lappeenranta university of technology ltkk

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LAPPEENRANNAN TEKNILLINEN KORKEAKOULUEnergiatekniikan osasto

LAPPEENRANTA UNIVERSITY OF TECHNOLOGY Department of Energy Technology

RESEARCH REPORT EN A-33

LTKK

DESIGN OF A SWITCHED RELUCTANCE GENERATOR

Thomas Heese Juha Pyrhonen

FOREIGN SALES PROHIBITED

1996

%

ISBN 951-764-077-3 ISSN 0785-823X

H

DISTRIBUTION RESTRICTED TO U S. ONLY '»

DISCLAIMER

Portions of this document may be illegible electronic image products. Images are produced from the best available original document.

ABSTRACTLAPPEENRANTA UNIVERSITY OF TECHNOLOGY

Department of Energy Technology Section of Electric Power Engineering

Thomas Heese, researcherJuha Pyrhonen, associate professor, doctor of technology

DESIGN OF A SWITCHED RELUCTANCE GENERATORLUT, Department of Energy Technology, September 1996, 105 pages, 61 pictures, 10 tables, 1 appendix

Research Report EN A-33

ISBN 951-764-077-3 ISSN 0785-823X UDK: 621.313

Key Words: Electrical Machines, Switched Reluctance Machines, Generators

This paper presents the design of a low voltage switched reluctance generator for variable speed applications showing the design of its construction and commutation unit. For the realisation of the control system the control strategy is presented. The principle and the theory of switched reluctance generators are described in this context. Also an overview of existing generator technology for these applications is given.

The results gained suggest that switched reluctance machines can also advantageously be used as generators if the generating operation is considered within the design process. Compared with the existing technology a higher output power and efficiency is reached over the whole speed range.

Lappeenranta, September 1996

Thomas Heese, Juha Pyrhonen

J

2

Contents

Preface.............................................................................................................................................1

Contents..........................................................................................................................................2

List of Symbols.............................................................................................................................4Tiivistelma...................................................................................................................................... 9

1 Introduction...........................................................................................................................10

2 Generators for Variable Speed Applications..................................................................12

2.1 DC Generator............................................................................................................... 13

2.2 Alternator....................................................................................................................... 15

2.3 Weak Spots of Existing Technology........................................................................18

2.4 Supposed Improvements and Advantages of Switched Reluctance Technology21

3 Principle and Theory of Switched Reluctance Generators......................................... 24

3.1 Construction................................................................................................................. 24

3.1.1 Basic Characteristics........................................................................................... 25

3.1.2 Envelope and Internal Dimensions.................................................................. 27

3.1.3 Pole Geometry.....................................................................................................30

3.1.4 Windings............................................................................................................... 32

3.2 Working Principle........................................................................................................32

3.2.1 Rotor Position Dependency............................................................................... 33

3.2.2 Torque and Currents.......................................................................................... 37

3.2.3 Mathematical Description.................................... 39

3.2.4 Energy Conversion............................................................................................. 41

3.3 Commutation Unit.....................................!................................................................ 46

3.3.1 Classic Converter................................................................................................47

3.3.2 (»+l)-switch converter..................................................... :...............................48

3.3.3 Boost and Buck Converter............................................................................... 49

3.3.4 Bifilar Winding Converter..................................................................................51

3.3.5 Other Converter Topologies............................................................................. 52

3.4 Dynamic Operation......................................................................................................52

3.4.1 Single-Pulse Operation....................................................................................... 53

3.4.2 Chopping.............................................................................................................. 55

3.5 Control System.............................................................................................................55

3.5.1 Structure............................................................................................................... 56

3.5.2 Control Modes and Strategy.............................................................................56

3.5.3 Sensorless Control...............................................................................................58

Contents 3

4 Generator Design................................................................................................................ 59

4.1 Construction................................................................................................................. 60

4.1.1 Basic Characteristics............................................................................................62

4.1.2 Envelope and Internal Dimensions................................................................... 63

4.1.3 Pole Size and Geometry......................................................................................66

4.1.4 Winding................................................................................................................. 68

4.1.5 Further Estimations............................................................................................ 72

4.2 Commutation Unit................................................................................................. 73

4.2.1 Topology................................................................................................................75

4.2.2 Transistors............................................................................................................ 76

4.2.3 Diodes.................................................................................................................... 78

4.2.4 Zener Diode................................................................... 79

4.3 Control System....................................................................................................... 80

4.3.1 Control Strategy................................................................................................... 80

4.3.2 Sensing.................................................................................................................. 82

5 Simulation Results...............................................................................................................845.1 Input...............................................................................................................................85

5.2 Output..............................................................................................................................90

5.3 Phase Current................................................................................................................93

5.4 Efficiency.......................................................................................................................95

5.5 Losses..............................................................................................................................97

6 Conclusion and Prospects...................................................................... 101

7 References............................................................................................................................102

Appendix A: Measuring Results of an Alternator.........................................................106

Appendix B: True Scale Figures of the Generator....................................................... 118

Appendix C: Conclusion of Characteristic and Dimension Values..........................120

Appendix D: Tables of the Simulation Results..........................................................121

List of Symbols

•'i comer

AcuAcu+insul

Acu wire

Ainsul

ArAglotr

AglotS

Aslotsnet

A wire

B•BioB2.5

B30ddrdsD•DcUwireDrDrmDsDsbDSh•Dwire

EErEtfstk

HHei

bzpeak

hIb

comer area winding copper areacross sectional winding area with insulation

nominal cross sectional copper area

insulation areaarea of rotor cross sectionrotor slot area

stator slot areanet stator slot areacross sectional wire area with insulationmagnetic flux densityflux density at 10 kA/mflux density at 2.5 kA/mflux density at 30 kA/mthickness of insulation layerrotor slot depthstator slot depthduty cycle

nominal copper diameter of a wire rotor diameter minor rotor diameter ' stator lamination diameter

stator slot bottom diameter

shaft diametermaximum wire diameter with insulationmodulus of elasticitymodulus of elasticity in rolling directionmodulus of elasticity in transverse directionlamination stacking factormagnetic field strengthcoercive forcephase currentdiode currentpeak currenttransistor currentmodulus of inertiacontinuous drain current

List of Symbols 5

Idc output currentIdm peak of pulsed drain currentfomean diode mean current■fopeak diode peak current^DRMS diode RMS current

■lexc excitation currentfpRM repetitive peak forward currentIo output currenth phase currentfppeak phase peak current/r reverse current■^Tmean transistor mean current■^Tpeak transistor peak current/trms transistor RMS currentJ moment of inertiaK20 nominal capacityL phase inductanceU aligned inductanceLaO unsaturated aligned phase inductanceLds drain-source internal parasitic inductanceu overall lengthLoh overhang length of windingLratio inductance ratioLstk stack lengthLu unaligned inductanceLuO unsaturated unaligned phase inductance

m number of phasesNp number of turns per poleNpalh number of parallel paths per phaseNr number of rotor polesNs number of stator polesNstrokes/rev number of strokes per revolutionMvp number of parallel wires per turn per poleP10 core losses at 1 Tf lOmax maximum core losses at 1 TPl5 core losses at 1.5 TP ISmax maximum core losses at 1.5 Tfexc mean electrical excitation powerPl power lossesPlosses total power losses

List of Symbols 6

P mech

•Pout

Pshaft

Pjpeak

rRP wiremax

P wiremin

RoRiPiP3T?DS(on)

PphDC

PshPthjc

Sfill^fillinsul

t

toif

tonfP

tr

tststk

TTPAV(in)

PcmaxPexcThigh

TjPlow

ToffTon

TpuRV

Trev

Tshaft

Tstroke

Plot

mean mechanical input power

mean electrical output power

shaft power

peak of transistor leakage power

radius of comer at stator slot bottomphase resistancemaximum wire resistance per length

minimum wire resistance per length minor rotor radius

rotor radiusradius of stator slot bottom stator outside radius

drain-source on-resistance direct-current phase resistance shaft radius thermal resistance slot fill factorslot fill factor with consideration of insulation time

turn-off time

turn-on time

pulse duration rotor pole width

stator pole widthlayer thickness of the lamination stackingtemperaturetorqueaverage input torque

maximum permissible junction temperatureexcitation periodperiod of high leveljunction temperatureperiod of low levelnon-conducting periodconducting periodtorque per unit rotor volumerevolution periodshaft torquestroke periodtotal period

List of Symbols 7

uU

Udis

UusUv

Ugas

Ugs

Umax

C/nUo ut

Ur

Ure f

UrestUrrm

US

V

Vi

We

Wr°ssWet

WFe

Wpe

W*

WcuWexc

Wf

WpeWm

IWi(in)

Wm(inl)

VW(in2)

IWi(out)

Wr

Wiot

X

Jr

%

phase voltage

voltage

discharged voltage

drain-source voltage forward voltage

gassing voltage

gate-source voltage

maximum charged voltage

nominal voltage

output voltage

continuous reverse voltage

reference voltage

rest voltagerepetitive peak reverse voltage

supply voltagevelocityfirst critical speedtotal iron volume

gross electromagnetic volumenet electromagnetic volumevolume of rotor ironvolume of stator ironcoenergycopper weight with insulationexcitation energystored field energytotal iron weightmechanical energytotal mechanical input energymechanical input energy while excitation periodmechanical input energy while output periodmechanical output energyrotor iron weight

total weight

abbreviation for comer area calculation rotor yoke thickness stator yoke thickness

List of Symbols 8

a

Pr

Ardiff

Ps

Ps diff

Ps lot

Ps lotback

8 e en

Vgen

PPmax

Pstart

ee0

0c0D

6q0S

P

PA

pc u

Pe

PFe

PresFe

a

ov

Ts

(0

■^riax

tycAU

constant for calculation of temperature influence on resistivity abbreviation for comer area calculation rotor pole arcabbreviation for rotor slot area calculation stator pole arcabbreviation for stator slot area calculationabbreviation for insulation area calculationabbreviation for insulation area calculationair gap lengthexcitation penaltystroke angleefficiency

generator efficiencynumber of working poles per phasemaximum relative permeability of iron

relative permeability of ironrotor position angleturn-on angleturn-off angledwell angleextinction anglesensor positionresistivityabsolute overlap ratio resistivity of copper effective overlap ratio density of iron resistivity of iron mechanical stress yield point rotor pole pitch

stator pole pitch

angular velocity first critical angular velocity maximum angular velocity phase flux linkagemaximum flux linkage at commutation voltage error

Tiivistelma

Tutkimus esittelee pienjannitteisen molemminpuolin avonapaisen reluktanssigeneraattorin suunnittelua. Kone on tarkoitettu ajoneuvogeneraattoriksi ja toimii siten vaihte- levalla nopeudella. Tyossa kehitetaan koneen konstraktio ja perehdytaan erityisesti kommutoinnin ajoitukseen optimaalisen tuloksen saavuttamiseksi.

Tyossa esitellaan aluksi molemminpuolin avonapaisen reluktanssigeneraattorin toimin- taperiaate ja tarkastellaan konetyyppiin liittyvaa teoriaa. Lisaksi tarkastellaan nykyisin kaytettyjen generaattorityyppien ominaisuuksia ja puutteita.

Tyossa saavutetut tulokset osoittavat, etta molemminpuolin avonapainen reluktanssi- kone voidaan haluttaessa suunnitella erityisesti generaattorikayttoon. Simulointitulos- ten perusteella talla konetyypilla on mahdollista saada nykyisia konetyyppeja suurempi lahtoteho samasta konetilavuudesta ja etenkin hyotysuhdetta voidaan kohottaa merkit- tavasti nykytekniikan tasosta.

10

1 Introduction

The history of low voltage generators for variable speed applications dates back to

the beginning of this century. Since then the technologies used have changed. First

the DC generator was used. Later it was not powerful enough anymore and replaced

by the alternator. The demands are still increasing steadily and the limits of the

alternator technology are almost reached nowadays. Thus innovative technologies

have to be developed. The switched reluctance technology should be able to meet the

new demands.

Switched reluctance motors are examined in the literature for recent years. Nowadays

they have started to compete with inverter-fed induction motors. Whereas switched reluctance generators have been left almost unexplored. Only few machines for

four-quadrant operation have been built [12]. Nevertheless it can be expected that

switched reluctance generators will be as competitive and advantageous than the

motors.

The advantages of the switched reluctance technology are

• high output power,

• high efficiency,

• no extra excitation winding,

• no brushes,

• simple and robust construction,

• and fault tolerance.

As a main field of application the generator is considered to be used for the on-board

power supply in motor vehicles. This requires that the generator is capable of

supplying loads with direct current and has power reserves for charging the battery. A

constant output voltage over the whole speed range is demanded. It should be as

maintenance-free as possible and tolerate external loading, like vibrations,

temperature changes, dirt and damp. Low weight, compact dimensions, low noise

and long life are essential. Most important is that it is easy and inexpensive to

produce in large quantities within mass-production. The task of this work is to design

a generator which fulfils these requirements by using the advantages of the switched

reluctance technology.

The work begins with an overview of the existing DC generator and alternator

technologies. Their weak spots and on the other hand the supposed improvements

Chapter 1: Introduction 11

and advantages of the switched reluctance technology are pointed out. Lots of effort

has been put on working out the principle and theory of switched reluctance

generators in general. All characteristics of the construction are presented and the

working principle is described in detail. The usable converter topologies for the

commutation are summarised. The dynamic operation and the control system are

other contents. Based on this important knowledge the design of the generator is

made. It is distinguished in the construction and commutation unit design. The

control strategy and the sensing for the realisation of the control are also given.

Simulation results are obtained and evaluated for input and output characteristics,

efficiency, phase current and losses. Finally, a conclusion and prospects are given.

12

2 Generators for Variable Speed Applications

The major field of application for generators with variable speed and low output

power is the electricity generation in motor vehicles. The electric systems of motor

vehicles are working on DC current and the voltage is 12 V, or for bigger vehicles

24 V. All circuits contain a battery for energy storage, a generator for energy

conversion and several loads with different demands on power and time

characteristic.

The biggest load is the starting motor. It needs from 800 W to 3,000 W, but only for

a very short period of time. The time characteristic of the loads can be categorised in

continuous, prolonged and brief loads. Continuous loads are ignition, electric fuel

pump and electric gasoline injection. The car radio, different lamps and the heater

form the category of prolonged loads. Brief loads like electric window lifter, electric

radiator fan, rear window heating etc. form the largest category. Table 2.1 shows the

power requirement of the mentioned loads.

Table 2.1: Power requirement of the loads in motor vehicles

Starting motor 800... 3,000 WIgnition 20 WFuel pump 50... 70 WGasoline injection 70... 100 WCar radio 10... 15 WLamps (altogether) approx. 200 WHeater 20... 60 WWindow lifter 150 WRadiator fan 200 WRear window heating 120 W

The task of the generator is to provide electric power for supplying the loads and for

storage in battery. The first generator type used in variable speed applications was the

DC generator. Later the DC generator was replaced by the alternator. Both generator

types, the rectification and the control are described in the following. The weak spots

of these generator types and the improvements and advantages of switched reluctance

technology are pointed out afterwards. For a further overview on the electrical part of

car technology see references [14],[17],[44],[45].

Chapter 2: Generators for Variable Speed Applications 13

2.1 DC Generator

Figure 2.1 shows the construction of a DC generator. The stationary stator frame (1)

has pole shoes (7) and carries the excitation winding (8). The rotor core (2) is made

of laminated iron and is fitted on the shaft. In the rotor core the armature winding is

embedded. Because this winding is on the rotating part, brushes (9) are needed. They

are made of carbon and are put on the commutator (4). Also the electric terminal (3),

the commutator end shield (5) and the drive end shield (6) are shown in the figure.

2 3 5

The operating principle works the way that AC voltage is induced in the armature

winding due to the magnetic field variations during rotation. It is rectified by the

commutator and the resulting DC current is picked off at the commutator segments

by the brushes. DC generators for these applications are shunt-wound machines. The

armature winding and the excitation winding are connected in parallel. This has the

effect that the necessary excitation current is produced by the machine itself. It is

tapped from the armature current. This is the principle of self-excitation.

A voltage regulator is required for all DC generators to keep the generator voltage in

a tolerance range over the entire speed range irrespective of the load. The regulation


principle consists of regulating the excitation current as a function of the generated

voltage. The excitation current is regulated by a regulating contact which interrupts

the excitation current when a voltage tolerance range is exceeded and is contacted

again when a minimum set value is reached. This voltage regulator protects the

electric loads against overvoltage and prevents the battery from being overcharged. It

also takes the electro-chemical properties of the battery into account, like the

temperature-depending charging voltage.

Besides a voltage regulator DC generators need an extra current regulator which

protects the machine against overloading. To protect the battery from discharging at

low speeds an independent electromagnetic relay is also required to interrupt the

connection between the generator and the battery.

The speed versus generator current curve (see Figure 2.2) shows the characteristic

behaviour of the generator in interaction with the regulation. At speeds close to the

per unit idle speed of the internal combustion engine of motor vehicles, in many

cases above it, the charging voltage is reached and the generator is connected to the

battery through the automatic cut-out relay. At this point the generator starts to deliver power, though higher speed is needed until the maximum generator current is

reached. When the maximum current is reached it is limited by the current regulator

and kept constant. The maximum rotational speed is limited by the commutation

because of the danger of overheating and heavy wear on the carbon brushes.

Engine idle speed range

Per unit speed

Figure 2.2: Maximum output current characteristic curve of a DC generator


2.2 Alternator

The most common alternator type is the claw-pole alternator currently installed

almost in every motor vehicle. Figure 2.3 shows the construction of a claw-pole

alternator. In the laminated stator core (6) the three-phase stator winding is embedded

in slots. The stator is clamped between the slip-ring end shield (1) and the drive end

shield (10). The rotor (7) carries the poles and the DC excitation winding. This

winding consists of a single circular coil enclosed by the claw-poles. To supply the

excitation current, carbon brushes are put on slip rings which are mounted on the

shaft. Also the fan (8) and the pulley (9) are mounted on the shaft.

Figure 2.3: Construction of an alternator [44]

Alternators need an electrical rectification because during rotation AC voltage is

induced in the three-phase stator winding. This is done by a bridge circuit of six

power diodes (3). For the conversion of the three-phase current to excitation current

three exciter diodes (4) are needed. All these diodes are fixed on a diode plate (2)

which fulfils the function of a heat sink at the same time.

The output voltage of alternators has to be regulated. It must be kept in a tolerance

range over the whole speed range. Unlike DC generators alternators need only a

voltage regulator which works the same way than the voltage regulators used for DC


generators. The excitation current is diminished, when the voltage tolerance range is

exceeded and increased again after a minimum set value is reached. The regulator (5)

is connected to the brush holders and, depending on the type, sometimes mounted

straight on them like in figure 2.3.

Generally different types of regulators exist but the latest invented hybrid regulator is

mostly used nowadays. Other regulator types are the conventional electromagnetic

vibrating-type and the transistor regulator. The advantages of the hybrid regulator are

compact construction, high reliability, small amount of components and connections.

The main component of the hybrid regulator is an integrated circuit that combines all

control functions. Basically the hybrid regulator is a further development of the

transistor regulator.

The invention of the transistor regulator was a large progress in regulator technology

because it has no mechanical contacts and moving parts anymore, thus it is

maintenance free. It is also a lot smaller and lighter than the conventional

electromagnetic vibrating-type regulator and insensitive to vibrations. These

advantages allow the transistor regulator to be mounted directly on the alternator.

Other positive features are short switching times, narrow regulation tolerances,

allowance of high switching currents, spark-free switching and electronic

temperature compensation. The conventional electromagnetic vibrating-type

regulator is not used anymore because of the obvious advantages of the new regulator

types.

Figure 2.4 shows the total connection diagram for an alternator with generation,

rectification, pre-excitation, excitation and regulation. The interaction of the three

generator circuits for pre-excitation, excitation and generation can be seen. The

pre-excitation starts when the ignition is switched on and the excitation current

supplied by the battery flows through the generator warning lamp to the excitation

winding of the rotor. From there it flows through the regulator to ground. The

pre-excitation is necessary because at low speeds the remanence in the iron core is

not sufficient to build up a magnetic field just by a self-excitation strong enough to

generate the desired minimum voltage for the excitation circuit. At least the

generated voltage has to be higher than the voltage drop of the in series connected

negative rectifier diode and excitation diode.

When the desired minimum voltage is reached, the excitation circuit starts to work

and the excitation is taken straight from the generated current. No external power

source is needed after that. The alternator excites itself. At the same time the


generator warning lamp goes out and signals that current is delivered by the

generator. For the excitation some current of the phase windings is rectified by the

excitation diodes and supplied to the excitation winding. Through the regulator and

the negative rectifier diodes the path goes back to the phase windings. The excitation

circuit has the task to produce the magnetic field which is necessary to induce the

output voltage in the three-phase stator winding.

Generator warning lamp

Ignitionswitch

Positiverectifierdiodes

Exciterdiodes'

Battery

NegativerectifierdiodesExcitation winding

Regulator

Figure 2.4: Alternator connection diagram with generation, rectification,

pre-excitation, excitation and regulation

The generation circuit supplies the current for charging of the battery and for

coincidence of the loads. Thus it is divided into load and battery current. Before it

can be delivered, the AC current of the three-phase stator winding has to be rectified.

This is done by the bridge circuit which consists of the positive and negative rectifier

diodes.

A schematic diagram of the speed versus generator current curve is shown in figure

2.5. The figure shows the characteristic behaviour of alternators in interaction with

the regulation. The schematic diagram has been verified by measurements that have

been made within this work (see Appendix A and especially Figure A.4). In contrast


to DC generators alternators already deliver an output current at the per unit idle

speed of the internal combustion engine of motor vehicles. This has the advantage

that the battery can be kept in a good state of charge even in winter and while driving

in town with frequent waiting times. The output current at idle speed reaches

approximately one third of the absolute maximum output current.

Engine idlespeedrange

Per unit speed

Figure 2.5: Maximum output current characteristic curve of an alternator

The maximum output current increases rapidly with an increase of the speed at low

speeds. At high speeds it increases slightly with an increase of speed. It is not kept

constant like for DC generators because alternators are not equipped with current

regulation. Compared with DC generators the reached maximum output current is

always higher. The maximum rotational speed is limited by centrifugal force and

appearing vibrations.

2.3 Weak Spots of Existing Technology

As already mentioned, DC generators were used at first for low output power and

variable speed applications but nowadays they are almost not used anymore. The

main reason for this can be seen from the maximum output current characteristic

curve which was already shown in figure 2.2. It can be seen that the speed range is

severely restricted to a range not broad enough for modem variable speed

applications. Especially for motor vehicles the output characteristic does not meet the

demands because no energy is supplied at the per unit idle speed. This will cause a

discharge of the battery while driving in town because of the high average proportion

of waiting times in town driving. The development of the average proportion of


waiting times in town driving from 1950 to 1990 is illustrated in figure 2.6 and it can

be observed that the situation has not become better.

Figure 2.6: Development of average proportion of waiting times in town driving from 1950 to 1990

Another disadvantage of DC generators is the need of maintenance due to the wear of

the carbon commutator brushes. A high output power can be reached only with large

dimensions and high weight. The advantage and the reason for former use is the

simple, mechanical rectification by the commutator. Since semiconductor

components are common and inexpensive, the mechanical rectification is not needed

or advantageous anymore. Rectification can be better and easier made by bridge

circuits of power diodes.

Nowadays the alternator is used for low output power and variable speed

applications. It has some advantages compared with DC generators. Especially the

maximum output current characteristic curve (already shown in figure 2.5) is more suitable. The alternator supplies energy over a broader speed range and even at the

per unit idle speed of the combustion engine of motor vehicles. Also the output

power is higher and that is important because the demand of output power has increased. Figure 2.7 shows the rapid increase of the required generator output for

motor vehicles since 1950.

Another advantage of alternators is the electronic rectification of the three-phase

current with diodes, because it makes the mechanical rectification by the commutator

superfluous. This, together with the fact that the rotor winding is only for the

excitation, decreases the wear of the brushes because the coal of the brushes will be


rubbed off more slowly and because the excitation current is a lot smaller than the

output current. This guarantees a longer service life. Mostly the brushes or the

bearings wear out first after around 100,000 km. The diodes perform also an

automatic relay which cuts the alternator from the battery if the alternator voltage

drops below the battery voltage. Alternators are also lighter than DC generators and

they can better tolerate external influences like high temperatures, damp, dirt and

vibrations. The disadvantage of alternators is their smaller efficiency.

1200 T

1000 --

800 --

Figure 2.7: Development of generator output from 1950 to 1990

As just pointed out alternators have some advantages compared with DC generators,

but still they have their weak spots. One main disadvantage is that they provide only

approximately one third of the maximum output power at idle speed (see Chapter

2.2). This can cause the discharging of the battery under unfavourable conditions, for

example in winter time when many loads are switched on and long waiting times

occur at the same time.

The other main disadvantage of alternators is the low efficiency. Especially at high

speeds the efficiency decreases noticeably. This can be seen from the measurement

results documented in the Appendix A. Figure A.5 shows the decrease of efficiency

with increasing speed. In the same picture it can also be seen that the efficiency

decreases with a decrease of the load. Alternators reach a reasonable efficiency only

at nominal output power and not too high speed. The low alternator efficiency reacts,

for example negatively on the fuel consumption of motor vehicles, as it is

investigated in reference [25].


The constantly increasing power demand and the changed traffic conditions led to

such requirements that the DC generator was not capable of fulfilling them anymore.

The alternator solved the problems that cropped up with the new demands.

Nowadays the development is going still in the direction that higher and higher

electric power is demanded. It can be noticed that the alternators are almost reaching

their output power limits and new technology or different system suppositions, like a

higher voltage level, are necessary to fulfil the requirements of modem car

technology. Switched reluctance generators can exceed the alternator limits, and they

have also other advantages.

2.4 Supposed Improvements and Advantages of Switched

Reluctance Technology

Comparisons of switched reluctance machines with other machine types have been

made and they are reported in literature [5],[15],[28],[35],[47]. Most of them are

concentrating on motor applications and are quite general, but some of them also

point out that the advantages of switched reluctance machines can be recognised in

all four quadrants of operation (see Figure 3.1).

The first main advantage of switched reluctance generators is the high output power.

A higher output power compared with other machine types is reached because more

copper can be fitted in the large slot area. Over a broad speed range and especially at

low speeds the output power is higher than for alternators. Only at very high speeds it

is lower. The maximum output power is supplied over a broad range at medium

speeds.

Figure 2.8 shows a schematic comparison of the maximum output current of the three

generator types versus the per unit speed range of the internal combustion engine of a

motor vehicle. It can be seen in the figure that compared with the alternator the

maximum output current of switched reluctance generators is around three times

higher at idle speed and still higher until the motor overspeed range is reached. In the

overspeed range it is smaller, but this speed range is rarely used for driving. The

output current behaviour is almost equal to the output power behaviour because of

the nearly constant average voltage.

The other main benefit of switched reluctance generators is the high efficiency.

Contrarily to alternators, it is almost constant over the whole speed range and nearly


independent from the load. This will react positively on the fuel consumption of

motor vehicles, as investigated in reference [25].

Engine idle Switched reluctance Engine overspeed range generator speed range

Alternator

DC generator

Per unit speed

Figure 2.8: Maximum output current characteristic curve for the different

generator types

The high efficiency is reached because the losses are low and this leads to a small

temperature rise [22]. Because of this the additional fan losses are low, too. The fan

is needed for the cooling of the heat produced by the other losses and can be less

powerful if they are smaller. The fan losses are also positively effected by the lower

absolute speed of switched reluctance generators compared with alternators, because

the fan losses increase intensely with the speed. As pointed out in chapter 2.3 and

verified in Appendix A, the fan losses are the major part of the losses of alternators,

especially at high speeds. Thus the overall efficiency of switched reluctance

generators is much higher than for alternators.

Another advantage is that no extra excitation winding is needed. This saves an

additional excitation circuit and the necessity of slip rings and brushes. The simple

construction which enables inexpensive mass production is also a positive aspect.

The construction is compact as well, so the size is as small as the size of alternators

in the same range.

The fault tolerance of switched reluctance machines together with the commutation

should also be mentioned. The reason for this is the lack of excitation and the

independence of the phases. An open circuit in a phase circuit does not produce any

generated voltage and a short circuit condition does not produce any fault current,

because there is no field winding or permanent magnet for excitation. If one phase is


faulted, the healthy ones can operate almost unaffected because of the independence

of the phases. Commutation units of the form of the classic converter (see chapter

3.3.1) have no shoot-through path and thus the DC supply can be shorted only if the

phase winding itself is short circuited. Additional information on the behaviour of

switched reluctance machines under internal and external fault conditions is given in

the references [1],[2],[26].

The disadvantages of switched reluctance generators are the high level of current

ripple and the control dependent on rotor position, which requires a rotor position

feedback. They are also known for producing higher acoustic noise [51]. The main

advantages of high output power and high efficiency compensate these

disadvantages.

24

3 Principle and Theory of Switched Reluctance Generators

Switched reluctance machines are widely used for motor applications and because of

this most of the published theory is about motoring operation. Only a bit of

information on switched reluctance generators can be extracted from the literature.

On the other hand motoring and generating are operating states of one machine. This

is the reason why motor theory and generator theory are connected. Figure 3.1

illustrates the four quadrant operation of a machine. The theory mentioned in this

chapter refers to literature, if mentioned, or is verified by investigations with the

simulation tool PC-SRD [30],[31]. This chapter gives an overview of the switched

reluctance machine theory with special attention to the characteristics of generating

operation.

Forward

r<ov> 0

Generating

T> 0 v > 0

Motoring

Motoring0

GeneratingT< 0 T> 0v<0 v< 0

Reversei

Figure 3.1: Speed over torque diagram for four quadrant machine operation

3.1 Construction

The main construction characteristic of switched reluctance machines is that they

have salient stator and rotor poles which differ in number. Basically the motion can

be rotary or linear and the rotor interior or exterior, but interior rotors with rotary

motion are most common. The way of motion and the arrangement of the rotor

determine the cross section layout. Only the most commonly used construction is

described here. Another basic characteristic is that only the stator poles are equipped

with windings and the rotor carries no windings. Usually the windings of two

opposite poles form one phase winding. Both the rotor and the stator are made of

Chapter 3: Principle and Theory of Switched Reluctance Generators 25

laminated iron. Figure 3.2 shows the cross section of a three phase 6/4-switched

reluctance machine to give a first impression of the construction.

Figure 3.2: Cross section of a three phase 6/4-switched reluctance machine

3.1.1 Basic Characteristics

Switched reluctance machines can be distinguished by the number of phases m, stator

Nt and rotor poles Nt. Different combinations of these main design criteria enable afunctional machine. It must be mentioned that the one and two phase machines need

assistance for starting if they are used for motor applications. Table 3.1 shows

different possible phase and pole combinations most commonly used in practice [27].

The combinations supported by the PC-SRD can be seen in reference [30].

All combinations included in the table are so called regular designs. A regular design

means that the stator and rotor poles are symmetric about their centre lines and

equally spaced around the rotor and stator respectively. Most of the practical

switched reluctance machine designs are included in the table, but irregular machines

are existing, too, as it can be seen in reference [27]. This reference also gives an

overview of different motor designs. The stroke angle e = 360°/(mA/r) and the number

of strokes per revolution Mtrokes/rev = rnNr can be calculated from the number of

phases and rotor poles. These characteristic values are also included in the table.


Table 3.1: Phase and pole combinations

Number of Phasesm

Number of Stator Poles

Ns

Number of Rotor Poles Nt

Number of Working Poles

per Phase p

Stroke Angle£

Strokes per RevolutionN .strokes/rev

1 2 2 1 180.00 22 4 2 1 90.00 42 8 4 2 45.00 83 6 2 1 60.00 63 6 4 1 30.00 123 12 8 2 15.00 243 18 12 3 10.00 363 24 16 4 7.50 484 8 6 1 15.00 244 16 12 2 7.50 485 10 4 1 18.00 205 10 6 1 12.00 305 10 8 1 9.00 406 12 10 1 6.00 606 24 20 2 3.00 1206 12 14 1 4.29 847 14 10 1 5.14 707 14 12 1 4.29 84

Other characteristics of a switched reluctance machine are the absolute and effective

torque zones and the absolute and effective overlap ratios. The absolute torque zone

is the angle through which one phase can produce a non-zero torque in motoring

operation. For a regular motor it is maximally 180°/Nt. In generating operation this is

the maximum zone where a positive output current is available. In this operating

mode a better name would be absolute current zone. The effective value of this

dimension is comparable to the smaller pole arc of the overlapping rotor and stator

poles and it gives the angle where useful torque or respectively useful output current

can be produced.

The absolute overlap ratio is defined as the ratio of the absolute torque zone to the

stroke angle. Its value is equal to mil. For a regular motor a value of at least one is

necessary so that torque can be produced at all rotor positions, but a value of one is

not sufficient because the nominal torque can never be provided throughout the

whole absolute torque zone by only one phase. For a generator the same feature can

be seen for the output current.

The effective overlap ratio is defined by the ratio of the effective torque zone and

the stroke angle respectively. It is always smaller than the value of the absolute

overlap ratio. The ratio is approximately equal to the stator pole arc divided by the


stroke angle if the stator pole arc is smaller than the rotor pole arc for a regular

machine, which is normal in common conditions. A value of at least one is necessary

to get a starting torque at every rotor position but not sufficient for avoiding torque

ripple. In generating operation there is no need for a starting torque, because it is

given by the driving machine. For a steady output current a value bigger than one of

the effective overlap ratio is necessary.

3.1.2 Envelope and Internal Dimensions

The internal and envelope dimensions mainly determine the machine performance.

The envelope dimensions are the stator lamination diameter A and the overall length

Le which is measured over the end turn overhangs of the winding. These dimensions

define the gross electromagnetic volume Vgross- The net electromagnetic volume Vnet

is defined by the stack length Lstk and the stator lamination diameter. The stack length

is an inner dimension and the overall length can be calculated from it by

Le=Lstk+ 2 L0h with L0h as the overhang length of the winding. The overhang length

is approximately equal to the stator pole width ts which is introduced later in this

chapter. All these and some more inner dimensions (stator slot bottom diameter Ab,

shaft diameter Ah, minor rotor diameter Am, rotor diameter A and air gap length 8) are illustrated in figure 3.3. The figure shows the longitudinal cross section of a

machine and the main parts of the construction are named.

Some ratios of the above mentioned dimensions can be used for machine

characterisation. One is the standard or split ratio which is defined by the rotor

diameter divided by the stator diameter. Dc/Ds can vary between 0.4 and 0.7 but for

most designs it is between 0.5 and 0.55 [27] and tends to be larger with a higher

number of poles. According to the reference [10] a suitable value should be between

0.57 and 0.63. Another characterising ratio is the length per diameter ratio given' exactly by the stack length and the rotor diameter. A typical value for Atk/A is 1.

From the net electromagnetic rotor volume and the torque T the torque per unit rotor

volume rpURv can be estimated as

^puRV —f D“4k

(3.1)

According to table 3.2 the Tpurv value enables a rough categorisation of the machine

and shows the extent of machine utilisation which is mostly limited by the used


cooling method. Usually this value is used as a starting point for the first rough

estimation of a new machine design.

Stator

Stator pole

Rotor

Rotor pole

End turn overhang

Winding

Stator yoke

Figure 3.3: Longitudinal machine cross section (rotor in aligned position)

Other inner dimensions can be seen from the cross-section of a machine. Figure 3.4

shows the cross section of a three phase 6/4-machine, including the inner dimensions

shaft radius Rsh, minor rotor radius Rq, rotor radius Ru radius of stator slot bottom R2. stator outside radius Rz, rotor pole arc /Jr, stator pole arc /5S, rotor pole width /, and

stator pole width ts.

Table 3.2: Machine categorisation from the torque per unit rotor volume [ 27 j

Machine category T durv in kNm/m3Small totally enclosed machines 2.5-7Integral-kW industrial machines 7-30High-performance servomotors 15-50Aerospace machines 30-75Large liquid-cooled machines 100 - 250

All important information of a machine construction is given with the mentioned

basic dimensions and all other necessary values can be calculated from them, like the rotor tooth width


tt=2Rx sin^L

the stator tooth width

K -2(^i+<$)sin^-^

the rotor pole pitch

KTr = 2ft, sin

and the stator pole pitch

ts = 2 (ft, +5 )sin

Other important derivative values are the stator slot area

Aio*-[%ARi+sT]{y-Y

+ [ft, - (R, + 5)] ^jl - sin' Psdiff D Pstiff~ ft; COS

(3.2)

(3.3)

(3.4)

(3.5)

(3.6)

with

2


where the winding is embedded, the stator iron volume

v,„ = {* [*? - ft+S f ] ■- WA-} (3.7)

and the rotor iron volume

(3.8)

with Asiotr as the rotor slot area which is calculated in the same way than the stator

slot area, but the values R2, (Ri+S), Ns and j3s have to be replaced by Ru Ro, Nr and jSr

and the within used abbreviation f3sm then changed to /Wf respectively.

Also some derivative dimensions can be defined. Mainly the rotor slot depth

dT = Rx-Rq, the stator slot depth ds = R2-(R\+S), the rotor yoke thickness yT = Ro-Rsh and the stator yoke thickness ys = R3-R2 are important to mention and they are

especially used during the designing process because of their better clarity in

connection to the electric and magnetic phenomena occurring in a machine.

3.1.3 Pole Geometry

Figure 3.4 has already shown the basic pole geometry, but variations especially for

the stator poles are common and sometimes advantageous depending on the

intention. Figure 3.5 shows some different possible modifications of the stator pole

geometry. Modifications of the rotor pole geometry are not so common and, because

of that, not mentioned here.

One very useful and advantageous modification of the standard pole geometry

(Figure 3.5 (a)) is shown in figure 3.5 (b). The radius at the comers of the slot bottom

increases the stiffness of the poles against lateral deflection and also stabilises the

stator. This has a positive effect on acoustic noise reduction, but on the other hand

the usable slot area for embedding of the winding is decreased. The comer area taken

by the radius r is

A,'comercomerasa.-------COS2 2 1 (3.9)

with

and


^corner = 2 arcscomer (3.10)

The stator slot area is recalculated Asiots(new) = Asi0ts(old) - 2 Acomer with Asi0ts(old)

calculated by equation (3.6). The loss of usable slot area taken away by the radius is

in practice not so significant because the round wires are not fitting exactly into the

comer, so the area is partly unusable for the winding anyway.

(a) (C)(b) (d)

Figure 3.5: Details of stator pole geometry

The slight taper in figure 3.5 (c) concentrates the saturation near the air gap and

decreases the magnetic voltage drop over the pole. On the other hand, the slot area

will be decreased and the required quantity of iron and thus the machine weight is

increased.

Pole overhangs (Figure 3.5 (d)) have the advantage that the pole width can be

extended almost without reducing the slot area. The negative consequence is that

ready wound coils can only be used if the coil is made wide enough and pressed

against the poles after it has been slipped over the pole overhangs. This method has

the disadvantage of an extra end turn overhang and can only be used if the slot fill

factor is small. Anyway, the production is more complicated and thus its costs are

increased.

Basically a pole geometry with multiple teeth is possible but they are not very

common. In reference [27] it is mentioned that their benefits are liable to be restricted


to low speeds and they have the same disadvantage concerning the winding than a

pole geometry with overhangs as well.

3.1.4 Windings

The windings of switched reluctance machines are simpler than those of other machine types and an extra winding for excitation is not needed. Only one coil is

wound on each stator pole and it is not necessary to make use of special winding

patterns. Normally the windings of opposite poles comprise to one phase. They can

be connected in series or in parallel.

Basically the winding can be defined by the slot fill factor Sen, the number of turns

per pole Np and the number of parallel paths per phase /Vpath. The theoretical

maximum achievable slot fill factor is restricted to itlA because round wires can not

be joined to each other without leaving some empty space in-between. In practice the

theoretical slot fill factor can not be reached because of the area losses by the

insulation, the distance that has to be kept from the air gap and the geometrical

circumstances. A realistic maximum slot fill factor for an insulated slot area is

between 0.6 and 0.7.

The slot fill factor also determines if pre-wound windings can be used. In that case

the slot fill factor should be smaller than around 0.4. This value ensures that the

ready wound winding can be slipped over the poles. It has to be also permissible by

the pole geometry (see chapter 3.1.3).

3.2 Working Principle

The working principle of switched reluctance machines is based on the change of the

magnetic reluctance depending on the rotor position. The rotor tries to adjust the

position with the smallest magnetic reluctance and produces a torque. For a generator

with a torque given by a driving machine, a voltage which will cause a current will be

induced in the stator winding. Because the rotor poles are without a winding, the

excitation and the output current must be taken from the same winding. Thus the

current of each phase has to be switched depending on the rotor position.


3.2.1 Rotor Position Dependency

As already mentioned, the working principle is based on the rotor position. To

describe this dependency it is easier and enough to concentrate just on the positions

according to one phase. Then two positions and two zones can be distinguished. The

positions are the aligned and the unaligned position.

The rotor is in the aligned position according to one phase when one pair of the rotor

poles is exactly aligned with the stator poles on which the winding of this phase is

wound. Figure 3.6 illustrates the aligned position on the phase in the horizontal axis

for a 6/4-switched reluctance machine.

Figure 3.6: 6/4-switched reluctance machine in the aligned position on the phasewhich is marked

In this position the magnetic reluctance of the flux path is lowest because most of the

reluctance is in the air gap and the gap is smallest in this position. Because the

reluctance is at its minimum, the phase inductance is at its maximum. The reluctance

in the iron is lower than in the air gap but can not be neglected, because the long path

through the iron also absorbs a significant magneto motive force. The iron is also

susceptible to saturation, especially in the stator and rotor yokes. Because of these

reasons the aligned inductance will be reduced.

The aligned position is a stable position. A current in this phase can not produce a

torque because the magnetic reluctance is already at its minimum. If the rotor is

displaced to either side, a restoring torque tends to return the rotor towards the

position of minimum reluctance - the aligned position.


The rotor is in the unaligned position according to one phase when the interpolar axis

of the rotor is aligned with the stator poles on which the winding of this phase is

wound. Figure 3.7 illustrates the unaligned position on the horizontal axis for the

same 6/4-switched reluctance machine.

Figure 3.7: 6/4-switched reluctance machine in the unaligned position on the

phase which is marked

In this position the magnetic reluctance is at its highest because of the large air gap.

Because the reluctance is at its maximum, the phase inductance is at its minimum. The iron is unreceptive to saturation in this position because the current when

saturation begins has to be much higher than in the aligned position. This is because

the leakage flux is relatively much greater and the winding is laid out to avoid high

saturation even in the aligned position.

If the phase is excited, the unaligned position is an unstable equilibrium. There is no

torque in this position, but if the rotor is displaced to either side, a torque appears that

tends to displace the rotor further until it is aligned with the next aligned position.

The intermediate positions can be summarised to two zones. The direction of forward

motion is always set counterclockwise. Then the intermediate positions of the first

zone are those that are taken while the rotor turns from the unaligned towards the

aligned position. Respectively, when the rotor turns from the aligned towards the

following unaligned position, the intermediate positions of the second zone are taken.

Figure 3.8 shows these two zones for the same 6/4-switched reluctance machine.


In the first zone the magnetic reluctance decreases towards the aligned position, thus

the inductance increases. Especially with the start of pole overlap the inductance

changes rapidly because of the smaller air gap. Before overlap there is only a slight

increase. In the second zone the inductance shows a contrary behaviour. It decreases

with further rotation. With the start of pole overlap also the iron starts to be

susceptible to saturation. Before the pole overlap there is only the possibility of local

saturation of the pole comers.

direction ofrotation

unaligned

Zone 2

aligned

Zone 1

unaligned

Figure 3.8: 6/4-switched reluctance machine with the two zones of intermediate

rotor positions

If the phase is excited in the first zone, the appearing torque assists the

counterclockwise rotation towards the aligned position. Thus this zone is relevant forthe motoring operation. In the second zone the appearing torque counteracts against the counterclockwise rotation and a driving torque is necessary to enable the

movement towards the unaligned position. Thus this zone is relevant for generating

operation.

The influence of the different rotor positions can be also described by the

magnetisation and inductance curves. These figures give a closer survey and form the

basis for the further mathematical description. Figure 3.9 shows a set of

magnetisation curves. The flux linkage y/ versus the current i is presented for one

phase.


This set of magnetisation curves is for the rotor in several positions between the

unaligned and aligned positions. The aligned curve is the highest and the unaligned

curve is the lowest. Before the start of pole overlap the curves do not vary a lot and

rise almost linearly, but with the begin of overlap they rise sharply and their shape

gets closer to that of the aligned curve. Just before alignment they change less again.

V

i

Figure 3.9: Set of magnetisation curves for one phase [27]

Figure 3.10 shows the shape of the phase inductance curves versus the rotor positions

between the two zones for different phase currents. The curves are periodic with the

rotor pole pitch which is equal to the width of the two zones, thus only this part of

the curves is included in the figure. As already mentioned above, the inductance L is

a function of the rotor position angle G. From the figure it can be seen that the

inductance is not only a function of the rotor position but a function of the rotor

position and the phase current as well. The phase current dependency is caused by the

influence of saturation. With an increase of the current the inductance decreases.

The most used inductances in switched reluctance machine theory are the unsaturated

unaligned inductance Lu0 and the unsaturated aligned inductance Lao which are

included in the figure. For a good electrical behaviour and a high output power of the

generator the unaligned inductance should be as low as possible and the unsaturated

aligned inductance as high as possible. Typical motor designs have a ratio Lao /Luo

around 10 [27]. Basically, the higher this ratio is the more output power can be

delivered by a generator. The reason for this will be clear after the energy conversion

diagram is introduced in chapter 3.2.4.


Zone 1 Zone 2

increasing/current

unaligned aligned unaligned

Figure 3.10: Inductance versus rotor position angle with the effect of saturation as

the current increases

3.2.2 Torque and Currents

When current flows in one phase, the appearing torque tends to move the rotor into a

position where the magnetic reluctance will be minimised, which is equal to the maximisation of the inductance. Thus the rotor movement is always in the direction

of increasing inductance. The direction of the phase current is insignificant for this

behaviour. Therefore a positive torque can be produced only in zone 1 and the

periodic equivalents in counterclockwise rotation. Respectively a negative torque will

be produced in zone 2. For generating operation only this negative torque of zone 2 is

useful. Because of this the phase current has to be switched during a revolution

according to the operating state of the machine. Otherwise the efficiency will be

decreased or, in the worst case, the machine will not operate. How this commutation

of the phase current can be realised is the topic of chapter 3.3.

The total torque is assembled by the instantaneous torques of each phase. More

phases are needed to produce an unidirectional torque at all rotor position. The torque

waveform gets more constant with an increase of the number of phases. For switched

reluctance motors torque ripple is usual and a lot of articles have been published

about the research and progress on torque ripple reduction, like [48] and [50]. The

negative torque used for generating has a ripple, too, and causes a rippled output

current. Generators with a low number of phases do not usually produce a steady

current. The current is pulsating instead and sometimes the peak of the pulse can be

very high and sharp. These peaks have to be limited by a careful construction design


and by a suitable control strategy (see chapter 3.5). Otherwise the commutation

devices might be destroyed.

Figure 3.11 shows the output current waveform for a 6/4-switched reluctance

generator with 12 V supply voltage and 1.5 kW output power at a speed of 3,000 rpm

computed by the simulation tool PC-SRD. It can be seen that the positive current

peak is quite sharp. This is because the excitation is taken straight from the output current in the beginning and only later from the supply. The negative part of the

waveform is wider and the peak is a lot higher, so a high output is reached.

PC Link curr» r>~A x 1.0*2

Peter position x 1.0*1

Figure 3.11: DC link current versus rotor position for a 6/4-switched reluctance

generator with 12 V supply voltage and 1.5 kW output power at a

speed of 3,000 rpm

The necessary input torque for generation of the DC link current in figure 3.11 is

shown in figure 3.12. This torque has to be provided by the driving machine. From

the figure it can be seen that also the input torque has very high peaks like the

generated output current.

Torque versus rotor positionie < Nm > x l.Oel

12.00 18.00-0.25--0.50--0.75--1.00-

-1.25--1.50-

Rotor position < deq ) x l.Oel

Figure 3.12: Torque versus rotor position for a 6/4-switched reluctance generator

with 12 V supply voltage and 1.5 kW output power at 3,000 rpm


3.2.3 Mathematical Description

The mathematical description of the switched reluctance machine is based on the

voltage equation and the energy balance. The equations are derived for an one-phase

model with neglecting skin and hysteresis effects and magnetic coupling of the

phases. The voltage equation of one phase is

u = Ri+M$. (3.11)at

with the phase resistance R, the phase current i and the phase flux linkage iff. The flux

linkage depends on the phase current and rotor position angle d which are changing

with time. The power balance

ui = Ri2 + i dif/ di . diff dd■+i (3.12)

di dt dd dtis got by multiplying the voltage equation with the phase current. The used energy

ui dt — R ?dt+i ^ di+i ^ dd — R i2dt+dWt + dWm (3.13)

consists of the change in mechanical work dWm,. stored field energy dW{ and

resistance losses. The magnetical energy depends on the current and the rotor

position and its change is given by

dWf=^di+^-dd.f di dd

Thus the change of the mechanical energy is

(3.14)

(3.15)

The energy stored in the magnetic field at a certain operative condition can be calculated by

W(=ji diff =iy/-j\]/di, (3.16)

(3.17)

and its partial derivation regarding the current is

di di l di di

Equation (3.15) has given the change of mechanical energy and it can be written

easier by using equation (3.17). It equals then

(3.18)

The torque equals the derivation of the mechanical energy regarding the rotor

position and it is


dWm ,d y dW{ do de de

(3.19)

This equation can be simplified more by replacing the stored field energy with the

coenergy defined by/

W‘=\\}fdi. (3.20)o

The graphic definition of the coenergy is shown by figure 3.13. Also the graphic

interpretation of the stored field energy is given in the figure. The knowledge of the

different energy types is needed for understanding the energy conversion principle

(Chapter 3.2.4).

The flux linkage for the coenergy calculation is

y/ = j(Us-Ri)dt (3.21)

with Us as the supply voltage.

From the figure can be seen straight that the sum of the stored field energy and

coenergy is

Wf+W*=z>. (3.22)

The derivation of the coenergy regarding the rotor position is

dW* = . dyr dW{ dQ dG d6

(3.23)

By replacing this result in equation (3.19) the torque produced by one phase can be

calculated from


rM)=Mi=const

(3.24)

The equations (3.20), (3.21) and (3.24) are the general expressions used for switched

reluctance machine calculations. For the realisation of machine designs these

equations have to be solved, but an analytical solution can be found only if the effects

of saturation are neglected. With neglecting the saturation the magnetisation curves

become linear and the instantaneous torque is then

T 1 .2 dL2 dO

(3.25)

For a good machine design the effect of saturation can not be neglected and the

equations (3.20), (3.21) and (3.24) have to be solved. This requires computer-based

simulation because the torque is a function of phase current and rotor position and

affected by saturation, especially intensely at the pole comers. Another reason is that

the instantaneous torque and current vary with the rotor position. Thus the average

torque can be determined only by integration over a period of rotation. Different

computer-based simulation tools or models are reported in literature which are based

on those equations. The already mentioned simulation tool PC-SRD is among them

[6],[29],[31],[32],[33],[41].

3.2.4 Energy Conversion

The energy conversion principle can be best explained by using the energy

conversion diagram which is also called i-yr diagram. An advantage of this diagram

is that the average torque can be derived from the areas on the diagram. This method

for deriving the average torque is used for computer based simulations, for example

the simulation tool PC-SRD uses it [29]. Figure 3.14 shows a diagram like that

computed by the PC-SRD.

Some suppositions have to be set so that the energy conversion diagram can be used.

The machine must rotate at constant speed and a constant voltage has to be supplied

to one phase. For the here described generating operation the voltage is supplied

close before the rotor reaches the aligned position and the commutation takes place

after the aligned position, but before the next unaligned position. The working

principle is explained neglecting all losses for an easier understanding. Thus in the

fundamental figures of the energy conversion diagram (Figure 3.15 to 3.17) which

are used for explanation of the principle, the losses are neglected, too.


The energy conversion diagram can be separated into two periods. The first period is

the excitation period. It starts with the supply of the voltage to the phase and ends

with the commutation. Its necessity is justified because switched reluctance

generators are singly excited machines and the excitation energy must be supplied

every stroke. The second period is the output period after commutation during which

the output current is provided to the power supply. This period stretches as far as the

next unaligned position is reached.

Flux linkage versus currentU-s x 1.0e-2

8.50-

1.00-

7.50-

5.50-

5.00-

4.00-

3.50-

3.00-

2.50-

2.00-

1.50-

1.00-

Figure 3.14: Energy conversion diagram computed by the PC-SRD

Figure 3.15 shows the part of the energy conversion diagram for the first period.

During this period the excitation energy WeXC combines with the mechanical input

energy W^mi; to build up the stored field energy Wf. No energy is supplied to the

output during this period. It is all stored in the magnetic field.

The magnified part of figure 3.15 shows the mechanical output energy Wm(0Ut). It is a

part of the energy supplied by the source but it is not stored in the magnetic field.

Instead it is converted to mechanical work and produces a small positive torque. This

is caused by the switch-on of the excitation before the aligned position is reached. It

seems that the mechanical output energy is wasted in the generating operation, but

the produced positive torque can be used by another phase depending on the number

of phases, the position in which the excitation will be switched on and the moment of

commutation. If these dependencies suit, the torque will be taken over straight from

another phase and thus the necessary driving torque will be decreased.


Moment of commutation

m(out)

Figure 3.15: Energy conversion diagram: Excitation period

In the figure the area taken by the mechanical output energy is rather small compared

with the others, but the area will increase with an switch-on of the excitation far

before the aligned position. Thus it can not always be neglected. The production of

mechanical output energy can only be avoided if the excitation is not switched on

before the aligned position is reached. In this case the time for building up the stored

field energy is very short and only a low flux linkage will be reached until the

moment of commutation. This flattens the energy conversion loop and the output

power will be low. Because of this the mechanical output energy can not be avoided

if the machine is supposed to work at high capacity.

Figure 3.16 shows the part of the energy conversion loop for the second period.

During this period the stored field energy Wf = Wexc + Wm(ini) is released as output

energy. At the same time the mechanical input energy Wm(in2) is converted straight to

output energy. When the unaligned position is reached, the stored field energy is

completely exhausted and the flux linkage and the phase current reaches zero.

Figure 3.17 shows the complete energy conversion diagram. Both periods together

form the energy conversion loop. The area inside the loop is the total mechanical

input energy = Wm(i„i) + Wm(in2). The average torque taken from the driving

machine can be calculated from it as


(3.26)

The mechanical input power equals the effective output energy if the excitation

current is taken from the same source than the output current is provided to.

Depending on the commutation circuit different sources for excitation and output are

possible (see chapter 3.3.3). Then the excitation energy has to be added to the total mechanical input energy to get the total input energy. Also the total output energy is

increased by the excitation energy.

0 i

Figure 3.16: Energy conversions diagram: Output period

The output capability of switched reluctance generators clearly depends on the

available area of the i-y/ diagram. To achieve a high specific output, it is important to

have a large inductance ratio and a high aligned saturation flux linkage. This ensures

a large usable area for the energy conversion loop between the unaligned and aligned

magnetisation curves.

The energy flow in a switched reluctance generator can be characterised by the

excitation penalty

(3.27)

with Pexc as the average electrical excitation power and Pout as the average electrical

output power. Ideally the excitation penalty would be zero, but this is impossible


because it would require a zero air gap and non-saturable iron. Thus the excitation

penalty should be as small as possible.

Figure 3.17: Complete energy conversion diagram

If the excitation and output sources are equal, the efficiency is

77 = -out (3.28)

1 mech

with Pmech as the mean mechanical input power. For different sources the efficiency

is

V = P + px exc 1 mech(3.29)

3.3 Commutation Unit

Switched reluctance generators need essentially a commutation unit, because

unipolar current pulses have to be supplied every stroke for excitation. The

magnitude and amplitude of the excitation current pulses have to be controlled to

fulfil the requirements of the output power control and of the commutation

components. Also a reverse voltage has to be supplied for demagnetisation to get the

output current. The commutation in the converter is a current commutation. This

means that the current in one phase has to be reduced to zero and the current in the

following phase build up from zero.


The commutation unit is required to raise the current in the on-going phase in the

minimum time to get enough excitation and to minimise current disturbances. For

this it needs a sufficiently high forcing voltage at each operation point, so that the current is injected quickly enough into the winding. This is critical at high speeds

since the available time is decreased, because the time for excitation is inversely

proportional to the rotation speed. At low speeds the current has to be limited

because of appearing high current peaks which could destroy the commutation

components. It also has to have a high demagnetising voltage to provide efficient

energy extraction during the demagnetisation interval, which is important for a highly

cyclical energy exchange between the converter and the generator, and it has to

permit an extension of the excitation period.

Another requirement is to provide independent control of the phase currents for the

possibility of an overlap, so that excitation can be supplied to one phase while

extracting it simultaneously from the other phase. Obvious requirements are high

efficiency, low switch to phase ratio and as low converter power rating as possible to

save production costs, high reliability and robustness and low noise and current

pulsation. The converter current rating is determined at low speeds, whereas the

voltage rating is fixed by the maximum speed.

The converter topologies can be distinguished into groups by the voltages used for

magnetisation and demagnetisation and their ability to provide independent phase

control. Single-rail circuits are characterised by having the same voltage available for

magnetisation and demagnetisation, whereas dual-rail circuits use different voltages.

Single phase circuits allow an independent control of each phase, whereas multiple

phase circuits can not cope with phase overlap. These are the key parameter that

affect the inverter selection, and most important is whether the generator operates

with or without an overlapping current through its speed range.

Lots of effort has been lately put on the task to develop new and cheap converter

topologies for motoring operation, as it can be seen from the literature

[4],[7],[13],[18], [19],[40]. The main attempt was to reduce the number of switches

per phase, and many different converter circuits with a reduced amount of switches

have been designed. Other publications concentrate on comparative evaluations like

[49] and a basic general overview is given in references [27],[48]. Every converter

circuit mentioned in the literature can not be used for generating operation because

some of them do not allow to deliver energy to the source during the demagnetisation


interval. The usable converter topologies for generating operation are described in

this chapter.

3.3.1 Classic Converter

The classic converter is the most popular converter topology, especially for

four-quadrant operation. Sometimes it is also called standard or asymmetric bridge

converter. The connection diagram of the classic converter for a three-phase machine

is shown in figure 3.18. It consists of two active switches and two diodes for each

phase. Thus the number of switches is twice the number of phases, which is the

highest switch per phase ratio of a converter topology. The advantage of this high

ratio is that the phases can be controlled independently of each other. Because of this

the classic converter belongs to the group of single phase converters and, because it

works only on one voltage level, it is also a single-rail converter.

S1\D1A

Figure 3.18: Classic converter topology for a three-phase machine

The classic converter enables three connecting states independent for each phase. The

first connecting state is when the switches SI and S2 are connected. At that time the

excitation current flows and builds up the magnetic field. This is the converter state

during the excitation period of the generator. The other important state for generating

operation is when both switches (SI and S2) are turned off. Then the demagnetisation takes place and the output current is delivered to the supply. This is

the converter state during the output period. The third possible state is called

freewheeling and only one of the switches (SI or S2) is connected. This state is

necessary for soft chopping (see chapter 3.4.2) but not essentially necessary for

generating operation, because chopping is not advantageous in generating operation.


The classic converter has many advantages. The most important is that the current

overlap does not affect. Thus the phases can be controlled independently. The full

supply voltage is applied to the winding in either direction of polarity and the

components have a low voltage rating. It has also some disadvantages of which the

most significant is the high total number of switches which equals a high switch to

phase ratio. Others are the need of a DC link filter, the low demagnetisation voltage

at high speeds and the high voltage drop across the converter switches which is a

significant fraction of the supply voltage in low-voltage applications.

3.3.2 (n+l)-switch converter

The (n+l)-switch converter is named after the number of switches used. The number

of switches is one higher than the number of phases. This is one switch more than the

minimum possible number (for example compare chapters 3.3.3 and 3.3.4). Sometimes this converter is also called Miller or common switch converter. It is

derived from the classic converter by substituting switches and diodes. The

connection diagram of the (n+l)-switch converter for a three-phase machine is shown

in figure 3.19. It consists of one common diode and active switch for all phases and

another diode and active switch for each phase. The disadvantage of the low switch

per phase ratio is that the phases can not be controlled independently of each other.

The (n+l)-switch converter belongs to the group of multiple phase and single-rail

converters.

Figure 3.19: (n+l)-switch converter for a three-phase machine

Like the classic converter, also the (n+l)-switch converter enables the three

connecting states for excitation, output and freewheeling. The main limitation is that


the demagnetisation of any of the phases is impossible when the switch SI is turned

on. Thus it does not tolerate phase overlapping and therefore its capability is very

limited. This is the major disadvantage of the (n+1)-switch converter and limits its

operational area to low speed applications. Its benefits are the reduced number of

switches and the low converter power rating which reduces the production costs.

3.3.3 Boost and Buck Converter

Boost and buck converters (for their connection diagrams see Figure 3.20 and 3.21)

are almost solely used for generating operation. One reason is that they do not allow

the freewheeling state. Thus they enable soft chopping but it does not affect

generating operation. Only two connecting states independent for each phase are

allowed. The first connecting state is when the switch S is connected. This is during

the excitation period. The other state is when the switch S is switched off and the

output current is delivered through the diode D to the supply.

Figure 3.20: Boost converter topology for a three-phase generator

Boost and buck converters are dual-rail converters because the excitation circuit is

separated from the output circuit and the voltage levels of both circuits have to be

different. One advantage of these converter topologies is that each phase can be

controlled independently. This is characteristic for single phase converters. Another

advantage is that only one switch per phase is needed. This is the lowest possible

switch per phase ratio. The major disadvantage is that two independent voltage

sources are needed.


Characteristic for boost converters is that the output voltage has to exceed the input

voltage. This leads to a problem at slow speeds because the high reverse voltage

across the phase winding extinguishes the flux too quickly and the energy conversion

is cut off with only a fraction of its maximum possible output. The boost converter is

sometimes also called up converter

Figure 3.21: Buck converter topology for a three-phase generator

Buck converters are characterised by a lower output voltage than input voltage. This

has the advantage that the problem of boost converters does not appear in buck

converters. The lower output voltage leads to a longer output period with a slower

extinction of the flux. A higher output can be reached because a fuller energy

conversion loop is obtained. The buck converter is sometimes also called down

converter.

3.3.4 Bifilar Winding Converter

The bifilar winding converter, like the boost and buck converters, uses the smallest

possible number of power devices. Just one switch is required per phase and this

leads to the lowest possible switch per phase ratio. Figure 3.22 shows the connection

diagram of a bifilar winding converter for a three-phase machine. The converter

allows two connecting states independent for each phase. At first, when the switch S

is connected, the magnetic field for the excitation is build up. After the switch S is

switched off, the output current is delivered through the diode D to the supply. These

are the two possible states. The bifilar winding converter can not operate in the

freewheeling state and thus soft chopping is enabled, which does not affect generating operation.


O-

Ad A A

s

O'Figure 3.22: Bifilar winding converter for a three-phase machine

The advantages of the bifilar winding converter are the low switch per phase ratio

and the full reverse voltage. A negative point is the need of an extra winding for each

phase. This causes additional costs and reduces the efficiency, because additional

copper losses are associated with the auxiliary winding. Also voltage spikes resulting from imperfect magnetic coupling can appear and necessitate the use of snubbers. A

high voltage rating is necessary.

3.3.5 Other Converter Topologies

Several other converter topologies are developed but most of them are restricted to

motoring operation. Only converters which can connect the reverse voltage to the

phase winding through freewheeling diodes are useful for generating operation.

Common for motoring operation are, for example, C-dump or modified C-dump

converters. They recover the stored energy by dumping it in a capacitor and the

trapped energy is returned to the source by using a chopper. These converters need

additional components and their control is complicated but they need only one active

switch more than the minimum. For generating operation the chopper components

and the dump capacitor have to be very large, even larger than for motoring

operation, because the energy returned to the supply is a lot higher. Also the

additional losses associated with the reactive elements enable their use for generating

operation.

Other quite common converters for motoring operation are converters which use a

resistor for suppression. The advantage of these converters is that they have low


production costs because they require just the minimum number of switches without

an auxiliary bifilar winding. Because they dissipate the stored energy or at least parts

of it in the resistor, they can not be used for generating operation.

3.4 Dynamic Operation

The dynamic operation of switched reluctance machines depends on the commutation

unit and the control strategy. The operation modes are single-pulse operation and

chopping. Both operation modes are described in this chapter. All commutation units

allow single-pulse operation and hard chopping and most of them also allow soft

chopping (compare chapter 3.3). The control strategy builds on these different

operation modes depending on its task. Especially in motoring operation chopping is

used very often to smooth the output torque and to control the current at low speeds.

3.4.1 Single-Pulse Operation

The single-pulse operation is the main operation mode because the flux in switched

reluctance machines is not constant and has to be build up from zero every stroke.

This is realised by switching the supply voltage on at the turn-on angle 6q and off at

the turn-off angle 6c- The switching is made by the active switches of the

commutation unit. The turn-off angle is often also called commutation angle, because

at this rotor position the reverse voltage is supplied through the commutation diodes

to the phase winding. Figure 3.23 shows the characteristic waveforms of the idealised

inductance, voltage, flux linkage and phase current for single-pulse operation.

The waveforms are typical for generating operation at middle speeds. At low and

high speeds the waveform shape can vary, but the general appearance is not very

different. The inductance waveform is idealised between the aligned La and

unaligned inductance L^. The other waveforms can be related to the rotor position

from it. The supply voltage Us is switched on while the inductance is rising and

before the aligned position is reached. The commutation takes place behind the

aligned position but still far before the unaligned position so that the output period is

long enough to deliver a sufficient output current. At the commutation angle the active switches are switched off and the reverse voltage is supplied through the

diodes. The flux linkage reaches its maximum y/c at the moment of commutation,

whereas the maximum current peak /peak is reached later. At the extinction angle 9q


the voltage, flux linkage and phase current are back to zero and the diodes are closed

again.

Idealised inductance

Aligned

Unaligned

Voltage

Flux linkage

■ Phase current

Excitationperiod

Figure 3.23: Single-pulse waveforms for generating operation

Ideally the switch-on angle should be close to the aligned position because otherwise

a small positive torque is produced by the supply current of the battery. On the other

hand, the excitation will not be sufficient if the period is too short. Especially at high

speeds the disadvantage of positive torque production has to be accepted (compare

chapter 3.2.4). The angle difference between the turn-off and the tum-on angle is

called dwell angle It is the angle that stretches across the excitation period. The

control of switched reluctance machines uses both the tum-on and the turn-off and

thus also the dwell angle. In generating operation the output power and the height of

the peak currents are depending on these angles.


3.4.2 Chopping

Chopping is necessary in motoring operation to control the current at low speeds and

to smooth the output torque. It is realised by using the freewheeling or reversing state

of the commutation unit which were already explained in chapter 3.3. The types ofchopping are distinguished in voltage pulse-width modulation and current regulation.

Both types of chopping can be realised by soft and hard chopping. In soft chopping

the supply voltage is switched off by using the freewheeling state, whereas in hard

chopping the voltage is reversed by using the reversing state of the commutation unit.

The characteristic of voltage pulse-width modulation is that the state of the

commutation unit is switched at high frequency with a fixed duty cycle during the

dwell period. For current regulation the state is switched during the dwell period

depending on the current being greater or smaller than a reference current. Thus the

duty cycle is variable.

Chopping is not advantageous in generating operation because the peak of the output

current appears during the output period and not during the excitation or dwell period

(see chapter 3.4.1) when chopping is used. Thus chopping reduces only the excitation

current but that is not desirable and has no direct influence on the peak of the output

current. Other strategies have to be used to reduce the high peak of the output

current, especially at slow speeds.

3.5 Control System

Switched reluctance machines need a control system because the current waveform

shape and its magnitude must be controlled in relation to the variations of speed and

load. This task is quite difficult to fulfil because the relationships between torque,

current, speed and firing angles are highly non-linear and vary as a function of speed

and load. The control strategy has to cope with these difficulties and sometimes it has

to fulfil also the requirements of peak current regulation. Another difficulty is that

switched reluctance machines have no axis transformation like AC motors and no

field oriented control principle has been developed for them. Thus it is necessary to

use high-speed real time controllers which operate with phase currents and voltages

directly. Also the switching precision is critical in switched reluctance drives and a

precision of 0.5° or even 0.25° is desirable, as it is pointed out in reference [27].

Motors are normally controlled by closed-loop speed and sometimes torque control,

whereas generators are controlled by keeping the output voltage constant. The


parameters for the control are the turn-on and the turn-off angles. A rotor position

feedback is necessary to synchronise the switching of the commutation devices

depending on the firing angles with the rotor position. The rotor position can be

obtained by direct or indirect sensing. The conventional way is to use direct position

sensing and it is realised by using a slotted disk together with optical interrupters,

Hall-effect or other type of sensors. The indirect rotor position sensing is a popular

field for investigations and research and many articles have been published, like

[8],[9],[16],[21],[23],[36],[37],[38]. It is described later in this chapter.

3.5.1 Structure

The structure of the control system for switched reluctance generators is shown in

figure 3.24. The controller, commutation unit and switched reluctance generator are

considered as a black box for the reason of simplicity. The system input value is a

reference voltage UKfwhich is generally kept constant depending on the voltage level

of the source and loads. The system output is the output voltage Uout of the generator

and varies with load and speed. It has to be kept constant and thus a voltage error AU is derived by comparison with the reference voltage after feedback. The voltage error

together with the rotor position 6 and angular velocity (0 feedback is the input of the

controller which has to estimate the firing angles 0O and 0c for the commutation unit.

The commutation unit then switches the phase currents i\, i% and h of the generator.

This all put together results in the structure of the control system.

AU CommutationUnit

Controller SR-Generator

Figure 3.24: Control system structure for a three-phase generator

3.5.2 Control Modes and Strategy

Different control modes for switched reluctance motors are mentioned in the

literature [3],[27]. The modes are normal, boost and long dwell and are distinguished

according to the values of the firing angles and the resulting characteristics. The


references mention only one mode for generating or braking operation, but

simulations with the PC-SRD have shown that the three modes can be observed also

in generating operation. Figure 3.25 shows the current waveforms of the three control

modes for generating operation.

Normal

Boost

Long dwell

Figure 3.25: Phase current waveforms for normal, boost and long dwell control

modes

The normal mode is characterised by a short excitation period with the tum-on

angle 6q close before and the turn-off angle 0c close behind the aligned position.

Only a small negative torque is produced during excitation before the aligned

position is reached. Because the excitation period is short, the output period is also

short and thus the output power is small. A positive effect is that the current peak

/peak is small, too. This control mode is most suitable at low speeds for restricting the

current peak.

Compared with the normal mode the boost mode has a longer excitation period and

thus also a longer output period. More output power is generated and the current peak

is higher. The negative torque produced during excitation is still quite small. This


mode should be used at medium speeds. Because of the higher speed a longer

excitation period is needed to reach the nominal output power.

The long dwell or also called the advanced mode has the longest excitation period

with the turn-on angle far before and turn-off angle far after the aligned position. The

first smaller current peak of the current waveform for the long dwell mode, which

can be seen in the figure, produces a worth mentioning negative torque because of the

turn-on of the excitation far before the aligned position. The output period isextended and thus a high output power is reached. A negative feature is the high

output current peak. This mode is supposed to be used at high and very high speeds

to reach a high output power. There is no clear distinction between the modes.

Basically the control strategy can be realised in two ways. The first and the easier

possibility is to vary just the turn-on angle and to keep the turn-off angle constant at a

sufficiently high value. This has the consequence that very high current peaks can

appear at low speeds together with high load, which may not be tolerated by the

commutation unit. At low load the ratio of peak current and RMS-current can be

high, but these current peaks will not cause damage to the commutation, because

their level is lower than in the other situation. This control strategy is mainly based

on the long dwell mode with the turn-off angle far behind the aligned position.

The other possibility is to vary both firing angles. Then a smoother output current

waveform is reached and the critical high current peaks are avoided. The reason for

this is that all control modes are used in their suitable speed ranges. This control

strategy is more sophisticated but has the mentioned major advantages.

3.5.3 Sensorless Control

The sensorless control can be distinguished into four schemes. The schemes are

open-loop control, passive waveform detection, active probing and observers. In

open-loop control the dwell period is controlled but the firing angles are not

synchronised to the rotor position. These controllers are unstable and they have to be

stabilised by using other external values, like torque or current, to recognise load or

speed changes. They are not useful in generating operation because the firing angles

have to be kept exactly in position to keep the output voltage constant and to avoid

high current peaks.


The passive waveform detection mainly relies on characteristics in the phase current

waveform, for example maximum or minimum. Phase current measurements are

necessary to realise this scheme. Reference [23] illustrates the realisation of such a

scheme that detects the change of current ripple and converts it to a rotor position

signal, but it can provide the signal only at low speeds. References [36],[37],[38]

describe a sensing technique that uses the current rise and fall times. Restrictions to

low speeds are mentioned and the successful detection of the rotor position is related to chopping operation. Another method is to measure the mutual induced voltage in

an unexcited phase as it is described in reference [16]. It is suitable for low speeds,

low voltage and high current drives with single switch per phase converters. In

generating operation passive waveform detection does not seem very suitable

because the high current peaks appear at low speeds and thus switched reluctance

generators should operate at higher speeds.

For sensing with active probing, a square-wave voltage is applied to an unexcited

phase. The resulting current pulses vary with the phase inductance. The minimum

and the maximum are reached with the aligned and unaligned positions. The rotor

position can be detected from this. The references [8],[9],[21] describe the realisation

of position sensing with active probing. Problems occur with a small number of

phases because of phase overlap and the references mention that the realisation is

most reliable for machines with at least three or preferably four phases.

The most demanding control scheme uses observers. A state observer is a mathematical simulation of the machine running on-line on a microcomputer in

parallel with the drive. Measured currents and voltages are the input for a model

which gives then the rotor position and speed.

59

4 Generator Design

Before the generator design can be made, some suppositions have to be defined. The

main suppositions are supply voltage, speed-range and size. A common 12 V battery

is chosen for the power supply, as it is used in motor vehicles. This is the cheapest

and most reliable solution. It also opens the easiest possibility of using the generator

in the most common field of applications - in motor vehicles. A detailed description

of battery characteristics is given in the references [14] and [17].

Table 4.1 includes the main battery characteristics. It can be seen that different

characteristic voltages are necessary to describe the battery behaviour because the

voltage depends on the state of charge. Besides the conventional nominal voltage

also rest, discharged, maximum charged and gassing voltages are introduced. Also

the nominal capacity is included. This capacity is defined by the amount of current

which can be delivered during 20 hours of discharging at 27° C with a constant

current.

Table 4.1: Main battery characteristics

Nominal voltage C/N= 12 VRest voltage U rest = 12.72 VDischarged voltage t/dis= 11.76... 11.88 VMaximum charged voltage Umax = 15.6 ... 16.2 VGassing voltage UR as = 14.4 VNominal capacity K 20 = 84 Ah

The voltage drops down to the rest voltage after charging of the battery and it will be

held. If the battery is partly discharged, the rest voltage will be reached after a few

seconds of charging. The lowest possible voltage is reached when the battery is

discharged. Analogously the maximum voltage is reached when the battery is fully

charged but before reaching that level the battery water will start to decompose at the gassing voltage. Thus the gassing voltage should not be exceeded. Figure 4.1

illustrates this voltage behaviour versus time for charging and discharging.

The voltage behaviour of batteries is also depending on the temperature. The above

mentioned values of the voltage levels are applied to 20° C and they decrease in

colder surroundings. Thus a voltage of 14 V has been chosen as operating voltage of

the generator to surely avoid the decomposition of the battery water at the gassing

voltage of 14.4 V. It also provides some clearance for the control system.

Chapter 4: Generator Design 60

UN14.4 t

13.8 "

13.2 --

— Charging —Discharging

12.0 --

11.4 --

0123456789 10

Figure 4.1: Battery voltage versus time for charging and discharging

The speed range of the generator is chosen according to the speed range of the

internal combustion engine of motor vehicles to provide the best output characteristic

for this main application. A speed range multiplied by a constant ratio factor is also

suitable. This can be realised by the variation of the pulley size. It can be suited in the

same way for other applications with a different speed range. The speed range of

combustion engines spans from the idling speed 800 rpm up to 8,000 rpm. At a speed

of 6,000 rpm the overspeed range begins, so this range is rarely used for driving.

Speeds around 3,000 to 4,000 rpm are used mostly.

The size of the switched reluctance generator should be around the size of large

alternators for 12 V applications. Then the new generator with its supposed higher

output power would be advantageous in this point. The outer stator diameter of these

alternators is around 150 mm, the outer length is usually a bit smaller than the

diameter and the weight is around 7 kg.

4.1 Construction

Before geometrical details of the construction can be designed the magnetic material

has to be chosen because it has a major influence on the machine performance. Its

typical magnetic values, magnetisation curve, core losses and mechanical properties

have to be known before a design can be made. The material has to fulfil the special

demands of switched reluctance machines, like high commutation frequency, high


harmonics of the flux density waveform and high saturation, especially of the pole

comers. Thin lamination is desirable, and Silicon steels are preferred [27].

Here is chosen a cold rolled, non-oriented electrical steel of grade DK-66 which

contains 1.3 per cent of Silicon. The layer thickness of the lamination stacking rstk is

selected to 0.5 mm. For the lamination stacking factor fs± is chosen the value 0.97.

The important magnetic and mechanical properties of this steel are summarised in

table 4.2.

Table 4.2: Properties of DK-66

Resistivity P resFE = 2.8* 10'3 £2/mRelative permeability at 2*104 T and 50 Hz P start — 290

Maximum relative permeability at 50 Hz P max = 5000Flux density at 2.5* 103 A/m DC B 25= 1.65 TFlux density at 10* 103 A/m DC B io= 1.83 TFlux density at 30* 103 A/m DC B 30 = 2.06 TCoercive force at DC Hc = 90 A/mGuaranteed maximum core losses at 1.0 T and 50 Hz P 10max = 2.6 w/kgGuaranteed maximum core losses at 1.5 T and 50 Hz P 15max = 6.0 w/kgCore losses at 1.0 T f 10 = 2.4 W/kgCore losses at 1.5 T P15 = 5.4 W/kgDensity Pfe = 7740 kg/m3Modulus of elasticity in rolling direction £r=1.8443*10nkg/(ms2)

Modulus of elasticity in transverse direction £, = 2.119*10n kg/(ms2)

Yield point C7y=2.845*108N/m2

Even though this material is non-oriented it should be mentioned that the property

values are different in the rolling and traverse direction, for example the permeability

is higher and the core losses are lower in rolling direction. Table 4.2 includes average

or worst case values so that they can be used safely for further calculations.

This steel is a common material in many AC machines and especially in

high-efficiency applications because the Silicon reduces the core losses. The major

advantage of this material is the high saturation flux density as can be seen from the

magnetisation curve in figure 4.2. This fact is decisive for the use in switched

reluctance machines to reach a good output power.


2.00 •

1.80 ■

1.00-

0.40 •

0.20*

2.00 2.60 3.000.60Ax* x 1.0*4

Figure 4.2: Magnetisation curve of DK-66 as integrated into the PC-SRD

4.1.1 Basic Characteristics

In order to get a competitive machine the number of phases should be as low as

possible. This guarantees low production costs because of the easy construction and a

commutation unit with a small amount of switches. A one-phase generator has the

minimum number of phases but it has only an absolute current output zone of one

half. This means that output current can be produced maximum over only one half of

each revolution. The other half of the revolution is over a blank zone and can not be

used for current generation. This is definitely too low utilisation of a machine. To get

output current almost over a full revolution the absolute current zone has to be at

least one. This together with the already mentioned demand fulfils a two-phase

generator. Thus a two-phase generator is chosen.

Table 3.1 shows two different possible rotor and stator pole combinations for

two-phase machines. In reference [20] the influence of the number of poles per phase

in switched reluctance motors has been researched. It concludes that both single- and

multiple-pole-pair-per-phase motors have their advantages depending on the

application. Because of this an analysis of two-phase generators with single- and

multiple-pole-pairs-per-phase has been made with the PC-SRD in this work to

examine the influence for generator applications. The results show that the generator

with eight stator poles and four rotor poles has only disadvantages compared with the

other one. The peak currents are higher, a more precise controller is needed and the

geometry is more complicated. Thus the number of stator poles is chosen to 4 and the


number of rotor poles to 2 respectively. Then the stroke angle is 90° and the number

of strokes per revolution is 4.

4.1.2 Envelope and Internal Dimensions

For the design of the geometrical dimensions a starting point has to be found to

enable simulations with the PC-SRD. This can be done by solving equation (3.1) for

typical values. An average torque of around 10 Nm is necessary to reach the output

power of 1.5 kW at slow speeds. From table 3.2 the value for the torque per unit rotor volume can be chosen to 35 kNm/m3 to get a good performing and utilised machine.

Equation (3.1) can be solved by using these values together with a common stack

length per rotor diameter ratio of 1. Then the stack length and rotor diameter are

calculated to around 72 mm. For a rotor diameter per stator lamination diameter ratio

of 0.5 which is typical for machines with a small number of poles, the stator

lamination diameter is 144 mm. This fulfils the supposition for the approximated

generator size and with a stack length of 72 mm the overall length will be also less

than 150 mm.

A large shaft diameter is desirable to maximise the lateral stiffness of the rotor. It

raises the first critical resonance speed and reduces the acoustic noise. Thus the shaft

diameter is chosen quite large to 20 mm. The rotor yoke has to be sufficient to carry

the rotor flux, which means, that it should be at least half the rotor pole width,

because the flux divides into two equal parts when it leaves the rotor poles. For a

rotor yoke of half the rotor pole width the minor rotor diameter can be calculated by

Am = Ah+ tT with tT given by equation (3.2). For a typical rotor pole arc of 45° the

result is 47.5 mm (for the pole arc selection and optimisation see chapter 4.1.3).

The air gap length is initially chosen to 0.5 mm. This is larger than the minimum

limit of 0.2 mm which is caused by the very difficult production situation under this

limit. The last missing parameter value is the stator slot bottom diameter. The facts for the stator yoke are equal to those for the rotor yoke except that the stator yoke

thickness has in addition a major influence on the acoustic noise of the generator.

Thus the stator yoke should be chosen thicker than ts /2 to increase the stiffness and thus to reduce acoustic noise. A suitable value is 2/3 ts. The stator slot bottom

diameter can be calculated by Dsb = DS- 4/3 ts with ts given by equation (3.3). With a

typical stator pole arc of 45° it equals to 106.5 mm.


Now the corresponding radiuses can be calculated from the diameter values. The

shaft radius is 10 mm, the minor rotor radius 23.75 mm, the rotor radius 36 mm, the

stator slot bottom radius 53.25 mm and the stator radius is 72 mm.

After the starting point for the simulations with the PC-SRD has been found, the

geometrical dimensions are varied and the effect on certain characteristic values is

examined. The geometrical dimensions are varied over a range around their starting

value. The observed characteristics are the inductance ratio L^o, shaft torque Tshaft,

shaft power fshaft, efficiency t}, total power losses P\0sses, diode peak current /Dpeak,

transistor peak current /rpeak and the output current /Dc. The values of the shaft torque, shaft power and output current are negative in generating operation and thus

the absolute value is taken. The results of these variations of the geometrical dimensions are summarised in table 4.3.

Table 4.3: Effect of an increase of the geometrical dimensions on characteristic

values; the symbols are standing for: 0 / almost no changes,

+ / increase, - / decrease, (+) or (-) / slight increase or decrease

R sh Ro Ri Ri R 3 8 •t-stk

1* ratio 0 - + - 0 - 0

abs(7 shaft) + - + 0 (-) - -

abs(P shaft) ■ + - + 0 (-) - -

77 - + - + (+) - +

P Losses + - + - - + -

I Dpeak + - + 0 0 0 -

f Tpeak ■ + - 0 + - + -

abs(/Dc) + - + + (-) - -

In the table it can be seen that a large shaft radius results besides the higher lateral

stiffness of the rotor in an increase of the output power. Decrease of the efficiency

and increase of the peak currents of the commutation devices come along with the

higher output power. Thus the shaft radius should not be made larger than it already

is.

The variation of the minor rotor radius shows that it has a significant influence on the

output power. To get a high output power this radius should be small but, as already

mentioned, the rotor yoke has to be wide enough to carry the rotor flux. Thus it

should not be made smaller to avoid high saturation of the rotor iron and it is finally

chosen to 24 mm.


The rotor radius is the best parameter to be changed to reach a high output power

because an increase of this dimension increases the output power significantly. This

is quite surprising because the slot area is decreased and thus less copper can be fitted

in, but still the output power rises. This can be explained from the energy conversion

diagram (see chapter 3.2.4). Because of the higher inductance ratio the area between

the unaligned and the aligned magnetisation curves will be enlarged and thus the

energy conversion loop will be bigger. Very positive is also the fact that the critical

transistor peak current does not rise with an increase of the output power.

The rotor radius is chosen to its highest value that can be used with the chosen minor

rotor radius and this is 37.5 mm. A higher value would cause very high saturation of

the rotor iron and the rotor yoke would have to be enlarged. Then the larger minor

rotor radius would decrease the output power. Changes of the minor rotor radius and

the rotor radius effect contrary on the characteristics and mainly the difference

between these dimensions (rotor tooth length) determines the inductance ratio and

thus the output power. This is confirmed by reference [43].

The influence of the stator slot bottom radius is rather small. It mainly effects the slot

area and with a larger radius more copper can be fitted in. This will slightly increase

the output power. It is positive that the generator will become more efficient at the

same time. Thus the stator slot bottom radius is enlarged to 56 mm. The

disadvantages are that the transistor peak current is raised and the stiffness of the

stator yoke is reduced, but they can be compensated by the right choice of the stator

radius.

The stator radius has only a slight effect on most of the characteristics for the

designing process. Thus the main criterion for its choice is the stator stiffness to

reduce the acoustic noise. Positive, but not significant, is the reduction of the

transistor peak current with a larger radius. To compensate the yoke thickness

reduction from the enlargement of the stator slot bottom radius, the stator radius is

chosen to 74 mm.

Highly significant is the influence of the air gap length as it is pointed out in

reference [34]. A small air gap effects positively on all characteristics without

exception and thus it should be as small as possible. The absolute minimum given by

the production possibilities is 0.2 mm [27]. The air gap length is finally chosen a bit

wider to 0.3 mm to keep some clearance to the limit to ensure the production.


An increase of the stack length gives lower peak currents and the efficiency will be

higher, but on the other hand the output power will be decreased. Thus a good

compromise between these characteristics has to be found. Because the influence on the peak currents is more sufficient the stack length is chosen to 75 mm. A small

stack length also enlarges the influence of end effects. The effect of end core flux on

the machine performance is presented in reference [24].

The optimum choice of the values of all dimensions had been verified for different

speeds and load conditions. From these finally settled dimensions the longitudinal generator cross section can be drawn. It is shown scaled down in figure 4.3 and truly

scaled in figure B.2 in Appendix B.

Figure 4.3: Longitudinal cross section of the generator

4.1.3 Pole Size and Geometry

The stator and the rotor poles have to be designed. The pole sizes are determined

mainly by the stator and rotor pole arcs. The other dimensions effecting on the pole

sizes are already fixed in the previous chapter. A good starting point for the rotor and

stator pole arc is 45°. This value equals to half of the stroke angle and is the most

common choice because it enables output current to be produced almost during a

whole revolution and enough clearance between the rotor and stator poles.


In most applications the stator and rotor pole arcs have approximately the same size

because otherwise the dead zone, where no torque or output current is produced,

would be extended. Basically the increase of one pole arc decreases the output

current. This is a disadvantage but, on the other hand, the peak currents will be

decreased, too. If both pole arcs are enlarged in the same way the current ripple will

get lower for the same output current, but to reach the same output power with a

larger stator pole arc a higher slot fill factor of the winding is necessary, because with

an increase of the stator pole arc the slot area for the winding decreases. Thus the

stator pole arc of 45° is not changed to keep the size of the slot area and the rotor pole

arc is enlarged to 47.5° to reduce the peak currents. Enlarging both pole arcs does not

reduce current ripple significantly because a two-phase machine with an effective

overlap ratio less than 1 always produces a pulsating output current.

The most suitable pole geometry is the modification (b) introduced in figure 3.5. It is

chosen because it increases the stiffness of the poles and stabilises the stator yoke

which affects on noise reduction. Also it does not decrease the usable slot area

significantly and it is quite easy to produce compared with other modifications. The

radius of the comer area is chosen quite high to 5 mm to reduce acoustic noise. Now

all the required information for drawing the cross section of the generator is given

and it is shown scaled down in figure 4.4 and truly scaled in figure B.l in

Appendix B.

Figure 4.4: Cross section of the generator

Modification (d) in figure 3.5 could have been another solution but the pole

overhangs are not necessary because the stator pole arc is not enlarged and thus the


slot area is large enough to fit in the winding. Different pole profiles for motoring

operation are discussed in the reference [34]. For generating operation it can not be

said if some of this profiles would be advantageous and a more complicated profile

would increase the production costs. Thus the traditional profile used with the pole

geometry in figure 3.5 is not changed.

4.1.4 Winding

The winding has a major influence on the machine performance. It determines mainly

the phase current behaviour, especially the peak current and the output power. Because of that the winding design has to be carefully and well suited.

First, the slot fill factor has to be chosen. Because of its influence on the electrical behaviour it should be as high as possible because with an increase of the slot fill

factor the output power and efficiency will be increased. Another advantage is that

the copper losses will be decreased, but the slot fill factor is limited by the geometry

of the slot and the essential insulation. The only disadvantage of a high slot fill factor

is that pre-wound windings can not be used.

Afterwards the number of turns per pole has to be chosen. Generally with an increase

in the number of turns per pole the output power and the peak current will be

decreased. A good compromise according to these two criteria has to be found and

especially at low speeds the peak currents have to be limited. Otherwise suitable

commutation devices can not be found.

The windings of opposite poles can be connected in series or parallel. Simulations

with the PC-SRD have shown that the basic machine performance does not differ

between serial and parallel connected windings if the number of turns per pole is

chosen respectively. For parallel connected windings the number of turns per pole

would have to be double compared to serial ones. Generally, serial connected

windings have a better behaviour according to the influence of harmonics. Thus

serial windings have been chosen here. The number of parallel paths per phase is

then 1.

Various simulations with the PC-SRD have shown that the optimum fixed number of

turns per pole for the serial connected winding over the whole speed range is 12. This

value provides the desired output power of 1.5 kW over a broad speed range and it

limits the peak currents at low speeds so that a good but not the desired output power


can be reached at these speeds, too. Limitations of the output power at low and very

high speeds have to be made anyway if a fixed number of turns per pole is used, and

the number of turns per poles has to be fixed to realise an easy and cheap winding.

With Np that equals to 12 and %u around 0.6 the wire diameters will be very high and

with the phase current waveform high eddy current losses will be caused. A solution

for this is to use smaller wire diameters and to connect them in parallel. This has also

the advantage that a higher slot fill factor can be reached because smaller wires can

be better fitted into the given slot area geometiy. A suitable wire diameter is 1 mm.

For the above estimated generator geometry the slot area can be calculated with equation (3.6) and it is 805 mm2. The usable slot area will be decreased by the area of

the pole comers that is taken away by the radius r because of the chosen pole geometry (see chapter 4.1.3). ACOmer equals to 9.56 mm2 and is calculated from

equation (3.9) with the geometric dimensions mentioned in the previous chapters, thus the real slot area is 786 mm2. The windings have to be insulated from the stator

core iron and the two windings in the slot from each other. This will reduce the

usable slot area, too. The area taken away by an insulation layer of the thickness d around the slot and of the thickness 2d between the windings is

= 2 d (2^-2/?,-3d-25-r)+[(/?, +S+df-(R1 +S)2]^l

+ -(#2- J)2j^'°'back T ^corner _ (r~df](4.1)

withA>iot -4r(27r~NsPs)’

'slotback M\7Z-N, arcsin 5, 12

and /Corner already given by equation (3.10). The net stator slot area can then be

calculated as

Alotsnet Alois 2Acomer Ansul • (4.2)

For sufficient insulation the insulation layer thickness should be at least 0.2 mm and the net slot area then equals to 755.5 mm2.

A very suitable and common wire for all small electrical machine windings and for

many other applications is the enamelled round copper wire with DFV quality and

grade 2 insulation thickness. The wire insulation is a THEIC-modified polyester

imide enamel according to EEC 317-8 standard which has good chemical and


electrical properties. Because of its hard surface it can resist mechanical stresses. The

enamel insulation belongs to the temperature class H, which guarantees that it can

tolerate temperatures up to 180° C. It can also tolerate quite high temperature

changes without any damage. If the wires are prepared with paraffin before coiling,

machines can be used for the winding process, which will decrease the production

costs. All these characteristics seem very likely for this type of wire. The technical

specifications for the wire with 1 mm nominal copper diameter for a temperature of

20° C are shown in table 4.4.

Table 4.4: Wire specifications

Nominal diameter of copper D CUwire — 1 Him

Nominal cross sectional copper area A cuwire = 0.7854 mm2

Minimum resistance per length R' wiremin = 0.02115 D/mMaximum resistance per length R' wiremax = 0.02240 D/m

Average resistivity Pcu= 1.7102*10-8 Dm

Maximum diameter with insulation D wire = 1.0930 mm

Cross sectional area with insulation A wire = 0.9383 mm2

Wire density with insulation P wire = 7613 kg/m3

Finally, the number of parallel wires per turn per pole jVwp has to be estimated. From

the cross sectional area of the winding with insulation Acu+insui = NpNwpAwm the slot

fill factor with consideration of the insulation can be calculated as

SfiUinsui = 2 Acu+insui/Asiotsnet with Asi0tsnet given by equation (4.2). This factor should be

smaller than 0.75 to be sure that the windings will fit into the net stator slot area.

From these equations the number of parallel wires per turn per pole can be calculated

to 24. This gives a slot fill factor with consideration of the insulation of 0.715 and the copper area Acu = 7/pMvpAwirecu equals then to 226.2 mm2. The slot fill factor

without the consideration of the insulation is then Sfm = 2 Acu/Asiots = 0.576. This

high slot fill factor makes it impossible to use pre-wound windings, but concerning

the electrical behaviour a slot fill factor lower than 0.4 is not suitable because the

output power will be decreased for slow and high speeds and the efficiency decreased

over the whole speed range. Figure 4.5 shows a possible arrangement of the wires in

the slot area and it confirms that the wires can be fitted.

The winding properties are completely defined now and the direct-current resistance

of one phase can be approximated as

(4.3)


and for a temperature of 20° C it equals to 6.3 m£l For higher temperatures the

resistivity of the copper rises and thus the phase resistance will be increased. The

temperature-depending resistivity is

p(T) = p(20° C) [1 + a (7-20° C)] (4.4)

with a that equals to 0.0038 for copper. Machines are usually reaching a stable

temperature of around 80° C while operation. Depending on the characteristics of the

surroundings the temperatures can rise even higher. For the following calculations a

temperature of 90° C has been scheduled to ensure that the generator will work

properly in the warm surrounding of the internal combustion engine of motor vehicles. The resistivity of the copper equals then to 2.1651*10'8 Qm. This means an

increase of around 25 %. The direct-current phase resistance rises to 8 mfl.

The phase resistance for non-direct currents is basically higher than for direct currents because of the influence of the skin effect. Here the influence of the skin

effect can be neglected because of the small diameter of the used wires. Thus the

direct-current phase resistance can be used as an approximation for the phase

resistance.


4.1.5 Further Estimations

After all the basic geometrical dimensions have been set, some other interesting

values can be estimated, like the length, weight and moment of inertia. The overall

length Le can be approximated to 133.5 mm from Le = Lstk+2L0h with L„h almost equal to the stator pole width ts. For the total length of the generator the width of the

shields with the bearings and the fan must be added to the overall length, but all this

together still fulfils the previously made suppositions for the generator size.

The weight of the generator Wtot can be approximated from the weight of the used

iron and copper. The total iron weight Wpe equals to Wr? = ppe We with ppe given in

table 4.2 and We as the total iron volume which can be calculated by adding the rotor

and stator iron volume given by the equations (3.7) and (3.8). Its value is 6.7 kg. The

copper weight with insulation Wcu is given approximately by

(4.5)

with the already mentioned dimensions and pwire and Awire from table 4.4. The copper

weight equals then to 2.4 kg. All together the weight is then 9.1 kg. This value will

be increased by the weight of shaft, shields, bearings, fan and armature. Compared

with alternators the weight is higher, but this is thoroughly justified by the higher

output.

For the calculation of the moment of inertia J the geometry of the rotor pole teeth is

assumed to be a rectangular parallelepiped with the side lengths Lstk, tx and (R\ - Rq) for simplification. Then it can be calculated from

(4.6)2

+ Ptehlk{Rl-Ro)tr +

with the previous set dimensions and ppe given in table 4.2. The result is 7.94* 10"4 kgm2.

Further, it has to be checked that the mechanical properties of the generator are

satisfactory. The maximum operating speed has to be lower than the first critical

speed. Two approaches are used for calculating the first critical speed. The first

approach is introduced in reference [42] and based mainly on the mechanical

characteristics of the iron material. The first critical angular velocity Q\ can be

calculated from


Qx =nl3■^stk

£7PpeA-

(4.7)

with £ as the modulus of elasticity, 7 as the modulus of inertia and Ar as the area of

the rotor cross section. Table 4.2 includes two values for the modulus of elasticity.

For this calculation is taken the lower value in rolling direction £r to estimate the

worst case. The modulus of inertia can be calculated from the moment of inertia

given by equation (4.6) with

7 = (4.8)

The area of the rotor cross section is Ar= VrFe/£stk with VrFe given by equation (3.8).

The result for the first critical speed calculated with this approach is very high, so

that definitely no danger appears.

The second approach is introduced in reference [27] and based on the shaft

quantities. An equation for the first critical speed Vi is given, and converted to

Si-units it is

Vj =9.236*10 •^slk V^tk^r" (4.9)

where 7?Sh is the shaft radius in m, Lstk the stack length in m and WT the rotor weight

in kg. The unit of the result is rpm. The first critical speed is calculated to around

41,500 rpm. This is clearly above the maximum speed of the generator.

The rotor has to tolerate the centrifugal force at maximum rotational speed. If the

rotor is assumed to be cylindrical, the mechanical stress cr is calculated according to

reference [42] by

= Ppe^l ^max (4.10)

with Qmzx as the maximum angular velocity. For a maximum speed of 12,000 rpm the stress is 1.72*107 Pa. Compared with the yield point of the iron given in table 4.2

the safety factor is 16.5, which is sufficient.

4.2 Commutation Unit

The commutation unit has to fulfil the demands given by the generator. The devices

are mainly determined by the current they have to commutate. Current peak and

waveform are important criteria for the device selection. Mainly it is enough to

concentrate on the worst case currents for the transistors and diodes to ensure their


proper operation. Attention has to be paid also on the commutation losses. For surethey should be as small as possible to maximise the efficiency, and their influence is huge because they are a major part of the total losses. Because of the low voltage and

the high current the voltage drop across the diodes and the transistor resistance has to

be small. In the selection of the converter topology one has to consider the phase

overlap at high speeds and output power.

The worst case transistor current waveform is shown in figure 4.6. It is characterised

by a slight linear increase after the transistor is switched on and after around 5 ms it

starts to rise rapidly up to the peak Apeak = 255 A. At this moment after the

conducting period Ton = 6.5 ms the transistor is switched off and the current drops to

zero. After the non-conducting period T0ff= 18.5 ms the transistor is switched on

again and the same current waveform is following. Thus the whole period Ttot is

25 ms. The mean value of the transistor current Amean equals to 11.3 A and the RMS

value Arms is 35.1 A.

VA

240 -

160 -

120 -

Figure 4.6: Transistor current (worst case for commutation)

Figure 4.7 shows the waveform of the worst case of the diode current. After the

transistors have been switched off the current commutates through the diodes and

rises immediately up to around 260 A. Then it rises slightly up to the peak

Apeak = 340 in the next 2.7 ms. From there it drops almost linearly down to zero. This

takes 4.1 ms and thus the diode is conducting for the conducting period Ton=6.8 ms

altogether. After the non-conducting period T0ff= 14.6 ms the diode is conducted

again and the same waveform follows. Thus the whole period Act is 21.4 ms. The


mean value of the diode current /Dmean equals to 65.3 A and the RMS value /drms is

135.6 A.

VA

240-

200-

Figure 4.7: Diode current (worst case for commutation)

4.2.1 Topology

The classic converter topology is chosen which was introduced in chapter 3.3.1. The

most important reason for this choice is that the phases can be controlled independent

from each other. This is necessary because of the phase overlap at high speeds and

output power. From the other converter topologies mentioned in chapter 3.3.1 the

boost and buck converters are able to cope with phase overlap but they need two independent voltage sources, which is not allowed here. Also the bifilar winding

converter could be used, but the need of the second winding stays in contrast to the

supposition made to enable good efficiency and easy and inexpensive production.

The disadvantage of the classic converter is the high number of switches, which

causes high commutation losses. Thus special attention has to be paid on loss

reduction when selecting the devices.

Figure 4.8 shows the topology of the commutation unit. The commutation of phase

one Phi is made by the transistors T1 and T2 together with the diodes D1 and D2

corresponding to the classic converter topology. Phase two Ph2 is commutated by the

transistors T3 and T4 together with the diodes D3 and D4. The zener diode Z is to


protect against voltage peaks which can appear by sudden changes of the load or

during the switch-off time of transistors because of parasitic inductances.

T3 iT1 i

Figure 4.8: Commutation unit topology

Generally, commutation units of switched reluctance machines need a capacitor filter

to smooth the low-frequency link current. This can be done by using a large

capacitor, but it can be renounced here because the battery U has a huge capacity

itself.

4.2.2 Transistors

Power MOSFETs are most suitable for this commutation unit because they can

switch the high currents. Another reason is the low driving power because they are

voltage controlled and thus only a small current is needed for the control. Also the

frequency range and the switching times fulfil the demands. The chosen transistor

type is the SEMITRANS M power MOSFET module SKM 101 AR which is

produced by SEMIKRON. It is an N-channel enhancement mode MOSFET. The data

sheet is included in reference [46] and the most important absolute maximum ratings

and characteristic values are summarised in table 4.5. In context with the table it

should be mentioned that the given switching times can be used for rough


orientation. Exact values can only be measured in the practical circuit because they

depend on the base and collector current waveform.

Table 4.5: Maximum ratings and characteristics of SEMITRANS M power

MOSFET module SKM 101 AR

Maximum drain-source voltage U DS = 50 VMaximum continuous drain current 7d = 200 APeak value of pulsed drain current /dm = 600 AMaximum gate-source voltage t/ gs = 20 VDrain-source on-resistance R DS(on) — 3 m£2Internal parasitic inductance L ds = 20 nHTurn-on time ron = 540 nsTurn-off time t off =960 nsMaximum junction temperature Tj=150°C

It can not be seen in the table if the MOSFET is capable of tolerating the current

waveform shown in figure 4.6 because the peak current is higher than the maximum

continuous drain current. On the other hand, it is lower than the maximum peak value

of a pulsed drain current, but the current of 600 A is allowed to flow for only the

maximum time of 1 ms and that non-repetitive. The most important limiting value

concerning the permissible current rating of a power MOSFET is the maximum permissible junction temperature Tcmax- Hence, if the maximum permissible junction

temperature is not exceeded, the transistor will operate properly. It can be calculated

byAmax = A ~ Apeak Ahjc (4.11)

with the maximum junction temperature 7j given in table 4.5, Prpeak as the peak of

the transistor leakage power and Pthjc as the thermal resistance under pulse

conditions. The peak of the leakage power equals to

Apeak = Apeak % A>S(on) ’ (412)

because for a MOSFET in the fully conducting state the voltage is proportional to the

current and thus it behaves like an ohmic resistance. This is described by the

on-resistance Pcston) which increases with the junction temperature. This is taken into

account by the factor of 2 in the equation, because at a junction temperature close to

150 °C its value is almost double compared to the case temperature of 25 °C. The

thermal resistance under pulse conditions is a function of the pulse duration rp and

can be taken from Fig. 52 on page B6-6 of reference [46]. It equals to 0.015 °C/W for

the pulse duration of 1.5 ms and a duty cycle D of 0.06. Then the peak leakage power


is 390 W, and the maximum permissible junction temperature is 144 °C. Thus the

current can be tolerated if the junction temperature is kept below this limit.

The peak voltage which will arise from the current drop during turn-off of the

transistor has to be observed, as well. Its maximum value is not allowed to exceed

the maximum drain-source voltage Uus- Thus the inequation

us+L^ <yDS (4.13)dt (off)

must be fulfilled with U$ as the supply voltage and Lds as the internal parasitic

inductance. If the current is assumed to fall linearly the minimum allowed turn-off

time /off can be approximated to

AaS^Tpeak^off > uDS~us

(4.14)

and its value is around 145 ns. Compared with the turn-off time of 960 ns of the

transistor given in table 4.5 this value is much lower and thus it is insured that the

voltage peak caused by the internal parasitic inductance will not exceed the

maximum drain-source voltage. It should be mentioned that the parasitic inductances

of the connecting wires were neglected in this calculation. In addition the zener diode

is responsible for ensuring the safety of the transistors and diodes towards. high

frequency voltage peaks.

Concerning the commutation losses it is important that the transistor has a very low

on-resistance because it determines the losses. This is given by the chosen type,

because an on-resistance of 3 m£2 is very low for a MOSFET. Finally, it can be

concluded that the chosen MOSFET type fulfils the set demands.

4.2.3 Diodes

Schottky diodes are most suitable here because they can tolerate the high currents and

compared with other diodes they have a lower forward voltage drop, which effects

significantly on the commutation losses. Other reasons are the low capacitance,

absence of stored charge, zero switching losses and the fact that they can withstand

reverse voltage transients. The chosen diode type is the PBYR40045CT which is

produced by PHILIPS. It is a schottky barrier double rectifier diode. The data sheet is

included in reference [39] and the most important absolute maximum ratings and

characteristic values are summarised in table 4.6.


Table 4.6: Maximum ratings and characteristics of PHILIPS schottky diode

PBYR40045CT

Maximum continuous reverse voltage C7r = 45 VMaximum repetitive peak reverse voltage U rrm = 45 VMaximum output current Io — 400 AMaximum repetitive peak forward current per diode 7FRM = 3000 AMaximum forward voltage (200 A, 25 °C) UF = 0.69 VTypical forward voltage (200 A, 125 °C) UF = 0.58 VMaximum forward voltage (200 A, 150 °C) UF = 0.63 VTypical forward voltage (400 A, 125 °C) I/F = 0.75 VMaximum reverse current (25 °C) 7R = 4mAMaximum reverse current (125 °C) 7r = 400 mAMaximum junction temperature T, = 150 °C

The table shows that this diode can tolerate the high current whose waveform was

shown in figure 4.7 because its peak is even lower than the maximum continuous

output current. The low forward voltage has a very positive effect on the losses

because it causes the main part of the commutation loses. It is only 0.75 V at high

current and decreases with a lower current.

4.2.4 Zener Diode

The zener diode is to protect the commutation unit from voltage peaks which can

appear because of sudden changes of the load or during the switch-off time of the

transistors because of parasitic inductances. It is a semiconductor P-N junction diode that has a controlled reverse-bias breakdown voltage and thus it can be used to clamp

the voltage of the commutation unit and the supply circuit.

The zener diode type chosen is BZY91C18 and is produced by SEMTTRON (see also

reference [11]). It is recommended for transient suppression because of the very short

conducting time of around 5 ns. This is much quicker than the turn-off time of the

transistor and thus it is able to protect against the quick voltage peaks arising with the

transistor switch-off. It also has a high continuous power dissipation of 75 W which

is necessary to protect against the voltage peaks arising with sudden changes of the

load. These voltage peaks are slower but, on the other hand, more powerful than the

peaks arising during the transistor switch-off. A power dissipation of 75 W for the

zener diode should be enough, and higher values are hard to find. For example, if the

generator output is for a short while higher than the demand of the loads, most of the

power is dissipated in the battery because of its very small inner resistance. The diode


has to tolerate only the fast transients. This diode type has a break-down voltage of

18 V. This is a bit higher than the nominal output voltage of the generator of 14 V

but it is usual for transient suppression applications.

4.3 Control System

The control system has to keep the output voltage of the generator constant. The

voltage varies with changes of speed and load. Most suitable is a constant voltage of

14 V. This ensures charging of the battery and provides clearance to its gassing

voltage. The control system can be realised according to the structure shown in figure

3.24. The controller needs voltage and rotor position feedbacks.as input. It derives

the firing angles for the commutation from the voltage error and the speed according

to the control strategy. '

The optimum speed range of the generator is between 1,200 rpm and 12,000 rpm

which is 1.5 times the speed of internal combustion engines of motor vehicles. At

speeds under 1,200 rpm the transistor peak currents are becoming tremendous. Thus

the speed range has to be restricted to this minimum limit. Only small maximum

output power is supplied at speeds over 12,000 rpm but basically the generator is able

to operate above this limit.

The control strategy has to be chosen in a way that the transistor peak currents are

restricted to 250 A. This is necessary at low speeds. It will ensure the safe operation

of the commutation unit. Good efficiency and high maximum output power are also

demanding the choice of the control strategy. In addition the control strategy should

be as simple as possible to make the controller as inexpensive as possible. The

sensing should enable fast reaction and provide sufficient precision.

4.3.1 Control Strategy

The control strategy has to be chosen in the way that both firing angles are controlled.

This is necessary because otherwise the transistor peak currents at low speeds can not

be kept under 250 A. The dwell period has to be enlarged with an increase of speed

or load by changing the control modes. Because of the variation of both firing angles

the control modes can be used in their suitable speed range. This will affect positively on the efficiency.


The control strategy chosen builds on three discrete load levels over different speed

ranges. The load levels are no, medium and maximum output power. The speed

ranges are determined by the maximum output power. They mainly cover 1,000 rpm

ranges except at low and high speeds. Smaller ranges are necessary at low speeds

because the influence of firing angle variations is high. At speeds over 8,000 rpm the

turn-on angle is at its minimum and the turn-off angle at its maximum. Table 4.7

summarises the firing angles for the different load levels over the speed ranges. The

angles in the table are given in mechanical degrees according to the aligned position

of the first phase at 180°. The second phase will be aligned at 270° and thus an angle

of 90° degrees has to be added to the firing angle values in the table for the second

phase. Then the first phase is aligned again at 0° and the second one at 90°.

Table 4.7: Discrete firing angles of the controller for the load levels over the

speed ranges

v/rpm0O / 0c in ° for

no output power0o / 0c in ° for

medium output power0o / 0c in ° for

maximum output1200-1500 180/180 160/210 157/2101500-2000 it " 149/2102000-3000 ii 150/210 142/2103000-4000 ii 140/2154000-5000 u 145/215 139 / 2205000-6000 ii 137/2256000-7000 n 130/2257000-8000 n 135/220 121/2258000-9000 n 115/227

>9000 ii 135/225

The angles at the maximum output power for each speed range are chosen so that

they are optimum for the lowest speed in the range. This will ensure that the peak

currents are limited because they decrease with an increase of the speed. The

disadvantage is that the maximum output power is decreased a bit at the higher

speeds in the range. The angles at medium load are chosen that they provide an

output power between 1.0 kW and 0.5 kW. It decreases with an increase of the speed.

At no output power the turn-on and turn-off angle are identical and thus the dwell

angle is zero, so that no output power is supplied.

The controller has to change the firing angles according to the voltage error and the

speed. The fastest change can be after one stroke if the sensing enables it because this

control strategy can not influence the turn-off angle after the excitation has started. If

the. voltage error AU is between -0.1 V and 0.1 V the output power chosen can be


kept and no change is necessary. Between -0.3 V and -0.1 V the controller has to

change to a higher output level, so that the output voltage will rise. If the voltage

error is between 0.1 V and 0.3 V the output power level has to be decreased to

decrease the output voltage. If the voltage error is less than -0.3 V maximum output

power has to be chosen to protect the battery from becoming discharged. Over a

voltage error of 0.3 V the generator has to be switched off by changing to the no

output power level to ensure that the gassing voltage of the battery is not exceeded.

The changes of the speed have to be done by the controller according to the table.

This strategy will enable in the average all load conditions and keep the output

voltage almost constant. It should be also mentioned that too high output power can

be taken over by the battery for a short while. The battery can also supply a part of

the output power if it is too low.

The precision of the firing angles can be 1° or even less because of the low number

of phases the pole arcs are large compared with other machines. A precision of 0.5°

or 0.25°, as it was mentioned in chapter 3.5, is here not necessary. The tolerance can

be enlarged by choosing the turn-off angle for the maximum output power level at the lowest speed range one or two degrees in advance than mentioned in the table but

with the disadvantage of a decreased maximum output power at these speeds.

4.3.2 Sensing

Direct position sensing is chosen. Indirect sensing with active probing can not be

used because of the low number of phases. State observers demand an expensive

microcomputer and a model of the generator which is not known. It is enough to use

one sensor and obtain the signal from the rotor poles while rotation. The sensor

signal of the shaft position feedback obtained in such way is shown in figure 4.9. The

high level is made by the rotor poles.

£■ stroke

— zhigh

■ low

Figure 4.9: Sensor signal of the shaft position feedback

The period of one revolution is


T = 60(4.15)

the period of the high level is

the period of the low level is

and the excitation period is

60 9c-90 exc v 2tc

(4.16)

(4.17)

(4.18)

with v as the speed in rpm. The unit of the results is seconds. From equation (4.15)

the period of one stroke can be calculated by

T =■‘stroke N.(4.19)

strokes/rev

Table 4.8 shows the periods of time for different speeds. It can be seen that the stroke

period is shorter than the low level period. This has the disadvantage that the sensing

is too slow to enable the controller to react after each stroke. The delay will be

utmost two strokes. At speeds between 1,200 rpm and 1,500 rpm a delay of one

stroke can be realised if the sensor is placed in the right position because of the short

excitation period. The position for the sensor can be calculated by

0S = 2^1 - —j - 0O • (4.20)

and it is equal to 70.5°. A good position for the sensor then is 65° to provide some

clearance to the limit. This enables fast control after one stroke at the smallest speed

range, where it is most necessary, because of the high transistor peak currents and the

long period of one stroke. This should be fast enough for motor vehicle applications

because speed changes of the driving engine are quite small within the delay time of

the sensing because of the high inertia.

Table 4.8: The periods of time for different speeds

v/rpm 1200 1500 3000 6000 9000 12000T tot / ms 50 40 20 10 6.66 5T high / HIS 6.6 5.28 2.64 1.32 0.88 0.66T low / ms 18.4 14.72 7.36 3.68 2.45 1.84T stroke / mS 12.5 10 5 2.5 1.665 1.25T exc / ms 7.36 6.78 4.167 2.638 2.074 1.556

84

5 Simulation Results

The simulation results are obtained by simulations with the PC-SRD. They describe

the performance of the whole system including generator, commutation and control. The results are put together in a way that shows the system behaviour versus the

speed range and different load conditions. The speed range spans from 1,200 rpm to

12.000 rpm and the output power is varied in the four steps of 0.1 kW, 0.5 kW,

1.0 kW and the maximum output power. The maximum output power versus speed is

shown in figure 5.1. It is important to mention that the nominal output power of

1.5 kW is not reached at low and high speeds because it influences other

characteristic values and will be noticed in the following figures.

1600 T

1400 --

1200 --

1000 --

800 - •

600 - -

400 - -

200--

1000 2000 3000 4000 5000 6000 7000 8000 9000 10000 11000 12000

Figure 5.1: Maximum output power versus speed

The output power is kept constant or at its maximum to imitate the influence of the

controller. This is done by varying the firing angles. The turn-off angle is varied

throughout its range in 5° steps and the turn-on angle in 1° steps to reduce the

simulation effort with the PC-SRD. Otherwise many simulation runs have to be made

until the desired output power is obtained and different solutions are possible. At low

speeds and under maximum output power the turn-on angle is exceptionally varied in

0.5° steps, because the reaction of the generator on the control of the angles is more

sensible. The summary of the results is distinguished into input, output and inner

characteristics, efficiency and losses. The figures are derived from the tables included

in Appendix D. Also the waveforms of some dimensions are presented for different

speeds. The speeds are chosen to 1,200 rpm, 4,500 rpm and 9,000 rpm to cover the whole range.

Chapter 5: Simulation Results 85

5.1 Input

The generator input consists of mechanical and electrical input. Mechanical input is

the shaft torque provided by the driving machine. The shaft power corresponds with

it. Electrical input is the excitation current supplied by the battery. It builds up the

magnetic field.

The average shaft torque versus speed is shown in figure 5.2 for the four load

conditions. It can be seen that it decreases significantly with the speed and depends

also on the load. Less output power has to be provided with lower load and thus the

mechanical input decreases, because only the mechanical input is converted to output

power. The shaft torque decreasing with the speed can be explained by the equation

7'shaft CO = f shaft together with figure 5.4. As the figure shows, the shaft power is

almost constant over the speed range and thus the shaft torque indirectly proportional

to the angular velocity. This explains the curve shape in figure 5.2.

T Shaft/Nm14.0 T

13.0-

12.0" —max (1.5 kW)11.0 - —1.0 kW10.0- —0.5 kW9.0-

— 0.1 kW

7.0--6.0 - -

5.0-

4.0 - -3.0-2.0-

1000 2000 3000 4000 5000 6000 7000 8000 9000 10000 11000 12000

Figure 5.2: Average shaft torque versus speed for different load conditions

The shaft torque at the maximum load is partly influenced by the maximum output

power decreased at low and high speed. At low speeds it rises with the speed until the

nominal output power is supplied. At this point the shaft torque is at its maximum.

Also at high speeds it is lower than expected for the same reason. The curve differs a

bit from the ideal shape at low speeds because of the sensitivity of the generator

related to the control. The firing angles are not chosen accurately enough because

otherwise, as already mentioned, the simulation effort would be tremendous. This can


be, and sometimes even better, noticed from the other figures included in this

chapter.

Besides the average shaft torque, the waveform of the torque is of interest. It is

shown in figure 5.3 for three speeds at the maximum output power. Actually, the

total torque of both phases and the torque of just one phase is included, but in parts

(a) and (b) it can not be noticed because they overlap totally. This can be explained

by the total independence of the phases at these speeds. Thus the waveforms of single

phases are just added to the total waveform. They do not affect each other. The

difference can be seen only in part (c) of the figure. The torque of single phases

intersects and thus the total waveform does not overlap.

The figure shows that the torque is pulsating and has quite high peaks. With an

increase of the speed the peak is getting sharper but its maximum value is decreasing.

The comparison of the peak value with the average torque shows that their ratio is

increasing with the speed from around 2.5 up to 9.5. Compared with the. output

torque produced by the internal combustion engine of a motor vehicle for driving, the

average torque and the peak torque are small. Thus the pulsating torque will cause

just a small ripple and is not a problem in this kind of application.

The peak is also a bit postponed because of the postponed turn-off angle. The

turn-off angles for the different speeds are (a) 210°, (b) 220° and (c) 227°. It can be

seen that the torque is taken over already before the turn-off angle. It is stored in the

field energy at first because it can not be delivered to the supply before the turn-off of

the transistors. At 9,000 rpm the waveform for a single phase shows a positive torque

which is produced by the supply current because of the turn-on angle far before the

aligned position caused by the long dwell control mode. This positive torque overlaps

with the negative torque of the other phase. It is taken straight over by it and thus it is

not wasted.

The average shaft power is shown in figure 5.4. It is constant over the speed range for

a constant output. At the maximum output power it is not constant because of the not

always reached nominal output power. The waveform has almost the same shape

than the waveform of maximum output power. This quite similar behaviour of input

and output points towards almost constant total losses versus speed and load.


(a)Torque versus rotor position

< Nm ) x l.Uel

1.-0.40-

-0.80-

-1.20-

-1.40-

-2.00-

-2.40-

-2.80-

-3.20-

10 1.60 3.60

Rotor position ( dea ) x 1.0e2

(b)

Torque versus rotor position< Nm > x l.Oel

1.-0.40-

-0.80-

-1.20-

-1.40-

-2.00-

-2.40-

!0 2 --------------------------------------- 2"80

Rotor position < dea > x 1.0e2

(C)

Torque versus rotor position< Nm > x l.Oel

0.-0.25-

-0.50-

-0.75-

-1.00-

-1.26-

-1.60-

-1.75-

10 1.00—2.00 3.20

Rotor position ( deq > x 1.0e2

Figure 5.3: Shaft torque versus rotor position for (a) 1200 rpm, (b) 4500 rpm and(c) 9000 rpm at the maximum output power

Electrical input is necessary to build up the magnetic field. This is done by the excitation current provided by the supply. The excitation current versus speed for the

different load conditions is shown in figure 5.5. The figure shows that the excitation

current is high at low speeds. This is caused by the small back-EMF which enables

an increase of the excitation current forced by the almost full supply voltage. The

reason for this small back-EMF is that the excitation takes part around the aligned

position at low speeds. Close to the aligned position the inductance remains nearly


constant and only a changing inductance generates a sufficient back-EMF which

consumes part of the supply voltage.

P shaft/W — max (1.5 kW)2000 T 1.0 kW

0.5 kW1800--0.1 kW

1600 - -

1400 --

1200 - -

1000--

800 -

600 -

400 - -

200--

1000 2000 3000 4000 5000 6000 7000 8000 9000 10000 11000 12000

Figure 5.4: Average shaft power versus speed for different load conditions

—max (1.5 kW) —1.0 kW —0.5 kW — 0.1 kW

1000 2000 3000 4000 5000 6000 7000 8000 9000 10000 11000 12000

Figure 5.5: Excitation current versus speed for different load conditions

At medium speeds the excitation current is at its minimum, because the back-EMF is

bigger because of the advanced beginning of the excitation. Another main influence

on the excitation current besides the back-EMF is the control mode, and the normal

control mode is still used at medium speeds. The advantage of the normal control

mode is that only a very small positive torque is produced and its influence on the


excitation current can not be noticed. For low output power the excitation current

stays at its minimum also at high speeds because the normal control mode can be

used over the whole speed range.

At higher speeds the control mode changes to boost mode and the positive torque can

not be neglected any longer. The produced positive torque is quite small and thus the

excitation current increases only slightly. At high speeds the control mode changes to

long dwell mode and a noticeable positive torque is produced. Thus the excitation

current rises. For maximum output the excitation current decreases even in long

dwell mode at speeds over 8000 rpm because of the not reached nominal output.

The disadvantage of the small back-EMF at low speeds can be noticed also from the

peak of the excitation current. It is shown in figure 5.6, and very high peak currents

appear at slow speeds. The ratio of peak current to average current is around 11 for

output power higher than 500 W. It should be mentioned that already lots of effort

were taken to reduce these current peaks during construction and controller design. These high peak currents are very critical because they almost exceed the limits of

available transistors. Also high voltage peaks can appear during switch-off of the

transistors because of the parasitic inductances (compare chapter 4.2.2). The

behaviour of peak current at higher speeds is similar to the mean current behaviour

for the same reasons. The increase of the peak currents at high speeds and high

output power is again caused by the change of the control modes as it was already

explained for the mean current.

/rpeak/A

—max (1.5 —1.0 kW —0.5 kW — 0.1 kW

250 --

225 -

200-

175 -

150--

125 --

100-

1000 2000 3000 4000 5000 6000 7000 8000 9000 10000 11000 12000

Figure 5.6: Transistor peak current versus speed for different load conditions


5.2 Output

Output is provided by the DC link current. The current is directly proportional to the

output power according to equation Pcu = kc U because of the constant controlled

voltage. Thus it is not shown here because its behaviour versus speed and load is equal to the output power behaviour which is shown in figure 5.7. Of interest are

mainly just the nominal output current of 107 A and the waveforms shown later.

PoutAV —max (1.5 kW)1.0 kW1600 T0.5 kW

1400 -- — 0.1 kW

1200 - -

1000--

800 - ■

600 - -

400 - ■

200--

1000 2000 3000 4000 5000 6000 7000 8000 9000 10000 11000 12000

Figure 5.7: Output power versus speed for different load conditions

The output power is kept constant according to the demands of the load. Above the

power of 1 kW it can not be kept constant over the whole speed range because for

some speeds the maximum output power is then reached. From the curve of

maximum output power it can be seen that the nominal output power can not be

reached over the whole speed range. At low speeds up to 1,400 rpm it has to be

reduced for limiting the excitation peak current. At speeds over 8,000 rpm the output

power is decreasing because the excitation period is too short to enable a sufficient

excitation and it can not be extended above the already reached maximum. In these

cases the battery has to provide the power if an output higher than the maximum is

demanded.

For the use in motor vehicles it is not momentous that the maximum output power is

lower than the nominal output power at these speeds. An output power of 1.25 kW at

the speed of 1,200 is already quite high and at least higher than for alternators. If the

battery gets partly discharged while the combustion engine is at idling speed, it can

be charged again at a higher speeds during driving. The reduced output power at high


speeds does not have a major influence because these speeds are rarely reached. At

the speed of 9,000 rpm the overspeed range of the internal combustion engine starts

(the ratio of 1.5 from generator to engine speed has to be taken into account). It can

be concluded that the generator shows good performance over the speed range and it

is particularly suitable for motor vehicle applications.

Concerning the DC link current the waveform is of interest. Figure 5.8 shows the DC

link current at the speed of 1,200 rpm for the maximum output power. The DC link

current is composed by the transistor and diode currents of both phases. At the speed

of 1,200 rpm almost no phase overlap can be noticed. Thus the positive parts of the

current are almost equivalent to the transistor currents and the negative parts to the

diode currents. The periods of the positive and negative parts are almost the same.

Also it can be seen well in the figure that the current is pulsating and high peaks

appear. The positive peak is 250 A and the negative one is 315 A. On the average the

negative part predominates. Thus the generator delivers output power.

DC Link current

2.00-

1.20-0.80-

2.00 2.401. >0 2.80-0.40--0.80-

-2.00-

Rotor position x 1.0*2

Figure 5.8: DC link current versus rotor position for 1200 rpm at the maximum

output power

Figure 5.9 shows the DC link current at the speed of 4,500 rpm for maximum output

power. At this speed a phase overlap can be noticed. The negative output current

pulse is extended and overlaps with the positive excitation current pulse of the next

phase. The excitation current is straight supplied by the output current pulse of the

previous phase. The peaks are decreased to 85 A and 245 A.


DC Link currentfT x 1.0e2

0.40-

2.40 2.80 3.201. >0

-0.40-

-0.80-

-1.20-

-2.00-

-2.20-

Rotor position x 1.0o2


output power

Figure 5.10 shows the DC link current at a speed of 9,000 rpm for maximum output

power. At this speed the phase currents overlap completely. The turn-on of the

second phase is at an angle of 115° and the first phase is turned off later at an angle of

137°. The positive current pulse is very short now because the negative output current pulse is still more extended and supplies straight the excitation of the other phase. The positive peak is increased again up to 135 A because of the change of the control

mode to long dwell mode. The negative peak is more decreased down to 195 A.

DC Link currentA x 1.01

1.40-

1.20-1.00-0.80-

0.40-

0.20-

1.20 2.00 2.40 2.80 3.20

-0.40-

-1.00--1.20-

-1.80-

Potor positi' 1.0o2


output power


From the comparison of the figures of the DC link current waveforms it can be

concluded that the pulse of the negative output current is extended with the speed.

Also its peak value decreases and the peak appears earlier after commutation.

Respectively the positive pulse is shortened at higher speeds. Its peak value is at the

maximum at low speeds, medium at medium speeds and increases again at high

speeds. The rising time of the current up to the peak increases with higher speeds.

5.3 Phase Current

Figure 5.11 presents the average phase current. It is almost constant versus speed at

not maximum output power. This shows that the losses are almost constant versusspeed because the output current is constant, too. At 1 kW output power the phase

current increases a bit at high speeds. This is caused by the higher excitation current

because of the changed control mode. The phase current at maximum output power is

influenced by the not always reached maximum output power. Thus it decreases at high speeds and is also not at its maximum at low speeds. The increase at speeds

from 5,000 rpm to 8,000 rpm is caused by the higher excitation current for the same

reason than at the lower output power. The phase current is higher at low speeds for

all load conditions because of the very high excitation current.

—max (1.5 kW) —1.0 kW —0.5 kW — 0.1 kW

1000 2000 3000 4000 5000 6000 7000 8000 9000 10000 11000 12000

Figure 5.11: Phase current versus speed for different load conditions

The phase peak current is shown in figure 5.12. It equals the peak of the diode

current. The equality with the diode peak current is obvious because the diode peak

current is much higher than the transistor peak current. The phase peak current has


also almost the same height as the output current. The excitation current of the other

phase overlaps only with the diode current and at the time when the diode current

peak appears is the excitation current still small. Thus the peak value of the output

current is decreased only slightly.

—max (1.5 kW)350 T1.0 kW325 --0.5 kW300 -0.1 kW275 --

250 --225 --200-- ■

175--

150 - -125 --100-

1000 2000 3000 4000 5000 6000 7000 8000 9000 10000 11000 12000

Figure 5.12: Phase peak current versus speed for different load conditions

The figure shows that the peak value decreases with higher speeds and smaller loads.

The ratio of peak to mean value of the phase current is at low speeds between 4.5 and

7.5. It rises with a decrease of the load and is lower at high speeds. The ratio is lower

for the output current because of the higher mean value of the output current resulting

from the two phases. These current peaks are not so problematic than the transistor

current peaks because the diode can easily tolerate them and the diode current is not

switched off at its peak, like the transistor current. The diode current falls steadily

and unforced down to zero after a while.

Figure 5.13 shows the phase current waveform for different speeds. The influence of

the different control modes can be seen clearly by comparison with figure 3.25. The

excitation and output periods increase with higher speeds. At 9,000 rpm the first peak

of the excitation current comes from the produced positive output torque (see also

chapter 3.5.2).


(a)Current versus rotor position

Phase ips ) x 1.0e23.20-]

2.80-

2.40-

2.00-

1.20-0.80-

2.80Rotor position < deg > x 1.0e2

(b)Current versus rotor position

Phase current < amps > x 1.0e22.80-1

2.00-

1.20-

0.80-

2.80 3.20Rotor position < deg > x 1.0e2

(c)Current versus rotor position

Phase current ( amps ) x 1.0e22.00-1

1.50-

1.25-

1.00-0.76-

0.26-

2.000.80 2.40 2.80____ 3.20Rotor position ( deg > • t. 0e2

Figure 5.13: Phase current versus rotor position for (a) 1200 rpm, (b) 4500 rpm and

(c) 9000 rpm at the maximum output power

5.4 Efficiency

Besides the output power, the efficiency shows the superiority of the switched

reluctance generator. Figure 5.14 presents the efficiency of the pure switched

reluctance generator without consideration of the commutation and fan losses. It can

be seen that the generator has a very high efficiency. It reaches for middle output

power 90 % and even sometimes a bit more. At maximum output power it is worst

over most of the speed range but still over 80 % and at high speeds it also reaches

90 %. For low output power the efficiency is high at low speeds but it drops down to


around 80 % at high speeds. The current-depending copper losses are the reason for

the reduced efficiency at high output power. At low output power the windage losses

which increase squared with the speed are becoming significant at high speeds and

thus the efficiency decreases.

h gen in100 T

—max (1.5 kW) —1.0 kW —0.5 kW - 0.1 kW

1000 2000 3000 4000 5000 6000 7000 8000 9000 10000 11000 12000

Figure 5.14: Generator efficiency versus speed for different load conditions

Unfortunately, values for the efficiency of a pure alternator were not found and the

measurement results reported in Appendix A are obtained with the influence of the

controller and fan. The fan losses are estimated from the measurements, but the effort

to measure the commutation losses would be too high. Thus the switched reluctance

generator efficiency can not be compared with the efficiency of a pure alternator.

Figure 5.15 shows the generator efficiency with consideration of the commutation

losses. As expected, this efficiency is lower than the efficiency of the pure generator

shown in figure 5.14. It can be seen that this efficiency is still quite high. It reaches a

maximum of 85 % and is always above 75 %. Its behaviour versus speed and load is

almost equal to the pure generator efficiency. The influence of the load is a bit

stronger because the commutation losses are current dependent.

Compared with the efficiency of an alternator with consideration of the same losses,

which is estimated in Appendix A and shown in figure A.7, the switched reluctance

generator efficiency is a lot higher. The alternator efficiency is around 50 % whereas

the switched reluctance generator efficiency is around 75 %.


77 in %100 T

—max (1.5 kW) —1.0 kW —0.5 kW — 0.1 kW

1000 2000 3000 4000 5000 6000 7000 8000 9000 10000 11000 12000

Figure 5.15: Generator efficiency versus speed for different load conditions with

consideration of the commutation losses

The switched reluctance generator efficiency without consideration of the fan losses

varies only slightly with speed and load. If fan losses are considered the efficiency

will be lower and it will decrease with an increase of the speed. Also it will decrease

with a decrease of the load because the fan losses will become dominant. The

efficiency of the alternator with consideration of the fan losses varies significantly

with speed and load as it can be seen from figure A.5 in Appendix A. It goes down to

very low values under unfavourable conditions. It can be expected that this will not

happen for the switched reluctance generator because its efficiency without

consideration of the fan losses is much higher and the fan losses will be also lower

than for an alternator as it is pointed out in the following chapter.

5.5 Losses

The total losses of the switched reluctance generator can be mainly distinguished into

copper, iron, windage, commutation and fan losses. Simulation results are obtained

by the PC-SRD except for the fan losses and thus the figures in this chapter do not include the fan losses. About the fan losses of the switched reluctance generator it

can be said that they are lower than those of an alternator. The total losses of the

switched reluctance generator are smaller because of the better efficiency. Thus the

heat produced by the losses will be smaller and a less powerful fan can be used.

Hence, the fan itself will produce fewer losses. The fan losses are also positively

affected by the lower absolute speed of switched reluctance generators compared


with alternators, because the fan losses increase intensely with the speed. The

switched reluctance generator operates at a speed of 1.5 times the speed of an internal

combustion engine of a motor vehicle, whereas alternators operate usually at 2 times

the engine speed.

Figure 5.16 shows the losses versus speed for maximum output power. At this load

condition the copper losses are the major part of the total losses because they are

proportional to the square value of the current. Thus the behaviour of the total losses

is mainly influenced by copper losses. They are very high at low speeds because ofthe high excitation current. They are also influenced by the not reached nominal output power and thus they decrease at high speeds. The commutation losses are the

other main fraction of the total losses in this load condition. They are also current dependent but only partly proportional to the square value. Their main part is linear

proportional to the current. Versus the speed they are almost constant and at high

speeds they decrease because of the not reduced output power. The iron and windage

losses can be almost neglected at the maximum output power because they are much

lower than copper and commutation losses.

P l/w —total500 T — copper

—commutation— iron— windage

450-

400 * •

350 - ■

300 -

250 - -

200--

150-

100-

1000 2000 3000 4000 5000 6000 7000 8000 9000 10000 11000 12000

Figure 5.16: Losses versus speed for maximum output power

The losses for an output power of 1 kW are shown in figure 5.17. The copper and

commutation losses still determine the total losses. They are almost in the same

range. Only at low speeds the copper losses exceed the commutation losses because

of the high excitation current. The iron and windage losses are still a small fraction.

Only at high speeds the influence of the windage losses can be noticed by a slight

increase of the total losses.


PJW —total275 T —copper

—commutation— iron— windage

250 -

225 --

200-

175 -

150 -

125 -

100 -

1000 2000 3000 4000 5000 6000 7000 8000 9000 10000 11000 12000

Figure 5.17: Losses versus speed for 1.0 kW output power

Figure 5.18 shows the losses versus speed for an output power of 0.5 kW. The

commutation losses are the biggest fraction of the total losses. They are almost

constant over the speed range. The copper losses are smaller and only as high as the

commutation losses at low speeds because of the influence of the high excitation

current. They decrease with an increase of the speed because less excitation current is

supplied because of the rising back-EMF. Also the control mode is not changed at

this load condition and thus does not cause an increase of the excitation current at

high speeds.

PlAV —total125 T —copper

—commutation —iron —windage100 -

1000 2000 3000 4000 5000 6000 7000 8000 9000 10000 11000 12000



Iron and windage losses are still smaller than the commutation and the copper losses

but they are giving a noticeable contribution to the total losses at this load condition.

The iron losses are almost constant over the speed range whereas the windage losses

increase with higher speeds. The windage losses are dependent on the speed and not

on the current. They increase proportionally to the square value of the speed. This

time the windage losses do not cause a visible increase of the total losses at high

speeds because the copper losses decrease simultaneously.

The losses for the output power of 0.1 kW are shown in figure 5.19. Because of the

small output power, the current is small and thus the current-depending losses are

small, too. The lowest losses are the copper losses. The commutation losses are

highest at low and medium speeds whereas the windage losses are dominating at high

speeds. The behaviour of the total losses is determined by the windage losses already

at middle speeds and significant at high speeds. At low speeds the influence of the

high excitation current can still be noticed.

•Pl/W —total— copper—commutation— iron— windage22--

1000 2000 3000 4000 5000 6000 7000 8000 9000 10000 11000 12000


101

6 Conclusion and Prospects

The task of this work has been to design a low voltage switched reluctance generator

for variable speed applications. As appropriate and main field of application the

generator is considered to be used for the on-board power supply in motor vehicles.

As basis for the designing process the principle and theory of switched reluctance

generators have been worked out. The construction and the commutation unit are

designed in detail. The strategy for the realisation of the control system is given. The

performance of the whole system is presented by the obtained simulation results. An

overview, of the existing technology for variable speed applications has been

presented to complete the expositions of the topic.

The switched reluctance generator, which has been designed in this work, fulfils the

required demands, like high output power and efficiency. It is capable of supplying a

nominal output power of 1.5 kW and the efficiency is above 75 %. These values are

reached almost over the whole speed range and the efficiency varies only slightly

over the output power range. The performance of the generator exceeds the

characteristics of the nowadays alternator technology used. The better efficiency will

affect positively on the fuel consumption of motor vehicles.

Prospective work could be to complete the design of the control system based on the

recommended strategy. The next step then would be to build and investigate a

prototype generator.

102

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[18] Krishnan, R.; Materu, P.N.: “Analysis and Design of Low-Cost Converter forSwitched Reluctance Motor Drives”. IEEE Transactions on IndustryApplications, Vol. 29, No. 2,1993, pp. 320-326.

[19] Le-Huy, H.; Viarouge, P.; Francoeur, B.: “A Novel Unipolar Converter for Switched Reluctance Motor”. IEEE Transactions on Power Electronics, Vol. 5, No. 4, 1990, pp. 469-475.

[20] Lovatt, H.C.; Stephenson, J.M.: “Influence of Number of Poles per Phase in Switched Reluctance Motors”. IEE Proceedings-B, Vol. 139, No. 4, 1992, pp. 307-314.

[21] MacMinn, S.R.; et al.: “Application of Sensor Integration Techniques toSwitched Reluctance Motor Drives”. IEEE Transactions on IndustryApplications, Vol. 28, No. 6,1992, pp. 1339-1343.

[22] Materu, P.N.; Krishnan, R.: “Estimation of Switched Reluctance Motor Losses”. IEEE Transactions on Industry Applications, Vol. 28, No. 3, 1992, pp. 668-679.

[23] Matsuo, T.; Lipo, T.A.: “Rotor Position Detection Scheme for Synchronous Reluctance Motor Based on Current Measurements”. IEEE Transactions on Industry Applications, Vol. 31, No. 4,1995, pp. 860-868.

[24] Michaelides, A.M.; Pollock, C.: “Effect of End Core Flux on the Performance of the Switched Reluctance Motor”. IEE Proceedings of Electric Power Applications, Vol. 141, No. 6,1994, pp. 308-316.

[25] Michels, K.; Schmedes, H.G.: “EinfluB des Generators auf den Kraftstoff- verbrauch”. Motortechnische Zeitschrift, 56. Jahrgang, Nr. 12, 1995, pp. 728-733.


[26] Miller, T.J.E.: “Faults and Unbalance Forces in the Switched Reluctance Machine”. IEEE Transactions on Industry Applications, Vol. 31, No. 2, 1995, pp.319-328.

[27] Miller, T.J.E.: Switched Reluctance Motors and Their Control. Magna Physiscs Publishing and Clarendon Press, Oxford, 1993.

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[29] Miller, T.J.E.; McGilp, M.: “Nonlinear Theory of the Switched Reluctance Motor for Rapid Computer-Aided Design”. IEE Proceedings-B, Vol. 137, No. 6, 1990, pp. 337-347.

[30] Miller, T.J.E.; McGilp, M.: PC-SRD4: User’s Manual. SPEED Consortium, University of Galsgow, 1991.

[31] Miller, T.J.E.; McGilp, M.: “PC CAD for Switched Reluctance Drives”. ElectricMachines and Drives Conference, London, 1987, IEE Conference Publication, No. 282, pp. 360-366.

[32] Moallem, M.; Ong, C.M.: “Predicting the Steady-State Performance of a Switched Reluctance Machine”. IEEE Transactions on Industry Applications, Vol. 27, No. 6,1991, pp. 1087-1097.

[33] Moallem, M.; Ong, C.M.: “Predicting the Torque of a Switched Reluctance Machine from its Finite Element Field Solution”. IEEE Transactions on Energy Conversion, Vol. 5, No. 4,1990, pp. 733-739.

[34] Moallem, M.; Ong, C.M.; Unnewehr, L.E.: “Effect of Rotor Profiles on the Torque of a Switched-Reluctance Motor”. IEEE Transactions on Industry Applications, Vol. 28, No. 2,1992, pp. 364-369.

[35] Moghbelli, H.; Adams, G.E.; Hoft, R.G.: “Performance of a 10-Hp Switched Reluctance Motor and Comparison with Induction Motors”. IEEE Transactions on Industry Applications, Vol. 27, No. 3,1991, pp. 531-538.

[36] Panda, S.K.; Amaratunga, G.A.J.: “Analysis of the Waveform-Detection Technique for Indirect Rotor-Position Sensing of Switched Reluctance Motor Drives”. IEEE Transactions on Energy Conversion, Vol. 6, No. 3, 1991, pp. 476-483.

[37] Panda, S.K.; Amaratunga, G.A.J.: “Waveform Detection Technique for Indirect Rotor-Position Sensing of Switched-Reluctance Motor Drives: Part 1: Analysis”. IEE Proceedings-B, Vol. 140, No. 1, 1993, pp. 80-88.

[38] Panda, S.K.; Amaratunga, G.A.J.: “Waveform Detection Technique for Indirect Rotor-Position Sensing of Switched-Reluctance Motor Drives: Part 2: Experimental Results”. IEE Proceedings-B, Vol. 140, No. 1, 1993, pp. 89-96.


[39] Philips (Publ.): Data Handbook: Power Devices. 1990.

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[41] Pulle, D.W.J.: “New Data Base for Switched Reluctance Drive Simulation”. IEE Proceedings-B, Vol. 138, No. 6,1991, pp. 331-337.

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[46] Semikron (Publ.): Leistungshalbleiter. 1992.

[47] Staton, D.A.; Soong, W.L.; Miller, T.J.E.: “Unified Theory of Torque Production in Switched Reluctance and Synchronous Reluctance Motors". IEEE Transactions on Industry Applications, Vol. 31, No. 2,1995, pp. 329-337.

[48] Steiert, U.: “Drehmomentsteuerung einer Reluktanzmaschine mil beidseitig ausgepragten Polen und geringer Drehmomentwelligkeit". Dissertation Universitat Karlsruhe, 1992.

[49] Vukosavic, S.; Stefanovic, V.R.: “SRM Inverter Topologies: A Comparative Evaluation”. IEEE Transactions on Industry Applications, Vol. 27. No 6. 1991, pp. 1034-1047.

[50] Wallace, R.S.; Taylor, D.G.: “A Balanced Commutator for Switched Reluctance Motors to Reduce Torque Ripple”. IEEE Transactions on Power Electronics, Vol. 7, No. 4,1992, pp. 617-626.

[51] Wu, C.Y.; Pollock, C.: “Analysis and Reduction of Vibration and Acoustic Noise in the Switched Reluctance Drive”. IEEE Transactions on Industry Applications, Vol. 31, No. 1,1995, pp. 91-98.

106

Appendix A: Measuring Results of an Alternator

A commonly used claw-pole alternator with a nominal output power of 770 W has

been examined. Over a speed range from 1,340 to 10,400 rpm the root-mean-square

of the output voltage, the torque, the mechanical input power and the

root-mean-square of the output current have been measured under different load

conditions. The generator was first driven by a solid rotor high-speed induction

motor, but to examine a broader speed range another induction motor was used as

driving machine at slow speeds. A 12 V battery was used as excitation power supply. The measurement set-up was made according to Figure 2.4.

With the solid rotor high-speed induction motor as driving machine, the lowest

measurable speed was 3,000 rpm because the induction motor was not able to

produce the necessary torque and stopped when the load was switched on. Thus

another series of measurements was made with the driving motor for low speeds. The

low speed limit was then caused by the generator because it was not capable of

producing the necessary output for the excitation. At speeds over 10,000 rpm the

vibrations of the test rack were getting so high that it would have been dangerous to

continue to increase the speed.

Four different load conditions have been measured. At first the measurements were

made without any extra load - just the battery and the excitation. The measured

values and the derived results for the output power and efficiency are included in the

tables A.1 and A.2. The tables show that the output current for the high speed

measurements was higher, because the battery was less charged. The results would be

more comparable if the output current had the same value, but to get a general

impression of the generator performance the results are useful.

Starting from this “no extra load”-condition the load was increased in three steps

until the nominal output current was generated. The results for the “load 1’’-condition

are shown in the tables A.3 and A.4. The results for the “load 2”-condition can be

seen in the tables A.5 and A.6. The most convincing results were reached at the

nominal output and they are included in the tables A.7 and A.8. For an actual

comparison of the different load conditions it should be mentioned that the output

voltage is decreased a bit with higher load and higher output current respectively.

This is caused by the higher voltage drop of the rectifying diodes at higher currents.

The tables mentioned already include all the necessary information but for a better

understanding and overview the important values are concluded in figures A.1, A.2,

Appendix A: Measuring Results of an Alternator 107

A.3 and A.5. Figure A.l shows the absolute value of the torque versus speed for the

different load conditions. It can be seen that the input torque shows a different

behaviour according to the load condition. At low loads the torque increases mainly

with the increase of the angular velocity but at high loads the torque decreases with

the velocity. The effect at low load is caused by the increase of losses, especially the

fan losses (see below). At high load the influence of the losses can not be seen this

straight from the torque behaviour because the high output power dominates the

behaviour and less torque is generally needed at higher speeds.

abs(7)/Nm5.0 T —no extra load

— load 1 —load 2 —loads

4.5 --

4.0"

3.5 -

3.0--

2.5--

2.0-

1.0--

1000 2000 3000 4000 5000 6000 7000 8000 9000 10000 11000

Figure A.1: Absolute value of torque versus speed for the different load conditions

Figure A.2 shows the absolute value of the mechanical input power versus speed for

the different load conditions. This figure illustrates the influence of the losses better

than the previous one because the contrary influence of the angular velocity is not

affecting the mechanical input power. It can be seen that the mechanical input power

increases for all load conditions with the increase of speed. This is caused by the

speed-depending increase of the losses.

Figure A.3 concludes the output power versus speed for the different load conditions.

It can be seen that the output power is held almost constant over a very broad speed

range and only at slow speeds some problems occur for high loads. At low loads the

generator is able to deliver the necessary output through the whole speed range but at

“load 2”-condition the generator is not able to produce the output power at speeds

under 2,000 rpm and at “load 3”-condition at speeds under 2,500 rpm. Thus only the

maximum reachable output current was measured for the “load 3”-condition under


2,500 rpm (see Table A.8). It is impossible to get other values, because the load is

overtaken by the battery and thus it is quickly discharged. With the discharge of the

battery the voltage drops quickly and useful results can not be measured anymore.

abs(f mech)/W

2500 T

2000 --

1500 --

1000--

— no extra load— load 1 —load 2— load3

500 -

1000 2000 3000 4000 5000 6000 7000 8000 9000 10000 11000

Figure A.2: Absolute value of mechanical input power versus speed for the

different load conditions

P outAV

900 T

800 - -

700 --

600 -

500--

—no extra load — load 1 —load 2 —load 3

400 - -

300 - -

200--

1000 2000 3000 4000 5000 6000 7000 8000 9000 10000 11000

Figure A.3: Output power versus speed for the different load conditions

Figure A.4 shows the maximum output current versus speed. The current curve has

the same behaviour than expected in the theory (compare Figure 2.5). Especially

remarkable is that the nominal current can only be reached at speeds higher than


3,000 rpm. Under this speed the maximum output current decreases rapidly with a

decrease of the speed. This behaviour explains the low maximum output power of

alternators at low speeds.

I max/A

1000 2000 3000 4000 5000 6000 7000 8000 9000 10000 11000

Figure A.4: Maximum current versus speed

Most convincing is figure A.5. It illustrates the efficiency versus speed for different

load conditions^ It can be seen that the efficiency goes down with the increase of the

speed independently of the load condition. The low efficiency for the “no extra

load"-condition is not very convincing because almost no output power is supplied.

Only the battery is slightly charged. Almost all the mechanical input power is needed

straight to cover the losses, especially at high speeds. At low speeds quite a good

efficiency is reached for all load conditions but at high speeds the efficiency is rather

poor. The maximum efficiency reached is 65 %. This is quite good, but the maximum

efficiency at nominal output is only 50 %.

The large decrease of the efficiency with an increase of the angular velocity indicates

that some of the losses are highly speed-depending. The fan losses are the most

reasonable explanation because the air resistance is highly speed-depending. To

estimate the fan losses two more measurement series were made with the driving

machine for high speeds. The first series was with the excitation turned off and for

the second series also the fan was taken away. The results are included in the tables A.9 and A. 10. From these results the fan losses can be estimated and they are

included in table Aril.


77 in %70.0 T — no extra load

— load 1

— load 2— load 3

60.0 - -

50.0 - -

40.0 - -

30.0 - -

20.0 - -

10.0-

1000 2000 3000 4000 5000 6000 7000 8000 9000 10000 11000

Figure A.5: Efficiency versus speed for the different load conditions

Figure A.6 illustrates the measurement results and the derived fan losses. It can be

seen that the fan losses are the major part of the losses. Especially at high speeds they

rise very high up to 680 W at 8,000 rpm and at higher speeds even more. The curve

for the measurement results without excitation and fan shows the height of the rest of

the losses but it is difficult to distinguish them. They are mainly frictional losses in

the bearings and particularly the speed-depending part of the losses seems to be from

the air resistance of the clutches between the alternator and the driving machine.

abs(Pmcch)/W1200 T

— estimated fan losses —no excitation— no excitation and no fan

1000 --

800 --

600 --

400 --

200 --

4 v/rpm

Figure A.6: Absolute value of mechanical input power versus speed for the not

excited generator with and without fan and estimated fan losses


Finally, after estimation of the fan losses the alternator efficiency without

consideration of the fan losses can be estimated. It is shown in figure A.7 for nominal

output. Its value is around 50 % and decreases slightly with the speed.

77 in %

Figure A.7: Estimated efficiency versus speed at nominal output power without

fan losses

The tables of the measuring results are following on the next pages.


Table A. 1: Measuring results of the alternator without extra load at high speeds

v/rpm TfNm f rms/A C/rms/V P mech/W P out/W 77 in %3043 -0.736 6.8 14.10 -234.6 95.9 40.93498 -0.802 8.8 14.15 -293.8 124.5 42.44010 -0.766 8.2 14.12 -321.7 115.8 36.04507 -0.714 7.7 14.11 -337.0 108.6 32.25002 -0.722 7.6 14.11 -378.2 107.2 28.45502 -0.718 7.0 14.11 -413.7 98.8 23.95980 -0.760 6.9 14.10 -475.9 97.3 20.46519 -0.814 6.4 14.10 -555.7 90.2 16.26969 -0.854 6.2 14.11 -623.2 87.5 14.07399 -0.948 6.1 14.10 -734.6 86.0 11.78075 -1.124 5.6 14.10 -950.4 79.0 8.38836 -1.180 4.9 14.13 -1013.7 69.2 6.89177 -1.328 5.5 14.11 -1158.1 77.6 6.79691 -1.228 5.2 14.11 -1064.4 73.4 6.9

10391 -1.382 5.4 14.11 -1290.1 76.2 5.9

Table A.2: Measuring results of the alternator without extra load at low speeds

v/rpm r/Nm / rms/A C/ms/V f mech/W P out/W 77 in %1340 -0.83 2.9 14.22 -116.5 41.2 35.41500 -0.65 2.8 14.20 -102.1 39.8 38.92000 -0.42 2.5 14.19 -88.0 35.5 40.32500 -0.35 2.9 14.18 -91.6 41.1 44.93000 -0.29 2.5 14.19 -91.1 35.5 38.93500 -0.28 2.7 14.20 -102.6 38.3 37.44000 -0.30 3.3 14.18 -125.7 46.8 37.2


Table A.3: Measuring results of the alternator for load 1 at high speeds

v/rpm 7YNm ■^rms/A t/rms/V P mech/W Pout/W 77 in %3008 -1.236 13.5 14.08 -389.3 190.1 48.83500 -1.188 14.9 14.10 -435.4 210.1 48.34012 -1.102 14.3 14.06 -463.0 201.1 43.44505 -1.012 13.5 14.07 -477.4 189.9 39.85001 -0.990 13.7 14.07 -518.5 192.8 37.25508 -0.966 13.3 14.06 -557.1 187.0 33.66016 -0.980 13.0 14.06 -617.4 182.8 29.66515 -1.008 12.7 14.07 -687.7 178.7 26.07008 -1.048 12.6 14.08 -769.1 177.4 23.17550 -1.140 12.5 14.08 -901.3 176.0 19.58010 -1.336 12.0 14.07 -1120.7 168.8 15.18824 -1.334 11.5 14.10 -1138.8 162.2 14.29166 -1.500 12.0 14.07 -1305.8 168.8 12.99681 -1.378 11.9 14.06 -1199.9 167.3 13.9

10379 -1.494 12.0 14.06 -1330.8 168.7 12.7

Table A.4: Measuring results of the alternator for load 1 at low speeds

v/rpm r/Nm ^rms/A t/rms/V P mech/W P out/W rj in %1340 -1.81 8.0 13.90 -254.0 111.2 43.81500 -1.65 10.0 14.11 -259.2 141.1 54.42000 -1.09 10.3 14.06 -228.3 144.8 63.42500 -0.85 10.3 14.07 -222.5 144.9 65.13000 -0.72 10.0 14.05 -226.2 140.5 62.13500 -0.66 10.1 14.05 -241.9 141.9 58.74000 -0.61 10.5 14.06 -255.5 147.6 57.8



v/rpm 77Nm ■^rms/A C/rms/V P mech/W P out/W Tj in %3000 -2.974 34.5 13.98 -934.3 482.3 51.64009 -2.498 35.8 14.01 -1048.7 501.6 47.84503 -2.286 35.5 14.03 -1078.0 498.1 46.25008 -2.132 35.1 13.99 -1118.0 491.0 43.95505 -2.016 35.0 13.99 -1162.1 489.7 42.16001 -1.906 34.7 13.99 -1197.7 485.5 40.56495 -1.864 34.1 14.00 -1267.7 477.4 37.76996 -1.858 34.5 14.01 -1361.2 483.3 35.57557 -1.892 34.2 14.00 -1497.4 478.8 32.08063 -2.010 33.5 13.99 -1697.1 468.7 27.68770 -1.970 33.5 14.00 -1673.1 469.0 28.09110 -2.168 33.8 13.99 -1864.1 472.9 25.49627 -1.990 33.4 13.96 -1721.8 466.3 27.1

10326 -2.046 33.5 13.96 -1817.8 467.7 25.7


v/rpm r/Nm •^rms/A U rms/V P mech/W P out/W 77 in %2000 -4.10 34.0 14.03 -858.7 477.0 55.62500 -3.00 32.6 13.98 -785.4 455.7 58.03000 -2.48 32.8 13.98 -779.1 458.5 58.93500 -2.14 32.5 13.99 -784.4 454.7 58.04000 -1.93 32.8 14.00 -808.4 459.2 56.8



v/rpm 77Nm ■f rms/A t/rms/V P mech/W Pout/W 77 in %3611 -4.808 57.5 14.14 -1818.3 813.1 44.74493 -3.592 55.0 13.98 -1689.9 768.9 45.54994 -3.518 54.0 13.95 -1839.7 753.3 40.95496 -3.204 53.9 13.95 -1844.1 751.9 40.85999 -3.138 54.5 13.96 -1971.3 760.8 38.66473 -3.054 54.2 13.96 -2070.3 756.6 36.56997 -2.994 54.2 13.96 -2193.9 756.6 34.57518 -2.884 53.4 13.95 -2270.6 744.9 32.88022 -2.800 53.7 13.96 -2352.1 749.7 31.98688 -2.780 53.4 13.95 -2362.1 744.9 31.59028 -2.850 54.0 13.97 -2469.4 754.4 30.59543 -2.754 53.6 13.93 -2382.4 746.6 31.3

10249 -2.736 53.5 13.92 -2465.7 744.7 30.2


v/rpm T/Nm 7 rms /A 7/ rms/V P mech/W P out/W 77 in %1340 10.01500 14.02000 34.02500 -4.52 45.5 13.11 -1183.3 596.5 50.43000 -4.71 52.5 13.86 -1479.7 727.7 49.23500 -4.49 55.4 14,01 -1645.7 776.2 47.24000 -3.80 55.0 13.95 -1591.7 767.3 48.2


Table A.9:

Table A.10:

Measuring results of the alternator without excitation at high speeds

v/rpm 77Nm P mech /W3000 -0.32 -1013500 -0.37 -1364000 -0.42 -1764500 -0.48 -2265000 -0.55 -2885500 -0.62 -3576000 -0.70 -4406500 -0.78 -5317020 -0.87 -6407475 -0.99 -7758015 -1.16 -9748500 -1.30 -1157

Measuring results of the alternator without excitation and fan at high

speeds

v/rpm T/Nm -Pmech/W3000 -0.08 -253500 -0.08 -294000 -0.09 -384505 -0.09 -425000 -0.11 -585495 -0.13 -756000 -0.14

OO

oot

6505 -0.15 -1027000 -0.22 -1617500 -0.26 -2048005 -0.35 -293


Table A.ll: Derived fan losses from the alternator measurements

v/rpm P mech/W3000 753500 1054000 1404500 1855000 2305500 2806000 3506500 4307000 4807500 5708000 680

118

Appendix B: True Scale Figures of the Generator

Scale:mm

Figure B.l: Cross section of the generator

Appendix B: True Scale Figures of the Generator 119

Scale: 1:1 Unit: mm

Figure B.2: Longitudinal cross section of the generator

120

Appendix C: Conclusion of Characteristic and Dimension

Values

Nominal voltage

Nominal current

Nominal output power

Minimum speed Maximum speed

Number of stator poles

Number of rotor poles

Shaft radius

Minor rotor radius

Rotor radius

Radius of stator slot bottom

Stator outside radius

Stack length

Overall length

Air gap length

Stator pole arc

Rotor pole arc

Radius of comer at stator slot bottom

Lamination stacking factor

Layer thickness of the lamination stacking

Number of parallel path per phase

Number of turns per pole

Slot fill factor

Thickness of insulation layer

Slot area

Copper area

Direct-current phase resistance (20 °C)

Direct-current phase resistance (90 °C)

Iron weight

Copper weight

Total weight

Moment of inertia

Z7n=14V

7n= 107 A

PN= 1.5 kW

Vmin= 1,200 rpm

Vmax= 12,000 rpm

Ns = 4

Nr= 2

RSh = 10 mm

Ro = 24 mm

R\ = 37.5 mm

i?2 = 56 mm

i?3 = 74 mm

L$tk = 75 nun

Le= 133.5 mm

<5= 0.3 mm

A = 45°

A =47.5° r-5 mm

/stk = 0.97

rstk= 0.5 mm

Npath = 1

Nv = 12

Sfin= 0.576

d = 0.2 mm Asiot= 786 mm2

Acu = 226 mm2

PphDC(20) = 6.3 m£2

PphDC(9o> =8.0 mQ WFe= 6.7 kg

Wcu = 2.4 kg

Wtot= 9.1 kg / = 7.94*10"4 kgm2

121

Appendix D: Tables of the Simulation Results

Table D.l: Simulation results of the generator at maximum output power (part 1)

v/rpm T shaii/Nm P shaf/W T] gen HI % I dc/A 6oin° 0cin° fiVW P ou,/W 77 tot in %1200 13.0 1633 82.8 89.5 157 210 408 1253 76.71300 13.5 1840 82.5 100.5 153 210 461 1407 76.51400 13.3 1954 82.9 107.0 150 210 479 1498 76.71500 12.0 1881 84.2 105.0 149 210 432 1470 78.12000 9.0 1877 86.3 107.5 142 210 384 1505 80.23000 5.7 1801 87.9 105.0 140 215 340 1470 81.64500 3.8 1799 88.8 106.0 135 220 324 1484 82.56000 2.9 1824 88.8 107.5 130 225 335 1505 82.57000 2.5 1827 88.8 107.5 121 225 336 1505 82.48000 2.0 1716 88.0 100.0 115 227 337 1400 81.69000 1.6 1537 88.8 90.5 115 227 289 1267 82.4

12000 0.9 1176 90.1 70.0 115 227 205 980 83.3

Table D.2: Simulation results of the generator at maximum output power (part 2)

v/rpm / p/A /pocak/A IcJA /rocak/A I Doeafc/A fcu/W PeVW P cott/W Pwit/W1200 67.0 315 22.6 253 315 263.5 17.7 126.4 0.141300 73.8 334 23.9 253 334 302.3 19.0 139.1 0.171400 76.8 341 23.5 237 341 315.1 19.5 143.9 0.201500 72.6 327 20.3 196 327 279.1 18.8 134.1 0.232000 69.7 307 16.1 113 307 238.9 17.9 127.0 0.403000 66.1 275 13.7 86 275 202.3 15.6 120.9 0.904500 67.0 246 14.0 97 246 184.2 15.2 122.6 2.036000 71.4 231 17.9 144 231 185.3 15.6 130.4 3.607000 73.5 221 19.9 132 221 182.3 16.6 132.1 4.908000 73.7 216 24.0 153 216 182.6 17.3 130.5 6.409000 66.1 194 21.1 134 194 147.3 16.6 116.5 8.10

12000 50.7 150 15.7 97 150 86.7 15.1 88.4 14.40

Table D.3: Simulation results of the generator at 1 kW output power (part 1)

v/rpm T shafi/Nm P shaf/W 7? sen in % /dc/A 0o in" 0c in" P u=t/W Pout/W 7? tot in %1200 9.66 1214 85.8 69.2 162.5 210 264 " 969 79.81300 8.96 1219 86.5 70.1 161.0 210 253 981 80.51400 8.36 1226 87.1 70.9 159.5 210 247 993 81.01500 7.86 1235 87.5 71.8 158.0 210 242 1005 81.42000 5.81 1217 88.8 71.7 152.0 210 220 1004 82.53000 3.84 1207 89.9 71.8 142.0 210 205 1005 83.34500 2.54 1195 90.8 71.9 140.0 215 191 1007 84.26000 1.86 1165 91.4 70.5 131.0 215 181 987 84.77000 1.62 1184 91.6 71.9 135.0 220

OO 1007 85.0

8000 1.41 1185 91.7 72.3 130.0 220 180 1012 85.49000 1.23 1163 91.6 70.8 134.0 225 180 991 85.2

12000 0.94 1176 90.1 70.2 115.0 227 205 983 83.6

Appendix D: Tables of the Simulation Results 122

Table D.4: Simulation results of the generator at 1 kW output power (part 2)

v/rpm /p/A I Pocak/A / cx(/A ■Itdoi/A 1 Doeak/A PcuAV PrAV f con/W /’winAV1200 49.8 262 ' 15.4 178 262 158.1 14.2 91.1 0.141300 49.0 261 14.1 153 261 150.1 14.0 89.1 0.171400 48.5 259 13.2 133 259 144.5 13.9 87.9 0.201500 48.3 257 12.5 117 257 140.8 13.8 87.4 0.232000 46.3 243 10.5 61 243 122.3 13.4 83.7 0.403000 45.8 220 10.0 32 220 108.0 13.5 82.8 0.904500 44.9 195 9.0 31 195 95.1 12.6 81.7 2.036000 44.5 174 9.3 28 174 83.4 13.2 80.6 3.607000 44.7 167 8.8 34 167 81.9 12.7 81.4 4.908000 45.2 159 9.0 32 159 78.4 13.1 82.0 6.409000 45.2 154 9.9 75 154 77.1 12.7 82.0 8.10

12000 50.7 150 15.7 97 150 86.7 15.1 88.4 14.40

Table D.5: Simulation results of the generator at 0.5 lcW output power (part 1)

v/rpm rshafl/Nm Pshaf/W V gen in % /dc/A 0O in0 0c in” P Lto/W Pou/W 7? tot in %1200 4.87 612 90.0 37.0 172.5 210 108 518 84.61300 4.24 577 90.5 34.7 171.5 210 98 486 84.21400 4.07 596 90.6 35.9 170.0 210 100 503 84.31500 3.85 604 90.8 36.4 169.0 210 100 510 84.42000 2.77 579 91.4 35.3 165.0 210 92 494 85.43000 1.91 600 92.0 36.5 157.0 210 92 511 85.24500 1.25 590 92.6 36.2 149.0 210 86 507 85.96000 0.92 578 92.9 35.5 143.0 210 82 497 86.07000 0.80 586 92.9 36.1 139.0 210 83 505 86.28000 0.70 589 92.9 36.3 145.0 215 83 508 86.39000 0.62 584 92.8 35.9 142.0 215 83 503 86.1

12000 0.47 584 92.1 35.7 143.0 220 86 500 85.6

Table D.6: Simulation results of the generator at 0.5 kW output power (part 2)

v/rpm / p/A f Pocak/A Axe/A ■^Tocak/A I Dpeal/A Pcu/W PreAV Pcon/W PwinAV

1200 26.3 176 7.8 84 176 52.0 9.2 46.3 0.141300 24.7 170 7.4 65 170 45.4 9.0 43.3 0.171400 25.2 173 7.3 5.7 173 46.5 9.1 44.2 0.201500 25.3 174 7.1 50 174 46.4 9.1 44.5 0.232000 24.0 165 6.4 32 165 40.7 8.9 42.3 0.403000 24.4 153 6.1 27 153 38.2 9.2 43.2 0.904500 23.7 133 5.6 22 133 32.2 9.5 42.2 2.036000 23.0 119 5.2 19 119 27.9 9.7 41.1 3.607000 23.2 113 5.2 18 113 26.9 10.0 41.5 4.908000 22.9 109 4.7 20 109 26.2 9.4 41.3 6.409000 22.6 103 4.6 19 103 24.5 9.6 40.8 8.10

12000 22.3 93 4.5 22 93 22.2 9.5 40.4 14.40

Appendix D: Tables of the Simulation Results 123


v/rpm T sbaf/Nm P shaf/W 1} gen in % I dc/A 0oin° 9cin° fuo/W P ou/W T] lot in %1200 0.91 115 90.3 6.8 174.0 205 23.2 95 82.21300 0.97 126 90.9 7.6 173.5 205 24.1 106 84.41400 0.83 122 91.0 7.2 173.0 205 23.1 101 83.21500 0.76 119 91.1 7.1 172.5 205 22.3 99 83.42000 0.55 116 91.7 7.0 171.0 205 20.5 98 84.23000 0.38 119 92.7 7.3 178.0 210 18.6 102 85.84500 0.25 117 92.2 7.1 175.0 210 18.4 100 85.46000 0.19 121 91.3 7.3 172.0 210 19.8 102 84.57000 0.16 119 90.2 7.1 171.0 210 20.5 100 84.28000 0.15 122 89.2 7.2 169.0 210 22.1 101 82.8

9000 0.13 123 87.9 7.2 168.0 210 23.5 101 82.112000 0.10 127 83.5 7.0 164.0 210 29.3 98 77.4


v/rpm / p/A I Plicak/A WA / TDcal/A I Doeak/A PcuAV Pr/W Pcom/W Pwu/W

1200 8.1 60 4.7 30 60 4.4 6.6 12.0 0.141300 8.3 66 4.5 29 66 4.8 6.5 12.6 0.171400 8.0 64 4.4 28 64 4.4 6.4 12.1 0.201500 7.8 63 4.3 26 63 4.1 6.2 11.8 0.23

.2000 7.1 59 3.6 22 59 3.4 5.8 10.9 0.403000 6.2 59 2.6 19 59 3.2 4.6 10.0 0.904500 5.6 52 2.1 14 52 2.5 4.5 9.3 2.036000 5.5 48 1.8 12 48 2.3 4.7 9.2 3.607000 5.2 45 1.8 11 45 2.1 4.6 8.8 4.908000 5.2 43 1.6 10 43 2.0 4.8 8.9 6409000 5.1 41 1.5 9 41 1.9 4.8 87 8.10

12000 4.8 36 1.3 8 36 1.6 4.9 84 14 40

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