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 + İ1,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+ İ1,oc (8.27)
where
İ'2 = (w2/wl) İ2
and
İ'3 = (w3/wl) 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.
Labels: Electricity and Magnetism