# 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