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29 March, 14:04

A three-phase 25-kVA, 480-V, 60-Hz alternator, operating under balanced steady-state conditions, supplies a line current of 20 A per phase at a 0.8 lagging power factor and at rated voltage.

Determine the power triangle for this operating condition.

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  1. 29 March, 16:49
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    The apparent power is S = 9.6 kVA;

    The true power is P = 7.68 kW;

    The reactive power is Q = 7.075 kVAr (inductive)

    Explanation:

    There are three types of electrical power the apparent power S (V*I), true power P (V*I*cos (theta)) and reactive power Q (V*I*sin (theta)). The power factor is the same as cos (theta) So we can find theta by applying acos to it:

    theta = acos (0.8) = 36.87º

    Now we can compute the power triangle:

    S = V*I = 480*20 = 9.6 kVA

    P = V*I*cos (theta) = 9.6 * (0.8) = 7.68 kW

    Q = V*I*sin (theta) = 9.6*|sin (36.87) | = 9.6| (-0.737) | = 7.075 kVAr (inductive)
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