What transposition is and why it is needed

What transposition is

Transposition is the regular exchange of the positions of the three phase conductors along a line. Each phase occupies each of the three positions for one-third of the length of a complete transposition cycle. The exchange is done at special transposition towers.

   Section 1    Section 2    Section 3
 pos1  a ---------- c ---------- b
 pos2  b ---------- a ---------- c
 pos3  c ---------- b ---------- a
      |<- l/3 ->|<- l/3 ->|<- l/3 ->|

Why it is required

1. Equal inductance and capacitance per phase. With unsymmetrical spacing (for example horizontal or vertical arrangement), each phase sees different distances to the other two. So each phase has a different flux linkage, inductance and capacitance. Transposition gives every phase the same average spacing, $D_{eq} = \sqrt[3]{D_{ab}D_{bc}D_{ca}}$, and so equal parameters:

$$L = 2\times10^{-7}\ln\frac{D_{eq}}{r'}\ \text{H/m per phase}$$

2. Balanced voltage drops. With unequal reactances, a balanced load current produces unequal drops, and the receiving-end voltages become unbalanced. Transposition keeps the receiving end balanced.
3. No complex (imaginary) inductance terms. Without transposition the flux-linkage equations contain $a$-operator terms. These make power transfer between phases appear, and the per-phase model fails. Transposition removes them, so the line can be treated as balanced and analysed per phase.
4. Reduced interference with communication lines. The induced voltages from the three phases cancel over a cycle. This reduces electromagnetic and electrostatic interference with nearby telephone and communication circuits.
5. Reduced unbalance in charging currents and neutral (ground) currents.

In practice, lines are transposed at switching stations or every few tens of kilometres. Even when a line is not physically transposed, it is usually calculated as transposed, because the error is small.