0. Electric Machinery PowerPoint Slides Chapter 2 Transformers
to accompany
Electric Machinery
Sixth Edition
A.E. Fitzgerald
Charles Kingsley, Jr.
Stephen D. Umans
Chapter 2
Transformers

1. Transformer with open secondary.
Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display.
Transformer with open secondary.
Figure 2.4
2-1

2. No-load phasor diagram.
Figure 2.5

3. Ideal transformer and load.
Figure 2.6

4. Three circuits which are identical at terminals ab when the transformer is ideal.
Figure 2.7

5. Equivalent circuits for Example 2
Equivalent circuits for Example 2.2 (a) Impedance in series with the secondary. (b) Impedance referred to the primary.
Figure 2.8

6. Schematic view of mutual and leakage fluxes in a transformer.
Figure 2.9

7. Steps in the development of the transformer equivalent circuit.
Figure 2.10

8. Equivalent circuits for transformer of Example 2
Equivalent circuits for transformer of Example 2.3 referred to (a) the high-voltage side and (b) the low-voltage side.
Figure 2.11

9. Approximate transformer equivalent circuits.
Figure 2.12

10. Cantilever equivalent circuit for Example 2.4.
Figure 2.13

11. No-Load Test (or Open-Circuit Test)
Short-Circuit Test

12. (high-voltage side open) (low-voltage side shorted)
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:

13. Open-Circuit Test (high-voltage side open)
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)
Voltmeter
Ammeter
Wattmeter
220 V
2.5A
100W

14. Short-Circuit Test (low-voltage shorted)
Voltmeter
Ammeter
Wattmeter
150 V
4.55A
215W

15. 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.

16. Voltage Regulation

17. Voltage Regulation – Example
Determine the voltage regulation in percent for the following load conditions.
75% full load, 0.6 power factor lagging
1Ø, 10kVA, 2200/220V, 60Hz

18. b) 75% full load, 0.6 power factor leading

19. 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.
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.

20. 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.

21. Common three-phase transformer connections; the transformer windings are indicated by the heavy lines.
Figure 2.19

22. 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.

23. 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.

25. 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 j0.016Ω. The 3Ø transformer supplies a 3Ø, 120kVA, 230V, 0.85 PF (lag) load.
Draw a schematic diagram sowing the transformer connection
Determine the transformer windwing currents.
Determine the primary voltage (line-to-line) required.
Determine the voltage regulation.
Schematic diagram sowing the transformer connection

26. b) c) d)

27. 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,
Determine the base values of voltages, currents, and impedances for both high-voltage and low-voltage sides.
Express the exciting current in per-unit form for both sides.
Obtain the equivalent circuit in per-unit form.

28. a) b) c)