# Winding EMFs in a 3-Phase Induction Motor; Stator EMF and Rotor EMF

Let suffixes "s" and "r" be used for stator and rotor quantities, respectively. Then,

ππ  = Stator applied voltage per phase

ππ  = Number of stator winding turns in series per phase

ππ = Number of rotor winding turns in series per phase

Ο = Resultant flux in air gap

πΈπ  = Stator induced EMF per phase

πΈπ0 = EMF induced in the rotor per phase when the rotor is at standstill

πΈππ  = EMF induced in the rotor per phase when the rotor is rotating at a slip π

ππ  = Resistance of stator winding per phase

ππ = Resistance of rotor winding per phase

πΏπ0 = Rotor inductance per phase at standstill due to leakage flux

ππ0 = Leakage reactance of the rotor winding per phase when the rotor is at standstill

ππ = Supply frequency

ππ = Frequency of the induced EMF in the rotor at a slip π

πππ  = Leakage reactance of rotor winding per phase when the rotor is rotating at a slip π

πππ  = Distribution factor of stator winding

πππ = Distribution factor of rotor winding

πππ  = Coil span factor of stator winding

πππ = Coil span factor of rotor winding

Then, the induced EMF in the stator winding per phase is given by,

$$\mathrm{πΈ_π = 4.44\: π_{ππ } \:π_{ππ }\: π_π \:\varphi\: π_π … (1)}$$

The induced EMF per phase in the rotor when the rotor is at standstill is given by,

$$\mathrm{πΈ_{π0} = 4.44 \:π_{ππ}\: π_{ππ}\: π_π \: \varphi\: π_π … (2)}$$

The induced EMF per phase in the rotor when the rotor is rotating at a slip 's' is given by,

$$\mathrm{πΈ_{ππ } = π πΈ_{π0}}$$

$$\mathrm{\therefore πΈ_{ππ } = 4.44 π_{ππ} π_{ππ}\: π \:π_π \:\varphi \:π_π … (3)}$$

Now, let,

• πππ  πππ  = ππ€ = Winding factor of stator
• πππ πππ = ππ€π = Winding factor of rotor

Then,

$$\mathrm{πΈ_π = 4.44 π_{π€π }\: π_π \:\varphi \:π_π … (4)}$$

And

$$\mathrm{πΈ_{ππ } = 4.44 π_{π€π} π π_π \varphi π_π … (5)}$$

Now, taking the ratio of eqns. (4) and (5), we get,

$$\mathrm{\frac{πΈ_{π }}{πΈ_{ππ }}=\frac{π_{π€π } π_{π }}{π_{π€π} π_{π}}=\frac{π_{ππ }}{π_{ππ}}= π_{πππ}… (6)}$$

Where, Nes and Ner are known as effective stator and rotor turns per phase, respectively.

And ππππ is known as effective turns ratio of an induction motor.

Also,

$$\mathrm{\frac{πΌ′_π}{πΌ_π}=\frac{π_{ππ}}{π_{ππ }}=\frac{1}{π_{πππ}}… (7)}$$

From equation (6), it is clear that the ratio between stator and rotor EMFs is constant at standstill. This ratio depends upon the turns ratio modified by the distribution and coil span factors of the windings. Hence, an induction motor behaves like a transformer. The number of slots in stator and rotor may be different, thus, the factors for the stator and rotor windings are not the same.