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1. Derive dV(x)/dx and dI(x)/dx.2. Derive the second order equations in relation to V(x) and I(x).3. Solve for the general solution for V(x).4. Solve for the general solution for I(x).5. Determine the characteristic impedance.6. What role does the attenuation, phase, and propagation constants play in the general solution?7. Determine specific solutions using boundary conditions at x=0; V(x) = Vr, and I(x) = Ir and at x= L; V(x) = Vs, and I(x) =Is.8. Determine the ABCD Matrix.9. Given the SWAN AWG=4 transmission line, determine the attenuation, propagation, and impedance characteristic.Aluminum
Conductor Steel Reinforced (ACSR) Cables
Alcan Cable manufactures a full line of ACSR cables which
are used in overhead transmission and distribution line
applications. Alcan offers various conductor designs and
Product Construction
ACSR is a concentric-lay-stranded conductor consisting of
a single core wire or a stranded steel central core with one
or more layers of 1350 H19 stranded aluminum wires. Steel
core wires are protected from corrosion by galvanizing,
aluminum-clad alloy or zinc – 5\% aluminum mischmetal
alloy coating. Standard, High, Extra and Ultra High strength
steel are also available. All ACSR cables are also available in
a non-specular finish.
Specifications
Alcan’s ACSR cables meet or exceed industry requirements
per ASTM specifications B230, B232, B498, and B500.
Product Features
ACSR conductors provide dependable performance
for many years under adverse weather conditions. The
combination of the aluminum and steel in the conductor
design offer both efficient conductivity and high tensile
strength making ACSR cable the most economical solution
for overhead power transmission and distribution projects.
7
ACSR
Aluminum Conductor Steel Reinforced
ASTM: B230, Specification for Aluminum 1350-H19 Wire for Electrical Purposes
B232, Specification for Concentric-Lay-Stranded Aluminum Conductors, Coated Steel Reinforced (ACSR)
B498, Specification for Zinc-Coated (Galvanized) Steel Core Wire for Aluminum Conductors Steel Reinforced (ACSR)
Physical Properties
SIZE
CODE WORD
TURKEY
SWAN
SWANATE
SPARROW
SPARATE
ROBIN
RAVEN
QUAIL
PIGEON
PENGUIN
WAXWING
PARTRIDGE
MERLIN
LINNET
ORIOLE
IBIS
LARK
PELICAN
FLICKER
HAWK
HEN
OSPREY
PARAKEET
DOVE
EAGLE
PEACOCK
SWIFT
KINGBIRD
ROOK
GROSBEAK
EGRET
FLAMINGO
STARLING
REDWING
COOT
TERN
CUCKOO
CONDOR
DRAKE
MALLARD
RUDDY
CANARY
CORNCRAKE
REDBIRD
TOWHEE
RAIL
CARDINAL
ORTOLAN
CURLEW
BLUEJAY
FINCH
BUNTING
GRACKLE
SKYLARK
BITTERN
PHEASANT
DIPPER
MARTIN
PLOVER
LAPWING
FALCON
CHUKAR
MOCKINGBIRD
BLUEBIRD
KIWI
THRASHER
JOREA
STRANDING
Number & Diameter (In.)
Nominal Diameter (In.)
AWG
or kcmil
6
4
4
2
2
1
1/0
2/0
3/0
4/0
266.8
266.8
336.4
336.4
336.4
397.5
397.5
397.5
477
477
477
477
556.5
556.5
556.5
556.5
605
636
636
636
636
636
666.6
715.5
715.5
795
795
795
795
795
795
900
900
954
954
954
954
954
1033.5
1033.5
1113.0
1113.0
1192.5
1192.5
1272.0
1272.0
1272.0
1351.5
1351.5
1431.0
1431.0
1590.0
1590.0
1780.0
2034.5
2156.0
2167.0
2312.0
2515.0
Aluminum
Steel
6 x 0.0661
6 x 0.0834
7 x 0.0772
6 x 0.1052
7 x 0.0974
6 x 0.1181
6 x 0.1327
6 x 0.1489
6 x 0.1672
6 x 0.1878
18 x 0.1217
26 x 0.1013
18 x 0.1367
26 x 0.1137
30 x 0.1059
18 x 0.1486
26 x 0.1236
30 x 0.1151
18 x 0.1628
24 x 0.1410
26 x 0.1354
30 x 0.1261
18 x 0.1758
24 x 0.1523
26 x 0.1463
30 x 0.1362
24 x 0.1588
36 x 0.1329
18 x 0.1880
24 x 0.1628
26 x 0.1564
30 x 0.1456
24 x 0.1667
26 x 0.1659
30 x 0.1544
36 x 0.1486
45 x 0.1329
24 x 0.1820
54 x 0.1213
26 x 0.1749
30 x 0.1628
45 x 0.1414
54 x 0.1291
20 x 0.2184
24 x 0.1994
48 x 0.1410
45 x 0.1456
54 x 0.1329
45 x 0.1515
54 x 0.1383
45 x 0.1573
54 x 0.1436
45 x 0.1628
54 x 0.1486
36 x 0.1880
45 x 0.1681
54 x 0.1535
45 x 0.1733
54 x 0.1582
45 x 0.1783
54 x 0.1628
45 x 0.1880
54 x 0.1716
84 x 0.1456
72 x 0.1681
84 x 0.1602
72 x 0.1735
76 x 0.1744
76 x 0.1819
1 x 0.0661
1 x 0.0834
1 x 0.1029
1 x 0.1052
1 x 0.1299
1 x 0.1181
1 x 0.1327
1 x 0.1489
1 x 0.1672
1 x 0.1878
1 x 0.1217
7 x 0.0788
1 x 0.1367
7 x 0.0884
7 x 0.1059
1 x 0.1486
7 x 0.0961
7 x 0.1151
1 x 0.1628
7 x 0.0940
7 x 0.1053
7 x 0.1261
1 x 0.1758
7 x 0.1015
7 x 0.1138
7 x 0.1362
7 x 0.1059
1 x 0.1329
1 x 0.1880
7 x 0.1085
7 x 0.1216
19 x 0.0874
7 x 0.1111
7 x 0.1290
19 x 0.0926
1 x 0.1486
7 x 0.0886
7 x 0.1213
7 x 0.1213
7 x 0.1360
19 x 0.0977
7 x 0.0943
7 x 0.1291
7 x 0.0971
7 x 0.1329
7 x 0.1097
7 x 0.0971
7 x 0.1329
7 x 0.1010
7 x 0.1383
7 x 0.1049
19 x 0.0862
7 x 0.1085
19 x 0.0892
1 x 0.1880
7 x 0.1121
19 x 0.0921
7 x 0.1155
19 x 0.0949
7 x 0.1189
19 x 0.0977
7 x 0.1253
19 x 0.1030
19 x 0.0874
7 x 0.1122
19 x 0.0961
7 x 0.1157
19 x 0.0814
19 x 0.0850
Complete
Conductor
0.198
0.250
0.257
0.316
0.325
0.354
0.398
0.447
0.502
0.563
0.509
0.642
0.684
0.720
0.741
0.743
0.783
0.806
0.814
0.846
0.858
0.883
0.879
0.914
0.927
0.953
0.953
0.930
0.940
0.977
0.990
1.019
1.000
1.051
1.081
1.040
1.063
1.092
1.092
1.108
1.140
1.131
1.162
1.165
1.196
1.175
1.165
1.196
1.212
1.245
1.259
1.293
1.302
1.338
1.316
1.345
1.382
1.386
1.424
1.427
1.465
1.504
1.545
1.602
1.681
1.762
1.735
1.802
1.880
80.0
101.8
110.8
134.6
159.0
176.9
190.8
211.3
203.2
8 x 0.1000
12 x 0.0921
12 x 0.0961
12 x 0.1059
12 x 0.1151
12 x 0.1214
12 x 0.1261
12 x 0.1327
16 x 0.1127
1 x 0.1670
7 x 0.0921
7 x 0.0961
7 x 0.1059
7 x 0.1151
7 x 0.1214
7 x 0.1261
7 x 0.1327
19 x 0.0977
0.367
0.461
0.481
0.530
0.576
0.607
0.631
0.664
0.714
Steel
Core
0.0661
0.0834
0.1029
0.1052
0.1299
0.1181
0.1327
0.1489
0.1672
0.1878
0.1217
0.236
0.1367
0.265
0.318
0.1486
0.288
0.345
0.1628
0.282
0.316
0.378
0.1758
0.304
0.341
0.409
0.318
0.1329
0.1880
0.326
0.365
0.437
0.333
0.387
0.463
0.1486
0.266
0.364
0.364
0.408
0.489
0.283
0.387
0.291
0.399
0.329
0.291
0.399
0.303
0.415
0.315
0.431
0.326
0.446
0.1880
0.336
0.461
0.347
0.475
0.357
0.489
0.376
0.515
0.437
0.337
0.481
0.347
0.407
0.425
WEIGHT
(Lbs./1000 Ft.)
PERCENT OF
TOTAL WEIGHT
Rated
Strength
(Lbs.)
Total
Aluminum
Steel
Aluminum
Steel
1190
1860
2360
2850
3640
3550
4380
5300
6620
8350
6880
11300
8700
14100
17300
9900
16300
20300
11800
17200
19500
23800
13700
19800
22600
27800
21600
13800
15700
22600
25200
31500
23700
28400
34600
16800
22100
27900
28200
31500
38400
24400
31900
25600
33500
28500
25900
33800
27700
36600
29800
39100
32000
41900
26400
34100
43600
36200
46300
38300
49100
42200
54500
51000
46800
60300
49800
56700
61700
36.0
57.4
67.0
91.2
106.6
115.0
145.2
182.8
230.5
290.8
289.1
366.9
364.8
462.0
526.4
431.0
546.0
621.8
517.3
613.9
655.3
746.4
603.3
716.1
765.2
870.7
778.8
642.8
689.9
818.2
874.2
987.2
857.9
983.7
1109.3
803.6
895
1023
1022
1093
1233.9
1013
1158
1074
1228
1123
1075
1227.1
1163
1329
1254
1430
1342
1531
1286
1432
1634
1521
1735
1611
1838
1790
2042
2072
2163
2508
2301
2523
2749
24.4
39.0
39.0
61.9
61.9
78.1
98.6
124.1
156.4
197.4
249.9
251.3
315.3
316.5
317.7
372.5
374.1
375.2
447.1
449.4
448.9
450.4
521.4
524.3
524.2
525.4
570.1
596.0
596.3
599.1
599.0
600.5
628.2
674.0
675.3
745.1
749
749
748
749
750.7
848
848
899
899
899
899
898.4
973
973
1049
1054
1123
1128
1192
1198
1205
1273
1279
1348
1355
1498
1505
1685
1929
2040
2052
2188
2383
11.6
18.4
28.0
29.3
44.7
36.9
46.6
58.7
74.1
93.4
39.2
115.6
49.5
145.5
208.7
58.5
171.9
246.6
70.2
164.5
206.4
296.0
81.9
191.8
241.0
345.3
208.7
46.8
93.6
219.1
275.2
386.7
229.7
309.7
434.0
58.5
146
274.0
274.0
344
483.2
165
310
175
329
224
176
328.7
190
356
205
376
219
403
94
234
429
248
456
263
483
292
537
387
234
468
249
335
366
67.8
67.9
58.2
67.9
58.1
67.9
67.9
67.9
67.9
67.9
86.4
68.5
86.4
68.5
60.4
86.4
68.5
60.4
86.4
73.2
68.5
60.4
86.4
73.2
68.5
60.4
73.2
92.7
86.4
73.2
68.5
60.8
73.2
68.5
60.8
92.7
83.7
73.2
73.2
68.5
60.8
83.7
73.2
83.7
73.2
80.1
83.7
73.2
83.7
73.2
83.7
73.7
83.7
73.7
92.7
83.7
73.7
83.7
73.7
83.7
73.7
83.8
73.7
81.3
89.2
81.3
89.2
86.7
86.7
32.2
32.1
41.8
32.1
41.9
32.1
32.1
32.1
32.1
32.1
13.6
31.5
13.6
31.5
39.6
13.6
31.5
39.6
13.6
26.8
31.5
39.6
13.6
26.8
31.5
39.6
26.8
7.3
13.6
26.8
31.5
39.2
26.8
31.5
39.2
7.3
16.3
26.8
26.8
31.5
39.2
16.3
26.8
16.3
26.8
19.9
16.3
26.8
16.3
26.8
16.3
26.3
16.3
26.3
7.3
16.3
26.3
16.3
26.3
16.3
26.3
16.3
26.3
18.7
18.7
18.7
10.8
13.3
13.3
5200
10400
11300
13600
16000
17300
18700
20700
28400
148.8
253.8
276.3
335.5
396.3
440.9
475.7
526.8
674.6
74.9
95.9
104.4
126.8
149.7
166.6
179.7
199.0
191.4
73.9
157.9
171.9
208.7
246.6
274.3
296.0
327.8
483.2
50.3
37.8
37.8
37.8
37.8
37.8
37.8
37.8
28.4
49.7
62.2
62.2
62.2
62.2
62.2
62.2
62.2
71.6
High Strength ACSR
GROUSE
PETREL
MINORCA
LEGHORN
GUINEA
DOTTEREL
DORKING
COCKHIN
BRAHMA
0.1670
0.276
0.288
0.318
0.345
0.364
0.378
0.398
0.489
15
ACSR
Aluminum Conductor Steel Reinforced
Electrical Properties
SIZE & STRANDING
CODE WORD
TURKEY
SWAN
SWANATE
SPARROW
SPARATE
ROBIN
RAVEN
QUAIL
PIGEON
PENGUIN
AWG
or kcmil
6
4
4
2
2
1
1/0
2/0
3/0
4/0
Aluminum/
Steel
6/1
6/1
7/1
6/1
7/1
6/1
6/1
6/1
6/1
6/1
DC
(Ohms/1000 Ft.)
@20°
0.6419
0.4032
0.3989
0.2534
0.2506
0.2011
0.1593
0.1265
0.1003
0.0795
WAXWING
PARTRIDGE
MERLIN
LINNET
ORIOLE
IBIS
LARK
PELICAN
FLICKER
HAWK
HEN
OSPREY
PARAKEET
DOVE
EAGLE
PEACOCK
SWIFT
KINGBIRD
ROOK
GROSBEAK
EGRET
FLAMINGO
STARLING
REDWING
COOT
TERN
CUCKOO
CONDOR
DRAKE
MALLARD
RUDDY
CANARY
CORNCRAKE
REDBIRD
TOWHEE
RAIL
CARDINAL
ORTOLAN
CURLEW
BLUEJAY
FINCH
BUNTING
GRACKLE
SKYLARK
BITTERN
PHEASANT
DIPPER
MARTIN
PLOVER
LAPWING
FALCON
CHUKAR
MOCKINGBIRD
BLUEBIRD
KIWI
THRASHER
JOREA
266.8
266.8
336.4
336.4
336.4
397.5
397.5
397.5
477.0
477.0
477.0
477.0
556.5
556.5
556.5
556.5
605.0
636.0
636.0
636.0
636.0
636.0
666.6
715.5
715.5
795.0
795.0
795.0
795.0
795.0
795.0
900.0
900.0
954.0
954.0
954.0
954.0
954.0
1033.5
1033.5
1113.0
1113.0
1192.5
1192.5
1272.0
1272.0
1272.0
1351.5
1351.5
1431.0
1431.0
1590.0
1590.0
1780.0
2034.5
2156.0
2167.0
2312.0
2515.0
18/1
26/7
18/1
26/7
30/7
18/1
26/7
30/7
18/1.
26/7
30/7
18/1
26/7
30/7
36/1
18/1
26/7
30/19
26/7
30/19
36/1
45/7
54/7
26/7
30/19
45/7
54/7
20/7
48/7
45/7
54/7
45/7
54/7
45/7
54/19
45/7
54/19
36/1
45/7
54/19
45/7
54/19
45/7
54/19
45/7
54/19
84/19
72/7
84/19
72/7
76/19
76/19
0.0644
0.0637
0.0510
0.0506
0.0502
0.0432
0.0428
0.0425
0.0360
0.0358
0.0357
0.0354
0.0309
0.0307
0.0305
0.0300
0.0282
0.0267
0.0269
0.0268
0.0267
0.0266
0.0256
0.0238
0.0236
0.0217
0.0216
0.0215
0.0215
0.0214
0.0213
0.0191
0.0190
0.0180
0.0179
0.0180
0.0180
0.0179
0.0167
0.0165
0.0155
0.0154
0.0144
0.0144
0.0135
0.0135
0.0135
0.0127
0.0127
0.0120
0.0120
0.0108
0.0108
0.0097
0.0085
0.0080
0.0080
0.0075
0.0069
GROUSE
PETREL
MINORCA
LEGHORN
GUINEA
DOTTEREL
DORKING
COCHIN
BRAHMA
80.0
101.8
110.8
134.6
159.0
176.9
190.8
211.3
203.2
8/1
12/7
12/7
12/7
12/7
12/7
12/7
12/7
16/19
RESISTANCE
AC-60-HZ(Ohms/1000 Ft.)
60 HZ REACTANCE 1 FOOT EQUIVALENT SPACING
Inductive (Ohms/1000 Ft.)
@25° C
0.6553
0.4119
0.4072
0.2591
0.2563
0.2059
0.1633
0.1301
0.1034
0.0822
@50° C
0.750
0.4794
0.4633
0.3080
0.2966
0.2474
0.1972
0.1616
0.1208
0.1066
@75° C
0.8159
0.5218
0.5165
0.3360
0.3297
0.2703
0.2161
0.1760
0.1445
0.1157
Capacitive
(Megohms-1000 Ft.)
0.7513
0.7149
0.7102
0.6785
0.6737
0.6600
0.6421
0.6241
0.6056
0.5966
0.0657
0.0652
0.0523
0.0517
0.0513
0.0443
0.0438
0.0434
0.0369
0.0367
0.0366
0.0362
0.0318
0.0314
0.0314
0.0311
0.0290
0.0281
0.0278
0.0277
0.0275
0.0273
0.0263
0.0244
0.0242
0.0225
0.0225
0.0223
0.0222
0.0222
0.0220
0.0200
0.0197
0.0188
0.0186
0.0188
0.0188
0.0186
0.0175
0.0172
0.0163
0.0161
0.0152
0.0151
0.0145
0.0144
0.0142
0.0136
0.0134
0.0129
0.0127
0.0117
0.0116
0.0106
0.0096
0.0090
0.0092
0.0086
0.0081
0.0723
0.0714
0.0574
0.0568
0.0563
0.0487
0.0481
0.0477
0.0405
0.0403
0.0402
0.0389
0.0348
0.0347
0.0345
0.0341
0.0378
0.0307
0.0306
0.0300
0.0301
0.0299
0.0290
0.0269
0.0267
0.0247
0.0246
0.0243
0.0244
0.0242
0.0241
0.0218
0.0216
0.0206
0.0204
0.0205
0.0206
0.0205
0.0191
0.0189
0.0178
0.0176
0.0167
0.0165
0.0159
0.0157
0.0155
0.0148
0.0147
0.0141
0.0134
0.0127
0.0126
0.0115
0.0104
0.0098
0.0099
0.0092
0.0087
0.0788
0.0778
0.0625
0.0619
0.0614
0.0528
0.0525
0.0519
0.0441
0.0439
0.0438
0.0434
0.0379
0.0377
0.0375
0.0371
0.0347
0.0334
0.0332
0.0330
0.0328
0.0326
0.0314
0.0292
0.0290
0.0268
0.0267
0.0266
0.0265
0.0263
0.0261
0.0237
0.0235
0.0224
0.0221
0.0223
0.0223
0.0222
0.0208
0.0201
0.0193
0.0191
0.0181
0.0179
0.0173
0.0170
0.0169
0.0161
0.0159
0.0152
0.0151
0.0138
0.0137
0.0125
0.0112
0.0105
0.0106
0.0100
0.0093
0.576
0.565
0.560
0.549
0.544
0.544
0.539
0.533
0.528
0.524
0.522
0.517
0.518
0.512
0.510
0.505
0.505
0.509
0.507
0.502
0.500
0.495
0.498
0.490
0.486
0.492
0.488
0.484
0.484
0.482
0.477
0.479
0.474
0.474
0.470
0.473
0.474
0.470
0.468
0.464
0.462
0.458
0.456
0.452
0.455
0.451
0.447
0.447
0.442
0.442
0.438
0.434
0.430
0.424
0.416
0.409
0.411
0.405
0.399
0.2110
0.1625
0.1491
0.1233
0.1045
0.0945
0.0875
0.0792
0.0790
0.2362
0.2072
0.1932
0.1638
0.1426
0.1301
0.1229
0.1125
0.1089
0.2612
0.2394
0.2233
0.1894
0.1653
0.1513
0.1424
0.1311
0.1348
@25° C
0.1201
0.1152
0.11533
0.1100
0.1081
0.1068
0.1040
0.1017
0.0992
0.0964
Inductive (Ohms/1000 Ft.)
16
HIGH STRENGTH ACSR
0.2065
0.1583
0.1454
0.1198
0.1014
0.0911
0.0845
0.0763
0.0764
@50° C
0.1390
0.1314
0.1239
0.1235
0.1176
0.1191
0.1138
0.1117
0.1083
.01047
@75° C
0.1439
0.1369
0.1303
0.1277
0.1206
0.1224
0.1163
0.1135
0.1095
0.1053
GMR (Ft.)
0.0934
0.0197
0.0881
0.0217
0.0877
0.0221
0.0854
0.0244
0.0843
0.0255
0.0856
0.0240
0.0835
0.0265
0.0824
0.0277
0.0835
0.0263
0.0818
0.0283
0.0814
0.0290
0.0803
0.0304
0.0818
0.0284
0.0801
0.0306
0.0795
0.0313
0.0786
0.0328
0.0792
0.0319
0.0806
0.0300
0.0805
0.0301
0.0786
0.0327
0.0780
0.0335
0.0769
0.0351
0.0780
0.0335
0.0767
0.0355
0.0756
0.0372
0.0780
0.0335
0.0764
0.0352
0.0763
0.0361
0.0759
0.0368
0.0756
0.0375
0.0744
0.0392
0.0755
0.0374
0.0744
0.0392
0.0751
0.0378
0.0742
0.0396
0.0745
0.0391
0.0748
0.0385
0.0757
0.0404
0.0739
0.0401
0.0729
0.0420
0.0731
0.0416
0.0702
0.0436
0.0723
0.0431
0.0710
0.0451
0.072
0.0427
0.072
0.0445
0.070
0.0466
0.071
0.0459
0.070
0.0480
0.070
0.0472
0.069
0.0495
0.069
0.0498
0.068
0.0521
0.067
0.0534
0.066
0.0553
0.065
0.0588
0.068
0.0570
0.065
0.0600
0.064
0.0621
60 HZ REACTANCE 1 FOOT EQUIVALENT SPACING
Inductive (Ohms/1000 Ft.)
Capacitive
(Megohms-1000 Ft.)
@25° C
@50° C
@75° C
0.6547
0.1047
0.1129
0.1150
0.6193
0.1019
0.1161
0.1282
0.6125
0.1017
0.1176
0.1269
0.5972
0.0998
0.1148
0.1227
0.5845
0.0979
0.1117
0.1189
0.5760
0.0970
0.1102
0.1169
0.5697
0.0956
0.1093
0.1150
0.5618
0.0945
0.1074
0.1129
0.5507
0.0934
0.1047
0.1121
Notes:
1. DC reesistance is based on 16.946 ohn-cmil/ft. 61.2\% IACS for 1350 wires and 129.64 ohm-cmil/ft. 8\% IACS for the steel core at 20° C with stranding increment as per ASTM B232.
09
IL IR
d Vix)
VR
dy
BC
1 + ZU 를
d I (x)
dx
Itzy
IR
Specific
Midnighty Y (Her var ( 14 21
Soln
1415
Vs
N
1+2
VR
SV(x)
A B CD Matrix
Geverd
YA
ix
Ich J Sil
Impedance Characteristia
propagation Constant
Attenuation Content
AV
Is
It AIA
mum, zaxom?
lav
Vs
+
vrov
VO)
-y (ax.)
y (a)
Vpp = V(+)
. 4x

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