A 4-pole, three-phase induction motor is supplied from 50 Hz AC supply and the full-load speed of the motor is 1455 r.p.m. What are the values of slip and frequency of the rotor induced e.m.f. at standstill respectively?

Concept:

A synchronous motor rotates due to the interlocking of stator R.M.F. poles and rotor poles. Due to this Interlocking, the rotor always rotates at the synchronous speed.

The difference between the rotor speed (N) and the rotating magnetic flux speed (Ns) is called slip.

The motor slip is usually expressed as a percentage of synchronous speed (NS) and is represented by the symbol s.

Mathematically, Percentage slips, \(\% \;s = \left[ {\frac{{{N_s}\;-\;N}}{{{N_s}}}} \right] \times 100\)

Or fractional slip,  \(s = \frac{{{N_s}\;-\;N}}{{{N_s}}}\)

The frequency of rotor-induced emf = sf

Where s is the slip

f is the supply frequency

Calculation:

Number of poles (P) = 4

Frequency (f) = 50 Hz

Full load speed = 1455 rpm

\(N_s = \frac{120f}{P} = \frac{120\times50}{4} = 1500 ~RPM\)

\(Slip ~(s) = \frac{{{N_s}\;-\;N}}{{{N_s}}}= \frac{1500 - 1455}{1500} = 0.03\)

At standstill, fr = 50 Hz