Electric Power Generation, Transmission, and Distribution

Note that the balance of thermal and elastic elongation of the conductor yields an equilibrium tension
of approximately 3700 lbs and a sag of 13.3 ft. The calculations of the previous section, which ignored
elastic effects, results in lower tension, 3440 lb, and a greater sag, 14.7 ft.
Slack is equal to the excess of conductor length over span length. The preceding table can be replaced
by a plot of the catenary and elastic curves on a graph of slack vs tension. The solution occurs at the
intersection of the two curves. Figure 14.5 shows the tension versus slack curves intersecting at a tension
of 3700 lb, which agrees with the preceding calculations.

14.2.3 Sag Change Due to Ice Loading

As a final example of sag-tension calculation, calculate the sag and tension for the 600-ft Drake span
with the addition of 0.5 inches of radial ice and a drop in conductor temperature to 0 8 F. Employing Eq.
(14.17), the weight of the conductor increases by:

wice¼ 1 : 244 t(Dþt)

wice¼ 1 :244(0:5)(1: 108 þ 0 :5)¼ 1 :000 lb=ft

As in the previous example, the calculation uses the conductor’s zero tension length at 60 8 F, which is
the same as that found in the previous section, 599.81 ft. The ice loading is specified for a conductor
temperature of 0 8 F, so the ZTL(0 8 F), usingEq. (14.24), is:

ZTL(0F)¼ 599 :81[1þ(10: 6  10 ^6 )(060)]¼ 599 :43ft

As in the case of sag-tension at elevated temperatures, the conductor tension is a function of slack and
elastic elongation. The conductor tension and the conductor length are found at the point of intersec-
tion of the catenary and elastic curves (Fig. 14.6). The intersection of the curves occurs at a horizontal
tension component of 12,275 lb, not very far from the crude initial estimate of 12,050 lb that
ignored elastic effects. The sag corresponding to this tension and the iced conductor weight per unit
length is 9.2 ft.
In spite of doubling the conductor weight per unit length by adding 0.5 in. of ice, the sag of the
conductor is much less than the sag at 167 8 F. This condition is generally true for transmission
conductors where minimum ground clearance is determined by the high temperature rather than the
heavy loading condition. Small distribution conductors, such as the 1=0 AWG ACSR in Table 14.1,
experience a much larger ice-to-conductor weight ratio (4.8), and the conductor sag under maximum
wind and ice load may exceed the sag at moderately higher temperatures.

5000

4500

4000

3500

3700 Ibs

Elastic

Catenary

3000

2500

2000

0.5 0.75 1 1.25 1.5

Slack / Elongation, ft

Tension, Ibs

FIGURE 14.5 Sag-tension solution for 600-ft span of Drake at 167 8 F.