Electrical Power Systems

374 Electrical Power Systems
The elastic property of wire is measured by its modulus of elasticity. The modulus of
elasticity is defined as the stress per unit area divided by the deformation per unit length.
Since
s = T
A kg/m2
where
s = stress per unit area (kg/m2 )
T = conductor tension (kg)
A = actual cross section of conductor (m 2 )
Elongation e of the conductor due to the tension is
e =
stress
modulus of elasticity
... (15.1)
... (15.2)
Elongation is high if modulus of elasticiy is low. Thus, a small change in the length of
conductor causes large effect on sag and tension of conductor.
Sag and stresses in conductors are dependent on the following things:
1. Initial tension put on them when they are clamped in place.
2. Weight of the conductors themselves.
3. Ice or sleet chinging to them.
4. Wind pressure.
Stress depends on sag, any span can be used provided the poles or towers are high enough
and strong enough. The matter is merely one of extending the catenary in both directions. Cost
of towers sharply increases with height and loading.
15.2 EECT O TEMPERATURE CHANGE
Sag and stress vary with temperature because of the thermal expansion and contraction of the
conductor. Temperature rise of conductor increase the length of conductor, and hence sag
increases and tension decreases. A temperature fall causes opposite effect. Maximum stress
occurs at the lowest temperature, when the line has contracted and is also possibly covered with
ice and sleet.
If conductor stress is constant while the temperature changes, the change in length of the
conductor is
Dl = l 0 aDt ...(15.3)
where
Dt = t 1 – t 0, Dl = l 1 – l 0
where
t 0 = initial temperature
l 0 = conductor length at initial temperature t 0
l 1 = conductor length at t 1.
a = coefficient of linear expansion of conductor per degree centigrade.
Dt = change in temperature in degree centigrade.
Dl = change in conductor length in meter.
If the temperature is constant while the conductor stress changes (i.e., loading), the change
in length of the conductor is