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.

 

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 \(P=S \cdot |PF|\).

 

Ok, my apologies, but I wrote an inexact equation on the assumption it would be understood. I did, in fact, mean

, 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?

 

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

 

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.

 

You seem to have a handle on it now. Well done!