You may start with sag equation:
S=w*L^2/8/T where:
S = mid-span sag (m)
w = conductor weight (N/m)
L = horizontal span length (m)
T = conductor tension (N)
The conductor tension T is the tension at the low point of the cable
Usually To=0.2-0.3 NBL [Nominal Break Load]
w=Wc[Kg/km]*9.81/1000
The difference in distance between the straight line between the supports and the distance along the parabola arc (the stretched conductor length) is called the slack. For a level span the slack is given by:
K=8*S^2/3/L
K = slack (m)
S = mid-span sag (m)
L = span length (m)
As the temperature increases, the unstretched conductor length will increase by an amount equal to: Δ L = α*dT* S where:
α = the coefficient of thermal expansion
dT = the temperature increase in deg C
S = the span length in metres
wind load on the conductor will increase the apparent weight of the conductor resulting in an in increase in tension.
Ice build up on the conductor will increase the apparent diameter and weight of the conductor
Aging: conductor sag over time may increase due to the effects of strand settling in and
metallurgical creep.
The increase in tension will increase the cable length due to elastic stretch by an amount given by: dL=(T-To)/E/A where:
To = the initial tension in newtons
T = the final tension
E = the coefficient of elasticity
A = the cross section of the conductor in metres.
See-for instance:
NETWORK LINES STANDARD GUIDELINES FOR OVERHEAD LINE DESIGN-ERGON ENERGY