Subject overview
Three-Phase Systems
Balanced star and delta connections, three-phase power and generator phase voltages separated by 120 electrical degrees.
01 Star Connection
Variables
- Upphase RMS voltage
- Vvolt
- Ipphase RMS current
- Aampere
- φload phase angle
- radradian
- ULline RMS voltage
- Vvolt
- ILline RMS current
- Aampere
- Ptotal active power
- Wwatt
- Qtotal reactive power
- varvar
- Stotal apparent power
- VAvolt-ampere
Key Formulas
Line voltages are differences of phase-voltage phasors. For equal magnitudes separated by 120°, this gives the factor √3 in a star connection. In delta, the corresponding phasor subtraction applies to the line currents. Total complex power is the sum over three equal loads.
Balanced sinusoidal three-phase supply and identical passive phase loads. Neutral current is zero in balanced star. Relations do not describe unbalanced loads or floating-neutral voltage shifts.
Calculate
Type prefixes directly: 1.5k, 250m or 20u. Results: 3 significant figures.
Balanced sinusoidal three-phase supply and identical passive phase loads. Neutral current is zero in balanced star. Relations do not describe unbalanced loads or floating-neutral voltage shifts.
Enter the required input values to calculate.
02 Delta Connection
Variables
- Upphase RMS voltage
- Vvolt
- Ipphase RMS current
- Aampere
- φload phase angle
- radradian
- ULline RMS voltage
- Vvolt
- ILline RMS current
- Aampere
- Ptotal active power
- Wwatt
- Qtotal reactive power
- varvar
- Stotal apparent power
- VAvolt-ampere
Key Formulas
Line voltages are differences of phase-voltage phasors. For equal magnitudes separated by 120°, this gives the factor √3 in a star connection. In delta, the corresponding phasor subtraction applies to the line currents. Total complex power is the sum over three equal loads.
Balanced sinusoidal three-phase supply and identical passive phase loads. Neutral current is zero in balanced star. Relations do not describe unbalanced loads or floating-neutral voltage shifts.
Calculate
Type prefixes directly: 1.5k, 250m or 20u. Results: 3 significant figures.
Balanced sinusoidal three-phase supply and identical passive phase loads. Neutral current is zero in balanced star. Relations do not describe unbalanced loads or floating-neutral voltage shifts.
Enter the required input values to calculate.
03 Three-Phase Generator
Variables
- Upphase peak voltage
- Vvolt
- ffrequency
- Hzhertz
- telapsed time
- ssecond
- u1phase 1 voltage
- Vvolt
- u2phase 2 voltage
- Vvolt
- u3phase 3 voltage
- Vvolt
Key Formulas
Three identical windings displaced by 120 electrical degrees generate equal-amplitude sinusoidal voltages. Their instantaneous sum vanishes in a balanced system. Electrical frequency equals mechanical rotational frequency times the number of pole pairs.
Ideal balanced generator with 120° electrical phase separation and equal amplitudes. The three phase voltages sum to zero. Change elapsed time to inspect the instantaneous state.
Calculate
Type prefixes directly: 1.5k, 250m or 20u. Results: 3 significant figures.
Ideal balanced generator with 120° electrical phase separation and equal amplitudes. The three phase voltages sum to zero. Change elapsed time to inspect the instantaneous state.
Enter the required input values to calculate.
Schematic curve; no numerical scale.
Schematic curve; no numerical scale.
Schematic curve; no numerical scale.
Schematic curve; no numerical scale.