Table Of ContentFuzzy Logic Control
in Energy Systems
with design applications in MatLab/Simulink
_
ş
Ismail H. Alta
The Institution of Engineering andTechnology
PublishedbyTheInstitutionofEngineeringandTechnology,London,UnitedKingdom
TheInstitutionofEngineeringandTechnologyisregisteredasaCharityinEngland&
Wales(no.211014)andScotland(no.SC038698).
†TheInstitutionofEngineeringandTechnology2017
Firstpublished2017
TheInstitutionofEngineeringandTechnology
MichaelFaradayHouse
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Herts,SG12AY,UnitedKingdom
www.theiet.org
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AcataloguerecordforthisproductisavailablefromtheBritishLibrary
ISBN978-1-78561-107-0(hardback)
ISBN978-1-78561-108-7(PDF)
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PrintedintheUKbyCPIGroup(UK)Ltd,Croydon
Contents
Preface xi
Acknowledgments xv
1 Introduction 1
1.1 Introduction 1
1.2 Fuzziness 3
1.3 Fuzzy membership functions 4
1.4 Fuzzy sets 5
References 5
2 Fuzzy sets 7
2.1 Introduction 7
2.2 Fuzzy sets and fuzzy membership functions 13
2.2.1 Triangular membership function 13
2.2.2 Trapezoid membership function 17
2.2.3 Gaussian membership function 22
2.2.4 Bell membership function 23
2.2.5 Cauchy membership function 24
2.2.6 Sinusoid membership function 26
2.2.7 Sigmoid membership function 32
2.3 Properties of fuzzy membership functions 36
2.4 Fuzzy set operations 43
2.4.1 Intersection: t-norm 43
2.4.2 Union: t-conorm 46
2.4.3 Complement 48
2.4.4 De Morgan laws 52
2.5 Adjustment of fuzziness 53
2.6 Problems 55
References 60
3 Fuzzy partitioning 63
3.1 Introduction 63
3.2 Theoretical approaches 66
3.3 Fuzzy partition examples inenergy systems 67
3.4 Problems 83
References 87
4 Fuzzy relation 89
4.1 Introduction 89
4.2 Fuzzy relation 89
4.3 Operation with fuzzy relations 99
4.3.1 Intersectionof two fuzzy relations 99
4.3.2 Union of two fuzzy relations 99
4.3.3 Negation of a fuzzy relation 100
4.3.4 Inverse of afuzzy relation 102
4.3.5 Composition of fuzzy relations 102
4.3.6 Compositional rule of inference 108
4.3.7 The relational joint 110
4.4 Binary relations 110
4.5 The extension principle 112
4.5.1 The cylindrical extension 113
4.6 Fuzzy mapping 117
4.7 Problems 122
References 126
5 Fuzzy reasoning andfuzzy decision-making 127
5.1 Introduction 127
5.2 Fuzzy implications 127
5.3 Approximate reasoning 134
5.4 Inference rules of approximate reasoning 136
5.4.1 Entailment rule of inference 137
5.4.2 Conjunction rule of inference 137
5.4.3 Disjunction rule of inference 137
5.4.4 Negation rule of inference 138
5.4.5 Projection rule of inference 138
5.4.6 Generalized modus ponens rule of inference 139
5.4.7 Compositional rule of inference 139
5.5 Fuzzy reasoning 140
5.5.1 Inference engine with single inputsingle rule 142
5.5.2 Inference engine with multiple input single rule 143
5.5.3 Inference engine with multiple input multiple rule 146
5.6 Problems 156
References 158
6 Fuzzy processor 161
6.1 Introduction 161
6.2 Mamdani fuzzy reasoning 161
6.2.1 Fuzzification 166
6.2.2 Fuzzy rule base 168
6.2.3 Fuzzy conclusion 168
6.2.4 Defuzzification 171
6.3 Takagi–Sugeno fuzzy reasoning 178
6.4 Tsukamoto fuzzy reasoning 185
6.5 Problems 189
References 196
7 Fuzzy logic controller 199
7.1 Introduction 199
7.2 Physical system behaviors and control 200
7.3 Fuzzy processor for control 210
7.3.1 Fuzzy rules: the modeling of thoughts 211
7.3.2 The input–output interaction 218
7.4 Modeling the FLCin MATLAB 222
7.5 Modeling the FLCin Simulink 231
7.6 Problems 244
References 248
8 System modelingandcontrol 251
8.1 Introduction 251
8.2 System modeling 252
8.3 Modeling electrical systems 259
8.4 Modeling mechanical systems 271
8.4.1 Mechanical systemswithlinear motion 272
8.4.2 Mechanical systemswithrotational motion 279
8.5 Modeling electromechanical systems 282
8.5.1 Field subsystem 286
8.5.2 Armature subsystem 287
8.5.3 Mechanical subsystem 287
8.5.4 Electromechanic interaction subsystem 288
8.5.5 Modeling DCmotors 290
8.5.6 Modeling ACmotors 301
8.6 Problems 301
References 307
9 FLCin powersystems 309
9.1 Introduction 309
9.2 Excitation control 312
9.2.1 Excitation system modeling 315
9.2.2 State–space model of excitation systems 321
9.2.3 FLC of excitation systems 323
9.3 LF control 328
9.3.1 Small signal modeling of power systems 329
9.3.2 FLC design for LFC 335
9.4 FLCin power compensation 347
9.4.1 Powerfactor improvement 348
9.4.2 Busvoltage control 351
9.5 Problems 356
References 359
10 FLC inwindenergy systems 363
10.1 Introduction 363
10.2 Wind turbine 364
10.3 Electrical generator 368
10.3.1 Dynamic modeling of induction generator 370
10.3.2 Self-excited induction generator 375
10.4 FLC examples in WEC systems 380
10.5 Problems 395
References 398
11 FLC inPVsolar energy systems 403
11.1 Introduction 403
11.2 PVcell modelings 406
11.2.1 Reference I–Vcharacteristics of a PVpanel 410
11.2.2 Effects of changes insolar irradiation and
temperature 413
11.2.3 PVpanel modeling in Simulink 418
11.2.4 APVarray emulator 426
11.3 MPPsearch in PVarrays 429
11.3.1 MPPbylookup tables 430
11.3.2 MPPsearch algorithm based on measurements of
S and T 431
X X
11.3.3 MPPsearch algorithm based on voltage and current
measurements 432
11.3.4 MPPsearch algorithm based on online repetitive
method 434
11.4 MPPT of PVarrays 435
11.4.1 Constant maximumpower angle approach 436
11.4.2 Online load matching approach 441
11.5 Problems 453
References 456
12 Energy management andfuzzy decision-making 459
12.1 Introduction 459
12.2 Distributed generation and control 461
12.3 Energy management in a renewable integrationsystem 463
12.3.1 Centralized control of distributed renewable
energy systems 463
12.3.2 Distributed control of renewable energy systems 484
12.4 Problems 490
References 492
Index 495
Preface
This book is about fuzzy logic controller (FLC) and its applications in energy
systems.Itaimstogiveaninsightintoaclearunderstandinganddesignapproaches
(cid:2) (cid:2)
ofFLCsinMATLAB andMATLAB/Simulink environment.Itincludesabasic
theoryoffuzzysetsandFLtopreparethereaderforabetterunderstandingoffuzzy
partitioning, fuzzy relation and fuzzy decision-making processing, which are
requiredfordesigningFLCs.Afuzzyunitcalledfuzzyprocessorisdevelopedand
designed to be used as a fuzzy decision maker and a FLC depending on the
application problem.
Energy system is one of the application areas of FL. It is used to manage,
control and operate electrical energy systems. Examples in the book are related
to the control, operation and management of electrical energy utilization. The fol-
lowing examples on FLC and fuzzy management are discussed and studied in the
scope of the book.
● DCmotor speed and torque control
● excitation and load–frequency control in power systems
● multiarea load–frequency control in power systems
● wind energy controlsystems(WECS)
● photovoltaic (PV)solar energy control systems
● maximum power point tracking in PVsystems
● energy management in WECS
● energy management in PVsystems
The book addresses undergraduate and graduate students as well as practicing
engineersinelectricalpower,energyandcontrolsystems.Theywillbeabletoget
sufficient knowledge of FL theory and a clear understanding of designing fuzzy
decision maker and controller in MATLAB and Simulink. Those who study the
bookwillbeabletodeveloptheirownfuzzyprocessorlibraryanddesigntheirown
FL toolbox for the special problems they study. With the given examples, the
readers will also get to know the modeling and simulation of electrical power and
energy systems.
AnovelFLCdesignapproach inbothMATLABandSimulink isgiveninthe
book such that the user can see every step of the FL processor with the ability to
interfere the code in MATLAB.m files and also in operational Simulink blocks.
TheFLCdesignapproachwillmakethereadersnotjustassoftwareusersbutalso
software developers.
Chapters 1–7 can be used as an accompanying textbook for teaching Fuzzy
LogicandFuzzyDecisionMakingasanundergraduatecourse.Chapters1–8canbe
used as a textbook for teaching Fuzzy Logic Control in undergraduate or graduate
levels. Chapters 5–9canbeusedinagraduate courseabout FLCinPowerSystem
ControlassumingthatstudentshaveabasicknowledgeoffuzzysettheoryandFL.
Chapters5–7and10–12canbeusedasanadvancedgraduatecourseaboutFLCin
RenewableEnergyandDistributedGeneration.Chapters10–12canalsobeusedin
an advanced graduate course to teach FL-controlled wind and PV energy conver-
sion systems.
The book is organized into 12 chapters.
Chapter1.Introduction.Abriefhistoryoffuzzysettheoryanditsapplication
areasaresummarizedinthischapter.Theconceptoffuzziness,fuzzymembership
functions and fuzzy subsetsisintroduced.
Chapter2.Fuzzysets.Typesandpropertiesoffuzzysetsarestudied.Modeling
of fuzzy sets in MATLAB and MATLAB/Simulink are shown and MATLAB
function files are developed to be used as a part of user-defined toolbox library.
Fuzzy intersection,union and complement are also studied in this chapter.
Chapter 3. Fuzzy partitioning. Fuzzy subclasses and partitioning of the uni-
verses into fuzzy subsets are studied in this chapter. The importance of and
meaning of the portioning are discussed withexamples.
Chapter 4. Fuzzy relation. The concept of fuzzy relation, two-dimensional
fuzzy sets, fuzzy extension principle, fuzzy projection and binary and n-ary fuzzy
relationsarediscussedinthischapter.Representingverbaltermsandexpressionsas
fuzzy relationsare also introduced in this chapter.
Chapter 5. Fuzzy reasoning and fuzzy decision-making. Approximate reason-
ing,fuzzyreasoningandfuzzydecision-makingprocessesaregiveninthischapter.
Single-input single-rule, single-input multiple-rules and multiple-input multiple-
rule base systems are studied and examples are given. The concept of fuzzy rea-
soning is studied and user-defined MATLAB files are used to support the opera-
tional behaviors of fuzzy decision-making.
Chapter 6. Fuzzy processor. Fuzzy reasoning and fuzzy decision-making
processes are carried ahead with multiple inputs, multiple rules and multiple
decisions as the fuzzy processor. Known fuzzy reasoning algorithms such as
Mamdani fuzzy reasoning, Sugeno fuzzy reasoning and Tsukamoto fuzzy reason-
ing are discussed and steps toward FLCsare given.
Chapter 7. Fuzzy logic controller. FLC is given in this chapter. Rule devel-
opment,thewayofputtingexperts’ideasintorulesandinferencesystemstructure
are studied. From crisp input variables to crisp output, all processes are discussed
andshown.Defuzzification,ruleprocessing,fuzzyreasoningandcrispoutputafter
defuzzification are explained. User-developed FLC examples are given.
Chapter 8. System modeling and control. Mathematical modeling of physical
systems is given in this chapter. The methods obtaining differential equations,
simulation diagrams and state–space models of physical systems are studied.
Runge–Kutta numerical solution method is discussed and user-based MATLAB
software is developed to showthe meaning of controlling physical systems asone
oftheapplication areasofFL.Thereaderwillbeabletodevelophis/herownFLC
code in MATLAB and MATLAB Simulink. Examples of controlling electrical,
mechanical and electromechanical systems will be given.
Chapter 9. FLC in power systems. Application of FLC and decision maker to
excitation control,load–frequencycontrolandpowercompensationisdiscussedin
this chapter. Single and multiarea control of power systems are also studied as
examples in the chapter.
Chapter 10. FLC in wind energy systems. Application of FL control and
decision-making processes to wind energy conversion systems is given in this
chapter. After giving problems and control issues in wind energy conversion sys-
tems, the utilization of FL in solving these problems is shown.
Chapter 11. FLC in PV solar energy systems. Application of FL control and
decision-making processes inPVsolar systemsisgiven inthischapter.Maximum
power point tracking, sun tracking, voltage control, battery charging and manage-
ment of the generated power are studied.
Chapter12.Energymanagementandfuzzydecision-making.Theuseoffuzzy
decision-making and control process in energy management systems is studied in
thischapter.EnergymanagementinPVsolarandwindenergysystemsisdiscussed
and examples are given.
Chapter 1
Introduction
Abriefhistoryoffuzzysettheoryanditsapplicationareasaresummarized inthis
chapter.Theconceptoffuzziness,fuzzymembershipfunctionsandfuzzysubsetsis
introduced.
1.1 Introduction
Manywordsweusearbitrarilyinourdailylifeareusuallyfuzzyintermsofverbal
meanings.Whenexpressingordescribingasystemoranevent,weusewordssuch
asold,young,tall,short,cold,warm,hot,sunny,cloudy,fast,slow,etc.,whichare
fuzzy in nature. We, the humans, use uncertain, vogue and muddy words when
discussing something or taking decisions to perform some actions. Depending on
his/herage,wecallapersonold,middleaged,young,veryoldandveryyoung.We
pressthegasorbrakemoreorlessaccordingtotheroadconditionwhetheritisdry,
slippery,ramporflat.Ifthelightsinourstudyroomarelow,weincreasebrightness
alittle, else wedecrease it. Allthese examples showhowourbrainacts and takes
decisions during the situations that are uncertain and fuzzy.
Studies on systems with uncertainty and muddy data have reached a new era
with the publication of the article ‘‘Fuzzy sets’’ by Lotfi A. Zadeh [1]. Although
this article was first published in 1965, the use of fuzzy logic (FL) has increased
afterthesecondhalfofthe1970swhenLotfiA.Zadehpublishedtwomorearticles
[2,3], in which the application of fuzzy set theory to uncertain systems and
decision-making was described. FL applications have been gaining a high speed
ever since the Japanese started using them in commercially available appliances.
Nowadays,it ispossible tofind fuzzy-based applicationsinalmost every area [4].
Some of the utilization areas of FL are listed next.
FLisusedinrobotics,automation,trackingsystems,temperaturecontrol,flow
control, motion control, commercial products and many more utilization areas of
automatic control systems [4–7]. It is used in information systems as a database
tool to store and recall knowledge, uncertain data, experts’ ideas and operational
behavior of machines. Image processing, signal aliasing and human–machine
interactionarealsosomeoftheapplicationareaswhereFLisused[4].Itispossible
to find many more FL-based applications in social and medical sciences as
well [4]. FL is also used as a mathematical tool in areas such as function optimi-
zation, filtering, curve fitting, etc. [4].
