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**ENERGY CONVERSION ONE (Course 25741)**

CHAPTER SEVEN INDUCTION MOTORS

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**SUMMARY 2. Basic Induction Motor Concepts**

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

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**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

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**INDUCTION MOTORS INTRODUCTION**

It was shown how amortisseur windings on a synchronous motor could develop a starting torque without 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 called induction machine, because the rotor voltage is induced in rotor windings rather than being physically connected by wires

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**INDUCTION MOTORS INTRODUCTION**

Cutaway diagram of typical large cage rotor induction motor

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**INDUCTION MOTORS INTRODUCTION**

Sketch of Cage Rotor

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**INDUCTION MOTORS INTRODUCTION**

Typical wound rotors for induction motors, slip rings & bars connecting rotor windings to slip rings can be seen

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**INDUCTION MOTORS INTRODUCTION**

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

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**INDUCTION MOTORS INTRODUCTION**

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”

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**INDUCTION MOTORS CONSTRUCTION**

A cage induction rotor consists 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 a cage rotor because 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 maintenance due to wear associated with brushes & slip rings, therefore wound motor induction motors are rarely used

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**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

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**BASIC INDUCTION MOTOR CONCEPTS**

Development of Induced Torque

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**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

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**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

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**BASIC INDUCTION MOTOR CONCEPTS**

Flowchart showing induction motor operation

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**BASIC INDUCTION MOTOR CONCEPTS**

Note: in normal operation, both BR & BS rotate together at syn. Speed nsync while 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

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**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%)

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**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

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**BASIC INDUCTION MOTOR CONCEPTS**

Electrical Frequency on Rotor An induction motor works by inducing voltages in rotor of machine & because of that sometimes called rotating 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

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**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

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**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?

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**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?

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**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 = x 60=3 Hz or fr=p/120 (nsync-nm)=4/120 ( )=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 nm r/min Tload=5252 x 10 / (1710) = 30.7 lb . ft

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**EQUIVALENT CIRCUIT OF AN INDUCTION MOTOR**

Basis of an induction motor is on induction of voltage & current in its rotor (Transformer Action) equivalent circuit of an induction motor is very similar to equivalent 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”

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**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 source such as internal generated voltage EA in a syn. Machine The equivalent circuit of induction motor can be derived from a knowledge of “transformers” and from what already know about “variation of rotor frequency” with speed in induction motors The induction motor model developed by starting with transformer model, and then realizing variable rotor frequency & other induction motor effects

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**EQUIVALENT CIRCUIT OF AN INDUCTION MOTOR**

Transformer Model of an Induction Motor Per-phase equivalent circuit of an induction motor

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**TRANSFORMER MODEL of INDUCTION MOTOR**

As shown there is certain resistance & self inductance in primary (stator) windings which 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)

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**TRANSFORMER MODEL of INDUCTION MOTOR**

Magnetization curve of induction motor

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**TRANSFORMER MODEL of INDUCTION 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 motor which greatly increase reluctance of flux path & therefore reduces coupling between primary & secondary windings Higher reluctance caused by air gap means a higher magnetizing reactance XM in equivalent circuit will have a much smaller value (larger susceptance BM) than its value in an ordinary transformer

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**TRANSFORMER MODEL of INDUCTION MOTOR**

Primary internal stator voltage E1 coupled to secondary ER by an ideal transformer with an effective turns ratio aeff Effective turns ratio aeff easy to determined for a wound-rotor motor ratio of conductors per phase on stator to conductors per phase on rotor, modified by any pitch & distribution factor differences It is rather difficult to determine aeff clearly in cage of a case rotor motor because there are no distinct windings on cage rotor

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**TRANSFORMER MODEL of INDUCTION 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 current of induction motor are very similar to corresponding components in a transformer equivalent circuit Induction motor equivalent circuit differs from transformer equivalent circuit primarily in effects of varying rotor frequency on rotor voltage ER and secondarily in rotor resistance RR and jXR

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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)

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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

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ROTOR CIRCUIT MODEL reactance of an induction motor rotor depends 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:

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