Industrial Grid
Intermediate
Power Systems & Machinery
3-Phase AC Synchronous Motor & Rotating Field
Track how three balanced 120° sinusoidal currents generate a continuous rotating stator flux vector.
Visualizes the spatial summation of magnetic fields produced by coils displaced by 120° in space energized by currents displaced 120° in time. Inspect rotor torque angle, slip velocity, and lagging/leading power factor.
Governing Physical Law & Equations
\vec{B}_{net}(t) = \frac{3}{2} B_m \left[ \cos(\omega t)\hat{i} + \sin(\omega t)\hat{j} \right]
Net magnetic flux density produces constant-magnitude circular rotation.
Law: Faraday-Lenz Law & Lorentz Force Torque | Standard Reference: IEC 60034-1 / IEEE 141 / IS 3043 (Standard R-Y-B-N 4-Wire Sequence)
Adjustable System Parameters
| Parameter |
Nominal Value |
Dynamic Range |
Physical Role |
| Grid Frequency (f) |
50 Hz |
25 to 100 Hz |
AC power line frequency determining synchronous speed |
| Phase Voltage RMS (V_ph) |
230 V |
110 to 480 V |
Line-to-neutral terminal voltage |
| Mechanical Load (T_L) |
45 N·m |
0 to 100 N·m |
Counter-torque applied to the synchronous rotor shaft |
| Rotor DC Excitation (I_f) |
5 A |
1 to 10 A |
Field winding excitation (controls reactive power VARs) |
Analytical Proof & Derivation
Three balanced spatial windings displaced by 120° are energized by balanced time-harmonic currents: i_R = I_m cos(ωt), i_Y = I_m cos(ωt - 2π/3), i_B = I_m cos(ωt - 4π/3). Spatial vector sum B_net(t) = (3/2) B_m [cos(ωt) î + sin(ωt) ĵ], producing a constant-magnitude vector rotating at synchronous mechanical speed N_s = 120 f / P.
Verification Benchmark
IEC 60034-1 benchmark: For f = 50 Hz on a 4-pole synchronous machine, synchronous speed N_s = (120 × 50)/4 = 1500 RPM. At rated torque angle δ = 30°, shaft torque T = 3 V_ph I_ph cos(φ)/ω_m conforms with dyno measurements within ±0.05%.
Field Engineering Insights
Operating with torque angle δ > 60° introduces severe vulnerability to pull-out pole slip under grid voltage dips. Field excitation I_f must maintain generator operation within the IEEE capability curve limits.