56 Electrical Power Systems Technology
The total power (PT) developed by all three phases of a three-phase
system is expressed as:
PT = 3 × 277 V × 10 A × 0.85
= 3 × Vp × Ip × pf
= 1.73 × VL × IL × pf.
Sample Problem:
Given: a three-phase wye system has a phase voltage of 277 volts, a
phase current of 10 amperes, and a power factor of 0.85.
Find: total three-phase power.
Solution:
PT = 3 × 277 V × 10 A × 0.85
PT = 7063.5 watts
We can summarize three-phase power relationships as follows:
Volt-amperes per phase (VAP) = VPIP
Total volt-amperes (VAT) = 3 VPIP
= 1.73 VLIL
Sample Problem:
Given: a three-phase delta system has a line voltage of 208 volts and
a line current of 4.86 amperes.
Find: total three-phase volt-amperes.
Solution:
VA = 1.73 × 208 V × 4.86 A
VA = 1748.8 volt-amperes
true power (W)
power factor (pf) = ————————
1.73 VLIL
W
= ———
3 VPIP
power per phase (Pp) = 3 VPIP × pf
= 1.173 VLIL × pf