A singlecircuit threephase transmission line is composed of

A single-circuit, three-phase transmission line is composed of Parakeet conductors with flat horizontal spacing of 19.85 ft between adjacent conductors. Determine the characteristic impedance and the propagation constant of the line at 60 Hz and 50 degree C temperature. Solution: At 50 degree C and 60 Hz, from Table A.3, for Parakeet conductors, r = 0.1832 Ohm/mi X_a = 0.423 Ohm/mi D_eq = cubicroot Squareroot 19.85^3 times 2 ft = 25 ft At 25 ft, X_d(inductive) = 0.3906 Ohm/mi Therefore, z = 0.1832 + j(0.423 + 0.3906) Ohm/mi = 0.834/77.31 degree Ohm/mi X_a^\' = 0.0969 times 10^-6 Ohm middot mi y = j/X_a\' + X_d = 10^-6 90 degree/0.0955 +0.0955 S/mi Characteristic impedance: Z_c = Squareroot z/y = Squareroot 0.834 77.31 degree Ohm = 400.6/-6.345 degree Ohm Propagation constant: gamma = Squareroot zy = Squareroot 0.834 times 5.1975 times 10^-6/77.31 degree + 90 degree mi^-1 = 2.08 times 10^-3 mi^-1

Solution

There is a formulae for finding inductive reactance spacing factor Xd at 60 Hz frequency

X_d= 0 .2794 log d (ohms per mile per conductor)

where d = separation in ft

For three-phase lines
d = D_eq

Hence at 25 ft   X_d=0.2794 log (25)=0.3906 ohms per mile