# NCEES #111



## cruzy (Oct 26, 2010)

Why do they divide 12.5 by sqrt 3 for doing the single phase equivalent of Van? It is a delta load, where there isn't even a neutral to consider. I know I am wrong, just don't get why at all.


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## cableguy (Oct 26, 2010)

Because they're working with line current in the solution. They have to drop out of the line to line voltage and go to a phase voltage in order to do a voltage sum on the line.

They convert the line-to-line voltage to a phase voltage, add the phase current x impedance voltage value, and then go back to line-to-line at the end by multiplying by sqrt(3).


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## nmh0408 (Oct 26, 2010)

cableguy said:


> Because they're working with line current in the solution. They have to drop out of the line to line voltage and go to a phase voltage in order to do a voltage sum on the line.
> They convert the line-to-line voltage to a phase voltage, add the phase current x impedance voltage value, and then go back to line-to-line at the end by multiplying by sqrt(3).



In addition dont forget a 30 degrees phase shift between the Phase and Line to Neutral Voltages.


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## cableguy (Oct 26, 2010)

Absolutely - since they drove a nail through Vab at 0 degrees, everything else depends on it.

If they nail down an angle, then you should probably keep track of angles in your solution.


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## knight1fox3 (Oct 26, 2010)

I'm fairly certain this problem has been discussed in a few other threads but didn't the solution basically use a delta to wye conversion to make the math easier in drawing the single-line diagram? In doing that it really simplifies the problem. But that is where the sqrt(3) comes from. The analysis will work out the same whether the load is configured in delta or wye, but the math is easier with the load configured in wye.


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## electric (Oct 26, 2010)

It seems for this problem, the delta load is insignificant. Basically all the calculations are done for the transmission line. Even if the load had been Y, still you would end up with the same answer. Is that correct?


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## cruzy (Oct 26, 2010)

cableguy said:


> Because they're working with line current in the solution. They have to drop out of the line to line voltage and go to a phase voltage in order to do a voltage sum on the line.
> They convert the line-to-line voltage to a phase voltage, add the phase current x impedance voltage value, and then go back to line-to-line at the end by multiplying by sqrt(3).


But when they convert the line-line voltage to a phase voltage, in delta those two have the same value. I took it as if the line current given already had the sqrt 3 built in, meaning the phase current was (70 angle -20)/sqrt3. Still not getting it. How can the 12.5 kV in that delta config be divided by sqrt 3? there's no neutral to take care of the lower voltage.


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## Flyer_PE (Oct 27, 2010)

cruzy said:


> But when they convert the line-line voltage to a phase voltage, in delta those two have the same value. I took it as if the line current given already had the sqrt 3 built in, meaning the phase current was (70 angle -20)/sqrt3. Still not getting it. How can the 12.5 kV in that delta config be divided by sqrt 3? there's no neutral to take care of the lower voltage.


For a balanced system, the load configuration (delta or wye) doesn't matter. In a balanced wye, since the current in the neutral is zero, you can remove the neutral conductor and the system will still work just fine. Just because there's no neutral conductor, doesn't mean there isn't a point in space that is at neutral potential to the three phases.


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## nmh0408 (Oct 27, 2010)

Flyer_PE said:


> cruzy said:
> 
> 
> > But when they convert the line-line voltage to a phase voltage, in delta those two have the same value. I took it as if the line current given already had the sqrt 3 built in, meaning the phase current was (70 angle -20)/sqrt3. Still not getting it. How can the 12.5 kV in that delta config be divided by sqrt 3? there's no neutral to take care of the lower voltage.
> ...



Some people refer to it as the "Y-Equivelent", whcih make calculation easier.


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## cableguy (Oct 27, 2010)

Heck, Kaplan thinks there are 2 of them. N and n. And they're both different. Magic!


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