Transposition and transposition cycle layouts

Transposition is the exchange of the positions of the phase conductors at regular intervals along the line, so that each conductor occupies each position for an equal length.

Why transposition is done

• With unsymmetrical spacing, each phase has different flux linkages and charges, so the inductance and capacitance of the phases are unequal.
• This causes unequal voltage drops and unbalanced receiving-end voltages even for a balanced load.
• Transposition makes the average $L$ and $C$ of every phase equal, so the line is balanced and can be analysed per phase with $D_{eq} = \sqrt[3]{D_{12}D_{23}D_{31}}$.
• It reduces interference with nearby communication (telephone) lines, because the induced voltages from the three sections cancel.
• In practice transposition is done at switching stations or every few tens of km.

Complete transposition cycle: 3-φ single circuit

The line length is divided into three equal sections; each phase takes positions 1, 2 and 3 in turn.

 Pos  Sec I     Sec II    Sec III
  1   a ------\ c ------\ b ------
  2   b ------\ a ------\ c ------
  3   c ------  b ------  a ------
      |<-l/3->| |<-l/3->| |<-l/3->|

Complete transposition cycle: 3-φ double circuit

Both circuits are transposed together, and the same pattern is kept in every section: the two middle conductors belong to the same phase, and the top conductor of each circuit is the same phase as the bottom conductor of the other (in Section I, a is opposite c', b opposite b', and c opposite a').

  Sec I         Sec II        Sec III
 a o   o c'    c o   o b'    b o   o a'
 b o   o b'    a o   o a'    c o   o c'
 c o   o a'    b o   o c'    a o   o b'
 |<--l/3-->|   |<--l/3-->|   |<--l/3-->|

In each section the phases shift by one position, and over the full cycle every phase of each circuit occupies every position once.