A celluloid template, shaped to the
form of the suspended conductor, is used to scale the distance from the
conductor to the ground and to adjust structure locations and heights to (1)
provide proper clearance to the ground; (2) equalize spans; and (3) grade the
line.
The template is cut as a parabola on the maximum sag
(usually at 49#C) of the ruling span and should be extended by computing the
sag as proportional to the square of the span for spans both shorter and longer
than the ruling span.
By extending the template to a span of several thousand
feet, clearances may be scaled on steep hillsides. The form of the template is
based on the fact that, at the time when the conductor is erected, the
horizontal tensions must be equal in all spans of every length, both level and
inclined, if the insulators hang plumb.
This is still very nearly true at the maximum temperature.
The template, therefore, must be cut to a catenary or, approximately, a
parabola. The parabola is accurate to within about one-half of 1% for sags up
to 5% of the span, which is well within the necessary refinement.
Since vertical ground clearances are being established, the
49 deg C no-wind curve is used in the template. Special conditions may call for
clearance checks. For example, if it is known that a line will have high
temperature rise because of load current, conductor clearance should be checked
for the estimated maximum conductor temperature.
One crossing over a navigable stream was designed for 88 deg
C at high water. Ice and wet snow many times cause weights several times that
of the 1/2-in radial ice loading, and conductors have been known to sag to
within reach of the ground.
Such occurrences are not normally considered in line design,
and when they occur, the line is taken out of service until the ice or snow
drops. Checks made afterward have nearly always shown no permanent deformation.
The template must be used subject to a “creep” correction
for aluminum conductors. Creep is a nonelastic conductor stretch which
continues for the life of the line, with the rate of elongation decreasing with
time.
For example, the creep elongation during the first 6 months
is equal to that of the next 91/2 years. All conductors of all materials are
subject to creep, but to date only aluminum conductors have had intensive
study. Creep is not substantial in other conductors, but the conductor
manufacturers should be consulted.
The IEEE Committee Report, “Limitations on Stringing and
Sagging Conductors,” in the December 1964 Transactions of the IEEE Power Group
discusses creep, and the reader should examine that report.
Creep causes a continuous slow increase in the sag of the
line which must be estimated and allowed for. The aluminum-conductor
manufacturers will furnish creep-estimating curves, and most sag-tension
computer programs now available are capable of calculating sags with and
without creep.
These curves are at approximately constant temperatures,
around 15.5 to 21 deg C, and plot stress against elongation, one curve for each
period of time, 1 h, 1 day, 1 month, 1 year, 10 years, etc. The values are
integrated values for the period and are considered to be reasonable estimates.
The temperature used is a reasonable average of the year’s
temperature across the center of the United States. Precise values for creep
are impossible to determine, since they vary with both temperature and tension,
which are continuously varying during the life of the line.
From Fig. 3 of the committee report in Ref. 53, it is found
that a 1000-ft span of 954,000-cmil 48/7 ACSR when subjected to a constant
tension of approximately 18% of its ultimate strength at a temperature of 15.5
deg C will have a sag increase in 1 day of approximately 5.5 in; in 10 days, 13
in; in 1 year, 27 in; in 10 years, 44 in; and in 30 years, 52 in.
Unless it is known that the line will have a life of less
than 10 years, not less than 10 years’ creep should be allowed for. Creep has
come into consideration in transmission-line design only during the past 35
years, and to date no standards have been established for handling it.
Probably the simplest approach is to check all close
clearance points on the profile with a template made with no creep allowance
and to specify higher structures at these points if the addition of liberal
creep sag infringes on the required clearances.
It is possible to prestress the creep out of small
conductors, but for large conductors this requires time and special tensioning
facilities not normally available. Also the time lost in constructing an EHV
line will more than pay for the extra structure height required to compensate
for the creep. Prestressing changes the modulus of elasticity, and this new
modulus should be used in the design.
The vertical weight supported at any structure is the weight
of the length of conductor between low points of the sag in the two adjacent
spans. For bare-conductor weights, this distance between low points can be
scaled by using a template of the sag at any desired temperature.
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