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ThreePhase Kva and Power FactorAuthor: E.E. Kimberly Power in a threephase load is the sum of the powers in the three component parts of the load. Where the load is Yconnected, as in Fig. 95 (a), the power is the same whether the phases are balanced or unbalanced. Thus,
When the load is balanced, and Also, Therefore, or (96) Where the load is Δconnected, as in Fig. 95 (b), the following relation holds whether the phases are balanced or unbalanced:
When the load is balanced, and Also, Therefore,
(97) Similarly, it may be shown that the number of reactive voltamperes (vars, reactive power, fictitious power) in a threephase load is the algebraic sum of the reactive voltamperes of the component parts of the load. Voltamperes of a capacitive portion of a load must be taken opposite in sign to voltamperes of an inductive portion in the algebraic sum. When the load is balanced, the number of reactive voltamperes is
(98) The total number of voltamperes (apparent power) in a threephase load is the square root of the sum of the squares of the power and the reactive voltamperes. The method of combining the several kinds of voltamperes graphically is shown in Fig. 911.
The power factor of a threephase load is the ratio of the power to the total voltamperes. The foregoing definitions are predicated on the assumption of sinusoidal currents and voltages only. For some purposes, such as the calculation of condenser capacity required for powerfactor correction (see Chapter 25), the threephase quantities are used in an equivalent singlephase diagram.


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