# Complex Power and Power Factor

Discussion in 'Homework Help' started by Teppod, Feb 5, 2011.

1. ### Teppod Thread Starter New Member

Feb 5, 2011
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Given: S=1500 VA
pf=0.866 lagging

Find reactive power.

We are given a value for complex power, which is a real number, and a value for the power factor, which is lagging. Since S=P+jQ, I would like to conclude that Q=0, but the existence of a power factor is throwing me off. Is it possible to have a lagging power factor and still have a purely real value for complex power? If so, how? Any help is greatly appreciated.

2. ### Georacer Moderator

Nov 25, 2009
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Actually, it is $\vec{S}=P+jQ$, so it is $S^2=P^2+Q^2$. A PF of 0.866 lagging means that the current comes behind the voltage, that usually is the angle reference.

Remember that $P=S \cdot |PF|$.

3. ### Teppod Thread Starter New Member

Feb 5, 2011
5
0
Ok, my apologies, but I wrote an inexact equation on the assumption it would be understood. I did, in fact, mean $\vec{S}=P+jQ$, so $\vec{S}$=1500 VA in the given information. I also understand the meaning of a lagging power factor.

To elaborate a bit on the work I've done, using $cos^{-1}=(pf)$, the fact that pf is lagging and letting $\theta_{v}$ be zero as a reference, I found the power factor angle to be approx. -30 degrees. This gives me a rf of about -.5. The fact that I have a non-zero value there means that $V_{eff}I_{eff}$ would have to be zero for $\vec{S}$ to be wholly real, except that it can't be because that would make $\vec{S}=0$.

So, to reiterate my question, how is it possible that $\vec{S}$ is a wholly real number if Q≠0, or where has my logic gone off the rails?

Last edited: Feb 5, 2011
4. ### t_n_k AAC Fanatic!

Mar 6, 2009
5,448
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I imagine the confusion has arisen because you have concluded that the quoted 1500VA is a real number - rather than a complex value.

I take it that the "1500" is the magnitude of the complex value. If the pf were unity then indeed the 1500 would be the real component with jQ=0. But the pf is 0.866 lagging, which requires the apparent power to be a complex value. The complex value is implicit in the statement of non-unity power factor conditions.

In other words

S=1300-j750 VA

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5. ### Teppod Thread Starter New Member

Feb 5, 2011
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Another part of my confusion actually stems from the fact that I'm trying to solve a problem for a take-home quiz (due Mon. morning) covering material we have not yet covered in our lecture. Go figure, but I think you may be onto something here.

Let me see if I follow your logic. Stating "If the complex power is 1500 VA with a power factor of 0.866 lagging..." indicates that $\vec{S}=1500\angle-30^{\circ} VA$ (angle taken from previous post), which, in rectangular notation, is $750\sqrt{3}-j750 VA$. From there I can break out the reactive power. That makes a lot of sense, thank you.

6. ### t_n_k AAC Fanatic!

Mar 6, 2009
5,448
782
You seem to have a handle on it now. Well done!