2.7 Transformers in Three-Phase Circuits 85
more efficient than an equivalent number of two-winding transformers. Transformers
having a primary and multiple secondaries are frequently found in multiple-output dc
power supplies for electronic applications. Distribution transformers used to supply
power for domestic purposes usually have two 120-V secondaries connected in series.
Circuits for lighting and low-power applications are connected across each of the
120-V windings, while electric ranges, domestic hot-water heaters, clothes-dryers,
and other high-power loads are supplied with 240-V power from the series-connected
secondaries.
Similarly, a large distribution system may be supplied through a three-phase
bank of multiwinding transformers from two or more transmission systems having
different voltages. In addition, the three-phase transformer banks used to interconnect
two transmission systems of different voltages often have a third, or tertiary, set of
windings to provide voltage for auxiliary power purposes in substations or to sup-
ply a local distribution system. Static capacitors or synchronous condensers may be
connected to the tertiary windings for power factor correction or voltage regulation.
Sometimes A-connected tertiary windings are put on three-phase banks to provide a
low-impedance path for third harmonic components of the exciting current to reduce
third-harmonic components of the neutral voltage.
Some of the issues arising in the use of multiwinding transformers are associated
with the effects of leakage impedances on voltage regulation, short-circuit currents,
and division of load among circuits. These problems can be solved by an equivalent-
circuit technique similar to that used in dealing with two-circuit transformers.
The equivalent circuits of multiwinding transformers are more complicated than
in the two-winding case because they must take into account the leakage impedances
associated with each pair of windings. Typically, in these equivalent circuits, all
quantities are referred to a common base, either by use of the appropriate turns ratios
as referring factors or by expressing all quantities in per unit. The exciting current
usually is neglected.
2.7 TRANSFORMERS IN THREE-PHASE
CIRCUITS
Three single-phase transformers can be connected to form a
three-phase transformer
bank
in any of the four ways shown in Fig. 2.19. In all four parts of this figure, the wind-
ings at the left are the primaries, those at the right are the secondaries, and any primary
winding in one transformer corresponds to the secondary winding drawn parallel to it.
Also shown are the voltages and currents resulting from balanced impressed primary
line-to-line voltages V and line currents I when the ratio of primary-to-secondary
turns N1/N2
= a
and ideal transformers are assumed. 4 Note that the rated voltages
and currents at the primary and secondary of the three-phase transformer bank de-
pends upon the connection used but that the rated kVA of the three-phase bank is three
times that of the individual single-phase transformers, regardless of the connection.
4 The relationship between three-phase and single-phase quantities is discussed in Appendix A.