# EMF equation of an alternator and solved problems

An alternator or a synchronous generator is a device used to convert mechanical energy to Alternating current electric current. The EMF equation of an alternator is a mathematical expression to calculate the effective value of EMF induced in each phase of an alternator or a synchronous generator.

According to Faraday’s law of electromagnetic induction, the average emf induced per conductor is:

Where,

Φ is the flux per pole in weber.

t is the time taken for rotation.

If ‘P’ is the number of poles in the alternator and n is the speed of rotation in radials per minute, the change in flux can be given by

Also the time take for rotation is given by

Hence,

The frequency of the induced EMF is given by

Substituting equation [2] in equation [1]

Let ‘Z’ be the number of conductors per phase and ‘T’ be the number of turns per phase. Every phase contains two turns of the conductor so Z=2T. The average EMF induced in each phase is given by:

The above equation represents the average value of EMF induced per phase of an alternator. As you know the induced voltage is sinusoidal in nature.

The RMS value of a sinusoidal AC voltage is 1.11 times its average value. Hence effective RMS value of EMF induced per phase can be found by multiplying Equation [3] by 1.11.

Considering the pitch factor kp and the distribution factor kd also, the equation [4] for the RMS value of the voltage generated in each phase of an AC synchronous generator may be rewritten as follows:

The EMF equation of an alternator is given above. The pitch factor kp and the distribution factor kd can be calculated from the following formulae:

Where,

α is the slot angle and m is the number of slots per pole per phase.β is the angular distance between a full pitch and short pitch coils. For a full pitch coil, β = 0, and hence kp is 1.

## Solved example:

Let us find the solution for the following problem using the emf equation of an alternator.

Problem: A 3-phase, 50 Hz alternator is running at 600 rpm has a 2-layer winding, 12 turns/coil, 4 slots/pole/phase, and coil-pitch of 10 slots. Let us find the induced EMF per phase if the flux/pole is 0.035 webers.

### Solution

Given data:

The number of poles can be calculated as follow:

The total number of slots

Slot angle

Slot angle

The emf equation of an alternator is