In one line
Three identical coils placed 120° apart on the same rotor (or stator) of an alternator produce three equal sinusoidal EMFs that are 120° out of phase with each other.
Explained simply
Imagine three people pedalling a tandem bicycle with pedals set at equal angles apart: at every moment someone is pushing, so the ride is smooth. Single-phase power pulses (it drops to zero 100 times a second at 50 Hz), but three-phase power delivered to a balanced load is constant, which is why large motors and the grid use three phases.
Technically, in a three-phase alternator, three windings R, Y and B are displaced by 120° electrical. As the magnetic field rotates, each winding sees the same EMF waveform, but each reaches its peak one-third of a cycle after the previous one.
How it works
- Coil R generates \( e_R = E_m\sin\omega t \).
- Coil Y, 120° behind, generates \( e_Y = E_m\sin(\omega t - 120^\circ) \).
- Coil B, 240° behind, generates \( e_B = E_m\sin(\omega t - 240^\circ) \).
- The order in which phases reach their maximum (R-Y-B) is the phase sequence; reversing two lines reverses a motor's direction.
- For a balanced system, \( e_R + e_Y + e_B = 0 \) at every instant, and the phasor sum is zero.
Advantages over single phase: more power for the same conductor material, constant power to balanced loads, three-phase motors are self-starting, and alternators of the same frame size give more output.
Key formula
\( e_R = E_m\sin\omega t,\; e_Y = E_m\sin(\omega t - 120^\circ),\; e_B = E_m\sin(\omega t - 240^\circ) \)
\( E_m \) = peak EMF of each phase (V), \( \omega = 2\pi f \) (rad/s), angles in degrees; 120° displacement is in electrical degrees.
Quick example
At \( \omega t = 90^\circ \): \( e_R = E_m \), \( e_Y = E_m\sin(-30^\circ) = -0.5E_m \), \( e_B = E_m\sin(-150^\circ) = -0.5E_m \). Sum \( = 0 \). In India, the three-phase supply is 415 V line (about 400 V nominal) and 230–240 V phase, 50 Hz; houses receive one phase and neutral.
Common mistakes
- Thinking the three phases have different frequencies or amplitudes.
- Writing \( e_B = E_m\sin(\omega t + 240^\circ) \); it is \( -240^\circ \) (equivalently \( +120^\circ \)).
- Forgetting that the instantaneous sum is zero only for a balanced system.
How MU asks it
Asked as "Explain the generation of three-phase EMF with waveforms and phasor diagram" (5 marks) or "State advantages of three-phase systems". For full marks: sketch three coils 120° apart, write the three equations, draw the three waveforms and the phasor diagram, state phase sequence, and list three or four advantages.