Subcommittee Subcomm ittee Chairs Computer & Analytical Methods EDWIN LIU, Chair Nexant, Inc. 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]
IEEE POWER ENGINEERING SOCIETY Power System Analysis, Computing and Economics Committee Chair 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
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
baughman@mai baughma
[email protected] l.utexas.edu s.edu
[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]
Distribution System Analysis Subcomm Subcommittee ittee
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] [email protected] u
IEEE 4 Node Test Feeder
Systems EconomicsChair ROSS BALDICK, ECE Dept. , ENS 502 The University of Texas at Austin Austin, TX 78712 Vox: 512-471-5879 Fax: 512-471-5532
[email protected] baldick@ece .utexas.edu Past Chair JOANN V. STARON Nexant Inc/ Inc/ PCA 1921 S. Alma School Road Suite 207 Mesa, AZ 85210 Vox: 480-345-7600 Fax: 480-345-7601 joann.staron@pca-co joann.staro
[email protected] rp.com
The Institute of Electrical and Electronics Engineers, Inc.
IEEE 4 Node Test Feeder The system to be use in testing transformer models is shown in Figure 1: 2
1
3
4
25 00 ft ft..
[I34]
2000 ft.
Infinite Bus Bu s
[I12]
Figure 1 – IEEE 4 Node Test Feeder
Both the primary line (Node1-Node 2) and the secondary line (Node 3-node4) will be constructed using the pole configuration shown in Figure 2. 2.5 ' a
4.5 '
b
c 3.0' 4.0'
n 24.0'
Figure 2 – Pole Configuration Phase Conductor: 336,400 26/7 GMR = 0.0244 ft., Resistance = 0.306 Ω/mile, Diameter = 0.721 inch Neutral Conductor: Conductor: 4/0 6/1 ACSR ACSR GMR = 0.00814 ft., Resistance = 0.592 Ω/mile, Diameter = 0.563 inch
The Institute of Electrical and Electronics Engineers, Inc.
Load
The source is a 12.47 kV line-to-line infinite bus.
Three-Phase Transformer Data: Con onne nect ctio ion n
kVA kVA
Steptep-D Dow own n Step-Up
6,0 6,000 6,000
kVLL kVLL-- kVL kVLL-l L-low ow R -
X-
high 12 12.4 .47 7 12 2..47
% 6.0 6.0 6.0
4.16 4.16 24.9
% 1.0 1.0 1.0
Open Wye – Open Delta: (Two Single Phase Transformers Each Rated) Con onne nect ctio ion n kVA kVA
kV-h kV-hig igh h
kV kV--lo low w
Step-Down 2000 Step-Up 2000
7.2 7.2
4.16 24.9
R% 1.0 1.0
X% 6.0 6 6..0
Closed Connections Load Data: Balanced
Unbalanced
1800 0.9 lag
1275 0.85 lag
1800 0.9 lag
1800 0.9 lag
1800 0.9 lag
2375 0.95 lag
Phase-1
kW Power Factor Phase-2
kW Power Factor Phase-3
kW Power Factor
Open Connection Load Data: Phase-1
kW Power Factor
Balanced
Unbalanced
1200 0.9 lag
850 0.85 lag
1200 0.9 lag
1200 0.9 lag
1200 0.9 lag
1583.33 0.95 lag
Phase-2
kW Power Factor Phase-3
kW Power Factor
Loads are connected in grounded wye for four wire line configurations and connected in closed delta for three wire line configurations.
Line Impedances 4-wire configuration:
Phase impedance matrix: zy
=
0 .1 .1 55 55 9+ 0 .5 .50 17 17 j 0.4 0.4666 666+ 1. 1.0482 0482j j 0.15 0.158 8 + 0.4 0.423 236j 6j
0.1535 5+ 0.384 0.3849j 9j 0.153
0.158+ 0.4236j 0.4236j
0.4615 0.4615+ 1. 1.0651j 0651j
Ω/mile
Sequence impedances: 27j zy pos = 0.3061 0.3061+ 0.6 0.627j
Ω/mile
zyzero = 0.773 0.7735 5+ 1. 1.9373j 9373j
Ω/mile
Three wire configuration:
Phase impedance matrix: zd
=
0 .0 .0 95 95 3+ 0 .8 .85 15 15 j 0.4 0.4013 013+ 1. 1.4 4 133j 0.095 0.0953 3+ 0.7 0.7802j 802j
0.726 266j 6j 0.0953+ 0.7 0.7802j 802j 0.4 0.4013 013+ 1. 1.4 4133j 0.0953+ 0.7
Ω/mile
Sequence impedances: Ω/mile
272jj zd pos = 0.3 0.306 06+ 0.6272 0.6 9855jj zdzero = 0 .5919+ 2. 2.9855
Ω/mile
The Institute of Electrical and Electronics Engineers, Inc.
Standard Wye-Delta and Delta – Wye Connections A A
B
a
C
b
c
B
C
a
b
c
a
A
a
B
b
C
c
n
Delta - Wye Step Up
B
G
G
c
Open Wye-Delta Step Down
N
c
b
A
a
b
Delta – Wye Step Down
B
Wye – Delta Step Up
A
A
C
N
Wye-Delta Step Down
n
B
a
b
c
Open Wye-Delta Step Up
The Institute of Electrical and Electronics Engineers, Engineers, Inc.
Solutions Step-Down with Balanced Loading Standard 30 degree connections are assumed for wye-delta and delta-wye banks V1 = Vag for wye connections and Vab for delta connections V2 = Vbg for wye connections and Vbc for delta connections V3 = Vcg for wye connections and Vca for delta connections Connection Node-2 V1 V2 V3 Node-3 V1 V2 Node-4V3 V1 V2 V3 Current 1-2 Ia Ib Ic Current 3-4 Ia Ib Ic Node 2 Van Vbn Vcn Vng
Gr Y - Gr Y
Gr Y -D
Y-D
D - Gr Y
D-D
Open Gr.Y-D
7107/-0 /-0.3 7140 7140/-1 /-12 20.3 7121 7121/1 /119 19.6 .6
7113/-0 /-0.3 7112/-.0 /-.03 3 12340/2 /29 9.7 1 12 2339/29 /29.7 6984/0 /0.4 .4 7132/ 132/-1 -120 20.3 .3 71 713 33/3/-12 120 0.4 123 2349 49/-9 /-90 0.4 123 2349 49/-9 /-90 0.4 716 7167/-1 7/-121 21.7 .7 7123/ 123/11 119.6 9.6 712 7124/1 4/119 19.6 .6 123 12318 18/1 /149 49.6 .6 123 2321 21/1 /14 49.6 729 293/ 3/12 120.5 0.5
2247.6/.6/-3 3.7 2269 2269/-1 /-12 23.5
3906/-3 /-3.5 3915/ 915/-1 -123 23.6 .6
3906/-3 /-3.4 2249/-3 /-33.7 391 3915/5/-12 123 3.6 226 263/3/-1 153.4
3911/26 /26.5 391 3914/ 4/-9 -93.6 3.6
3701/-0 /-0.9 407 076/ 6/-1 -126 26.5 .5
2256/11 /116.4
3909/11 /116.3
3909/1 /11 16.3
3905/14 /146.4
3572/11 /110.9
1918/-9 /-9.1 2061 2061/-1 /-12 28.3 1981/11 /110.9
3437/-7 /-7.8 3497/ 497/-1 -129 29.3 .3 3388/11 /110.6
3437/-7 /-7.8 1920/-3 /-39.1 3 34 497/7/-12 129 9.3 205 054/4/-1 158.3 3388/1 /11 10.6 1 19 986/80 /80.9
3442/22 /22.3 34 349 97/-9 7/-99.4 9.4 3384/14 /140.7
3384/-3 /-3.5 380 804. 4.9/9/-1 130 30.2 .2 3246/10 /106.5
347.9 .9/-3 /-34 4.9 32 323.7 3.7/-1 /-154 54.2 .2 336.8/85.0
334.8/-3 .8/-34 4.5 335.8/-3 .8/-34 4.7 335.0/.0/-3 35.7 335.8/-3 .8/-34 4.7 380.9/-6 .9/-65 5.2 335 35.4/-1 .4/-154 54.9 .9 33 335.9 5.9/-1 /-154 54.6 .6 33 331.8 1.8/-1 /-154 54.0 .0 33 335.8 5.8/-15 /-154.6 4.6 387 87.4/-1 .4/-12 25.2 337.4/85.4 335.9/85.3 341.6/85.6 336.0/85.4 0
10 1042 42.8/.8/-34 34.9 .9 97 970.2 0.2/-1 /-154 54.2 .2 1009.6/8 .6/85 5.0
100 006.6 6.6/-6 /-64.7 4.7 10 1006 06.6/-6 .6/-64 4.7 10 1041 41.9/-6 .9/-64.9 4.9 10 1006 06.7/-3 .7/-34.7 4.7 659 59.3/-6 .3/-65 5.2 100 006.7 6.7/17 /175.4 5.4 10 1006 06.7/1 .7/175 75.4 .4 97 973.7 3.7/17 /175.9 5.9 10 1006 06.7/-1 .7/-154 54.6 .6 665 65.7/1 .7/175 75.6 .6 1007.2/5 .2/55 5.3 10 100 07.2/5 .2/55 5.3 1007.0/5 .0/55 5.0 1007.2/8 .2/85 5.4 670 670.5/5 .5/54 4.8
2 22 259/86 /86.4
7116/-.03 7131/-120.3 7121/119.6 3.6/169.5
The Institute of Electrical and Electronics Engineers, Engineers, Inc.
Step-Down with Unbalanced Loading Standard 30 degree connections are assumed for wye-delta and delta-wye banks V1 = Vag for wye connections and Vab for delta connections V2 = Vbg for wye connections and Vbc for delta connections V3 = Vcg for wye connections and Vca for delta connections Connection Node-2 V1 V2 V3 Node-3 V1 V2 V3 Node-4 V1 V2 V3 Current 1-2 Ia Ib Ic Current 3-4 Ia Ib Ic Node 2 Van Vbn Vcn Vng
Gr Y - Gr Y
Gr Y -D
Y-D
D - Gr Y
D-D
Open Gr.Y-D
7164/-0 /-0.1 7110 110/-120 /-120.2 .2 7082 082/119 /119.3 .3
7113/-0 /-0.2 714 7144/-1 4/-12 20.4 0.4 711 7111/1 1/119.5 19.5
7112/-0 /-0.2 714 7144/-1 4/-12 20.4 0.4 711 7112/11 2/119. 9.5 5
12350/29 /29.6 123 12314/-9 14/-90 0.4 123 12333/1 33/14 49.8 9.8
12341/29 /29.8 123 237 70/-9 0/-90 0.5 1230 2302/ 2/14 149 9.5
6952/0.7 /0.7 7172/-1 72/-12 22.0 73 7313 13/1 /12 20.5 0.5
2305/-2 /-2.3 2255 255/-123 /-123.6 .6 2203/11 /114.8
3896/-2 /-2.8 397 3972/-1 2/-12 23.8 3.8 3875/11 /115.7
3896/-2 /-2.8 397 3972/-1 2/-12 23.8 3.8 3874/11 /115.7
2290/-3 /-32.4 226 2261/-1 1/-15 53.8 2214/85 /85.2
3902/2 /27 7.2 397 972 2/-93. /-93.9 9 3871/14 /145.7
3632/0 /0.1 .1 4121/-1 21/-12 27.6 3450/10 /108.9
2175/-4 /-4.1 1930 930/-126 /-126.8 .8 1833/10 /102.8
3425/-5 /-5.8 364 3646/-1 6/-13 30.3 0.3 3298/10 /108.6
3425/-5 /-5.8 364 3646/-1 6/-13 30.3 0.3 3298/10 /108.6
2157/-3 /-34.2 193 1936/-1 6/-15 57.0 1849/73 /73.4
3431/24 /24.3 364 647 7/-100 /-100.4 .4 3294/13 /138.6
3307/-1 /-1.5 3907/-1 07/-13 31.9 3073/10 /103.1
230.1/.1/-3 35.9 34 345.7 5.7/-1 /-152 52.6 .6 455.1/84.7
308.5/.5/-4 41.5 31 314.6 4.6/-1 /-145 45.5 .5 389.0/85.9
309.8/.8/-4 41.7 285.7/.7/-2 27.6 31 315.5 5.5/-1 /-145 45.2 .2 402.7/402.7/-14 149.6 9.6 387.2/85.9 3 34 49.1/74.4
689.7 89.7//-35 35.9 .9 1036 036/-152 /-152.6 .6 1364/84 /84.7
100 10083.8 83.8//-71 71.0 .0 108 1083.8/ 3.8/-7 -71 1.0 6 69 95.5 .5/-6 /-66. 6.0 0 849 849.9/1 .9/17 77.0 7.0 849 849.9/1 .9/17 77.0 7.0 103 1033/17 3/177 7.1 1098.7/6 .7/63 3.1 109 1098.7/6 .7/63 3.1 1352/55 /55.2
361.7/.7/-4 41.0 424.8/.8/-7 73.8 283.5 283.5/-1 /-153 53.0 .0 440.3 440.3/-1 /-118 18.5 .5 366.5/93.2 0 1084 084/-41. /-41.0 0 735.2/ 5.2/-7 -73. 3.8 8 849.7 49.7/-1 /-153 53.0 .0 5 56 69.9/ 9.9/1 176.3 1099/93 /93.2 762.0/6 .0/61 1.5
7116/-0.3 7142/-120.4 7109/119.6 4.27/171.6
The Institute of Electrical and Electronics Engineers, Engineers, Inc.
Step-Up with Balanced Loading Standard 30 degree connections are assumed for wye-delta and delta-wye banks V1 = Vag for wye connections and Vab for delta connections V2 = Vbg for wye connections and Vbc for delta connections V3 = Vcg for wye connections and Vca for delta connections Connection Node-2 V1 V2 V3 Node-3 V1 V2 V3 Node-4 V1 V2 V3 Current 1-2 Ia Ib Ic Current 3-4 Ia Ib Ic Node 2 Van Vbn Vcn Vng
Gr Y - Gr Y 7126/-0 /-0.3 7145 145/-1 /-120 20.4 .4 7137/11 /119.6
Gr Y -D 7128/-0 /-0.3 7145/-1 5/-120 20.3 .3 7137/11 /119.6
Y-D
D - Gr Y
D-D
Open Gr.Y-D
7127/-0 /-0.3 714 7145/5/-12 120.4 0.4 7138/11 /119.6
12361/2 /29 9.7 12 1237 372 2/-9 /-90 0.4 12348/14 /149.6
12361/2 /29 9.7 123 2372 72/-9 /-90 0.4 12348/14 /149.6
7001/-0 /-0.3 718 183 3/-1 /-12 21.5 7281/120 /120.5 .5
13675/-3 /-3.3 23746/5 /56 6.7 23746/5 /56 6.7 1371 3715/-1 /-12 23.4 3.4 23 23722/-6 22/-63 3.4 237 23722/-6 22/-63.4 3.4 13 1369 698/1 8/116 16.6 .6 23 2369 698/1 8/176 76.7 .7 23 2369 698/1 8/176 76.7 .7
13697/26 /26.7 13 1371 710 0/-9 /-93 3.4 13 1368 681/1 1/14 46.6
23723/26 /26.7 237 3746 46/-9 /-93 3.4 23 236 698 98/14 /146.6 6.6
24603/54 /54.1 219 193 38/-6 8/-68.6 8.6 22 2243 433/1 3/178 78.7 .7
13631/-3 /-3.5 23680/5 /56 6.6 23681/5 /56 6.6 1368 3682/-1 /-12 23.5 3.5 23 23663/-6 63/-63 3.6 236 23664/-6 64/-63.6 3.6 13 1366 661/1 1/116 16.5 .5 23 2362 625/1 5/176 76.5 .5 23 2362 625/1 5/176 76.5 .5
13653/26 /26.6 13 1367 678 8/-9 /-93 3.5 13 1364 644/1 4/14 46.5
23657/26 /26.6 236 3688 88/-9 /-93 3.5 23 236 625 25/14 /146.5 6.5
24558/54 /54.0 219 190 00/-6 0/-68.7 8.7 22 2238 380/1 0/178 78.6 .6
293.0 .0//-2 29.3 29 291.9 1.9/-1 /-149 49.3 .3 292.3/90.6
291.6/-2 .6/-29 9.1 292.4/.4/-2 29.34 .34 29 291.9 1.9/-14 /-149.6 9.6 292.4 292.4/-1 /-149 49.3 .3 293.7/90.7 292.4/90.7
2 29 92.4/-2 .4/-29 9.3 29 292.4 2.4/-1 /-149 49.3 .3 2 29 92.4/90.7
292.4/.4/-2 29.3 29 292 2.4/-149 .4/-149.3 .3 292.4/90.7
346.7/.7/-6 61.3 34 349.8 9.8/-1 /-121 21.4 .4
146.7/.7/-2 29.3 14 146.2 6.2/-1 /-149 49.3 .3 146.4 .4/9 /90 0.6
146.4/0 .4/0.7 .7 146.7/0 .7/0--.7 14 146.4 6.4/-11 /-119.3 9.3 146.4 146.4/-1 /-119 19.3 .3 146.4/1 .4/12 20.7 1 14 46.4/1 .4/12 20.7
146.5 .5/0 /0.7 .7 14 146.2 6.2/-1 /-119 19.4 .4 146.6/1 .6/12 20.6
146.4 .4//-2 29.3 14 146 6.4/-149 .4/-149.3 .3 146.4/9 .4/90 0.7
100.9 .9//-0 0.9 10 101.2 1.2/-1 /-121 21.4 .4 100.2/1 .2/11 18.7
0
7130/-0.3 7144/-120.3 7136/119.6 3.10/174.9
The Institute of Electrical and Electronics Engineers, Inc.
Step-Up with Unbalanced Loading Standard 30 degree connections are assumed for wye-delta and delta-wye banks
V1 V2 = = Vag Vbg for for wye wye connections connections and and Vab Vbc for for delta delta connections connections V3 = Vcg for wye connections and Vca for delta connections Connection Node-2 V1 V2 V3 Node-3 V1 V2 V3 Node-4 V1 V2 V3 Current 1-2 Ia Ib Ic Current 3-4 Ia Ib Ic Node 2 Van Vbn Vcn Vng
Gr Y - Gr Y
Gr Y -D
Y-D
D - Gr Y
D-D
Open Gr.Y-D
7161/-0 /-0.1 7120/120/-1 120.3 20.3 7128/1 128/11 19.3
7121/-0 /-0.4 7147 147/-120 /-120.3 .3 7150 150/11 /119.5 9.5
7120/-0 /-0.4 7147/-1 47/-12 20.3 7150/1 50/119 19.6 .6
12364/2 /29 9.8 12 12362/2 /29 9.8 123 2391 91/-9 /-90 0.5 1239 392 2/-9 /-90 0.4 123 2333 33/14 /149 9.6 1233 334 4/149. /149.5 5
7001/0 /0.0 .01 1 72 720 07/-1 /-12 21.3 72 726 64/120 /120.5
13839/-2 /-2.1 .1 13 136 663 63/-1 /-123 23.3 .3 13 136 655 55/11 /115.1 5.1
23703/57 /57.2 24 2404 040/0/-63 63.6 .6 23 2357 576/1 6/176 76.1 .1
23703/57 /57.2 24 2404 040/0/-63 63.6 .6 23 2357 576/1 6/176 76.1 .1
13792/27 /27.7 23675/27 /27.2 24762/55 /55.0 13 137 733 33/-9 /-93.5 3.5 24060 24060\-9 \-93.6 3.6 22 2275 756/6/-68 68.8 .8 13 136 641 41/14 /145.4 5.4 2 235 3573 73/14 /146.0 6.0 22 2245 455/1 5/17 77.6
13815/-2 /-2.2 .2 13 136 614 14/-1 /-123 23.4 .4 13 136 615 15/11 /114.9 4.9
23637/57 /57.1 23 2399 995/5/-63 63.8 .8 23 2349 496/1 6/175 75.9 .9
23637/57 /57.1 23 2399 995/5/-63 63.8 .8 23 2349 495/1 5/175 75.9 .9
13768/27 /27.7 23610/27 /27.2 24716/54 /54.9 13 136 684 84/-9 /-93.6 3.6 24015 24015/-9 /-93.7 3.7 22 2272 728/8/-68 68.9 .9 13 136 600 00/14 /145.2 5.2 2 234 3492 92/14 /145.9 5.9 22 2239 398/1 8/17 77.5
216.8/-3 .8/-34 4.0 29 293 3.3/-1 .3/-14 49.2 366.7/9 .7/96 6.7
332.6/.6/-2 28.1 26 269.5 9.5/-1 /-155 55.6 .6 275.5/ .5/100.3
333.5/.5/-2 28.2 309.3/.3/-3 35.2 312.3/-3 .3/-34 4.8 368.9/.9/-5 52.6 26 269.6 9.6/-1 /-155 55.4 .4 24 249 9.5/-1 .5/-146 46.5 .5 248 248.1/-1 .1/-147 47.2 .2 29 295.5 5.5/-1 /-119 19.5 .5 274.3/100.2 319.3 .3/9 /98 8.1 316.5/98.7 0
108.6/.6/-3 34.0 14 147 7.0/-1 .0/-14 49.2 183.6/9 .6/96 6.7
156.4/.4/-4 4.8 12 124.2 4.2/-1 /-117 17.2 .2 158.4/1 .4/12 28.7
156.4/.4/-4 4.8 12 124.2 4.2/11 /117.2 7.2 158.4/1 .4/12 28.7
109.0/.0/-4 4.1 156.4/.4/-3 34.8 107.3/.3/-5 5.6 14 146 6.2/-119 .2/-119.4 .4 12 124.2 4.2/-1 /-147 47.2 .2 85.4/-1 85.4/-119 19.5 .5 183.8/1 .8/12 27.0 15 158.5/9 .5/98 8.7 106.7/1 .7/12 27.4
7123/-0.3 7146/-120.2 7149/119.5 2.79/-173.9
The Institute of Electrical and Electronics Engineers, Inc.
