Delft University of Technology MATERIALS ENGINEERING Department Marine and Transport Technology Mekelweg 2 2628 CD Delft the Netherlands Phone +31 (0)15-2782889 Fax +31 (0)15-2781397 www.mtt.tudelft.nl
Specialization: Transport Engineering and Logistics Report number: 2012.TEL.7729
Title: Electrical drives – Design choices and selection guidance
Author: M.C. de Graaf
Title (in Dutch) Elektrische aandrijving – Ontwerp keuzes en selectie begeleiding
Assignment: literature Confidential: no
Initiator (university): ir. W. van den Bos Initiator (company): -
Supervisor: ir. W. van den Bos Date: November 01, 2012
Student: M.C. de Graaf Assignment type: Literature Supervisor (TUD): Ir. W. van den Bos Creditpoints (EC): 10 Supervisor (Company) - Specialization: TEL
Report number: 2012.TEL.7729 Confidential: No
Subject: Electric motors
Electric motors or complete electrical drives are being used more and more throughout the industry. Also the transportation section nowadays utilizes more and more electric powered machines. Engineers have to be aware of this development and have to be capable to provide designs which comply with this new demand.
A lot of information can be found about these electric motors and drives throughout different sources. The problem however is that not all the information engineers and students need can be found in one single book. Also in the curriculum very little attention is paid regarding this subject. Because of this a lot of unnecessary mistakes are made during the design phase.
Your assignment is to give an overview of the state of the art regarding the electric motor and the electrical drive. A complete overview is desired of the different possibilities with both a theoretic background as well as actual performance data of these machines through the use of equations and graphs. In addition practical information and examples have to be given so that students can understand and use this document during design classes.
The report should comply with the guidelines of the section. Details can be found on the website. The professor,
Table of Contents
Preface ... 9 Summary ... 11 List of symbols ... 13 Terminology ... 15 Introduction ... 171 Brief history of the electric motor and generator ... 19
2 Electric motors ... 21
2.1 DC motors ... 21
2.1.1 Working principle ... 21
2.1.2 Permanent magnet DC (PMDC) ... 29
2.1.3 Separately excited motor ... 30
2.1.4 Shunt motor ... 32 2.1.5 Series motor ... 33 2.1.6 Compound motor ... 35 2.1.7 Closing remarks ... 36 2.2 AC motors ... 37 2.2.1 Asynchronous motor ... 37 2.2.2 Synchronous motor... 45 2.3 Other motors ... 50 2.3.1 Stepper motor ... 50 2.3.2 Brushless DC motor ... 51 2.3.3 Hysteresis motor ... 51 2.3.4 Reluctance motor ... 52
2.3.5 Axial flux motor ... 53
2.3.6 Universal motor ... 54 2.3.7 Coreless DC motor ... 54 2.3.8 Pancake DC motor ... 54 2.3.9 Torque motor ... 55 2.3.10 Electrostatic motor ... 55 2.3.11 Piezoelectric motor ... 55 3 Generators ... 57 3.1 DC generator ... 57 3.1.1 General information ... 57
3.1.2 Separately excited generator ... 59
3.1.3 Shunt generator ... 60
3.1.5 Compound generator ... 62
3.2 AC generators ... 63
3.2.1 Asynchronous generator ... 63
3.2.2 Synchronous generator ... 65
4 Coupling ... 71
4.1 Different coupling possibilities ... 71
4.2 Heat development... 73 4.3 Design limitations... 74 5 Batteries ... 77 6 Frequency controllers ... 79 6.1 Operating principle ... 79 6.2 Different controllers ... 81 6.2.1 Cycloconverter ... 81 6.2.2 PWM ... 82 6.2.3 PAM ... 82 6.2.4 Vector modulation ... 83 6.2.5 Field-oriented control ... 84 6.3 Lifespan ... 84
6.4 Multiple devices setup ... 85
6.4.1 Parallel machines ... 85
6.4.2 Series machines ... 86
7 Reading manufacturer’s data charts ... 87
7.1 Categories ... 87
7.2 Given parameters ... 92
7.3 Remaining information ... 94
8 Component dimensioning and selection examples ... 97
8.1 Automated MTS-trailer ... 97
8.1.1 Wishes and demands ... 97
8.1.2 Calculations ... 98
8.1.3 Component selection ... 103
8.2 Windmill ... 105
8.2.1 Whishes and demands ... 105
8.2.2 Calculations ... 105
8.2.3 Component selection ... 107
8.3 Crane... 108
8.3.1 Whishes and demands ... 108
8.4 Conveyer belt ... 113
8.4.1 Whishes and demands ... 113
8.4.2 Calculations ... 113
8.4.3 Component selection ... 115
9 Conclusion and recommendations ... 117
Source indication ... 119
Appendix A: Principle of electromechanical energy conversion ... 123
Appendix B: Eddy currents... 127
Preface
This report is a literature assignment which is a standard part of the curriculum for the master study Transportation Engineering and Logistics, and thus is conducted in the name of the Department of Transportation Engineering at the faculty of 3Me of the Technical University of Delft.
This report discusses a very (electro-) technical subject and is intended for technical
students. Attempts have been made to write this report in such a way that also readers with a limited knowledge about these subjects can read it, but at least a basic understanding of the principles of electrical engineering is assumed to be known.
I would also like to use this opportunity to thank my supervisor Ir. W. van de Bos for his guidance and advice during this thesis.
Summary
Since the start of the industrial revolution better, stronger and more efficient engines have been invented. Starting with the steam engine soon the petrol and diesel engine came to live and eventually of course the electric engine. Especially the electric engine nowadays has a wide variety of fields in which it is applied. Because of its advantages over conventional engines, that need liquid fuel, and the ongoing development more and more companies try to make the switch to these electric motors and electrical drives.
A lot of knowledge about these drives is available through books and the internet but the problem that engineers that have to choose these drives soon face is that this information is scattered. Also the huge variety in different types adds to this loss of overview. Due to the ever increasing share of electrical drives in propulsion technique at least a basic knowledge of these systems is very important though. The need for a complete, clear and concise source of information is thus high. The purpose of this report is then also to give a clear overview of the state of art of the electrical drives with the addition of some practical information and examples.
The most important part of an electric drive is the driving force behind it all, which is either the motor or the generator. These machines know many distinctive DC or AC types, of which the PMDC, separately excited, shunt, series, compound, induction and synchronous
motor/generator are the most common ones. These machines are all based upon the same phenomenon that occurs when a current carrying wire is placed in a magnetic field.
Whenever this happens a force is generated. With the use of clever constructions this physics principle can be turned into highly efficient machines.
Other components are required to create an electric drive though as well. These include a transmission, control unit and in some cases a battery. All these components need to be dimensioned and installed carefully. Transmission for instance which can be either a direct coupling, elastic coupling, gearwheel (gearbox), belt, snare, chain or a CVT are very sensitive to misalignment, vibrations and overheating. Control units for induction and synchronous machines (also known as frequency controllers) are mainly limited by the maximum current they can handle. However also this component has many variants with all kinds of operating methods, among which are cycloconverters, PWM, PAM, vector
modulation and field-oriented control. Batteries can be even a bigger problem since these are not only limited by technical aspects but by economical factors as well since they can be very expensive. Due to these influences only four types are available nowadays which are suited for most applications. These types are lead-acid, Nickel metal hydride, zebra and lithium-ion.
The purpose of this report has been fulfilled by giving a theoretical background of the working principle and the different types of the most important parts in an electric drive. Although not every aspect is discussed as thorough as others the electric motor and generator have been presented along with the means to control these machines, the possibilities to connect these machines to their loads and a possibility to either drain or store their power. This theory was then completed with practical information and calculation examples which combine all the theory of electric drives, giving an overview for several different applications.
Although these machines are well designed and reasonably rigid and reliable they do need to be selected carefully. This is one of the most important tasks of an engineer. Though it is true that the manufacturer is responsible for delivering a quality machine, it is the engineer’s responsibility to ensure correct usage of the machine. This includes factors like sudden loss of supply voltage, sudden loss of load on the motor, environmental contaminations, correct and rigid mounting of the machine and even the global location of the machine (since most machines are only designed to be used up to 1000 m above sea level).
This report forms a solid base for engineers to consult regarding all these factors that have to be thought about in a design process. It presents the state of the art regarding electric drive systems and gives both technical and non-technical persons a clear insight in the world of one of the most frequently used and versatile propulsion systems currently available. For very complex design problems this report might only function as an orientation guide though and it is recommended that detailed topic specific literature is also consulted in these cases.
List of symbols
Symbol Quantity Unit
α Angle ⁰ δ Load angle ⁰ η Efficiency - μ Friction coefficient - ξ Efficiency - ρ Density kg/m3 Φ Magnetic flux Wb
ω Angular velocity Rad/s
A Area m2
a Acceleration Rad/s2
B Flux density T
C Capacitance F
Ccr Combined radiation and convection heat transfer coefficient W/(m2⁰C)
c Constant -
cw Air drag coefficient -
d Diameter m
E Voltage V
E0 Induced voltage V
Eh Hysteresis loss J
Es Externally supplied voltage V
F Force N
f Frequency Hz
frol Rolling resistance coefficient -
g Gravitational acceleration m/s2 H Dissipated energy W I Current A Ia Armature current A i Transmission ratio - J Moment of inertia kgm2 K Machine constant - l Length m M Mass kg
m Number of stator phases -
N Number of loops -
n Motor speed Rpm
P Power W
p Number of poles -
Q Reactive power VAR
q Motor constant - R Resistance Ω Ra Armature resistance Ω r Radius m S Apparent power VA s Slip - T Torque Nm ΔT Temperature difference ⁰C t Time s Δt Time interval s
t0 Braking time constant s
U Voltage V Ua Armature voltage V v Speed m/s W Energy J Xc Capacitive reactance Ω Xs Synchronous reactance Ω x Distance m
Z Motor constant that depends upon the number of turns and the type of the armature windings
Terminology
Throughout this entire report certain terms will return frequently. Since these terms are quite important and fundamental in the field of electrical engineering they will be explained here. Stator: The stationary part of an electrical machine.
Rotor: The rotating part of an electrical machine.
Armature: The power-producing component of an electrical machine. In a motor the armature (commonly) consists out of a metal core surrounded by windings and is also referred to as the rotor. In a generator the armature windings generate the electric current. The armature can be either the rotor or the stator.
Magnetic field: The magnetic field is the driving force of most electrical machines. It can be provided by either electromagnets or permanent magnets mounted on either the rotor or the stator.
Electromotive force (emf): A voltage generated by a battery or by the magnetic
force according to Faraday's Law, which states that a time varying magnetic field will induce an electric current.
Magnetomotive force (mmf): Any physical driving (motive) force that produces magnetic flux. Magnetomotive force is so named because it plays a role in magnetic circuits analogous to that of electromotive force in electric circuits.
Introduction
Since the start of the industrial revolution better, stronger and more efficient engines have been invented. Starting with the steam engine soon the petrol and diesel engine came to live and eventually of course the electric engine. Especially the electric engine nowadays has a wide variety of fields in which it is applied. Because of its advantages over conventional engines, that need liquid fuel, and the ongoing development more and more companies try to make the switch to these electric motors and electrical drives.
A lot of knowledge about these drives is available through books and the internet but the problem that engineers that have to choose these drives soon face is that this information is scattered. Also the huge variety in different types adds to this loss of overview. Because of this engines are selected that are wrongly dimensioned or are more costly than necessary. It is thus in the engineers interest, as well as his employers and eventually everyone’s interest that the right choice is made.
The purpose of this report is to give a clear overview of the state of art of the electrical drives with the addition of some practical information and examples. In order to give engineers a clear and complete overview some boundaries are required. The scope of this report is limited to a number of factors. For starters future technologies that are still under
development at this time will not be looked at. Besides the motors and generators also other important parts of a drive system are discussed, like the gearbox, batteries and frequency controller. These other components will however not be discussed as thorough as the motors and will be limited to a number of design aspects that engineers have to watch out for. The final limitation is that although most motor and generator types will be presented, some variants that are special combinations of these types, or specialized versions of a specific type, may not be mentioned.
The structure of this report is as follows. First off the history of the electric motor and generator discusses the invention and development of these machines in chapter 1. These machines are then discussed in detail in chapters 2 and 3 for the electric motor and
generator respectively. The subsequent chapters handle the other components of the drive system. Chapter 4 discusses the coupling, chapter 5 the batteries and chapter 6 the
frequency controllers. Chapter 7 will explain certain aspects regarding the manufacturer’s data about these electric machines and this information will be used in chapter 8 where a number of examples are given which all require the selection of an electrical drive system. The report is than finished with a conclusion and some recommendations.
1 Brief history of the electric motor and generator
Before a lot of in dept information is given a brief historical overview will be given. This chapter will present the development of one of the most important actuators of the modern age, starting with the discovery of a phenomenon 192 years ago. As will soon become clear there is no one who is acclaimed to be the sole inventor of the DC motor, since this device is the result of a long process involving many people.1820: Hans Oersted discovers the generation of a magnetic field by electric currents through the observation of a compass needle.
1821: the British scientist Michael Faraday demonstrates the conversion of electrical energy into mechanical energy by electromagnetic means. A free-hanging wire was dipped into a pool of mercury, on which a permanent magnet was placed. When a current passed through the wire, the wire rotated around the magnet, showing that the current gave rise to a close circular magnetic field around the wire.
1822: The English mathematician and physicist Peter Barlow built the first Barlow wheel. In this apparatus a wheel is lowered until a spoke just touches a pool of mercury which is situated beneath it. When a voltage is applied to the wheel’s supports, the wheel will start to rotate.
1828: A Hungarian physicist, Ányos Jedlik, demonstrated the first device to contain the three main components of practical DC motors: the stator (the part that remains
stationary), rotor (the moving part) and commutator (a rotary electrical switch that periodically reverses the current direction between the rotor and the external circuit). The device
employed no permanent magnets, as the magnetic fields of both the stationary and revolving components were produced solely by the currents flowing through their windings.
1831-1834: During this period inventions are made all over the world by a lot of different people. These inventions concern both the electric motor as well as generators. The most influential people in this period are Michael Faraday (British), Joseph Henry (USA), Savatore dal Negro (Italian), Hippolyte Pixii (French), William Ritchie (British), William Sturgeon (British), Heinrich Friedrich Emil Lenz (German) and
Guiseppe Domenico Botto (Italian).
1834: Moritz Hermann Jacobi (German-speaking Prussian, naturalized Russian) constructs an
electric motor. His motor lifts a weight of 12 pounds with a speed of one foot per second, which is equivalent to about 15 watts of mechanical power. About a year after he made his invention he clearly states that he was not the sole inventor of the electromagnetic motor. He indicates the priority of the inventions of Botto and Dal Negro. Nevertheless Jacobi was the first person to make a usable rotating electric motor.
1834-1854: In these years the development continues in a rapid pace. More and more individuals try to improve and sell their engines. During this period also the first electric driven (toy) vehicles were build. These vehicles range from cars, to boats, to trains. A highlight in this period is the first U.S. patent for an electric motor granted to Thomas Davenport (USA) in 1837.
1856: Werner Siemens (German) invents the electric generator. He is also the first one to use windings in slots. This new invention transforms the design of electrical machines and in the decades to come all previous designs drop out of the market. Even up to date almost every electric motor still has this basic design.
1871: Zénobe Théophil Gramme (Belgium) invents the anchor ring. Subsequently he incorporates this into Siemens machine solving the problem of a pulsating DC production. 1886: Improvements to various parts of the electric motor continue to take place in the years leading up to 1886 when Frank Julian Sprague (USA) invented the first practical DC motor. The reason this was the first practical DC motor is because it was a non-sparking motor
capable of constant speed under variable loads. In the same year Sprangue’s company also introduced another important invention, namely a method to return power to the main supply systems of equipment driven by electric motors. His method of returning power to main supply systems was important in the development of the electric train and the electric elevator.
1882-1893: During this period several people, the most prominent being Nikola Tesla (Croatian, naturalized US-American), Galileo Ferraris (Italian),
Charles Schenk Bradley (US-American), Friedrich August Haselwander (German),
Michael Dolivo-Dobrowolsky (Russian, naturalized Swiss) and Jonas Wenström (Swedish), all made contributions in the invention of the multi-phase AC systems and the induction motor.
Although the art of the electric motor/generator would continue to evolve during the next century, leading to a wide range of highly efficient machines, (most of) the basic knowledge was now known. Application of electric motors revolutionized industry. Industrial processes were no longer limited by power transmission using line shafts, belts, compressed air or hydraulic pressure. Instead every machine could be equipped with its own electric motor, providing easy control at the point of use, and improving power transmission efficiency. Electric motors applied in agriculture eliminated human and animal muscle power for tasks such as handling grain or pumping water. Household uses of electric motors reduced heavy labor in the home and made higher standards of convenience, comfort and safety possible.
2 Electric motors
There are a lot of different electrical motors. Often they are divided into three different groups; the DC motors, asynchronous motors and synchronous motors. In this chapter the different types of motors will be discussed. For the contents of this chapter the basic principles of electromechanical energy conversion, which can be found in appendix A, are assumed to be known.
Paragraph 2.1 gives more information about the DC motors. In the second paragraph both the synchronous and the asynchronous motor are presented, since these are both AC
motors, and then in paragraph 2.3 the remaining types of motors that haven’t been discussed yet are presented.
2.1 DC motors
In this paragraph the DC motor will be discussed. This will be done by starting with a
theoretical background in paragraph 2.1.1. This explains how this motor transforms the basic principles of electromechanical energy conversion into a working motor as well as some other important parts. The subsequent paragraphs present the different variations to this basic DC motor design. In these paragraphs more engineering relevant details are given like equations and torque-speed curves. This section is than finished with some final remarks.
2.1.1 Working principle
Continuing where the basic principles of electromechanical energy conversion stopped (see appendix A), a way is needed to make sure that the rotor keeps rotating. The way a DC motor does this is with the use of a so called commutator. The simplest form of such a commutator can be found in a two-pole brushed DC motor, which will be used here in order to give a clear and simple explanation. Also other important parts and factors will be
discussed subsequently. 2.1.1.1 Commutator
A commutator is a rotary electrical switch that periodically reverses the current direction between the rotor and the external circuit. This is achieved by the construction of the commutator. The external circuit is connected by a set of brushes (see section 2.1.1.2) to a disc consisting of 2 conducting halves separated by an insulating strip, the commutator. The way this works can be seen in Figure 2.1.
When the coil is powered, a magnetic field is generated around the armature. The left side of the armature is pushed away from the left magnet and drawn toward the right, causing rotation. The armature continues to rotate. When the armature becomes horizontally aligned, the commutator reverses the direction of current through the coil. Because of this the
process can be repeated over and over again while the torque remains in the same direction. Although the working principle of the DC motor is now fully explained this simple design suffers from a few problems. The first problem occurs when the armature is in a horizontal position. In this position the torque is zero and thus the motor would not be able to start. If it is already started though the momentum of the load and rotor would cause the motor the turn beyond this point and keep functioning. There is however a second problem with this
horizontal no torque position that occurs during normal operation. Each time the commutator passes this point it shorts out the battery (directly connects the positive and negative
terminals) for a moment. This shorting wastes energy and drains the battery needlessly. These problems can be solved rather simply by starting the motor with an external torque and increasing the spacing between the commutator halves so that the brushes (see section 2.1.1.2) can’t touch both halves simultaneous anymore. These solutions might not however be suitable for every application though. Besides the clear disadvantage of the solution to the first problem, the result of the solution to the second problem is that the developed torque is not smooth anymore but slightly pulsating. Another disadvantage is that, since the coils have a measure of self inductance, the current flowing through them cannot suddenly stop. This current attempts to jump the space between the commutator segment and the brush, causing arcing.
Unlike the demonstration motor above, DC motors are commonly designed with more than two poles. The advantage of more poles is that they don’t suffer (as much) from any of the before mentioned problems.
2.1.1.2 Brushes
The commutator is supplied with power through a set of brushes, see Figure 2.2. These brushes consist of conductive material that makes mechanical (sliding) contact with the commutator. Different brush types make contact with the commutator in different ways. Because copper brushes have the same hardness as the commutator segments, the rotor cannot be spun backwards against the ends of copper brushes without the copper digging into the segments and causing severe damage. Consequently strip/laminate copper brushes only make tangential contact with the commutator, while copper mesh and wire brushes use an inclined
contact angle touching their edge across the segments of a commutator that can spin in only one direction. The softness of carbon brushes permits direct radial end-contact with the commutator without damage to the segments, permitting easy reversal of rotor direction, without the need to reorient the brush holders for operation in the opposite direction. These different orientation possibilities are visible in Figure 2.3.
Using this technique of applying brushes also brings some limitations to the motor though. The biggest
disadvantage is that brushes and copper segments wear. On small power machines the brushes may last as long as the product, but larger heavy duty machines require regular replacement of brushes and occasional resurfacing of the
commutator. Because of this regular required
maintenance this type of motor is not suited for all applications, like for instance
service on aerospace equipment where maintenance is not possible.
Another consequence of the use of brushes is that the power range of these machines is limited. Because of the "brush drop" due to the resistance of the sliding contact, the efficiency of DC motors is limited. A brush drop of several volts makes low-voltage machines very inefficient. Unlike the brushed DC motor, the induction motors which do not use commutators or brushes are much more energy efficient (more on this can be found in paragraph
2.2.1). Besides the brush drop which creates a lower power range boundary, also an upper power range boundary is created by the brushes. Since the current density in the brush is limited and the maximum voltage on each segment of the commutator is also limited very large DC motors (> several MW) cannot be built with this technique. The largest motors and generators are all AC machines.
New developments in the field of power engineering have made this technique of brushes and commutators outdated. With the widespread availability of power semiconductors it is now economical to provide electronic switching of the current in the motor windings. This has resulted in the development of the so called "brushless direct current" motors (see section 2.3.2). In these motors the rotor position determines when the stator windings switch polarity. Their operating life is determined only by bearing lifetime.
2.1.1.3 Electromotive force
As has been explained previously a rotating coil that is subjected to a magnetic field will induce a voltage over its terminals. This is true no matter what causes the rotation. This means that as soon as a DC motor is started the rotor will induce a voltage that opposes the externally supplied voltage. This phenomenon is called counter-electromotive force (cemf). The polarity and value of the induced voltage are the same as those obtained when the motor operates as a generator. This means that the resulting net voltage acting in the electrical circuit is equal to Es – Eo, where Es is the externally supplied voltage and Eo is given by the next formula:
0
60
Z n
E
[2.1] In this formula:Z = a constant that depends upon the number of turns on the armature and the type of winding
n = the speed of rotation of the motor [rpm] Φ = the flux per pole [Wb]
2.1.1.4 Magnetic field
In the example given in this paragraph the magnetic field is generated by a pair of permanent magnetic shells. Unlike the Permanent magnet DC motor (see paragraph 2.1.2) every DC motor actually uses electromagnets to generate the magnetic field. These are also referred to as field windings.
Electromagnet consists of a conductive wire, usually copper, wrapped around a piece of metal. When a current flows through the wire a magnetic field is created around the coiled wire, magnetizing the metal as if it were a permanent magnet.
Electromagnets are useful preferred over permanent magnets because they can be turned on and off.
2.1.1.5 Rotor
A rotor normally is composed out of several windings, forming a coil, wrapped around a metal core. Opposite to the example that has been given so far a rotor (also referred to as
armature) can also be equipped with several coils. As a consequence obviously this also means that the commutator needs to have multiple isolated segments.
The core which hasn’t been discussed yet is not made out of one solid piece. The reason for this is that the core is also subjected to the stationary magnetic field. As it turns the core cuts flux lines and thus induces a voltage according to
faraday’s law. Because of this voltage eddy currents are induced in the rotating armature. This is demonstrated in Figure 2.4 for a cylindrical core. For a short theoretical background of eddy currents please read appendix B. These eddy currents cause large I2R losses. These losses cause rapid heating of the core. In order to reduce the eddy currents the core is laminated with sections that are insulated from each other. As can be seen in Figure 2.5 this reduces the eddy currents and thus the temperature of the core.
2.1.1.6 Armature reaction
The current that flows through the armature conductors creates a magnetomotive force that distorts and weakens the flux coming from the stator poles. This phenomenon occurs in both motors and generators and is known as the armature reaction. This phenomenon is best seen in Figure 2.6. When a motor runs at no-load, the small current flowing in the armature doesn’t affect the flux Φ1 coming from the poles (Figure 2.6a). If the armature carries its normal current it produces a strong magnetomotive force which in turn creates a flux Φ2 (Figure 2.6b). The resulting flux Φ3
can be seen in Figure 2.6c. As can be seen the magnetic field is distorted. This unequal distribution leads to two important effects.
Figure 2.4 Eddy currents in cylindrical core
Figure 2.5 Eddy currents in laminated core
Figure 2.6 a, b and c Magnetic field of stator, rotor and resulting respectively
First the neutral zone shifts to the left, against the direction of rotation. Neutral zones are those places on the armature surface where the flux density is zero. In a no-load situation this would be precisely between the poles. In these places the brushes are normally placed. Shifting of these neutral zones results in poor commutation and sparking at the brushes. The armature reaction and the resulting magnetic field as well as the newly obtained neutral zone are sketched in Figure 2.8 and Figure 2.7 respectively. Secondly an unstable situation could arise in which the speed increases with load.
Commutating poles
The problem of the armature reaction can be countered with the use of
commutating poles. These commutating poles are installed between the
magnetic poles and develop a
magnetomotive force that is equal and opposite to that of the armature. In this way the distortion of the magnetic field is neutralized, but only in the narrow region covered by the commutating poles (Figure 2.9). Since this is the area where commutation takes place it is no
problem for motors driving normal loads that the Figure 2.9 Commutating poles Figure 2.8 Armature reaction Figure 2.7 Resulting magnetic field
field under the main poles remains distorted. In special cases it could however be necessary to add another feature to further neutralize the armature reaction.
Compensating windings
In some applications of DC motors the armature current changes constantly producing very sudden changes in the armature reaction. For such motors the commutating poles don’t neutralize the armature reaction enough. Under these conditions torque and speed are difficult to control and flashovers may occur across the commutator. To prevent this problem special compensating windings are installed. These windings are placed in slots that are cut into the pole faces (see Figure 2.10) and they are connected in series with the armature.
Figure 2.10 Compensating windings
The principle behind the compensating windings is the same as for the commutating poles, but because these windings are more locally distributed the armature reaction is completely neutralized. The usage of compensating windings also has some other advantages with respect to design and performance, namely:
- A shorter air gap can be used because demagnetizing of the armature is no longer a problem. The use of a shorter gap means that the shunt field strength can be reduced and thus the coil can be smaller.
- The inductance of the armature circuit is reduced, consequently the armature current can change more quickly and the motor gives a much better response (especially in big machines).
- The peak torque can briefly be 3 to 4 times as high as the rated torque. The reason is that the effective flux in the air gap falls of rapidly with increasing current because of armature reaction.
2.1.1.7 Starting an DC motor
Starting a DC motor is not as easy as it may sound. If the full voltage would be applied to a stationary motor the starting current would be very high and several things could happen, like for instance:
- Burning out the armature
- Heavy sparking, causing damage to the commutator and brushes - Breaking the shaft due to mechanical shock
For this reason DC motors must be equipped with a way to limit the starting current. This can be done with a variable resistor or a Face-plate starter.
Figure 2.11 Face-plate starter
Figure 2.11 shows the schematic of a manual face-plate starter. As the contact arm moves to the right and completes the circuit the supply voltage Es causes full field current Ix to flow. The armature current I is however limited by a series of resistors. As the motor begins to turn the cemf Eo builds up and the armature current decreases. When the motor reaches a steady speed the contact arm is moved one resistor further. Because of this the current increases to a higher level and the process is repeated until the contact arm touches the last contact. The electromagnet and the spring form a fail-safe which makes sure that the motor stops, and stays off, when the supply voltage is interrupted and reestablished again.
Just like with the commutator also this method is outdated. Electronic methods nowadays are used to limit the starting current.
2.1.1.8 Stopping an DC motor
Just like starting a motor sounds easier then it is, the same is true for stopping a motor. Although a motor will eventually stop when no more voltage is supplied due to friction and windage losses, the inertia of the rotor and the load could still let it run for over an hour (this method is known as coasting). Since for most applications this in unacceptable and a quick stop is desired two stopping methods will be discussed here, dynamic braking and plugging. Dynamic braking
With dynamic braking the connection with the power supply is severed and the motor is reconnected with a resistor. The voltage Eo will immediately produce an armature current. However, this current flows in the opposite direction of the original current. This means that also a reverse torque is developed which brings the motor to a rapid and smooth stop. If the speed decreases, so does Eo and thus also the braking current and torque, finally becoming zero when the rotor comes to a standstill.
Plugging
To stop a motor even faster the method of plugging can be used. In this method the
terminals of the supply voltage are reversed, and thus also the current through the armature. By reversing the current the source voltage Es and the cemf Eo are now in the same direction and increase each other. This increased net voltage can produce an enormous current that would destroy most components. In order to limit this current a resistor is placed in series with the reversing circuit just like was done with dynamic braking. Unlike dynamic braking where the source voltage disappears, with plugging the source voltage remains active even
disconnected immediately or the motor will start spinning in reverse. Figure 2.12 shows a graph of the braking time plotted against the remaining speed for the different braking methods discussed.
Figure 2.12 Braking times
Braking time constant
As can be seen in the graph above the braking time can be expressed in a time constant t in much the same way as the electrical time constant of a capacitor that discharges into a resistor. Essentially, t is the time it takes for the speed of the motor to drop to 36.8% of its initial value. It is much easier to draw the speed-time curves by defining a new time constant to though. This new time constant is defined as the time for the speed to decrease to 50% of its original value. These two time constants are related to one another by the following equation:
0.693
o
t
t
[2.2]Although providing the prove is beyond the scope of this report it can be proven that the new time constant to is given by:
2 1 0 1
131.5
J n
t
P
[2.3] In this formula:to = time for the motor speed to fall to one-half its previous value [s]
J = moment of inertia of the rotating parts, referred to the motor shaft [kgm2] n1 = initial speed of the motor when braking starts [rpm]
P1 = initial power delivered by the motor to the braking resistor [W] 131.5 = a constant [exact value = (30/π)2log
e2] 0.693 = a constant [exact value = loge2]
This equation assumes that the braking effect is entirely due to the energy dissipated in the braking resistor. In general, the motor is subjected to an extra braking torque due to windage losses and friction, and so the braking time will be less than that given by this formula. 2.1.1.9 Speed control
The speed of a DC motor can be controlled in two different ways, either by changing the armature voltage or by changing the flux.
Armature speed control: By changing the armature voltage the speed can be controlled. If the voltage is increased so is the speed and vise versa. This will also be immediately clear once the equation for the angular velocity is given. This equation can be found in the following paragraphs per motor type.
Field speed control: The second option to change the speed is to change the field flux. These two parameters are correlated inverse, so if the field flux is increased the speed decreases.
Note that by applying these methods and thus changing any of the parameters other factors may be influenced as well. For instance the torque delivered or the heat generated could change. Depending on the type of motor and the magnitude of the change this could cause problems. These consequences, if any, will be discussed in the subsequent paragraphs explaining the different motor types.
2.1.2 Permanent magnet DC (PMDC)
The DC motor that was used in the previous paragraph as an example is a PMDC. Such motors that use permanent magnets to generate the flux instead of electromagnets have several advantages. These are:
- No electromagnets are needed, so less energy is consumed, less heat is generated and less space is required (this results in a higher efficiency).
- Since permanent magnets are used the flux is always present so there is no risk of run-away due to field failure.
- Since the magnets have a permeability nearly equal to that of air the effective air gap is increased. Because of this the armature reaction is lower than when soft-iron pole pieces are used. The result is that the magnetic field doesn’t get distorted. - Because of a reduced armature reaction commutation is improved, the overload capacity of the motor is better and the long air gap reduces the inductance of the armature which results in a faster response to changes in armature current. There are however also some disadvantages to PMDC motors.
- Only practical in smaller (< 5hp) and lower torque motors.
- The magnets are ceramic or rare-earth/cobalt alloys. Because of this they are expensive.
- Because no electromagnets are used it is not possible to obtain higher speeds by field weakening.
The PMDC motor is often classified under the separately excited motor since, although no secondary power source is needed, the rotor and stator are independent of one another. Because of these similarities for more information about speed-torque curves and more please continue to section 2.1.3.
2.1.3 Separately excited motor
The rotor and stator are each connected from a different power supply. This gives another degree of freedom for controlling the motor over for instance the shunt motor. A schematic drawing of a separately excited DC motor is given in Figure 2.13.
Recalling from equation A1.4 that
E
B l
d
and realizing that the armature voltage equals the cemf plus the losses, or in formula:U
a
E
I
aR
a, these equations can be rewritten into the next equation which gives us the angular velocity for this type of motor.a a a p
U
I
R
K
[2.4] In this formula: Ua = armature voltage [V] Ia = armature current [A] Ra = armature resistance [Ω] K = machine constant Φp = main pole flux [Wb]Since the armature resistance is small the second term in this equation can be neglected. This means that the speed is only dependent on the armature voltage and the main pole flux and not the load. Because the main pole flux is generated by an external power source (or in case of the PMDC by the permanent magnets themselves) this flux is kept maximal at all times. This in turn means that the torque-speed curves can be varied from zero to the
nominal speed by changing the armature current. Special care has to be taken with regard to the main flux though. Although this normally is kept constant at the maximum value it could drop due to an interruption in the electrical circuit. This so called weakening of the field would cause the speed to increase. The speed could then become so high that the armature
windings break free out of their slots and collide with the stator damaging the motor. Although the equations for all other factors can be derived from equation 2.4 with the additional knowledge that the torque
T
K
pI
a, they are all given below.The torque is given by:
2 2 a p p a a U K K T R R
[2.5]And the armature voltage is given by: a
a p p
T R
U
K
K
[2.6]One very important equation is equation 2.5 because this gives the relation between the torque and the speed of the motor. These so called torque-speed curves can be seen in Figure 2.14 for different armature voltages.
Figure 2.13 Separately excited DC motor
Figure 2.14 Torque-speed characteristic for different armature voltages with load-line As can be seen in the graph above the motor can deliver the required torque up until the nominal speed is reached. Although previously a warning has been given for the
consequences of field weakening this technique can also be used to increase the motors speed and enable it to deliver more torque. This normally can be done to a factor of about 1,5. Besides the before mentioned motor damage heating also becomes a problem, as will be discussed next.
As has been mentioned before the current is highest during the acceleration of the motor from standstill. The heat losses are given by:
2
loss a a
P
I
R
[2.7]Rewriting equation 2.4 gives the formula for the armature current.
a p a a
U
K
I
R
[2.8]Since during acceleration the angular velocity is almost zero the second term can be neglected and the startup armature current becomes:
, a a start a U I R [2.9]
This current used to be limited with the help of a face plate starter as has been explained in section 2.1.1.7. Nowadays this is done with the help of a chopper which in theory eliminates any losses. Because the current is limited also the torque is limited.
max p max
T
K
I
[2.10]Including this extra boundary into the torque-speed curve that was previously given, the entire torque-speed range of the motor is obtained. This complete graph is shown in Figure 2.15.
Figure 2.15 Complete torque-speed curve
2.1.4 Shunt motor
Instead of having the rotor and stator both being driven by a separate power source, a shunt motor has the stator and rotor windings connected to the same power source in parallel. A simple version of the electrical circuit is given in Figure 2.16.
Because the windings are connected in parallel the current in the circuit is divided into two. Because the shunt winding is made of a small diameter wire the resistance is high. This means that only a small fraction of the current (< 5%) flows through this winding and most current flows through the armature winding. Since the torque equation is the same as for the separately excited motor this equation is not repeated here. Following from the same torque equation also the
torque-speed curve is the same. This information can thus all be found in section 2.1.3.
An extra graph that is given contains not only the torque-speed relationship, but also the torque-current dependency. As can be seen in Figure 2.17 if the torque increases (thus the motor is mechanically loaded) the speed decreases only slightly and the current increases. The reason is that once the speed decreases also the cemf decreases and thus the armature current increases. Because the speed only decreases slightly over a large torque range shunt motors are also called constant speed motors. This characteristic makes it extremely suitable for applications where a constant speed under varying loads is desired, like for instance in cranes and elevators.
The advantages of a shunt motor are that it can’t run-away (even under no-load conditions) and that its speed can be controlled very precisely in a wide range without high losses. A disadvantage would be that the start-up torque is less than that of for instance a series motor.
Figure 2.17 Torque-speed and torque-current curve (the speed, torque and current are given in per-unit values)
2.1.5 Series motor
As the name suggests the stator and rotor windings are connected in series (see Figure 2.18). As a result of this the field current and the armature current are the same. This means that the flux is now proportional to the armature
current ( '
p K Ia
) and thus the torque is proportional to I2
.
The advantage of this is that
it gives the highest torque percurrent ratio over all other dc motors. It is therefore used in starter motors of cars and elevator motors.
The equations given in the section 2.1.3 are still valid for this type of engine, with the alteration that the torque is given by equation 2.11, with K” being a constant.
'' 2
p a a
T K I K I [2.11]
Rewriting the formula’s previously given with this new torque equation gives the following results: '' '' a
T
U
K T
K
[2.12] '' a a a a U I R K I
[2.13] '' 2 '' 2(
)
aK U
T
K
R
[2.14]From this last equation it follows that the torque and speed are inverse correlated and that a series motor should not be used unloaded since then the speed becomes very high, possibly even higher than the motor can bear. This equation also enables the drawing of the torque-speed curve.
Figure 2.19 Torque-speed characteristic for different armature voltages and load-lines
Also the series motor suffers from heat losses which limit the maximum current that can be supplied. These heat losses are dependent on the armature current according to the following equation: '' a a a U I K
R [2.15]Also the series motor requires some sort of current limiting device during startup (when ω = 0). Including this maximum current limitation in the torque-speed curve, results in the graph given in Figure 2.20. Note that unlike the separately excited motor the method of field weakening doesn’t work on this type of motor.
Figure 2.20 Complete torque-speed curve
A final remark that has to be made concerns the accuracy of this type of engine. As can be derived from equation 2.14 the motor is less sensitive to changes in the armature voltage at high speeds. The disadvantage of this is that it can’t be controlled very well at those speeds.
2.1.6 Compound motor
Where the previous types of motors all had their own characteristic electrical circuits the compounded motor actually is a combination of these previous types. The stator is connected to the rotor through a combination of shunt and series windings, see Figure 2.21. If the magnetomotive forces of the shunt and series windings add up together, the motor is called cumulatively compounded. If they subtract from each other, then it is called a differentially compounded motor.
Cumulative compound: The cumulative compound motor is one of the most common DC motors because it provides high starting torque and good speed regulation at high speeds. When the motor runs at no-load, the armature current I in the series winding is low and the magnetomotive force of the series field can be neglected. The shunt field is fully excited though and thus the motor behaves like a shunt motor, or in other words it does not tend to run away at no-load. As the load increases so does the magnetomotive force of the series field while the shunt field remains the same. This means that the total magnetomotive force increases and thus the motor speed falls with increasing load. Recalling that the shunt motor can provide smooth operation at full speed, but cannot start with a large load attached, and the series motor can start with a heavy load, but its speed cannot be controlled the
cumulative compound motor combines the best of both these types of motors into one. This makes it acceptable for most applications.
For this type of motor the torque is given by:
s p
aT
K
I
[2.16]In this formula: K = constant
Φs = series field flux [wb] Φp = shunt field flux [Wb] Ia = armature current [A]
Differential compound: As can be quickly understood the differential compound motor pretty much behaves the opposite of the cumulative compound motor. This is logical since the windings aren’t working together but against each other. As a result of this the
magnetomotive force decreases with increasing load. This means that the speed increases when the load increases. Such a situation may lead to instability and thus this type of motor is unsuitable for any application.
Figure 2.22 shows the torque-speed curves the compound motors as well as the shunt and series motor. Again the units are on a per-unit basis.
Figure 2.22 Torque-speed curve for different motor types
2.1.7 Closing remarks
Now that the basic and most common DC motors have been presented this paragraph list a number of things that are valid for all DC motor types. First a number of disadvantages of the above presented DC motors:
- Brush wear: Since they need brushes to connect the rotor winding. Brush wear occurs, and it increases dramatically in low‐pressure environment. So they cannot be used in artificial hearts. If used on aircraft, the brushes would need replacement after one hour of operation.
- Sparks from the brushes may cause an explosion if the environment contains explosive materials.
- RF noise from the brushes may interfere with nearby electronic devices.
Note that these disadvantages concern the commutator and brush section of the motor. These problems can be overcome as will be explained later in paragraph 2.3.
Although the torque-speed curves are given and fields of application have been mentioned for the different motors, there are still some uncertainties about the actual size, output, etc. of these motors. To give some more insight about these matters the following table gives common values for a number of important motor characteristics for engineers.
Table 1 - DC motor characteristics P kW 33 184 336 526 738 1025 U V 440 550 440 520 520 470 I A 89 363 830 1074 1532 2336 n Rpm 916 4137 2236 1618 963 1323 T Nm 339 425 1437 3106 7318 7399 η - 0.795 0.913 0.912 0.935 0.923 0.9354 M Kg 310 400 860 1440 2550 2700 lxwxh mm 905x 360x 831 1013x 360x 831 1270x 450x 1049 1447x 560x 1300 1820x 716x 1406 1508x 906x 1734
2.2 AC motors
In this paragraph the AC motor will be discussed. There are two types of AC motors, the asynchronous and the synchronous motor. The asynchronous motor will be presented in paragraph 2.2.1 and the synchronous motor in paragraph 2.2.2. Unlike the DC motors the working principle will be discussed per motor type.
2.2.1 Asynchronous motor
In this paragraph the asynchronous motor is discussed. In order to give a clear overview first the working principle will be discussed and the construction of the motor. When the
theoretical background is known more practical information is given like for instance the torque-speed curves and the fields of application for this type of motor.
2.2.1.1 Working principle
The asynchronous motor (also called induction motor) carries this name because the stator and rotor are turning asynchronous. This will be further explained in this paragraph as well as how to start, stop and control this type of motor. Because of the vast amount of information available on this subject only a superficial summary is given in this paragraph. Interested readers should also read chapters 13, 14 and 15 from Electrical Machines, Drives, and Power Systems by Theodore Wildi [55].
2.2.1.1.1 Magnetic field
Since this is an AC motor the stator is powered with alternating current. This can be either single-phase or polyphase AC current. The explanation given here is based upon the
Figure 2.23 3-phase stator
Since there are 3 pole pairs and the current is 3-phase the dominant pole pair switches between A, B and C. As a result the magnetic field now rotates with the AC oscillations. This is demonstrated in Figure 2.24.
Figure 2.24 Magnetic field rotation with AC oscillations
In section 2.1.1.5 it was described how dividing the core into laminated parts could reduce the eddy currents. This solution works for all rotating metal structures that are subjected to a stationary magnetic field. In an ac machine the soft magnetic pole caps that are inserted into the electromagnets are however subjected to an alternating magnetic field (see Figure 2.25a). This also induces eddy currents in the material and results in significant heating of the material. Since this is not desirable the same solution to reduce these eddy currents can be used. The difference is that the laminations are now made lengthwise due to the different
laminations from one another again the eddy currents are reduced to acceptable levels, see Figure 2.25b and c.
Figure 2.25 a, b and c Eddy currents in stationary iron core subjected to alternating magnetic field
2.2.1.1.2 Rotor
Unlike the previously discussed DC motors the rotor of an asynchronous motor is not connected to any external electrical circuit which supplies it with power, instead the rotor is shorted. Once the motor is turned on and the stator field starts rotating, the rotor ‘sees’ this rotating field. The changing flux induces a current in the rotor windings and since the rotor is short-circuited this current starts to flow. These currents in turn create magnetic fields in the rotor that interact with the stator field. Due to Lenz's law the direction of the magnetic field is such as to eliminate the source of the change in current. As a result of this the rotor will start to rotate in the direction of the rotating stator magnetic field to make the relative speed
between rotor and rotating stator magnetic field zero. If the motor is unloaded the rotor will be accelerated until this happens. Once this point is reached the rotor ‘sees’ no more flux
change and thus no more current is induced which will cause the rotor to slow down again. If the motor has to accelerate a load however the rotor speed will remain less than that of the magnetic field and the induced current is high enough to develop the required torque. The asynchronous motor is divided into two different
types according to the kind of rotor they use. The two types are the squirrel-cage rotor and the wound rotor. Squirrel-cage rotor: This rotor is composed of bare copper bars which are pushed into slots. The ends of the copper bars are connected by two copper rings, so that they are all short-circuited together. A typical squirrel-cage is shown in Figure 2.26.
Wound rotor: A wound rotor has a 3-phase winding, similar to the one on the stator. The winding is uniformly distributed
in the slots and is usually connected in 3-wire wye. The ends of these windings are connected to three rings which turn with the rotor. With the use of brushes these slip-rings are connected to external resistors. These resistors are used during the start-up period and the brushes are short-circuited during normal operation.
Also these rotor cores are subjected to eddy currents. Like explained in section 2.1.1.5 this means that the core isn’t a solid metal piece but consists out of several laminations.
2.2.1.1.3 Slip
As has just been explained the rotor is turning slower than the rotating stator magnetic field. A new term is needed to describe this phenomenon: the slip. The formula for this is given below. 1 s r r s s s
[2.17] Figure 2.26 Squirrel-cage
In this formula ωs and ωr are the angular velocities of the stator and rotor respectively. Since during start-up the rotor is still standing still the slip equals one. During normal operation this value normally lies between 0,01 to 0,08.
2.2.1.1.4 Starting an induction motor
The starting current in both the stator and rotor are high so a prolonged starting period (such as occur with high-inertia loads) has to be kept as short as possible or even avoided or else overheating becomes a problem. This problem can be prevented by reducing the starting voltage. This however also elongates the start-up time. Whether or not this is acceptable depends on the application for which it is used.
2.2.1.1.5 Stopping an induction motor
Just like it was the case with the DC motors there are several ways to stop an induction motor. Again the simplest option would be to remove the power source powering the revolving stator magnetic field. This however results in a very long stopping time which is usually unacceptable. The other options are plugging or braking with DC.
Plugging: With plugging two stator leads are interchanged. As a result of this the revolving stator magnetic field changes direction and thus starts to decelerate the rotor. The advantage of this method is that it works fast. The disadvantage is that besides all the kinetic energy in the system the stator also keeps supplying the rotor with electromagnetic power. All of this energy needs to be dissipated as heat. The result is that the heat dissipated in the rotor during plugging is three times the original kinetic energy of all the rotating parts. Because of this motors should not be plugged to often because high motor temperatures can melt the rotor bars or overheat the stator windings.
Braking with DC: Another option is to replace the AC source with a DC source. The magnetic field has now become stationary and decelerates the rotor. The advantage of this method over plugging is that the dissipated heat is only equal to the original kinetic energy of all the rotating parts. The disadvantage is of course that the braking time is longer than with plugging. The energy dissipated in the rotor is independent of the DC current, but a lower DC current increases the braking time. However the DC current can be up to three times as high as the rated current of the motor.
2.2.1.1.6 Exceptional conditions
Just like field weakening worked for some DC motors also asynchronous motors can be boosted a little. Normally these motors work fine within a 10% range of the nominal voltage and a 5% range of the nominal frequency, or if both these values are varied the sum of their percentages should be below 10%. Keep in mind though that increasing the load or the supply voltage can significantly increase the temperature of the motor and cause damage. Another known problem is called single-phasing. As has been said in the beginning of this paragraph a three-phase system has been used throughout this section of the report. If one line of this 3-phase line is opened for some reason then the motor continues to run as a single-phase motor and the current drawn from the remaining lines will almost double. Besides the obvious danger of overheating also the torque-speed curve is affected by this problem, see Figure 2.27.
Figure 2.27 Torque-speed curves under single-phase conditions Two final factors that are easily overlooked are:
1. The frequency variation due to a difference in national standards. In the USA the power grid is based upon a 60Hz system but Europe works on a 50Hz system. Using an engine made in another country is possible but care has to be taken in order to prevent overheating or other damage. This can be achieved by changing the voltage for instance.
2. All motors are designed to work without problems up to 1000m above sea level. At higher altitudes the motor temperature may become too high due to the fact that the thinner air results in poorer cooling.
2.2.1.2 Torque-speed curves
Because rewriting the basic principles for this type of motor is difficult and not relevant this derivation is left out and the final equations are given.
2 1 ( ) s s s q I c U s q [2.18] And 2 2 1 ( ) s field U s q T c s q
[2.19]With Is = effective current per phase in the stator [A] q = motor constant (for large motors around 5) Us = effective voltage per phase in the stator [V] T = torque [Nm]
c = constant s = slip
Equation 2.19 enables the drawing of the torque-speed curve. This graph is given in Figure 2.28.
Figure 2.28 Torque-speed curve
Although this torque-speed curve is important the motor runs at speeds close to nominal speed most of the time, supplying a torque varying between zero and maximum torque. Between these limits the torque-speed curve is almost linear, see Figure 2.29. The slope of the line depends mainly upon the rotor resistance (the lower the resistance, the steeper the slope). Because of this it is possible to write down an equation that very closely (accuracy better than 5%) predicts the speed under certain conditions, once the speed under other conditions is known.
This equation is: 2 x x n x n n n x T R E s s T R E [2.20]
With n = subscript referring to the known load conditions x = subscript referring to the unknown load conditions s = slip
T = torque [Nm]
R = rotor resistance [Ω] E = stator voltage [V]
Note that this equation is only valid under the restriction that
2 x x n n E T T E . 2.2.1.2.1 Speed control
When driven by a fixed frequency, loading the motor reduces the rotation speed. When used in this way, induction motors are usually run so that in operation the speed is kept above the peak torque point because then the motor will tend to run at reasonably constant speed. Below this point, the speed tends to be unstable and the motor may stall or run at reduced shaft speed. It used to be hard to control the frequency, which mend that induction motors could only be used in fixed speed applications but with the development of electronics it is simple to control the frequency nowadays. Because of that the induction motor now has replaced the DC motor in many applications.
The theoretical unloaded speed (with slip approaching zero) of the induction motor is controlled by the number of pole pairs and the frequency of the supply voltage. The synchronous speed ns in revolutions per minute (RPM) is given by:
120 s f n p [2.21] In this formula:
f = frequency of the source [Hz] p = number of poles
If the frequency is decreased the flux increases. In order to keep the flux equal the voltage has to be decreased simultaneous. If the frequency is increased the flux decreases. Since the voltage cannot be increased the torque decreases. This means that up until the nominal speed the motor can deliver the same maximal torque. At higher speeds the torque
decreases, but the power remains the same.
Out of equation 2.19 it becomes clear that there are several ways to change the speed of the motor. Previously only the option to control the speed by controlling the frequency of the magnetic stator field is discussed. The reason for that is because the other speed controlling options are respectively changing rotor parameter q (by changing the rotor resistance), changing the number of pole pairs or changing the voltage Us. These options haven’t been mentioned before because they aren’t preferable. This is because changing the rotor
resistance leads to more heat losses, changing the number of pole pairs only allows a limited number of speeds and changing the voltage Us only has a narrow range to control the speed and is therefore only applied in fine tuning.
