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Delta and Wye Circuit Equations

Typical 3-Phase Wiring Diagrams and Equations for Resistive Heaters

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Definitions

For Both Wye and Delta (Balanced Loads) Wye and Delta Equivalent
VP = Phase Voltage
VL = Line Voltage
IP = Phase Current
IL = Line Current
R = R1 = R2 = R3 = Resistance of each branch
W = Wattage

WDELTA = 3 WWYE
WODELTA = ¾ WDELTA
WOWYE = ½ WWYE

Equations

3-Phase Wye (Balanced Load) 3-Phase Open Wye (No Neutral)

3-Phase Wye

IP = I L
VP = VL/1.73
WWYE = VL2/R = 3 (VP2)/R
WWYE = 1.73VLIL

3-Phase Open Wye

IPO = I LO
VPO = VL/2
WOWYE = 1/2 ( VL /R)
WOWYE = 2 (VPO2/R)

3-Phase Delta (Balanced Load) 3-Phase Open Delta

3-Phase Delta

IP = I L/1.73
VP = VL
WDELTA = 3(VL2)/R
WDELTA = 1.73VLIL

3-Phase Open Delta

VP = VL
IPO1 = I PO3 = I LO2
ILO3 = 1.73 I PO1
WODELTA = 2(VL2/R)