Chapter 1: Modelling Power System Components

Composite Conductors

So far we have considered only solid round conductors. However as mentioned at the beginning of Section 1.1, stranded conductors are used in practical transmission line. We must therefore modify the equations derived above to accommodate stranded conductors. Consider the two groups of conductors shown in Fig. 1.9. Of these two groups conductor x contains n identical strands of radius rx while conductor y contains m identical strands of radius ry . Conductor x carries a current I the return path of which is through conductor y . Therefore the current through conductor y is - I .

Fig. 1.9 Single-phase line with two composite conductors.

Since the strands in a conductor are identical, the current will be divided equally among the strands. Therefore the current through the strands of conductor x is I / n and through the strands of conductor y is -I/m . The total flux linkage of strand a is given by

 (1.44)

We can write (1.44) as

 (1.45)

The inductance of the strand a is then given by

 (1.46)

In a similar way the inductances of the other conductors are also obtained. For example,

 (1.47)

The average inductance of any one of the strands in the group of conductor x is then

 (1.48)

Conductor x is composed of n strands that are electrically parallel. Even though the inductance of the different strand is different, the average inductance of all of them is the same as Lav, x . Assuming that the average inductance given above is the inductance of n parallel strands, the total inductance of the conductor x is

 (1.49)

Substituting the values of La , Lbetc. in the above equation we get

 (1.50)

where the geometric mean distance ( GMD ) and the geometric mean radius ( GMR ) are given respectively by

 (1.51) (1.52)

The inductance of the conductor y can also be similarly obtained. The geometric mean radius GMRy will be different for this conductor. However the geometric mean distance will remain the same.