Question

Calculate the camacitance-to-neutral in F/m and the admittance-to-neutral in S/km for the three-phase line in problem Neglect the effect of the earth plane.

Answer 1

The answer is given below

Step-by-step explanation:

A 60 Hz three-phase, three-wire overhead line has solid cylindrical conductors arranged in the form of an equilateral triangle with 4 ft conductor spacing. Conductor diameter is 0.5 in.

Given that:

The spacing between the conductors (D) = 4 ft

1 ft = 0.3048 m

D = 4 ft = 4 × 0.3048 m = 1.2192 m

The conductor diameter = 0.5 in

Radius of conductor (r) = 0.5/2 = 0.25 in = 0.00635 m

Frequency (f) = 60 Hz

The capacitance-to-neutral is given by:

`C_n=(2\pi \epsilon_0)/(ln((D)/(r) )) =(2\pi *8.854*10^(-12))/(ln(1.2192/0.00635))=1.058*10^(-11)\ F/m`

The admittance-to-neutral is given by:

`Y_n=j2\pi fC_n=j*2\pi *60*1.058*10^(-11)*(1000\ m)/(1\ km)=j3.989*10^(-6)\ S/km`