Representation of Lines

The manner in which lines and cables are represented depends on their length and the accuracy required. There are three broad classifications of length: short, medium and long. The actual line or cable is a distributed constant circuit, that is it has resistance, inductance and capacitance distributed evenly along its length, as shown in Figure 3.25.

Except for long lines the total resistance, inductance and capacitance of the line are concentrated to give a lumped-constant circuit. The distances quoted are only a rough guide.

Table 3.2a Overhead-line constants at 50 Hz (British) (per phase, per km)

Voltage: No. and area of conductors (mm)2:

132 kV

275 kV

400 kV

l x 113

l x 258

2x 113

2 x 258

2 x 258

4x 258

Resistance (R)

V

0.155

0.068

0.022

0.034

0.034

0.017

Reactance (XL)

V

0.41

0.404

0.335

0.323

0.323

0.27

Susceptance (1/Xc)

S x 10~6

7.59

7.59

9.52

9.52

9.52

10.58

Charging current (Ic)

A

0.22

0.22

0.58

0.58

0.845

0.945

Surge impedance

V

373

371

302

296

296

258

Natural load

MW

47

47

250

255

540

620

XL/R ratio

2.6

5.9

4.3

9.5

9.5

15.8

Thermal rating:

Cold weather (below

MVA

125

180

525

760

1100

2200

5 °C)

Normal (5-18 ° C)

MVA

100

150

430

620

900

1800

Hot weather (above

MVA

80

115

330

480

790

1580

18 °C)

Table 3.2b Typical characteristics of bundled-conductor E.H.V. lines

Number of subconductors in bundle

Country

Line voltage and number of circuits (in parentheses)

Diameter of subconductors

Radius of circle on which subconductors are arranged

Resistance of bundle

Inductive reactance at 50 Hz

Susceptance at 50 Hz

1

kV

mm

mm

V/km

V/km

mS/km

Japan

275 (2)

27.9

0.0744

0.511

3.01

Canada

300 (2)

35.0

0.0451

0.492

2.33

Australia

330 (1)

45.0

0.0367

0.422

2.78

Russia

330 (1)

30.2

0.065

0.404

2.82

Italy

380 (1)

50.0

0.0294

0.398

2.84

Average (one

0.048

0.442

2.75

conductor):

2

Japan

275 (2)

25.3

200

0.0444

0.374

4.35

Canada

360 (1)

28.1

299

0.04

0.314

3.57

Australia

330 (1)

31.8

190.5

0.0451

0.341

3.34

U.S.A.

345 (1)

30.4

228.6

0.0315

0.325

3.55

Italy

380 (1)

31.5

200

0.0285

0.315

3.57

Russia

330 (1)

28.0

200

0.04

0.321

3.43

Average (two

0.040

0.323

3.58

conductors):

3

Sweden

380 (1)

31.68

260

0.018

0.29

3.85

Russia

525 (1)

30.2

230

0.0212

0.294

3.88

4

Germany

380 (2)

21.7

202

0.0316

0.260

4.3

Germany

500 (1)

22.86

323

0.0285

0.272

4.0

Canada

735 (1)

35.04

323

0.0121

0.279

3.9

Table 3.2c Overhead-line parameters - USA

Line voltage (kV)

345

345

500

500

735

735

Conductors per phase at 18 in spacing

1

2

2

4

3

4

Conductor code

Expanded

Curlew

Chuker

Parakeet

Expanded

Pheasant

Conductor diameter (inches)

1.750

1.246

1.602

0.914

1.750

1.382

Phase spacing (ft)

28

28

38

38

56

56

GMD (ft)

35.3

35.3

47.9

47.9

70.6

70.6

  • 8 Xa
  • 60 Hz inductive reactance V/mile < XD

i Xa + Xd

  • 0.3336
  • 0.4325
  • 0.7661
  • 0.1677
  • 0.4325
  • 0.6002
  • 0.1529
  • 0.4694
  • 0.6223
  • 0.0584
  • 0.4694
  • 0.5278
  • 0.0784
  • 0.5166
  • 0.5950
  • 0.0456
  • 0.5166
  • 0.5622
  • 8X'
  • 60 Hz capacitive reactance MV-miles X0D

i xa + XD

  • 0.0777
  • 0.1057
  • 0.1834
  • 0.0379
  • 0.1057
  • 0.1436
  • 0.0341
  • 0.1147
  • 0.1488
  • 0.0126
  • 0.1147
  • 0.1273
  • 0.0179
  • 0.1263
  • 0.1442
  • 0.0096
  • 0.1263
  • 0.1359

Z0(V)

374.8

293.6

304.3

259.2

276.4

Natural loading MVA

318

405

822

965

1844

1955

Conductor d.c. resistance at 25 °C (V/mile)

0.0644

0.0871

0.0510

0.162

0.0644

0.0709

Conductor a.c. resistance (60 Hz) at 50 °C (V/mile)

0.0728

0.0979

0.0599

0.179

0.0728

0.0805

XA = component of inductive reactance due to flux within a 1 ft radius.

XD = component due to other phases.

Total reactance per phase = XA + XD.

Xa = 0.2794 log10 (-1—NTTTw I V/mile.

10 [N(GMK)(A)n-1]1/n J

Xd = 0.2794 log10(GMD) V/mile. / 1

XA and XD are similarly defined for capacitive reactance and XA = 0.0683 log101-N-1 ^N I MV-miles; XD = 0,0683 log10(GMD)MV-miles.

GMR = geometric mean radius in feet; V [Nr(A) ] ' J

GMD = geometric mean diameter in feet;

N = number of conductors per phase;

A = S/2 sin (p/N); N > 1 A = 0; N = 1;

S = bundle spacing in feet; r = conductor radius in feet.

Data adapted from Edison Electric Institute.

Table 3.3 Underground cable constants at 50 Hz (per km)

Size

2

mm2

132 kV

275 kV

400 kV

355

645

970

1130

1935

Rating (soil g = 120 °C cm/W)

A

550

870

1100

1100

1600

MVA

125

200

525

525

1100

Resistance (R) at 85 °C

V

0.065

0.035

0.025

0.02

0.013

Reactance (XL)

V

0.128

0.138

0.22

0.134

0.22

Charging current (lc)

A

7.90

10.69

15.70

17.77

23.86

Xl/R Ratio

2.0

4.0

CO

CO

6.6

16.8

 
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