NEC Problem 536 using handbook

[Byk]

I am trying to solve all of the problems in the practice exam using only reference book.

However, I cannot solve this one. I know that problem gives us the formula to use for line to ground capacitance and then we use that to convert it to capacitive reactance.

I was wondering if we can somehow use formula for the average capacitive reactance to neutral ( I understand that it it handbook is to neutral not to the ground) 

Also, can someone please break down GMR formula for me.



I understand the r prime however, I am not sure what to use for d. Should it be d12, d23 or d13?

Thanks in advance!

 

[jd5191]

I was wondering if we can somehow use formula for the average capacitive reactance to neutral ( I understand that it it handbook is to neutral not to the ground) 

Yes. Calculate your average reactance to neutral which gives you an answer in ohm-miles, divide by number of miles to get your ohms. As long as you use either all inches or all ft in the 'Ln' part of the equation. You'll get the right answer.

Also, can someone please break down GMR formula for me.

View attachment 20321

I understand the r prime however, I am not sure what to use for d. Should it be d12, d23 or d13?

Before I answer the question, note that this problem's equation calls for "GMRc" and not "GMR". GMRc uses the radius of the conductor and not 0.7788r.

GMR is used when you have multiple conductors in one phase of a line, and you need to calculate an equivalent radius of the multiple conductors in a single phase, note that it is not the distance between phases! The diagram below from the handbook shows multiple conductors in a single phase only. In this problem, GMRc = radius.

 

[akyip]

I am trying to solve all of the problems in the practice exam using only reference book.

However, I cannot solve this one. I know that problem gives us the formula to use for line to ground capacitance and then we use that to convert it to capacitive reactance.

I was wondering if we can somehow use formula for the average capacitive reactance to neutral ( I understand that it it handbook is to neutral not to the ground) 

Also, can someone please break down GMR formula for me.

View attachment 20321

I understand the r prime however, I am not sure what to use for d. Should it be d12, d23 or d13?

Thanks in advance!

As @jd5191 mentioned above, one of the very confusing things that the NCEES reference handbook was use GMRc for the transmission line capacitance formulas. You actually just use the actual conductor radius for the transmission line capacitance. For the case of Problem 536, it's only 1 conductor per phase, so just use the conductor's actual radius (not the GMR - GMR is for calculating transmission line inductance).

Also, since each phase of the transmission line is just 1 conductor per phase, the bundled conductor formulas do not apply in this problem. The bundled conductors are used for cases where each phase has more than one (sub-)conductor. The Deq in the formula refers to GMD = geometric mean distance. That is a function of how the phases are spaced apart, not bundling.

I believe the formula they gave specifically in Problem 536 is actually the same as the capacitance to neutral formula given in Page 72 of the reference handbook - just expressed in different units. I took a shot in deriving this.

I was able to come to close to the correct answer using the 3 different formulas provided between Problem 536 and the NCEES reference handbook formulas.

Please see my work attached.

 

[Byk]

As @jd5191 mentioned above, one of the very confusing things that the NCEES reference handbook was use GMRc for the transmission line capacitance formulas. You actually just use the actual conductor radius for the transmission line capacitance. For the case of Problem 536, it's only 1 conductor per phase, so just use the conductor's actual radius (not the GMR - GMR is for calculating transmission line inductance).

Also, since each phase of the transmission line is just 1 conductor per phase, the bundled conductor formulas do not apply in this problem. The bundled conductors are used for cases where each phase has more than one (sub-)conductor. The Deq in the formula refers to GMD = geometric mean distance. That is a function of how the phases are spaced apart, not bundling.

I believe the formula they gave specifically in Problem 536 is actually the same as the capacitance to neutral formula given in Page 72 of the reference handbook - just expressed in different units. I took a shot in deriving this.

I was able to come to close to the correct answer using the 3 different formulas provided between Problem 536 and the NCEES reference handbook formulas.

Please see my work attached.

View attachment 20334

View attachment 20335

View attachment 20336

View attachment 20337

@akyip Thank you so much for posting your work.

I did everything exactly the same. However, I did not substitute GMRc for rc.

How did you know that GMRc is actually rc? 

When reading the handbook ti says GMRc is calculated the same way as GMR with the virtual radius rl replaced with the subconductor's radius r. 

 

[akyip]

@akyip Thank you so much for posting your work.

I did everything exactly the same. However, I did not substitute GMRc for rc.

How did you know that GMRc is actually rc? 

When reading the handbook ti says GMRc is calculated the same way as GMR with the virtual radius rl replaced with the subconductor's radius r. 

This was something I was taught by a review session from Zach Stone, specifically about the NCEES reference handbook. GMRc should really be rc for the transmission line capacitance formulas.

In general:

When calculating transmission line inductance, you use GMR.

When calculating transmission line capacitance, you use actual conductor radius r.

 

[Byk]

@Zach Stone, P.E. would you be kind and chime in why would you use Rc for the vaule GMRc?

The handbook states "GMRc is calculated the same way as GMR with the virtual radius rl replaced with the subconductor's radius r."

 

[jd5191]

This was something I was taught by a review session from Zach Stone, specifically about the NCEES reference handbook. GMRc should really be rc for the transmission line capacitance formulas.

Are you saying capacitance doesn't change no matter how many conductors you have? I would think the formulas in the handbook are correct and you need to calculate GMRc based on the number of conductors you have.

 

[akyip]

Are you saying capacitance doesn't change no matter how many conductors you have? I would think the formulas in the handbook are correct and you need to calculate GMRc based on the number of conductors you have.

No, what I'm trying to say is that you use either the actual radius of the conductor (for a single conductor per phase) or the equivalent radius of multiple bundled conductors per phase.

For the case of bundled sub-conductors per phase:

Let r = actual radius of each sub-conductor, and d = spacing distance between sub-conductors

Then, the equivalent radius you use for the denominator inside the ln of the capacitance formulas become:

r, 2-conductor bundle = sqrt(r * d)

r, 3-conductor bundle = 3-root(r * d * d)

r, 4-conductor bundle = 4-root(r * d * d * sqrt(2) * d)

 

[jd5191]

No, what I'm trying to say is that you use either the actual radius of the conductor (for a single conductor per phase) or the equivalent radius of multiple bundled conductors per phase.

For the case of bundled sub-conductors per phase:

Let r = actual radius of each sub-conductor, and d = spacing distance between sub-conductors

Then, the equivalent radius you use for the denominator inside the ln of the capacitance formulas become:

r, 2-conductor bundle = sqrt(r * d)

r, 3-conductor bundle = 3-root(r * d * d)

r, 4-conductor bundle = 4-root(r * d * d * sqrt(2) * d)

Ok so that's no different than the handbook. I thought you were saying you learned something different.