ENERGY CONVERSION ONE (Course 25741)

1. ENERGY CONVERSION ONE(Course25741) CHAPTER SEVEN INDUCTION MOTORS

2. SUMMARY 1. Induction Motor Construction 2. Basic Induction Motor Concepts The Development of Induced Torque in an Induction Motor The Concept of Rotor Slip The Electrical Frequency on the Rotor 3. The Equivalent Circuit of an Induction Motor The Transformer Model of an induction Motor The Rotor Circuit Model The Final Equivalent Circuit 4. Powers and Torque in Induction Motor Losses and Power-Flow diagram Power and Torque in an Induction Motor Separating the Rotor Copper Losses and the Power Converted in an Induction Motor’s Equivalent Circuit 5. Induction Motor Torque-Speed Characteristics Induced Torque from a Physical Standpoint The Derivation of the Induction Motor Induced-Torque Equation Comments on the Induction Motor Torque Speed Curve Maximum (Pullout) Torque in an Induction Motor 6. Variations in Induction Motor Toque-Speed Characteristics Control of Motor Characteristics by Cage Rotor Design Deep-Bar and Double-Cage rotor design, Induction Motor Design Classes

3. SUMMARY 7. Starting Induction Motors 8. Speed Control of Induction Motor Induction Motor Speed Control by Pole Changing. Speed Control by Changing the Line Frequency. Speed Control by Changing the Line Voltage. Speed Control by Changing the Rotor Resistance. 9. Determining Circuit Model Parameters The No-Load Test The DC Test The Locked-Rotor Test 10. Determining Circuit model parameters No-load test/ DC test for stator resistance Locked-Rotor test 11. Induction Generator induction generator operating alone/ induction Generator application Induction motor ratings

4. INDUCTION MOTORSINTRODUCTION • It was shown how amortisseur windings on a synchronous motor could develop a starting torquewithout necessity of supplying an external field current to them • Amortisseur windings work so well that a motor could be built without syn. motor’s main dc field circuit • A machine with only amortisseur winding is calledinduction machine, because the rotor voltage is induced in rotor windings rather than being physically connected by wires

5. INDUCTION MOTORSINTRODUCTION • Cutaway diagram of typical large cage rotor induction motor

6. INDUCTION MOTORSINTRODUCTION • Sketch of Cage Rotor

7. INDUCTION MOTORSINTRODUCTION • Typical wound rotors for induction motors, slip rings & bars connecting rotor windings to slip rings can be seen

8. INDUCTION MOTORSINTRODUCTION • Cutaway of a wound-rotor induction motor • Note:brushes and slip rings are shown, also rotor windings skewed to eliminate slot harmonics

9. INDUCTION MOTORSINTRODUCTION • Distinguishing feature:no dc field current required to run machine • Although it is possible to use an induction machine as either motor or generator, it has many disadvantages as a generator & so is rarely used as Gen. • INDUCTION MOTOR CONSTRUCTION • Same physical stator as syn. machine with different rotor construction • There are “cage rotor” & “wound rotor”

10. INDUCTION MOTORSCONSTRUCTION • A cage induction rotorconsists of a series of conducting bars laid into slots carved in face of rotor & shorted at either end by large shorting rings • This design is referred to as acage rotorbecause of conductors arrangement on rotor • A wound rotor has a complete set of 3 phase windings that are mirror images of windings on stator • The 3 phase of rotor windings are usually Y-connected and end of 3 rotor wires tied to slip rings on rotor shaft • The rotor currents accessible at stator brushes, where they can be examined & where extra resistance can be inserted into rotor circuit • This can be used to modify torque-speed characteristic of motor • Wound rotor motors more expensive, & require more maintenancedue to wearassociated with brushes & slip rings, therefore wound motor induction motors are rarely used

11. BASIC INDUCTION MOTOR CONCEPTS • Its operation is basically same as amortisseur windings on syn. motors • Development of Induced Torque • Again a BS is developed, which is rotating counter-clockwise in Figure of  next slide • Speed of magnetic field’s rotation is : nsync=120fe/p • voltage induced in a rotor bar: eind=(v x B).l v=velocity of bar relative to magnetic field B=magnetic flux density vector l= length of conductor in magnetic field

12. BASIC INDUCTION MOTOR CONCEPTS • Development of Induced Torque

13. BASIC INDUCTION MOTOR CONCEPTS • relative move of rotor w.r.t. BS result in an induced voltage in rotor bar • Velocity of upper rotor bars w.r.t. BS is to right • Induced voltage in upper bars is out of page,while induced voltage in the lower bars is into page • This results in a current flow out of upper bars & into lower bars • Since rotor assembly is inductive, peak rotor current flow produces a rotor magnetic field BR

14. BASIC INDUCTION MOTOR CONCEPTS • Induced torque in machine is: Tind =kBR x BS • resulting torque is counterclockwise & rotor accelerates in this direction • There is a finite upper limit on motor’s speed • If induction motor’s rotor were turning at syn. Speed, then rotor bars would be stationary relative to BS & there would be no induced voltage eind=0 no rotor current & BR=0  Tind=0 • Rotor will slow down, due to friction losses • An induction motor can speed up to near-syn. Speed, however it can never reach syn. speed

15. BASIC INDUCTION MOTOR CONCEPTS • Flowchart showing induction motor operation

16. BASIC INDUCTION MOTOR CONCEPTS • Note:in normal operation, both BR & BS rotate together at syn. Speed nsyncwhile rotor itself turn at a slower s peed • Concept of Rotor Slip • Voltage induced in rotor bar depends on relative speed of rotor with respect to BS • Since behavior of induction motor depends on motor voltage & current, it is more logical to talk about this relative speed • Two terms commonly used to define relative motion of rotor & BS, “slip speed” & “slip” • “slip speed” defined as difference between syn. Speed & rotor speed nslip=nsync-nm

17. BASIC INDUCTION MOTOR CONCEPTS • In which: nslip= slip speed of machine nsync= speed of magnetic fields nm= mechanical shaft speed of motor • “slip” is relative speed expressed on a per-unit or percentage basis: s=nslip/nsync (x100%) s= [nsync-nm] / nsync (x100%) or in terms of angular velocity: • s= [ωsync-ωm] / ωsync (x100%)

18. BASIC INDUCTION MOTOR CONCEPTS • If rotor turn at syn. speed  s=0 • while if rotor stationary  s=1 • all normal motor speeds fall somewhere between those 2 limits • mechanical speed of rotor shaft can be expressed in terms of syn. speed & slip • nm= (1-s)nsync or ωm=(1-s)ωsync

19. BASIC INDUCTION MOTOR CONCEPTS • Electrical Frequency on Rotor • An induction motor works by inducing voltages in rotor of machine& because of that sometimes calledrotating transformer • Like a transformer, primary (stator) induces a voltage in secondary (rotor) but : Unlike a transformer, secondary frequency is not necessarily same as primary frequency • If rotor of motor locked so that can not move, rotor will have the same frequency as stator

20. BASIC INDUCTION MOTOR CONCEPTS • on the other hand, if rotor turns at syn. Speed, frequency on rotor will be zero • what will rotor frequency be for any arbitrary rate of rotor rotation ? • at nm=0 r/min, rotor frequency fr=fe Hz, and slip s=1 • at nm=nsyn fr=0 and slip is s=0 • with any speed in between, rotor frequency is directly proportional to difference between speed of magnetic field nsync & speed of rotor nm S=[nsync-nm] / nsync • rotor frequency can be expressed as : fr=s fe

21. BASIC INDUCTION MOTOR CONCEPTS • alternative forms of last expression: • fr=[nsync-nm] / nsync . fe • since : nsync=120 fe/p  • fr= (nsync-nm)p/(120fe) fe • fr= p/120 (nsync-nm) • Example: A 208 V, 10 hp, 4 pole, 60 Hz, Y connected induction motor has a full-load slip of 5 percent • (a) what is syn. Speed of motor?

22. BASIC INDUC. MOTOR CONCEPTS….EXAMPLE: • (b) what is rotor speed of this motor at rated load? • (c) what is rotor frequency of this motor at rated load? • (d) what is shaft torque of this motor at rated load?

23. BASIC INDUCTION MOTOR CONCEPTS • SOLUTION: (a) nsync=120 fe/p=120x60/4=1800 r/min (b) nm=(1-s) nsync =(1-0.05)(1800)=1710 r/min (c) fr=s fe = 0.95 x 60=3 Hz or fr=p/120 (nsync-nm)=4/120 (1800-1710)=3 Hz • (d) Tload = Pout/ωm= [10 x 746]/[1710 x 2π x 1/60]= 41.7 N.m shaft load torque in English units: Tload=5252 P/n where T is in lb-feet , P in hp, and nmr/min Tload=5252 x 10 / (1710) = 30.7 lb . ft

24. EQUIVALENT CIRCUIT OF AN INDUCTION MOTOR • Basis of an induction motoris on induction of voltage & current in its rotor (Transformer Action) • equivalent circuit of an induction motoris very similar toequivalent circuit of a transformer • “induction motor” is called a “singly excited”machine (opposed to “doubly excited”syn. machine) since power is supplied to only “stator circuit”

25. EQUIVALENT CIRCUIT OF AN INDUCTION MOTOR • Since an induction motor does not have an independent field circuit, its model will not contain an internal voltage sourcesuch as internal generated voltage EAin a syn. Machine • The equivalent circuit of induction motorcan be derived from a knowledgeof“transformers”and from what already know about “variation of rotor frequency” with speedin induction motors • The induction motor model developed by starting with transformer model, and then realizing variable rotor frequency & other induction motor effects

26. EQUIVALENT CIRCUIT OF AN INDUCTION MOTOR • Transformer Model of an Induction Motor • Per-phase equivalent circuit of an induction motor

27. TRANSFORMER MODEL ofINDUCTION MOTOR • As shown there is certain resistance & self inductance in primary (stator) windingswhich must be represented in equivalent circuit of machine • Stator resistance called R1 & stator leakage reactance called X1 • These appear right at input to machine model • Flux in machine is the integral of applied voltage E1 • Curve of magneto-motive force versus flux, (magnetization curve) compared to similar curve for power transformer (next slide)

28. TRANSFORMER MODEL ofINDUCTION MOTOR • Magnetization curve of induction motor

29. TRANSFORMER MODEL ofINDUCTION MOTOR • Note:slope of induction motor’s magneto-motive force-flux curve is much shallower than curve of a good transformer • because there is an air gap in an induction motorwhich greatly increase reluctanceof flux path &therefore reduces coupling between primary & secondary windings • Higher reluctance caused by air gap means a higher magnetizing reactanceXM in equivalent circuit will have a much smaller value (larger susceptance BM) than its value in an ordinary transformer

30. TRANSFORMER MODEL ofINDUCTION MOTOR • Primary internal stator voltage E1 coupled to secondary ERby an ideal transformerwith an effective turns ratio aeff • Effective turns ratio aeffeasy to determined for a wound-rotor motor • ratio of conductors per phase on statorto conductors per phase on rotor,modified by any pitch & distribution factor differences • It is rather difficult to determine aeff clearlyin cage of a case rotor motorbecause there are no distinct windings on cage rotor

31. TRANSFORMER MODEL ofINDUCTION MOTOR • In either case there is an effective turns ratio for motor • Voltage ER produced in rotor in turn produces a current flow in shorted rotor (or secondary) circuit of machine • Primary impedance& magnetization currentof induction motor are very similar tocorresponding components in a transformer equivalent circuit • Induction motor equivalent circuit differs from transformer equivalent circuitprimarily in effects of varying rotor frequency on rotor voltage ERand secondarily inrotor resistance RR and jXR

32. ROTOR CIRCUIT MODEL • A voltage induced in rotor windings when 3 phase voltage applied to stator windings • The greater the relative motion between rotor & stator magnetic fields, the greater the resulting rotor voltage & rotor frequency • The largest relative motion occurs when rotor is stationary, called locked-rotor or blocked-rotor condition • So largest voltage & rotor frequency are induced in rotor at that condition (locked rotor)

33. ROTOR CIRCUIT MODEL • Smallest voltage (0 V) and frequency (0 Hz) occur when rotor moves at same speed as stator magnetic field (having no relative motion) • magnitude & frequency of induced voltage in rotor at any speed between these extremes is proportional to the slip of motor • If magnitude of induced rotor voltage at locked-rotor is ER0 magnitude at any slip : ER=s ER0 frequency of induced voltage: fr=sfe rotor has both resistance & reactance; RR a constant (except for ski effect) , reactance affected in a complicated way by slip

34. ROTOR CIRCUIT MODEL • reactance of an induction motor rotordepends on: inductance of rotor& frequency of voltage and current in rotor • XR=ωr LR = 2π fr LR (realizing : fr=sfr)  XR=2πsfeLR=s XR0(XR0:blocked-rotor reactance) • Resulted equivalent circuit of rotor: