ungrounded wye-delta transformer bank … wye-delta transformer bank backfeed voltage ... v bg sw c...

45
Ungrounded Wye-Delta Transformer Bank Backfeed Voltage W. H. Kersting Milsoft Utility Solutions

Upload: trantram

Post on 04-May-2018

265 views

Category:

Documents


6 download

TRANSCRIPT

Page 1: Ungrounded Wye-Delta Transformer Bank … Wye-Delta Transformer Bank Backfeed Voltage ... V BG SW C SW B Source 120 volt SW A E E CG E ... • Ungrounded Wye-Delta

Ungrounded Wye-Delta Transformer Bank Backfeed Voltage

W. H. Kersting Milsoft Utility Solutions

Page 2: Ungrounded Wye-Delta Transformer Bank … Wye-Delta Transformer Bank Backfeed Voltage ... V BG SW C SW B Source 120 volt SW A E E CG E ... • Ungrounded Wye-Delta

Introduction •  Loadstobeserved–  Three-phaseinduc4onmotor–  120/240voltsingle-phaseloads

•  Transformerconnec4on– Groundedwye-delta

•  Developsbackfeedshortcircuitcurrentsforupstreamgroundfaults

– Ungroundedwye-delta•  Purposeofthispaper

Page 3: Ungrounded Wye-Delta Transformer Bank … Wye-Delta Transformer Bank Backfeed Voltage ... V BG SW C SW B Source 120 volt SW A E E CG E ... • Ungrounded Wye-Delta

TypicalSystemOne-LineDiagram

4-wire, gr. wye 1/0 QuadraplexInfinite Bus

12,470 VSingle-Phase Loads

M Induction Motor

1 2 3 4

Page 4: Ungrounded Wye-Delta Transformer Bank … Wye-Delta Transformer Bank Backfeed Voltage ... V BG SW C SW B Source 120 volt SW A E E CG E ... • Ungrounded Wye-Delta

The Three-Phase System

Page 5: Ungrounded Wye-Delta Transformer Bank … Wye-Delta Transformer Bank Backfeed Voltage ... V BG SW C SW B Source 120 volt SW A E E CG E ... • Ungrounded Wye-Delta

30 Degree Step-Down Connection

N

+ +

- -

-

+

+

++

+

a

+

-

+

-

+

-

+

-

n

+

-

+

-

-

23V

- NGV

ANVT BNVT

CNVT

anVt

nbVt

bcVtacI

bnI

naI

cbI+

_

caVt

c

b

bcV

anV

nbV

cI

bI

aI

0Z

2Z

bZ

cZ

1Z

BI

AI

NI

CI

ANV

CNV ABV

BNV

abV

bcV

caVRated Primary

Rated Secondaryt

kVLNn

kVLL=

Page 6: Ungrounded Wye-Delta Transformer Bank … Wye-Delta Transformer Bank Backfeed Voltage ... V BG SW C SW B Source 120 volt SW A E E CG E ... • Ungrounded Wye-Delta

30DegreeStep-UpConnec4on

N

+ +

- -

-

+

+

++

+

a

+

-

+

-

+

-+

-

n

+

-

+

-

-

23V

- NGV

anVt

nbVt

bcVtacI

bnI

naI

cbI+

_

caVt

c

b

bcV

anV

nbV

cI

bI

aI

0Z

2Z

bZ

cZ

1Z

BI

AI

NI

CI

BNVT

CNVT

ANVT

ANV

BNV

CNV ABV

acVcaV

abVcbV

bcVbaV

Page 7: Ungrounded Wye-Delta Transformer Bank … Wye-Delta Transformer Bank Backfeed Voltage ... V BG SW C SW B Source 120 volt SW A E E CG E ... • Ungrounded Wye-Delta

Voltage Equations for NMSU Connection

[ ] [ ] [ ]

[ ]

2 0 0 00 0 1 00 0 0 1

2 0 0 0where: 0 0 1 0

0 0 0 1

anAN

nbBN t

bcCN

ca

ABC anbc

t

VtVT

VtVT n

VtVT

Vt

VTLN AV Vt

AV n

⎡ ⎤⎡ ⎤ ⎡ ⎤ ⎢ ⎥⎢ ⎥ ⎢ ⎥ ⎢ ⎥= ⋅ ⋅⎢ ⎥ ⎢ ⎥ ⎢ ⎥⎢ ⎥ ⎢ ⎥ ⎢ ⎥⎣ ⎦⎣ ⎦

⎣ ⎦

= ⋅

⎡ ⎤⎢ ⎥= ⋅ ⎢ ⎥⎢ ⎥⎣ ⎦

[ ] [ ] [ ]

[ ]

0.5 0 00.5 0 010 1 00 0 1

0.5 0 00.5 0 01where: 0 1 00 0 1

anAN

nbBN

bc tCN

ca

anbc ABC

t

VtVT

VtVT

Vt nVT

Vt

Vt BV VTLN

BVn

⎡ ⎤ ⎡ ⎤⎡ ⎤⎢ ⎥ ⎢ ⎥⎢ ⎥⎢ ⎥ ⎢ ⎥= ⋅ ⋅ ⎢ ⎥⎢ ⎥ ⎢ ⎥⎢ ⎥⎢ ⎥ ⎢ ⎥ ⎣ ⎦

⎣ ⎦⎣ ⎦

= ⋅

⎡ ⎤⎢ ⎥⎢ ⎥= ⋅⎢ ⎥⎢ ⎥⎣ ⎦

N

+ +

- -

-

+

+

++

+

a

+

-

+

-

+

-+

-

n

+

-

+

-

-

23V

- NGV

ANVT BNVT

CNVT

anVt

nbVt

bcVt

acIbnI

naI

cbI+

_

caVt

c

b

bcV

anV

nbV

cI

bI

aI

0Z

2Z

bZ

cZ

1Z

BI

AI

NI

CI

Page 8: Ungrounded Wye-Delta Transformer Bank … Wye-Delta Transformer Bank Backfeed Voltage ... V BG SW C SW B Source 120 volt SW A E E CG E ... • Ungrounded Wye-Delta

Current Equations for NMSU Connection

[ ] [ ] [ ]

[ ]

0.5 0.5 0 01 0 0 1 0

0 0 0 1

0.5 0.5 0 01where: 0 0 1 0

0 0 0 1

naA

bnB

cbtC

ac

ABC anbc

t

II

II

InI

I

I AI ID

AIn

⎡ ⎤⎡ ⎤ ⎡ ⎤ ⎢ ⎥⎢ ⎥ ⎢ ⎥ ⎢ ⎥= ⋅ ⋅⎢ ⎥ ⎢ ⎥ ⎢ ⎥⎢ ⎥ ⎢ ⎥ ⎢ ⎥⎣ ⎦⎣ ⎦

⎣ ⎦

= ⋅

⎡ ⎤⎢ ⎥= ⋅ ⎢ ⎥⎢ ⎥⎣ ⎦

[ ] [ ] [ ]

[ ]

5 1 31 5 311 1 361 1 3

5 1 31 5 31where: 1 1 361 1 3

naa

bnb

cbc

ac

anbc abc

II

II

II

I

ID Dd I

Dd

⎡ ⎤ ⎡ ⎤⎡ ⎤⎢ ⎥ ⎢ ⎥− − − ⎢ ⎥⎢ ⎥ ⎢ ⎥= ⋅ ⋅ ⎢ ⎥⎢ ⎥ ⎢ ⎥− −⎢ ⎥⎢ ⎥ ⎢ ⎥ ⎣ ⎦−⎣ ⎦⎣ ⎦

= ⋅

⎡ ⎤⎢ ⎥− − −⎢ ⎥= ⋅⎢ ⎥− −⎢ ⎥−⎣ ⎦

N

+ +

- -

-

+

+

++

+

a

+

-

+

-

+

-+

-

n

+

-

+

-

-

23V

- NGV

ANVT BNVT

CNVT

anVt

nbVt

bcVt

acIbnI

naI

cbI+

_

caVt

c

b

bcV

anV

nbV

cI

bI

aI

0Z

2Z

bZ

cZ

1Z

BI

AI

NI

CI

Page 9: Ungrounded Wye-Delta Transformer Bank … Wye-Delta Transformer Bank Backfeed Voltage ... V BG SW C SW B Source 120 volt SW A E E CG E ... • Ungrounded Wye-Delta

Ini6alStudyofNMSUTransformers

█NMSU Power Lab Transformers@Each rated: 0.5 kVA, 120−120/240 Volts, 𝑍↓𝑡 =0+1𝑗0.036 PU 

N

+ +

- -

-

+

+

++

+

a

+

-

+

-

n

+

-

-- NGV

ANVT BNVT

CNVT

anVt

nbVt

bcVt+

_

caVt

c

b

0Z

2Z

bZ

cZ

1Z

B

G

A

C

_+__

+

AGV

CGV

BGV

SW C

SW B

Source120 volt

SW A

AGE

CGE

BGE

+__

+

+ +

Page 10: Ungrounded Wye-Delta Transformer Bank … Wye-Delta Transformer Bank Backfeed Voltage ... V BG SW C SW B Source 120 volt SW A E E CG E ... • Ungrounded Wye-Delta

No-LoadStudiesofNMSUSystem

•  Standard30degreeconnec4onssothesecondarywillhavebalancedthree-phasevoltages

•  Developequa4onsforsteadystate•  Modifyfor– SW-Aopen– SW-Bopen– SW-Copen

Page 11: Ungrounded Wye-Delta Transformer Bank … Wye-Delta Transformer Bank Backfeed Voltage ... V BG SW C SW B Source 120 volt SW A E E CG E ... • Ungrounded Wye-Delta

The NMSU System

N

+ +

- -

-

+

+

++

+

a

+

-+

-

n

+

-

-- NGV

ANVT BNVT

CNVT

anVt

nbVt

bcVt+

_

caVt

c

b

0Z

2Z

bZ

cZ

1Z

120 LGSource

B

G

A

C

+

_+__

+

AGV

CGV

BGV

SW A

SW C

SW B

Turns ratio: 120 0.5240tn = =

Source LG Voltages: [ ]120/0

120/ 120120/120

ABCELG⎡ ⎤⎢ ⎥= −⎢ ⎥⎢ ⎥⎣ ⎦

Source LL Voltages: [ ]207.8/30

207.8/ 90207.8/90

ABCELL⎡ ⎤⎢ ⎥= −⎢ ⎥⎢ ⎥⎣ ⎦

Assumption: With one switch open the two remaining primaries will share the line-to-line voltage equally.

Page 12: Ungrounded Wye-Delta Transformer Bank … Wye-Delta Transformer Bank Backfeed Voltage ... V BG SW C SW B Source 120 volt SW A E E CG E ... • Ungrounded Wye-Delta

KVL On Secondary Terminals

( )

( )

on secondary 0

1 1 1 1 02 21 0

0 0

an nb bc ca

AN AN BN CNt t t t

AN BN CNt

AN BN CN t

kVLVt Vt Vt Vt

VT VT VT VTn n n n

VT VT VTnVT VT VT n

+ + + =

⋅ + ⋅ + ⋅ + ⋅ =⋅ ⋅

⋅ + + =

+ + = ⋅ =

N

+ +

- -

-

+

+

++

+

a

+

-

+

-

n

+

-

-- NGV

ANVT BNVT

CNVT

anVt

nbVt

bcVt+

_

caVt

c

b

0Z

2Z

bZ

cZ

1Z

B

G

A

C

_+__

+

AGV

CGV

BGV

SW C

SW B

Source120 volt

SW A

AGE

CGE

BGE

+__

+

+ +

Page 13: Ungrounded Wye-Delta Transformer Bank … Wye-Delta Transformer Bank Backfeed Voltage ... V BG SW C SW B Source 120 volt SW A E E CG E ... • Ungrounded Wye-Delta

All Switches Closed

1. 1. 2. 2. 3.

A AN NG AN

B BN NG BN

C CN NG

ELG VT V VTELG VT V VTELG VT V

= +

= +

= + 3. 14. 0 4.

25. 0 5.

CN

an AN ant

nb an

VT

V VT Vtn

Vt Vt

= − + ⋅⋅

= − +

.

16. 0 6.

17. 0 7.

8. 0 +

nb

bc BN bct

ca CN cat

AN BN CN

Vt

Vt VT Vtn

Vt VT Vtn

VT VT V

= − + ⋅

= − + ⋅

= + 8. NGV

Page 14: Ungrounded Wye-Delta Transformer Bank … Wye-Delta Transformer Bank Backfeed Voltage ... V BG SW C SW B Source 120 volt SW A E E CG E ... • Ungrounded Wye-Delta

All Switches Closed - Results

[ ] [ ]

[ ]

[ ] [ ] [ ]

120/0120/0

120/0120/ 120

240/ 120120/120

240/120

00 0

0

120/0120/ 120120/120

ABC anbc

NG AG AN

ABC ABC

VTLN Vt

V E VT VNG

VSLG VTLN VNG

⎡ ⎤⎡ ⎤ ⎢ ⎥⎢ ⎥ ⎢ ⎥= − =⎢ ⎥ ⎢ ⎥−⎢ ⎥ ⎢ ⎥⎣ ⎦

⎣ ⎦

⎡ ⎤⎢ ⎥= − = = ⎢ ⎥⎢ ⎥⎣ ⎦

⎡ ⎤⎢ ⎥= + = −⎢ ⎥⎢ ⎥⎣ ⎦

Page 15: Ungrounded Wye-Delta Transformer Bank … Wye-Delta Transformer Bank Backfeed Voltage ... V BG SW C SW B Source 120 volt SW A E E CG E ... • Ungrounded Wye-Delta

SW-AOpen

N

+ +

- -

-

+

+

++

+

a

+

-+

-

n

+

-

-- NGV

ANVT BNVT

CNVT

anVt

nbVt

bcVt+

_

caVt

c

b

0Z

2Z

bZ

cZ

1Z

B

G

A

C

_+__

+

AGV

CGV

BGV

SW C

SW B

Source120 volt

SW A

AGE

CGE

BGE

+__

+

+ +

SW-A open and B and C closed:

( )

207.8/ 901 103.9/ 902

103.9/900

0.5 0 0 00.5 0 0 010 1 0 207.8/ 900 0 1 207.8/90

BC BC

BN BC

CN BN

AN AN CN

anAN

nbBN

bc tCN

ca

NG

VT ELL

VT VT

VT VTVT VT VT

VtVT

VtVT

Vt nVT

VtV EL

= = −

= ⋅ = −

= − =

= − + =

⎡ ⎤ ⎡ ⎤ ⎡ ⎤⎡ ⎤⎢ ⎥ ⎢ ⎥ ⎢ ⎥⎢ ⎥⎢ ⎥ ⎢ ⎥ ⎢ ⎥= ⋅ ⋅ =⎢ ⎥⎢ ⎥ ⎢ ⎥ ⎢ ⎥−⎢ ⎥⎢ ⎥ ⎢ ⎥ ⎢ ⎥⎣ ⎦

⎣ ⎦ ⎣ ⎦⎣ ⎦=

[ ] [ ] [ ]

60/18060/180

120/ 120120/120

BG CN

ABC

L VT

VNG VTLN VNG

− =

⎡ ⎤⎢ ⎥= − = −⎢ ⎥⎢ ⎥⎣ ⎦

Page 16: Ungrounded Wye-Delta Transformer Bank … Wye-Delta Transformer Bank Backfeed Voltage ... V BG SW C SW B Source 120 volt SW A E E CG E ... • Ungrounded Wye-Delta

SW-B Open

N

+ +

- -

-

+

+

++

+

a

+

-+

-

n

+

-

-- NGV

ANVT BNVT

CNVT

anVt

nbVt

bcVt+

_

caVt

c

b

0Z

2Z

bZ

cZ

1Z

B

G

A

C

_+__

+

AGV

CGV

BGV

SW C

SW B

Source120 volt

SW A

AGE

CGE

BGE

+__

+

+ +

( )

207.8/1501 103.9/1502

103.9/ 300

0.5 0 0 103.9/ 300.5 0 0 103.9/ 3010 1 0 00 0 1 207.8/150

CA CA

CN CA

AN CN

BN CN AN

anAN

nbBN

bc tCN

ca

VT ELL

VT VT

VT VTVT VT VT

VtVT

VtVT

Vt nVT

Vt

= =

= ⋅ =

= − = −

= − + =

−⎡ ⎤ ⎡ ⎤ ⎡ ⎤⎡ ⎤⎢ ⎥ ⎢ ⎥ ⎢ −⎢ ⎥⎢ ⎥ ⎢ ⎥ ⎢= ⋅ ⋅ =⎢ ⎥⎢ ⎥ ⎢ ⎥ ⎢⎢ ⎥⎢ ⎥ ⎢ ⎥ ⎢⎣ ⎦

⎣ ⎦ ⎣ ⎦⎣ ⎦

[ ] [ ] [ ]

60/60120/060/60

120 /120

NG BC BN

ABC

V ELG VT

VLG VTLN VNG

⎥⎥⎥⎥

= − =

⎡ ⎤⎢ ⎥= + = ⎢ ⎥⎢ ⎥⎣ ⎦

Page 17: Ungrounded Wye-Delta Transformer Bank … Wye-Delta Transformer Bank Backfeed Voltage ... V BG SW C SW B Source 120 volt SW A E E CG E ... • Ungrounded Wye-Delta

SW-C Open

N

+ +

- -

-

+

+

++

+

a

+

-+

-

n

+

-

-- NGV

ANVT BNVT

CNVT

anVt

nbVt

bcVt+

_

caVt

c

b

0Z

2Z

bZ

cZ

1Z

B

G

A

C

_+__

+

AGV

CGV

BGV

SW C

SW B

Source120 volt

SW A

AGE

CGE

BGE

+__

+

+ +

( )

207.8/301 103.9/302

103.9/ 1500

0.5 0 0 103.9/300.5 0 0 103.9/3010 1 0 207.8/ 1500 0 1 0

AB AB

AN AB

BN AN

CN AN BN

anAN

nbBN

bc tCN

ca

VT ELL

VT VT

VT VTVT VT VT

VtVT

VtVT

Vt nVT

Vt

= =

= ⋅ =

= − = −

= − + =

⎡ ⎤ ⎡ ⎤ ⎡ ⎤⎡ ⎤⎢ ⎥ ⎢ ⎥ ⎢ ⎥⎢ ⎥⎢ ⎥ ⎢ ⎥ ⎢ ⎥= ⋅ ⋅ =⎢ ⎥⎢ ⎥ ⎢ ⎥ ⎢ −⎢ ⎥⎢ ⎥ ⎢ ⎥ ⎢⎣ ⎦

⎣ ⎦ ⎣ ⎦⎣ ⎦

[ ] [ ] [ ]

60/ 60120 / 0

120 / 12060 / 60

NG AB AN

ABC

V ELG VT

VLG VTLN VNG

⎥⎥

= − = −

⎡ ⎤⎢ ⎥= + = −⎢ ⎥⎢ ⎥−⎣ ⎦

Page 18: Ungrounded Wye-Delta Transformer Bank … Wye-Delta Transformer Bank Backfeed Voltage ... V BG SW C SW B Source 120 volt SW A E E CG E ... • Ungrounded Wye-Delta

New Mexico State Power Lab

This circuit was set up in the New Mexico State University (NMSU) power lab. The purpose was to verify the Mathcad results. Understand that the Mathcad routine assumes “ideal” transformers while the Lab uses real transformers which have shunt impedances and capacitance.

N

+ +

- -

-

+

+

++

+

a

+

-

+

-

n

+

-

-- NGV

ANVT BNVT

CNVT

anVt

nbVt

bcVt+

_

caVt

c

b

0Z

2Z

bZ

cZ

1Z

B

G

A

C

_+__

+

AGV

CGV

BGV

SW C

SW B

Source120 volt

SW A

AGE

CGE

BGE

+__

+

+ +

Page 19: Ungrounded Wye-Delta Transformer Bank … Wye-Delta Transformer Bank Backfeed Voltage ... V BG SW C SW B Source 120 volt SW A E E CG E ... • Ungrounded Wye-Delta

Mathcad vs. Lab Results

MathcadResults NMSULabResults

SW-A SW-B SW-C ANVT 8.5 104 102

BNVT 106 2.4 105

CNVT 101 102 6.3

NGV 55 55 55

anVt 8.5 104 104

nbVt 8.5 104 104

bcVt 213 4.7 209

caVt 201 204 12.8

AGV 55 120 120

BGV 120 61 120

CGV 120 120 63

SW-A SW-B SW-C ANVT 0 103.9 103.9

BNVT 103.9 0 103.9

CNVT 103.9 103.9 0

NGV 60 60 60

anVt 0 103.9 103.9

nbVt 0 103.9 103.9

bcVt 207.8 0 207.8

caVt 207.8 207.8 0

AGV 60 120 120

BGV 120 60 120

CGV 120 120 60

Page 20: Ungrounded Wye-Delta Transformer Bank … Wye-Delta Transformer Bank Backfeed Voltage ... V BG SW C SW B Source 120 volt SW A E E CG E ... • Ungrounded Wye-Delta

NMSU System with Single-Phase Load

25 Unknowns 12 voltages 13 currents

N

+ +

- -

-

+

+

++

+

a

+

-+

-

n

+

-

-- NGV

ANVT BNVT

CNVT

anVt

nbVt

bcVt+

_

caVt

c

b

0Z

2Z

bZ

cZ

1Z

120 LGSource

B

G

A

C

+

_+__

+

AGV

CGV

BGV

1SL

2SL3SL

aI

nI

bI

1IL

2IL 3IL

AI

BI

CI

naI

cbIacI

bnI

SW C

SW A

SW B

_+

_

+

_AGE

CGE

+BGE

Page 21: Ungrounded Wye-Delta Transformer Bank … Wye-Delta Transformer Bank Backfeed Voltage ... V BG SW C SW B Source 120 volt SW A E E CG E ... • Ungrounded Wye-Delta

Single-Phase Loading WindMil and Mathcad

•  WindMil PQ single-phase loads

•  Using WindMil results the constant impedance loads computed for Mathcad

[ ]0.5/18.20.45/25.80.55/31.8

SL⎡ ⎤⎢ ⎥= ⎢ ⎥⎢ ⎥⎣ ⎦

[ ]25.4 8.326.8 13.082.7 51.2

jZL j

j

+⎡ ⎤⎢ ⎥= +⎢ ⎥⎢ ⎥+⎣ ⎦

Page 22: Ungrounded Wye-Delta Transformer Bank … Wye-Delta Transformer Bank Backfeed Voltage ... V BG SW C SW B Source 120 volt SW A E E CG E ... • Ungrounded Wye-Delta

WindMil and Mathcad Full-Load Results

WindMil Mathcad AI 8.59/-29.3 8.59/-29.3

BI 4.29/150.7 4.29/150.7

CI 4.29/150.7 4.29/150.7

aI 6.64/-26.9 6.64/-26.9

bI 6.24/148.1 6.24/148.1

cI 0 0

anV 116.0/-3.9 116.0/-3.9

nbV 115.8/-3.8 115.8/-3.8

abV 231.8/-3.8 231.8/-3.8

NGV 0 0

Page 23: Ungrounded Wye-Delta Transformer Bank … Wye-Delta Transformer Bank Backfeed Voltage ... V BG SW C SW B Source 120 volt SW A E E CG E ... • Ungrounded Wye-Delta

Open Switch Studies •  Majorpurposeofthetotalstudywastodeterminewhathappenswhenoneofthethreeupstreamswitchesisopen

•  Studiestobecompletedwiththesingle-phaseloads– SW-Aopen– SW-Bopen– SW-Copen

Page 24: Ungrounded Wye-Delta Transformer Bank … Wye-Delta Transformer Bank Backfeed Voltage ... V BG SW C SW B Source 120 volt SW A E E CG E ... • Ungrounded Wye-Delta

SW-A Open - Currents

Page 25: Ungrounded Wye-Delta Transformer Bank … Wye-Delta Transformer Bank Backfeed Voltage ... V BG SW C SW B Source 120 volt SW A E E CG E ... • Ungrounded Wye-Delta

SW-A Open - Voltages

N

+ +

- -

-

+

+

++

+

a

+

-+

-

n

+

-

-- NGV

ANVT BNVT

CNVT

anVt

nbVt

bcVt+

_

caVt

c

b

0Z

2Z

bZ

cZ

1Z

120 LGSource

B

G

A

C

+

_+__

+

AGV

CGV

BGV

1SL

2SL

3SL

aI

nI

bI

1IL

2IL 3IL

AI

BI

CI

naI

cbIacI

bnI

SW C

SW A

SW B

_+

_

+

_AGE

CGE

+BGE

1) Only voltage on transformers is BCV

a) 12BN BCVT V= ⋅

b) 12CN BCVT V= − ⋅

i) 1bc BN

tVt VT

n= ⋅

ii) 1ca BN

tVt VT

n= − ⋅

iii) ( )

KVL: 0 0 0 0

an nb bc ca

t AN BN BN

AN BN BN

AN

Vt Vt Vt Vtn VT VT VTVT VT VTVT

+ + + =

⋅ + − =

+ − =

=

Page 26: Ungrounded Wye-Delta Transformer Bank … Wye-Delta Transformer Bank Backfeed Voltage ... V BG SW C SW B Source 120 volt SW A E E CG E ... • Ungrounded Wye-Delta

SW-A Open – Mathcad Results

N

+ +

- -

-

+

+

++

+

a

+

-+

-

n

+

-

-- NGV

ANVT BNVT

CNVT

anVt

nbVt

bcVt+

_

caVt

c

b

0Z

2Z

bZ

cZ

1Z

120 LGSource

B

G

A

C

+

_+__

+

AGV

CGV

BGV

1SL

2SL

3SL

aI

nI

bI

1IL

2IL 3IL

AI

BI

CI

naI

cbIacI

bnI

SW C

SW A

SW B

_+

_

+

_AGE

CGE

+BGE

0, 103.9/ 90, 103.9/9060/180

0, 207.8/ 90, 207.8/9060/180120/ 120120/120

60 0.5120

AN BN CN

NG

an nb bc ca

AG AN NG

BG BN NG

CG CN NG

VT VT VTVVt Vt Vt VtVS VT VVS VT VVS VT V

Ratio

= = − =

=

= = = − =

= + =

= + = −

= + =

= =

Page 27: Ungrounded Wye-Delta Transformer Bank … Wye-Delta Transformer Bank Backfeed Voltage ... V BG SW C SW B Source 120 volt SW A E E CG E ... • Ungrounded Wye-Delta

SW-B Open - Currents

N

+ +

- -

-

+

+

++

+

a

+

-+

-

n

+

-

-- NGV

ANVT BNVT

CNVT

anVt

nbVt

bcVt+

_

caVt

c

b

0Z

2Z

bZ

cZ

1Z

120 LGSource

B

G

A

C

+

_+__

+

AGV

CGV

BGV

1SL

2SL

3SL

aI

nI

bI

1IL

2IL 3IL

AI

BI

CI

naI

cbIacI

bnI

SW C

SW A

SW B

_+

_

+

_AGE

CGE

+BGE

1) 0 alwayscI =

a) 0BI = i) 0cbI =

ii)

Because 00

Therefore: 0 and 0 0 0

c

ac

C A

ac an nb cb

a b c

II

I II I I II I I

=

=

= =

= = = =

= = =

Page 28: Ungrounded Wye-Delta Transformer Bank … Wye-Delta Transformer Bank Backfeed Voltage ... V BG SW C SW B Source 120 volt SW A E E CG E ... • Ungrounded Wye-Delta

SW-B Open - Voltages

N

+ +

- -

-

+

+

++

+

a

+

-+

-

n

+

-

-- NGV

ANVT BNVT

CNVT

anVt

nbVt

bcVt+

_

caVt

c

b

0Z

2Z

bZ

cZ

1Z

120 LGSource

B

G

A

C

+

_+__

+

AGV

CGV

BGV

1SL

2SL

3SL

aI

nI

bI

1IL

2IL 3IL

AI

BI

CI

naI

cbIacI

bnI

SW C

SW A

SW B

_+

_

+

_AGE

CGE

+BGE

1) All currents are zero

a) Since the load currents are zero the center tap voltages and an nbVt Vt must be zero i) Therefore: 0ANVT =

(1) With 0AI = the primary neutral is shifted up to the terminal A (2) This causes and CN CA AN CAVT V VT V= = −

Page 29: Ungrounded Wye-Delta Transformer Bank … Wye-Delta Transformer Bank Backfeed Voltage ... V BG SW C SW B Source 120 volt SW A E E CG E ... • Ungrounded Wye-Delta

SW-B Open – Mathcad Results

N

+

-

-+

+

a

+

-+

-

n

+

-

- NGV

BNVT

CNVT

anVt

nbVt

bcVt+

_

caVt

c

b

2Z

bZ

cZ

1Z

120 LGSource

B

G

A

C

+

_+__

+

AGV

CGV

BGV

1SL

2SL

3SL

aI

nI

bI

1IL

2IL 3IL

AI

BI

CI

naI

cbIacI

bnI

SW C

SW A

SW B

_+

_

+

_AGE

CGE

+BGE

0, 207.8/ 30, 207.8/150120/0

0, 415.7/ 30, 415.7/150120/0317.5/ 19.1120/120

317.5 2.65120

AN BN CN

NG

an nb bc ca

AG AN NG

BG BN NG

CG CN NG

VT VT VTVVt Vt Vt VtVS VT VVS VT VVS VT V

Ratio

= = − =

=

= = = − =

= + =

= + = −

= + =

= =

Page 30: Ungrounded Wye-Delta Transformer Bank … Wye-Delta Transformer Bank Backfeed Voltage ... V BG SW C SW B Source 120 volt SW A E E CG E ... • Ungrounded Wye-Delta

SW-C Open – Mathcad Results

N

+ +

- -

-

+

+

++

+

a

+

-+

-

n

+

-

-- NGV

ANVT BNVT

CNVT

anVt

nbVt

bcVt+

_

caVt

c

b

0Z

2Z

bZ

cZ

1Z

120 LGSource

B

G

A

C

+

_+__

+

AGV

CGV

BGV

1SL

2SL

3SL

aI

nI

bI

1IL

2IL 3IL

AI

BI

CI

naI

cbIacI

bnI

SW C

SW A

SW B

_+

_

+

_AGE

CGE

+BGE

0, 207.8/ 150, 207.8/30120/0

0, 415.7/ 150, 415.7/30120/0120/ 120317.5/19.1

317.5 2.65120

AN BN CN

NG

an nb bc ca

AG AN NG

BG BN NG

CG CN NG

VT VT VTVVt Vt Vt VtVS VT VVS VT VVS VT V

Ratio

= = − =

=

= = = − =

= + =

= + = −

= + =

= =

Page 31: Ungrounded Wye-Delta Transformer Bank … Wye-Delta Transformer Bank Backfeed Voltage ... V BG SW C SW B Source 120 volt SW A E E CG E ... • Ungrounded Wye-Delta

Summary of Open Switches

Page 32: Ungrounded Wye-Delta Transformer Bank … Wye-Delta Transformer Bank Backfeed Voltage ... V BG SW C SW B Source 120 volt SW A E E CG E ... • Ungrounded Wye-Delta

12.47 kV System Data

5 mile

4-wire, gr. wye

500 ft.

1/0 quadraplex

Single-Phase Loads

Induction MotorInfinite Bus

12,470 V

Four Wire Centered Tapped Ungrd. Y-D Transformer System

3 single-phasetransformers

Primary Line: 336,400 26/7 ACSR and 4/0 ACSR Secondary Line: 1/0 AA Quadraplex Lighting Transformer: 25 kVA, 7200-120/240 volts, 0.012 0.017LZt j= + per-unit Power Transformers: 10 kVA, 7200-240 volts, 0.16 0.014PZ j= + per-unit

Single-Phase 120 volt loads: 1 1

2 2

3.0, 0.95 lag5.0, 0.90 lag

kVA PFkVA PF

= =

= =

Single-Phase 240 volt load: 3 38.0, 0.85 lagkVA PF= =

Induction Motor:

25, Line-to-line voltage = 240 volt0.0336 0.08 per-unit0.0394 0.08 per-unit

2.1 per-unit

s

r

m

kVAZ jZ jZ j

=

= +

= +

=

Page 33: Ungrounded Wye-Delta Transformer Bank … Wye-Delta Transformer Bank Backfeed Voltage ... V BG SW C SW B Source 120 volt SW A E E CG E ... • Ungrounded Wye-Delta

12.47 kV System Unknowns

█For Mathcad Routine@ 39 unknowns 

System Voltages: , , , , , , , , , NG an nb bc ca an nb ab bc caV V V V V VL V VL VL VL Transformer Voltages: , , , , , , AN BN CN an nb bc caVT VT VT Vt Vt Vt Vt Voltage Drop: , , , , , A B C a b cv v v v v v Line Currents: , , , , , A B C a b cI I I I I I Transformer Currents: , , , na bn cb acI I I I Load Currents: 1 2 3, , , , , a b cIL IL IL IM IM IM

N

+ +

- -

-

+

+

++

+

a

+

-

+

-

+

-+

-

n

+

-

+

-

-

2 3V

- NGV

Cv

Bv

AvANVT BNVT

CNVT

av

bv

cv

Motor

anVt

nbVt

bcVtacI

bnI

naI

cbI+

_

caVt

c

b

bcV

anV

nbVn I

aIM

cIM

bIM

0Z

2 Z

bZ

cZ

1 Z1ZL

2ZL3ZL

SourceN I

B

G

A

C

+

_+__

+

AGV

CGV

BGV

SW B

12.47 kV

AI

BI

CI

aI

bI

cI

SW A

AGE

BGE

+__

+

CGE

SW C

+__

+

+

Page 34: Ungrounded Wye-Delta Transformer Bank … Wye-Delta Transformer Bank Backfeed Voltage ... V BG SW C SW B Source 120 volt SW A E E CG E ... • Ungrounded Wye-Delta

WindMil and Mathcad •  Beforecheckingfortheopenswitchcondi4onstheMathcadrou4neneededtobeverifiedbyrunningWindMiltogetthecorrectanswersunderafull-loadcondi4on.

•  WindMilwasfirstrun.TheMathcadrou4neassumesalinearsystemsotheresultsofWindMilwereusedtocomputethesingle-phaseloadequivalentimpedances.

Page 35: Ungrounded Wye-Delta Transformer Bank … Wye-Delta Transformer Bank Backfeed Voltage ... V BG SW C SW B Source 120 volt SW A E E CG E ... • Ungrounded Wye-Delta

The Three-Phase System – Full Load WindMil and Mathcad Results

N

+ +

- -

-

+

+

++

+

a

+

-

+

-

+

-+

-

n

+

-

+

-

-

2 3V

- NGV

Cv

Bv

Av

ANVT BNVT

CNVT

av

bv

cv

Motor

anVt

nbVt

bcVt

acIbnI

naI

cbI+

_

caVt

c

b

bcV

anV

nbVnI

cI

bI

aI

aIM

cIM

bIM

0Z

2Z

bZ

cZ

1Z1ZL

2ZL3ZL12.5 kV

Source

BI

AI

NI

CI

B

G

A

C

+

_+__

+

AGV

CGV

BGV

SW A

SW C

SW B

[ ] [ ] [ ]

[ ]

7200/0 7074.7/ 0.4 109.7/2.07200/ 120 , 7228.3/ 120.4 57.7/5.1, 103.1/ 1.57200/120 7221.5/120.4 212.7/0.3

2.51/ 27.61.77/ 172.11.48/108.9

ABC ABC NG

ABC

VS VT V VL

I

−⎡ ⎤ ⎡ ⎤ ⎡ ⎤⎢ ⎥ ⎢ ⎥ ⎢ ⎥= − = − = = −⎢ ⎥ ⎢ ⎥ ⎢ ⎥⎢ ⎥ ⎢ ⎥ ⎢ ⎥⎣ ⎦ ⎣ ⎦ ⎣ ⎦

−⎡ ⎤⎢= −⎢⎢⎣

[ ] [ ]

[ ] [ ]

101.0/ 43.7 27.4/ 16.2, 132.4/164.7 , 48 / 5/ 27.4

62.4 / 52.5 27.6/ 31.5

212.7/0.3 44.9/ 71.0221.4/ 117.7 , 53.1/ 172.4223.9/119.4 62.4/52.5

V

abc anbI IL

VM IM

− −⎡ ⎤ ⎡ ⎤⎥ ⎢ ⎥ ⎢ ⎥= = −⎥ ⎢ ⎥ ⎢ ⎥⎥ ⎢ ⎥ ⎢ ⎥−⎦ ⎣ ⎦ ⎣ ⎦

−⎡ ⎤ ⎡ ⎤⎢ ⎥ ⎢ ⎥= − = −⎢ ⎥ ⎢ ⎥⎢ ⎥ ⎢ ⎥⎣ ⎦ ⎣ ⎦

oltage Unbalance = 3.04%, Current Unbalance = 16.69%

Page 36: Ungrounded Wye-Delta Transformer Bank … Wye-Delta Transformer Bank Backfeed Voltage ... V BG SW C SW B Source 120 volt SW A E E CG E ... • Ungrounded Wye-Delta

•  SinceWindMilandMathcadresultsareiden4cal– ConfidencethattheMathcadrou4neiscorrect– WillusetheMathcadrou4netostudytheopenswitchcondi4ons•  SW-AOpenwithmotorandsingle-phaseloads•  Allotherswitchesopenwithmotoroff

Page 37: Ungrounded Wye-Delta Transformer Bank … Wye-Delta Transformer Bank Backfeed Voltage ... V BG SW C SW B Source 120 volt SW A E E CG E ... • Ungrounded Wye-Delta

SW-A Open with Motor and Single-Phase Loads

[ ] [ ]117.3/ 21.0 71.7/ 168.6169.3/ 106.0 78.6/ 101.8214.0/107.1 125.6/46.5

Voltage Unbalance = 29.7% Current Unbalance = 36.5%

Negative sequence relay on motor will disco

VM IM− −⎡ ⎤ ⎡ ⎤

⎢ ⎥ ⎢ ⎥= − = −⎢ ⎥ ⎢ ⎥⎢ ⎥ ⎢ ⎥⎣ ⎦ ⎣ ⎦

nnect motor

Page 38: Ungrounded Wye-Delta Transformer Bank … Wye-Delta Transformer Bank Backfeed Voltage ... V BG SW C SW B Source 120 volt SW A E E CG E ... • Ungrounded Wye-Delta

SW-A Open With No Motor

[ ] [ ]0 3600/ 180

6235.4/ 90 , 3600/ 180, 7200/ 1206235.4/ 90 7200/120

Note that the LG voltage on the transformer side of the open phase A will be 3600 volts. It is no

ABC NG ABCVT V VS−⎡ ⎤ ⎡ ⎤

⎢ ⎥ ⎢ ⎥= − = − = −⎢ ⎥ ⎢ ⎥⎢ ⎥ ⎢ ⎥−⎣ ⎦ ⎣ ⎦

[ ]

t zero.

00

207.8/ 90207.8/90

With no 120/240 voltages across the single-phase 120/240 volt loads, the load currents will be zero.

abcVLN

⎡ ⎤⎢ ⎥⎢ ⎥=⎢ ⎥−⎢ ⎥⎣ ⎦

Page 39: Ungrounded Wye-Delta Transformer Bank … Wye-Delta Transformer Bank Backfeed Voltage ... V BG SW C SW B Source 120 volt SW A E E CG E ... • Ungrounded Wye-Delta

SW-B Open With No Motor

Page 40: Ungrounded Wye-Delta Transformer Bank … Wye-Delta Transformer Bank Backfeed Voltage ... V BG SW C SW B Source 120 volt SW A E E CG E ... • Ungrounded Wye-Delta

SW-C Open With No Motor

Page 41: Ungrounded Wye-Delta Transformer Bank … Wye-Delta Transformer Bank Backfeed Voltage ... V BG SW C SW B Source 120 volt SW A E E CG E ... • Ungrounded Wye-Delta

NMSU System •  Thesystemwascreatedinordertoanalyzehowtheungroundedwye-deltabankbehavesundernormalandabnormalcondi4ons–  Thesystemwasstudiedunderano-loadcondi4onusingaMathcadrou4ne

–  ThesystemwassetupintheNMSUpowerlaboratorytochecktheresultsfortheno-loadcondi4on

–  Theresultswereverifiedtakingintoaccountthe“ideal”vs.realtransformers

Page 42: Ungrounded Wye-Delta Transformer Bank … Wye-Delta Transformer Bank Backfeed Voltage ... V BG SW C SW B Source 120 volt SW A E E CG E ... • Ungrounded Wye-Delta

12.47 kV System

•  Ungrounded Wye-Delta – Can serve 120/240 volt single-phase loads and a

three-phase induction motor – Problems when one phase is open

•  Voltage unbalance on motor will cause the motor relay to trip the motor off •  If the open phase is serving the center tap transformer

there will be a nominal line-to-ground voltage of 3600 volts at transformer side of the open switch

Page 43: Ungrounded Wye-Delta Transformer Bank … Wye-Delta Transformer Bank Backfeed Voltage ... V BG SW C SW B Source 120 volt SW A E E CG E ... • Ungrounded Wye-Delta

12.47 System Conculations (cont.)

– Whentheopenswitchisservingoneofthepowertransformerstheline-to-groundvoltageatthetransformersideoftheopenswitchis19,049volts

– The19,049voltsis2.654mestheratedline-to-groundvoltageofthesystem

Page 44: Ungrounded Wye-Delta Transformer Bank … Wye-Delta Transformer Bank Backfeed Voltage ... V BG SW C SW B Source 120 volt SW A E E CG E ... • Ungrounded Wye-Delta

Conclusions

•  Thecombina4on120/240voltsingle-phaseloadandthree-phaseinduc4onmotorcanbeservedbyagroundedwye-deltaorungroundedwye-deltabank– Groundedwye-deltabank

• Willcon4nuetoservebothloadswithanopenphase•  Problemswithbackfeedshortcircuitcurrentonupstreamgroundfaults

Page 45: Ungrounded Wye-Delta Transformer Bank … Wye-Delta Transformer Bank Backfeed Voltage ... V BG SW C SW B Source 120 volt SW A E E CG E ... • Ungrounded Wye-Delta

Conclusions (cont.) – Ungroundedwye-deltabank

•  Cannotservecombina4onloadswithanopenphase•  Anopenphaseresultsinaveryhighline-to-groundvoltageatthetransformersideoftheopenswitch