__Multiwinding Transformers __

In many electrical installations it is desired to have an interconnection between several circuits (or networks) operating at different voltage levels. Most conveniently this can be done with a multi winding transformer which has one or several primary windings and several secondary windings. The simplest unit in this class is a three-winding transformer widely used in high-voltage networks.

A three-winding transformer has three electrically isolated windings. These are the H.V. winding with *w*_{1} turns, the M.V. (medium voltage) winding with *w*_{2} turns, and the L.V. winding with *w*_{3} turns. The respective voltages may, for example, be 220 kV, 38.5 kV, and 11 kV. The three windings (one primary and two secondaries ) are put on a common core which does not differ from that of a double winding transformer. The magnetizing current in the primary winding of a three-winding transformer excites in the core a magnetic flux which induces in all the three windings emfs proportional to their turns. If the load currents in the M.V. and L.V. windings are *İ*_{2} and *İ*_{3}, the mmf in the primary must be such as to balance the de-magnetizing effect of mmfs of the two secondary currents and also to supply a magnetizing mmf. Therefore

*İ*_{1}*w*_{1} = *İ*_{2}*w*_{2}+ *İ*_{3}*w*_{3} + *İ*_{1,oc}*w _{3}* (8.26)

and the primary current may be treated as a sum of the referred (or transferred) currents in the second and third windings and of the magnetizing current [see Eq. (8.10a)]

*İ*_{1}=* İ'*_{2}+* İ'*_{3}+* İ*_{1,oc }(8.27)

where

*İ'*_{2} = (*w*_{2}/*w*_{l}) *İ*_{2}

and

*İ'*_{3 }= (*w*_{3}/*w*_{l}) *İ*_{3}

As is seen, power in a three-phase transformer is simultaneously transferred to two secondary circuits, one associated with the second winding and the other with the third winding.

I t is highly improbable that the load currents in the two second dary circuits , *İ*_{2} and *İ*_{3}, could be at their maximum values and in phase at the same time. Therefore it is usual to design the primary winding for a rated power which is smaller than the sum of the rated powers of the secondary windings. The rated power of a three-winding transformer' is the apparent power of the highest-rated winding.

A three-winding transformer has three transformation (or turns) ratios

*n*_{12} = *w*_{1}/*w*_{2}, *n*_{13} = *w*_{1}/*w*_{3}, *n*_{23} = *w*_{2}/*w*_{3}, = *n*_{13}/*n*_{12}

The above ratios are found at the open-circuit voltages, as for a double-winding transformer, Eq. (8.13).

A more recent trend has been to use three-winding, transformers in which the H.V. and M.V. windings are interconnected as an autotransformer, with the usual transformer connection applied only to the L.V. winding electrically insulated from the H.V. and M.V. windings.