Unbalanced Three Phase : How to calculate total power ?

Discussion in 'Homework Help' started by kbarb, Jul 17, 2015.

  1. kbarb

    Thread Starter New Member

    Dec 29, 2008
    6
    0
    In our building, we have a four wire 208v/120v Wye service.

    I'm trying to measure the watts used by a subpanel, but the loads are unbalanced.

    For example, for the 208v lines (black, red, blue) I get :
    -- 42A
    -- 84A
    -- 80A

    I know about P = √3 Vl × Il × cos φ where cos φ = power factor, but that's for balanced scenarios, right ?

    I'm going to have to guess at the power factor - most of the loads are lighting & computers/monitors.

    But anyone know how to calculate the total power draw ?

    If you look on this page, Three Phase Current - Simple Calculation and look at the "Balanced Voltages" section it implies that for unbalanced systems you can still calc as such :
    • the line to neutral (phase) voltage VLN = 208/√3 = 120 V
    • phase 1 apparent power = 42 x 120 = 5040 VA = 5.04 kVA
    • phase 2 apparent power = 84 x 120 = 10080 VA = 10.08 kVA
    • phase 3 apparent power = 80 x 120 = 9600 VA = 9.6 kVA
    • Total three phase power = 5.04 + 10.08 + 9.6 = 24.72 kVA
    Anyone know if this is correct ?
     
  2. WBahn

    Moderator

    Mar 31, 2012
    17,716
    4,788
    Yes, that looks correct.

    As you say, you would have to guess at the power factor and that could have a significant effect on your real power.

    As a quick sanity check, you can take the average of the three currents (which would be 68.7 A) and throw that at the balanced three-phase formula and see if you get something that is in the ball park of when you do the per-leg unbalanced computation. In this case that comes out to 24.74 kVA, which is a pretty small ballpark.

    Looking at the formulas, these work out exactly.
     
  3. kbarb

    Thread Starter New Member

    Dec 29, 2008
    6
    0
    Thanks a lot for your very fast reply.
    And I like your sanity check exercise - I can always use a bit of that.
    Thanks again,

    Kent
     
  4. KL7AJ

    AAC Fanatic!

    Nov 4, 2008
    2,039
    287
    Yikes....this is not as simple as it appears. But yes....it is probably unsolvable without knowing the power factor.
     
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