EMF Equation of a Synchronous Generator

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)

• Z_ph = number of series-connected conductors per phase

• T_ph = number of series-connected turns per phase

• Kc = coil span factor

• K_d = 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).