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2013 | Book

Introduction Read chapter Read first chapter

Electrical Machines

Author: Slobodan N. Vukosavic

Publisher: Springer New York

Book Series : Power Electronics and Power Systems

Part of: Springer Professional "Wirtschaft+Technik" , Springer Professional "Technik"

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About this book

Electrical Machines primarily covers the basic functionality and the role of electrical machines in their typical applications. The effort of applying coordinate transforms is justified by obtaining a more intuitive, concise and easy-to-use model.

In this textbook, mathematics is reduced to a necessary minimum, and priority is given to bringing up the system view and explaining the use and external characteristics of machines on their electrical and mechanical ports. Covering the most relevant concepts relating to machine size, torque and power, the author explains the losses and secondary effects, outlining cases and conditions in which some secondary phenomena are neglected.

While the goal of developing and using machine mathematical models, equivalent circuits and mechanical characteristics persists through the book, the focus is kept on physical insight of electromechanical conversion process. Details such as the slot shape and the disposition of permanent magnets and their effects on the machine parameters and performance are also covered.

Table of Contents

Frontmatter
Chapter 1. Introduction
Abstract
This chapter provides introduction to electromechanical energy conversion and rotating power converters. This chapter explains the role of electrical machines in electrical power systems, industry applications, and commercial and residential area and supports the need to study electrical machines and acquire skills in their modeling, supplying, and control. This chapter also discusses notation and system of units used throughout this book, specifies target knowledge and skills to be acquired, and explains prerequisites. This chapter concludes with remarks on further studies.
Slobodan N. Vukosavic
Chapter 2. Electromechanical Energy Conversion
Abstract
Electrical machines contain stationary and moving parts coupled by an electrical or magnetic field. The field acts on the machine parts and plays key role in the process of electromechanical conversion. For this reason, it is often referred to as the coupling field. This chapter presents the most significant principles of creating a force or torque on the machine moving parts. In all the cases considered, the force appears due to the action of the electrostatic or magnetic field on the moving parts of the machine. Depending on the nature of the coupling field, the machines can be magnetic or electrostatic.
Slobodan N. Vukosavic
Chapter 3. Magnetic and Electrical Coupling Field
Abstract
Electromechanical conversion is based on forces and torques of electromagnetic origin. The force exerted upon a moving part can be the consequence of electrical or magnetic field. The field encircles and couples both moving and nonmoving parts of electromechanical converter. Therefore, the field is also called coupling field. In this chapter, some basic notions are given for electromechanical energy converters with electrical coupling field and converters with magnetic coupling field.
Slobodan N. Vukosavic
Chapter 4. Magnetic Circuit
Abstract
This chapter introduces and explains magnetic circuits of electrical machines. Basic laws and skills required to analyze magnetic circuits are reinstated and illustrated on examples and solved problems. The terms such as magnetic resistance, magnetomotive force, core flux, and winding flux are recalled and applied. Dual electrical circuit is introduced, explained, and applied in solving magnetic circuits. Basic properties of ferromagnetic materials are recalled, including saturation phenomena, eddy current losses, and hysteresis losses. Laminated magnetic circuits as the means of reducing the iron losses are explained and analyzed.
Slobodan N. Vukosavic
Chapter 5. Rotating Electrical Machines
Abstract
This chapter provides basic information on cylindrical machine. Typical machine windings are introduced and explained, along with the basic forms of magnetic circuits with slots and teeth. This chapter introduces common notation, symbols, and conventions in representing the windings, their magnetic exes, their flux, and magnetomotive force. Typical losses and power balance charts are explained and presented for cylindrical motors and generators. Calculation of the magnetic field energy in the air gap of cylindrical machines is given at the end of this chapter, along with considerations regarding the torque per volume ratio.
Slobodan N. Vukosavic
Chapter 6. Modeling Electrical Machines
Abstract
This chapter introduces, develops and explains generalized mathematical model of electrical machines. It explains the need for modeling, introduces and explains approximations and neglected phenomena, and formulates generalized model as a set of differential and algebraic equations.
Slobodan N. Vukosavic
Chapter 7. Single-Fed and Double-Fed Converters
Abstract
In this chapter, examples of single-fed and double electromechanical converters are analyzed and explained. In both cases, the torque changes are analyzed in cases where the windings have DC currents and AC currents of adjustable frequency. Revolving magnetic field created by AC currents in the windings is introduced and explained. Using the previous considerations, some basic operating principles are given for DC current machines, induction machines, and synchronous machines.
Slobodan N. Vukosavic
Chapter 8. Magnetic Field in the Air Gap
Abstract
This chapter presents an analysis of the magnetic and electrical fields in the air gap of a cylindrical machine. It is assumed that the fields come as a consequence of electrical current in the windings. The magnetic field in the air gap is created by the currents in both stator and rotor, which generate the corresponding stator and rotor magnetomotive forces.
Slobodan N. Vukosavic
Chapter 9. Energy, Flux, and Torque
Abstract
Magnetic field in the air gap is obtained from electrical currents in stator and rotor windings. Another source of the air gap field can be permanent magnets that may be placed within magnetic circuits of either stator or rotor. The stator and rotor fields in the air gap are calculated in the previous chapter. Interaction of the two fields incites the process of electromechanical conversion.
Slobodan N. Vukosavic
Chapter 10. Electromotive Forces
Abstract
Electromotive forces induced in windings of electrical machines are analyzed and discussed in this chapter. Analysis includes transformer electromotive forces and dynamic electromotive forces. The rms values, the waveforms, and harmonics are derived for concentrated and distributed windings. For real windings that have conductors distributed in a limited number of slots, the electromotive forces are calculated by introducing, explaining, and using chord factors and belt factors. Discussion includes design methods that suppress low-order harmonics in electromotive forces. This chapter concludes with the analysis of distributed windings with sinusoidal change of conductor density. Calculation of flux linkage and electromotive force in such windings shows that they achieve suppression of all harmonic distortions and operate as ideal spatial filters.
Slobodan N. Vukosavic
Chapter 11. Introduction to DC Machines
Abstract
Prior to commissioning the first electrical power stations, electrical energy was mostly obtained from batteries, chemical sources of electrical current. The batteries provide DC voltages and currents at their output terminals. It is for this reason that the first experiments and applications of electrical machines have been made with DC current electrical machines. Electrical engineers have studied the principles of operation of these machines and analyzed their characteristics, and they found the way of designing and manufacturing DC machines.
Slobodan N. Vukosavic
Chapter 12. Modeling and Supplying DC Machines
Abstract
In this chapter, mathematical model is developed for DC machines with excitation windings and DC machines with permanent magnet excitation. The block diagram of the model is used to provide a brief introduction to the torque control. Steady-state equivalent circuits are derived and explained for armature and excitation windings. These circuits are used to introduce and analyze mechanical characteristic of separately excited DC machine and determine the steady-state speed. The chapter provides basic elements for the control of the rotor speed. Steady-state operation of DC generators is explained along with basic output characteristics. Typical applications of DC machines are classified on the basis of the speed and torque changes within the four quadrants of T em –Ω m plane. On that ground, the basic requirements are specified for the power supply of the armature windings. The operation of switching power converter with H-bridge is briefly explained, along with the basic notions on pulse-width modulation (PWM). The impact of pulsed power supply on the machine operation is considered by studying the ripple of the armature current. The chapter closes with an overview of most common power converter topologies used in supplying DC machines.
Slobodan N. Vukosavic
Chapter 13. Characteristics of DC Machines
Abstract
Working with DC machines requires the knowledge on their electrical and mechanical properties, parameters, and limitations. This chapter introduces and explains the concept of rated quantities and discusses the maximum permissible currents in continuous, steady-state service of DC machines. It also defines the safe operating area of DC machines in T em –Ω m plane, both in steady-state operation and during transients. For the sake of readers that meet electrical machines for the first time, the concepts of rated current, rated voltage, mechanical characteristics, natural characteristics, rated speed, rated torque, and rated power are introduced and explained in this chapter. The need to use machines at higher speeds and with reduced flux is discussed and explained, introducing at the same time the constant flux operating region and the field-weakening operating region. The problems of removing the heat caused by the conversion losses are analyzed along with the performance restrictions imposed by temperature limits. Besides, an insight is given into possible short-term overload operation of DC machines. Principal conversion losses in DC machines are analyzed, discussed, and included in power balance. This chapter closes by discussing permissible operating areas in torque-speed plane. The steady-state safe operating area in T em –Ω m plane is also called exploitation characteristics. It is introduced and explained along with the transient safe operating area, also called the transient characteristic. Discussion and examples within this chapter are focused on separately excited DC machines.
Slobodan N. Vukosavic
Chapter 14. Induction Machines
Abstract
The operating principles of induction machines and basic data concerning constructions of their stator and rotor are presented in this chapter. This chapter includes some basic information regarding construction of induction machines. Discussed and described are the stator windings, the rotor short-circuited cage winding, and slotted and laminated magnetic circuits of both stator and rotor. Fundamentals on creating the revolving magnetic field are reinstated for the three-phase stator winding. Basic operating principles of an induction machine are illustrated on simplified machine with one short-circuited rotor turn. The torque expression is developed and used to predict basic properties of mechanical characteristic. For the purpose of studying the electrical and mechanical properties of induction machines, corresponding mathematical model is developed in Chap. 15 and used within the next chapters. Chapter 16 deals with the steady-state operation, steady-state equivalent circuit and relevant parameters, mechanical characteristics, losses, and power balance. Variable speed operation of induction machines is discussed in Chap. 17, with analysis of constant frequency-supplied induction machines and introduction and analysis of variable frequency-supplied induction machines, fed from PWM-controlled three-phase inverters.
Slobodan N. Vukosavic
Chapter 15. Modeling of Induction Machines
Abstract
This chapter introduces and explains mathematical model of induction machines. This model represents transient and steady-state behavior in electrical and mechanical subsystems of the machine. Analysis and discussion introduces and explains Clarke and Park coordinate transforms. The model includes differential equations that express the voltage balance in stator and rotor windings, inductance matrix which relates flux linkages and currents, Newton differential equation of motion, expression for the air-gap power, and expression for the electromagnetic torque. The model development process starts with replacing the three-phase machine with two-phase equivalent. Namely, the three-phase voltages, currents, and flux linkages are transformed in two-phase variables by appropriate transformation matrix which implements 3Φ/2Φ transform, also called Clarke coordinate transform. Two-phase model is formulated in stationary coordinate frame. The drawbacks and difficulties in using this model are the rationale for introducing and applying Park coordinate transform, which results in the machine model in synchronous dq coordinate frame. Necessary techniques and procedures of applying and using coordinate transforms are explained in detail, including representation of machine vectors by complex numbers. The operable model of induction machines is obtained in dq coordinate frame which revolves synchronously with the stator field. The merits and practical uses of the model in dq frame are explained at the end of the chapter.
Slobodan N. Vukosavic
Chapter 16. Induction Machines at Steady State
Abstract
In this chapter, steady state operation of induction machines is studied with the aim to derive the equivalent circuit and mechanical characteristic of induction machine. The steady state model is derived from the dynamic model, developed and explained in the previous chapter. The voltage balance equations at steady state are used to develop the steady state equivalent circuit of the machine with squirrel cage rotor. At the same time, the concept of the equivalent transformer is introduced to derive the same steady state equivalent circuit. The equivalent circuit is used to determine the steady state currents, torque, power, losses, and fluxlinkages. Typical resistances and inductances of the equivalent circuit are explained and discussed, along with typical experimental procedures for their measurement and estimation. The system of relative units is introduced and explained, along with benefits that come from its use. Characteristic examples are studied to develop skills in working with relative units and selecting the base quantities used in scaling the absolute values into relative values. The functions that approximate the mechanical characteristic of induction machine and typical mechanical loads are introduced and explained. Natural mechanical characteristic is analyzed along with the start-up mode, rated operation, and no load operation. Breakdown torque is studied and explained in both motor and generator modes. Stable and unstable equilibrium points on mechanical characteristic are discussed and explained. The influence of machine resistances and reactances on the start-up torque, breakdown torque, breakdown slip, and coefficient of efficiency is analyzed and explained. This chapter proceeds by summarizing energy losses in windings, magnetic circuits, and mechanical losses due to rotation. Calculation of steady state losses is explained on the basis of the steady state equivalent circuit. The losses are presented in the form of power balance chart drawn for induction machine that operates in motoring mode. Simplified power balance is derived by splitting the air-gap power into rotor losses and mechanical power, according to the relative slip s. This chapter ends with deriving power balance chart for induction generator and discussing generator operating mode of induction machines.
Slobodan N. Vukosavic
Chapter 17. Variable Speed Induction Machines
Abstract
This chapter discusses the means for the speed change of induction machines. The speed regulation is required in both generators and motors. Induction machines that serve as generators in wind power stations revolve at variable speed. Therefore, the machine and the associated equipment must ensure conversion of mechanical work in electrical energy at variable speed. The machines used as motors often serve in motion control applications, where the speed changes in continuous manner.
Slobodan N. Vukosavic
Chapter 18. Synchronous Machines
Abstract
The following chapters study principles of operation, construction, mathematical model, and basic characteristics of synchronous machines. Along with induction machines, synchronous machines belong to the group of AC machines. Their operating principles are different. The rotor of induction machines revolves at the speed slightly lower than the synchronous speed, thus their name asynchronous machines. The rotor of synchronous machines revolves at the synchronous speed.
Slobodan N. Vukosavic
Chapter 19. Mathematical Model of Synchronous Machine
Abstract
This chapter introduces and explains mathematical model of synchronous machines. The model considers three-phase synchronous machines with excitation windings or permanent magnets on the rotor. This model does not include damper windings, which are introduced and explained in Chap. 21. The model represents transient and steady state behavior in electrical and mechanical subsystems of synchronous machines. Analysis and discussion introduce and explain Clarke and Park coordinate transforms. The model includes differential equations that express the voltage balance in stator and rotor windings, inductance matrix which relates flux linkages and currents, Newton differential equation of motion, expression for the air gap power, and expression for the electromagnetic torque. The model development process is very similar to that of the induction machine, which is detailed in Chap. 15. Therefore, some considerations are shortened or removed. The model obtained in this chapter is suitable for both isotropic (cylindrical) and anisotropic (salient pole) machines. This chapter closes with some basic considerations on the reluctant torque and synchronous reluctance machines.
Slobodan N. Vukosavic
Chapter 20. Steady-State Operation
Abstract
Mathematical model of electrical machine contains differential and algebraic equations describing the machine operation in given supply conditions and given load. Using the model, it is possible to derive the changes of the rotor speed, electromagnetic torque, the air-gap flux, and phase currents during transients and in steady-state conditions. The model is needed to design the power supply of the machine and to devise control algorithm. At the same time, the model is used to predict performance of the machine in operating conditions of interest and to evaluate whether the machine is suitable for given application.
Slobodan N. Vukosavic
Chapter 21. Transients in Sychronous Machines
Abstract
In this chapter, transient response of synchronous machines connected to stiff network is analyzed and discussed. Analysis of transients in electrical and mechanical subsystems of synchronous machines is relatively complex due to a relatively large number of state variables, such as the rotor position and speed, and the winding currents and flux linkages. Complexity of mathematical model does not help the process of understanding the nature of transients and hinders deriving corresponding conclusions. The analysis can be simplified by introducing the assumption that transients in electrical subsystem decay considerably faster than those of mechanical subsystem. In this way, analysis of transients in mechanical subsystem can be performed by using steady state model of electrical subsystem. In this way, results are made more legible and intuitive.
Slobodan N. Vukosavic
Chapter 22. Variable Frequency Synchronous Machines
Abstract
This chapter studies the operation and characteristics of three-phase synchronous machines connected to three-phase inverters, static power converters capable of adjusting the stator voltages by means of changing the width of the voltage pulses supplied to the stator terminals. The average voltage of the pulse train is adjusted to suit the machine needs. Variable speed operation of synchronous machine is achieved with variable frequency and variable amplitude of stator voltages. This chapter introduces and explains some basic torque and speed control principles. The need of controlling the stator currents is discussed and explained. Fundamental principles of stator current control are introduced, relying on PWM-controlled three-phase inverter as the voltage actuator. Field-weakening performance of inverter-supplied synchronous machines with buried magnets and surface-mounted magnets is analyzed and explained. The limits of constant power operation in field-weakening mode are determined, explained, and expressed in terms of the stator self-inductance. Based upon the study of operating limits of the machine and operating limits of associated three-phase inverter, steady-state operating area and transient operating area are derived in T−Ω plane and studied for inverter-supplied synchronous machines.
Slobodan N. Vukosavic
Backmatter
Metadata
Title
Electrical Machines
Author
Slobodan N. Vukosavic
Copyright Year
2013
Publisher
Springer New York
Electronic ISBN
978-1-4614-0400-2
Print ISBN
978-1-4614-0399-9
DOI
https://doi.org/10.1007/978-1-4614-0400-2