- EMF Definition: Electromotive force (EMF) in a DC generator is defined as the voltage generated by the movement of conductors through a magnetic field.
- Faraday’s Law: This law explains that the induced EMF in a generator’s conductor is proportional to the rate at which it cuts through the magnetic field lines.
- Generator Components: A DC generator consists of conductors, magnetic fields, armature, poles, and winding paths that collectively contribute to EMF production.
- Types of Winding: Wave winding involves fewer parallel paths, generally two, affecting the EMF calculation, whereas lap winding has a parallel path for each pole.
- EMF Equation of DC Generator: The total EMF for the generator is calculated by multiplying the EMF of one conductor by the number of conductors connected in series per path.
The EMF equation of a DC generator can be derived in two steps:
- Find the average induced EMF of one armature conductor.
- Multiply by the conductors connected in series in each parallel armature path.
Derivation for Induced EMF of One Armature Conductor
For one mechanical revolution of a conductor,
Let,
Φ = useful Flux per pole in webers (Wb)
and
P = number of poles in the DC generator.
Therefore,
Total flux cut by one conductor per revolution
And,
Time taken for one revolution
Here N is armature speed in revolutions per minute (rpm).
Under Faraday’s law of induction, the magnitude of average induced EMF equals flux cut divided by time. The commutator rectifies the alternating conductor EMF at the brushes. The induced conductor EMF is denoted by e, and its polarity follows Lenz’s law for the chosen reference direction and flux.
Therefore,
Average induced EMF of one conductor
The average induced EMF of one conductor is
Derivation for Induced EMF for DC Generator
Let Z be the total number of active armature conductors, divided among A parallel paths.
Here,
Z = total number of active armature conductors
A = number of parallel armature paths
Then,
Z/A = number of conductors connected in series in each path
Each correctly connected parallel path has the same brush-to-brush generated EMF.
Therefore,
The generated EMF E equals the average EMF of one conductor multiplied by Z/A, the number of series conductors in one parallel path.
Generated EMF of a DC generator
Simplex wave-wound generator
The number of parallel paths is A = 2.
Therefore,
Generated EMF for a simplex wave winding is
Simplex lap-wound generator
Here, the conductors are grouped into one parallel path per pole.
That is, A = P for a simplex lap winding.
Therefore,
Generated EMF for a simplex lap-wound generator
Multiplex windings use different path counts, so use the actual value of A.
