Transformer
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Transformer Current & Voltage Practice
Wye connected windings: Have a common connection point Have two voltages available “L-L & L-N” Has only one current Line current
Delta connected windings: Have no common connection point Have only one voltage available “L-L” Delta can be closed “connected” in more than one way Has two currents Line current Phase or winding current
Definitions • Delta: Phase voltage is line voltage but phase current is not line current. – Line current ÷ √3= phase current – Line voltage = Phase voltage
• Wye: Phase voltage is not line voltage but phase current is line current. – Line voltage ÷ √3= phase voltage – Line current = phase current
HS Line 230 kV LS Line 23 kV Transformer 3 Ø 230/13280/23000 Gnd. Wye 25 MVA
230 kV B
A
C
H2
H1
W1
H3
W2
W3
W5
W4
W6
N X1
X2
X3
23 kV a
b
c
HS Line 115 kV LS Line 12 kV Transformer: 3 3 Ø 115/12000/6928 Gnd. Wye 40MVA
Voltage on HS 115 kV. Only one voltage because it is delta
201 B
A
C
H2
H1
H3
Voltage on LS 12,000 & 6,928 because it is wye connected 116
W2
W 3
16.6/1
Transformer Ratio 16.6/1
W 5
N X1
W 6 X2
X3
b
c
1925 a
LS Line 23 kV Transformer ? MVA
B
A
C
H2
H1
H3
W3
W2
W5
W6
N X1
X2
X3
b
c
1255 a
Typical GSU Transformer Connection
System
A
B
H1
C
H2
H3 N
W6
W4
W5
W3
W2 W1
X1
X2
a
b
Generator
X3 c
Transformer Solutions • Information: 230/23kV 25 MVA transformer 230 kV
•
What is the voltage A-B, B-C, C-A ?
•
What is the voltage a-b, b-c, c-a?
•
What is the voltage a-n, b-n, c-n?
•
What is the voltage across W1, W2, W3? 230 kV
•
What is the voltage across W4, W5, W6?
13,280 kV
•
What is the current in line A, B, C ?
25 MVA / 230 kV / √3 = 62.76 amps
•
What is the current in W1, W2, W3?
•
What is the current in W4, W5, W6?
23 kV 13,280 kV
25 MVA / 3 = 8.33 MVA /230 kV = 36.3 amps 25 MVA / 23 kV / √3 = 627.56 amps
Transformer Solutions • Information: Δ-Υ 230/23kV 25 MVA transformer 230 kV (Given)
•
What is the voltage on High voltage line?
•
What is the voltage on low voltage line?
•
What is the voltage on low voltage phase? 13,280 kV ( V 𝐿 − 𝐿
•
What is the voltage across W1, W2, W3? 230 kV (Same as the line for Δ winding)
•
What is the voltage across W4, W5, W6?
•
What is the current in line A, B, C ?
•
What is the current in W1, W2, W3?
•
What is the current in W4, W5, W6?
23 kV (Given) ÷ √3)
13,280 kV ( L-N voltage) 25 𝑀𝑉𝐴 ÷ 230,000 ÷ 3 = 62.75
25 𝑀𝑉𝐴 ÷ 230,000 ÷ √3 ÷ √3 = 36.23 25 MVA / 23 kV / √3 = 627.56 amps
Transformer Solutions •
What is the current in line a, b, c?
Same as winding W4, W5, W6= 627.556 amps
•
On the delta side of the transformer
The line current ÷ √3 = Winding Current ; 62.76 ÷ √3 = 36.23
Calculating three phase transformer MVA Voltage X Current X three windings 230,000 X 36.3 amps = 8,349,000 x 3 (windings)= 25,047,000 = 25 MVA 13,280 X 627.57 amps = 8,334,129 X 3 (windings)= 25,002, 388 = 25MVA
Transformer Ratio 3 Phase 230/23 kV 25 MVA Transformer is 230/ 23 kV Ratio is NOT this ration but is the ration of the voltages across the windings. W1 230 kV, W4 13,280 Ratio is 230,000 / 13,280 = 17.32/1
A
B
C
H2
H1
H3
W1
W2
W4
W5
W3
W6
N
Note: W4 current/ W1 current = 627.56/36.3 = 17.3 627.56 amps X 13,280 volts = 8.3 MVA 36.3 amps X 230,000 volts = 8.3 MVA 8.3 MVA X 3 (windings) =25 MVA
X1
a
X2
X3
b
c
How Are They Connected?
H
H primary
H primary
secondary
H
H
H primary
secondary
H
H
H
secondary
H
H
H
W1
A
B
H1
H2
W2
H3
W3
W5
W4
C
W6
N
X1
a
X2
b
X3
c
Both transformers are Δ-Υ but notice the Δ windings are not closed the same
A
B
H1
H2
W 1
W 2
N
X1
A H1
B
C
H2
H3
W 1
N
W 2
W 3
W 5
W 4 X1
a
a
W 6 X2
X3
b
c
H3
W 3
W 5
W 4
C
W 6 X2
X3
b
c
Single Phase Transformer information: HV 115 kV LV 7200 V Capacity 16,670 KVA primary
Primary amps 16,670,000 ÷ 115,000 = 145 amps
Secondary amps 16,670,000 ÷ 7,200 = 2315 amps Turns Ratio 115,000 ÷7200 = 15.97/1 Current ratio Check 2315÷145 = 15.97/1
secondary
Calculating single phase transformer MVA Voltage X Current 115,000 X 145 amps = 16,675,000= 16.67MVA 7,200 X 2315 amps = 16,668,000 = 16.67 MVA
Transformer Information For Practice Calculations • • • • • •
3Ø, Δ-Υ 115/12 kV 25MVA 3Ø, Δ-Υ 115/23 kV 40 MVA 3Ø, Δ- Δ 23/ 13.8 kV 5 MVA 3Ø Υ- Υ 4160/ 2400 5 MVA 3Ø, Δ- Δ 115/ 13.8 kV 10 MVA 1Ø Υ- Δ 230/22 kV 350 MVA
Delta and Wye 3-phase circuits : Electronics Worksheet
Wye connected windings: Have a common connection point Have two voltages available “L-L & L-N” Has only one current Line current
Delta connected windings: Have no common connection point Have only one voltage available “L-L” Delta can be closed “connected” in more than one way Has two currents Line current Phase or winding current
Definitions • Delta: Phase voltage is line voltage but phase current is not line current. – Line current ÷ √3= phase current – Line voltage = Phase voltage
• Wye: Phase voltage is not line voltage but phase current is line current. – Line voltage ÷ √3= phase voltage – Line current = phase current
HS Line 230 kV LS Line 23 kV Transformer 3 Ø 230/13280/23000 Gnd. Wye 25 MVA
230 kV B
A
C
H2
H1
W1
H3
W2
W3
W5
W4
W6
N X1
X2
X3
23 kV a
b
c
HS Line 115 kV LS Line 12 kV Transformer: 3 3 Ø 115/12000/6928 Gnd. Wye 40MVA
Voltage on HS 115 kV. Only one voltage because it is delta
201 B
A
C
H2
H1
H3
Voltage on LS 12,000 & 6,928 because it is wye connected 116
W2
W 3
16.6/1
Transformer Ratio 16.6/1
W 5
N X1
W 6 X2
X3
b
c
1925 a
LS Line 23 kV Transformer ? MVA
B
A
C
H2
H1
H3
W3
W2
W5
W6
N X1
X2
X3
b
c
1255 a
Typical GSU Transformer Connection
System
A
B
H1
C
H2
H3 N
W6
W4
W5
W3
W2 W1
X1
X2
a
b
Generator
X3 c
Transformer Solutions • Information: 230/23kV 25 MVA transformer 230 kV
•
What is the voltage A-B, B-C, C-A ?
•
What is the voltage a-b, b-c, c-a?
•
What is the voltage a-n, b-n, c-n?
•
What is the voltage across W1, W2, W3? 230 kV
•
What is the voltage across W4, W5, W6?
13,280 kV
•
What is the current in line A, B, C ?
25 MVA / 230 kV / √3 = 62.76 amps
•
What is the current in W1, W2, W3?
•
What is the current in W4, W5, W6?
23 kV 13,280 kV
25 MVA / 3 = 8.33 MVA /230 kV = 36.3 amps 25 MVA / 23 kV / √3 = 627.56 amps
Transformer Solutions • Information: Δ-Υ 230/23kV 25 MVA transformer 230 kV (Given)
•
What is the voltage on High voltage line?
•
What is the voltage on low voltage line?
•
What is the voltage on low voltage phase? 13,280 kV ( V 𝐿 − 𝐿
•
What is the voltage across W1, W2, W3? 230 kV (Same as the line for Δ winding)
•
What is the voltage across W4, W5, W6?
•
What is the current in line A, B, C ?
•
What is the current in W1, W2, W3?
•
What is the current in W4, W5, W6?
23 kV (Given) ÷ √3)
13,280 kV ( L-N voltage) 25 𝑀𝑉𝐴 ÷ 230,000 ÷ 3 = 62.75
25 𝑀𝑉𝐴 ÷ 230,000 ÷ √3 ÷ √3 = 36.23 25 MVA / 23 kV / √3 = 627.56 amps
Transformer Solutions •
What is the current in line a, b, c?
Same as winding W4, W5, W6= 627.556 amps
•
On the delta side of the transformer
The line current ÷ √3 = Winding Current ; 62.76 ÷ √3 = 36.23
Calculating three phase transformer MVA Voltage X Current X three windings 230,000 X 36.3 amps = 8,349,000 x 3 (windings)= 25,047,000 = 25 MVA 13,280 X 627.57 amps = 8,334,129 X 3 (windings)= 25,002, 388 = 25MVA
Transformer Ratio 3 Phase 230/23 kV 25 MVA Transformer is 230/ 23 kV Ratio is NOT this ration but is the ration of the voltages across the windings. W1 230 kV, W4 13,280 Ratio is 230,000 / 13,280 = 17.32/1
A
B
C
H2
H1
H3
W1
W2
W4
W5
W3
W6
N
Note: W4 current/ W1 current = 627.56/36.3 = 17.3 627.56 amps X 13,280 volts = 8.3 MVA 36.3 amps X 230,000 volts = 8.3 MVA 8.3 MVA X 3 (windings) =25 MVA
X1
a
X2
X3
b
c
How Are They Connected?
H
H primary
H primary
secondary
H
H
H primary
secondary
H
H
H
secondary
H
H
H
W1
A
B
H1
H2
W2
H3
W3
W5
W4
C
W6
N
X1
a
X2
b
X3
c
Both transformers are Δ-Υ but notice the Δ windings are not closed the same
A
B
H1
H2
W 1
W 2
N
X1
A H1
B
C
H2
H3
W 1
N
W 2
W 3
W 5
W 4 X1
a
a
W 6 X2
X3
b
c
H3
W 3
W 5
W 4
C
W 6 X2
X3
b
c
Single Phase Transformer information: HV 115 kV LV 7200 V Capacity 16,670 KVA primary
Primary amps 16,670,000 ÷ 115,000 = 145 amps
Secondary amps 16,670,000 ÷ 7,200 = 2315 amps Turns Ratio 115,000 ÷7200 = 15.97/1 Current ratio Check 2315÷145 = 15.97/1
secondary
Calculating single phase transformer MVA Voltage X Current 115,000 X 145 amps = 16,675,000= 16.67MVA 7,200 X 2315 amps = 16,668,000 = 16.67 MVA
Transformer Information For Practice Calculations • • • • • •
3Ø, Δ-Υ 115/12 kV 25MVA 3Ø, Δ-Υ 115/23 kV 40 MVA 3Ø, Δ- Δ 23/ 13.8 kV 5 MVA 3Ø Υ- Υ 4160/ 2400 5 MVA 3Ø, Δ- Δ 115/ 13.8 kV 10 MVA 1Ø Υ- Δ 230/22 kV 350 MVA
Delta and Wye 3-phase circuits : Electronics Worksheet
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