Module 6. Power system stability. 6.1 Introduction
|
|
- Anabel Little
- 7 years ago
- Views:
Transcription
1 Module 6 Power system stability 6.1 Introduction In general terms, power system stability refers to that property of the power system which enables the system to maintain an equilibrium operating point under normal conditions and to attain a state of equilibrium after being subjected to a disturbance. As primarily synchronous generators are used for generating power in grid, power system stability is generally implied by the ability of the synchronous generators to remain in synchronism or in step. On the other hand, if the synchronous generators loose synchronism after a disturbance, then the system is called unstable. The basic concept of synchronism can be explained as follows. In the normal equilibrium condition, all the synchronous generators run at a constant speed and the difference between the rotor angles of any two generators is constant. Under any disturbance, the speed of the machines will deviate from the steady state values due to mismatch between mechanical and electrical powers (torque) and therefore, the difference of the rotor angles would also change. If these rotor angle differences (between any pair of generators) attain steady state values (not necessarily the same as in the pre-disturbance condition) after some finite time, then the synchronous generators are said to be in synchronism. On the other hand, if the rotor angle differences keep on increasing indefinitely, then the machines are considered to have lost synchronism. Under this out of step condition, the output power, voltage etc. of the generator continuously drift away from the corresponding pre-disturbance values until the protection system trips the machine. The above phenomenon of instability is essentially related with the instability of the rotor angles and hence, this form of instability is termed as rotor angle instability. Now, as discussed above, this instability is triggered by the occurrence of a disturbance. Depending on the severity of the disturbance, the rotor angle instability can be classified into two categories: Small signal instability: In this case, the disturbance occurring in the system is small. Such kind of small disturbances always take place in the system due to random variations of the loads and the generation. It will be shown later in this chapter that under small perturbation (or disturbance), the change in the electrical torque of a synchronous generator can be resolved into two components, namely, a) synchronizing torque (T s ) - which is proportional to the change in the rotor angle and b) damping torque (T d ), which is proportional to the change in the speed 250
2 of the machine. As a result, depending on the amounts of synchronizing and damping torques, small signal instability can manifest itself in two forms. When there is insufficient amount of synchronizing torque, the rotor angle increases steadily. On the other hand, for inadequate amount of damping torque, the rotor angle undergoes oscillations with increasing amplitude. These two phenomena are illustrated in Fig In Fig. 6.1(a), both the synchronizing and damping torques are positive and sufficient and hence, the rotor angle comes back to a steady state value after undergoing oscillations with decreasing magnitude. In Fig. 6.1(b), the synchronizing torque is negative while the damping toque is positive and thus, the rotor angle envelope is increasing monotonically. Fig. 6.1(c) depicts the classic oscillatory instability in which Ts is positive while Td is negative. Figure 6.1: Influence of synchronous and damping torque In an integrated power system, there can be different types of manifestation of the small signal instability. These are: 251
3 a. Local mode: In this type, the units within a generating station oscillate with respect to the rest of the system. The term local is used because the oscillations are localized in a particular generating station. b. Inter-area mode: In this case, the generators in one part of the system oscillate with respect to the machines in another part of the system. c. Control mode: This type of instability is excited due to poorly damped control systems such as exciter, speed governor, static var compensators, HVDC converters etc. d. Torsional mode: This type is associated with the rotating turbine-governor shaft. This type is more prominent in a series compensated transmission system in which the mechanical system resonates with the electrical system. Transient instability: In this case, the disturbance on the system is quite severe and sudden and the machine is unable to maintain synchronism under the impact of this disturbance. In this case, there is a large excursion of the rotor angle (even if the generator is transiently stable). Fig. 6.2 shows various cases of stable and unstable behavior of the generator. In case 1, under the influence of the fault, the generator rotor angle increases to a maximum, subsequently decreases and settles to a steady state value following oscillations with decreasing magnitude. In case 2, the rotor angle decreases after attaining a maximum value. However, subsequently, it undergoes oscillations with increasing amplitude. This type of instability is not caused by the lack of synchronizing torque; rather it occurs due to lack of sufficient damping torque in the post fault system condition. In case 3, the rotor angle monotonically keeps on increasing due to insufficient synchronizing torque till the protective relay trips it. This type of instability, in which the rotor angle never decreases, is termed as first swing instability. Figure 6.2: Illustration of various stability phenomenon Apart from rotor angle instability, instability can also occur even when the synchronous generators are maintaining synchronism. For example, when a synchronous generator is supplying power to an induction motor load over a transmission line, the voltage at the load terminal can progressively 252
4 reduce under some conditions of real and reactive power drawn by the load. In this case, loss of synchronism is not an issue but the challenge is to maintain a stable voltage. This type of instability is termed as voltage instability or voltage collapse. We will discuss about the voltage instability issue later in this course. Now, for analysing rotor angle stability, we have to first understand the basic equation of motion of a synchronous machine, which is our next topic. 6.2 Equation of motion of a synchronous machine The equation of motion of a synchronous generator is based on the fact that the accelerating torque is the product of inertia and its angular acceleration. In the MKS system, this equation can be written as, J d2 θ m dt 2 = T a = T m T e (6.1) In equation (6.1), J The total moment of inertia of the rotor masses in Kg m 2 θ m The angular displacement of the rotor with respect to a stationary axis, in mechanical radians t Time in seconds T a The net accelerating torque, in N-m T m The mechanical or shaft torque supplied by the prime mover less retarding torque due to rotational losses, in N-m T e The net electrical or electromagnetic torque in N-m Under steady state operation of the generator, T m and T e are equal and therefore, T a is zero. In this case, there is no acceleration or deceleration of the rotor masses and the generator runs at constant synchronous speed. The electrical torque T e corresponds to the air gap power of the generator and is equal to the output power plus the real power loss of the armature winding. Now, the angle θ m is measured with respect to a stationary reference axis on the stator and hence, it is an absolute measure of the rotor angle. Thus, it continuously increases with time even with constant synchronous speed. However, in stability studies, the rotor speed relative to the synchronous speed is of interest and hence, it is more convenient to measure the rotor angular position with respect to a reference axis which also rotates at synchronous speed. Hence, let us define, θ m = ω sm t + δ m (6.2) In equation (6.2), ω sm is the synchronous speed of the machine in mechanical radian/sec. and δ m (in mechanical radian) is the angular displacement of the rotor from the synchronously rotating reference axis. From equation (6.2), dθ m dt = ω sm + dδ m dt or, 253 dδ m dt = dθ m dt ω sm (6.3)
5 d 2 θ m dt 2 = d2 δ m dt 2 (6.4) Equation (6.3) shows that the quantity dδ m represents the deviation of the actual rotor speed dt from the synchronous speed in mechanical radian per second. Substituting equation (6.4) into equation (6.1) one gets, J d2 δ m dt 2 = T a = T m T e (6.5) Now. let us define the angular velocity of the rotor to be ω m = dθ m. From equation (6.5) we get, dt Jω m d 2 δ m dt 2 = ω m T a = ω m T m ω m T e Or, Jω m d 2 δ m dt 2 = P a = P m P e (6.6) In equation (6.6), P a, P e and P m denote the accelerating power, electrical output power and the input mechanical power (less than the rotational power loss) respectively. The quantity Jω m is the angular momentum of the rotor and at synchronous speed, it is known as the inertia constant and is denoted by M. Strictly, the quantity Jω m is not constant at all operating conditions since ω m keeps on varying. However, when the machine is stable, ω m does not differ significantly from ω sm and hence, Jω m can be taken approximately equal to M. Hence, from equation (6.6) we obtain, M d2 δ m dt 2 = P a = P m P e (6.7) Now, in machine data, another constant related to inertia, namely H-constant is often encountered. This is defined as; H = stored kinetic energy in megajoules at synchronous speed machine rating in MVA Or, H = 1 Jω 2 sm = 1 Mω sm MJ/MVA = 1 Mω sm sec. (6.8) 2 S mc 2 S mc 2 S mc In equation (6.8), the quantity S mc is the three phase MVA rating of the synchronous machine. Now, from equation (6.8), Substituting for M in equation (6.7), we get, M = 2HS mc ω sm MJ/mech. rad (6.9) 2H d 2 δ m ω sm dt 2 = P a S mc = P m P e S mc (6.10) In equation (6.10), both δ m and ω sm are in mechanical units. Now, the corresponding quantities 254
6 in electrical units are given as, ω s = P 2 ω sm; δ = P 2 δ m; (6.11) In equation (6.11), P is the number of pole in the generator, ω s is the synchronous speed of the machine in electrical radian/sec. and δ (in electrical radian) is the angular displacement of the rotor from the synchronously rotating reference axis. Substituting equation (6.11) in equation (6.10) we get, 2H ω s d 2 δ dt 2 = P a = P m P e per unit (6.12) Equation (6.12) is known as the swing equation of the synchronous machine. As this is a second order differential equation, it can be written as a set of two first order differential equations as below. 2H ω s dω dt = P m P e per unit (6.13) dδ dt = ω ω s (6.14) In equations (6.13) - (6.14), the quantity ω is the speed of the synchronous machine and is expressed in electrical radian per second. Now, in the above two equations, no damping of the machine is considered. If damping is considered (which opposes the motion of the machine), a term proportional to the deviation of the speed (from the synchronous speed) is introduced in equation (6.13). Therefore, the modified equation becomes; 2H ω s dω dt = P m P e d(ω ω s ) per unit (6.15) In equation (6.15), d is called the damping co-efficient. However, in the presence of damping, equation (6.14) does not change. Therefore, in the presence of damping, this pair of equations ((6.14) and (6.15)) describe the motion of the synchronous machine. With this introduction of motion of synchronous machine, we are now ready to address the various stability issues. From the next lecture we will start with transient stability analysis. 255
SYNCHRONOUS MACHINES
SYNCHRONOUS MACHINES The geometry of a synchronous machine is quite similar to that of the induction machine. The stator core and windings of a three-phase synchronous machine are practically identical
More information13 ELECTRIC MOTORS. 13.1 Basic Relations
13 ELECTRIC MOTORS Modern underwater vehicles and surface vessels are making increased use of electrical actuators, for all range of tasks including weaponry, control surfaces, and main propulsion. This
More informationDually Fed Permanent Magnet Synchronous Generator Condition Monitoring Using Stator Current
Summary Dually Fed Permanent Magnet Synchronous Generator Condition Monitoring Using Stator Current Joachim Härsjö, Massimo Bongiorno and Ola Carlson Chalmers University of Technology Energi och Miljö,
More information8 Speed control of Induction Machines
8 Speed control of Induction Machines We have seen the speed torque characteristic of the machine. In the stable region of operation in the motoring mode, the curve is rather steep and goes from zero torque
More informationDynamic states of three-phase induction motors. Selected problems
Computer Applications in Electrical Engineering Dynamic states of three-phase induction motors. Selected problems Ryszard Nawrowski, Zbigniew Stein, aria Zielińska Poznań University of Technology 61-965
More informationMEASURING INSTRUMENTS. By: Nafees Ahmed, Asstt, Prof, EE Deptt, DIT, Dehradun
MEASURING INSTRUMENTS By: Nafees Ahmed, Asstt, Prof, EE Deptt, DIT, Dehradun MEASURING INSTRUMENTS The device used for comparing the unknown quantity with the unit of measurement or standard quantity is
More informationSynchronous motor. Type. Non-excited motors
Synchronous motor A synchronous electric motor is an AC motor in which the rotation rate of the shaft is synchronized with the frequency of the AC supply current; the rotation period is exactly equal to
More informationManufacturing Equipment Modeling
QUESTION 1 For a linear axis actuated by an electric motor complete the following: a. Derive a differential equation for the linear axis velocity assuming viscous friction acts on the DC motor shaft, leadscrew,
More information300 MW Variable Speed Drives for Pump-Storage Plant Application Goldisthal
May 24 MW Variable Speed Drives for Aurélie Bocquel APCG / 4BOC4 (MW-Goldisthal 1-5-24).PPT MW Variable Speed Drives for Content Major benefits of the cyclo-converter driven doubly-fed induction machines
More informationTechnical Guide No. 100. High Performance Drives -- speed and torque regulation
Technical Guide No. 100 High Performance Drives -- speed and torque regulation Process Regulator Speed Regulator Torque Regulator Process Technical Guide: The illustrations, charts and examples given in
More informationBasics of Electricity
Basics of Electricity Generator Theory PJM State & Member Training Dept. PJM 2014 8/6/2013 Objectives The student will be able to: Describe the process of electromagnetic induction Identify the major components
More informationPhysics 41 HW Set 1 Chapter 15
Physics 4 HW Set Chapter 5 Serway 8 th OC:, 4, 7 CQ: 4, 8 P: 4, 5, 8, 8, 0, 9,, 4, 9, 4, 5, 5 Discussion Problems:, 57, 59, 67, 74 OC CQ P: 4, 5, 8, 8, 0, 9,, 4, 9, 4, 5, 5 Discussion Problems:, 57, 59,
More informationSlide 10.1. Basic system Models
Slide 10.1 Basic system Models Objectives: Devise Models from basic building blocks of mechanical, electrical, fluid and thermal systems Recognize analogies between mechanical, electrical, fluid and thermal
More informationMechanical Principles
Unit 4: Mechanical Principles Unit code: F/601/1450 QCF level: 5 Credit value: 15 OUTCOME 4 POWER TRANSMISSION TUTORIAL 2 BALANCING 4. Dynamics of rotating systems Single and multi-link mechanisms: slider
More informationMotor Fundamentals. DC Motor
Motor Fundamentals Before we can examine the function of a drive, we must understand the basic operation of the motor. It is used to convert the electrical energy, supplied by the controller, to mechanical
More informationPower Electronics. Prof. K. Gopakumar. Centre for Electronics Design and Technology. Indian Institute of Science, Bangalore.
Power Electronics Prof. K. Gopakumar Centre for Electronics Design and Technology Indian Institute of Science, Bangalore Lecture - 1 Electric Drive Today, we will start with the topic on industrial drive
More informationRotation: Moment of Inertia and Torque
Rotation: Moment of Inertia and Torque Every time we push a door open or tighten a bolt using a wrench, we apply a force that results in a rotational motion about a fixed axis. Through experience we learn
More informationUnit 4 Practice Test: Rotational Motion
Unit 4 Practice Test: Rotational Motion Multiple Guess Identify the letter of the choice that best completes the statement or answers the question. 1. How would an angle in radians be converted to an angle
More informationPhysics 9e/Cutnell. correlated to the. College Board AP Physics 1 Course Objectives
Physics 9e/Cutnell correlated to the College Board AP Physics 1 Course Objectives Big Idea 1: Objects and systems have properties such as mass and charge. Systems may have internal structure. Enduring
More informationLecture L22-2D Rigid Body Dynamics: Work and Energy
J. Peraire, S. Widnall 6.07 Dynamics Fall 008 Version.0 Lecture L - D Rigid Body Dynamics: Work and Energy In this lecture, we will revisit the principle of work and energy introduced in lecture L-3 for
More informationPractice Exam Three Solutions
MASSACHUSETTS INSTITUTE OF TECHNOLOGY Department of Physics Physics 8.01T Fall Term 2004 Practice Exam Three Solutions Problem 1a) (5 points) Collisions and Center of Mass Reference Frame In the lab frame,
More informationUnderstanding Poles and Zeros
MASSACHUSETTS INSTITUTE OF TECHNOLOGY DEPARTMENT OF MECHANICAL ENGINEERING 2.14 Analysis and Design of Feedback Control Systems Understanding Poles and Zeros 1 System Poles and Zeros The transfer function
More informationTransient analysis of integrated solar/diesel hybrid power system using MATLAB Simulink
Transient analysis of integrated solar/diesel hybrid power system using ATLAB Simulink Takyin Taky Chan School of Electrical Engineering Victoria University PO Box 14428 C, elbourne 81, Australia. Taky.Chan@vu.edu.au
More informationSOLID MECHANICS BALANCING TUTORIAL BALANCING OF ROTATING BODIES
SOLID MECHANICS BALANCING TUTORIAL BALANCING OF ROTATING BODIES This work covers elements of the syllabus for the Edexcel module 21722P HNC/D Mechanical Principles OUTCOME 4. On completion of this tutorial
More informationEquivalent Spring Stiffness
Module 7 : Free Undamped Vibration of Single Degree of Freedom Systems; Determination of Natural Frequency ; Equivalent Inertia and Stiffness; Energy Method; Phase Plane Representation. Lecture 13 : Equivalent
More informationKeywords: synchronous generator, synchronous motor, automatic voltage regulator, V- curves, synchronizing power, hunting, excitation system
SYNCHRONOUS MACHINES Tze-Fun Chan Hong Kong Polytechnic University, Hong Kong, China Keywords: synchronous generator, synchronous motor, automatic voltage regulator, V- curves, synchronizing power, hunting,
More informationSOLID MECHANICS TUTORIAL MECHANISMS KINEMATICS - VELOCITY AND ACCELERATION DIAGRAMS
SOLID MECHANICS TUTORIAL MECHANISMS KINEMATICS - VELOCITY AND ACCELERATION DIAGRAMS This work covers elements of the syllabus for the Engineering Council exams C105 Mechanical and Structural Engineering
More informationChapter 3 AUTOMATIC VOLTAGE CONTROL
Chapter 3 AUTOMATIC VOLTAGE CONTROL . INTRODUCTION TO EXCITATION SYSTEM The basic function of an excitation system is to provide necessary direct current to the field winding of the synchronous generator.
More informationChen. Vibration Motor. Application note
Vibration Motor Application note Yangyi Chen April 4 th, 2013 1 Table of Contents Pages Executive Summary ---------------------------------------------------------------------------------------- 1 1. Table
More informationANALYTICAL METHODS FOR ENGINEERS
UNIT 1: Unit code: QCF Level: 4 Credit value: 15 ANALYTICAL METHODS FOR ENGINEERS A/601/1401 OUTCOME - TRIGONOMETRIC METHODS TUTORIAL 1 SINUSOIDAL FUNCTION Be able to analyse and model engineering situations
More informationPrecise Modelling of a Gantry Crane System Including Friction, 3D Angular Swing and Hoisting Cable Flexibility
Precise Modelling of a Gantry Crane System Including Friction, 3D Angular Swing and Hoisting Cable Flexibility Renuka V. S. & Abraham T Mathew Electrical Engineering Department, NIT Calicut E-mail : renuka_mee@nitc.ac.in,
More informationEDUMECH Mechatronic Instructional Systems. Ball on Beam System
EDUMECH Mechatronic Instructional Systems Ball on Beam System Product of Shandor Motion Systems Written by Robert Hirsch Ph.D. 998-9 All Rights Reserved. 999 Shandor Motion Systems, Ball on Beam Instructional
More information6. Synchronous machine dynamics
1 6. Synchronous machine dynamics In the middle of eighties, the present Type 59 synchronous machine model program was implemented and put into practical use in EMTP. In the first half of nineties, also
More informationMotors and Generators
Motors and Generators Electro-mechanical devices: convert electrical energy to mechanical motion/work and vice versa Operate on the coupling between currentcarrying conductors and magnetic fields Governed
More informationSpeed Control Methods of Various Types of Speed Control Motors. Kazuya SHIRAHATA
Speed Control Methods of Various Types of Speed Control Motors Kazuya SHIRAHATA Oriental Motor Co., Ltd. offers a wide variety of speed control motors. Our speed control motor packages include the motor,
More informationFXA 2008. UNIT G484 Module 2 4.2.3 Simple Harmonic Oscillations 11. frequency of the applied = natural frequency of the
11 FORCED OSCILLATIONS AND RESONANCE POINTER INSTRUMENTS Analogue ammeter and voltmeters, have CRITICAL DAMPING so as to allow the needle pointer to reach its correct position on the scale after a single
More informationChapter 10 Rotational Motion. Copyright 2009 Pearson Education, Inc.
Chapter 10 Rotational Motion Angular Quantities Units of Chapter 10 Vector Nature of Angular Quantities Constant Angular Acceleration Torque Rotational Dynamics; Torque and Rotational Inertia Solving Problems
More information226 Chapter 15: OSCILLATIONS
Chapter 15: OSCILLATIONS 1. In simple harmonic motion, the restoring force must be proportional to the: A. amplitude B. frequency C. velocity D. displacement E. displacement squared 2. An oscillatory motion
More informationINSTRUMENTATION AND CONTROL TUTORIAL 2 ELECTRIC ACTUATORS
INSTRUMENTATION AND CONTROL TUTORIAL 2 ELECTRIC ACTUATORS This is a stand alone tutorial on electric motors and actuators. The tutorial is of interest to any student studying control systems and in particular
More informationAvailable online at www.sciencedirect.com Available online at www.sciencedirect.com
Available online at www.sciencedirect.com Available online at www.sciencedirect.com Procedia Procedia Engineering Engineering () 9 () 6 Procedia Engineering www.elsevier.com/locate/procedia International
More informationMODELLING AND SIMULATION OF MICRO HYDRO POWER PLANT USING MATLAB SIMULINK
MODELLING AND SIMULATION OF MICRO HYDRO POWER PLANT USING MATLAB SIMULINK Auwal Abubakar Usman 1, Rabiu Aliyu Abdulkadir 2 1 M.Tech (Power System Engineering), 2 M.Tech (Instrumentation and Control) Sharda
More informationIntroduction. Chapter 1. 1.1 The Motivation
Chapter 1 Introduction 1.1 The Motivation Hydroelectric power plants, like real systems, have nonlinear behaviour. In order to design turbine controllers, it was normal practice in the past, when computer
More informationReactive Power Control of an Alternator with Static Excitation System Connected to a Network
Reactive Power Control of an Alternator with Static Excitation System Connected to a Network Dr. Dhiya Ali Al-Nimma Assist. Prof. Mosul Unoversity Dr. Majid Salim Matti lecturer Mosul University Abstract
More informationVerification of Short Circuit Test Results of Salient Poles Synchronous Generator
Verification of Short Circuit Test Results of Salient Poles Synchronous Generator Abdul Jabbar Khan 1, Amjadullah Khattak 2 1 PG Student, University of Engineering and Technology, Peshawar, Department
More informationApplication Information
Moog Components Group manufactures a comprehensive line of brush-type and brushless motors, as well as brushless controllers. The purpose of this document is to provide a guide for the selection and application
More informationMechanics lecture 7 Moment of a force, torque, equilibrium of a body
G.1 EE1.el3 (EEE1023): Electronics III Mechanics lecture 7 Moment of a force, torque, equilibrium of a body Dr Philip Jackson http://www.ee.surrey.ac.uk/teaching/courses/ee1.el3/ G.2 Moments, torque and
More informationCandidate Number. General Certificate of Education Advanced Level Examination June 2014
entre Number andidate Number Surname Other Names andidate Signature General ertificate of Education dvanced Level Examination June 214 Physics PHY4/1 Unit 4 Fields and Further Mechanics Section Wednesday
More informationInductance. Motors. Generators
Inductance Motors Generators Self-inductance Self-inductance occurs when the changing flux through a circuit arises from the circuit itself. As the current increases, the magnetic flux through a loop due
More informationPower Quality Paper #3
The Effect of Voltage Dips On Induction Motors by: M D McCulloch 1. INTRODUCTION Voltage depressions caused by faults on the system affect the performance of induction motors, in terms of the production
More informationEquipment: Power Supply, DAI, Synchronous motor (8241), Electrodynamometer (8960), Tachometer, Timing belt.
Lab 9: Synchronous motor. Objective: to examine the design of a 3-phase synchronous motor; to learn how to connect it; to obtain its starting characteristic; to determine the full-load characteristic of
More informationMagnetic electro-mechanical machines
Magnetic electro-mechanical machines Lorentz Force A magnetic field exerts force on a moving charge. The Lorentz equation: f = q(e + v B) f: force exerted on charge q E: electric field strength v: velocity
More informationUnit - 6 Vibrations of Two Degree of Freedom Systems
Unit - 6 Vibrations of Two Degree of Freedom Systems Dr. T. Jagadish. Professor for Post Graduation, Department of Mechanical Engineering, Bangalore Institute of Technology, Bangalore Introduction A two
More informationEE 402 RECITATION #13 REPORT
MIDDLE EAST TECHNICAL UNIVERSITY EE 402 RECITATION #13 REPORT LEAD-LAG COMPENSATOR DESIGN F. Kağan İPEK Utku KIRAN Ç. Berkan Şahin 5/16/2013 Contents INTRODUCTION... 3 MODELLING... 3 OBTAINING PTF of OPEN
More informationSimple Harmonic Motion
Simple Harmonic Motion 1 Object To determine the period of motion of objects that are executing simple harmonic motion and to check the theoretical prediction of such periods. 2 Apparatus Assorted weights
More informationProf. Krishna Vasudevan, Prof. G. Sridhara Rao, Prof. P. Sasidhara Rao
6 Synchronous motor 6.1 Principle of operation In order to understand the principle of operation of a synchronous motor, let us examine what happens if we connect the armature winding (laid out in the
More informationDC motors: dynamic model and control techniques
DC motors: dynamic model and control techniques Luca Zaccarian Contents 1 Magnetic considerations on rotating coils 1 1.1 Magnetic field and conductors.......................... 1 1.2 The magneto-motive
More informationLab 14: 3-phase alternator.
Lab 14: 3-phase alternator. Objective: to obtain the no-load saturation curve of the alternator; to determine the voltage regulation characteristic of the alternator with resistive, capacitive, and inductive
More informationTime Response Analysis of DC Motor using Armature Control Method and Its Performance Improvement using PID Controller
Available online www.ejaet.com European Journal of Advances in Engineering and Technology, 5, (6): 56-6 Research Article ISSN: 394-658X Time Response Analysis of DC Motor using Armature Control Method
More informationApplications of Second-Order Differential Equations
Applications of Second-Order Differential Equations Second-order linear differential equations have a variety of applications in science and engineering. In this section we explore two of them: the vibration
More informationCenter of Gravity. We touched on this briefly in chapter 7! x 2
Center of Gravity We touched on this briefly in chapter 7! x 1 x 2 cm m 1 m 2 This was for what is known as discrete objects. Discrete refers to the fact that the two objects separated and individual.
More informationSOLID MECHANICS DYNAMICS TUTORIAL MOMENT OF INERTIA. This work covers elements of the following syllabi.
SOLID MECHANICS DYNAMICS TUTOIAL MOMENT OF INETIA This work covers elements of the following syllabi. Parts of the Engineering Council Graduate Diploma Exam D5 Dynamics of Mechanical Systems Parts of the
More informationDevelopment of the Induction Motor for Machine Tool Spindles and Servo Amplifier SANMOTION S
New Products Introduction Development of the Induction Motor for Machine Tool Spindles and Servo Amplifier SANMOTION S Takashi Sekiguchi Masahiro Kidou Yuusuke Shimura Yuji Ide Masahisa Koyama Michio Kitahara
More informationMounting instructions. Acceleration Transducer B12. B 26.B12.10 en
Mounting instructions Acceleration Transducer B12 B 26.B12.10 en B12 3 Contents Page Safety instructions.............................................. 4 1 Scope of supply..............................................
More informationInduction Motor Theory
PDHonline Course E176 (3 PDH) Induction Motor Theory Instructor: Jerry R. Bednarczyk, P.E. 2012 PDH Online PDH Center 5272 Meadow Estates Drive Fairfax, VA 22030-6658 Phone & Fax: 703-988-0088 www.pdhonline.org
More informationLet s first see how precession works in quantitative detail. The system is illustrated below: ...
lecture 20 Topics: Precession of tops Nutation Vectors in the body frame The free symmetric top in the body frame Euler s equations The free symmetric top ala Euler s The tennis racket theorem As you know,
More informationLOSSELESS STARTING METHOD FOR THE WOUND ROTOR INDUCTION MOTOR
LOSSELESS STARTING METHOD FOR THE WOUND ROTOR INDUCTION MOTOR Sergiu Ivanov Mihai Rdulescu University of Craiova, Romania INDA Craiova Faculty of Electrical Engineering 30, Mr#e#ti Street 107, Decebal
More informationGENERATOR DIFFERENTIAL PROTECTION RELAY STABILITY VIS-A -VIS SELECTION OF CTS MR. H. C. MEHTA & MR. JAY MEHTA Power Linker Group Co.
GENERATOR DIFFERENTIAL PROTECTION RELAY STABILITY VIS-A -VIS SELECTION OF CTS MR. H. C. MEHTA & MR. JAY MEHTA Power Linker Group Co., Mumbai ABSTRACT : For generator differential protection, one set of
More informationFREQUENCY CONTROLLED AC MOTOR DRIVE
FREQUENCY CONTROLLED AC MOTOR DRIVE 1.0 Features of Standard AC Motors The squirrel cage induction motor is the electrical motor motor type most widely used in industry. This leading position results mainly
More informationWhat Is Regeneration?
What Is Regeneration? Braking / Regeneration Manual Regeneration Overview Revision 1.0 When the rotor of an induction motor turns slower than the speed set by the applied frequency, the motor is transforming
More informationActive Vibration Isolation of an Unbalanced Machine Spindle
UCRL-CONF-206108 Active Vibration Isolation of an Unbalanced Machine Spindle D. J. Hopkins, P. Geraghty August 18, 2004 American Society of Precision Engineering Annual Conference Orlando, FL, United States
More informationUSER MANUAL THE RESOLVER
USR MANUAL TH RSOLVR ICP Department 4 has developed and produced a wide range of transmitter type resolvers for military and industrial applications. From a mechanical viewpoint, these products have been
More informationAccuracy and Tuning in CNC Machine Tools
FAMA Technical Article/001 Accuracy and Tuning in CNC Machine Tools Introduction: This article explains how it is possible to achieve a better performance on High Speed CNC Machine Tools. Performance is
More informationPhysics 1A Lecture 10C
Physics 1A Lecture 10C "If you neglect to recharge a battery, it dies. And if you run full speed ahead without stopping for water, you lose momentum to finish the race. --Oprah Winfrey Static Equilibrium
More informationSample Questions for the AP Physics 1 Exam
Sample Questions for the AP Physics 1 Exam Sample Questions for the AP Physics 1 Exam Multiple-choice Questions Note: To simplify calculations, you may use g 5 10 m/s 2 in all problems. Directions: Each
More informationLab 8: DC generators: shunt, series, and compounded.
Lab 8: DC generators: shunt, series, and compounded. Objective: to study the properties of DC generators under no-load and full-load conditions; to learn how to connect these generators; to obtain their
More informationPower System review W I L L I A M V. T O R R E A P R I L 1 0, 2 0 1 3
Power System review W I L L I A M V. T O R R E A P R I L 1 0, 2 0 1 3 Basics of Power systems Network topology Transmission and Distribution Load and Resource Balance Economic Dispatch Steady State System
More informationPHYS 101-4M, Fall 2005 Exam #3. MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
PHYS 101-4M, Fall 2005 Exam #3 Name MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. 1) A bicycle wheel rotates uniformly through 2.0 revolutions in
More informationThe dynamic equation for the angular motion of the wheel is R w F t R w F w ]/ J w
Chapter 4 Vehicle Dynamics 4.. Introduction In order to design a controller, a good representative model of the system is needed. A vehicle mathematical model, which is appropriate for both acceleration
More informationNO LOAD & BLOCK ROTOR TEST ON THREE PHASE INDUCTION MOTOR
INDEX NO. : M-142 TECHNICAL MANUAL FOR NO LOAD & BLOCK ROTOR TEST ON THREE PHASE INDUCTION MOTOR Manufactured by : PREMIER TRADING CORPORATION (An ISO 9001:2000 Certified Company) 212/1, Mansarover Civil
More informationHow to Turn an AC Induction Motor Into a DC Motor (A Matter of Perspective) Steve Bowling Application Segments Engineer Microchip Technology, Inc.
1 How to Turn an AC Induction Motor Into a DC Motor (A Matter of Perspective) Steve Bowling Application Segments Engineer Microchip Technology, Inc. The territory of high-performance motor control has
More informationDynamics of Offshore Wind Turbines
Proceedings of the Twenty-first (2011) International Offshore and Polar Engineering Conference Maui, Hawaii, USA, June 19-24, 2011 Copyright 2011 by the International Society of Offshore and Polar Engineers
More informationAwell-known lecture demonstration1
Acceleration of a Pulled Spool Carl E. Mungan, Physics Department, U.S. Naval Academy, Annapolis, MD 40-506; mungan@usna.edu Awell-known lecture demonstration consists of pulling a spool by the free end
More informationMathematical Modeling and Dynamic Simulation of a Class of Drive Systems with Permanent Magnet Synchronous Motors
Applied and Computational Mechanics 3 (2009) 331 338 Mathematical Modeling and Dynamic Simulation of a Class of Drive Systems with Permanent Magnet Synchronous Motors M. Mikhov a, a Faculty of Automatics,
More informationdspace DSP DS-1104 based State Observer Design for Position Control of DC Servo Motor
dspace DSP DS-1104 based State Observer Design for Position Control of DC Servo Motor Jaswandi Sawant, Divyesh Ginoya Department of Instrumentation and control, College of Engineering, Pune. ABSTRACT This
More informationPENDULUM PERIODS. First Last. Partners: student1, student2, and student3
PENDULUM PERIODS First Last Partners: student1, student2, and student3 Governor s School for Science and Technology 520 Butler Farm Road, Hampton, VA 23666 April 13, 2011 ABSTRACT The effect of amplitude,
More informationINTRODUCTION TO SYNCHRONIZING AUTOMATIC SYNCHRONIZING CONSIDERATIONS AND APPLICATIONS
INTRODUCTION TO SYNCHRONIZING AUTOMATIC SYNCHRONIZING CONSIDERATIONS AND APPLICATIONS INTRODUCTION It is the intention of this presentation to provide an explanation of the automatic synchronizing process,
More informationUNIT II : SYNCHRONOUS MOTORS
UNIT II : SYNCHRONOUS MOTORS It is known, that the direct current generator operates satisfactorily as a motor. Moreover, there is practically no difference in the construction of the DC generator and
More informationReactive Power and Importance to Bulk Power System OAK RIDGE NATIONAL LABORATORY ENGINEERING SCIENCE & TECHNOLOGY DIVISION
Reactive Power and Importance to Bulk Power System OAK RIDGE NATIONAL LABORATORY ENGINEERING SCIENCE & TECHNOLOGY DIVISION Outline What is Reactive Power and where does it come from? Why is it important?
More informationGenerator Stator Protection, under/over voltage, under /over frequency and unbalanced loading. Ramandeep Kaur Aujla S.NO 250447392
1 Generator Stator Protection, under/over voltage, under /over frequency and unbalanced loading By Ramandeep Kaur Aujla S.NO 250447392 ES 586b: Theory and applications of protective relays Department of
More informationPHYSICS 111 HOMEWORK SOLUTION #9. April 5, 2013
PHYSICS 111 HOMEWORK SOLUTION #9 April 5, 2013 0.1 A potter s wheel moves uniformly from rest to an angular speed of 0.16 rev/s in 33 s. Find its angular acceleration in radians per second per second.
More informationAcceleration Introduction: Objectives: Methods:
Acceleration Introduction: Acceleration is defined as the rate of change of velocity with respect to time, thus the concepts of velocity also apply to acceleration. In the velocity-time graph, acceleration
More informationSoil Dynamics Prof. Deepankar Choudhury Department of Civil Engineering Indian Institute of Technology, Bombay
Soil Dynamics Prof. Deepankar Choudhury Department of Civil Engineering Indian Institute of Technology, Bombay Module - 2 Vibration Theory Lecture - 8 Forced Vibrations, Dynamic Magnification Factor Let
More informationv v ax v a x a v a v = = = Since F = ma, it follows that a = F/m. The mass of the arrow is unchanged, and ( )
Week 3 homework IMPORTANT NOTE ABOUT WEBASSIGN: In the WebAssign versions of these problems, various details have been changed, so that the answers will come out differently. The method to find the solution
More informationDesign and Analysis of Switched Reluctance Motors
Design and Analysis of Switched Reluctance Motors İbrahim ŞENGÖR, Abdullah POLAT, and Lale T. ERGENE Electrical and Electronic Faculty, İstanbul Technical University, 34469, Istanbul, TURKEY sengoribrahim@gmail.com,
More informationTennessee State University
Tennessee State University Dept. of Physics & Mathematics PHYS 2010 CF SU 2009 Name 30% Time is 2 hours. Cheating will give you an F-grade. Other instructions will be given in the Hall. MULTIPLE CHOICE.
More informationBASIC VIBRATION THEORY
CHAPTER BASIC VIBRATION THEORY Ralph E. Blae INTRODUCTION This chapter presents the theory of free and forced steady-state vibration of single degree-of-freedom systems. Undamped systems and systems having
More informationAP1 Oscillations. 1. Which of the following statements about a spring-block oscillator in simple harmonic motion about its equilibrium point is false?
1. Which of the following statements about a spring-block oscillator in simple harmonic motion about its equilibrium point is false? (A) The displacement is directly related to the acceleration. (B) The
More informationSpring Simple Harmonic Oscillator. Spring constant. Potential Energy stored in a Spring. Understanding oscillations. Understanding oscillations
Spring Simple Harmonic Oscillator Simple Harmonic Oscillations and Resonance We have an object attached to a spring. The object is on a horizontal frictionless surface. We move the object so the spring
More informationScholars Research Library
Available online at www.scholarsresearchlibrary.com Scholars Research Library Archives of Applied Science Research, 2010, 2 (2):380-387 (http://scholarsresearchlibrary.com/archive.html) ISSN 0975-508X
More information