Multiwinding Transformers

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 w₁ turns, the M.V. (medium­ voltage) winding with w₂ turns, and the L.V. winding with w₃ 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 İ₂ and İ₃, 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

İ₁w₁ = İ₂w₂+ İ₃w₃ + İ_1,ocw₃ (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)]

İ₁= İ’₂+ İ’₃+ İ_1,oc (8.27)

where

İ’₂ = (w₂/w_l) İ₂

and

İ’₃ = (w₃/w_l) İ₃

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 , İ₂ and İ₃, 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

n₁₂ = w₁/w₂, n₁₃ = w₁/w₃, n₂₃ = w₂/w₃, = n₁₃/n₁₂

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.