Wye / Delta Line-to-Phase Voltage and Current
The mapping between line and phase (winding) quantities for both three-phase connections.
Example
You enter
- Connection wye
- Line-to-line voltage (V) 208
- Line current (A) 10
- Power factor (0-1) 1
You get
- Phase (winding) voltage 120.1 V
- Phase (winding) current 10 A
- Apparent power 3603 VA
Checked against published worked examples from: EC&M (Endeavor Business Media), author Mike Holt.
Details, formula, and sources
Scopein a wye the line voltage is root-3 times the phase voltage while currents are equal; in a delta the line current is root-3 times the phase current while voltages are equal, with the connection-independent apparent power. The equipment nameplate governs the connection.
Formula or tableWye: V_line = root-3 x V_phase, I_line = I_phase. Delta: V_line = V_phase, I_line = root-3 x I_phase. Connection-independent S = root-3 x V_line x I_line; P = S x PF. root-3 = 1.73205.
Source and editionFirst-principles three-phase winding relations; classical balanced three-phase theory.
Free accessFirst-principles physics; no licensed source required.
What governsEstimate. AHJ and licensed professional govern.
API field namesconfiguration, line_voltage_v, line_current_a, power_factor, phase_voltage_v, phase_current_a, power_va
- Balanced system the relations assume a balanced three-phase system; the root-3 factor is exact for balanced sinusoidal quantitiesbalanced three-phase theory
- Connection the equipment nameplate governs the actual connection (wye/star or delta)equipment nameplate