Electric Power Generation, Transmission, and Distribution

Note that the conductor length depends solely on span and sag. It is not directly dependent on
conductor tension, weight, or temperature. The conductor slack is the conductor length minus the span
length; in this example, it is 0.27 ft (0.0826 m).

14.2.1 Sag Change with Thermal Elongation

ACSR and AAC conductors elongate with increasing conductor temperature. The rate of linear thermal
expansion for the composite ACSR conductor is less than that of the AAC conductor because the steel
strands in the ACSR elongate at approximately half the rate of aluminum. The effective linear thermal
expansion coefficient of a non-homogenous conductor, such as Drake ACSR, may be found from the
following equations (Fink and Beatty):

EAS¼EAL

AAL

ATOTAL



þEST

AST

ATOTAL



(14:22)

aAS¼aAL

EAL

EAS



AAL

ATOTAL



þaST

EST

EAS



AST

ATOTAL



(14:23)

whereEAL ¼Elastic modulus of aluminum, psi
EST ¼Elastic modulus of steel, psi
EAS ¼Elastic modulus of aluminum-steel composite, psi
AAL ¼Area of aluminum strands, square units
AST ¼Area of steel strands, square units
ATOTAL¼Total cross-sectional area, square units
aAL ¼Aluminum coefficient of linear thermal expansion, per 8 F
aST ¼Steel coefficient of thermal elongation, per 8 F
aAS ¼Composite aluminum-steel coefficient of thermal elongation, per 8 F
The elastic moduli for solid aluminum wire is 10 million psi and for steel wire is 30 million psi.
The elastic moduli for stranded wire is reduced. The modulus for stranded aluminum is assumed to be
8.6 million psi for all strandings. The moduli for the steel core of ACSR conductors varies with stranding
as follows:
.27.5 106 for single-strand core
.27.0 106 for 7-strand core
.26.5 106 for 19-strand core
Using elastic moduli of 8.6 and 27.0 million psi for aluminum and steel, respectively, the elastic
modulus for Drake ACSR is:

EAS¼(8: 6  106 )

0 : 6247

0 : 7264



þ(27: 0  106 )

0 : 1017

0 : 7264



¼ 11 : 2  106 psi

and the coefficient of linear thermal expansion is:

aAS¼ 12 : 8  10 ^6

8 : 6  106

11 : 2  106



0 : 6247

0 : 7264



þ 6 : 4  10 ^6

27 : 0  106

11 : 2  106



0 : 1017

0 : 7264



¼ 10 : 6  10 ^6 =F

If the conductor temperature changes from a reference temperature,TREF, to another temperature,T,
the conductor length,L, changes in proportion to the product of the conductor’s effective thermal
elongation coefficient,aAS, and the change in temperature,T–TREF, as shown below:

LT¼LTREF(1þaAS(TTREF)) (14:24)