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Double check apparent power definition

  1. Oct 27, 2015 #1
    Hey just to make sure,
    can we say apparent power S = V^2 / Z

    for a complex impedance Z?
    And do we have to worry about conjugates at all?

    Cheers
     
  2. jcsd
  3. Oct 27, 2015 #2

    anorlunda

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    The total power S = VI. Where S, V and I are all complex. I prefer that to $$\frac{V^2}{Z}$$ because VI works for any circuit.

    Is apparant power the same as total power? I'm not exactly sure what you mean by apparent power.

    Edit: no conjugations were needed.
     
  4. Oct 27, 2015 #3

    Averagesupernova

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    I always thought apparent power is the voltage across the complex impedance multiplied by the current through the complex impedance. So, V * I, or V^2 / Z, or I^2 * Z. I don't think I have heard of a definition of total power. But that just might be semantics.
     
  5. Oct 27, 2015 #4
    First, you have the complex power:
    $$
    \mathbf{S} = \mathbf{V}\overline{\mathbf{I}}
    $$
    where ##\mathbf{V},\mathbf{I}## are RMS phasors. The overline means to take the complex conjugate.

    The apparent power is defined as:
    $$
    |\mathbf{S}| = |\mathbf{V}\overline{\mathbf{I}}| = |\mathbf{V}||\overline{\mathbf{I}}| = |\mathbf{V}||\mathbf{I}| = \frac{|\mathbf{V}|^2}{|\mathbf{Z}|}
    $$
    which is consumed by the impedance ##\mathbf{Z}## with the voltage ##\mathbf{V}## across it.
     
  6. Oct 27, 2015 #5
    Yeah Averagesupernova, I think that's right, I always think of it as being the hypotenuse of the reactive and real power.
     
  7. Oct 27, 2015 #6
    Hi Miles, thanks.
    Ah ok, it is for magnitudes. But what about if I still wanted it all to be in terms of comples voltages, currents and powers?

    Specifically because I'm trying to work out a newton raphson here:

    https://www.physicsforums.com/threa...on-matlab-not-converging.839961/#post-5270803

    Using the aforementioned power equation. I'm trying to work out the complex voltages for 4 busses in Matlab. Where I have worked out the matricies for the complex power for each bus and the admittance matrix.


    Thank you
     
  8. Oct 28, 2015 #7
    ##\mathbf{V}## and ##\mathbf{Z}## are complex.

    When you need the apparent power, then you could just, for instance, use the 'abs' function in MATLAB to find ##|\mathbf{V}|,|\mathbf{Z}|##.
     
  9. Oct 28, 2015 #8
    Hey Miles,
    Yeah I actually tried that yesterday, but now I'm thinking I can't use apparent power. So is it incorrect to say that:

    Complex power = complex voltage * complex admittance?
    like P + Q = V^2 / (R + X)

    I think one thing that might be wrong is my jacobian.
    From what I remember NR uses the form y = f(x)
    where y is a constant (in this case the powers) and x is the voltages ('volts' matrix), so my function is
    (volts)^2)*Y_mat

    so the jabobian is:
    (2*volts*Y_mat)

    ? Or have I not differentiated that properly?
     
    Last edited: Oct 28, 2015
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