Capacitance to neutral? PPI Exam 1 Question 68

[akyip]

Hey guys,

PPI Exam 1 question 68 is about solving for a 1-phase, 2-wire distribution system's capacitive reactance per unit length. I tried to solve this using the NCEES-provided reference handbook.

In the NCEES reference handbook, the formula for average capacitance to neutral is given as:

C = 2 * pi * epsilon 0 / ln(D eq / GMR)

But the solution to this problem uses:

C = pi * epsilon 0 / ln(D / r)

Why is the capacitance formula different for a 1-phase, 2-wire system? Why does it not have the 2 multiplier? Why does it only use conductor radius instead of GMR?

Thanks for any input on this!

 

[speakeelsy PE]

Hey guys,

PPI Exam 1 question 68 is about solving for a 1-phase, 2-wire distribution system's capacitive reactance per unit length. I tried to solve this using the NCEES-provided reference handbook.

In the NCEES reference handbook, the formula for average capacitance to neutral is given as:

C = 2 * pi * epsilon 0 / ln(D eq / GMR)

But the solution to this problem uses:

C = pi * epsilon 0 / ln(D / r)

Why is the capacitance formula different for a 1-phase, 2-wire system? Why does it not have the 2 multiplier? Why does it only use conductor radius instead of GMR?

Thanks for any input on this!

single phase formulas are different that 3 phase formulas for this. Check out Zach's online course Ch8.7 Transmission Lines. It doesn't really give an explanation though.

For more explanation check out Power systems Analysis by Grainger and Stevenson -- Chapter 5.3 Capacitance of a Two-wire line, and 5.4 Capacitance of a Three-Phase Line - it's got the derivation of both formulas!

Looks like it all stems from C=q/V

for single phase C=q/(Vab/2)

divided by 2 because it's capacitance to ground or neutral, so the 2's cancel

for 3phase C=q/Van

so the 2's don't cancel. 

Also remember GMRc in the handbook = radius, and GMR = r'  (it's dumb)

 

[DLD PE]

Also the capacitive reactance formula:

Xc =  1 / (2*pi*f*C) is a useful formula but I don't recall seeing it in the NCEES handbook.

 

[speakeelsy PE]

Also the capacitive reactance formula:

Xc =  1 / (2*pi*f*C) is a useful formula but I don't recall seeing it in the NCEES handbook.

page 36 but it's in a weird format

 

[DLD PE]

Yes, that format could cause hesitation under real exam conditions.

 

[akyip]

Thanks for the responses, guys!

Going over Zach's Oct. 2020 live class notes on my own. I'll have to see his transmission lines notes when I get there.