wye-delta center tapped xfm test feeder

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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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Page 1: Wye-Delta Center Tapped Xfm Test Feeder

ChairMARTIN L. BAUGHMANProfessor EmeritusThe University of Texas at Austin5703 Painted Valley DriveAustin, TX 78759Vox: 512-345-8255Fax: [email protected]

Vice ChairCHEN-CHING LIUDept. of Electrical Eng. University of WashingtonBox 352500Seattle, WA 98195Vox: 206-543-2198Fax: [email protected]

SecretaryROGER C. DUGANSr. ConsultantElectrotek Concepts, Inc.408 N Cedar Bluff RdKnoxville, TN 37923Vox: 865-470-9222Fax: [email protected] & Analytical Methods

EDWIN LIU, ChairNexant, Inc.101, 2nd street, 11FSan Francisco CA 94105Vox: 415-369-1088Fax: [email protected]

Distribution Systems AnalysisSANDOVAL CARNEIRO, JR, ChairDept. of Electrical EngineeringFederal Univ. of Rio de JaneiroRio de Janeiro, RJ, BrazilVox: 55-21-25628025Fax: 55-21-25628628 [email protected]

Intelligent System ApplicationsDAGMAR NIEBUR, ChairDepartment of ECEDrexel University3141 Chestnut StreetPhiladelphia, PA 19104Vox: (215) 895 6749Fax: (215) 895 [email protected]

Reliability, Risk & Probability ApplicationsJAMES D. MCCALLEY, ChairIowa State UniversityRoom 2210 Coover HallAmes, Iowa 50011Vox: 515-294-4844Fax: [email protected]

Systems EconomicsROSS BALDICK, ChairECE Dept. , ENS 502The University of Texas at AustinAustin, TX 78712Vox: 512-471-5879Fax: [email protected]

Past ChairJOANN V. STARONNexant Inc/ PCA1921 S. Alma School RoadSuite 207Mesa, AZ 85210Vox: 480-345-7600Fax: [email protected]

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

November 2004

Page 2: Wye-Delta Center Tapped Xfm Test Feeder

The Institute of Electrical and Electronics Engineers, Inc.

1

IEEE Four-Wire Delta Test Feeder

The 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

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.

Figure 2 – Three-Phase Circuit

Page 3: Wye-Delta Center Tapped Xfm Test Feeder

The Institute of Electrical and Electronics Engineers, Inc.

2

Equivalent SourceBalanced 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.

Figure 3 – Pole Configuration

Phase Conductors: 556,500 26/7 ACSRGMR = 0.0313 ft., Resistance = 0.1859 Ω/mile, Diameter = 0.927 inch

Neutral Conductor: 4/0 6/1 ACSRGMR = 0.00814 ft., Resistance = 0.492 Ω/mile, Diameter = 0.563 inch

Length of line = 5 miles

Primitive four -wire impedance matrix:

Kron reduced equivalent three-wire impedance matrix:

zp

0.2812 1.383j

0.0953 0.7266j

0.0953 0.8515j

0.0953 0.7524j

0.0953 0.7266j

0.2812 1.383j

0.0953 0.7802j

0.0953 0.7674j

0.0953 0.8515j

0.0953 0.7802j

0.2812 1.383j

0.0953 0.7865j

0.0953 0.7524j

0.0953 0.7674j

0.0953 0.7865j

0.6873 1.5465j

/mile

zabc

0.3375 1.0478j

0.1535 0.3849j

0.1559 0.5017j

0.1535 0.3849j

0.3414 1.0348j

0.158 0.4236j

0.1559 0.5017j

0.158 0.4236j

0.3465 1.0179j

/mile

Page 4: Wye-Delta Center Tapped Xfm Test Feeder

The Institute of Electrical and Electronics Engineers, Inc.

3

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

Figure 4 – Quadraplex Cable

Phase Conductor: 4/0 AAGMR = 0.0158 ft., Resistance = 0.484 Ω/mile, Diameter = 0.522 inch

Neutral Conductor: 4/0 6/1 ACSRGMR = 0.00814 ft., Resistance = 0.592 Ω/mile, Diameter = 0.563 inch

Insulation Thickness = 0.2 inchLength of Secondary = 100 ft.

Four Wire Impedance Matrix:

Kron Reduced Equivalent Three-Wire Impedance Matrix:

zq

0.5793 1.466j

0.0953 1.2741j

0.0953 1.2741j

0.0953 1.3004j

0.0953 1.2741j

0.5793 1.466j

0.0953 1.2741j

0.0953 1.2251j

0.0953 1.2741j

0.0953 1.2741j

0.5793 1.466j

0.0953 1.3004j

0.0953 1.3004j

0.0953 1.2251j

0.0953 1.3004j

0.6873 1.5465j

/mile

zsec

0.8491 0.4984j

0.3455 0.361j

0.3651 0.3064j

0.3455 0.361j

0.8112 0.6044j

0.3455 0.361j

0.3651 0.3064j

0.3455 0.361j

0.8491 0.4984j

/mile

Page 5: Wye-Delta Center Tapped Xfm Test Feeder

The Institute of Electrical and Electronics Engineers, Inc.

4

Transformer DataPower Transformers Phase A: 10 kVA, 7200-120/240, ZP = 0.016 + j0.014 per-unit

Lighting Transformers Phase B &C: 25 kVA, 7200-120/240, ZL =0.012 + j0.017 per-unit

For an interlaced lighting transformer:

per-unit

Impedances in Ohms per the circuit diagram of Figure 5:

Ohms

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

Figure 5 – Transformer Connection Diagram

Page 6: Wye-Delta Center Tapped Xfm Test Feeder

The Institute of Electrical and Electronics Engineers, Inc.

5

Load DataThree-Phase Induction Motor:

25 Hp, 240 volt

Ohms

Slip = 0.035

Three-phase motor admittance and impedance matrices for slip = 0.035

NEMA Voltage and Current Unbalance Equation:

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

YMabc

0.7452 0.4074j

0.3547 0.4997j

0.0999 0.0923j

0.0999 0.0923j

0.7452 0.4074j

0.3547 0.4997j

0.3547 0.4997j

0.0999 0.0923j

0.7452 0.4074j

S

ZMabc

1.0991 1.3888j

0.8996 1.0723j

0.9987 0.3165j

0.9987 0.3165j

1.0991 1.3888j

0.8996 1.0723j

0.8996 1.0723j

0.9987 0.3165j

1.0991 1.3888j

Page 7: Wye-Delta Center Tapped Xfm Test Feeder

The Institute of Electrical and Electronics Engineers, Inc.

Ungrounded Wye-Delta Solution

Source LG Voltages Source LL Voltages

V V

Primary Line Voltage Drops End of Line LG Voltages

V

Transformer Primary LN Voltages Transformer Primary LL Voltages

V V

Page 8: Wye-Delta Center Tapped Xfm Test Feeder

The Institute of Electrical and Electronics Engineers, Inc.

Neutral to Ground Voltage at Transformer Primary

V

Primary Windings Ideal Voltages Primary Line, Neutral and Ground Currents

V A

Transformer Secondary Windings Ideal Voltages Transformer Secondary Terminal Voltages

A V

Transformer Secondary Winding Currents Secondary Line, Neutral and Ground Currents

A A

Secondary Line Voltage Drops Single-Phase Load Voltages

V V

Single-Phase Load Currents Single-Phase Complex Powers

Page 9: Wye-Delta Center Tapped Xfm Test Feeder

The Institute of Electrical and Electronics Engineers, Inc.

A kVA

Motor LL Voltages Motor Line Currents

V A

Transformer Operating kVAs

INDUCTION MOTOR ANALYSIS

Stator Input Complex Power Rotor Currents

A

Losses Converted Shaft Power

W kW

NEMA Unbalances

%

Grounded Wye-Delta Solution

Page 10: Wye-Delta Center Tapped Xfm Test Feeder

The Institute of Electrical and Electronics Engineers, Inc.

Source LG Voltages Source LL Voltages

V V

Primary Line Voltage Drops End of Line LG Voltages

V V

Transformer Primary LN Voltages Transformer Primary LL Voltages

V V

Neutral to Ground Voltage at Transformer Primary

Page 11: Wye-Delta Center Tapped Xfm Test Feeder

The Institute of Electrical and Electronics Engineers, Inc.

V

Primary Windings Ideal Voltages Primary Line, Neutral and Ground Currents

V A

Transformer Secondary Windings Ideal Voltages Transformer Secondary Terminal Voltages

A V

Transformer Secondary Winding Currents Secondary Line, Neutral and Ground Currents

A A

Secondary Line Voltage Drops Single-Phase Load Voltages

V V

Page 12: Wye-Delta Center Tapped Xfm Test Feeder

The Institute of Electrical and Electronics Engineers, Inc.

Single-Phase Load Currents Single-Phase Complex Powers

A kVA

Motor LL Voltages Motor Line Currents

V A

Transformer Operating kVAs

INDUCTION MOTOR ANALYSIS

Stotor Input Complex Power Rotor Currents

A

Losses Converted Shaft Power

W kW

NEMA Unbalances

%

Leading Open Wye-Delta Solution

Page 13: Wye-Delta Center Tapped Xfm Test Feeder

The Institute of Electrical and Electronics Engineers, Inc.

Source LG Voltages Source LL Voltages

V V

Primary Line Voltage Drops End of Line LG Voltages

V V

Transformer Primary LN Voltages Transformer Primary LL Voltages

V V

Neutral to Ground Voltage at Transformer Primary

Page 14: Wye-Delta Center Tapped Xfm Test Feeder

The Institute of Electrical and Electronics Engineers, Inc.

V

Primary Windings Ideal Voltages Primary Line, Neutral and Ground Currents

V A

Transformer Secondary Windings Ideal Voltages Transformer Secondary Terminal Voltages

A V

Transformer Secondary Winding Currents Secondary Line, Neutral and Ground Currents

A A

Secondary Line Voltage Drops Single-Phase Load Voltages

V V

Page 15: Wye-Delta Center Tapped Xfm Test Feeder

The Institute of Electrical and Electronics Engineers, Inc.

Single-Phase Load Currents Single-Phase Complex Powers

A kVA

Motor LL Voltages Motor Line Currents

V A

Transformer Operating kVAs

INDUCTION MOTOR ANALYSIS

Stotor Input Complex Power Rotor Currents

A

Losses Converted Shaft Power

W kW

NEMA Unbalances

%

Lagging Open Wye-Delta Solution

Page 16: Wye-Delta Center Tapped Xfm Test Feeder

The Institute of Electrical and Electronics Engineers, Inc.

Source LG Voltages Source LL Voltages

V V

Primary Line Voltage Drops End of Line LG Voltages

V V

Transformer Primary LN Voltages Transformer Primary LL Voltages

V V

Page 17: Wye-Delta Center Tapped Xfm Test Feeder

The Institute of Electrical and Electronics Engineers, Inc.

Neutral to Ground Voltage at Transformer Primary

V

Primary Windings Ideal Voltages Primary Line, Neutral and Ground Currents

V A

Transformer Secondary Windings Ideal Voltages Transformer Secondary Terminal Voltages

A V

Transformer Secondary Winding Currents Secondary Line, Neutral and Ground Currents

A A

Secondary Line Voltage Drops Single-Phase Load Voltages

V V

Page 18: Wye-Delta Center Tapped Xfm Test Feeder

The Institute of Electrical and Electronics Engineers, Inc.

Single-Phase Load Currents Single-Phase Complex Powers

A kVA

Motor LL Voltages Motor Line Currents

V A

Transformer Operating kVAs

INDUCTION MOTOR ANALYSIS

Stotor Input Complex Power Rotor Currents

A

Losses Converted Shaft Power

W kW

NEMA Unbalances

%