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

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  • Ungrounded Wye-Delta Transformer Bank Backfeed Voltage

    W. H. Kersting Milsoft Utility Solutions

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

    Transformerconnec4onGroundedwye-delta

    Developsbackfeedshortcircuitcurrentsforupstreamgroundfaults

    Ungroundedwye-delta Purposeofthispaper

  • TypicalSystemOne-LineDiagram

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

    12,470 VSingle-Phase Loads

    M Induction Motor

    1 2 3 4

  • The Three-Phase System

  • 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=

  • 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

  • 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

  • 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

  • Ini6alStudyofNMSUTransformers

    NMSU Power Lab [email protected] rated: 0.5 kVA, 120120/240 Volts, =0+10.036 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

    +__

    +

    + +

  • No-LoadStudiesofNMSUSystem

    Standard30degreeconnec4onssothesecondarywillhavebalancedthree-phasevoltages

    Developequa4onsforsteadystate ModifyforSW-AopenSW-BopenSW-Copen

  • 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 0.5240t

    n = =

    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.

  • 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

    +__

    +

    + +

  • 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

  • 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

    = =

    = = =

    = + =

  • 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

    =

    = =

  • 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

    = =

    = + =

  • 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

    = =

    = + =

  • 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

    +__

    +

    + +

  • 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

  • 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

  • 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

    + = + +

  • 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

  • Open Switch Studies Majorpurposeofthetotalstudywastodeterminewhathappenswhenoneofthethreeupstreamswitchesisopen

    Studiestobecompletedwiththesingle-phaseloadsSW-AopenSW-BopenSW-Copen

  • SW-A Open - Currents

  • 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 BC

    VT V=

    b) 12CN BC

    VT V=

    i) 1bc BNt

    Vt VTn

    =

    ii) 1ca BNt

    Vt VTn

    =

    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

    + + + =

    + =

    + =

    =

  • 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

    = = =

    =

    = = = =

    = + =

    = + =

    = + =

    = =

  • 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

    =

    =

    = =

    = = = =

    = = =

  • 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= =

  • 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

    = = =

    =

    = = = =

    = + =

    = + =

    = + =

    = =

  • 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

    = = =

    =

    = = = =

    = + =

    = + =

    = + =

    = =

  • Summary of Open Switches

  • 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 12 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

    =

    = +

    = +

    =

  • 12.47 kV System Unknowns

    For Mathcad [email protected] 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

    +__

    +

    +

  • WindMil and Mathcad Beforecheckingfortheopenswitchcondi4onstheMathcadrou4neneededtobeverifiedbyrunningWindMiltogetthecorrectanswersunderafull-loadcondi4on.

    WindMilwasfirstrun.TheMathcadrou4neassumesalinearsystemsotheresultsofWindMilwereusedtocomputethesingle-phaseloadequivalentimpedances.

  • 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%

  • SinceWindMilandMathcadresultsareiden4calConfidencethattheMathcadrou4neiscorrectWillusetheMathcadrou4netostudytheopenswitchcondi4ons SW-AOpenwithmotorandsingle-phaseloads Allotherswitchesopenwithmotoroff

  • 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

  • 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

    =

  • SW-B Open With No Motor

  • SW-C Open With No Motor

  • NMSU System Thesystemwascreatedinordertoanalyzehowtheungroundedwye-deltabankbehavesundernormalandabnormalcondi4ons Thesystemwasstudiedunderano-loadcondi4onusingaMathcadrou4ne

    ThesystemwassetupintheNMSUpowerlaboratorytochecktheresultsfortheno-loadcondi4on

    Theresultswereverifiedtakingintoaccounttheidealvs.realtransformers

  • 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

  • 12.47 System Conculations (cont.)

    Whentheopenswitchisservingoneofthepowertransformerstheline-to-groundvoltageatthetransformersideoftheopenswitchis19,049volts

    The19,049voltsis2.654mestheratedline-to-groundvoltageofthesystem

  • Conclusions

    Thecombina4on120/240voltsingle-phaseloadandthree-phaseinduc4onmotorcanbeservedbyagroundedwye-deltaorungroundedwye-deltabankGroundedwye-deltabank

    Willcon4nuetoservebothloadswithanopenphase Problemswithbackfeedshortcircuitcurrentonupstreamgroundfaults

  • Conclusions (cont.) Ungroundedwye-deltabank

    Cannotservecombina4onloadswithanopenphase Anopenphaseresultsinaveryhighline-to-groundvoltageatthetransformersideoftheopenswitch