wye-delta center tapped xfm test feeder

of 27/27
Chair MARTIN L. BAUGHMAN Professor Emeritus The University of Texas at Austin 5703 Painted Valley Drive Austin, TX 78759 Vice Chair CHEN-CHING LIU Dept. of Electrical Eng. University of Washington Box 352500 Seattle, WA 98195 Vox: 206-543-2198 Fax: 206-543-3842 [email protected] Secretary ROGER C. DUGAN Sr. Consultant Electrotek Concepts, Inc. 408 N Cedar Bluff Rd Knoxville, TN 37923 Vox: 865-470-9222 Fax: 865-470-9223 [email protected] Computer & Analytical Methods EDWIN LIU, Chair Nexant, Inc. 101, 2nd street, 11F San Francisco CA 94105 Vox: 415-369-1088 Fax: 415-369-0894 [email protected] Distribution Systems Analysis SANDOVAL CARNEIRO, JR, Chair Dept. of Electrical Engineering Federal Univ. of Rio de Janeiro Rio de Janeiro, RJ, Brazil Vox: 55-21-25628025 Fax: 55-21-25628628 [email protected] Intelligent System Applications DAGMAR NIEBUR, Chair Department of ECE Drexel University 3141 Chestnut Street Philadelphia, PA 19104 Vox: (215) 895 6749 Fax: (215) 895 1695 [email protected] Reliability, Risk & Probability Applications JAMES D. MCCALLEY, Chair Iowa State University Room 2210 Coover Hall Ames, Iowa 50011 Vox: 515-294-4844 Fax: 515-294-4263 [email protected] Systems Economics ROSS BALDICK, Chair ECE Dept. , ENS 502 The University of Texas at Austin Austin, TX 78712 Vox: 512-471-5879 Fax: 512-471-5532 [email protected] Past Chair JOANN V. STARON Nexant Inc/ PCA 1921 S. Alma School Road Suite 207 Mesa, AZ 85210 Vox: 480-345-7600 The Institute of Electrical and Electronics Engineers, Inc. IEEE POWER ENGINEERING SOCIETY Power System Analysis, Computing and Economics Committee Subcommittee Chairs Distribution System Analysis Subcommittee IEEE Wye-Delta Center Tapped Transformer Test Feeder Data and Solutions Transformer Connections Ungrounded Wye-Delta Grounded Wye-Delta “Leading” Open Wye- Delta “Lagging” Open Wye-Delta

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IEEE POWER ENGINEERING SOCIETY Power System Analysis, Computing and Economics CommitteeChair MARTIN L. BAUGHMAN Professor Emeritus The University of Texas at Austin 5703 Painted Valley Drive Austin, TX 78759 Vox: 512-345-8255 Fax: 512-345-9880 [email protected] Vice Chair CHEN-CHING LIU Dept. of Electrical Eng. University of Washington Box 352500 Seattle, WA 98195 Vox: 206-543-2198 Fax: 206-543-3842 [email protected] Secretary ROGER C. DUGAN Sr. Consultant Electrotek Concepts, Inc. 408 N Cedar Bluff Rd Knoxville, TN 37923 Vox: 865-470-9222 Fax: 865-470-9223 [email protected]

Subcommittee ChairsComputer & Analytical Methods EDWIN LIU, Chair Nexant, Inc. 101, 2nd street, 11F San Francisco CA 94105 Vox: 415-369-1088 Fax: 415-369-0894 [email protected] Distribution Systems Analysis SANDOVAL CARNEIRO, JR, Chair Dept. of Electrical Engineering Federal Univ. of Rio de Janeiro Rio de Janeiro, RJ, Brazil Vox: 55-21-25628025 Fax: 55-21-25628628 [email protected] Intelligent System Applications DAGMAR NIEBUR, Chair Department of ECE Drexel University 3141 Chestnut Street Philadelphia, PA 19104 Vox: (215) 895 6749 Fax: (215) 895 1695 [email protected] Reliability, Risk & Probability Applications JAMES D. MCCALLEY, Chair Iowa State University Room 2210 Coover Hall Ames, Iowa 50011 Vox: 515-294-4844 Fax: 515-294-4263 [email protected] Systems Economics ROSS BALDICK, Chair ECE Dept. , ENS 502 The University of Texas at Austin Austin, TX 78712 Vox: 512-471-5879 Fax: 512-471-5532 [email protected] Past Chair JOANN V. STARON Nexant Inc/ PCA 1921 S. Alma School Road Suite 207 Mesa, AZ 85210 Vox: 480-345-7600 Fax: 480-345-7601 [email protected]

Distribution System Analysis Subcommittee

IEEE Wye-Delta Center Tapped Transformer Test FeederData and Solutions Transformer Connections Ungrounded Wye-Delta Grounded Wye-Delta Leading Open Wye- Delta Lagging Open Wye-Delta

November 2004

The Institute of Electrical and Electronics Engineers, Inc.

1

IEEE Four-Wire Delta Test FeederThe system to be used in testing four wire delta transformer models is shown in Figure 1. This system is used to model the following transformer connections: Ungrounded wye-delta Grounded wye-delta Leading open wye-open delta Lagging open wye-open delta

1Infinite Bus

5 miles [IABC ]

2

3

100 ft. [Iabc ]

4M

120/240

12.47 kV

Figure 1 Four Wire Delta Test Feeder Three-Phase Circuit: The three-phase circuit to be analyzed for the ungrounded wye-delta connection is shown in Figure 2. The grounded wye-delta connection will have a connection from the primary transformer neutral to the distribution line grounded neutral. The leading open wye open delta connection will ground the transformer primary neutral and remove the transformer on phase C. The lagging open wye open delta connection will remove the transformer on phase B from the original connection.VB B EB EA A

IBVA

+

+ G

+

+ZA

IA

VTAN

VTBN

ZB

EC

- IN

-

VNG

+

N

-

Ungrounded Wye Primary

Equivalent Generator

VTCN

ICVC

ZC

+C

++ San +

aZa

Ia+

Vtan-

+ + +

va

Ina Vtca Iac

nZb

Van In

ILan

VLanSab

IMa ILab VLca

Vtnb

IbnIcb + Vtbc + c Closed Delta Secondary

Vnb - vb b+ Vbc-

ILnb

Sbn +

VLnb

3-Phase Load or Motor

Ib VLbc Ic

IMb IMc

vc Secondary Loads

-

+

Figure 2 Three-Phase Circuit

The Institute of Electrical and Electronics Engineers, Inc.

2

Equivalent Source Balanced line-to-ground voltages of 7200 volts with abc rotation. Primary Line: The primary line will be constructed using the pole configuration shown in Figure 3.a2.5'

c

4.5' 3.0'

b

4.0'

n 24.0'

Figure 3 Pole Configuration Phase Conductors: 556,500 26/7 ACSR GMR = 0.0313 ft., Resistance = 0.1859 /mile, Diameter = 0.927 inch Neutral Conductor: 4/0 6/1 ACSR GMR = 0.00814 ft., Resistance = 0.492 /mile, Diameter = 0.563 inch Length of line = 5 miles Primitive four -wire impedance0.7266j 0.0953+ 0.8515j 0.0953+ matrix: 0.2812+ 1.383j 0.0953+ 0.0953+ 0.7266j 0.2812+ 1.383j 0.0953+ 0.7802j 0.0953+ zp = 0.0953+ 0.8515j 0.0953+ 0.7802j 0.2812+ 1.383j 0.0953+ 0.0953+ 0.7524j 0.0953+ 0.7674j 0.0953+ 0.7865j 0.6873+ Kron reduced equivalent three-wire impedance matrix: 0.3375+ 1.0478j 0.1535+ 0.3849j 0.1559+ 0.5017j 0.1535+ 0.3849j 0.3414+ 1.0348j 0.158 + 0.4236j zabc = 0.1559+ 0.5017j 0.158 + 0.4236j 0.3465+ 1.0179j /mile 0.7524j 0.7674j

/mile

0.7865j1.5465j

The Institute of Electrical and Electronics Engineers, Inc.

3

Secondary Line: The secondary line is quadraplex cable as shown in Figure 4.

b

a

c

nFigure 4 Quadraplex Cable Phase Conductor: 4/0 AA GMR = 0.0158 ft., Resistance = 0.484 /mile, Diameter = 0.522 inch Neutral Conductor: 4/0 6/1 ACSR GMR = 0.00814 ft., Resistance = 0.592 /mile, Diameter = 0.563 inch Insulation Thickness = 0.2 inch Length of Secondary = 100 ft. Four Wire Impedance Matrix: 0.5793+ 1.466j 0.0953+ 1.2741j 0.0953+ 1.2741j 0.0953+ 0.0953+ 1.2741j 0.5793+ 1.466j 0.0953+ 1.2741j 0.0953+ zq = 0.0953+ 1.2741j 0.0953+ 1.2741j 0.5793+ 1.466j 0.0953+ 0.0953+ 1.3004j 0.0953+ 1.2251j 0.0953+ 1.3004j 0.6873+ Kron Reduced Equivalent Three-Wire Impedance Matrix: 0.8491+ 0.4984j 0.3455+ 0.361j 0.3651+ 0.3064j zsec = 0.3455+ 0.361j 0.8112+ 0.6044j 0.3455+ 0.361j 0.3651+ 0.3064j 0.3455+ 0.361j 0.8491+ 0.4984j /mile1.3004j 1.2251j

/mile

1.3004j1.5465j

The Institute of Electrical and Electronics Engineers, Inc.

4

Transformer Data Power Transformers Phase A: per-unit

10 kVA, 7200-120/240,

ZP = 0.016 + j0.014 ZL =0.012 + j0.017

Lighting Transformers Phase B &C: 25 kVA, 7200-120/240, per-unit For an interlaced lighting transformer: Z A = 0.5 RL + j 0.8 X L Z a = Zb = RL + j 0.4 X L per-unit

Impedances in Ohms per the circuit diagram of Figure 5: Z A = 12.4416 + j 28.201 Z a = Zb = 0.006912 + j 0.003917 Z B = ZC = 82.944 + j 72.576 Ohms

The connection diagram for the three transformers connected in ungrounded wye-delta is shown in Figure 5.

+VAN

ZA IA

+ _

VTAN

_ +VBN IB ZB

+ _ Vtan + Vtnb _ + Vtbc _ + Vtca _

Za Ina Ibn Icb

Ia In Ib

Zb

+ _

VTBN

_VCN

+ _

ZC IC

+ _

Iac

Ic

VTCN

G

_

VNG +

Figure 5 Transformer Connection Diagram

The Institute of Electrical and Electronics Engineers, Inc.

5

Load Data Three-Phase Induction Motor: 25 Hp, 240 volt Z stator = 0.0774 + j 0.1843 Z rotor = 0.0908 + j 0.1843 Z m = 0 + j 4.8384 Slip = 0.035 Three-phase motor admittance and impedance matrices for slip = 0.035 0.7452 0.4074j 0.0999 0.0923j 0.3547+ 0.4997j S YMabc = 0.3547+ 0.4997j 0.7452 0.4074j 0.0999 0.0923j 0.0999 0.0923j 0.3547+ 0.4997j 0.7452 0.4074j 1.0991+ 1.3888j 0.9987 0.3165j 0.8996 1.0723j ZMabc = 0.8996 1.0723j 1.0991+ 1.3888j 0.9987 0.3165j 0.9987 0.3165j 0.8996 1.0723j 1.0991+ 1.3888j NEMA Voltage and Current Unbalance Equation: Unbalance = Lighting Loads: SLan = 3 kVA at 0.95 lagging power factor SLbn = 5 kVA at 0.85 lagging power factor SLab = 10 kVA at 0.90 lagging power factor Maximum Deviation from Average Average 100%

Ohms

The Institute of Electrical and Electronics Engineers, Inc.

Ungrounded Wye-Delta Solution

VB B EB EA A

IBVA

+

+

+

IA

ZA

VTAN

VTBN

ZB

+

G

EC

IN

-

VNG

- + N -

Ungrounded Wye Primary

Equivalent Generator

VTCN

ICVC

ZC

+C

+

a Za

Ia + Vtan nZb

+ +

va ILan In San

+ +

Van

VLan Sab VLnb ILab

IMa VLca

Ina Vtca Iac

+ Vtnb

Ibn Icb + Vtbc + c -

- b+

Vnb vb Ib Vbc

ILnb

Sbn +

3-Phase Load or Motor

IMb VLbc IMc

-

Ic vc Secondary

Loads

+

Closed Delta Secondary

Source LG VoltagesES AG = 7, 200/ 0 ES BG = 7, 200/ 120 ESCG = 7, 200/120

Source LL VoltagesES AB = 12, 470.77/ 30 ES BC = 12, 470.77/ 90 V ESCA = 12, 470.77/150

V

Primary Line Voltage Dropsv A = 8.6057/ 47.57 vB = 6.1279/ 104.47 vC = 4.5188/174.26 vN = 0

End of Line LG VoltagesV AG = 7,194.20/ 0.05

V

VBG = 7,194.10/ 120.01 VCG = 7,197.36/119.97

Transformer Primary LN VoltagesV AN = 7,130.94/ 0.08 VBN = 7, 228.90/ 120.43 VCN = 7, 226.22/120.42

Transformer Primary LL VoltagesV AB = 12, 458.27/ 29.97 VBC = 12, 464.38/ 90.01 V VCA = 12, 464.80/149.95

V

The Institute of Electrical and Electronics Engineers, Inc.

Neutral to Ground Voltage at Transformer PrimaryVNG = 63.3576/ 3.10

V Primary Line, Neutral and Ground CurrentsI A = 2.7513/ 29.37 I B = 1.7654/ 175.76

Primary Windings Ideal VoltagesVTAN = 7, 063.30/ 0.49 VTBN = 7, 040.38/ 120.05 VTCN = 7, 079.80/119.61

V

IC = 1.6112/113.29 I N = 0.0403/ 21.28 IG = 0.0403/158.72

A

Transformer Secondary Windings Ideal Voltages Transformer Secondary Terminal VoltagesVtan = 117.72/ 0.49 Vtnb = 117.72/ 0.49 Vtbc = 234.68/ 120.05 Vtca = 235.99/119.61Van = 117.14/ 0.51 Vnb = 116.99/ 0.48

A

Vab = 234.13/ 0.50 V Vbc = 234.68/ 120.05 Vca = 235.99/119.61

Transformer Secondary Winding Currents CurrentsI na = 73.67/ 26.59 Ibn = 91.56/ 31.61 I cb = 52.96/ 175.76 I ac = 48.34/113.29

Secondary

Line,

Neutral

and

Ground

I a = 114.93/ 41.32 Ib = 138.02/161.37

A

I c = 58.91/ 55.09 I n = 10.59/ 51.66 I g = 8.69/ 50.55

A

Secondary Line Voltage Dropsva = 1.0321/ 30.14 vb = 1.5515/ 172.65 vc = 0.4488/ 94.39 vn = 0

Single-Phase Load VoltagesVLan = 116.24/ 0.26 VLnb = 115.46/ 0.59 V VLab = 231.70/ 0.42

V

Single-Phase Load Currents

Single-Phase Complex Powers

The Institute of Electrical and Electronics Engineers, Inc.

ILan = 25.81/ 18.45 ILnb = 43.31/ 32.38 ILab = 43.16/ 26.26

VLan ( ILan ) San = 1000

* = 3.0 @ 0.95 PF * * = [email protected] 0.90 PF = 5.0 @ 0.85 PF kVA

A

Snb = Sab =

VLnb ( ILnb ) 1000 VLab ( ILab ) 1000

Motor LL VoltagesVLab = 231.70/ 0.42 VLbc = 233.37/ 119.81 V VLca = 234.70/119.53

Motor Line CurrentsIM a = 54.65/ 66.49 IM b = 55.54/178.15 IM c = 58.91/ 55.09

A

Transformer Operating kVAs* V ( IA) S A = AN = 17.11 + j 9.60 = 19.62 _ kVA @ 0.87 _ PF 1000 * V ( IB ) S B = BN = 7.26 + j10.50 = 12.76 _ kVA @0.57 _ PF 1000 * V ( IC ) SC = CN = 11.55 + j1.45 = 11.64 _ kVA @0.99 _ PF 1000

INDUCTION MOTOR ANALYSIS Stator Input Complex PowerS stator = 18.83 + j12.79 _ kVA S stator = 22.77 _ kVA @ 0.8271_ PF

Rotor CurrentsIrotora = 45.89/ 38.29 Irotorb = 48.63/ 154.15 A Irotorc = 50.24/ 81.13

LossesStatorloss = 738.65 Rotorloss = 634.91 Totalloss = 1,373.56

Converted Shaft Power WPconverted = 17.46 _ kW kW Pconverted = 23.40 _ Hp

NEMA Unbalances Vaverage = 233.2543 Maximum Deviation = 1.5561 1.5561 Vunbalance = 100 = 0.6671 % 233.2543 Grounded Wye-Delta Solution The Institute of Electrical and Electronics Engineers, Inc.

Vunbalance = 0.6671 % Iunbalance = 3.0525

VB B EB EA A IB VA

+

+

+

IA

ZA

VTAN

VTBN

ZB

+

G

EC

IN

-

VNG

- N + -

Ungrounded Wye Primary

Equivalent Generator

VTCN

ICVC

ZC

+C

++ San + ILnb Sbn Ib + VLbc Ic IMc Loads +

a Za

Ia + Vtan Ina + nZb

va ILan

Van In Vnb vb

VLan Sab VLnb ILab

+

-

IMa VLca

+ + Vtnb - b+ +

VLab

3-Phase Load or Motor

Vtca Iac

Ibn Icb Vtbc + c -

IMb

Vbc -

vc Secondary

Closed Delta Secondary

Source LG VoltagesES AG = 7, 200/ 0 ES BG = 7, 200/ 120 ESCG = 7, 200/120

Source LL VoltagesES AB = 12, 470.77/ 30 ES BC = 12, 470.77/ 90 V ESCA = 12, 470.77/150

V

Primary Line Voltage Dropsv A = 15.1049/ 38.92 vB = 5.1143/ 35.34 vC = 3.8637/ 68.05 vN = 0

End of Line LG VoltagesV AG = 7,188.25/ 0.08

V

VBG = 7,199.53/ 120.04 V VCG = 7,197.62/120.02

Transformer Primary LN VoltagesV AN = 7,188.25/ 0.08 VBN = 7,199.53/ 120.04 VCN = 7,197.62/120.02

Transformer Primary LL VoltagesV AB = 12, 457.98/ 29.97 VBC = 12, 464.22/ 90.01 V VCA = 12, 464.80/149.95

V

Neutral to Ground Voltage at Transformer Primary The Institute of Electrical and Electronics Engineers, Inc.

VNG = 0

V Primary Line, Neutral and Ground CurrentsI A = 3.3974/ 32.26 I B = 1.3949/ 155.69

Primary Windings Ideal VoltagesVTAN = 7,101.69/ 0.55 VTBN = 7, 046.53/ 120.16 VTCN = 7, 089.46/119.70

V

IC = 1.0480/ 99.22 I N = 0.8621/153.32 IG = 1.1719/124.49

A

Transformer Secondary Windings Ideal Voltages Transformer Secondary Terminal VoltagesVtan = 118.36/ 0.55 Vtnb = 118.36/ 0.55 Vtbc = 234.88/ 120.16 Vtca = 236.32/119.70Van = 117.62/ 0.55 Vnb = 117.48/ 0.52

A

Vab = 235.10/ 0.53 V Vbc = 234.88/ 120.16 Vca = 236.32/119.70

Transformer Secondary Winding Currents CurrentsI na = 92.89/ 30.34 Ibn = 111.05/ 33.87 I cb = 41.85/ 155.69 I ac = 31.44/ 99.22

Secondary

Line,

Neutral

and

Ground

I a = 115.49/ 42.45 Ib = 137.78/161.09

A

I c = 58.52/ 55.56 I n = 10.51/ 51.69 I g = 8.68/ 50.60

A

Secondary Line Voltage Dropsva = 1.0378/ 30.23 vb = 1.5485/ 172.90 vc = 0.4468/ 95.11 vn = 0

Single-Phase Load VoltagesVLan = 116.72/ 0.29 VLnb = 115.95/ 0.62 V VLab = 232.69/ 0.46

V

The Institute of Electrical and Electronics Engineers, Inc.

Single-Phase Load CurrentsILan = 25.70/ 18.49 ILnb = 43.12/ 32.41 ILab = 42.98/ 26.30

Single-Phase Complex PowersSan = VLan ( ILan ) 1000 * = 3.0 @ 0.95 PF * * = [email protected] 0.90 PF = 5.0 @ 0.85 PF kVA

A

VLnb ( ILnb ) Snb = 1000 VLab ( ILab ) Sab = 1000

Motor LL VoltagesVLab = 232.69/ 0.46 VLbc = 233.58/ 119.92 V VLca = 235.01/119.62

Motor Line CurrentsIM a = 54.45/ 66.28 IM b = 55.46/177.41 IM c = 58.52/ 55.56

A

Transformer Operating kVAsSA = V AN ( I A ) 1000 * = 20.67 + j13.00 = 24.42 _ kVA @0.85 _ PF

* V ( IB ) S B = BN = 8.16 + j 5.85 = 10.04 _ kVA @0.81_ PF 1000 * VCN ( IC ) SC = = 7.05 + j 2.68 = 7.54 _ kVA @ 0.93 _ PF 1000

INDUCTION MOTOR ANALYSIS Stotor Input Complex PowerS stator = 18.91 + j12.85 _ kVA S stator = 22.86 _ kVA @ 0.8272 _ PF

Rotor CurrentsIrotora = 46.67/ 38.46 Irotorb = 48.26/ 154.77 A Irotorc = 50.10/ 81.84

LossesStatorloss = 741.21 Rotorloss = 636.97 Totalloss = 1,378.18

Converted Shaft PowerPconverted = 17.53 _ kW kW Pconverted = 23.50 _ Hp

W

NEMA UnbalancesVunbalance = 0.5375 % Iunbalance = 1.8197

Leading Open Wye-Delta Solution The Institute of Electrical and Electronics Engineers, Inc.

VB B EB EA

IB A

+

+

VA

IA

ZA

+ VTAG - -

VTBG + ZB

G

EC

IN

_

G

Leading Open Wye-Open Delta

Equivalent Generator

VCG ICVC

+C

+

a Za

Ia + Vtan n Ina Zb

+ +

va ILan In San

+ +

Van

VLan Sab VLnb ILab

IMa VLca

+ Vtnb

Vca Icb

Ibn

- b+ +

Vnb vb Ib Vbc Ic vc Secondary

ILnb

Sbn +

3-Phase Load or Motor

IMb VLbc IMc

Vtbc + c Open Delta Secondary -

Loads

+

Source LG VoltagesES AG = 7, 200/ 0 ES BG = 7, 200/ 120 ESCG = 7, 200/120

Source LL VoltagesES AB = 12, 470.77/ 30 ES BC = 12, 470.77/ 90 V ESCA = 12, 470.77/150

V

Primary Line Voltage Dropsv A = 23.3548/ 21.30 vB = 14.10/ 18.11 vC = 11.81/10.64 vN = 0

End of Line LG VoltagesV AG = 7,178.25/ 0.07

V

VBG = 7, 202.92/ 120.11 V VCG = 7, 203.93/120.09

Transformer Primary LN VoltagesV AN = 7,178.25/ 0.07 VBN = 7, 202.92/ 120.11 V

Transformer Primary LL VoltagesV AB = 12, 457.10/ 29.97 VBC = 12, 464.20/ 90.01 VCA = 12, 465.13/149.95

V

Neutral to Ground Voltage at Transformer Primary

The Institute of Electrical and Electronics Engineers, Inc.

VNG = 0

V Primary Line, Neutral and Ground CurrentsI A = 4.1845/ 41.44

Primary Windings Ideal Voltages

VTAN = 7, 061.39/ 0.51 VTBN = 7, 035.15/ 121.03

I B = 1.845/ 127.42

V

IC = 0 I N = 2.1109/131.85 IG = 2.7298/102.88

A

Transformer Secondary Windings Ideal Voltages Transformer Secondary Terminal VoltagesVtan = 117.69/ 0.51 Vtnb = 117.69/ 0.51 Vtbc = 234.51/ 121.03Van = 116.78/ 0.42 Vnb = 116.64/ 0.40

A

Vab = 233.42/ 0.41 V Vbc = 234.51/ 121.03 Vca = 231.76/119.05

Transformer Secondary Winding Currents CurrentsI na = 116.00/ 40.64 Ibn = 135.08/ 42.12 I cb = 55.30/ 127.42

Secondary

Line,

Neutral

and

Ground

I a = 116.01/ 40.64 Ib = 141.71/160.77

A

I c = 55.30/ 52.58 I n = 10.49/ 51.96 I g = 8.87/ 49.96

A

Secondary Line Voltage Dropsva = 1.0372/ 28.49 vb = 1.5893/ 173.14 vc = 0.4032/ 93.07 vn = 0

Single-Phase Load VoltagesVLan = 115.87/ 0.18 VLnb = 115.06/ 0.50 V VLab = 230.93/ 0.34

V

The Institute of Electrical and Electronics Engineers, Inc.

Single-Phase Load CurrentsILan = 25.89/ 18.38 ILnb = 43.45/ 32.29 ILab = 43.30/ 26.18

Single-Phase Complex PowersSan = VLan ( ILan ) 1000 * = 3.0 @ 0.95 PF * * = [email protected] 0.90 PF = 5.0 @ 0.85 PF kVA

A

VLnb ( ILnb ) Snb = 1000 VLab ( ILab ) Sab = 1000

Motor LL VoltagesVLab = 230.93/ 0.34 VLbc = 233.20/ 120.78 V VLca = 230.83/118.95

Motor Line CurrentsIM a = 54.19/ 63.01 IM b = 58.36/175.71 IM c = 55.30/ 52.58

A

Transformer Operating kVAsSA = V AN ( I A ) 1000 * = 22.54 + j19.85 = 30.04 _ kVA @ 0.75 _ PF

* V ( IB ) S B = BN = 13.17 + j1.69 = 13.28 _ kVA @ 0.99 _ PF 1000

INDUCTION MOTOR ANALYSIS Stotor Input Complex PowerS stator = 18.56 + j12.61_ kVA S stator = 22.43 _ kVA @ 0.8271_ PF

Rotor CurrentsIrotora = 47.19/ 34.79 Irotorb = 50.24/ 158.18 A Irotorc = 46.27/ 80.19

LossesStatorloss = 727.81 Rotorloss = 625.57 Totalloss = 1,353.38

Converted Shaft PowerPconverted = 17.20 _ kW kW Pconverted = 23.06 _ Hp

W

NEMA UnbalancesVunbalance = 0.7103 % Iunbalance = 4.3100

Lagging Open Wye-Delta Solution The Institute of Electrical and Electronics Engineers, Inc.

VB B EB EA A

IBVA

+

+

IA

ZA

+ VTAN N

G

EC

IN

-

VNG

+

VTCN

Equivalent Generator

+ICVC ZC

+C

a Za

Ia + Vtan nZb

+ +

va ILan In San

+ +

Van

VLan Sab VLnb ILab

IMa VLca

Ina Vtca Iac

+ Vtnb

Ibn

- b+

Vnb vb Ib Vbc Ic vc Secondary

ILnb

Sbn +

3-Phase Load or Motor

IMb VLbc IMc

+ c

-

Loads

+

Source LG VoltagesES AG = 7, 200/ 0 ES BG = 7, 200/ 120 ESCG = 7, 200/120

Source LL VoltagesES AB = 12, 470.77/ 30 ES BC = 12, 470.77/ 90 V ESCA = 12, 470.77/150

V

Primary Line Voltage Dropsv A = 24.51/ 64.26 vB = 10.26/ 72.96 vC = 16.36/ 90.38 vN = 0

End of Line LG VoltagesV AG = 7,189.39/ 0.18

V

VBG = 7, 210.00/ 119.98 V VCG = 7,185.78/120.06

Transformer Primary LN VoltagesV AN = 7,189.39/ 0.18

Transformer Primary LL VoltagesV AB = 12, 458.03/ 29.97 VBC = 12, 464.22/ 90.01 V VCA = 12, 464.32/149.95

VVCN = 7,185.78/120.06

The Institute of Electrical and Electronics Engineers, Inc.

Neutral to Ground Voltage at Transformer PrimaryVNG = 0

V Primary Line, Neutral and Ground CurrentsI A = 4.2202/ 19.26 IB = 0

Primary Windings Ideal VoltagesVTAN = 7,101.50/ 0.95

VVTCN = 6,990.71/120.29

IC = 1.8647/ 60.80 I N = 2.2118/ 159.62 IG = 2.8708/169.27

A

Transformer Secondary Windings Ideal Voltages Transformer Secondary Terminal VoltagesVtan = 118.36/ 0.95 Vtnb = 118.36/ 0.95 Vtca = 233.02/120.59Van = 117.44/ 1.05 Vnb = 117.30/ 1.03

A

Vab = 234.74/ 1.04 V Vbc = 228.11/ 120.60 Vca = 233.02/120.59

Transformer Secondary Winding Currents CurrentsI na = 118.61/ 16.77 Ibn = 134.81/ 21.45 I ac = 55.94/ 60.80

Secondary

Line,

Neutral

and

Ground

I a = 119.75/ 43.91 Ib = 134.81/158.55

A

I c = 55.94/ 60.80 I n = 10.42/ 50.89 I g = 8.79/ 52.63

A

Secondary Line Voltage Dropsva = 1.0761/ 31.40 vb = 1.5204/ 175.23 vc = 0.4456/103.16 vn = 0

Single-Phase Load VoltagesVLan = 116.52/ 0.79 VLnb = 115.95/ 1.10 V VLab = 232.30/ 0.94

V

The Institute of Electrical and Electronics Engineers, Inc.

Single-Phase Load Currents

Single-Phase Complex PowersSan = VLan ( ILan ) 1000 VLnb ( ILnb ) 1000 VLab ( ILab ) 1000 * = 3.0 @ 0.95 PF * * = [email protected] 0.90 PF = 5.0 @ 0.85 PF kVA

ILan = 25.75/ 18.98 ILnb = 43.18/ 32.89 ILab = 43.05/ 26.79

A

Snb = Sab =

Motor LL VoltagesVLab = 232.30/ 0.94 VLbc = 226.91/ 120.37 V VLca = 231.65/120.50

Motor Line CurrentsIM a = 60.06/ 66.97 IM b = 51.20/172.76 IM c = 55.94/ 60.80

A

Transformer Operating kVAs* V ( IA) S A = AN = 28.67 + j 9.92 = 30.34 _ kVA @0.95 _ PF 1000 * V ( IC ) SC = CN = 6.85 + j11.52 = 13.40 _ kVA @ 0.51_ PF 1000

INDUCTION MOTOR ANALYSIS Stotor Input Complex PowerS stator = 18.36 + j12.49 _ kVA S stator = 22.21_ kVA @ 0.8268 _ PF

Rotor CurrentsIrotora = 50.41/ 41.89 Irotorb = 42.67/ 157.40 A Irotorc = 50.09/ 87.85

LossesStatorloss = 724.45 Rotorloss = 623.74 Totalloss = 1,348.20

Converted Shaft PowerPconverted = 17.01_ kW kW Pconverted = 22.80 _ Hp

W

NEMA UnbalancesVunbalance =1.4663 % Iunbalance = 8.1399

The Institute of Electrical and Electronics Engineers, Inc.