AC power
Star connection: line and winding voltage
- where
- line voltage (V)
- winding (phase) voltage (V)
- line current (A)
- winding (phase) current (A)
Explain this equation
Gives the line voltage and line current of a balanced star-connected load or winding, from the voltage across and current through each winding. Use it when reading motor nameplates or working with three-phase four-wire supplies.
V_ph is the voltage across one winding, from a line to the star point, and I_ph the current through it. V_L is the voltage between any two lines and I_L the current in each line.
In star, each line feeds straight into one winding, so line current and winding current are the same. The voltage between two lines is the difference between two phase voltages 120° apart, and that difference works out at √3 times either one.
230 V per winding gives about 398 V between lines, which is why a 230 V phase-to-neutral system is called a 400 V three-phase system. Double the winding current and the line current doubles.
Watch out: this assumes a balanced load. With an unbalanced load and no neutral, the star point can float and the winding voltages will no longer be V_L / √3.
Each star-connected winding runs between a line and the star point. For a balanced supply and load, its voltage is the line voltage divided by √3.
Line current equals winding current in star. Winding voltage is especially important when interpreting motor nameplates; the correct connection must match the stated supply and rating.
Enter your values to see the result.
Common mistake
Never assume every 400 V motor should run in star. Read its actual winding and connection ratings.
Limits
Balanced three-phase star load. A floating star point can move under unbalance; do not assume V_L/√3 then.
Sources
The tools calculate the displayed equation. They do not automatically choose cable sizes, approve installations, supply current regulatory tables, certify equipment or replace inspection and testing.