Debre Tabor University
Faculty of technology
POWER SYSTEM I
Mechanical design of transmission lines
1
Outline
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Introduction
Sag and tension calculations
Effect of wind and ice loading
Stringing chart
Sag template
2
INTRODUCTION
A proper mechanical design is one of the essentials in providing
good service to customers
 A large majority of service interruptions can be traced to physical
failures on the distribution system, broken wires, broken poles,
damaged insulation, damaged equipment, etc
 Of course, many of these service interruptions are more or less
un avoidable, but their numbers can be reduced if the design and
construction of the various physical parts can withstand, with
reasonable safety factors, not only normal conditions but also
some probable abnormal conditions
 The conductors and poles must have sufficient strength with a
predetermined safety factor to withstand the loads due to the line
itself and stresses imposed by ice and wind loads.
 Thus, the overhead line should provide satisfactory service over a
long period of time without the necessary for too much
maintenance
 Ultimate economy is provided by a good construction since
excessive maintenance or especially short life can be easily more
3
than overbalance a saving in the first cost.

The overhead line must have a proper strength to
withstand the stresses imposed on its component
parts by the line itself.
 These include

 stresses set up by the tension in conductors at dead end
points,
 compression stresses due to guy tension,
 vertical stresses due to the weight of conductors, and
 the vertical component of conductor tension

The tension in the conductors should be adjusted so
that it is well within the permissible load of the
material. This will mean in practice that one must
allow for an appreciable amount of sag.
4

In general, the factors affecting a mechanical design of the
overhead lines are:
1. Character of line route
2. Right of way
3. Mechanical loading
4. Required clearances
5. Types of supporting structures
6. Grade of construction
7. conductors
8.Types of insulators
9. Joint use by the utilities
5
Main Components of Overhead Lines
 In general, the main components of an overhead lines
are:
 Conductors:- which carry electric power from the sending
end station to the receiving end station
 Supports:- which may be poles or towers and keep the
conductors at a suitable level above the ground
 Insulators:- which are attached to support and insulate the
conductors from the ground
 Cross arms:- which provide support to the insulators
 Shield wires:- which provides grounding and communication
services for the overhead transmission line.
 Miscellaneous items:- such as phase plates, danger plates,
anti-climbing wires, etc
6
Conductor materials
 The conductor is one of the important items as most of the
capital outlay is invested for it. Therefore, proper choice of
material and size of conductor is of considerable importance
 The conductor material used for transmission and distribution
of electric power should have the following properties:
High electrical conductivity
High tensile strength in order to withstand mechanical stresses
Low cost so that it can be used for long distances
Low specific gravity so that weight per unit volume is small

All above requirements are not found in a single material.
Therefore, while selecting a conductor material for a particular
case, a compromise is made between the cost and the required
electrical and mechanical properties
7
Commonly used conductor materials

The most commonly used conductor materials for
overhead lines are
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copper,
aluminum,
steel cored aluminum,
galvanized steel and
cadmium copper
The choice of a particular material will depend up on
the cost, the required electrical and mechanical
properties and local conditions
 All conductors used for overhead lines are preferably
stranded in order to increase the flexibility

8
Copper:

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Copper is an ideal material for overhead lines owing to its high
electrical conductivity and grater tensile strength
It is always used in the hard drawn form as stranded conductor.
Although hard drawn decreases the electrical conductivity
slightly yet it increases the tensile strength considerably
The merits of this metal as a line conductor are:
i. It has a best conductivity in comparison to other metals.
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
The conductivity of copper, however depends upon the percentage of
impurities present in it, the more the impurities the lesser will be the
conductivity.
The conductivity of copper conductor also depends upon the method
by which it has been drawn.
ii.
It has higher current density, so for the given current rating,
lesser cross-sectional area of conductor is required and
hence it provides lesser cross-sectional area to wind loads
iii. The metal is quite homogeneous
iv. It has low specific resistance
v. It is durable and has a higher scrap value
9
Aluminum:
 Aluminum is cheap and light as compared to copper but it has much smaller
conductivity and tensile strength
 Next to copper aluminum is the conductor used in order of performance
as far as the conductivity is concerned.
 Its merits and demerits are:
i. It is cheaper than copper
ii. It is lighter in weight (the specific gravity of aluminum is lower than
that of copper, i.e an aluminum conductor has almost one half the
weight of equivalent copper conductor)
iii. It is second in conductivity (among the metals used for transmission).
Commercial hard-down aluminum wire at standard temperature has
approximately 60.6 percent conductivity in comparison to standard
annealed copper wire.
iv. For same ohmic resistance, its diameter is about 1.27 times that of
copper.
v. At higher voltages it causes less corona loss
vi. Since the diameter of the conductor is more, so it is subject to greater
wind pressure due to which greater is the swing of the conductor and
greater is the sag
vii. Since the conductors are liable to swing, so it requires larger cross
arms
10
viii. As the melting point of the conductor is low , so the
short circuit etc. will damage it .

ix. Joining of aluminum is much more difficult than that of any
other material
In the modern over head transmission system, bare aluminum
conductors are used (for purpose of heat dissipation) which are
classifies as:
AAC - All Aluminum Conductors
 AAAC - All Aluminum Alloy Conductors
 ACSR – Aluminum Conductors Steel Reinforced
 ACAR - Aluminum Conductors Alloy Reinforced
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Steel
•
•
No doubt it has got the greatest tensile strength, but it is least used for
transmission of electrical energy as it has got high resistance.
Bare steel conductors are not used since, it deteriorates rapidly owing
to rusting. Generally galvanized steel wires are used.
11

It has the following properties:
i)
It is lowest in conductivity
ii ) It has high internal reactance
iii ) It is much subjected to eddy current and hysteresis loss
iv ) In a damp atmosphere it is rusted

Hence its use is limited
Line supports
The supporting structures for overhead line
conductors are various types of poles and towers
called line supports
 In general, the line supports should have the
following properties

 High mechanical strength to withstand the weight of conductors and wind
load etc
 Light in weight without the loss of mechanical strength
 Cheap in cost and economical to maintain
 Longer life
 Easy accessibility of conductors for maintenance
12

The line supports used for transmission and distribution of electric power
are of various types
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Wooden poles
Steel poles
Reinforced concrete (R.C.C) poles
Lattice steel towers
Wooden poles:
These are made of seasoned wood and are suitable for lines of moderate
X- section area and of relatively shorter span, say up to 50 meters
Such supports are cheap, easily available, provide insulating properties and
therefore, are widely used for distribution purposes in rural areas as an
economical proposition
The wooden poles generally tend to rot below the ground level, causing
foundation failure. In order to prevent this, the portion of the pole below
the ground level is impregnated with preservative compounds like creosote
oil
Double pole structures of the ‘A’ or ‘H’ type are often used (see fig. below)
to obtain a higher transverse strength than could be economically provided
by means of a single poles
13

The main objections
wooden supports are:
to
(i). Tendency to rot below the
ground level
(ii). Comparatively smaller life
(20-25 years)
(iii). Cannot be used for voltages
higher than 20 kV
(iv). Less mechanical strength and
(v). Require periodical inspection
Figure
wooden poles
14
Steel poles:
 The steel poles are often used as a substitute for wooden poles
 They posses greater mechanical strength, longer life and permit
longer spans to be used
 Such poles are generally used for distribution purposes in the cities
 This type of supports need to be galvanized or painted in order to
prolong its life
 The steel poles are of three types
 Rail poles
 Tubular poles and
 Rolled steel joints
RCC poles:
 The RCC poles have become very popular as line supports in recent
years
 They have greater mechanical strength, longer life and permit longer
spans than steel poles.
15
Moreover, they give good
outlook,
require
little
maintenance and have good
insulating properties.
 Figure below shows R.C.C
poles for single and double
circuit
 The holes in the poles facilitate
the climbing of poles and at the
same time reduce the weight
of line supports
 The main difficulty with the use
of these poles is the high cost
of transport owing to their
heavy weight.

16
Steel tower:
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In practice, wooden, steel and reinforced concrete poles are used
for distribution purposes at low voltages, say up to 15 kV.
However, for long distance transmission at higher voltage, steel
tower are invariably employed
Steel towers have greater mechanical strength, longer life, can
withstand most sever climatic conditions and permit the use of
longer spans
The risk of interrupted service due to broken or punctured
insulation is considerably reduced owing to longer spans
Tower footings are usually grounded by driving rods into the
earth, this minimizes the lightning troubles as each tower acts as
a lightning conductor
17
18
Spacing between the conductor
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
The most suitable spacing
between the conductors can be
arrived at by mathematical
calculations.
It can only be obtained by
empirical formulae which have
been obtained from practical
considerations.
19

Generally the following formulae is used for obtaining spacing
between the conductors(phases):
Spacing (cm)  0.3048 x V  4.010
D
W
S
Where V = Voltage of system in kV
D = Diameter of Conductor in cm
S = sag in cm
W = weight of conductor in kg/m
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
In addition to phase conductors, a transmission line usually
includes one or two steel wires called shield wires. These wires
are electrically connected to the tower and to the ground, and,
therefore, are at ground potential.
In large transmission lines, these wires are located above the
phase conductors, shielding them from lightning.
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21
Insulators
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The overhead line conductors should be supported on the
poles or towers in such a way that currents from
conductors do not flow to earth through supports.
Provide Electrical insulation between live conductor and
earthed structure under operating and overvoltage
conditions.
To act as a reliable mechanical link between the structure
and the conductor and keep the mechanical integrity under
normal operating and overload conditions.
The insulators are mainly made of either glazed, porcelain
or toughened glass.
The dielectric strength of porcelain should be 15KV to
17KV for every one tenth inch thickness. Porcelain is
mechanically strong, less affected by temperature and has
minimum leakage problem.
22
 Toughened glass is also sometimes used for insulators because
it has higher dielectric strength (35KV for one tenth inch
thickness), But it has lower coefficient of thermal expansion.
And it condenses moisture very easily (since those reasons it
use is limited up to 33KV )
 In general, the insulators should have the following desirable
properties:
 High mechanical strength in order to withstand conductor load, wind
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load, etc
High electrical resistance of insulator material in order to avoid
leakage current to earth.
High relative permittivity of insulator material in order that dielectric
strength is high.
The insulator material should be non-porous, free from impurities and
cracks otherwise the permittivity will be lowered.
High ration of puncture strength to flashover.
23
Types of insulators
 In overhead transmission lines, the conductors are suspended from a
pole or a tower via insulators.
 There are several types of insulators but the most commonly used
are pin type, suspension type, strain insulator and shackle insulator
Pin type insulators
 consist of a single or multiple shells adopted to be mounted on a spindle
to be fixed to the cross arm of the supporting structure. Multiple shells
are provided in order to obtain sufficient length of leakage
 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 up to 33 kV. Beyond operating voltage of 33 kV, the
pin type insulators become too bulky and hence uneconomical.
24
Cause of insulator failure
 Insulators are required to withstand both mechanical and electrical
stresses
 The latter type is primarily 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
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 In flash over, an arc occurs between the line conductor and insulator pin
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(i.e, earth) and the discharge jumps across the air gaps, following shortest
distance
In case of flash-over, the insulator will continue to act in its proper
capacity unless extreme heat produced by the arc destroys the insulator
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
Puncture strength
Safety factor of insulator =
Flash-over voltage
26
Suspension type insulators
 The cost of pin type insulator increases rapidly as the working voltage is
increases. Therefore, this type of insulator is not economical beyond 33
kV.
 For high voltages (greater than 33 kV), it is a usual practice to use
suspension type insulators shown in figure below.
 They consists 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. The
number of discs in series would obviously depend upon the working
voltage
27
Advantages
(i). Suspension type insulators are cheaper than pin type insulators for
voltages beyond 33 kV
(ii). 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
(iii). If any one disc is damaged, the whole string does not become useless
because the damaged disc can be replaced by the sound one
(iv). The suspension arrangement provides greater flexibility to the line. The
connection at the cross arm is such that insulator string is free to swing in
any direction and can take up the position where mechanical stress are
minimum
(v). In case of increased demand on the transmission line, it is found more
satisfactory to supply the greater demand by raising the line voltage than
to provide another set of conductors. The additional insulation required
for the raised voltage can be easily obtained in the suspension
arrangement by adding the desired number of discs
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(vi). 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
Strain Insulators
 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 relive the line of
excessive tension, strain insulators are used
 For low voltage lines (less than 11 kV), shackle insulators are used as
strain insulators. However, for high voltage transmission lines, strain
insulators consists of assembly of suspension insulators as shown in
figure below.
 The discs of strain insulators are used in the vertical plane. When the
tension in line is exceedingly high, as at long river spans, two or more
strings are used in parallel
29
Shackle Insulators
 In early days, the shackle insulators were used as strain insulators. But now
a day, they are frequently used for low voltage distribution line.
 Such insulators can be used either in a horizontal position or a vertical
position
30
 They can be directly fixed to the pole with a bolt or to the cross arm.
Figure below shows a shackle insulator fixed to the pole. The conductor
in the groove is fixed with a soft binding wire
Figure: Shackle insulator
31
Potential distribution over suspension
insulators string
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A string of suspension insulators consists of a number of discs
connected in series.
each disc forms a capacitor C mutual capacitance or selfcapacitance.
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.
However, in actual practice, shunt capacitance C1 also exists
between metal fitting of each disc and tower or earth.
Due to shunt capacitance, charging current is not the same
through all the discs of the string.
Therefore, voltage across each disc will be different.
32
33
N.B:
V3 will be much more than V2 or V1
 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.
 The unit nearest to the conductor is under
maximum electrical stress.
•
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34
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.
String efficiency is decides the potential
distribution along the string.
 The greater the string efficiency, the more
uniform is the voltage distribution.
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35
Mathematical expression.
Consider he equivalent circuit for a 3-disc string.
 Let as assume self capacitance of each disc is C.
and shunt capacitance C1 is some fraction K of
self capacitance i.e., C1 = KC.
Applying Kirchhoff’s current law to
node A, we get:
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36

Applying Kirchhoff’s current law to node B, we get:
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Voltage between conductor and earth (i.e., tower) is:
37
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Voltage across top unit:
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Voltage across second unit from top,
 Voltage across third unit from top,
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%age String efficiency =
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38
Methods of Improving String Efficiency
 The
various methods for this purpose are :
1. By using longer cross-arms
2. By grading the insulators.
3. By using a guard ring.
39
Exercises
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:
1)
i.
ii.
the distribution of voltage over 3 insulators
string efficiency.
A 3-phase transmission line is being supported by three
disc insulators. The potentials across top unit (i.e., near
to the tower) and middle unit are 8 kV and 11 kV
respectively.
Calculate
(i) the ratio of capacitance between pin and earth to the
self-capacitance of each unit.
(ii) the line voltage and
(iii) string efficiency
2)
40
Transmission line design consideration
The design is based on optimization of electrical,
mechanical, environmental and economic factors.
1.Electrical Factors

◦ Types, size and number of bundle conductors per phase.
◦ Number of insulator disks, string arrangement, phase to
phase clearance, phase to tower clearance,…
◦ Number, type and location of shield wires.
◦ Line heights to satisfy conductor to ground clearance
and conductor spacing.
2. Mechanical Factors: Major focus of this factor are:
◦ Strength of conductors
◦ Strength of insulator strings
◦ Strength of support structure
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3.Environmental Factors
 It focuses on land usage and visual impacts.
◦ The Effects on local communities and population
centers.
◦ Land values
◦ Access to property and wildlife
◦ Use of public parks and facilities.
4.Economic Factors
◦ Optimum line design – meets technical design
criteria with lower overall cost.
◦ Overall cost include total installed cost as well as
cost of line losses over operating life of the line.
42
SAG IN OVERHEAD LINES
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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.
Fig. below (i) shows a conductor suspended between two
equivalent supports A and B. The conductor is not fully stretched
but is allowed to have a dip. The lowest point on the conductor is
O and the sag is S.The following points may be noted :
43
a)
b)
c)
d)
When the conductor is suspended between two supports at
the same level, it takes the shape of catenary. However, if the sag
is very small compared with the span, then sag-span curve is like
a parabola.
The tension at any point on the conductor acts tangentially. Thus
tension TO at the lowest point O acts horizontally as shown in
Fig. (ii).
The horizontal component of tension is constant throughout the
length of the wire.
The tension at supports is approximately equal to the horizontal
tension acting at any point on the wire. Thus if T is the tension at
the support B, then T = TO.
44
SAG AND TENSION CALCULATIONS
We shall now calculate sag and tension of a conductor when :
(i) supports are at equal levels and
(ii) supports are at unequal levels
A. When supports are at equal levels:
Consider a conductor between two equi-level supports A and B
with O as the lowest point as shown in Fig. It can be proved that
lowest point will be at the mid-span.
where:
l = Length of span
w = Weight per unit length of
conductor
T = Tension in the conductor
45
Consider a point P on the conductor. Taking the lowest point O
as the origin, let the co-ordinates of point P be x and y.
 Assuming that the curvature is so small that curved length is
equal to its horizontal projection (i.e., OP = x), the two forces
acting on the portion OP of the conductor are :
a) The weight wx of conductor acting at a distance x/2 from O.
b) The tension T acting at O.
Equating the moments of above two forces about point O, we get:

46
The maximum dip (sag) is represented by the value of y
at either of the supports A and B.
 At support A,

When supports are at unequal levels:
• conductors suspended between supports at unequal
levels.
• Fig.
shows a conductor suspended between two
supports A and B which are at different levels. The
lowest point on the conductor is O.
B.
•
47

Let:
l = Span length
h = Difference in levels between two supports
x1 = Distance of support at lower level (i.e., A) from O
x2 = Distance of support at higher level (i.e. B) from O
T = Tension in the conductor
48

If w is the weight per unit length of the conductor,
then:

49
•
Solving x1 and x2
•
Having found x1 and x2, values of S1 and S2 can be
easily calculated.

Ex 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 meters.
50
Effect of wind and ice loading
 The above formulae for sag are true only in still air and at
normal temperature when the conductor is acted by its weight
only
 In actual practice, a conductor may have ice coating and
simultaneously subjected to wind pressure
 Under the severest conditions of ice covering and wind, the
stress over the line is increased to the maximum.
 Under this condition the per unit length of the wire
w
experiences the following loading
i. The weight of the conductor w acting vertically downwards
ii. The ice loading wi
acting vertically downwards and
iii. The wind loading ww acting horizontally
51
Ice Loading:
 Let r be the radius of the conductor and t be the thickness of
ice (figure below)
 The volume of ice per unit length



 r  t   r 2 .1
2
Figure: Ice coated conductor
   2rt  t 2  .1
If  is the density of ice (912 kg/m3 ), the weight of ice per unit
length of conductor
wi    2rt  t 2  kg/m
52
Wind Loading:

Let P be the wind pressure in kg/m2; assuming the ice coating
of thickness t, the projected area per unit length on which the
wind is acting is
a = 2  r  t  .1 sq.meters
 wind loading w w per unit length will be
ww  2  r  t  .P kg/meter
Total vertical loading
 w  wi
Total loading (effective load acting on the conductor) is
We 
 w  wi   ww2
2
The load factor
q  We / w
53
Therefore sag can be calculated as
we L2
d
i.e T  H  approximation 
8T
54
Example
1.
A stress-crossing overhead transmission line has a span of 150
m over the stream. Horizontal wind pressure is 20 kg/m2 and
the thickness of ice is 1.25 cm. diameter of conductor is 2.80
cm and weight is 1520 kg/km, and an ultimate strength of
12900 kg. use a factor of safety of 2 and 912 kg/m3 for the
weight of ice. Using the parabolic method, determine the
following
a).Weight of ice in kg per meter
b).Total vertical load on conductor in kg/m
c). Horizontal wind force exerted on line in kg/m
d). Effective load acting on conductor in kg/m
e). Sag in meter
f).Vertical sag
55
Solution
a). Weight of Ice is
wi    2rt  t 2  kg / m

 912 x 2 x1.4 x10 x1.25 x10
2
2
 1.25 x10
2

2

 2865.1325  0.00035  0.00015625 
 1.45 kg/m
b). Total vertical load on the conductor is
wT  w  wi
 1520 kg/km  1.45 kg/m
 (1.520  1.45) kg/m
 2.97 kg/m
56
c). Horizontal wind force exerted on the transmission line is
ww  2  r  t  .P kg/m
 2 1.4 x102  1.25 x102  x 20 kg/m
 2  0.014  0.0125  x 20 kg/m
 1.06 kg/m
d). Effective load on the conductor is
we 
ww2  wT2
 1.06 2  2.97 2 kg/m
 9.9445 kg/m
 3.154 kg/m
57
e). Sag in meter using parabolic (approximate method) is
Ultimate strength
Factor safety
12900 kg

 6450 kg
2
we L2
d 
8T
3.154 x (150) 2

8 x 6450
T=
 1.3753 m
f). The vertical sag is
Vertical sag = dcos , but cos =
=1.3753 (
2.97
1.06
2.97
)
1.06
= 3.853 m
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Stringing chart


For use in the field work of stringing the conductors,
temperature- sag and temperature-tension charts are plotted
for the given conductor and loading conditions. Such curves are
called stringing charts (see figure below)
These charts are very helpful while stringing overhead lines
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Sag Template



For correct design and economy, the location of structures on
the profile with a template is very essential
Sag template is a convenient device used in the design of a
transmission line to determine the location and height of
structures
Sag template can be relied upon to provide the following:
1.
2.
3.
4.

Economic layout
Minimum errors in design and layout
Proper grading of structures
Prevention of excessive insulator swing
Generally two types of towers are used:
1. The standard or straight run or intermediate tower
2. The angle or anchor or tension tower
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





The straight run towers are used for straight runs and normal
conditions. The angle towers are designed to withstand heavy loading
as compared to standard towers because angle towers are used at
angles, terminals and other points where a large unbalanced pull may
be thrown on the supports
For standard towers, for normal or average spans, the sag and the
nature of the curve (Catenary or parabola) that the line conductor
will occupy under expected loading conditions is evaluated and
plotted on template
Template will also show the required minimum ground clearance by
plotting a curve parallel to the conductor shape curve. For the
standard tower and same height, the tower footing line can also be
plotted on the template
Tower footing line is used for locating the position of towers and
minimum ground clearance is maintained throughout.
Figure below shows the sag template used for locating towers. In fact
there are no clear-cut guide lines for locating the tower positions and
several other alternatives may be examined
Ground clearance depends on the voltage level and in the table gives
the span length and ground clearance at different voltage levels
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62
Q?
Thank you
63