Lesson 12a: Three Phase Induction Motors

2/26/2016Lesson 12a et332b.pptx1Lesson 12a: Three PhaseInduction MotorsET 332bAc Motors, Generators and Power SystemsLesson 12a et332b.pptx2Learning ObjectivesAfter this presentation you will be able to: Explain how a three-phase induction motor operatesCompute the synchronous speed of an inductionmotor and the slip between motor rotor and statormagnetic fieldCompute the power that crosses that air gap of aninduction motorExplain how the parameters of an induction motorcircuit model relate to its performanceIdentify model equations1

2/26/2016Lesson 12a et332b.pptx3Three-Phase Induction MotorsRotorMotor ConstructionStatorStator - magnetic structure(iron core) and winding thatcreate magnetic field.Connected to three-phasevoltagesRotor - iron core and conductorsthat rotate and drive the shaft of themotor. Conductors can be eithercopper bars (squirrel cage) orwound coils (wound-rotor)Lesson 12a et332b.pptx4Three-Phase Induction MotorsThe three-phase voltages Va, Vb and Vc create fluxes that add in spaceand time to create a rotating magnetic field without physical motion.Flux wave rotates at a speed given by:ns 120 fPWhere ns synchronous speedf ac voltage frequencyP number of poles(not pole pairs)2

2/26/2016Lesson 12a et332b.pptx5Synchronous SpeedExample 12a-1: Four pole motor operating on a 60 Hz system.What is the speed at which the magnetic field rotatesns 120 fPP 4 polesf 60 Hzns 120 60 1800 rpm4When supplied from 60 Hz system, ns is multiple of 60Lesson 12a et332b.pptx6Induction Motor OperationFor an Induction Motor to Rotate3-phase voltages produce rotating magnetic field instatorCurrent is induced in rotor by moving magnetic fieldInduced current in rotor produces a magnetic field inrotorField in rotor interacts with the field in the stator toproduce torque (rotor "chases" stator field)3

2/26/2016Lesson 12a et332b.pptx7Slip and Slip SpeedTo induce current in rotor there must be a speed difference between therotor and the rotating magnetic field. This speed difference is called slipspeedn sl n s n rWhere nsl slip speedns synchronous speednr rotor speedDefine slip as per unit values ns n rnsSlip increases as load increasesLesson 12a et332b.pptx8Slip and Developed TorqueAt start up nr 0. Assuming ns 1800 RPM determine the slips ns n r1800 0 s 1ns1800Slip is 1 at lockedrotor (startup)At full load torque motor spins at rated speedRated speed nr 1750 rpm: typical for 4 pole induction motors ns nr1800 1750 s 0.028ns1800Rated slips vary 0.020.05 of ns.Slip at No-load Rotor spins at nearly n , so n 1798 typical for unloadedsr4 pole motors ns n r1800 1798Slip is near zero when s 0.001there is no-load on the motorns18004

2/26/20169Lesson 12a et332b.pptxThree-Phase Induction MotorsAdvantagesSmooth Power TransferPower almost constant in 3-phasesystemsPower pulsates in single phase motorsSimple ConstructionNo brushes or other high maintenancepartsDisadvantagesCan not easily control speed10Lesson 12a et332b.pptxInduction Motor Torque-SpeedCharacteristicTypical Torque-Speed Characteristic of Induction MotorStartingTorqueBreakoverTorque200Motor design determinesspeed characteristic shape150OperatingrangeTm ( n) 100Starting torque is developedwhen n 0 rpm. In this caseapproximately 100 N-m5000200 400 600 800 1000 1200 1400 1600 1800nShape of torque speed characteristic depends on design ofmotor5

2/26/2016Lesson 12a et332b.pptx11Slip Speed & Rotor Voltage/FrequencyDifference between speed of rotating magnetic field and rotor calledslip speedn sl n s n rWhere nsl slip speedSlip speed increases as load increases and rotor frequency is a function ofslips P nsf r 120Where: ns synchronous speeds p.u slipfr frequency of rotor inducedvoltageLesson 12a et332b.pptx12Slip Speed & Rotor Voltage/FrequencyWith the rotor blocked n 0, s 1fr P ns f stator f BR120Where: fstator stator voltage frequencyfBR blocked rotor frequencyAt startup stator voltage frequency and rotor voltage frequency are equalIn operation slip not equal 1, so generally.Induced V max at s 1f r s f BRE r s E BRWhere: Er voltage induced in rotor at slip sEBR voltage induced with n 0 (Blocked rotor)6

2/26/201613Lesson 12a et332b.pptxMotor Rotor Circuit ModelMotor has resistance and inductive reactance. XL depends on f sox r 2 f r Lrx r 2 s f BR Lrx r s X BRRotor reactance interms of blockedrotor inductanceRotor currentRotor Impedancez r R r j x r R r j s XBRIr s E BRs E BR R r j x r R r j s X BRLesson 12a et332b.pptx14Motor Rotor Circuit ModelSome algebra givesIr E BR Rr j X BR s Rotor current dependson slip which is relatedto motor speedPhase angle of Zr depends on slip ( R changes), so impedance angleand Fp changes with motor slip. This means rotor current magnitudeand phase angle change with slipRotor current magnitudeIr E BR2 Rr 2 X BR s Rotor current phase angle X r tan 1 BR Rr s Rotor power factorFpr cos( r )Where r rotor current angle7

2/26/201615Lesson 12a et332b.pptxMotor Rotor Circuit ModelRotor 16Lesson 12a et332b.pptxInduction Motor Air Gap PowerDefine power transferred across the air gap in the induction motorSgap E BR I r*Where E BR E BR 0 In rectangular formI r I r - r Sgap E BR I r cos( r ) j E BR I r sin( r )With the following componentsPgap E BR I r cos( r )Q gap E BR I r sin( r )Pgap active power providing shaft power, friction, windage, and rotorresistance losses.Qgap reactive power that oscillates across air gapRotor Fp and the magnitude of the Ir determine gap active power, PgapEBR is assumed to be constant because it is proportional tothe flux density which is assumed to be constant8

2/26/201617Lesson 12a et332b.pptxActive Power Across Air-GapComponentsPgap Pmech PrclWherePmech active power converted to shaft powerPrcl rotor conductor lossesTotal 3-phase rotor lossesPrcl 3 I r R r2Lesson 12a et332b.pptx18Active Power Across Air-Gap3 Ir R rs2Total gap powerPgap 9

2/26/2016Lesson 12a et332b.pptx19Active Power Across Air-GapSlip related to the amount of mechanical load on motor.More mechanical load more active power across gapCombine power balance equations with definitions ofPgap and Prcl3 I r R r (1 s) s2PmechLesson 12a et332b.pptx20Active Power Across Air-GapRotor resistance effects the amount of mechanical powerdevelopedDivideRrsInto two parts: rotor loss resistance and theresistance that represents mechanical loadR r R r (1 s) Rrss10

2/26/201621Lesson 12a et332b.pptxActive Power Across Air-GapPer phase model of the rotor22Lesson 12a et332b.pptxDeveloped Torque and Mechanical PowerMechanical power in terms of ns and nrs ns n rnss 1-nrnsso 1 - s nrnsSubstitute into the previous equation for mechanical power3 Ir R r n r s ns2Pmech11

2/26/201623Lesson 12a et332b.pptxDeveloped Torque and Mechanical PowerMechanical power related to rotor resistance and currentTo find torque divide mechanical power by speed 2 180 R r E BR Td 2 2 s n R 2s r X BR s N-mLesson 12a et332b.pptx24Developed Torque and Mechanical PowerThis equation assumes an ideal stator – no losses.Used to generate torque-speed curves – rotor resistanceeffects the developed power and, therefore torque12

2/26/2016Lesson 12a et332b.pptx25Motor Losses Efficiency & Power FactorPin Electric power in to motorPscl Stator conductor losses; Pcore Core losses;Prcl Rotor conductor losses; Pfw Friction and windage;Pstray Stray losses;Pshaft Mechanical power output (rated HP);Pmech Electric power converted to mechanical power in rotor.Lesson 12a et332b.pptx26Developed Torque and Mechanical PowerPower convertedPgap PrclsTotal active power across air gapPrcl rotor conductor lossesPortion of active gap powerPmech Pgap (1 s) converted to mechanical powerPmech Pshaft Pfw Pstray13

2/26/201627Lesson 12a et332b.pptxPower Balance EquationsPower in must equal power out plus lossesPmechRated shaft power (HP):From stator side:Pshaft Pmech – Pfw-PstrayPgap Pin – Pscl-Pcore28Lesson 12a et332b.pptxPower Balance EquationsTotal apparent electric power inSin 3 I L VLLFind Pin from Fp and Sin valuesFp PinSinAlso, given a motor efficiency at an output level Po Pshaft PinPinCan find Pin14

2/26/2016Lesson 12a et332b.pptx29Example 12a-2A 3-phase 60 Hz, 75 Hp, 4 pole motor operates at a ratedterminal voltage of 230 V Under rated conditions it draws aline current of 186 A and has an efficiency of 90%. Thefollowing losses are measured:Core losses 1273 W Stator conductor losses 2102 WRotor conductor losses 1162 WFind: a) the input powerb) the total lossesc) the air gap powerd) the shaft speede) the motor power factorf) combined mechanical lossesLesson 12a et332b.pptx30Example 12a-2 Solution (1)a) Find input powerAnsb) Find the total lossesLosses are the difference between the input and output powersAns15

2/26/2016Lesson 12a et332b.pptx31Example 12a-2 Solution (2)c) Find the gap powerAnsLesson 12a et332b.pptx32Example 12a-2 Solution (3)d) Find shaft speedFrom aboveFind synchronous speed16

2/26/201633Lesson 12a et332b.pptxExample 12a-2 Solution (4)Anse) Motor power factor – ratio of apparent power to active powerAns34Lesson 12a et332b.pptxExample 12a-2 Solution (5)f) Combined mechanical lossesAns17

2/26/2016Lesson 12a et332b.pptx35Example 12a-3A 3-phase 230V, 25 HP, 60Hz, 4 pole motor rotor absorbs20,200 W when supplying an unknown shaft load. The rotorcopper losses are measured at 975 W when supplying thisload. The friction and windage losses are known to be 250W. Determinea) the shaft speed;b) mechanical power developed;c) torque developed in the rotor;d) shaft torque;e) percent of rated horsepower that the motor is delivering.Lesson 12a et332b.pptx36Example 12a-3 Solution (1)a) Motor speedb) Mechanical power developed is Pgap less rotor conductor lossesAns18

2/26/2016Lesson 12a et332b.pptx37Example 12a-3 Solution (2)c) Compute developed torque in lb-ftAnsd) Compute shaft torque with shaft powerAnsLesson 12a et332b.pptx38Example 12a-3 Solution (3)e) Percent Load19

2/26/2016Lesson 12a et332b.pptx39Full Induction Motor ModelPer phase circuit similar to transformerVs stator voltage (line voltage) Rfe equivalent core resistanceRs stator winding resistanceRr actual rotor resistanceXs stator leakage reactanceXBR actual blocked-rotor reactanceXM stator core magnetizing reactancea N1/N2 ratio of stator to rotor turnsLesson 12a et332b.pptx40Full Induction Motor ModelPer phase motor model-rotor quantities referred to stator.Where: I stator current1I2 Ir/a2: rotor current referred to statorR2 Rra2 rotor resistance referred to statorX2 XBRa2 blocked rotor reactance referred to the statorE2 Esa blocked rotor voltage referred to the stator20

2/26/2016Lesson 12a et332b.pptx41Full Induction Motor ModelRemember, R2 can be written as: R (1 s) 2R2 Rr a2 a2 r a Rrs The power, torque speed and efficiency can now be foundanalytically from the model if input, output and modelparameters are known.Lesson 12a et332b.pptx42Full Induction Motor ModelUse circuit analysis techniques to determine motorperformance21

2/26/201643Lesson 12a et332b.pptxFull Induction Motor ModelZ2 R2 j X2sZP Z 2 Z0Z 2 Z0RotorimpedanceZ0 Zin ZP Z1R fe j X MR fe j X MParallelcombination of corevalueswhere Z1 R1 j X1Total motor model impedance (per phase)I1 VZinE 2 I1 ZPStator currentInduced rotorvoltage referred tostatorLesson 12a et332b.pptx44Full Induction Motor ModelI2 E2Z2Rotor current referred to statorTotal power relationships2Pscl 3 I1 R1Total stator conductor losses2P rcl 3 I 2 R 2Pgap P rclsTotal rotor conductor losses (1 s) Pmech P rcl s Note: all power equations are for total three-phase power22

2/26/2016Lesson 12a et332b.pptx45Full Induction Motor ModelPshaft Pmech Pfw PstrayTD 7.04 Pmech(lb - ft)nrTshaft 7.04 Pshaft(lb - ft)nrFinallyPcore3 E 2 2 R feShaft power is mechanical powerdeveloped less mechanical lossesRotor developed torque.Where nr rotor speedShaft torqueThe stator core losses aredependent on the voltageLesson 12a et332b.pptx46End Lesson 12a: ThreePhase Induction MotorsET 332bAc Motors, Generators and Power Systems23

Lesson 12a: Three Phase Induction Motors ET 332b Ac Motors, Generators and Power Systems Lesson 12a_et332b.pptx 1 Learning Objectives Lesson 12a_et332b.pptx 2 After this presentation you will be able to: Explain how a three-phase induction motor operates Compute the synchronous speed of an induction motor and the slip between motor rotor and stator