ECE 325 Electric Energy System Components 6- Three-Phase Induction Motors. Instructor: Kai Sun Fall 2015

Similar documents
Basic parts of an AC motor : rotor, stator, The stator and the rotor are electrical

BASIC INDUCTION MOTOR CONCEPTS

Overview: Induction Motors. Review Questions. Why the Rotor Moves: Motor Speed

No-load And Blocked Rotor Test On An Induction Machine

Section Induction motor drives

Induction Motor Drive

15 Problem 1. 3 a Draw the equivalent circuit diagram of the synchronous machine. 2 b What is the expected synchronous speed of the machine?

Electric Machines I Three Phase Induction Motor. Dr. Firas Obeidat

Synchronous Machines - Structure

Prince Sattam bin Abdulaziz University College of Engineering. Electrical Engineering Department EE 3360 Electrical Machines (II)

ECE 325 Electric Energy System Components 7- Synchronous Machines. Instructor: Kai Sun Fall 2015

60 p. 2. A 200hp 600V, 60 Hz 3-phase induction motor has start code F. What line current should be expected at starting? 4 marks.

FUNDAMENTALS OF POWER SYSTEMS

Chapter 4. Synchronous Generators. Basic Topology

Lecture Set 8 Induction Machines

University of Jordan Faculty of Engineering & Technology Electric Power Engineering Department

Per Unit Analysis. Single-Phase systems

Induction Motors. The single-phase induction motor is the most frequently used motor in the world

Massachusetts Institute of Technology Department of Electrical Engineering and Computer Science Electric Machines

Representation of a Group of Three-phase Induction Motors Using Per Unit Aggregation Model A.Kunakorn and T.Banyatnopparat

Question 1 Equivalent Circuits

Synchronous Machines

Three Phase Induction Motors

Chapter 5 Three phase induction machine (1) Shengnan Li

EEE3405 ELECTRICAL ENGINEERING PRINCIPLES 2 - TEST

ISSN: [Basnet* et al., 6(3): March, 2017] Impact Factor: 4.116

Performance Improvement of Direct Torque Controlled Interior Permanent Magnet Synchronous Motor Drive by Considering Magnetic Saturation

Introduction to Synchronous. Machines. Kevin Gaughan

Lesson 17: Synchronous Machines

SERIES COMPENSATION: VOLTAGE COMPENSATION USING DVR (Lectures 41-48)

The Influence of the Load Condition upon the Radial Distribution of Electromagnetic Vibration and Noise in a Three-Phase Squirrel-Cage Induction Motor

Q.1 A) Attempt any three of the following: 12 Marks i) State why three phase induction motor never run on synchronous speed? Ans:

CHAPTER 5 SIMULATION AND TEST SETUP FOR FAULT ANALYSIS

JRE SCHOOL OF Engineering

Electrical Machines and Energy Systems: Operating Principles (Part 1) SYED A Rizvi

Chapter 6: Efficiency and Heating. 9/18/2003 Electromechanical Dynamics 1

3 d Calculate the product of the motor constant and the pole flux KΦ in this operating point. 2 e Calculate the torque.

Tutorial Sheet Fig. Q1

Bernoulli s equation may be developed as a special form of the momentum or energy equation.

UNIT I INTRODUCTION Part A- Two marks questions

MATHEMATICAL MODELING OF INDUCTION MOTORS

CHAPTER 3 INFLUENCE OF STATOR SLOT-SHAPE ON THE ENERGY CONSERVATION ASSOCIATED WITH THE SUBMERSIBLE INDUCTION MOTORS

ROEVER COLLEGE OF ENGINEERING & TECHNOLOGY ELAMBALUR, PERAMBALUR DEPARTMENT OF ELECTRICAL AND ELECTRONICS ENGINEERING ELECTRICAL MACHINES I

An Introduction to Electrical Machines. P. Di Barba, University of Pavia, Italy

Simulation and Analysis of Linear Permanent Magnet Vernier Motors for Direct Drive Systems

INDUCTION MOTOR MODEL AND PARAMETERS

Revision Guide for Chapter 15

INFLUENCE OF BROKEN ROTOR BARS LOCATION IN THE SQUIRREL CAGE INDUCTION MOTOR USING FINITE ELEMENT METHOD

18 Problem 1. 7 d Sketch a cross section of a switched reluctance machine and explain the principle of operation.

Sensorless PM Brushless Drives

Chapter 6. Induction Motors. Copyright The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

Synchronous Machines

Pulsed Magnet Crimping

How an Induction Motor Works by Equations (and Physics)

Tutorial 1 (EMD) Rotary field winding

Generators. What its all about

Overview Electrical Machines and Drives

J. Electrical Systems 6-3 (2010): A COMPARATIVE STUDY ON PERFORMANCE IMPROVEMENT OF A PHOTOVOLTAIC PUMPING SYSTEM

EELE 3332 Electromagnetic II Chapter 10

A NEW EQUIVALENT CIRCUIT OF THE THREE-PHASE INDUCTION MOTOR (CASE STUDIES:CURRENT AND POWER FACTOR OF THE MOTOR)

ECE 320 Energy Conversion and Power Electronics Dr. Tim Hogan. Chapter 1: Introduction and Three Phase Power

Equivalent Circuits with Multiple Damper Windings (e.g. Round rotor Machines)

Energy Converters. CAD and System Dynamics

ME 375 EXAM #1 Tuesday February 21, 2006

Modelling and Simulating a Three-Phase Induction Motor

ECEN 667 Power System Stability Lecture 18: Voltage Stability, Load Models

ME 375 FINAL EXAM SOLUTIONS Friday December 17, 2004

ELECTRIC POWER CIRCUITS BASIC CONCEPTS AND ANALYSIS

ME 375 FINAL EXAM Wednesday, May 6, 2009

MAHARASHTRA STATE BOARD OF TECHNICAL EDUCATION

Reduction of Unbalanced Magnetic Pull in Doubly-Fed Induction Machine

Tuning of High-Power Antenna Resonances by Appropriately Reactive Sources

Estimation of Temperature Rise in Stator Winding and Rotor Magnet of PMSM Based on EKF

LO 1: Three Phase Circuits

R. W. Erickson. Department of Electrical, Computer, and Energy Engineering University of Colorado, Boulder

Department of Mechanical Engineering Massachusetts Institute of Technology Modeling, Dynamics and Control III Spring 2002

EFFICIENCY DETERMINATION AND LOSSES SEGREGATION OF SINGLE-PHASE INDUCTION MOTORS

Chapter 17 Amplifier Frequency Response

Electrical Machines and Energy Systems: Operating Principles (Part 2) SYED A Rizvi

The synchronous machine (detailed model)

Improving Power System Transient Stability with Static Synchronous Series Compensator

ECE 3510 Root Locus Design Examples. PI To eliminate steady-state error (for constant inputs) & perfect rejection of constant disturbances

PESIT Bangalore South Campus Hosur road, 1km before Electronic City, Bengaluru -100 Department of Electronics & Communication Engineering

Revision Guide for Chapter 15

DIRECT TORQUE CONTROL OF THREE PHASE INDUCTION MOTOR USING FUZZY LOGIC SPEED CONTROLLER FOR STEADY/DYNAMIC STATE RESPONSE

CHAPTER 8 DC MACHINERY FUNDAMENTALS

DESIGN OF ELECTRICAL APPARATUS SOLVED PROBLEMS

01. The pole-zero plots of three discrete-time systems P, Q and R on the z-plane are shown below.

Homework #7 Solution. Solutions: ΔP L Δω. Fig. 1

Synchronous Machines

Lecture 23 Date:

Dynamic Simulation of a Three-Phase Induction Motor Using Matlab Simulink

Outcome of this lecture

د شوقي حامد عرفه ابراهيم

EE 742 Chapter 3: Power System in the Steady State. Y. Baghzouz

ECE 325 Electric Energy System Components 5 Transmission Lines. Instructor: Kai Sun Fall 2015

: 2 : EE-Conventional Test-10 (Solutions)

6 Chapter 6 Testing and Evaluation

MAE140 Linear Circuits Fall 2012 Final, December 13th

Control of Wind Turbine Generators. James Cale Guest Lecturer EE 566, Fall Semester 2014 Colorado State University

Transcription:

ECE 35 Electric Energy Sytem Component 6- Three-Phae Induction Motor Intructor: Kai Sun Fall 015 1

Content (Material are from Chapter 13-15) Component and baic principle Selection and application Equivalent circuit

Undertanding the Nameplate 3-phae, 60Hz, AC induction motor Rated power: 30.0 hp (=.4kW) Service factor: 1.15 (i.e. 115% of rated power for hort-term ue) Rated full-load current: 35.0A Rated voltage: 460V Rated peed: 1765rpm Continuou duty at ambient 40 o C Full-load nominal efficiency: 93.0% Frame ize: haft height of 8/4=7 inche; body length of 6 Inulation cla: F (155 o C for 0,000 hour lifetime) NEMA deign: B (normal tarting torque combined with a low current) Start inruh kva: G (5.60-6.9kVA) http://www.pdhonline.org/coure/e156/e156content.pdf 3

Principle component Stator (tacked lamination) Rotor (tacked lamination) Wound rotor Squirrel-cage rotor Air gap (0.4mm-4mm) 4

Stator Hollow, cylindrical core made up of tacked lamination. Stator winding i placed in the evenly paced lot punched out of the internal circumference of the lamination. 5

6

Wound Rotor Ha a 3-phae winding (uually in Y-connection) uniformly ditributed in rotor lot, imilar to the tator winding Rotor winding terminal are connected to three lip-ring which revolve with the rotor. 3 tationary bruhe connect the rotor winding to external reitor during the tart-up period and are hort-circuited during normal operation. 7

Squirrel-Cage Rotor More adopted in induction motor Intead of a winding, copper bar are puhed into the lot in the lamination Welded to two copper end-ring, all bar are hort-circuited at two end, o a to reemble a quirrel cage In mall and medium motor, the cage (bar and end-ring) are made of aluminum. 8

9

Principle of Operation: Faraday Law and Lorentz Force A magnet moving above a conducting ladder induce a voltage E=Blv and a current I in the conductor underneath according to Faraday law (the right-hand rule). Cut by the moving flux, the current-carrying conductor experience a Lorentz force (the left-hand rule) alway acting in a direction to drag it along the moving magnet When the ytem reache a teady tate, the ladder move in the ame direction a the magnet but ha a lower peed <v (why?) Roll up the ladder into a cylindrical quirrel-cage rotor and replace the magnet by a tator an induction motor Parallel conductor are hort-circuited by end-bar A and B Conductor are hort-circuited by end-ring A and B) 10

Rotating magnetic field Conider a tator having 6 alient pole with Y-connected tator winding carrying balanced 3-phae alternating current. i ( t) 10co 10co( t) a i ( t) 10co( 10 ) 10co( t 10 ) b i ( t) 10co( 10 ) 10co( t 10 ) c Poitive current: alway flowing into terminal A, B and C 11

Rotating Magnetic Field: Intant 1 =0: 6 pole together produce a magnetic field having eentially one broad N pole and one broad S pole 1

Rotating Magnetic Field: Intant 60 o : the magnetic field move CW by 60 o ; it angular peed equal 13

Rotating Magnetic Field: Intant 3 10 o : the magnetic field move CW by 10 o ; it angular peed equal 14

Rotating Magnetic Field For the tator producing a magnetic field having one pair of N-S pole The field rotate 360 o during one cycle of the tator current. The peed of the rotating field i necearily ynchronized with the frequency f of the ource, o it i called ynchronou peed =60f (r/min) With the phae equence A-B-C, the magnetic field rotate CW. If we interchange any two of the three line connected to the tator, the new phae equence will be A-C-B and the magnetic field will rotate CCW at the ynchronou peed 15

Phae group In practice, intead of uing a ingle coil per pole, the coil i ub-divided into or more coil lodged and taggered in adjacent lot connected in erie, i.e. a phae group Each phae group produce one N/S pole, o uing more phae group allow u to increae the number of pole (denoted by p) No. of group = No. of phae No. of pole = 3 p 16

Number of N-S pole and ynchronou peed Synchronou peed n =10f / p [r/min] f : frequency of the ource [Hz] p: number of pole If f=60hz, n =10f / 4 =30f =1800r/min n =10f / 8 =15f=900r/min 17

Starting of an induction motor 1. The magnetic field produced by the tator current rotate CW at ynchronou peed n.. Relative to the magnetic field, the rotor rotate CCW. 3. According to Faraday Law (right-hand rule), the rotor winding (bar) have induced voltage in the direction a indicated. 4. Large circulating current are created in rotor winding (bar) by the induced voltage 5. The current have the maximum value at the taring point becaue the rotor ha the maximum peed relative to the magnetic field. 6. The rotor winding rotate CW ubjected to Lorentz force (left-hand rule) in the direction a indicated 7. The rotor will accelerate until the total Lorentz force equal the friction 8. Once the rotor tart rotating CW, it peed relative to the filed will decreae, o it winding current and Lorentz force will decreae Can the rotor reach n? If it did, then it current and Lorentz force would be zero and friction would low the rotor down, o the anwer i: No, the rotor peed n<n at a teady tate. Since friction i very mall, the rotor peed n n at no load condition 18

Slip Slip: i the difference between ynchronou peed n and rotor peed n, expreed a a per unit or percent of ynchronou peed. n n r f (pu) n f f: frequency of the ource connected to the tator [Hz] f : frequency of the voltage and current induced in the rotor [Hz] n =10f / p: ynchronou peed [r/min] n: rotor peed [r/min] r =n/30, =n /30 : correponding angular peed of n and n [rad/] 19

Example 13-3 A 0.5 hp, 6-pole induction motor i excited by a 3-phae, 60 Hz ource. Calculate the lip, and the frequency of the rotor current under the following condition: a. At tandtill b. Motor turning at 500r/min in the ame direction a the revolving field c. Motor turning at 500r/min in the oppoite direction to the revolving field d. Motor turning at 000r/min in the ame direction a the revolving field Solution: n =10f/p=1060/6 = 100 r/min a. = (n -n)/n =(100-0)/100 =1 pu f =f=60hz b. = (100-500)/100 = 0.583 pu f =f=0.583 60Hz = 35 Hz c. = [100- (-500)]/100 =1.417 pu f =f=1.417 60Hz = 85 Hz d. = [100-000)]/100 = -0.667 pu f =f=-0.667 60Hz = -40 Hz Slip =1 0<<1 >1 <0 Rotor peed & freq n=0 f =f 0<n<n 0<f <f n<0 f >f n>n f <0 Operating mode Tranformer (tandtill) Motor Brake Generator (revered phae equence A-C-B) 0

Equivalent circuit: wound-rotor induction motor 1. When the motor i at tandtill (i.e. n=0, =1), it act exactly like a conventional tranformer. Aume a Y-connection for both the tator and rotor, and a turn ratio of 1:1. Conider the per-phae equivalent circuit: E g : ource voltage, line to neutral, x 1, r 1 : tator leakage reactance and winding reitance x, r : rotor leakage reactance and winding reitance X m, R m : magnetizing reactance and reitance modeling loe of iron, R x : windage and friction external reitance, connecting one lip-ring to the neutral of the rotor Note: I o may reach 40% of I p due to the air gap between the tator and rotor (much bigger than the air gap between the P and S winding of a tranformer), o we cannot eliminate the magnetizing branch. 1

For motor maller than hp R =r +R X R X For motor exceeding hp R =r +R X R X

. When the motor run at a lip, i.e. n=(1-)n R =r +R X R X 1 : 1 f f E = E 1, I = I 1, jx jx r and R X are the ame I E E 0 = E arctan x R j x R j x R ( x ) R 1 1 Note: the phaor on the primary ide (E 1 and I 1 ) and the econdary ide (E and I ) cannot be drawn in one phaor diagram becaue they have different frequencie 3

Phaor diagram on the rotor and tator I 1 and I have the ame effective value even though they have different frequencie I 1 = I E 1 and E have the ame effective value E 1 = E E 1 lead I 1 and E lead I both by 4

Simplified equivalent circuit: referred to the tator ide I I 1 R E1 jx I 1 E E R / jx Z 1 1 def Z R / jx E I 1 1 jx =jx 1 +jx E 1 Note: The value of R / will vary from R to a the motor goe from tart-up (=1) to n (=0) 5

I p r 1 jx 1 jx R E g jx m I o R m I 1 jx R 1 R I m I f Total power aborbed by the motor: Eg Eg R S j I1 ( r1 jx ) R X m Eg P I r I R m Stator iron loe P E R Stator copper loe P I r j 1 1 m f g / m R 1 1 1 Active power upplied to the rotor: P I R / r 1 Total I R loe in the rotor circuit P I R P jr 1 r Mechanical power developed by the motor 1 Pm Pr Pjr Pr (1 ) I1 R Torque developed by the motor 9.55Pm 9.55 Pr(1 ) 9.55Pr T n n (1 ) n Note: The torque only depend on P r 6

Active power flow I p r 1 jx 1 jx R P I r j 1 1 P E R f g / m E g I m jx m I o R m I f I 1 1 R P I R jr 1 1 Pm I R P / P 1 L e 7

Phaor diagram of the induction motor S=P+jQ I p r 1 jx 1 jx R I o I 1 jx E g jx m R m R 1 R I m I f Z 1 =r 1 +jx =acco(p/ S ) =actan(x/r 1 ) 8

Breakdown (maximum) Torque Eg I1 R co E g IZ 1 1 co Eg I1 b Z1 co R b Z 1 When Z 1 = R /, P r and torque T both reach their maximum value E g T b 9.55Pr 9.55 I1 R / n n 9.55 E 4 n Z1 co g Z 1 I 1 I 1 R / I 1 9

Example 13-5 A 3-phae induction motor having a ynchronou peed of 100 r/min draw 80 kw from a 3-phae feeder. The copper loe and iron loe in the tator amount to 5 kw. If the motor run at 115 r/min, calculate a. The active power tranmitted to the rotor P r =P e P j P f =80 5 =75 kw b. The rotor I R loe, i.e. P jr =(n -n)/n =(100-115)/100=0.04 P jr =P r =0.0475=3 kw c. The mechanical power developed P m =P r P jr =75 3 =7 kw d. The mechanical power delivered to the load, knowing that the windage and friction loe equal to kw P L =P m - P V =7 =70 kw e. The efficiency of the motor =P L /P e =70/80=87.5% f. The torque developed by the motor T m =9.55 P r /n = 9.5575000/100=597 Nm 30

Two-wattmeter method to meaure 3-phae active power 3-phae load in Y or connection P 1 = V ac I a co( - 30 o )=E L I L co( - 30 o ) P = V bc I b co( + 30 o )=E L I L co( + 30 o ) S 3 P3 jq3 P1 P j 3( P1 P ) Proof: S3 ELI L co( 30 ) co( 30 ) j 3ELI L co( 30 ) co( 30 ) E I co co30 j 3E I in in 30 L L L L 3E L I L c o j 3E L I L in 31

Example 13-7 a. Power upplied to the rotor P e =P 1 +P =70 kw b. Rotor I R loe P jr r 1 =0.34/=0.17 P j =3I 1 r 1 =378 0.17=3.1 kw P r =P e P j P f =70 3.1 =64.9 kw =(n -n)/n =(1800-1763)/1800=0.005 P jr =P r =0.00564.9=1.33 kw Two-wattmeter method 1763 r/min A 3-phae induction motor having a nominal rating of 100 hp (~75 kw) and a ynchronou peed of 1800 r/min i connected to a 3-phae 600 V ource. Reitance between two tator terminal =0.34. Calculate c. Mechanical power upplied to the load P m =P r P jr =64.9 1.33 =63.5 kw P L =P m - P V = 63.5 1. =6.3 kw =6.3 1.34 = 83.5 hp d. Efficiency =P L /P e =6.3/70=89% e. Torque developed at 1763 r/m T m =9.55 P r /n = 9.55649000/1800 =344 Nm 3

Two practical quirrel-cage induction motor 33

Torque-Speed Curve n n R R, Pr I1, I1 Eg / ( Z1 ) n 9.55Pr T n 9.55 E Rn g R Z1 n n n n ( ) Stable operating Region (n, T) no-load torque The curve i nearly linear between no-load and full-load becaue i mall and R / i big 9.55 Eg 9.55 Eg I1 Eg / R T ( n ) n R n R n 34

The 5 hp induction motor Torque-Speed Curve E g =440/1.73 V R =1. Z 1 =1.5+6j n =1800 r/min T 9.55 Eg Rn Z1 ( n n) n n R Torque-Slip Curve Current-Speed Curve T 9.55 E 1 g R Z R / n I 1 Z 1 Eg Rn n n 35

Torque-Speed Curve: 5 hp motor I 1 P r T n When the motor i talled, i.e. locked-rotor condition, the current i 5-6 time the full-load current, making I R loe 5-36 time higher than normal, o the rotor mut never remain locked for more than a few econd Small motor (15 hp and le) develop their breakdown torque at about 80% of n 36

Torque-Speed Curve: 5000 hp motor Big motor (1500+ hp) : Relatively low tarting (locked-rotor) torque Breakdown torque at about 98% of n Rated n i cloe to n 37

Effect of rotor reitance R Rated Torque =15Nm Current at the rated torque.5r Rated torque =15Nm Current at the rated torque 10R Rated torque =15Nm Current at the rated torque 38

T LR Effect of rotor reitance 9.55 E R 9.55 E Z g g 1 R n Z1 n R I 1, LR Z 1 E g R P jr I 1 R T b 9.55 E 4 n Z1 co g When R increae, tarting (locked-rotor) torque T LR increae, tarting current I 1,LR decreae, and breakdown torque T b remain the ame Pro & Con with a high rotor reitance R It produce a high tarting torque T LR and a relatively low tarting current I 1,LR However, at the rated torque, it produce a rapid fall-off in peed with increaing load becaue the torque-peed curve become flat, and the motor ha high copper loe and low efficiency and tend to overheat Solution For a quirrel-cage induction motor, deign the rotor bar in a pecial way o that the rotor reitance R i high at tarting and low under normal operation If the rotor reitance need to be varied over a wide range, a wound-rotor motor need to be ued. 39

Effect of the terminal voltage: Problem 13-33 A 3-phae, 300kW, 300V 60Hz, 1780 r/min induction motor i ued to drive a compreor. The motor ha a full-load efficiency of 9% and power factor of 86%. If the terminal voltage rie by 0% while the motor operate at full load, how doe each of the following change? P m, T n FL Same I 1,LR T b 0% 44% 9.55 E T ( n n ) g FL FL Rn I 1,FL PF (Q) Average motor temperature Flux per pole About the ame (iron winding ) 0% T Q= I 1 x+ E g /X m LR 9.55 Eg Z n 1 R T LR About the ame (P f P j P jr ) 44% Exciting current Iron loe >0% (conidering aturation) T b I 1, LR 9.55 E 4 n Z1 co Z E g g R 1 40

Aynchronou generator Connect the 5 hp, 1800 r/min, 60Hz motor to a 440 V, 3-phae line and drive it at a peed of 1845 r/min =(n -n)/n =(1800-1845)/1800= -0.05 R /=1./(-0.05)=-48 <0 The negative reitance indicate that power i flowing from the rotor to the tator (aynchronou generator mode) Power flow from the rotor to the tator: E = 440/1.73=54 V I 1 = E / -48+1.5+ j6 =54/46.88= 5.4A P r = I 1 R /= -1410 W <0 1410W flow from the rotor to the tator Mechanical power and torque input to it haft: P jr = I 1 R =35. W P m =P r +P jr =1410 + 35.=1445W T=9.55 P m /n=.3 Nm Total active power delivered to the line: P j = I 1 r 1 =44.1 W P f = E /R m =71.1 W P e =P r -P j -P f = 1410-44.1-71.7=194 W P 3 =3P e =388W Reactive power aborbed from the line: Q 3 =( I 1 x+ E /X m ) 3 =(176+586) 3 =86 var Complex power delivered to the line: S 3 =P 3 - Q 3 =388 - j86 VA co=86.% Efficiency of thi aynchronou generator =P e /P m =194/1445=89.5% 41

Tet to determine the equivalent circuit I p r 1 jx 1 jx r / R / I o I 1 jx E g jx m R m R X / I m I f Etimate r 1, r, X m, R m and x (note: r +R X =R where R X i the external reitance) 1. No-load tet. Locked-rotor tet 4

No-load tet At no-load, lip 0 R / i high, I 1 <<I o Step: 1. Meaure tator reitance R LL between any two terminal (auming a Y connection) r 1 =R LL /. Run the motor at no-load uing rated line-to-line voltage E NL. Meaure no-load current I NL and 3-phae active power P NL S 3E I NL NL NL Q S P NL NL NL R m P P 3I r P P 3I r NL f NL 1 f NL NL 1 ( E / 3) E ( P P) / 3 P 3I r NL NL f NL NL 1 X m ( ENL / 3) ( Q ) / 3 NL (Ignoring P V ) E Q NL 43 NL

Locked-rotor tet When the rotor i locked, lip =1, I P >>I o r =r /R /, neglect the magnetizing branch Step: 1. Apply reduced 3-phae voltage E LR to the tator o that the tator current I p the rated value. Meaure line-to-line voltage E LR, current I LR and 3-phae active power P LR S 3E I LR LR LR Q S P LR LR LR x Q 3I LR LR P 3I r 3 I r r P / (3 I ) r LR LR 1 LR LR LR 1 44

Example 15-1 45

Homework Aignment #5 Read Chapter 13.0-13.16, 15.0-15.9 Quetion: 13-16, 13-3, 13-4, 13-8, 15-, 15-3, 15-4, 15-5 Due date: hand in your olution to Deni at MK 05 or by email (doipov@vol.utk.edu) before the end of 11/4 (Wed) 46