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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,
ππ = Stator applied voltage per phase
ππ = Number of stator winding turns in series per phase
ππ = Number of rotor winding turns in series per phase
Ο = Resultant flux in air gap
πΈπ = Stator induced EMF per phase
πΈπ0 = EMF induced in the rotor per phase when the rotor is at standstill
πΈππ = 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
πΏπ0 = Rotor inductance per phase at standstill due to leakage flux
ππ0 = Leakage reactance of the rotor winding per phase when the rotor is at standstill
ππ = Supply frequency
ππ = Frequency of the induced EMF in the rotor at a slip π
πππ = Leakage reactance of rotor winding per phase when the rotor is rotating at a slip π
πππ = Distribution factor of stator winding
πππ = Distribution factor of rotor winding
πππ = Coil span factor of stator winding
πππ = Coil span factor of rotor winding
Then, the induced EMF in the stator winding per phase is given by,
$$\mathrm{πΈ_π = 4.44\: π_{ππ } \:π_{ππ }\: π_π \:\varphi\: π_π … (1)}$$
The induced EMF per phase in the rotor when the rotor is at standstill is given by,
$$\mathrm{πΈ_{π0} = 4.44 \:π_{ππ}\: π_{ππ}\: π_π \: \varphi\: π_π … (2)}$$
The induced EMF per phase in the rotor when the rotor is rotating at a slip 's' is given by,
$$\mathrm{πΈ_{ππ } = π πΈ_{π0}}$$
$$\mathrm{\therefore πΈ_{ππ } = 4.44 π_{ππ} π_{ππ}\: π \:π_π \:\varphi \:π_π … (3)}$$
Now, let,
- πππ πππ = ππ€ = Winding factor of stator
- πππ πππ = ππ€π = Winding factor of rotor
Then,
$$\mathrm{πΈ_π = 4.44 π_{π€π }\: π_π \:\varphi \:π_π … (4)}$$
And
$$\mathrm{πΈ_{ππ } = 4.44 π_{π€π} π π_π \varphi π_π … (5)}$$
Now, taking the ratio of eqns. (4) and (5), we get,
$$\mathrm{\frac{πΈ_{π }}{πΈ_{ππ }}=\frac{π_{π€π } π_{π }}{π_{π€π} π_{π}}=\frac{π_{ππ }}{π_{ππ}}= π_{πππ}… (6)}$$
Where, Nes and Ner are known as effective stator and rotor turns per phase, respectively.
And ππππ is known as effective turns ratio of an induction motor.
Also,
$$\mathrm{\frac{πΌ′_π}{πΌ_π}=\frac{π_{ππ}}{π_{ππ }}=\frac{1}{π_{πππ}}… (7)}$$
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.