Shorebrook Practice Problem #52

[BebeshKing PE]

Could someone please explain to me how they come up with the answer of the power and power supply per wire for each system? (single phase 2-wire, single phase 3-wire, 3phase, 3 wire, and 3 phase 4-wire)

Thank you,

 

[akyip]

I just started doing the Shorebrook PE exam, and this is indeed one of the weirder questions I found on this exam.

My take on this question is this.

It seems this question defines power in terms of phase voltage and line current.

1-phase, 2-wire system:

V ph = V LN

P 1-ph = V ph * I Line * cos(theta) = P total

P total / Total number of wires = (1/2) * V ph * I Line * cos(theta) = 0.50 * V ph * I Line * cos(theta)

1-phase, 3-wire system:

V ph = V LN

P 1-ph = V LN * I Line * cos(theta)

P total = 2 * P 1-ph = 2 * V LN * I Line * cos(theta)

P total / Total number of wires = (2/3) * V ph * I Line * cos(theta) = 0.67 * V ph * I Line * cos(theta)

3-phase, 3-wire (delta) system:

V ph = V L-L for a 3-phase delta system

P total = P 3-ph = sqrt(3) * V ph * I Line * cos(theta) = sqrt(3) * V L-L * I Line * cos(theta)

P total / Total number of wires = [ sqrt(3) / 3 ] * V ph * I Line * cos(theta) = 0.58 * V ph * I Line * cos(theta)

3-phase, 4-wire (wye) system:

V ph = V L-N for a 3-phase wye system

P total = P 3-ph = 3 * V ph * I Line * cos(theta) = 3 * V LN * I Line * cos(theta)

P total / Total number of wires = (3/4) * V ph * I Line * cos(theta) = 0.75 * V ph * I Line * cos(theta)

This is the best explanation I can think of for this question.

Another egregious thing I saw on another question for the Shorebrook PE exam was that one of the solutions had S = V* I instead of S = VI*.

 

[Dothracki PE]

The simple answer I can think is with a given power load in a system, the question is asking for the power in the individual feeder. So for the single phase (2 wire) system the entirety of the power is in one conductor. Whereas the 1ph (3 wire), 3ph Delta, and 3ph Wye systems will divide the load between the phase legs. 

I don't know if that's the correct explanation but I know that's how we factor in loads on panels schedules for various loads when we often get a mix of all 4 types of electrical connections in a project