Electric Power Generation, Transmission, and Distribution

rated breaking strength that are not to be exceeded upon installation or during the life of the line. These
conditions, along with the elastic and permanent elongation properties of the conductor, provide
the basis for determinating the amount of resulting sag during installation and long-term operation
of the line.
Accurately determined initial sag limits are essential in the line design process. Final sags and tensions
depend on initial installed sags and tensions and on proper handling during installation. The final
sag shape of conductors is used to select support point heights and span lengths so that the minimum
clearances will be maintained over the life of the line. If the conductor is damaged or the initial sags
are incorrect, the line clearances may be violated or the conductor may break during heavy ice or
wind loadings.

14.1 Catenary Cables

A bare-stranded overhead conductor is normally held clear of objects, people, and other conductors by
periodic attachment to insulators. The elevation differences between the supporting structures affect
the shape of the conductor catenary. The catenary’s shape has a distinct effect on the sag and tension
of the conductor, and therefore, must be determined using well-defined mathematical equations.

14.1.1 Level Spans

The shape of a catenary is a function of the conductor weight per unit length,w, the horizontal
component of tension,H, span length,S, and the maximum sag of the conductor,D. Conductor sag
and span length are illustrated in Fig. 14.1 for a level span.
The exact catenary equation uses hyperbolic functions. Relative to the low point of the catenary curve
shown in Fig. 14.1, the height of the conductor,y(x), above this low point is given by the following
equation:

y(x)¼

H

w

cosh

w

H

x



 1



¼

w(x^2 )

2 H

(14:1)

S

D L 2

x

X axis

y (x)

H

a = H/w

Y axis

T

FIGURE 14.1 The catenary curve for level spans.