A balanced three-phase supply provides three sinusoidal voltages of equal magnitude, displaced by 120° in phase. This arrangement gives a constant total power transfer for a balanced load, which is why it dominates industrial power distribution and large motor drives.
Star and delta connections
In a star connection the three windings share a neutral point; in a delta connection they form a closed triangle. The relationship between line and phase quantities depends on the connection, so always identify which quantity a measurement refers to before applying a formula.
Balanced three-phase power
Problem. A balanced load draws 20 A per line from a 400 V line-to-line supply at a power factor of 0.85. Calculate the active power.
Solution. P = √3 × 400 × 20 × 0.85 = 1.7321 × 400 × 20 × 0.85 = 11 778 W, approximately 11.8 kW.
Why balance matters
A balanced load draws equal currents with a 120° displacement, so the neutral current of a star-connected load is ideally zero. Unbalanced loads produce neutral current and unequal phase voltages, which is why phase balance is checked in industrial installations.
- The three phase voltages are equal in magnitude and 120° apart.
- Total instantaneous power of a balanced load is constant.
- Line and phase quantities differ by the connection type.
- Neutral current is ideally zero only for a balanced star load.
- Three phases are 120° apart.
- Balanced three-phase power is P = √3 V_L I_L cos φ.
- Star and delta connections change the line/phase relationship.
- Unbalanced loads create neutral current.
Worked example
A 400 V, 30 A balanced load at power factor 0.9 draws P = √3 × 400 × 30 × 0.9 = 18 706 W, about 18.7 kW.