Electrical Machines II. Week 5-6: Induction Motor Construction, theory of operation, rotating magnetic field and equivalent circuit

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1 Electrical Machines II Week 5-6: Induction Motor Construction, theory of operation, rotating magnetic field and equivalent circuit

2 Asynchronous (Induction) Motor: industrial construction Two types of induction motors industrial products

3 Asynchronous (Induction) Motor: Introduction Three-phase induction motors are the most common and frequently encountered machines in industry simple design, rugged, low-price, easy maintenance wide range of power ratings: fractional horsepower to 10 MW run essentially as constant speed from no-load to full load No dc current is required (for magnetic field production)

4 Asynchronous (Induction) Motor: Construction An induction motor has two main parts: a stationary stator consisting of a steel frame that supports a hollow, cylindrical core core, constructed from stacked laminations (for eddy current reduction), having a number of evenly spaced slots, providing the space for the stator winding Two basic design types depending on the rotor design squirrel-cage: conducting aluminum bus bars laid into slots and shorted at both ends by two aluminum shorting rings forming a squirrel-cage shaped circuit (squirrel-cage). wound-rotor: complete set of insulated three-phase wire windings exactly as the stator. Usually Y-connected, and the ends of the three rotor wires are tied to 3 slip rings on the rotor shaft. The rotor windings are shorted through brushes riding on the slip rings. Wound rotor IM have their rotor currents accessible at the stator brushes, where they can be examined and where extra resistance can be inserted into the rotor circuit. similar to the winding on the stator to modify the torque- speed characteristics. Stator of IM Squirrel cage rotor

5 Asynchronous (Induction) Motor: Stator Construction Stator with three symetrical (balanced) distributed phases, a, b. c (windings). There are 3 isolated balanced phase (windings), spaced with 120 (for 2-pole machine). 3-phase symmetrical stators winding is supplied by 3-phase symmetrical voltage supply 120 Stator windings Rotor winding air gap Air gap It must be as small as possible. Smaller air gap resulting in small magnetizing current needed for magnetic field. That field is important for effective electromechanical energy conversion.

6 Asynchronous (Induction) Motor: Rotor Construction bars ring ring rings resistors More expensive than squirrel cage rotor and require much maintenance because of the wear associated with their brushes and slip rings Squirrel cage rotor of induction motor Stator and rotor connections of a slip-ring

7 Asynchronous (Induction) Motor: Rotating magnetic field i a t = I m cos ωt i b t = I m cos ωt 120 i c t = I m cos ωt 240 A balanced 3-phase set of currents is applied to the coil Each current will create a magnetic flux distribution, but the 3-phases are displaced both in time and in space. The flux distribution due to the coil b is 120 degrees behind coil a and the flux due to the coil c is 120 degrees behind coil b.

8 Asynchronous (Induction) Motor: Rotating magnetic field At wt=0 the current in phase a is at a positive max. While the other 2 phases have negative currents With an amplitude of ½. By the right hand flux rule the net stator flux is directed as indicated forming an S pole to the left and N pole to the right. At wt=90 the current in phase a is zero while phase b is positive and phase c is negative. The right hand flux rule will determine the net stator flux is directed as indicated forming an S pole at the bottom and N pole at the top. A rotating magnetic field with constant magnitude is produced, rotating with a speed n s = 120 f P rpm n s : synchronous speed f : supply frequency P: number of stator poles

9 Asynchronous (Induction) Motor: Rotating magnetic field At ωt = 0 B ( t) B ( t) B ( t) B ( t) net a b c B sin( t) 0 B sin( t 120 ) 120 B sin( t 240) 240 M M M = = B M B M B M cos 120 x + sin 120 y + cos 240 x + sin 240 y = 3 2 B M 1 2 x 3 2 y 1 2 x 3 2 y 3 = 2 B M 3 y = 1.5 B M y = 1. 5 B M 90 x: unit vector in the x direction y: unit vector in the y direction 0.866= 3 2

10 Asynchronous (Induction) Motor: Principle of Operation When the stator winding of a three-phase induction motor is connected to a three phase power source, it produces a magnetic field that: (a) is constant in magnitude and (b) revolves around the periphery of the rotor at the synchronous speed. If f is the frequency of the current in the stator winding and P is the number of poles, the synchronous speed of the revolving field is Synchronous speed N s = 120 f P rpm The speed with which the stator magnetic field rotates The revolving field induces electromotive force (emf) in the rotor winding. e ind = (v B). l v: velocity of the bar relative to the magnetic field B: Magnetic flux density l: length of the conductor in the magnetic field It is the relative motion of the rotor compared to the stator magnetic field that produces voltage in the rotor bar.

11 Since the rotor winding forms a closed loop, the induced emf in each coil gives rise to an induced current in that coil. When a current-carrying coil is immersed in a magnetic field, it experiences a force (or torque) that tends to rotate it. The torque thus developed is called the starting torque. If the load torque is less than the starting torque, the rotor starts rotating. The force developed and thereby the rotation of the rotor are in the same direction as the revolving field. This is in accordance with Faraday s law of induction. Under no load, the rotor soon achieves a speed nearly equal to the synchronous speed. However, the rotor can never rotate at the synchronous speed because the rotor coils would appear stationary with respect to the revolving field and there would be no induced emf in them. In the absence of an induced emf in the rotor coils, there would be no current in the rotor conductors and consequently no force would be experienced by them. In the absence of a force, the rotor would tend to slow down. As soon as the rotor slows down, the induction process takes over again. In summary, the rotor receives its power by induction only when there is a relative motion between the rotor speed and the revolving field.

12 Asynchronous (Induction) Motor: Synchronous speed and slip Let N m (or ω m ) be the rotor speed at a certain load. With respect to the motor, the revolving field is moving ahead at a relative speed of: N r = N s N m ω r = ω s ω m The relative speed is also called the slip speed. This is the speed with which the rotor is slipping behind a point on a fictitious revolving pole in order to produce torque. However, it is a common practice to express slip speed in terms of the slip (s), which is a ratio of the slip speed to the synchronous speed. That is, Per unit Slip s = N r N s = N s N m N s N m = (1 s)n s ω m = (1 s)ω s When the rotor is stationary, the per-unit slip is 1 and the rotor appears exactly like a short-circuited secondary winding of a transformer.

13 Asynchronous (Induction) Motor: Synchronous speed and slip The frequency of the induced emf in the rotor winding is the same as that of the revolving field. However, when the rotor rotates, it is the relative speed of the rotor N r (or ω r ) that is responsible for the induced emf in its windings. Thus, the frequency of the induced emf in the rotor is: f r = PN r 120 = P(N s N m ) 120 = sf e = PN s 120 N s N m N s rotor frequency depends upon the slip of the motor. At standstill, the slip is 1 and the rotor frequency is the same as that of the revolving field. However, the rotor frequency decreases with the decrease in the slip. As the slip approaches zero, so does the rotor frequency. An induction motor usually operates at low slip. Hence the frequency of the induced emf in the rotor is low

14 Asynchronous (Induction) Motor: Equivalent Circuit The induction motor is similar to the transformer with the exception that its secondary windings are free to rotate As we noticed in the transformer, it is easier if we can combine these two circuits in one circuit but there are some difficulties When a balanced three-phase induction motor is excited by a balanced three-phase source, the currents in the phase windings must be equal in magnitude and 120 electrical apart in phase. The same must be true for the currents in the rotor windings as the energy is transferred across the air-gap from the stator to the rotor by induction.

15 Asynchronous (Induction) Motor: Equivalent Circuit However, the frequency of the induced emf in the rotor is proportional to its slip. Since the stator and the rotor windings are coupled inductively, an induction motor resembles a three-phase transformer with a rotating secondary winding. The similarity becomes even more striking when the rotor is at rest (blocked-rotor condition, s = 1). HOW???? The greater the relative motion between the rotor and stator magnetic fields, the greater the resulting rotor voltage E R and rotor frequency f r. The largest relative motion occurs when the rotor is stationary, or so-called blocked rotor or locked-rotor. The smallest occurs when E R is zero, when rotor moves at same speed as stator magnetic field.

16 Asynchronous (Induction) Motor: Equivalent Circuit Thus, it is concluded that the voltage induced in the rotor at any instance is directly proportional to the slip of the rotor E R = se R0 Where E R0 is the largest value of the rotor s induced voltage obtained at s = 1(locked rotor) The rotor voltage is induced in a rotor circuit which contains both resistance and reactance. The rotor resistance R R is constant (doesn t change with operation, except for the skin effect) and is slip independent. Rotor reactance is affected in a more complicated way

17 Asynchronous (Induction) Motor: Equivalent Circuit It is known that: X = ωl = 2πfL So, as the frequency of the induced voltage in the rotor changes, the reactance of the rotor circuit also changes: X = ωl = 2πf r L r = 2πsf e L r = sx r0 Where X r0 is the rotor reactance at the supply frequency (at blocked rotor) rotor equivalent circuit

18 Asynchronous (Induction) Motor: Equivalent Circuit To calculate the rotor current as Dividing both the numerator and denominator by s so nothing changes we get I R ER ( R jx ) Where E R0 is the induced voltage and X R0 is the rotor reactance at blocked rotor condition (s = 1) R R R ser0 ( R jsx ) I R = R R E R0 R0 s + jx R0 rotor equivalent circuit Rotor circuit model with all frequency (slip) effects encountered

19 Asynchronous (Induction) Motor: Equivalent Circuit Now as we managed to solve the induced voltage and different frequency problems, we can combine the stator and rotor circuits in one equivalent circuit Where: X a X eff R0 R a R I 2 2 eff R eff E a E a R 1 eff R0 eff I a N N S R

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