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Thread: 3 Phase unbalanced power formula

  1. #1
    Join Date
    Sep 2004

    3 Phase unbalanced power formula

    The basic formula for 3 phase balanced power is pretty straightforward, I(line) * V(line to line) * sqrt(3) * Power Factor.

    It gets trickier with an unbalanced delta load. I have a situation where the line currents are not all equal, the line voltages are not all equal, and the power factors (defined as the phase relationship between the voltage and current on one wire) are not all equal. It is running a big delta connected motor(a chiller), which probably has a couple of smaller loads connected open jaw or single phase(some oil pumps, jacket heaters, and miscellaneous stuff). There is no neutral connection.

    Given the situation above, how does one calculate the total power accurately?

    Lawrence Lile, P.E.

  2. #2
    Join Date
    Jun 2003

    Re: 3 Phase unbalanced power formula

    First calculate the power in each leg of the delta using

    P = I(phase)* V(phase) * power factor

    (Notice that V(phase) = V(line), but I(phase) is not equal to I(line))

    Total power is the sum of the power in each leg:

    Pt = P1+P2+P3

    The tricky part is finding the line current. It is the vector sum of the two phase current connected to that line. For balanced loads:

    I(line) = sqrt(3) * I(phase)

    but that doesn't hold for unbalanced loads. However, if the chiller load is really large compared to the single phase loads I would just use sqrt(3) times the largest phase current.


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