Three-Phase Kv-a and Power Factor

Author: E.E. Kimberly

Power in a three-phase load is the sum of the powers in the three component parts of the load. Where the load is Y-connected, as in Fig. 9-5 (a), the power is the same whether the phases are balanced or unbalanced. Thus,

When the load is balanced,

and Also,

Therefore,

or

(9-6)

Where the load is Δ-connected, as in Fig. 9-5 (b), the following relation holds whether the phases are balanced or unbalanced:

When the load is balanced,

and Also,

Therefore,

(9-7)

Similarly, it may be shown that the number of reactive volt-amperes (vars, reactive power, fictitious power) in a three-phase load is the algebraic sum of the reactive volt-amperes of the component parts of the load.

Volt-amperes of a capacitive portion of a load must be taken opposite in sign to volt-amperes of an inductive portion in the algebraic sum. When the load is balanced, the number of reactive volt-amperes is

(9-8)

The total number of volt-amperes (apparent power) in a three-phase load is the square root of the sum of the squares of the power and the reactive volt-amperes. The method of combining the several kinds of volt-amperes graphically is shown in Fig. 9-11.

Fig. 9-11. Volt-Ampere Diagram

The power factor of a three-phase load is the ratio of the power to the total volt-amperes. 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 power-factor correction (see Chapter 25), the three-phase quantities are used in an equivalent single-phase diagram.