Three Phase Transformer Banks 3 86379 F0

User Manual: 3-phase-transformer-banks-86379 F0

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Three-Phase
Transformer Banks
RENEWABLE ENERGY

THREE-PHASE TRANSFORMER BANKS
Courseware Sample

by
the staff
of
Lab-Volt Ltd.

Copyright © 2011 Lab-Volt Ltd.
All rights reserved. No part of this publication may be
reproduced, in any form or by any means, without the prior
written permission of Lab-Volt Ltd.

Printed in Canada
August 2011

Safety Symbols
The following safety symbols may be used in this manual and on the Lab-Volt
equipment:

Symbol

Description
DANGER indicates a hazard with a high level of risk which, if not
avoided, will result in death or serious injury.
WARNING indicates a hazard with a medium level of risk which,
if not avoided, could result in death or serious injury.
CAUTION indicates a hazard with a low level of risk which, if not
avoided, could result in minor or moderate injury.
CAUTION used without the Caution, risk of danger sign ,
indicates a hazard with a potentially hazardous situation which,
if not avoided, may result in property damage.
Caution, risk of electric shock

Caution, hot surface

Caution, risk of danger

Caution, lifting hazard

Caution, hand entanglement hazard

Direct current
Alternating current
Both direct and alternating current
Three-phase alternating current
Earth (ground) terminal
Protective conductor terminal
Frame or chassis terminal

A Three-Phase Transformer Banks

Safety Symbols
Symbol

Description
Equipotentiality
On (supply)
Off (supply)
Equipment protected
reinforced insulation

throughout

double

insulation

In position of a bi-stable push control

Out position of a bi-stable push control

Three-Phase Transformer Banks A

Foreword
Three-phase transformer banks serve the same purpose in three-phase circuits
as single-phase power transformers in single-phase circuits. This means that
three-phase transformer banks are primarily used to either step-up (i.e., to
increase) the voltage from the primary windings to the secondary windings, or to
step-down (i.e., to decrease) the voltage from the primary windings to the
secondary windings. Since three-phase ac power is widely used worldwide for
both power transmission and power distribution, three-phase transformer banks
are one of the most common electrical components and are essential to any
three-phase ac power network.
Many three-phase transformer configurations are possible when connecting the
primary and secondary windings of a three-phase transformer bank. Each
configuration presents different characteristics. When connecting a three-phase
transformer bank in a circuit, it is therefore important to determine which
characteristics are advantageous to the circuit, and to choose the three-phase
transformer configuration accordingly. The four most common three-phase
transformer configurations are the wye-wye, delta-delta, wye-delta, and deltawye configurations.
This course, Three-Phase Transformer Banks, teaches the basic concepts of
three-phase transformer banks. Students are introduced to the different
characteristics of three-phase transformer banks. They learn how to connect the
windings of three-phase transformer banks in wye or delta. Students are also
introduced to the four most common types of three-phase transformer
configurations: wye-wye, delta-delta, wye-delta, and delta-wye. They determine
the voltage, current, and phase relationships between the primary windings and
the secondary windings of three-phase transformer banks for each of these
configurations. Students also verify the theory presented in the manual by
performing circuit measurements and calculations.

Three-phase transformer bank used for power distribution.

A Three-Phase Transformer Banks

vii

Table of Contents
Introduction

Three-Phase Transformer Banks ............................................. 1
Introduction to three-phase power transformers. Types of
three-phase power transformers. Connecting the windings of
three-phase transformer banks in wye and in delta.

Exercise 1

Three-Phase Transformer Configurations .............................. 5
Common three-phase transformer configurations. Voltage,
current, and phase relationships of the four common threephase transformer configurations. Summary of the
characteristics of the four common three-phase transformer
configurations. Uses of three-phase transformer banks.

Appendix A

Equipment Utilization Chart .................................................... 27

Appendix B

Glossary of New Terms ........................................................... 29

Appendix C

Impedance Table for the Load Modules ................................ 31

Index of New Terms ............................................................................................. 33
Bibliography ......................................................................................................... 35
We Value Your Opinion! ...................................................................................... 37

A Three-Phase Transformer Banks

Sample Exercise
Extracted from
Student Manual

Exercise

Three-Phase Transformer Configurations
EXERCISE OBJECTIVE

When you have completed this exercise, you will know how to connect threephase transformer banks in wye-wye, delta-delta, wye-delta, and delta-wye
configurations. You will determine what are the voltage, current, and phase
relationships between the primary windings and the secondary windings of a
three-phase transformer bank for each of these configurations. You will be
familiar with the different uses of three-phase transformer banks in three-phase
ac power circuits.

DISCUSSION OUTLINE

The Discussion of this exercise covers the following points:





DISCUSSION

Common three-phase transformer configurations
Voltage, current, and phase relationships of the four common threephase transformer configurations
Summary of the characteristics of the four common three-phase
transformer configurations
Uses of three-phase transformer banks

Common three-phase transformer configurations
Many three-phase transformer configurations are possible when connecting
the primary and secondary windings of a three-phase transformer bank. Each
configuration presents different characteristics. When connecting a three-phase
transformer bank in a circuit, it is therefore important to determine which
characteristics are advantageous to the circuit, and to choose the appropriate
three-phase transformer configuration accordingly.
The four most common three-phase transformer configurations are wye-wye,
delta-delta, wye-delta, and delta-wye configurations. Each of these configurations
is shown in Figure 3. The letter (A, B, or C) beside each winding in Figure 3
identifies one of the transformers in a three-phase transformer bank. This allows
the primary and secondary windings of each transformer in the three-phase
transformer bank to be easily located in the diagrams of Figure 3.

A Three-Phase Transformer Banks

Exercise 1 – Three-Phase Transformer Configurations  Discussion

Three-phase transformer bank
L1

Primaries

Secondaries

Primaries

Secondaries

B
L2

C
L3

L3
C

(a) Wye-wye configuration

(b) Delta-delta configuration

Three-phase transformer bank
Secondaries

Three-phase transformer bank
L1

Primaries

Primaries
L2
B

L2
B

C
L3

Secondaries

C
N

N
(c) Wye-delta configuration

(d) Delta-wye configuration

Figure 3. The four most common three-phase transformer configurations.

As you can see from the figure, wye-connected windings use 4 wires, while deltaconnected windings use only 3 wires. When setting up a three-phase transformer
bank in a wye-delta or delta-wye configuration, this property allows the number of
wires in a three-phase ac circuit to be modified from 4 wires to 3 wires, or from
3 wires to 4 wires, respectively. Either of these configurations can be a significant
advantage, depending on the requirements of the particular application in which it
is used.

Voltage, current, and phase relationships of the four common threephase transformer configurations
The most determining characteristics of each three-phase transformer
configuration mentioned in the previous section (i.e., the wye-wye, delta-delta,
wye-delta, and delta-wye configurations) are their respective voltage, current,
and phase relationships between the primary windings and the secondary

Three-Phase Transformer Banks A

Exercise 1 – Three-Phase Transformer Configurations  Discussion
windings. The following three sections discuss these relationships for each threephase transformer configuration. Note that, as wye-wye and delta-delta
configurations have similar voltage, current, and phase relationships, both
configurations are covered in the same section. Also note that, in the following
sections, the turns ratio of each transformer in the three-phase transformer bank
is assumed to be equal to 1:1. This allows observation of the effects each
configuration has on the voltage, current, and phase relationships of the threephase transformer bank, independently of the turns ratio.
Wye-wye and delta-delta configurations
When a three-phase transformer bank is connected in either a wye-wye or a
delta-delta configuration, the voltage, current, and phase relationships between
the primary windings and the secondary windings are identical to the
relationships found in a conventional single-phase power transformer. This
means that the values of the line voltages and currents at the secondary are
equal to those of the line voltages and currents at the primary (neglecting
transformer losses). Also, the line voltage sine waves at the secondary are in
phase with the line voltage sine waves at the primary. The same is true for the
line current sine waves at the secondary with respect to the line current sine
waves at the primary.
Wye-delta configuration
When a three-phase transformer bank is connected in a wye-delta configuration,
the values and phases of the line voltages and currents at the secondary are
different from those at the primary. Thus, in a wye-delta configuration, the value
of the line voltages at the secondary is equal to that of the line voltages at the
primary divided by √3. Conversely, the value of the line currents at the secondary
is equal to that of the line currents at the primary multiplied by √3. Furthermore,
the line voltage sine waves at the secondary lag behind those at the primary
by 30°. The same is true for the line current sine waves at the secondary with
respect to the line current sine waves at the primary.
Delta-wye configuration
When a three-phase transformer bank is connected in a delta-wye configuration,
the values and phases of the line voltages and currents at the secondary are
different from those at the primary. Thus, in a delta-wye configuration, the value
of the line voltages at the secondary is equal to that of the line voltages at the
primary multiplied by √3. Conversely, the value of the line currents at the
secondary is equal to that of the line currents at the primary divided by √3.
Furthermore, the line voltage sine waves at the secondary lead those at the
primary by 30°. The same is true for the line current sine waves at the secondary
with respect to the line current sine waves at the primary.

Summary of the characteristics of the four common three-phase
transformer configurations
The following table gives a summary of the different characteristics of the four
three-phase transformer configurations presented in the previous section
(i.e., the wye-wye, delta-delta, wye-delta, and delta-wye configurations).

A Three-Phase Transformer Banks

Exercise 1 – Three-Phase Transformer Configurations  Discussion
Table 1. Summary of the characteristics of three-phase transformer configurations.
Three-phase transformer
configuration

Line voltage
relationship
(
.:
.)

Line current
relationship
(
.:
.)

Phase shift
(Sec. with
respect to
Pri.)

Number of
wires
(Pri.:Sec.)

1: 1

0°

4: 4

1: 1

0°

3: 3

√3: 1

1: √3

30°
(30° lag)

4: 3

1: √3

√3: 1

30°
(30° lead)

3: 4

Wye-wye configuration

B
A

Delta-delta configuration
A
B
A

Wye-delta configuration
A
B
A

Delta-wye configuration

Remember that the line voltage and current relationships presented in Table 1
are valid only when the turns ratio of the transformers in the three-phase
transformer bank is equal to 1:1. When the turns ratio of the transformers in the
three-phase transformer bank is not 1:1, the actual line voltages at the secondary
can be found by multiplying the primary line voltages by the voltage ratio
appropriate to the configuration of the three-phase transformer bank and the
inverse of the turns ratio (
.⁄
. ) of the transformers. Similarly, the actual line
currents at the secondary can be found by multiplying the primary line currents

Three-Phase Transformer Banks A

Exercise 1 – Three-Phase Transformer Configurations  Procedure Outline
by the current ratio appropriate to the configuration of the three-phase
transformer bank and the turns ratio (
.⁄
. ) of the transformers.

Uses of three-phase transformer banks
Three-phase transformer banks are used in three-phase ac power circuits for
basically the same reasons as single-phase power transformers in single-phase
ac circuits, i.e., to step-up or step-down the voltages in the circuit and to provide
electrical isolation between the primary windings and the secondary windings.
However, the special properties of certain three-phase transformer configurations
presented in the previous sections allow three-phase transformer banks to be
used in a few additional applications. The primary uses of three-phase
transformer banks in three-phase ac power circuits are summarized below.
1. Three-phase transformer banks allow the voltages in the three-phase
ac power circuit to be stepped-up (i.e., to be increased) or steppeddown (i.e., to be decreased).
2. Three-phase transformer banks provide electrical isolation between the
primary windings and the secondary windings.
3. Three-phase transformer banks connected in a wye-delta or in a deltawye configuration allow the number of wires in the three-phase ac power
circuit to be decreased from 4 to 3, or increased from 3 to 4, respectively.
4. Three-phase transformer banks connected in a wye-delta or in a deltawye configuration allow the incoming line voltages and currents to be
phase shifted -30° or 30°, respectively.

PROCEDURE OUTLINE

The Procedure is divided into the following sections:







Set up and connections
Voltage, current, and phase relationships in a wye-wye configuration
Voltage, current, and phase relationships in a wye-delta configuration
Voltage, current, and phase relationships in a delta-delta configuration
Voltage, current, and phase relationships in a delta-wye configuration

PROCEDURE
High voltages are present in this laboratory exercise. Do not make or
modify any banana jack connections with the power on unless otherwise
specified.

Set up and connections
In this section, you will set up a circuit containing a three-phase transformer bank
connected in a wye-wye configuration. You will then set the measuring
equipment required to study the voltage, current, and phase relationships of the
three-phase transformer bank.

A Three-Phase Transformer Banks

Exercise 1 – Three-Phase Transformer Configurations  Procedure
1. Refer to the Equipment Utilization Chart in Appendix A to obtain the list of
equipment required to perform this exercise.
Install the required equipment in the Workstation.
2. Make sure that the ac and dc power switches on the Power Supply are set to
the O (off) position, then connect the Power Supply to a three-phase
ac power outlet.
Connect the Power Input of the Data Acquisition and Control Interface to
a 24 V ac power supply. Turn the 24 V ac power supply on.
3. Connect the USB port of the Data Acquisition and Control Interface to a USB
port of the host computer.
4. Turn the host computer on, then start the LVDAC-EMS software.
In the Module Selector window, make sure that the Data Acquisition and
Control Interface is detected. Make sure that the Computer-Based
Instrumentation function for the Data Acquisition and Control Interface is
selected. Also, select the network voltage and frequency that correspond to
the voltage and frequency of your local ac power network, then click the OK
button to close the Module Selector window.

Three-Phase Transformer Banks A

Exercise 1 – Three-Phase Transformer Configurations  Procedure
5. Connect the equipment as shown in Figure 4.
Three-Phase Transformer Bank module

Local ac power network

,
(Ω)

Voltage
(V)

Frequency
(Hz)

120

171

220

629

240

686

Figure 4. Three-phase transformer bank connected in a wye-wye configuration.

The values of the resistive loads used in the circuits of this manual depend on your
local ac power network voltage and frequency. Whenever necessary, a table below
the circuit diagram indicates the resistance of each load resistor for ac power
network voltages of 120 V, 220 V, and 240 V, and for ac power network
frequencies of 50 Hz and 60 Hz. Make sure to use the component values
corresponding to your local ac power network voltage and frequency.

6. Make the necessary switch settings on the Resistive Load in order to obtain
the resistance value required.

Appendix C lists the switch settings required on the Resistive Load in order to
obtain various resistance values.

7. In the Metering window, make the required settings in order to measure the
rms values (ac) of the line voltages
. ,
. , and
. (inputs E1, E2,
and E3, respectively), and the line currents
. ,
. , and
. (inputs I1,
I2, and I3, respectively) at the secondary of the three-phase transformer
bank. Set two other meters to measure the line voltage
. and current
.
at the primary of the three-phase transformer bank (inputs E4 and I4,
respectively).

A Three-Phase Transformer Banks

Exercise 1 – Three-Phase Transformer Configurations  Procedure

Voltage, current, and phase relationships in a wye-wye configuration
In this section, you will measure the line voltages and currents at the secondary
of the three-phase transformer bank, as well as a line voltage and current at the
primary. Using the measured values, you will determine the voltage and current
relationships between the primary and secondary windings of the three-phase
transformer bank. You will then open the Phasor Analyzer and the Oscilloscope,
and use both instruments to determine the phase shift between the line voltages
at the secondary and the line voltages at the primary. Finally, you will confirm
that the voltage, current, and phase relationships measured when the threephase transformer bank is connected in a wye-wye configuration are coherent
with the theory presented in the exercise discussion.

8. On the Power Supply, turn the three-phase ac power source on.
9. In the Metering window, measure the line voltages
. ,
. , and
. at
the secondary of the three-phase transformer bank, as well as the line
voltage
. at the primary. Also, measure the line currents
. ,
. ,
at
the
secondary
of
the
three-phase
transformer
bank,
as
well
as
and
.
the line current
. at the primary. Record all values below.
.

10. Using the line voltage and current values you measured in the previous step,
determine the voltage and current relationships between the primary
windings and the secondary windings of the three-phase transformer bank
when it is connected in a wye-wye configuration.
Voltage relationship (
Current relationship (

.:
.:

11. In LVDAC-EMS, open the Phasor Analyzer and make the required settings to
at the
observe the phasors of the line voltages
. ,
. , and
.
secondary (inputs E1, E2, and E3, respectively), as well as the line
voltage
. at the primary of the three-phase transformer bank (input E4).
Set the phasor of the line voltage
. (input E4) at the primary as the
reference phasor.
Using the Phasor Analyzer, determine the phase shift between the line
voltage
. at the secondary and the line voltage
. at the primary of the
three-phase transformer bank.
Phase shift between

and

Three-Phase Transformer Banks A

Exercise 1 – Three-Phase Transformer Configurations  Procedure
12. In LVDAC-EMS, open the Oscilloscope and make the required settings to
observe the waveforms of the line voltages
. ,
. , and
. at the
secondary (inputs E1, E2, and E3, respectively), as well as the line
voltage
. at the primary of the three-phase transformer bank (input E4).
Using the Oscilloscope, determine the phase shift between the line
voltage
. at the secondary and the line voltage
. at the primary of the
three-phase transformer bank.
Phase shift between

and

Does the phase shift between the line voltage
. at the secondary and the
line voltage
at
the
primary
you
just
determined
confirm the phase shift
.
you obtained previously using the Phasor Analyzer?

 Yes

 No

13. Are the voltage, current, and phase relationships you determined for the
three-phase transformer bank connected in a wye-wye configuration
coherent with the theory presented in the exercise discussion?

 Yes

 No

14. On the Power Supply, turn the three-phase ac power source off.

Voltage, current, and phase relationships in a wye-delta
configuration
In this section, you will connect the three-phase transformer bank in a wye-delta
configuration. You will measure the line voltages and currents at the secondary
of the three-phase transformer bank, as well as a line voltage and current at the
primary. Using the measured values, you will determine the voltage and current
relationships between the primary and secondary windings of the three-phase
transformer bank. You will then use the Phasor Analyzer and the Oscilloscope to
determine the phase shift between the line voltages at the secondary and the line
voltages at the primary. Finally, you will confirm that the voltage, current, and
phase relationships measured when the three-phase transformer bank is
connected in a wye-delta configuration are coherent with the theory presented in
the exercise discussion.

A Three-Phase Transformer Banks

Exercise 1 – Three-Phase Transformer Configurations  Procedure
15. Connect the equipment as shown in Figure 5. In this circuit, only the
connections at the secondary windings of the three-phase transformer bank
have been modified with respect to the circuit used in the previous section.
Three-Phase Transformer Bank module

15
5

L2
6

8
13

L3
11

Local ac power network

,
(Ω)

Voltage
(V)

Frequency
(Hz)

120

171

220

629

240

686

Figure 5. Three-phase transformer bank connected in a wye-delta configuration.

16. On the Power Supply, turn the three-phase ac power source on.
17. In the Metering window, measure the line voltages
. ,
. , and
. at
the secondary of the three-phase transformer bank, as well as the line
voltage
. at the primary. Also, measure the line currents
. ,
. ,
at
the
secondary
of
the
three-phase
transformer
bank,
as
well
as
and
.
the line current
. at the primary. Record all values below.
.

Three-Phase Transformer Banks A

Exercise 1 – Three-Phase Transformer Configurations  Procedure
18. Using the line voltage and current values you measured in the previous step,
determine the voltage and current relationships between the primary and the
secondary windings of the three-phase transformer bank when it is
connected in a wye-delta configuration.
Voltage relationship (

Current r relationship (

19. Using the Phasor Analyzer and the Oscilloscope, determine the phase shift
between the line voltage
. at the secondary and the line voltage
. at
the primary of the three-phase transformer bank.
Phase shift between

and

20. Are the voltage, current, and phase relationships you determined for the
three-phase transformer bank connected in a wye-delta configuration
coherent with the theory presented in the exercise discussion?

 Yes

 No

21. On the Power Supply, turn the three-phase ac power source off.

Voltage, current, and phase relationships in a delta-delta
configuration
In this section, you will connect the three-phase transformer bank in a delta-delta
configuration. You will measure the line voltages and currents at the secondary
of the three-phase transformer bank, as well as a line voltage and current at the
primary. Using the measured values, you will determine the voltage and current
relationships between the primary and secondary windings of the three-phase
transformer bank. You will then use the Phasor Analyzer and the Oscilloscope to
determine the phase shift between the line voltages at the secondary and the line
voltages at the primary. You will confirm that the voltage, current, and phase
relationships measured when the three-phase transformer bank is connected in a
delta-delta configuration are coherent with the theory presented in the exercise
discussion. You will then reverse the connection of the windings at the secondary
of the three-phase transformer bank. You will observe the resulting phase shift
between the secondary and the primary line voltages using the Phasor Analyzer
and the Oscilloscope, and analyze the results.

A Three-Phase Transformer Banks

Exercise 1 – Three-Phase Transformer Configurations  Procedure
22. Connect the equipment as shown in Figure 6. In this circuit, only the
connections at the primary windings of the three-phase transformer bank
have been modified with respect to the circuit used in the previous section.
Three-Phase Transformer Bank module

8
11

Local ac power network

,
(Ω)

Voltage
(V)

Frequency
(Hz)

120

171

220

629

240

686

Figure 6. Three-phase transformer bank connected in a delta-delta configuration.

23. On the Power Supply, turn the three-phase ac power source on.
24. In the Metering window, measure the line voltages
. ,
. , and
. at
the secondary of the three-phase transformer bank, as well as the line
voltage
. at the primary. Also measure the line currents
. ,
. ,
and
. at the secondary of the three-phase transformer bank, as well as
the line current
. at the primary. Record all values below.
.

25. Using the line voltage and current values you measured in the previous step,
determine the voltage and current relationships between the primary and the

Three-Phase Transformer Banks A

Exercise 1 – Three-Phase Transformer Configurations  Procedure
secondary of the three-phase transformer bank when it is connected in a
delta-delta configuration.
Voltage relationship (
Current relationship (

.:
.:

26. Using the Phasor Analyzer and the Oscilloscope, determine the phase shift
between the line voltage
. at the secondary and the line voltage
. at
the primary of the three-phase transformer bank.
Phase shift between

and

27. Are the voltage, current, and phase relationships you determined for the
three-phase transformer bank connected in a delta-delta configuration
coherent with the theory presented in the exercise discussion?

 Yes

 No

28. On the Power Supply, turn the three-phase ac power source off.

A Three-Phase Transformer Banks

Exercise 1 – Three-Phase Transformer Configurations  Procedure
29. Reverse the connections at each of the secondary windings of the threephase transformer bank. The circuit should now be as shown in Figure 7.
Three-Phase Transformer Bank module

12
L2

13
3

2
6

10
15

Local ac power network

,
(Ω)

Voltage
(V)

Frequency
(Hz)

120

171

220

629

240

686

Figure 7. Three-phase transformer bank connected in a delta-delta configuration with reversed connections at the secondary
windings.

30. On the Power Supply, turn the three-phase ac power source on.
31. Using the Phasor Analyzer and the Oscilloscope, determine the phase shift
between the line voltage
. at the secondary and the line voltage
. at
the primary of the three-phase transformer bank.
Phase shift between

and

32. What happens to the phase shift between the line voltage
. at the
at
the
primary
when
the
connections
at
secondary and the line voltage
.
the secondary windings of the three-phase transformer bank are reversed?

Three-Phase Transformer Banks A

Exercise 1 – Three-Phase Transformer Configurations  Procedure
Do your results confirm that it is important to respect the winding polarity
when connecting the windings of a three-phase transformer bank? Briefly
explain why.

33. On the Power Supply, turn the three-phase ac power source off.

Voltage, current, and phase relationships in a delta-wye
configuration
In this section, you will connect the three-phase transformer bank in a delta-wye
configuration. You will measure the line voltages and currents at the secondary
of the three-phase transformer bank, as well as a line voltage and current at the
primary. Using the measured values, you will determine the voltage and current
relationships between the primary and secondary windings of the three-phase
transformer bank. You will then use the Phasor Analyzer and the Oscilloscope to
determine the phase shift between the line voltages at the secondary and the line
voltages at the primary. Finally, you will confirm that the voltage, current, and
phase relationships measured when the three-phase transformer bank is
connected in a delta-wye configuration are coherent with the theory presented in
the exercise discussion. You will then reverse the connections of the windings at
the secondary of the three-phase transformer bank. You will observe the
resulting phase shift between the secondary and the primary line voltages using
the Phasor Analyzer and the Oscilloscope, and analyze the results.

34. Connect the equipment as shown in Figure 8. In this circuit, only the
connections at the secondary windings of the three-phase transformer bank
have been modified with respect to the last circuit used in the previous
section.

A Three-Phase Transformer Banks

Exercise 1 – Three-Phase Transformer Configurations  Procedure

Three-Phase Transformer Bank module

12
L2

2
6
11

Local ac power network

,
(Ω)

Voltage
(V)

Frequency
(Hz)

120

300

220

1100

240

1200

Figure 8. Three-phase transformer bank connected in a delta-wye configuration.

35. Make the necessary switch settings on the Resistive Load in order to obtain
the resistance value required.

Three-Phase Transformer Banks A

Exercise 1 – Three-Phase Transformer Configurations  Procedure
36. On the Power Supply, turn the three-phase ac power source on.

The voltage and power ratings of the Resistive Load are significantly exceeded in
this manipulation. It is therefore important that you perform the remainder of this
step in less than 2 minutes to avoid damaging the Resistive Load.

In the Metering window, measure the line voltages
. ,
. , and
. at
the secondary of the three-phase transformer bank, as well as the line
voltage
. at the primary. Also measure the line currents
. ,
. ,
and
. at the secondary of the three-phase transformer bank, as well as
the line current
. at the primary. Record all values below.
.

On the Power Supply, turn the three-phase ac power source off.
37. Using the line voltage and current values you recorded in the previous step,
determine the voltage and current relationships between the primary and the
secondary of the three-phase transformer bank connected in a delta-wye
configuration.
Voltage relationship (
Current relationship (

.:
.:

38. On the Power Supply, turn the three-phase ac power source on.

Using the Phasor Analyzer and the Oscilloscope, determine the phase shift
between the line voltage
. at the secondary and the line voltage
. at
the primary of the three-phase transformer bank.
Phase shift between

and

On the Power Supply, turn the three-phase ac power source off.

A Three-Phase Transformer Banks

Exercise 1 – Three-Phase Transformer Configurations  Procedure
39. Are the voltage, current, and phase relationships you determined for the
three-phase transformer bank connected in a delta-wye configuration
coherent with the theory presented in the exercise discussion?

 Yes

 No

40. Reverse the connections at each of the secondary windings of the threephase transformer bank. The circuit should now be as shown in Figure 9.
Three-Phase Transformer Bank module

12
L2

2
6
11

Local ac power network

,
(Ω)

Voltage
(V)

Frequency
(Hz)

120

300

220

1100

240

1200

Figure 9. Three-phase transformer bank connected in a delta-wye configuration with reversed connections at the secondary
windings.

Three-Phase Transformer Banks A

Exercise 1 – Three-Phase Transformer Configurations  Conclusion
41. On the Power Supply, turn the three-phase ac power source on.

and

On the Power Supply, turn the three-phase ac power source off.
42. What happens to the phase shift between the line voltage
. at the
secondary and the line voltage
. at the primary when the connections at
the secondary windings of the three-phase transformer bank are reversed?

Is the effect of reversing the connections at the secondary windings of the
three-phase transformer bank connected in a delta-wye configuration similar
to what you observed in step 31 when the three-phase transformer bank is
connected in a delta-delta configuration?

 Yes

 No

43. Close LVDAC-EMS, then turn off all the equipment. Disconnect all leads and
return them to their storage location.

CONCLUSION

In this exercise, you learned how to connect three-phase transformer banks in
wye-wye, delta-delta, wye-delta, and delta-wye configurations. You also
determined the voltage, current, and phase relationships between the primary
windings and the secondary windings of a three-phase transformer bank for each
of these configurations. You saw the uses of three-phase transformer banks in
three-phase ac power circuits.

A Three-Phase Transformer Banks

Exercise 1 – Three-Phase Transformer Configurations  Review Questions

REVIEW QUESTIONS

1. What are the main differences between single-unit, three-phase power
transformers and three-phase transformer banks?

2. How is it possible to confirm that the wye-connected secondary windings of a
three-phase transformer bank are properly connected (i.e., that winding
polarity is respected)? Explain briefly.

3. How is it possible to confirm that the delta-connected secondary windings of
a three-phase transformer bank are properly connected (i.e., that winding
polarity is respected) before closing the delta? Explain briefly.

Three-Phase Transformer Banks A

Exercise 1 – Three-Phase Transformer Configurations  Review Questions
4. Consider a three-phase transformer bank connected in a delta-wye
configuration. Each winding at the primary of the three-phase transformer
bank is made of 800 turns of wire, while each winding at the secondary is
made of 1340 turns of wire. Knowing that the line voltage
. at the primary
at
the
secondary.
is equal to 208 V, determine the line voltage
.

5. Consider a three-phase transformer bank connected in a wye-delta
configuration. Each winding at the primary of the three-phase transformer
bank is made of 4800 turns of wire, while each winding at the secondary is
made of 1600 turns of wire. Knowing that the line voltage
. at the primary
is equal to 75 kV, determine the line voltage
. at the secondary.

A Three-Phase Transformer Banks

Sample
Extracted from
Instructor Guide

Exercise 1

Three-Phase Transformer Configurations

Exercise 1

Three-Phase Transformer Configurations

ANSWERS TO
PROCEDURE STEP
QUESTIONS

196 V

0.67 A

196 V

0.66 A

197 V

0.67 A

205 V

10. Voltage relationship (
Current relationship (

A Three-Phase Transformer Banks

.:
.:

.)
.)

0.68 A

205 V: 196 V

1: 0.96 (≅ 1: 1)

0.68 A: 0.67 A

1: 0.99 (≅ 1: 1)

It is normal that the line voltages measured at the secondary to be
slightly (about 5%) lower than expected. This is because the voltage regulation
of the three-phase transformer bank is not ideal, thereby resulting in a voltage
drop at the secondary. Due to this voltage drop, the line currents at the
secondary are also proportionally lower.

Exercise 1

Three-Phase Transformer Configurations

11. The resulting phasors of the line voltages at the primary and the secondary
of the three-phase transformer bank are shown in the following figure:
Phasor Analyzer Settings
Reference Phasor ................................ E4
Voltage Scale.............................100 V/div

Phasors of the line voltages at the primary and the secondary of the three-phase transformer
bank when it is connected in a wye-wye configuration.

Phase shift between

and

0.49°

Three-Phase Transformer Banks A

Exercise 1

Three-Phase Transformer Configurations

12. The resulting sine waves of the line voltages at the primary and the
secondary of the three-phase transformer bank are shown in the following
figure:
Oscilloscope Settings
Channel-1 Input ................................... E1
Channel-1 Scale ........................200 V/div
Channel-1 Coupling ............................ DC
Channel-2 Input ................................... E2
Channel-2 Scale ........................200 V/div
Channel-2 Coupling ............................ DC
Channel-3 Input ................................... E3
Channel-3 Scale ........................200 V/div
Channel-3 Coupling ............................ DC
Channel-4 Input ................................... E4
Channel-4 Scale ........................200 V/div
Channel-4 Coupling ............................ DC
Trigger Type .............................. Software
Time Base ................................... 5 ms/div
Trigger Source ................................... Ch1
Trigger Level ........................................... 0
Trigger Slope ..................................Rising

0.0°

Sine waves of the line voltages at the primary and the secondary of the three-phase
transformer bank when it is connected in a wye-wye configuration.

Phase shift between

and

0.0°

Yes
13. Yes
17.

118 V

0.40 A

116 V

0.40 A

117 V

0.40 A

A Three-Phase Transformer Banks

206 V

0.24 A

Exercise 1

Three-Phase Transformer Configurations

18. Voltage relationship (
Current relationship (

.:
.:

.)
.)

206 V: 117 V

1.76: 1 (≅ √3: 1)

0.24 A: 0.40 A

1: 1.67 (≅ 1: √3)

It is normal for the line current measured at the primary to be
slightly (about 5%) greater than expected. This is due to the magnetizing
current flowing in the primary. In order to find the actual value of the primary
current due to the flow of the secondary line current through the load, the value
of the magnetizing current flowing in the primary would need to be vectorially
subtracted from the measured primary current
..

19. The resulting phasors of the line voltages at the primary and the secondary
of the three-phase transformer bank are shown in the following figure:
Phasor Analyzer Settings
Reference Phasor ................................ E4
Voltage Scale.............................100 V/div

Phasors of the line voltages at the primary and the secondary of the three-phase transformer
bank when it is connected in a wye-delta configuration.

Three-Phase Transformer Banks A

Exercise 1

Three-Phase Transformer Configurations

The resulting sine waves of the line voltages at the primary and the
secondary of the three-phase transformer bank are shown in the following
figure:
Oscilloscope Settings
Channel-1 Input ................................... E1
Channel-1 Scale ........................200 V/div
Channel-1 Coupling ............................ DC
Channel-2 Input ................................... E2
Channel-2 Scale ........................200 V/div
Channel-2 Coupling ............................ DC
Channel-3 Input ................................... E3
Channel-3 Scale ........................200 V/div
Channel-3 Coupling ............................ DC
Channel-4 Input ................................... E4
Channel-4 Scale ........................200 V/div
Channel-4 Coupling ............................ DC
Trigger Type .............................. Software
Time Base ................................... 5 ms/div
Trigger Source ................................... Ch1
Trigger Level ........................................... 0
Trigger Slope ..................................Rising

30°

Sine waves of the line voltages at the primary and the secondary of the three-phase
transformer bank when it is connected in a wye-delta configuration.

Phase shift between

and

30.2°

20. Yes
24.

202 V

0.69 A

201 V

0.68 A

203 V

0.69 A

205 V

25. Voltage relationship (
Current relationship (

A Three-Phase Transformer Banks

.:
.:

.)
.)

0.73 A

205 V: 202 V

1: 0.99 (≅ 1: 1)

0.73 A: 0.69 A

1: 0.95 (≅ 1: 1)

Exercise 1

Three-Phase Transformer Configurations
26. The resulting phasors of the line voltages at the primary and the secondary
of the three-phase transformer bank are shown in the following figure:

Phasor Analyzer Settings
Reference Phasor ................................ E4
Voltage Scale.............................100 V/div

Phasors of the line voltages at the primary and the secondary of the three-phase transformer
bank when it is connected in a delta-delta configuration.

Three-Phase Transformer Banks A

Exercise 1

Three-Phase Transformer Configurations

0.0°

Sine waves of the line voltages at the primary and the secondary of the three-phase
transformer bank when it is connected in a delta-delta configuration.

Phase shift between

and

0.32°

27. Yes

A Three-Phase Transformer Banks

Exercise 1

Three-Phase Transformer Configurations

31. The resulting phasors of the line voltages at the primary and the secondary
of the three-phase transformer bank are shown in the following figure:
Phasor Analyzer Settings
Reference Phasor ................................ E4
Voltage Scale.............................100 V/div

Phasors of the line voltages at the primary and the secondary of the three-phase transformer
bank when it is connected in a delta-delta configuration with reversed connections at the
secondary windings.

Three-Phase Transformer Banks A

Exercise 1

Three-Phase Transformer Configurations

180°

Sine waves of the line voltages at the primary and the secondary of the three-phase
transformer bank when it is connected in a delta-delta configuration with reversed
connections at the secondary windings.

Phase shift between

and

180°

The
sign in the above phase shift indicates that the secondary line
can be considered leading or lagging the primary line
voltage
.
voltage
. by 180°.

32. Reversing the connections at the secondary windings of the three-phase
transformer bank introduces a 180° phase shift between the sine waves of
the line voltage
. at the secondary and the line voltage
. at the
primary.
Yes, the results confirm that it is important to respect the winding polarity
when connecting the windings of a three-phase transformer bank. Otherwise,
the phase shift between the line voltages at the primary and the line voltages
at the secondary significantly differs from what is expected.
36.

343 V

0.68 A

345 V

0.68 A

346 V

0.68 A

A Three-Phase Transformer Banks

204 V

1.22 A

Exercise 1

Three-Phase Transformer Configurations

37. Voltage relationship (
Current relationship (

.:
.:

.)
.)

204 V: 345 V

1: 1.69 (≅ 1: √3)

1.22 A: 0.68 A

1.79: 1 (≅ √3: 1)

38. The resulting phasors of the line voltages at the primary and the secondary
of the three-phase transformer bank are shown in the following figure:
Phasor Analyzer Settings
Reference Phasor ................................ E4
Voltage Scale.............................100 V/div

Phasors of the line voltages at the primary and the secondary of the three-phase transformer
bank when it is connected in a delta-wye configuration.

Three-Phase Transformer Banks A

Exercise 1

Three-Phase Transformer Configurations
The resulting sine waves of the line voltages at the primary and the
secondary of the three-phase transformer bank are shown in the following
figure:

Oscilloscope Settings
Channel-1 Input ................................... E1
Channel-1 Scale ........................200 V/div
Channel-1 Coupling ............................ DC
Channel-2 Input ................................... E2
Channel-2 Scale ........................200 V/div
Channel-2 Coupling ............................ DC
Channel-3 Input ................................... E3
Channel-3 Scale ........................200 V/div
Channel-3 Coupling ............................ DC
Channel-4 Input ................................... E4
Channel-4 Scale ........................200 V/div
Channel-4 Coupling ............................ DC
Trigger Type .............................. Software
Time Base ................................... 5 ms/div
Trigger Source ................................... Ch1
Trigger Level ........................................... 0
Trigger Slope ..................................Rising

30°

Sine waves of the line voltages at the primary and the secondary of the three-phase
transformer bank when it is connected in a delta-wye configuration.

Phase shift between

and

29.9°

39. Yes

A Three-Phase Transformer Banks

Exercise 1

Three-Phase Transformer Configurations

41. The resulting phasors of the line voltages at the primary and the secondary
of the three-phase transformer bank are shown in the following figure:
Phasor Analyzer Settings
Reference Phasor ................................ E4
Voltage Scale.............................100 V/div

Phasors of the line voltages at the primary and the secondary of the three-phase transformer
bank when it is connected in a delta-wye configuration with reversed connections at the
secondary windings.

Three-Phase Transformer Banks A

Exercise 1

Three-Phase Transformer Configurations

150°
.

Sine waves of the line voltages at the primary and the secondary of the three-phase
transformer bank when it is connected in a delta-wye configuration with reversed connections
at the secondary windings.

Phase shift between

and

150°

42. Reversing the connections at the secondary windings of the three-phase
transformer bank introduces an additional 180° phase shift between the sine
waves of the line voltage
. at the secondary and the line voltage
. at
the primary. The phase shift between the sine waves of the line voltage
.
at the secondary and the line voltage
. at the primary is thus modified
from 29.9° to 150°.
Yes

ANSWERS TO REVIEW
QUESTIONS

1. Single-unit, three-phase power transformers are constructed by winding
three single-phase power transformers around a single core. On the other
hand, three-phase transformer banks consist of three individual single-phase
power transformers that are grouped together. For a given power rating,
single-unit, three-phase power transformers are smaller, require less
material, and are less costly than three-phase transformer banks. However,
three-phase transformer banks are easier to maintain.

A Three-Phase Transformer Banks

Exercise 1

Three-Phase Transformer Configurations
2. It is possible to confirm that the wye-connected secondary windings of a
three-phase transformer bank are properly connected by, firstly, confirming
that the line voltage between any two windings is √3 times greater than the
phase voltage across either of the two windings. Then, secondly, by
confirming that the line voltage between the third winding and each of the
other two windings is also √3 times greater than the phase voltage measured
previously.
3. It is possible to confirm that the delta-connected secondary windings of a
three-phase transformer bank are properly connected before closing the
delta by, firstly, confirming that the voltage across two series-connected
windings is equal to the voltage across either of the two windings. Then,
secondly, by connecting the third winding in series and confirming that the
voltage across the three series-connected windings is equal to 0 V.
4. The line voltage
. at the secondary of the three-phase transformer bank
connected in a delta-wye configuration can be calculated using the following
equation:
.
.

√3

208 V 1340 turns
800 turns

√3

603 V

5. The line voltage
. at the secondary of the three-phase transformer bank
connected in a wye-delta configuration can be calculated using the following
equation:
.
.

.
.

1
√3

75 kV 1600 turns
4800 turns

1
√3

14.4 kV

Three-Phase Transformer Banks A

Bibliography
Boylestad, Robert L., Introductory Circuit Analysis, 11th ed., Upper Saddle River:
Prentice Hall, 2006, ISBN 978-0131730441.
Wildi, Theodore, Electrical Machines, Drives, and Power Systems, 6th ed., Upper
Saddle River: Prentice Hall, 2005, ISBN 978-0131776913.

A Three-Phase Transformer Banks

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