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PowerPoint Slides
to accompany
Electric Machinery
Sixth Edition
A.E. Fitzgerald
Charles Kingsley, Jr.
Stephen D. Umans
Chapter 2
Transformers
2-0
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Transformer with open secondary.
Figure 2.4
2-1
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No-load phasor diagram.
Figure 2.5
2-2
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Ideal transformer and load.
Figure 2.6
2-3
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Three circuits which are identical at
terminals ab when the transformer
is ideal.
Figure 2.7
2-4
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Equivalent circuits for Example 2.2 (a) Impedance
in series with the secondary. (b) Impedance referred
to the primary.
Figure 2.8
2-5
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Schematic view of mutual
and leakage fluxes in a
transformer.
Figure 2.9
2-6
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Steps in the
development
of the
transformer
equivalent
circuit.
Figure 2.10
2-7
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Equivalent circuits for transformer of Example 2.3
referred to (a) the high-voltage side and (b) the
low-voltage side.
Figure 2.11
2-8
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Approximate transformer equivalent circuits.
Figure 2.12
2-9
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Cantilever equivalent circuit for Example 2.4.
Figure 2.13
2-10
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No-Load Test (or Open-Circuit Test)
Short-Circuit Test
2-11
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Example:
Test are performed on a 1Ø, 10kVA, 2200/220V, 60Hz transformer and the following results
are obtained for Open-Circuit:
Open-Circuit Test
(high-voltage side open)
Short-Circuit Test
(low-voltage side shorted)
Voltmeter
220 V
150V
Ammeter
2.5A
4.55A
Wattmeter
100W
215W
The ratings of the windings are as follows:
2-12
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a) Derive the parameters for the approximate equivalent circuits referred to the low-voltage
side and the high-voltage side.
Open-Circuit Test (high-voltage side open)
2-13
Voltmeter
Ammeter
Wattmeter
220 V
2.5A
100W
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Short-Circuit Test (low-voltage shorted)
2-14
Voltmeter
Ammeter
Wattmeter
150 V
4.55A
215W
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b) Express the excitation current as a percentage of the rated current
This is (2.5/45.5) x 100% = 5.5% of the rated current of the winding
c) Determine the power factor for the no-load and short-circuit tests.
2-15
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Voltage Regulation
2-16
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Voltage Regulation – Example
Determine the voltage regulation in percent for the following load conditions.
a)
75% full load, 0.6 power factor lagging
1Ø, 10kVA, 2200/220V, 60Hz
2-17
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b)
2-18
75% full load, 0.6 power factor leading
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Autotransformer.
Example:
A 1Ø, 100kVA, 2000/200V two-winding transformer is connected
as an autotransformer as shown in Figure, such that more than
2000V is obtained at the secondary. The portion ab is the 200V
winding, and the portion bc is the 2000V winding. Compute the
kVA rating as an autotransformer.
2-19
A 1Ø, 100kVA, connected as an autotransformer can deliver
1100 kVA. Also note that the 200V winding must have
sufficient insulation to withstand a voltage of 2200V to
ground.
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Three-Phase Transformers
A set of three similar single-phase transformers may be connected to form a three-phase
transformer. The primary and secondary windings may be connected in either wye (Y) or
delta (Δ). There are therefore four possible connections:
Y- Δ: This connection is commonly used to step down a high voltage to a lower voltage.
Δ-Y: This connection is commonly used to step up voltage.
Δ- Δ: This connection has the advantage that one transformer can be removed for repair
and the ramaining two can continue to deliver three-phase power at a reduced rating of
58% of that of he original bank. This is known as the open-delta or V connection.
Y-Y: This connection is rarely used because of problems with the exciting current and
induced voltages.
2-20
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Common three-phase transformer connections; the
transformer windings are indicated by the heavy lines.
Figure 2.19
2-21
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Three-Phase Transformers – Phase Shift
Consider the phasor voltages, shown in Fig. 2.18, for the Y-Δ connections. The phasores
VAN and Va are aligned, but the line voltage VAB of the primary leads the line voltage Vab of
the secondary by 30°. It can be shown that Δ-Y connection also provides a 30° phase shift
between line-to-line voltages, whereas Δ-Δ and Y-Y connections have no phase shift in their
line-to-line voltages.
2-22
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Three-Phase Transformers – Single Phase Equivalent Circuit
The voltages and currents in one phase are the same as those in other phases (for
balanced load), except that there is a phase displacement of 120°. Therefore, analysis of
one phase is sufficient to determine the variables on the two sides of the transformer.
A single phase equivalent circuit can be conveniently obtained if all sources, transformer
windings, and loas impedances are considered to be Y-connected.
2-23
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2-24
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Three-Phase Transformers – Single Phase Equivalent Circuit
Example:
Three 1Ø, 50kVA, 2300/230V, 60Hz transformers are connected to form a 3Ø, 4000/230V
transformer bank. The equivalent impedance of each transformer referred to low voltage is
0.012+j0.016Ω. The 3Ø transformer supplies a 3Ø, 120kVA, 230V, 0.85 PF (lag) load.
a) Draw a schematic diagram sowing the transformer connection
b) Determine the transformer windwing currents.
c) Determine the primary voltage (line-to-line) required.
d) Determine the voltage regulation.
a) Schematic diagram sowing the transformer connection
2-25
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b)
c)
d)
2-26
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PER-UNIT (PU) System
Example:
The exciting current of a Ø, 10kVA, 2100/210V, 60Hz transformers is 0.25A when measured
on the high-voltage side. Its equivalent impedance is 10.4+j31.3Ω when referred to the
high-voltage side. Taking the transformer rating as base,
a) Determine the base values of voltages, currents, and impedances for both high-voltage
and low-voltage sides.
b) Express the exciting current in per-unit form for both sides.
c) Obtain the equivalent circuit in per-unit form.
2-27
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a)
b)
c)
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