# NCEES 121



## roadrunner (Apr 14, 2010)

A synchronous generator is 3 phase wye connected and rated 1131 kva, 2.4 kv, 0.9 lagging. the output current from the generator at rated full load is most nearly:

Why do you use the formula Sbase = Sq root 3 Vbase Ibase

I just used the S=VI formula and got it wrong. Tad confused


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## Flyer_PE (Apr 15, 2010)

S=VI* is valid for single-phase devices.

S=sqrt3VI* is the power equation for three-phase devices.


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## roadrunner (Apr 15, 2010)

Thanks Flyer! Hope you know how important to this forum you are, your help is GREATLY appreciated


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## kris7o2 (May 14, 2021)

Why is this not S=3*Vp*Ip... instead we used S=3*VL*IL


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## akyip (May 14, 2021)

kris7o2 said:


> Why is this not S=3*Vp*Ip... instead we used S=3*VL*IL


Typically, 3-phase voltage values are given as line-to-line voltages and 3-phase current values are given as line currents. If you are given 3-phase voltage/current/power values and they don't specify whether it's line-to-line or line-to-neutral values, you need to assume that:

the voltages given are line-to-line voltage values
the currents given are line current values
the power values given (W, VA, or VAR) are 3-phase power values
So here in this problem with the 3-phase synchronous generator, the 1131 KVA given is 3-phase apparent power and the 2.4 KV voltage given is line-to-line voltage. So |S 3-ph| = sqrt(3) x |V LL| x |I L|, and line current magnitude value |I L| = |S 3-ph| / (sqrt(3) x |V LL|).

I also attached a brief derivation of the apparent 3-phase power formula. Please note that this is *magnitude only* *|S 3-ph|.*


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## Zach Stone P.E. (May 15, 2021)

roadrunner said:


> A synchronous generator is 3 phase wye connected and rated 1131 kva, 2.4 kv, 0.9 lagging. the output current from the generator at rated full load is most nearly:
> 
> Why do you use the formula Sbase = Sq root 3 Vbase Ibase
> 
> I just used the S=VI formula and got it wrong. Tad confused



These are two different formulas. The first calculates the apparent power for a three-phase system or machine, and the second calculates the apparent power for a single-phase system or machine, or the per-phase power of a three-phase system or machine.

These two formulas are very commonly misused. If you'd like to dig further with more examples of how these can be used both correctly AND incorrectly, take a look at the following article:

Avoid These Three Phase Power Formula Mistakes! (Electrical PE Review)


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