Calculation of Diameter for Stranded Conductor

Calculation of Diameter for Stranded Conductor

The stranded conductor usually has a central wire which is surrounded by the layers of wires. These layers consists of 6, 12, 18, ...... wires successively. Thus the total strands are 7, 13, 19 ...... .   

Such a stranded conductor with 37 strands is shown in the Fig. 4.5.1.

Let d = Diameter of each strand

Then the total diameter of a stranded conductor (cable) is given by,

d_c = (2 n + 1) d

where n = Number of layers in which the strands are arranged around central strand.

The stranded conductor is specified as number of strands and diameter of strand.

For example 7/0.295 mm which indicates 7 strands with 0.295 mm diameter of each strand.

If at all the number of layers are not specified then the number of layers can be calculated as number of strands and layers are related to each other by the equation,

x = 3n² + 3n + 1

where          x - Number of strands

and    n = Number of layers

The standard number of strands in each successive layer from inner to outer is 6, 12, 18, 24          ...............

Example 4.5.1 A transmission line uses a hard drawn copper of area of cross-section of 200 mm with a conductor 61/2.24 mm. The span of the line is 160 m with supports at the level. The maximum stress for a conductor is 41 kg/mm with a factor of safety of 5.

Calculate : a) Sag in still air

b) Sag with a wind pressure of 1.35 kg/m and ice coating of 1.25 cm.

c) Vertical sag with conditions as in (b) above

Assume copper density as 8.9 gm/cm³ .

Solution : L - 160 m, S_f - 5, Maximum stress - 41 kg/mm²

To find maximum stress in conductor, use area of copper as 200 mm² .

Maximum stress in kg = 41 × 200 = 8200 kg

S_f = Maximum stress / Tension T  i.e. T = 8200 / 5 = 1640 kg

Now we want conductor diameter which is dc It consists of 61 strands, each of diameter 2.24 mm.

Review Questions

1. An overhead line is supported between two towers 250 m apart having a difference in their levels equal to 4 m. Calculate the sag at the lower support if the wind pressure is 39 kg/m of projected area. Factor of safety is 2.

The conductor data is :

Nominal copper area 110 mm² , stranded conductor 37/2.79 mm

Weight 844 kg/km, ultimate strength 7950 kg       

[Ans.: 0.6817 m]

2. A 132 kV transmission line uses ACSR conductor whose data are : nominal copper area 110 mm² ; size 30 + 7/2.79 mm; weight 844 kg/km²; ultimate strength 7950 kg. The line is subjected to a horizontal wind pressure of 40 kg/m of projected area and 1.25 cm radial ice coating. If the maximum permissible sag is 6 m, calculate the permissible span between the a two supports, allowing for a factor of safety of 2. Weight of ice is 915 kg/m³ .

[Ans.: 133.5511 m]