Question

a squirrel cage induction machine is driving a 700 N load through a wheel with a diameter of 0.5 m using the simplified gamma model and the machine parameters presented below calculate the followings:

a) The speed of the machine, assuming a flux linkage of 0.703:

b)Stator current phasor is:

c)Active power, reactive power, apparent power, and power factor from the point of view of the source

the parameters are:

-line to line voltage 480 v

- # poles 4

-Gride frequency 60 Hz

-stator Resistance 0.1

-Rotor Resistance 0.3

-Stator Leakage Reactance 0.5

-Rotor Leakage Reactance 0.6

- magnetizing reactance 25

Answer 1

a, The very basic formula

N = 120 *f/P with p poles and f frequency

= 120 * 60 / 4 = 1800 rpm

b.Stator current phasor-

The induction motor draws no load current I_o  which is phasor sum of Ic (core component )  and I_m (magnetising ). The total stator current drawn from supply is,

?₁ = ?_o + ?_2r'

where

I_2r' = K I_2r

Given-

stator Resistance 0.1

-Rotor Resistance 0.3

-Stator Leakage Reactance 0.5

-Rotor Leakage Reactance 0.6

- magnetizing reactance 25

From the phasor diagram -

Also given  flux linkage = 0.703 Wb/m²

We know stator current I_! = V/ Z₁ where Z₁ = r₁ + jx₁ + Z_f

where r₁ - stator resistance

  x₁ - stator reactance

Z_f - shunt reactance (magnetising rectance )

Hence stator current I₁ (phase ) = 480 / 3.14 / ( 0.1 + 0.6 + 25 ) = 10.78 A