Transposed Line in Power System

Transposed Line in Power System

Transposition is the periodic swapping of positions of the conductors of a transmission line, in order to reduce crosstalk and otherwise improve transmission. In telecommunications this applies to balanced pairs whilst in power transmission lines three conductors are periodically transposed.

For longer power lines without branches, wires are transposed according to the transposing scheme. At closely branched grids and where several electric circuits share a route (in particular when the lines operate at different voltages) on the same pylons the outside unbalance of the line, which is caused by the other electric circuits, dominates. In these cases one finds large deviations from the transposing schemes. For example, in some such transpositions, only two of the three conductors on the pylons change their place. Also transpositions on pylons near power substations are used to get an optimal arrangement of the feeding system without crossing of conductors.
As the mutual influence of electric circuits can change after new lines are installed or old lines dismantled, certain transpositions may disappear or be added after new construction in electricity mains. In the case of a twisted line the individual conductors of an electric circuit swap places, either in their whole course (at cables) or at certain points (at overhead lines). The mutual influence of electrical conductors is reduced by transposing. The unbalance of the line, which can lead to one-sided loads in three-phase systems, is also reduced. Transposing of overhead lines is usually realized at so-called transposing pylons. Transposing is an effective measure for the reduction of inductively linked normal mode interferences.

A transposing scheme is a pattern by which the conductors of overhead power lines are transposed at transposing structures. In order to ensure balanced capacitance of a three-phase line, each of the three conductors must hang once at each position of the overhead line.

At a transposition tower, the conductors change their relative places in the line. A transposing structure may be a standard structure with special cross arms, or may

be a dead-end structure. The transposing is necessary as there is capacitance between conductors, as well as between conductors and ground. This is typically not symmetrical across phases. By transposing, the overall capacitance for the whole line is approximately balanced. Transposing also reduce effects related to interference in communications circuits.

Inductance of Three-Phase Lines with Asymmetrical Spacing

It is rather difficult to maintain symmetrical spacing as shown in Fig. 1.6 while constructing a transmission line. With asymmetrical spacing between the phases, the voltage drop due to line inductance will be unbalanced even when the line currents are balanced. Consider the three-phase asymmetrically spaced line shown in Fig. 1.7 in which the radius of each conductor is assumed to be r . The distances between the phases are denoted by D_ab, D_bc and D_ca. We then get the following flux linkages for the three phases

	(1.01)
	(1.02)
	(1.03)

Fig. 1.7 Three-phase asymmetrically spaced line.

Let us define the following operator

(1.04)

Note that for the above operator the following relations hold

(1.05)

Let as assume that the current are balanced. We can then write

Substituting the above two expressions in (1.31) to (1.33) we get the inductance of the three phases as

	(1.06)
	(1.07)
	(1.08)

It can be seen that the inductance contain imaginary terms. The imaginary terms will vanish only when D_ab= D_bc= D_ca.

The inductance that are given in (1.06) to (1.08) are undesirable as they result in an unbalanced circuit configuration. One way of restoring the balanced nature of the circuit is to exchange the positions of the conductors at regular intervals. This is called transposition of line and is shown in Fig.1.8. In this each segment of the line is divided into three equal sub-segments. The conductors of each of the phases a, b and c are exchanged after every sub-segment such that each of them is placed in each of the three positions once in the entire segment. For example, the conductor of the phase-a occupies positions in the sequence 1, 2 and 3 in the three sub-segments while that of the phase-b occupies 2, 3 and 1. The transmission line consists of several such segments.

Fig. 1.8 A segment of a transposed line.

In a transposed line, each phase takes all the three positions. The per phase inductance is the average value of the three inductance calculated in (1.06) to (1.08). We therefore have

(1.09)

This implies

From (1.35) we have a + a² = - 1. Substituting this in the above equation we get

(1.10)

The above equation can be simplified as

(1.11)

Defining the geometric mean distance ( GMD ) as

(1.12)

equation (1.11) can be rewritten as

H/m

(1.13)

Notice that (1.13) is of the same form as for symmetrically spaced conductors. Comparing these two equations we can conclude that GMD can be construed as the equivalent conductor spacing. The GMD is the cube root of the product of conductor spacings.