[James_H._Harlow]_Electric_Power_Transformer_Engin(BookSee.org)

Voltage and current symmetry with respect to the three lines is obtained only in the delta and zigzag
connections. Delta-connected transformers do not introduce third harmonics or their multiples into the
power lines. The third-harmonic-induced voltage components are 360 apart. They are therefore all in
phase and cause a third-harmonic current to flow within the delta winding. This third-harmonic current
acts as exciting current and causes a third-harmonic voltage to be induced in each winding that is in
opposition to the third-harmonic component of voltage that was originally induced by the sinusoidal
exciting current from the lines. As a result, the third harmonic is eliminated from the secondary voltage.
Another advantage of the delta–delta connection, if composed of three single-phase transformers, is
that one transformer can be removed and the remaining two phases operated at 86.6% of their rating
in the open delta connection.
The principle disadvantage of the delta–delta connection is that the neutral is not available. As a result,
the phases cannot be grounded except at the corners. The insulation design is more costly because this
type of three-phase transformer connection has higher ground voltages during system fault or transient
voltages. Supplying an artificial neutral to the system with a grounding transformer can help to control
these voltages. The delta-connection insulation costs increase with increasing voltage. Consequently, this
type of connection is commonly limited to a maximum system voltage of 345 kV.
Differences in the voltage ratio of the individual phases causes a circulating current in both the primary
and secondary deltas that is limited only by the impedance of the units. Differences in the impedances
of the individual phases also causes unequal load division among the phases. When a current is drawn
from the terminals of one phase of the secondary, it flows in the windings of all three phases. The current
among the phases divides inversely with the impedance of the parallel paths between the terminals.
3.5.4.1.3 Delta–Wye and Wye–Delta Connections
The delta–wye or wye–delta connections have fewer objectionable features than any other connections.
In general, these combine most of the advantages of the wye–wye and delta–delta connections. Complete
voltage and current symmetry is maintained by the presence of the delta. The exciting third-harmonic
current circulates within the delta winding, and no third-harmonic voltage appears in the phase voltages
on the wye side. The high-voltage windings can be connected wye, and the neutral can be brought out
for grounding to minimize the cost of the insulation.
Differences in magnetizing current, voltage ratio, or impedance between the single-phase units are
adjusted by a small circulating current in the delta. All of these factors result in unbalanced phase voltages
on the delta, which causes a current to circulate within the delta.
If the primary windings of a four-wire, wye-connected secondary that is supplying unbalanced loads
are connected in delta, the unbalanced loading can be readily accommodated. There will be unbalanced
secondary voltages caused by the difference in the regulation in each phase, but this is usually insignificant.
Although the delta–wye connection has most of the advantages of the wye–wye and delta–delta, it still
has several disadvantages. This connection introduces a 30 phase shift between the primary and secondary
windings that has to be matched for paralleling. A delta–wye bank cannot be operated with only
two phases in an emergency. If the delta is on the primary side and should accidentally open, the unexcited
leg on the wye side can resonate with the line capacitance.
3.5.4.2 Multiwinding Transformers
Transformers having more than two windings coupled to the same core are frequently used in power
and distribution systems to interconnect three or more circuits with different voltages or to electrically
isolate two or more secondary circuits. For these purposes, a multiwinding transformer is less costly and
more efficient than an equivalent number of two winding transformers. The arrangement of windings
can be varied to change the leakage reactance between winding pairs. In this way, the voltage regulation
and the short-circuit requirements are optimized. The application of multiwinding transformers permits:
• Interconnection of several power systems operating at different voltages
• Use of a delta-connected stabilizing winding, which can also be used to supply external loads
• Control of voltage regulation and reactive power
• Electrical isolation of secondary circuits
• Duplication of supply to a critical load
• Connection for harmonic-filtering equipment
• A source for auxiliary power at a substation
Some of the problems with the use of multiwinding transformers are associated with the effect leakage
impedance has on voltage regulation, short-circuit currents, and the division of load among the different
circuits. All the windings are magnetically coupled to the leakage flux and are affected by the loading of
the other windings. It is therefore essential to understand the leakage impedance behavior of this type
of transformer to be able to calculate the voltage regulation of each winding and load sharing among
the windings. For three-winding transformers, the leakage reactance between each pair of windings must
be converted into a star-equivalent circuit. The impedance of each branch of the star circuit is calculated
as follows:
Z a = 0.5(Z ab + Z ca – Z bc ) (3.5.1)
Z b = 0.5(Z bc + Z ab – Z ca ) (3.5.2)
and
Z c = 0.5(Z ca + Z bc – Z ab ) (3.5.3)
where Z a , Z b , and Z c are the star-equivalent impedances in each branch, and Z ab , Z bc , and Z ca are the
impedances as seen from the terminals between each pair of windings with the remaining winding left
open circuit. The equivalent star-circuit reactances and resistances are determined in the same manner.
The four-winding transformer coupled to the same core is not commonly used because of the interdependence
of the voltage regulation of each winding to the loading on the other windings. The equivalent
circuit for a four-winding transformer is much more complicated, involving a complex circuit of six
different impedances.
After the loading of each winding is determined, the voltage regulation and load sharing can be
calculated for each impedance branch and between terminals of different windings. The currents in each
winding during a system fault can also be calculated in a similar fashion.
3.5.4.3 Autotransformers Connections
It makes no difference whether the secondary voltage is obtained from another coil or from the primary
turns. The same transformation ratio is obtained in either case. When the primary and secondary voltages
are obtained from the same coil, schematically, the transformer is called an autotransformer. The performance
of autotransformers is governed by the same fundamental considerations as for transformers
with separate windings. The autotransformer not only requires less turns than the two-winding transformer;
it also requires less conductor cross section in the common winding because it has to carry only
the differential current between the primary and secondary. As a result, autotransformers deliver more
external load than the internal-winding kVA ratings, depending on the voltage ratios of the primary and
secondary voltages, as shown in Figure 3.5.3 and the following formula:
Output/internal rating = V 1 /(V 1 – V 2 ) (3.5.4)
where
V 1 = voltage of the higher-voltage winding
V 2 = voltage of the lower-voltage winding
The internal rating, size, cost, excitation current, and efficiency of autotransformers are higher than
in double-wound transformers. The greatest benefit of the autotransformer is achieved when the primary
and secondary voltages are close to each other.
© 2004 by CRC Press LLC
© 2004 by CRC Press LLC