Download Determining Transformer Phase Angle Displacment

Determining Transformer
Phase Angle Displacement
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.
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.
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 ´.
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‘
B - B‘
C - C‘
= A1 – A2
= B1 – B2
= C1 – C2
A or A1 is the polarity end of the
winding
Secondary winding
a - a‘
b - b‘
c - c‘
= a1 – a2
= b1 – b2
= c1 – c2
a or a1 is the polarity end of the
winding
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
Winding Displacement Based on Connection
Type
Primary
Delta
Wye
Delta
Wye
Secondary
Wye
Delta
Delta
Wye
Displacement
30°
30°
None
None
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
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
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
Standard Delta Connection
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
?
H1
H2
H3
N
X1
X2
X3
Closing The Delta On Single Phase Banks
We Can Close These Deltas Any Way We Wish But Will They
Connect to Other Transformers
C
B
A
primary
primary
secondary
a
b
c
n
secondary
primary
secondary
V A-B
C
B
A
V B-C
V C-A
primary
primary
primary
V a-n
-
+
V c-n
-
+
+
-
V b-n
secondary
a
b
c
Van – vbn + vba = 0
n
secondary
secondary
V A-B
C
B
A
V B-C
V C-A
primary
primary
primary
V a-n
-
+
V c-n
-
+
+
-
V b-n
secondary
Van – vbn + vba = 0
a
Vba = -van+vbn
b
c
n
secondary
secondary
From Our Windings we see that van – vbn + vba = 0
Solving for Vba
High Side Vector
then vba = -van + vbn
V A-B
We Can Display The Equation Using Vectors & Find Vba
V ab
V C-A
V B-C
Low Side Vectors
V a-n
V a-n
V ab
V c-n
We Can Move a Vector Anywhere
We Want To As Long As We Don’t
Change The Length Or Direction
V ab
V ba
V b-n
-Van
V c-n
-Van
V ba
V b-n
We Can Display the Vector Addition Two ways With The same Result
Conclusion LS L-L Voltage Leads HS L-L voltage By 30 °
B
V A-B
A
H1
V B-C
V C-A
C
H2
H3
V a-n
-
+
N
V c-n
X1
+
-
+
X2
X3
V b-n
V A-B
b
V a-n
a
c
Van – vbn + vba = 0
V ab
V ab
Vba = -van+vbn
Conclusion V ab leads V AB by 30°
V C-A
V B-C
V b-n
V c-n
V ba
-Van
B
V A-C
C
H1
V B-A
V C-B
A
H2
H3
V a-n
-
+
-
N
V c-n
X1
+
-
+
X2
X3
V b-n
b
a
V A-B
Van – vcn + vca = 0
V a-n
V ac
Vca = -van+vcn
Conclusion V ac lags V AC by 30°
c
V C-A
V B-C
V ac
V b-n
V c-n
V ca
-Van
Specification: Phasing
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
H2
X2
30° LEADING SECONDARY
b
COUNTERCLOCKWISE
B
C
ROTATION
H2
X3
a
X2
c
H1
X3
30
H1
H3
H3
A
X1
X1
Ref
H1
H2
H3
S
F
S
F
A
S
N
X3
X2
X1
S
F
B
F
S
C
F
S
F
Reference Point
B
A
C
B
A
C
primary
primary
H1
H2
H3
secondary
secondary
N
X1
primary
X2
secondary
a
X3
b
c
a
b
B
c
C
H1
n
A
H2
a
A
c
H3
c
B
N
X1
X2
C
c
a
B
A
X3
b
b
C
a
b
Solve The Following Pairs of Transformers
A
B
C
CØ
primary
BØ
AØ
primary
primary
HV ________ LV By 30°
secondary
secondary
secondary
c
b
a
n
C
A
H1
B
H2
H3
HV ________ LV By 30°
N
Can These Transformers
Be Paralleled ?
X1
b
X2
c
X3
a
Solve The Following Pairs of Transformers
A
B
C
primary
primary
primary
HV ________ LV By 30°
secondary
secondary
secondary
c
b
a
n
A
B
H1
C
H2
H3
HV ________ LV By 30°
N
Can These Transformers
Be Paralleled ?
X1
b
X2
c
X3
a
Solve The Following Pairs of Transformers
C
B
A
primary
primary
primary
HV ________ LV By 30°
secondary
secondary
secondary
a
b
c
n
B
H1
HV ________ LV By 30°
N
Can These Transformers
Be Paralleled ?
C
X1
b
A
H2
X2
c
H3
X3
a
Solve The Following Pairs of Transformers
C
B
A
primary
primary
primary
HV ________ LV By 30°
secondary
secondary
secondary
a
b
c
n
C
H1
HV ________ LV By 30°
N
Can These Transformers
Be Paralleled ?
A
X1
c
B
H2
X2
a
H3
X3
b
Solve The Following Pairs of Transformers
C
B
A
primary
primary
primary
HV ________ LV By 30°
secondary
secondary
secondary
a
b
c
n
C
H1
HV ________ LV By 30°
N
Can These Transformers
Be Paralleled ?
A
X1
c
B
H2
X2
a
H3
X3
b
Practice 1
C
B
A
B
C
A
primary
H1
H2
primary
H3
AØ
N
c
Fig. 1
BØ
secondary
secondary
X1
primary
X2
X3
b
a
CØ
secondary
Fig. 2
n
a
b
c
B
A
H1
N
X1
b
Fig. 3
C
H2
H3
X2
X3
a
c
Practice 1 Solution
C
B
A
B
C
A
primary
H1
H2
primary
H3
AØ
BØ
secondary
secondary
N
X1
c
Fig. 1
primary
X2
X3
b
a
CØ
secondary
Fig. 2
n
a
b
c
V a-n
B
Solution
V A-B
A
C
V ab
H1
V ab
V C-A
V B-C
V c-n
V ba
H2
H3
V b-n
-Van
N
X1
b
Fig. 3
X2
X3
a
c
Practice 2
A
B
C
A
B
C
primary
AØ
secondary
n
a
b
c
primary
primary
BØ
secondary
primary
primary
AØ
CØ
BØ
secondary
secondary
secondary
Fig. 2
primary
CØ
secondary
Fig. 2
n
a
b
c
A
B
H1
N
X1
a
Fig. 3
C
H2
H3
X2
X3
b
c
Practice 2 Solution
A
B
C
A
B
C
primary
primary
AØ
primary
BØ
secondary
secondary
primary
CØ
AØ
secondary
primary
BØ
secondary
secondary
Fig.6
n
a
b
c
primary
CØ
secondary
Fig. 7
n
a
b
c
V a-n
A
V A-C
B
C
V ac
V ac
V C-B
H1
V b-n
V c-n
H2
H3
V ca
V B-A
-Van
N
X1
a
Fig. 8
X2
X3
b
c
Does HV Lead or Lag LV?
H1
N
Fig. 8
X1
H2
X2
H3
X3
Does HV Lead or Lag LV?
H1
N
Fig. 8
V x1-n
V H1-H3
V x1-x3
V x1-x2
V x1-x3
V H3-H2
V H2-H1
V x3-n
-V x1
V x2-n
V x3-x1
X1
H2
X2
H3
X3
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