Sag in Overhead Conductor

What is Sag?

Sag is defined as the different in level between points of supports and the lowest point on the conductor.
sag
Here AOB is the transmission line conductor. Two supports are at point A and at point B. AB is the horizontal line and from this horizontal line to point O, S is the sag when measured vertically.

Why Sag Provision is Mandatory in Transmission Line Conductors?

Sag is mandatory in transmission line conductor suspension. The conductors are attached between two supports with perfect value of sag. It is because of providing safety of the conductor from not to be subjected to excessive tension. In order to permit safe tension in the conductor, conductors are not fully stretched; rather they are allowed to have sag.
If the conductor is stretched fully during installation, wind exerts pressure on the conductor, hence conductor gets chance to be broken or detached from its end support. Thus sag is allowed to have during conductor suspension.
Some important points are to be mentioned:

  1. When same leveled two supports hold the conductor, bend shape arises in the conductor. Sag is very small with respect to the span of the conductor.
  2. Sag span curve is like parabolic.
  3. The tension in each point of the conductor acts always tangentially.
  4. Again the horizontal component of the tension of conductor is constant throughout conductor length.
  5. The tension at supports is nearly equal to the tension at any point of the conductor.

How to Calculate Sag?

Sag calculation is classified on two conditions.

  1. When supports are at equal levels
  2. When supports are not at equal levels

Now let us start discussion on two conditions.

Sag calculation for supports are at equal levels

Suppose, AOB is the conductor. A and B are points of supports. Point O is the lowest point and the midpoint.
Let, L = length of the span, i.e. AB
w is the weight per unit length of the conductor
T is the tension in the conductor.
We have chosen any point on conductor, say point P.
The distance of point P from Lowest point O is x.
y is the height from point O to point P.

Equating two moments of two forces about point O as per the figure above we get,


Sag calculation for supports are at unequal levels
sag calculation for supports are at unequal levels
Suppose AOB is the conductor that has point O as the lowest point.
L is the Span of the conductor.
h is the difference in height level between two supports.
x1 is the distance of support at the lower level point A from O.
x2is the distance of support at the upper level point B from O.
T is the tension of the conductor.
w is the weight per unit length of the conductor.
Now,


So, having calculated the value of x1 and x2, we can easily find out the value of sag S1 and sag S2.
The above formula are used to calculate sag when the conductor is in still air and ambient temperature is normal. Hence the weight of the conductor is its own weight.

What is the Effect of Ice and Wind on Sag?

  • The weight per unit length of the conductor is changed when wind blows at a certain force on the conductor and ice accumulate around the conductor.
  • Wind force acts on the conductor to change the conductor self weight per unit length horizontally in the direction of the air flow.
  • Ice loading acts on the conductor to change the conductor self weight per unit length vertically downward.
  • Considering wind force and ice loading both at a time, the conductor will have a resultant weight per unit length.
  • The resultant weight will create an angle with the ice loading down ward direction.

Let us assume, w is the weight of the conductor per unit length.
wi is the weight of ice per unit length
wi= density of ice × volume of ice per unit length

sag
ww is the force of wind per unit length
ww = wind pressure per unit area × projected area per unit length


So, the total weight of the conductor per unit length is


The sag in the conductor is given by

So the vertical sag

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