DC generator working and emf equation

A DC generator is a machine that turns mechanical power into DC electrical power. Its action is based on Faraday's laws of electromagnetic induction.

Working principle

1. When a conductor is moved in a magnetic field so that it cuts the lines of flux, an emf is induced in it: e = B l v (V). The direction is given by Fleming's right-hand rule.
2. The armature conductors, rotated by a prime mover, cut the flux of the N and S poles. The emf induced in a coil is alternating, because each conductor passes alternately under N and S poles.
3. The commutator is a mechanical rectifier. As the coil emf reverses, the commutator segment connection to the brush also reverses, so the brush polarity does not change.
4. The brushes deliver unidirectional current to the load. The magnitude depends on speed and flux.
5. Field excitation is supplied either by a separate source (separately excited) or by the machine itself (self-excited: shunt, series, compound).

 prime mover -> rotating armature -> commutator -> brushes -> load
   (N rpm)      (cuts flux Φ)       (AC to DC)

Energy flow: mechanical input − (friction, windage, iron, copper losses) = electrical output.

Derivation of EMF equation

Let P = number of poles, Φ = flux per pole (Wb), Z = total armature conductors, A = parallel paths, N = speed (rpm).

• Flux cut by a conductor in one revolution: dΦ = ΦP
• Time for one revolution: dt = 60/N s
• Average emf generated per conductor: e = dΦ/dt = ΦPN/60 volts
• Number of conductors in series in each parallel path = Z/A
• Emf of the generator = emf per path

E_g = (ΦPN/60) × (Z/A) = PΦZN / (60A) volts

For a given machine, E_g = KΦN with K = PZ/(60A), which shows that emf depends on the flux per pole and the speed.