Sag calculation in overhead line

Calculation of Sag:

The sag & tension of conductor may be calculated in the following condition:-
a) When the supports are at equal levels.
b) When the supports are at unequal levels.

i) Sag calculation when supports are at equal levels:

Lets,
A conductor is in the two equal level supports A and B.
O is the lowest point of the conductor.
l= length of the span.
w= weight per unit of length conductor.
T= Tension in the conductor.

A point has been considered on the conductor in the point P which is X length away from the point O & y length high from the bottom point of the conductor. It may be assumed that the curvature length ‘OP’ = x, and the following two forces will be acted on the portion ‘OP’ of the conductor.

  1. Weight of ‘OP’ portion conductor is WX which is acted at a distance x/2 from the point O.
  2. T tension is acted at point O.

The above two forces is equating movement about point O, we get

The value of y is the sag of conductor at point P.
As, at the support point A, x = l/2 and y = S,
Therefore, put the value of x and y in the equation (i), we get

ii)Sag calculation when support are at unequal level:
The unequal level suspension conductor is normal shown in hilly area.

Let,
A conductor is supported at two point A & B.
O is the lowest point of conductor.
l = Span length of conductor.
h = Different in levels between two supports
X1 = Distance of support at higher level A from & point O
X2 = Distance of support at higher level i.e B from O.
T = Tension in conductor,
W= Wight per unit length of the conductor.

After getting x1 & x2 value, the sag of conductor is easily calculated.

Effect of wind and ice loading:

Now , we describe the effect of wind and ice loading in sag calculation at overhead line.

The weight of ice acts in the same direction as the weight of conductor ( i.e vertically down wards ). The force due to the wind is assumed to act horizontally.

 

Lets,

Therefore, the total force on conductor is the vector sum of the above two forces which is shown in fig.

So, when the conductor has wind and ice loading
i) the sag of the conductor will be:-

This sag represents the slant sag in a direction making an angle θ to the vertical. We can easily calculate the value of slant slag by using the above formula.

ii) The vertical sag = S cos ϴ

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