Derivation of the EMF equation for DC Generator
The derivation of the EMF equation for the DC generator involves two components.
- Induced EMF of one conductor
- Induced EMF of the Generator
Derivation for Induced EMF of a Single Armature Conductor
For one rotation of the conductor.
Let,
- Ī¦ = Flux generated by each pole in Weber (Wb).
- P = number of poles in the DC generator.
Therefore,
- Total flux generated by all poles = Ī¦ x P.
and,
Time required to complete one revolution = 60/N
Where,
N represents the armature conductorās speed in revolutions per minute.
According to Faradayās law of induction, the induced emf of the armature conductor is indicated by āeā, which is comparable to the rate of cutting the flux.
Therefore,
e = dĪ¦ / dt, and e = total flow / time taken.
The induced EMF of a single conductor
e = Ī¦ P/(N/60) = Ī¦ P x (N/60) volts.
Derivation of Induced EMF for DC Generator.
Assume there are Z total number of conductors in a generator, and they are designed so that all parallel pathways are always in series.
Here,
- Z = Total number of conductors.
- A = the number of parallel pathways.
Then,
Z/A = the number of conductors connected in series.
Therefore,
Induced EMF of DC Generator
- E = the emf of one conductor multiplied by the number of conductors linked in series.
The induced emf of a direct current generator
e = Ī¦P x (N/60) x (Z/A) volts.
The number of parallel paths are only 2 = A.
Hence,
The induced emf of a wave type winding generator is
(Ī¦PN / 60) x (Z / 2) = Ī¦ZPN / 120 Volts.
Simple lap winding generator.
Here, the number of parallel pathways equals the number of conductors in one path.
i.e. P = A
Therefore,
The induced EMF for a lap-wound generator is
Eg = (Ī¦ Z N P) / (60 A) volts.
Construction And Working of a DC Generator
In 1831, Michael Faraday, a British physicist, devised the electromagnetic generator. The primary function of this device is to convert mechanical energy to electrical energy. There are several types of mechanical energy sources available, including hand cranks, internal combustion engines, water turbines, and gas and steam turbines. The generator provides capacity for all electrical power networks. An electric motor should be able to perform the generatorās converse function. The basic purpose of the motor is to convert electrical energy into mechanical energy. Generators and motors have many properties.
Table of Content
- DC Generator
- Construction of a DC generator
- Workings
- Types
- Losses in DC Machines
- Characteristics of DC Generator
- Characteristics of DC Series Generator
- Characteristics of DC Shunt Generators
- External Load Characteristics of the DC Compound Generator
- Efficiency of a DC Generator