Synchronous Generator and EMF Equation Derivation
A generator operating at synchronous speed is termed a synchronous generator, which converts mechanical power into electrical energy for grid integration. The derivation of the EMF equation for a synchronous generator is as follows:
Notation:
- P = number of poles
- ϕ = flux per pole (Weber)
- N = rotational speed (revolutions per minute, r.p.m)
- f = frequency (Hertz)
- Zph = number of series-connected conductors per phase
- Tph = number of series-connected turns per phase
- Kc = coil span factor
- Kd = distribution factor
Derivation: The flux cut by each conductor in one revolution is Pϕ Weber. The time to complete one revolution is 60/N seconds. The average EMF induced per conductor is given by:
Average EMF induced per phase will be given by the equation shown below:
Average EMF Equation Assumptions
The derivation of the average EMF equation is based on the following assumptions:
- Coils exhibit full pitch configuration.
- All conductors are concentrated within a single stator slot.
The root mean square (RMS) value of the induced EMF per phase is expressed as:Eph = Average Value×Form Factor Thus,
EMF Equation and Winding Factors
Equation (1) above represents the EMF equation of a synchronous generator.
Coil Span Factor (Kc)
The coil span factor is defined as the ratio of the induced EMF in a short-pitched coil to that in an identical full-pitched coil.
Distribution Factor (Kd)
The distribution factor is the ratio of the induced EMF in a distributed coil group (wound across multiple slots) to that in a concentrated coil group (wound in a single slot).
