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
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    Ok, my apologies, but I wrote an inexact equation on the assumption it would be understood. I did, in fact, mean [​IMG], 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
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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
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    You seem to have a handle on it now. Well done!
     
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