[James_H._Harlow]_Electric_Power_Transformer_Engin(BookSee.org)

3.5.4 Three-Phase Transformer Connections
Three-phase connections can be made either by using three single-phase transformers or by using a
three-phase transformer. Advantages of the three-phase transformer is that it costs less, the weight is less,
it requires less floor space, and has lower losses than three single-phase transformers. Circuit computations
involving three-phase transformer banks under balanced conditions can be made by dealing with
only one of the transformers or phases. It is more convenient to use line-to-neutral values, since transformer
impedances can then be added directly to transmission-line impedances. All impedances must
be converted to the same side of the transformer bank by multiplying them by the square of the voltage
ratio.
There are two basic types of three-phase transformers, core type and shell type. The magnetic circuit
of the shell type is very similar to three single-phase transformers. This type of transformer has a return
circuit for each phase of the magnetic flux. Consequently, the zero-sequence impedance is equal to the
positive-sequence impedance. The conditions with respect to magnetizing currents and zero-sequence
impedances are essentially the same as for single-phase transformers connected in the same way. The
center-phase coil is usually wound in a direction opposite to that of the two outer phases in order to
decrease the core yoke required between phases. This reversal of polarity is corrected when the leads are
terminated.
The magnetic circuit of each phase of a three-limb core-type transformer is mutually connected in
that the flux of one phase must return through the other two phases. In this type of transformer, the
total instantaneous magnetic flux in each core section due to the fundamental excitation current is zero.
However, in the wye–wye-connected transformer, there are third-harmonic voltages in the phases caused
by the third-harmonic current. These voltages and the resulting magnetic flux are all induced in the same
direction. Since there is no return path for this flux in the core, the flux must return through the relatively
low-reluctance path outside the core. The core-type transformer is occasionally manufactured with a
five-limb core. In this case, the magnetic circuit and performance characteristics are similar to that of
shell-type or single-phase transformers.
Unbalanced system faults and loads can cause significant zero-sequence magnetic flux to occur for
some three-phase connections. Unless a magnetic return path for this flux is provided, the flux returns
outside the core and can cause eddy-current heating in other transformer conductive components, such
as the tank. The existence of zero-sequence flux either within or outside the core depends on both core
configuration and winding connections. Three-phase transformer-core assemblies do not usually provide
full-capacity return legs for zero-sequence flux. Thus, if sufficient zero-sequence flux occurs, it will be
forced to return outside the core.
Three-phase transformer connections can be compared with each other with respect to:
• Ratio of kVA output to the kVA internal rating of the bank
• Degree of voltage symmetry with unbalanced phase loads
• Voltage and current harmonics
• Transformer ground availability
• System fault-current level
• Switching and system fault and transient voltages
In some cases, there may also be other operating characteristics to determine the most suitable
connection for each application.
3.5.4.1 Double-Wound Transformers
The majority of three-phase transformer connections are made by connecting the individual phases either
between the power-system lines, thus forming a delta connection, or by connecting one end of each phase
together and the other ends to the lines, thus forming a wye (also referred to as star) connection. For
these connections, the total rating of the internal windings is equal to the through-load rating. This
accounts for the popularity of these connections. For all other double-wound transformer connections,
the ratio is less than unity. For example, in the interconnected star or zigzag connection, the transformer
is capable of delivering a load equal to only 86.6% of the internal winding rating. Since the cost of a
transformer varies approximately with the three-quarter power of the internal kVA, the cost of an
interconnected star or zigzag transformer is approximately 5% higher than for a similar double-wound
transformer. All of these types of three-phase connections are shown in Figure 3.5.2.
3.5.4.1.1 Wye–Wye Connections of Transformers
Joining together the terminals of similar windings with the same polarity derives the neutral of the wye
connection. This neutral point is available and can be brought out for any desired purpose, such as
grounding or zero-sequence current measurements and protection. For high-voltage transmission systems,
the use of the wye-connected transformer is more economical because the voltage across the phase
of each winding is a factor of 1.73 less than the voltage between the lines. If the neutral point is grounded,
it is not necessary to insulate it for the line voltage.
If the neutral is not grounded, the fault current during a system line to ground fault is insignificant
because of the absence of a zero-sequence current path. If the neutral is grounded in the wye–wye
transformer and the transformer is made with a three-limb core, the zero-sequence impedance is still
high. As a result, the fault currents during a system line-to-ground fault are relatively low. For wye–wye
transformers made of three single-phase units or with a shell-type or five-limb core-type, the zerosequence
impedance is approximately equal to the positive-sequence impedance. The fault current during
a system ground fault for this case is usually the limiting factor in the design of the transformer. In all
types of wye-wye transformer connections, only the transformer positive-sequence impedance limits the
fault current during a system three-phase system fault.
With the wye connection, the voltages are symmetrical as far as the lines are concerned, but they
introduce third-harmonic (or multiples of the third harmonic) voltage and current dissymmetry between
lines and neutral. The third-harmonic voltage is a zero-sequence phenomenon and thereby is exhibited
in the same direction on all phases. If the transformer and generator neutrals are grounded, thirdharmonic
currents will flow that can create interference in telephone circuits. If the transformer neutral
is not grounded, the third-harmonic voltage at the neutral point will be additive for all three phases, and
the neutral voltage will oscillate around the zero point at three times the system frequency. Thirdharmonic
voltages are also created on the lines, which can subject the power system to dangerous
overvoltages due to resonance with the line capacitance. This is particularly true for shell-type threephase
transformers, five-limb core-type transformers, and three-phase banks of single-phase transformers.
For any three-phase connection of three-limb core-form transformers, the impedance to thirdharmonic
flux is relatively high on account of the magnetic coupling between the three phases, resulting
in a more stabilized neutral voltage. A delta tertiary winding can be added on wye–wye transformers to
provide a path for third-harmonic and zero-sequence currents and to stabilize the neutral voltage. The
tertiary in this application will be required to carry all of the zero-sequence fault current during a system
line-to-ground fault.
The most common way to supply unbalanced loads is to use a four-wire wye-connected circuit.
However, the primary windings of the transformer bank cannot be wye-connected unless the primary
neutral is joined to the neutral of the generator. In this case, a third-harmonic voltage exists from each
secondary line-to-neutral voltage because the generator supplies a sinusoidal excitation current. The
third-harmonic currents created by the third-harmonic voltages can be a source of telephone interference.
If the primary neutral is not connected to the generator, single-phase or unbalanced three-phase loads
in the secondary cannot be supplied, since the primary current has to flow through the high impedance
of the other primary windings.
3.5.4.1.2 Delta–Delta Connection
The delta–delta connection has an economic advantage over the wye–wye connection for low-voltage,
high-current requirements because the winding current is reduced by a factor of 1.73 to 58% of that in
the wye–wye connection.
© 2004 by CRC Press LLC
© 2004 by CRC Press LLC