This document discusses three-phase transformer configurations and phase angle displacement. It explains that a three-phase transformer can be constructed using either three single-phase transformers connected together, or a single pre-assembled three-phase transformer core. The document also discusses how the primary and secondary windings are labeled and how the phase angle displacement depends on the connection type, such as delta-wye resulting in a 30 degree phase shift. Several examples are provided to demonstrate how to determine if the high voltage leads or lags the low voltage based on the winding connections.

1. Determining Transformer
Phase Angle Displacement

2. Transformers Do Not Change Or Create
Phases
• A transformer can not act as a phase changing device and change
single-phase into three-phase or three-phase into single phase. To
make the transformer connections compatible with three-phase
supplies we need to connect them together in a particular way to
form a Three Phase Transformer Configuration.
• A three phase transformer or 3φ transformer can be constructed
either by connecting together three single-phase transformers,
thereby forming a so-called three phase transformer bank, or by using
one pre-assembled and balanced three phase transformer which
consists of three pairs of single phase windings mounted onto one
single laminated core.

3. Advantages Of A Three Phase Transformer
• The advantages of building a single three phase transformer is that for
the same kVA rating it will be smaller, cheaper and lighter than three
individual single phase transformers connected together because the
copper and iron core are used more effectively. As well as having
fewer bushings. The methods of connecting the primary and
secondary windings are the same, whether using just one Three
Phase Transformer or three separate Single Phase Transformers.

4. How We Label
• The standard method for marking three phase transformer windings
is to label the polarity end of three primary windings with capital
letters A, B and C, and the non polarity end of the winding as A´
(called A prime) B ´and C ´.
• The secondary windings are labeled with small (lower case) letters a,
b and c and a ´, b ´and c ´.

5. Another Method of Labeling
• Each winding has two ends and may be labeled 1 and 2.
• For example the A phase winding may be labeled A1 and A2
Primary Winding
A - A‘ = A1 – A2
B - B‘ = B1 – B2
C - C‘ = C1 – C2
A or A1 is the polarity end of the
winding
Secondary winding
a - a‘ = a1 – a2
b - b‘ = b1 – b2
c - c‘ = c1 – c2
a or a1 is the polarity end of the
winding

6. Phase Angle Displacement Between
Windings
•REMEMBER
• There is never any phase displacement or shift between two
windings
•REMEMBER
There MAY be a phase displacement or shift between the line
voltages of two transformers depending on how the windings are
connected

7. Winding Displacement Based on Connection
Type
Primary Secondary Displacement
Delta Wye 30°
Wye Delta 30°
Delta Delta None
Wye Wye None

8. Phase Angle Displacement Between
Transformer Banks
• To connect two transformers for parallel operation each transformer’s
line voltages must be in phase with the other transformer
• Transformers operating in parallel may be in the same substation
connected to the same bus or in substations at different locations
• If the voltages are not in phase with one another a fault condition will
exist when the connection is attempted

9. Delta - Wye Connection Displacement
•REMEMBER If one winding is connected ∆ and the other
winding connected Y there will always be a phase shift of 30 ⁰
between the line voltages
• Whether the shift is leading or lagging depends on how the ∆ is
closed
• If one transformer is leading and the other is lagging then the
associated phase voltages will have an angle of 60 ⁰ between them

10. Wye – Wye Transformers
• Wye – Wye transformers will have no phase angle shift between the
voltages on the primary and secondary
• Trying to connect a Δ – Y transformer to a Y- Y transformer will result
in a 30 ⁰ shift between the voltages on the secondary and they will
not connect

11. Standard Delta Connection
N
H1 H2 H3
X1 X2 X3
? ?
?
All Three Phase
Transformers will Have The
Delta Closed As Shown
Below
The Question Then
Becomes To which
Bushing Do We Connect
Our System Phases

12. Closing The Delta On Single Phase Banks
primary
secondary
primary
secondary
primary
secondary
A
a
B
C
b
c
n
We Can Close These Deltas Any Way We Wish But Will They
Connect to Other Transformers

13. primary
secondary
primary
secondary
primary
secondary
A
a
B
C
b
c
n
+ + +
- -
-
V A-B
V B-C
V C-A
V a-n
V b-n
V c-n
Van – vbn + vba = 0

14. primary
secondary
primary
secondary
primary
secondary
A
a
B
C
b
c
n
+ + +
- -
-
V A-B
V B-C
V C-A
V a-n
V b-n
V c-n
Van – vbn + vba = 0
Vba = -van+vbn

15. V a-n
V b-n
V c-n
-Van
V ba
V ab
High Side Vector
Low Side Vectors
V a-n
V b-n
V c-n -Van V ba
V ab
From Our Windings we see that van – vbn + vba = 0
Solving for Vba then vba = -van + vbn
We Can Display The Equation Using Vectors & Find Vba
We Can Display the Vector Addition Two ways With The same Result
V A-B
V B-C
V C-A
V ab
We Can Move a Vector Anywhere
We Want To As Long As We Don’t
Change The Length Or Direction
Conclusion LS L-L Voltage Leads HS L-L voltage By 30 °

16. N
H1 H2 H3
X1 X2 X3
A
B C
a
b c
V A-B
V B-C
V C-A
V a-n
V b-n
V c-n
+ +
+
-
- -
Van – vbn + vba = 0
Vba = -van+vbn
V a-n
V b-n
V c-n
-Van
V ba
V ab
V A-B
V B-C
V C-A
V ab
Conclusion V ab leads V AB by 30°

17. N
H1 H2 H3
X1 X2 X3
C
B A
c
b a
V A-C
V B-A
V C-B
V a-n
V b-n
V c-n
+ +
+
-
- -
Van – vcn + vca = 0
Vca = -van+vcn
V a-n
V b-n
V c-n
-Van
V ca
V ac
V A-B
V B-C
V C-A
V ac
Conclusion V ac lags V AC by 30°

18. Specification: Phasing
X1
X2
X3
H1
H2
H3
A
a
B
b
C
c
30
Ref
A B C
H1
S F
F
S
S
S F
F S
S F
F
H2
H3
N
X3
X2
X1
30° LEADING SECONDARY
ROTATION
COUNTERCLOCKWISE
H1
H2
H3 X1
X2
X3
Rotation
• Pick a fixed reference point
• Spin the circle such that the
H terminals pass the reference
point in the order 1-2-3
• CCW - Counterclockwise Rotation
if the circle rotates CCW
• CW - Clockwise Rotation
if the circle rotates CW
Displacement
• Pick a fixed reference point
• Spin the circle according to it’s
rotation from above
• Leading
If the X1 Terminal passes the
reference point before the H1
- Secondary leads the Primary
• Lagging
If the X1 Terminal passes the
reference point after the H1
- Secondary lags the Primary
• Displacement Angle
The angle between the H1 and
• X1 terminal
Reference Point

19. primary
secondary
primary
secondary
primary
secondary
A
a
B
C
b
c
n
N
H1 H2 H3
X1 X2 X3
A
B C
a
b c
N
H1 H2 H3
X1 X2 X3
C
B A
c
b a
A
B C
a
b
c
C
B A
c
b
a

20. primary
secondary
primary
secondary
primary
secondary
C
c
B
A
b
a
n
N
H1 H2 H3
X1 X2 X3
A
C B
c
b a
HV ________ LV By 30°
HV ________ LV By 30°
Can These Transformers
Be Paralleled ?
Solve The Following Pairs of Transformers
AØ
BØ
CØ

21. primary
secondary
primary
secondary
primary
secondary
C
c
B
A
b
a
n
N
H1 H2 H3
X1 X2 X3
B
A C
c
b a
HV ________ LV By 30°
HV ________ LV By 30°
Can These Transformers
Be Paralleled ?
Solve The Following Pairs of Transformers

22. primary
secondary
primary
secondary
primary
secondary
A
a
B
C
b
c
n
N
H1 H2 H3
X1 X2 X3
C
B A
c
b a
HV ________ LV By 30°
HV ________ LV By 30°
Can These Transformers
Be Paralleled ?
Solve The Following Pairs of Transformers

23. primary
secondary
primary
secondary
primary
secondary
A
a
B
C
b
c
n
N
H1 H2 H3
X1 X2 X3
A
C B
a
c b
HV ________ LV By 30°
HV ________ LV By 30°
Can These Transformers
Be Paralleled ?
Solve The Following Pairs of Transformers

24. primary
secondary
primary
secondary
primary
secondary
A
a
B
C
b
c
n
N
H1 H2 H3
X1 X2 X3
A
C B
a
c b
HV ________ LV By 30°
HV ________ LV By 30°
Can These Transformers
Be Paralleled ?
Solve The Following Pairs of Transformers

25. N
H1 H2 H3
X1 X2 X3
B
C A
b
c a
Fig. 1
N
H1 H2 H3
X1 X2 X3
A
B C
a
b c
Fig. 3
primary
secondary
primary
secondary
primary
secondary
C
n
B
A
a
b
c
Fig. 2
AØ BØ CØ
Practice 1

26. N
H1 H2 H3
X1 X2 X3
B
C A
b
c a
Fig. 1
N
H1 H2 H3
X1 X2 X3
A
B C
a
b c
Fig. 3
primary
secondary
primary
secondary
primary
secondary
C
n
B
A
a
b
c
Fig. 2
AØ BØ CØ
V A-B
V B-C
V C-A
V ab
Solution
Practice 1 Solution
V a-n
V b-n
V c-n
-Van
V ba
V ab

27. N
H1 H2 H3
X1 X2 X3
B
A C
b
a c
Fig. 3
primary
secondary
primary
secondary
primary
secondary
C
n
B
A
a
b
c
Fig. 2
AØ BØ CØ
primary
secondary
primary
secondary
primary
secondary
C
n
B
A
a
b
c
Fig. 2
AØ BØ CØ
Practice 2

28. N
H1 H2 H3
X1 X2 X3
B
A C
b
a c
Fig. 8
primary
secondary
primary
secondary
primary
secondary
C
n
B
A
a
b
c
Fig.6
AØ BØ CØ
primary
secondary
primary
secondary
primary
secondary
C
n
B
A
a
b
c
Fig. 7
AØ BØ CØ
V a-n
V b-n
V c-n
-Van
V ca
V ac
V A-C
V B-A
V C-B
V ac
Practice 2 Solution

29. N
H1 H2 H3
X1 X2 X3
Fig. 8
Does HV Lead or Lag LV?

30. N
H1 H2 H3
X1 X2 X3
Fig. 8
Does HV Lead or Lag LV?
V x1-n
V x2-n
-V x1
V x3-x1
V x1-x2
V x3-n
V x1-x3
V H1-H3
V H2-H1
V H3-H2
V x1-x3

31. Lets Keep it Simple
• If a transformer bank is connect so that the polarity of the any
winding is connected to AØ and the non-polarity of the same winding
is connected to CØ then the HS L-L voltage leads the LS L-L voltage by
30°
• A-Cʹ then HS leads
• If a transformer bank is connect so that the polarity of the any
winding is connected to AØ and the non-polarity of the same winding
is connected to BØ then the HS L-L voltage lags the LS L-L voltage by
30°
• A-Bʹ then HS lags