10/25/2012
Overview
•
•
•
•
16-Three Phase Transformers
Y-Y Transformer Connection
Y-Y Transformer Analysis
Delta-Delta Transformer Connection
Delta-Delta Transformer Analysis
ECEGR 450
Electromechanical Energy Conversion
2
Dr. Louie
Three-Phase Transformer Connections
Y-Connected Circuits
• We are generally more concerned with three
phase transformers
• Three-phase transformers can be composed of
three single-phase transformers or be wound on
the same core
• Many combinations are possible:




•
Recall from previous lectures:
 Line current = Phase current
 Line voltage = Phase voltage x
o
3 30
Vector Diagrams
Ia
Y-Y
Delta-Delta
Y-Delta
next lecture
Delta-Y
Va
Vc
Vc
Vca
Vab
Inc, Ic
Ina
n
Inc Inb
Vb
30o
Ina, Ia
Va
Ib
Ic
Inb, Ib
Vb
Vbc
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Y-Y Transformer
• Each side has a common
point, n or n’
• Neutral points usually
grounded
• Tertiary winding (Delta)
sometimes connected to
avoid distortion if
harmonics are present
• Phase voltages appear
across the coils on each
side
• Insulation is stressed to
only 58% of line voltage
Y-Y Transformer Analysis
Ia
I’a
+
Van
-
-
Ib’
+
Vbn
-
+
Vb’n’
Ic’
-
n
• Mutual flux in each core
are out of phase by 120o
•
a links primary and
secondary
• Faraday’s law: Van and
Va’n’ must be in phase
and lead a by 90o
Ia
+
Vc’n’
-
 similar result for b, c
phases
-
-
Ib
Ic
+
Vb’n’
-
Ic’
c
+
-
n
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Ib’
b
+
Vbn
Vcn
n’
5
+
Va’n’
Van
-
• Ampere’s Law: Ia and Ia’
are also in phase
I’a
a
+
 similar result for b, c
phases
-
Ic
+
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+
Va’n’
Ib
Vcn
Do not confuse this n with 1/a
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+
Vc’n’
-
n’
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10/25/2012
Y-Y Transformer Analysis
Three-Phase Transformer Analysis: Y-Y
Phasor Diagram for Ideal Y-Y Connected Transformer
• Let k be the transformer voltage gain
• For Y-Y transformers:
Vc’n’
Va'n'
Ic
Vcn
Ic’
therefore k = n
Ia
Ia’
Ia
k
Ia'
Va’n’
Van
N2
Van
N1
kVan
j
Vbn
Va'b '
Ib’
3 n
nVab
nVbn , Vb ' c '
nVbc
Vc 'n '
nVcn , Vc ' a '
nVca
Ia '
Ib '
Ic '
e
(secondary line voltage)
Recall: e 6
1 30
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Magnetizing reactance
and core loss (in parallel)
a’
a
n
b
Recall: phase currents
= line current for Y
connections
n’
c
primary
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b’
c’
secondary
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Per Phase Y-Y Analysis
Delta-Connected Circuits
• Per-phase equivalent of non-ideal Y-Y transformer
• Analyze like a single-phase transformer
•
Recall from previous lectures:
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 Line current = Phase current x 3
 Line voltage = Phase voltage (but per-phase voltage is line
voltage x 1
30 )
Vector Diagrams
3
Ia
a
jXm
j
nVab
• Three phase non-ideal Y-Y transformer model
• Want to model as per-phase equivalent
• Line currents
Ia
n
Ib
n
Ic
n
e
j
6
Per-Phase Y-Y Analysis
• Phase voltages
nVan , Va 'b '
3
j
6
3e 6
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Three-Phase Transformer Analysis: Y-Y
Vb 'n '
Vab
nVan
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Va 'n '
j
Va'n' 3e 6
Ib
Magnitudes shown
assuming N1 < N2
Vb’n’
Do not confuse this n with the neutral point
Ia
n
Rc
Vc ,Vca
Iba
Iac
Vbc
Icb
b
Ic
Iba
Iac
Vab
Vca
c
Vb , Vbc
Ia
30o
30o
Ib
Ic
Icb
Va, Vab
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Using Van as reference
Ib
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- Transformer
Three-Phase Transformer Analysis:
Ia Iab
+
• No neutral point
• Vab, Va’b’ in phase
• Iab, Ia’b’ in phase
Vab
-
Ia’
+
Va’b’
-
• Let k be the transformer voltage gain
• For - transformers:
Va'b '
Ib
 Similar results for b, c
phase
Ibc
+
Vbc
-
• Line-line voltages
appear across the coils
on primary and
secondary
• Best suited for lower
voltage applications
Ic
Ib’
+
Vb’c’
+
-
+
Va'b 'e
j
6
nVab e
3
n( 3Vane 6 )e
-
j
6
3
nVan (per phase voltage)
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a’
c
b
b’
c’
primary
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Per-Phase - Transformer
a
secondary
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• Need to convert each side of the transformer to Y
• Recall that: ZY Z
3
• Per-phase equivalent circuit of non-ideal transformer
jXm
3
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Rc
3
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Example
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Example
• Consider three, single-phase transformers. The
transformers have the following specifications:
• Nominal per-phase voltage on primary is 360V
and 120V on secondary
 720VA, 360/120V, RH = 18.9 , XH = 21.6 , RL =
2.1 , XL = 2.4 , RcH = 8.64k , XmH = 6.84k
 Nominal primary line voltage: 623.5V
 Nominal secondary line voltage: 207.8V
• Draw the per-phase equivalent circuit if the
transformers are connected as Y-Y
• What are the nominal line voltages on each side
of the transformer?
j6.84k
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j
6
3
j
Vc’a’
Three-Phase Transformer Analysis:
• Current Relationships
therefore k = n
Iab
Iab
k
n
Va'n'
Ic’
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• Voltage Relationships
N2
Vab
N1
kVab
Ia'b '
-
Ica
Vca
-
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8.64k
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10/25/2012
Example
Example
• Consider three, single-phase transformers. The
transformers have the following specifications:
•
•
•
•
 720VA, 360/120V, RH = 18.9 , XH = 21.6 , RL =
2.1 , XL = 2.4 , RcH = 8.64k , XmH = 6.84k
• Draw the per-phase equivalent circuit if the
transformers are connected as
• What are the nominal line voltages on each side
of the transformer?
Nominal
Nominal
Nominal
Nominal
primary line voltage: 360V
secondary line voltage: 120V
primary per-phase voltage: 208V
secondary per-phase voltage: 69V
j2.28k
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2.88k
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Summary
• Y-Y, Delta-Delta transformers result in magnitude
changes of k = n from primary to secondary
 No phase shifting occurs
• Y-Y transformers grant access to neutral point,
which is usually grounded to prevent distortion
• Delta-Delta transformers have no neutral point,
but are less prone to distortion
• Per phase analysis can be used on Y-Y, DeltaDelta transformers
 Ensure impedances and voltages are properly
converted
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