Inductance of Three Phase Double Circuit with Symmetrical Spacing

Inductance of Three Phase Double Circuit with Symmetrical Spacing

Consider the three phase double circuit with the conductors placed at the vertices of a regular hexagon which is shown in the Fig. 1.22.1.

Conductor x, y, z are forming one circuit whereas conductors x', y'and z' are forming another circuit.

Let us find out flux linkage of conductor x due to currents in other phases.

Example 1.22.1 Find the inductance per phase per km of double circuit 3 phase line system shown in the Fig. 1.22.2. The conductors are transposed and are of radius 6 mm each. The phase sequence is ABC.

Solution :

Example 1.22.2 A 3 phase circuit line consist of 7/4.75 mm hard drawn copper conductors. The arrangement of the conductors is shown in Fig. 1.22.3. The line is completely transposed. Calculate inductive reactance per phase per km of the system.

AU: Dec.-13, May-15, Marks 12

Solution : The stranded conductor is specified as no. of strands and diameter of each strand 7/4.75 mm hard drawn copper conductors are there.

d = Diameter of each strand = 4.75 mm.

Total diameter of stranded conductor, dc = (2n + l)d where n = No. of layers in which the strands are arranged around central strands.

If no. of layers are not specified then the no. of layers n are given by,

Example 1.22.3 Determine the inductance per km of a double circuit 3 $ line as shown in Fig. 1.22.4. The transmission line is transposed within each circuit and each circuit remains on its own side. The diameter of each conductor is 15 mm.

Solution :

Review Questions

1. Derive an expression for inductance of three phase double circuit line with symmetrical spacing.

2. Find the inductance per phase per km of double circuit 3 phase line system shown in the Fig. 1.22.5. The conductors are transposed and are cf radius 0.75 cm each. The phase sequence is ABC.

[Ans.: 0.6436 mH] 

4. A double circuit 3-phase 50 Hz line has its conductors at vertices of regular hexagon of side 3.5 m. The diameter of conductor is 2 cm. Find inductance and inductive reactance of a line per phase per km.      

[Ans.: 1.9928 mH, 0.3747 Q]