Let
Φ = flux/pole in weber
Z = total number of armture conductors
= No.of slots x No.of conductors/slot
P = No.of generator poles
A = No.of parallel paths in armature
N = armature rotation in revolutions per minute (r.p.m)
E = e.m.f induced in any parallel path in armature
Generated e.m.f Eg = e.m.f generated in any one of the parallel paths i.e E.
Average e.m.f geneated /conductor = dΦ/dt volt (n=1)
Now, flux cut/conductor in one revolution dΦ = ΦP Wb
No.of revolutions/second = N/60
Time for one revolution, dt = 60/N second
Hence, according to Faraday's Laws of Electroagnetic Induction,
E.M.F generated/conductor is
For a simplex wave-wound generator
No.of parallel paths = 2
No.of conductors (in series) in one path = Z/2
E.M.F. generated/path is
For a simplex lap-wound generator
No.of parallel paths = P
No.of conductors (in series) in one path = Z/P
E.M.F.generated/path
In general generated e.m.f
where A = 2 - for simplex wave-winding
= P - for simplex lap-winding
Terminal Voltage
DC generator output voltage is dependent on three factors : (1) the number of
conductor loops in series in the armature, (2) armature speed, and (3) magnetic field strength. In order to change the generator output, one of these three factors must be varied. The number of conductors in the armature can not be changed in a normally operating generator, and it is usually impractical to change the speed at which the armature rotates. The strength of the magnetic field, however, can be changed quite easily by varying the current through the field winding. This is the most widely used method for regulating the output voltage of a DC generator.DC Generator Ratings
A DC generator contains four ratings.
Voltage: Voltage rating of a machine is based on the insulation type and design of
the machine.
Current: The current rating is based on the size of the conductor and the amount of
heat that can be dissipated in the generator.
Power: The power rating is based on the mechanical limitations of the device that is used to turn the generator and on the thermal limits of conductors,bearings, and other components of the generator.
Speed: Speed rating, at the upper limit, is determined by the speed at which mechanical damage is done to the machine. The lower speed rating is based on the limit for field current (as speed increases, a higher field current is necessary to produce the same voltage).
