Power in Balanced Three-Phase Circuits

The total power delivered by a three-phase source, or consumed by a three-phase load, is found simply by adding the power in each of the three phases. In a balanced circuit, however, this is the same as multiplying the average power in any one phase by 3, since the average power is the same for all phases. Thus one has

P = 3 V_phI_ph cos φ

where V_ph and I_ph are the magnitudes of any phase voltage and phase current, cosφ is the load power factor, and φ is the power factor angle between the phase voltage ¯V_ph and the phase current ¯ I_ph corresponding to any phase. In view of the relationships between the line and phase quantities for balanced wye- or delta-connected loads, Equation can be rewritten in terms of the line-to-line voltage and the line current for either wye- or delta-connected balanced loading as follows:
P = √3 V_LI_Lcos φ

where V_L and I_L are the magnitudes of the line-to-line voltage and the line current. φ is still the load power factor angle as in Equation, namely, the angle between the phase voltage and the corresponding phase current.