THREE-PHASE CIRCUITS
Basic AC Power
In a balanced delta load, the line voltage (VL) is equal to the phase voltage (Vf), and the line
current (IL) is equal to the square root of three times the phase current (
). Equation (9-5)
3 If
is a mathematical representation of VL in a balanced delta load. Equation (9-6) is a mathematical
representation of IL in a balanced delta load.
VL = Vf
(9-5)
(9-6)
IL
3 If
In a balanced wye load, the line voltage (VL) is equal to the square root of three times phase
voltage (
), and line current (IL) is equal to the phase current (If). Equation (9-7) is a
3 Vf
mathematical representation of VL in a balanced wye load. Equation (9-8) is a mathematical
representation of IL in a balanced wye load.
(9-7)
VL
3 Vf
(9-8)
IL
If
Because the impedance of each phase of a balanced delta or wye load has equal current, phase
power is one third of the total power. Equation (9-10) is the mathematical representation for
phase power (Pf) in a balanced delta or wye load.
Pf = Vf If cosq
(9-10)
Total power (PT) is equal to three times the single-phase power. Equation (9-11) is the
mathematical representation for total power in a balanced delta or wye load.
PT = 3Vf If cosq
(9-11)
In a delta-connected load, VL = Vf and
so:
If
3 IL
3
PT
3 VL IL cos q
In a wye-connected load, IL = If and
so:
Vf
3 VL
3
PT
3 VL IL cos q
ES-09
Page 20
Rev. 0
