25-01-2013, 02:26 PM
Sag and Tension of Conductor
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INTRODUCTION
The energized conductors of transmission and distribution lines must be placed to totally eliminate the
possibility of injury to people. Overhead conductors, however, elongate with time, temperature, and
tension, thereby changing their original positions after installation. Despite the effects of weather
and loading on a line, the conductors must remain at safe distances from buildings, objects, and people
or vehicles passing beneath the line at all times. To ensure this safety, the shape of the terrain along
the right-of-way, the height and lateral position of the conductor support points, and the position of the
conductor between support points under all wind, ice, and temperature conditions must be known.
Bare overhead transmission or distribution conductors are typically quite flexible and uniform in
weight along their length. Because of these characteristics, they take the form of a catenary (Ehrenberg,
1935; Winkelmann, 1959) between support points. The shape of the catenary changes with conductor
temperature, ice and wind loading, and time. To ensure adequate vertical and horizontal clearance under
all weather and electrical loadings, and to ensure that the breaking strength of the conductor is not
exceeded, the behavior of the conductor catenary under all conditions must be known before the line is
designed. The future behavior of the conductor is determined through calculations commonly referred
to as sag-tension calculations.
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.
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.
Inclined Spans
Inclined spans may be analyzed using essentially the same equations that were used for level spans. The
catenary equation for the conductor height above the low point in the span is the same. However, the
span is considered to consist of two separate sections, one to the right of the low point and the other to
the left as shown in Fig. 14.2 (Winkelmann, 1959). The shape of the catenary relative to the low point is
unaffected by the difference in suspension point elevation (span inclination).
Conductor Tension Limits
The NESC recommends limits on the tension of bare overhead conductors as a percentage of the
conductor’s rated breaking strength. The tension limits are: 60% under maximum ice and wind load,
33.3% initial unloaded (when installed) at 608F, and 25% final unloaded (after maximum loading has
occurred) at 608F. It is common, however, for lower unloaded tension limits to be used. Except in areas
experiencing severe ice loading, it is not unusual to find tension limits of 60% maximum, 25% unloaded
initial, and 15% unloaded final. This set of specifications could easily result in an actual maximum
tension on the order of only 35 to 40%, an initial tension of 20% and a final unloaded tension level of
15%. In this case, the 15% tension limit is said to govern.