductor used in cables should be tined stranded copper or aluminium of high
conductivity. Stranding is done so that conductor may become flexible and carry more
current.
◦ The conductor size should be such that the cable carries the desired load current
without overheating and causes voltage drop within permissible limits.
◦ The cable must have proper thickness of insulation in order to give high degree of
safety and reliability at the voltage for which it is designed.
◦ The cable must be provided with suitable mechanical protection so that it may
withstand the rough use in laying it.
◦ The materials used in the manufacture of cables should be such that there is complete
chemical and physical stability throughout.
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The various parts are :
1. Cores or Conductors
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 Fig. is used for 3-phase service.
The conductors are made of tinned copper or aluminium and are usually
stranded in order to provide flexibility to the cable.
2. Insulation
Each core or conductor is provided with a suitable thickness of insulation, the
thickness of layer depending upon the voltage to be withstood 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 alkalies) in the soil and atmosphere, a metallic sheath of lead or
aluminium is provided over the insulation as shown in Fig.

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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 sheath against corrosion and from
mechanical injury due to armouring.
5. Armouring. Over the bedding, armouring is provided which consists of
one or two layers of galvanised 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
cables.
6. Serving. In order to protect armouring from atmospheric conditions, a
layer of fibrous material (like jute) similar to bedding is provided over
the armouring. This is known as serving.

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(i) the type of insulating material used in their manufacture
(ii) the voltage for which they are manufactured.
1. Low-tension (L.T.) cables — upto 1000 V
2. High-tension (H.T.) cables — upto 11,000 V
3. Super-tension (S.T.) cables — from 22 kV to 33 KV
4. Extra high-tension (E.H.T.) cables — from 33 kV to 66 kV
5. Extra super voltage cables — beyond 132 kV

(iii) A cable may have one or more than one core depending upon the type of service for

which it is intended. They are:

(i) single-core
(ii) two-core
(iii) three-core
(iv) four-core

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 Single-core low tension cable
 The cable has ordinary construction because the
stresses developed in the cable for low voltages (upto
6600 V) are generally small.
 It consists of one circular core of tinned stranded
copper (or aluminium) insulated by layers of
impregnated paper.
 The insulation is surrounded by a lead sheath which
prevents the entry of moisture into the inner parts.
 In order to protect the lead sheath from corrosion, an
overall serving of compounded fibrous material (jute
etc.) is provided.
 Single-core cables are not usually armoured in order to
avoid excessive sheath losses.
 The principal advantages of single-core cables are
simple construction and availability of larger copper
section.

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 1. Belted cables — upto 11 kV
2. Screened cables — from 22 kV to 66 kV
3. Pressure cables — beyond 66 kV.

1. Belted cables. These cables are used for voltages upto 11kV
• Fig. shows the constructional details of a 3-core belted cable.
• The cores are insulated from each other by layers of impregnated paper.
• Another layer of impregnated paper tape, called paper belt is wound round the grouped
insulated cores.
• The gap between the insulated cores is filled with fibrous insulating material (jute etc.) so as
to give circular cross-section to the cable.
• The cores are generally stranded and may be of non- circular shape to make better use of
available space.
• The belt is covered with lead sheath to protect the cable against ingress of moisture and
mechanical injury.
• The lead sheath is covered with one or more layers of armouring with an outer serving.
• The belted type construction is suitable only for low and medium voltages as the electrostatic
stresses developed in the cables for these voltages are more or less radial i.e., across the
insulation.

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 This type of cable was first designed by H. Hochstadter
and hence the name. Fig. shows the constructional
details of a typical 3-core, H-type cable.
 Each core is insulated by layers of impregnated paper.
 The insulation on each core is covered with a metallic
screen which usually consists of a perforated aluminium
foil.
 The cores are laid in such a way that metallic screens
make contact with one another.
 An additional conducting belt (copper woven fabric
tape) is wrapped round the three cores.
 As all the four screens (3 core screens and one
conducting belt) and the lead sheath are at earth potential,
therefore, the electrical stresses are purely radial and
consequently dielectric losses are reduced.
 Two principal advantages
1. The perforations in the metallic screens assist in the
complete impregnation of the c a b l e w i t h t h e
compound and thus the possibility of air pockets or
voids (vacuous spaces) in the dielectric is eliminated.
2. The metallic screens Downloaded
increase the heat dissipating
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 It is basically H-type cable but the screen round each core insulation is covered by its own lead sheath.

 There is no overall lead sheath but only armouring and serving are provided.

 The S.L. type cables have two main advantages over H-type cables.

1. Firstly, the separate sheaths minimise the possibility of core-to-core breakdown.

2. Secondly, bending of cables becomes easy due to the elimination of overall lead sheath.

 The disadvantage is that the three lead sheaths of S.L. cable are much thinner than the single sheath of H-
cable and, therefore, call for greater care in manufacture.

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 These cables are meant for use upto 33 kV,
but in particular cases their use may be
extended to operating voltages upto 66 kV.
 Two principal types of screened cables are
H- type cables and S.L. type cables.
a) H-type cables
b) S.L. type cables.(separate lead)

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 For voltages beyond 66 kV, solid type cables are unreliable because there is a
danger of breakdown of insulation due to the presence of voids.
 When the operating voltages are greater than 66 kV, pressure cables are used.
 In such cables, voids are eliminated by increasing the pressure of compound
and for this reason they are called pressure cables.
 Two types of pressure cables
A. oil-filled cables
B. gas pressure cables are commonly used

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 In such types of cables, channels or ducts are provided in the cable for oil
circulation.
 The oil under pressure (it is the same oil used for impregnation) is kept
constantly supplied to the channel by means of external reservoirs placed at
suitable distances (say 500 m) along the route of the cable.
 Oil under pressure compresses the layers of paper insulation and is forced into
any voids that may have formed between the layers.
 Due to the elimination of voids, oil-filled cables can be used for higher
voltages, the range being from 66 kV upto 230 kV.
 Oil-filled cables are of three types viz., single-core conductor channel, single-
core sheath channel and three-core filler-space channels.

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 The voltage required to set up ionisation inside a void increases as
the pressure is increased.
 Therefore, if ordinary cable is subjected to a sufficiently high
pressure, the ionisation can be altogether eliminated.
 At the same time, the increased pressure produces radial
compression which tends to close any voids.
 This is the underlying principle of gas pressure cables.
 The triangular section reduces the weight and gives low thermal
resistance but the main reason for triangular shape is that the lead
sheath acts as a pressure membrane.
 Moreover, maintenance cost is small and the
 nitrogen gas helps in quenching any flame.
 However, it has the disadvantage that
 the overall cost is very high
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 The cable conductor is provided with a suitable thickness
of insulating material in order to prevent leakage current.
The path for leakage current is radial through the insulation.
 The opposition offered by insulation to leakage current
is known as insulation resistance of the cable.
 For satisfactory operation, the insulation resistance of the
cable should be very high.
 Consider a single-core cable of conductor radius r1 and
internal sheath radius r2 as shown in Fig. Let l be the
length of the cable and r be the resistivity of the insulation.

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◦ Consider a very small layer of insulation of
thickness dx at a radius x. The length through which
leakage current tends to flow is dx and the area of
X-section offered to this flow is 2π x l.

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 Problem A single-core cable has a conductor diameter of
1cm and insulation thickness of 0·4 cm. If the specific
resistance of insulation is 5 × 10 14 Ωcm, calculate the
insulation resistance for a 2 km length of the cable.
Ans: 234MΩ

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 A single-core cable can be considered to be equivalent to two
long co-axial cylinders.
 The conductor (or core) of the cable is the inner cylinder
while the outer cylinder is represented by lead sheath which is
at earth potential.
 Consider a single core cable with conductor diameter d and
inner sheath diameter D (Fig).
 Let the charge per metre axial length of the cable be Q
coulombs and ε be the permittivity of the insulation material
between core and lead sheath.
 Obviously is relative permittivity.

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 The work done in moving a unit positive charge from point P through a
distance dx in the direc tion of electric field is Ex dx.
 Hence, the work done in moving a unit positive charge from conductor
to sheath, which is the potential difference V between conductor and
sheath, is given by :

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 The capacitance of a cable system is much more important than that of overhead line
because in cables (i) conductors are nearer to each other and to the earthed sheath (ii)
they are separated by a dielectric of permittivity much greater than that of air.

 Fig. 11.18 shows a system of capacitances in a 3-core belted cable used for 3-phase
system.
 Since potential difference exists between pairs of conductors and between each
conductor and the sheath, electrostatic fields are set up in the cable as shown in Fig.
 These electrostatic fields give rise to core-core capacitances Cc and conductor earth
capacitances Ce as shown in Fig.

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 The three Cc are delta connected whereas the three Ce are star connected,
the sheath forming the star point .
 The three delta connected capacitances Cc [See Fig. 11.19 (i)] can be
converted into equivalent star connected capacitances as shown in Fig.
11.19 (ii). It can be easily *shown that equivalent star- capacitance Ceq is
equal to three times the delta- capacitance Cc i.e. Ceq = 3Cc.

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Principle of HVDC system operation
 When using direct current to provide an asynchronous link between 2 AC
systems it is necessary to have to convertor stations one at each end connected
by a DC transmission line.
 The main equipments in a converter station are transformers and thyristor
valves.
 Chokes and filters are provided at each end to ensure smooth direct current and
suppress harmonics.
 At the sending and the thyristor valves act as rectifiers to convert AC into DC
which is transmitted over the line.
 At the receiving end the thyristor valves act as inverters to convert DC into AC
which is utilised at the receiving end.
 Single line diagram of hvdc transmission system is shown in figure

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 A and B are the two converter stations.
 Converter station A is supplied from the generating station G.
 In converter station at the sending end the voltage is stepped up to
appropriate value by step up transformer and then converted into direct
current by thyristor valves.
 Thus at the start of transmission line we have high voltage DC .
 This rectified current flows along the transmission line to the receiving
end converting station B where it is converted into three phase AC
current by thyristor valves and then stepped down by the step down
transformer to low voltage for further distribution.
 �� - �� represents the power losses due to the conversion and
transmission.

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 The converter at the sending end acts as a rectifier and is suitable for power
frequency ( that is frequency of generator) on its AC side while converter at the
receiving end acts as an inverter and its frequency is determined by frequency of
the load system.
 This frequency is independent of the sending end frequency provided the two
ends A and B are not additional connected by the three phase lines.
 The DC output voltage magnitude is controlled by varying the firing angle of the
thyristor valves in the converter.
 In rectifier the firing angle is between zero degree and 90 degree while in inverter
it is between 90 degree and 180 degree.
 As the DC output voltage is a function of cosine of the firing angle has the
converter voltage becomes negative when firing angle ∝ exceeds 90 degree.
 This makes the converter to operate as an inverter.
 The two converter at sending and receiving end are identical and whether they
have to work as a rectifier or inverter is determined by the direction of power
flow.
 In practical HVDC converter stations three phase bridge converters are employed
at both ends. Reversible operation of converters as well as bidirectional power
flow in hvdc link is possible simply by the control of firing angle..

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 In DC system the power transferred from one station to another station is governed only by the
magnitudes of terminal DC voltages at the two ends while in AC transmission system the power
transfer is governed by phase difference (that is magnitude as well as phase) of the voltages at both
ends.
 Thus the controllability of hvdc power is fast and stable.
 The current flows from higher voltage to lower voltage which are set by adjustment of firing or
extinction angles of the two converters (that is rectifier and inverter.)
 If �� is the voltage of the sending end and �� we are is the voltage at the receiving end then the line
current is given as
�� −��
 ��� =
�
 Where R is the resistance of the entire transmission link.
 The sending end voltage is given as
3 2 3���
 �� =(( ���� )cos∝ - ��� )
� �
 And receiving and voltage is given as
3 2 3���
 �� =(( ���� )cosβ - ��� )
� �

 here Alpha is the firing angle of rectifier beta is the extinction angle of inverter, ���� is the AC side
line to line RMS voltage at the sending end ���� is the the AC side line to line RMS voltage at the
receiving end .

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 ��� is the commutation reactance at the sending end
 ���� is the computation reactance at the receiving end.

 Thus the power transferred is given as

�� −��
 � = �� ��� = ��
�
 tap changes on the AC side take care of the voltage variations
on AC side and DC power is controlled by controlling the
sending and receiving and voltages �� and �� which is
possible by control of firing and extinction angle alpha and
beta respectively.

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1. Cheaper in cost
 Bipolar hvdc transmission lines require to pole conductors while AC transmission
system requires three conductors to carry power.
 HVDC transmission can utilise Earth return and therefore does not require a double
circuit while HVAC transmission always require a double circuit.
1
 The potential stress on the insulation in case of DC system is times that of in AC
√2
system for the same operating voltage.
 As operating voltage less insulation is required.
2. HVDC line can be built in stages
 The DC line can be built as monopolar line with ground return in the initial stage
and may be converted into a bipolar line on the later date when the load
requirement increases.
3. No skin effect
 There is no skin effect in DC so there is a uniform distribution of current over the
the section of the conductor that there is full utilisation of line conductor in case of
DC transmission while it is not so in case of AC transmission.

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4. Lower transmission losses
 HVDC transmission system needs only two conductors
and therefore the power losses in a DC line are lesser
than losses in DC line of the same power transfer
capability.
5. Line loading
 The permissible loading on any HV AC line is limited
by transient stability limit and line reactance to almost
one third of thermal rating of conductors no such limit
exist in case of hvdc lines.
6. greater reliability
7. lesser corona loss and radio interference

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1. Costly terminal equipment
 the converters required at both ends of the line have proved to be
reliable but they are much more expensive than the conventional
AC equipments.
2. More maintenance of line insulators
 maintenance of insulators in hvdc transmission line is more
3. Circuit breaking in multi-terminal DC systems is difficult and
costly
4. Voltage transformation
 voltage transformation is not easier in case of DC and hence it has
to be accomplished on the AC side of the system

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