# EMF Equation of a Synchronous Generator

The Derivation of **EMF Equation** of a synchronous generator is given below.

Let,

- P be the number of poles
- ϕ is Flux per pole in Webers
- N is the speed in revolution per minute (r.p.m)
- f be the frequency in Hertz
- Z
_{ph}is the number of conductors connected in series per phase - T
_{ph}is the number of turns connected in series per phase - K
_{c}is the coil span factor - K
_{d}is the distribution factor

Flux cut by each conductor during one revolution is given as **Pϕ** Weber

Time taken to complete one revolution is given by **60/N** sec

Average EMF induced per conductor will be given by the equation shown below

Average EMF induced per phase will be given by the equation shown below

The average EMF equation is derived with the following assumptions given below.

- Coils have got the full pitch.
- All the conductors are concentrated in one stator slot.

**Root mean square** (R.M.S) value of the EMF induced per phase is given by the equation shown below.

**E _{ph} = Average value x form factor**

Therefore,

If the coil span factor K_{c} and the distribution factor K_{d , }are taken into consideration than the Actual EMF induced per phase is given as

Equation (1) shown above is the EMF equation of the Synchronous Generator.

The Coil Span Factor is defined as the ratio of the induced emf in a coil when the winding is short pitched to the induced emf in the same coil when the winding is full pitched.

Distribution factor is defined as the ratio of induced EMF in the coil group when the winding is distributed in a number of slots to the induced EMF in the coil group when the winding is concentrated in one slot.