Sag calculation in overhead line
Calculation of Sag:
The sag & tension of the 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:
![](https://i2.wp.com/www.electricalunits.com/Image/power-system/sag40.gif?zoom=2&w=640)
Lets,
A conductor is in the two equal levels 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.
- Weight of ‘OP’ portion conductor is WXwhich is acted at a distance x/2 from the point O.
- T tension is acted at point O.
The above two forces are equating movement about point O, we get
![](https://i0.wp.com/www.electricalunits.com/Image/power-system/sag10.png?zoom=2&w=640)
The value of y is the sag of the 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
![](https://i0.wp.com/www.electricalunits.com/Image/power-system/sag2.png?zoom=2&w=640)
ii)Sag calculation when support is at the unequal level:
The unequal level suspension conductor is normal shown in a hilly area.
![](https://i2.wp.com/www.electricalunits.com/Image/power-system/sag5.png?zoom=2&w=640)
Let,
A conductor is supported at two points A & B.
O is the lowest point of the conductor.
l = Span length of the conductor.
h = Different in levels between two supports
X1 = Distance of support at higher level Afrom & point O
X2 = Distance of support at higher level i.e Bfrom O.
T = Tension in the conductor,
W= Weight per unit length of the conductor.
![](https://i0.wp.com/www.electricalunits.com/Image/power-system/sag3.png?zoom=2&w=640)
After getting x1 & x2 value, the sag of the conductor is easily calculated.
Effect of wind and ice loading:
Now, we describe the effect of wind and ice loading in sag calculation at the overhead line.
The weight of ice acts in the same direction as the weight of the conductor ( i.e vertically downwards ). The force due to the wind is assumed to act horizontally.
![](https://i0.wp.com/www.electricalunits.com/Image/power-system/sag45.gif?zoom=2&w=640)
Lets,
![](https://i1.wp.com/www.electricalunits.com/Image/power-system/sag6.png?zoom=2&w=640)
Therefore, the total force on the conductor is the vector sum of the above two forces which is shown in fig.
![](https://i0.wp.com/www.electricalunits.com/Image/power-system/sag7.png?zoom=2&w=640)
So, when the conductor has wind and ice loading
i) the sag of the conductor will be:-
![](https://i2.wp.com/www.electricalunits.com/Image/power-system/sag8.png?zoom=2&w=640)
This sag represents the slant sag in a direction making an angle θ to the vertical. We can easily calculate the value of the slant slag by using the above formula.
ii) The vertical sag = S cos Ï´
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