Lesson 12a: Three Phase Induction Motors - Engr.siu.edu

2/26/2016 Lesson 12a et332b.pptx 1 Lesson 12a: Three Phase Induction Motors ET 332b Ac Motors, Generators and Power Systems Lesson 12a et332b.pptx 2 Learning Objectives 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 magnetic field Compute the power that crosses that air gap of an induction motor Explain how the parameters of an induction motor circuit model relate to its performance Identify model equations 1

2/26/2016 Lesson 12a et332b.pptx 3 Three-Phase Induction Motors Rotor Motor Construction Stator Stator - magnetic structure (iron core) and winding that create magnetic field. Connected to three-phase voltages Rotor - iron core and conductors that rotate and drive the shaft of the motor. Conductors can be either copper bars (squirrel cage) or wound coils (wound-rotor) Lesson 12a et332b.pptx 4 Three-Phase Induction Motors The three-phase voltages Va, Vb and Vc create fluxes that add in space and time to create a rotating magnetic field without physical motion. Flux wave rotates at a speed given by: ns 120 f P Where ns synchronous speed f ac voltage frequency P number of poles (not pole pairs) 2

2/26/2016 Lesson 12a et332b.pptx 5 Synchronous Speed Example 12a-1: Four pole motor operating on a 60 Hz system. What is the speed at which the magnetic field rotates ns 120 f P P 4 poles f 60 Hz ns 120 60 1800 rpm 4 When supplied from 60 Hz system, ns is multiple of 60 Lesson 12a et332b.pptx 6 Induction Motor Operation For an Induction Motor to Rotate 3-phase voltages produce rotating magnetic field in stator Current is induced in rotor by moving magnetic field Induced current in rotor produces a magnetic field in rotor Field in rotor interacts with the field in the stator to produce torque (rotor "chases" stator field) 3

2/26/2016 Lesson 12a et332b.pptx 7 Slip and Slip Speed To induce current in rotor there must be a speed difference between the rotor and the rotating magnetic field. This speed difference is called slip speed n sl n s n r Where nsl slip speed ns synchronous speed nr rotor speed Define slip as per unit value s ns n r ns Slip increases as load increases Lesson 12a et332b.pptx 8 Slip and Developed Torque At start up nr 0. Assuming ns 1800 RPM determine the slip s ns n r 1800 0 s 1 ns 1800 Slip is 1 at locked rotor (startup) At full load torque motor spins at rated speed Rated speed nr 1750 rpm: typical for 4 pole induction motor s ns nr 1800 1750 s 0.028 ns 1800 Rated slips vary 0.020.05 of ns. Slip at No-load Rotor spins at nearly n , so n 1798 typical for unloaded s r 4 pole motor s ns n r 1800 1798 Slip is near zero when s 0.001 there is no-load on the motor ns 1800 4

2/26/2016 9 Lesson 12a et332b.pptx Three-Phase Induction Motors Advantages Smooth Power Transfer Power almost constant in 3-phase systems Power pulsates in single phase motors Simple Construction No brushes or other high maintenance parts Disadvantages Can not easily control speed 10 Lesson 12a et332b.pptx Induction Motor Torque-Speed Characteristic Typical Torque-Speed Characteristic of Induction Motor Starting Torque Breakover Torque 200 Motor design determines speed characteristic shape 150 Operating range Tm ( n) 100 Starting torque is developed when n 0 rpm. In this case approximately 100 N-m 50 0 0 200 400 600 800 1000 1200 1400 1600 1800 n Shape of torque speed characteristic depends on design of motor 5

2/26/2016 Lesson 12a et332b.pptx 11 Slip Speed & Rotor Voltage/Frequency Difference between speed of rotating magnetic field and rotor called slip speed n sl n s n r Where nsl slip speed Slip speed increases as load increases and rotor frequency is a function of slip s P ns f r 120 Where: ns synchronous speed s p.u slip fr frequency of rotor induced voltage Lesson 12a et332b.pptx 12 Slip Speed & Rotor Voltage/Frequency With the rotor blocked n 0, s 1 fr P ns f stator f BR 120 Where: fstator stator voltage frequency fBR blocked rotor frequency At startup stator voltage frequency and rotor voltage frequency are equal In operation slip not equal 1, so generally. Induced V max at s 1 f r s f BR E r s E BR Where: Er voltage induced in rotor at slip s EBR voltage induced with n 0 (Blocked rotor) 6

2/26/2016 13 Lesson 12a et332b.pptx Motor Rotor Circuit Model Motor has resistance and inductive reactance. XL depends on f so x r 2 f r Lr x r 2 s f BR Lr x r s X BR Rotor reactance in terms of blocked rotor inductance Rotor current Rotor Impedance z r R r j x r R r j s XBR Ir s E BR s E BR R r j x r R r j s X BR Lesson 12a et332b.pptx 14 Motor Rotor Circuit Model Some algebra gives Ir E BR Rr j X BR s Rotor current depends on slip which is related to motor speed Phase angle of Zr depends on slip ( R changes), so impedance angle and Fp changes with motor slip. This means rotor current magnitude and phase angle change with slip Rotor current magnitude Ir E BR 2 Rr 2 X BR s Rotor current phase angle X r tan 1 BR Rr s Rotor power factor Fpr cos( r ) Where r rotor current angle 7

2/26/2016 15 Lesson 12a et332b.pptx Motor Rotor Circuit Model Rotor Phase Shift Rotor Current Operating range Operating range 16 Lesson 12a et332b.pptx Induction Motor Air Gap Power Define power transferred across the air gap in the induction motor Sgap E BR I r * Where E BR E BR 0 In rectangular form I r I r - r Sgap E BR I r cos( r ) j E BR I r sin( r ) With the following components Pgap E BR I r cos( r ) Q gap E BR I r sin( r ) Pgap active power providing shaft power, friction, windage, and rotor resistance losses. Qgap reactive power that oscillates across air gap Rotor Fp and the magnitude of the Ir determine gap active power, Pgap EBR is assumed to be constant because it is proportional to the flux density which is assumed to be constant 8

2/26/2016 17 Lesson 12a et332b.pptx Active Power Across Air-Gap Components Pgap Pmech Prcl Where Pmech active power converted to shaft power Prcl rotor conductor losses Total 3-phase rotor losses Prcl 3 I r R r 2 Lesson 12a et332b.pptx 18 Active Power Across Air-Gap 3 Ir R r s 2 Total gap power Pgap 9

2/26/2016 Lesson 12a et332b.pptx 19 Active Power Across Air-Gap Slip related to the amount of mechanical load on motor. More mechanical load more active power across gap Combine power balance equations with definitions of Pgap and Prcl 3 I r R r (1 s) s 2 Pmech Lesson 12a et332b.pptx 20 Active Power Across Air-Gap Rotor resistance effects the amount of mechanical power developed Divide Rr s Into two parts: rotor loss resistance and the resistance that represents mechanical load R r R r (1 s) Rr s s 10

2/26/2016 21 Lesson 12a et332b.pptx Active Power Across Air-Gap Per phase model of the rotor 22 Lesson 12a et332b.pptx Developed Torque and Mechanical Power Mechanical power in terms of ns and nr s ns n r ns s 1- nr ns so 1 - s nr ns Substitute into the previous equation for mechanical power 3 Ir R r n r s ns 2 Pmech 11

2/26/2016 23 Lesson 12a et332b.pptx Developed Torque and Mechanical Power Mechanical power related to rotor resistance and current To find torque divide mechanical power by speed 2 180 R r E BR Td 2 2 s n R 2 s r X BR s N-m Lesson 12a et332b.pptx 24 Developed Torque and Mechanical Power This equation assumes an ideal stator – no losses. Used to generate torque-speed curves – rotor resistance effects the developed power and, therefore torque 12

2/26/2016 Lesson 12a et332b.pptx 25 Motor Losses Efficiency & Power Factor Pin Electric power in to motor Pscl 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.pptx 26 Developed Torque and Mechanical Power Power converted Pgap Prcl s Total active power across air gap Prcl rotor conductor losses Portion of active gap power Pmech Pgap (1 s) converted to mechanical power Pmech Pshaft Pfw Pstray 13

2/26/2016 27 Lesson 12a et332b.pptx Power Balance Equations Power in must equal power out plus losses Pmech Rated shaft power (HP): From stator side: Pshaft Pmech – Pfw-Pstray Pgap Pin – Pscl-Pcore 28 Lesson 12a et332b.pptx Power Balance Equations Total apparent electric power in Sin 3 I L VLL Find Pin from Fp and Sin values Fp Pin Sin Also, given a motor efficiency at an output level Po Pshaft Pin Pin Can find Pin 14

2/26/2016 Lesson 12a et332b.pptx 29 Example 12a-2 A 3-phase 60 Hz, 75 Hp, 4 pole motor operates at a rated terminal voltage of 230 V Under rated conditions it draws a line current of 186 A and has an efficiency of 90%. The following losses are measured: Core losses 1273 W Stator conductor losses 2102 W Rotor conductor losses 1162 W Find: a) the input power b) the total losses c) the air gap power d) the shaft speed e) the motor power factor f) combined mechanical losses Lesson 12a et332b.pptx 30 Example 12a-2 Solution (1) a) Find input power Ans b) Find the total losses Losses are the difference between the input and output powers Ans 15

2/26/2016 Lesson 12a et332b.pptx 31 Example 12a-2 Solution (2) c) Find the gap power Ans Lesson 12a et332b.pptx 32 Example 12a-2 Solution (3) d) Find shaft speed From above Find synchronous speed 16

2/26/2016 33 Lesson 12a et332b.pptx Example 12a-2 Solution (4) Ans e) Motor power factor – ratio of apparent power to active power Ans 34 Lesson 12a et332b.pptx Example 12a-2 Solution (5) f) Combined mechanical losses Ans 17

2/26/2016 Lesson 12a et332b.pptx 35 Example 12a-3 A 3-phase 230V, 25 HP, 60Hz, 4 pole motor rotor absorbs 20,200 W when supplying an unknown shaft load. The rotor copper losses are measured at 975 W when supplying this load. The friction and windage losses are known to be 250 W. Determine a) 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.pptx 36 Example 12a-3 Solution (1) a) Motor speed b) Mechanical power developed is Pgap less rotor conductor losses Ans 18

2/26/2016 Lesson 12a et332b.pptx 37 Example 12a-3 Solution (2) c) Compute developed torque in lb-ft Ans d) Compute shaft torque with shaft power Ans Lesson 12a et332b.pptx 38 Example 12a-3 Solution (3) e) Percent Load 19

2/26/2016 Lesson 12a et332b.pptx 39 Full Induction Motor Model Per phase circuit similar to transformer Vs stator voltage (line voltage) Rfe equivalent core resistance Rs stator winding resistance Rr actual rotor resistance Xs stator leakage reactance XBR actual blocked-rotor reactance XM stator core magnetizing reactance a N1/N2 ratio of stator to rotor turns Lesson 12a et332b.pptx 40 Full Induction Motor Model Per phase motor model-rotor quantities referred to stator. Where: I stator current 1 I2 Ir/a2: rotor current referred to stator R2 Rra2 rotor resistance referred to stator X2 XBRa2 blocked rotor reactance referred to the stator E2 Esa blocked rotor voltage referred to the stator 20

2/26/2016 Lesson 12a et332b.pptx 41 Full Induction Motor Model Remember, R2 can be written as: R (1 s) 2 R2 Rr a2 a2 r a Rr s The power, torque speed and efficiency can now be found analytically from the model if input, output and model parameters are known. Lesson 12a et332b.pptx 42 Full Induction Motor Model Use circuit analysis techniques to determine motor performance 21