Camara Problems 10 and 12

[googs19]

The solutions for Camara problems 10 and 12 show the following equation for reactive power:

Q=sqrt(3)*(V^2)/X

From what I can tell the square root of 3 should not be in this equation. Is there something I am missing, or is this just an incorrectly shown equation?

 

[crellis]

From the PPI passing zone forum:

"Answer 10: The sqrt(3) in the solution for Q and Xc is nonsense. Therefore, the solution is nonsense. We would need to be told if the capacitance is to be connected in delta or in wye to be able to execute this problem.

I have submitted this to the errata previously. I did not check if it is on the PPI web site errata."

 

[Wael]

Guys the sqrt(3) is there because it is 3 phase formula. similar to P= sqrt(3) VIPF.

from voltage level you can tell it is 3 phase problem if not said clearly.

 

[googs19]

Wael, in the case of finding the impedance of a system from the voltage and power the single phase and three phase equations are both Z=V^2/S

 

[Wael]

The way i thought about it is:

Q= sqrt (3) (V line) ((Vline)/Xc) (sin -90), where Vline/Xc = I across capacitance.

I also looked into Errata and didnt find anything about it. so the formula seems right for 3 phase system. I hope somebody can confirm or clarify.

 

[googs19]

Since the single phase equation is: Q(phase)=V(phase)*(V(phase)/Xc)

The 3 phase equations is 3 times this value: Q(3-phase)=3*Q(phase)=3*V(phase)*(V(phase)/Xc)

And then when you convert V(phase) to V(line): Q(3-phase)=3*(V(line)/sqrt(3))*((V(line)/sqrt(3))/Xc)

Which reduces to: Q(3-phase)=V(line)*(V(line)/Xc)

In the S=VI form since there is only one voltage, 3/sqrt(3) reduces to sqrt(3). However, since there are two voltages in the S=V^2/Z the sqrt(3) is completely canceled out.

 

[Wael]

I reported this question to PPI last night and I hope to hear the answer before the exam. Ill keep you updated

 

[crellis]

Wael, my response above was from the passing zone coordinator working for ppi. I agree that the sqrt(3) should not be there. Work it out for yourself using only phase voltages and per phase reactive power.

 

[Wael]

crellis,

Thanks for your response, for a reason I missed your first post. now it all makes perfect sense. sorry for th econfusion guys, and I wish all the best for all of us on friday.

 

[GreenNGold]

So is the answer to this question C) 9 uF?

 

[GreenNGold]

For power factor correction, are these the appropriate equations?

Q (single phase) = (Vph)^2 / Xc

Q (three phase) = (3 * Vph) / Xc

Q (three phase) = Vline^2 / Xc

And if so, what about when given a delta load? Since Vline = Vph we would get different answers?