Induction Machines-Theory

• The induction motor consists of a fixed core, the stator, carrying a three phase winding in slots on its bore.
• The stator winding is connected to the supply, and a uniform rotating magnetic filed is produced therein.
• It works based on principle of Electro-magnetic interaction
• Speed of the stator m.m.f is synchronous speed
• The speed of rotation,n, of the rotor is less than the synchronous speed by a fraction,s known as the slip
• A high ratio of resistance to reactance is desirable under starting conditions, but the resistance should be low for running near synchronous speed, the normal condition
• The induction motor is a machine of substantially constant speed, and fills the same role as the plain shunt motor among the dc machines
• The cage rotor is adaptable to any number of poles. whereas the slip-ring winding has to be made for one(or possibly two) definite values of p.
• leakage flux is greater than transformer in induction machine due to its air gap
Power relations:
• Power input to the stator per phase is P₁ = V₁I₁cosØ₁
• Power delivered by transformer action to the rotor, P₂
• The mechanical power developed at the rotor, P_m = (1-s)P₂
• Rotor power loss is I₂²r₂ = sP₂ = s.rotor input
• P₂:P_m:I₂²r₂ = 1:(1-s):s
• If the rotor had no resistance it could develop no torque
• condition for maximum torque is r₂ = ±sx₂
• Slip values for different operations: If s is positive and between 0 and 1 : Motor, If s is negative and -1 to 0 : generator, If s greater than unity: braking

 

Solved Problems
1.A 220-V, three-phase, two-pole, 50-Hz induction motor is running at a slip of 5 percent. Find:
(a) The speed of the magnetic fields in revolutions per minute
(b) The speed of the rotor in revolutions per minute
(c) The slip speed of the rotor
(d) The rotor frequency in hertz

SOLUTION:

(a) The speed of the magnetic fields is

(b) The speed of the rotor is

(c) The slip speed of the rotor is

(d) The rotor frequency is

2.A three-phase, 60-Hz induction motor runs at 890 r/min at no load and at 840 r/min at full load.
(a) How many poles does this motor have?
(b) What is the slip at rated load?
(c) What is the speed at one-quarter of the rated load?
(d) What is the rotor’s electrical frequency at one-quarter of the rated load?
SOLUTION
(a) This machine has 8 poles, which produces a synchronous speed of

(b) The slip at rated load is

(c) The motor is operating in the linear region of its torque-speed curve, so the slip at ¼ load will be

The resulting speed is

(d) The electrical frequency at ¼ load is