Table 5.1 Rule base for fuzzy PI controller (using 3 membership functions).88. Table 5.2 Rule base for fuzzy ..... Chapter 2. Wind Energy Conversion System (WECS) ..... In practice, different ..... which operate at higher rates than the turbine-level control. ... However, energy per unit of time is equal to power, so this is also the.
Maximum Power Point Tracking for Wind Energy Conversion System Using Fuzzy Modeling and Control By Eng. Ayman Nadeer Francees Ayad A Thesis Submitted to the Faculty of Engineering at Cairo University in Partial Fulfillment of Requirement for the Degree of
MASTER OF SCIENCE In ELECTRICAL POWER AND MACHINES ENGINEERING
FACULTY OF ENGINEERING, CAIRO UNIVERSITY GIZA, EGYPT OCTOBER 2009 1
Maximum Power Point Tracking for Wind Energy Conversion System Using Fuzzy Modeling and Control By Eng. Ayman Nadeer Francees Ayad A Thesis Submitted to the Faculty of Engineering at Cairo University in Partial Fulfillment of Requirement for the Degree of
MASTER OF SCIENCE In ELECTRICAL POWER AND MACHINES ENGINEERING Under the Supervision of: Prof. Dr. Abdel Latif Elshafei
FACULTY OF ENGINEERING, CAIRO UNIVERSITY GIZA, EGYPT OCTOBER 2009 2
Maximum Power Point Tracking for Wind Energy Conversion System Using Fuzzy Modeling and Control By Eng. Ayman Nadeer Francees Ayad A Thesis Submitted to the Faculty of Engineering at Cairo University in Partial Fulfillment of Requirement for the Degree of
MASTER OF SCIENCE In ELECTRICAL POWER AND MACHINES ENGINEERING Approved by the Examining Committee Prof. Dr. Abdel Latif Elshafei
(Thesis Advisor)
Electrical Power & Machines Department - Faculty of Engineering – Cairo University
Prof. Dr. Adel Shaltout
(Member)
Electrical Power & Machines Department - Faculty of Engineering – Cairo University
Prof. Dr. Fahmy Bendary
(Member)
Electrical Power & Machines Department - Faculty of Engineering –Benha University
FACULTY OF ENGINEERING, CAIRO UNIVERSITY GIZA, EGYPT OCTOBER 2009 3
To the spirit of my father
4
Acknowledgement As always, I thank and praise God by my side. Intelligence is not the only element which leads one to the road of success. Through the combination of hard work and dedication success is derived. All these elements inspire ideas, concepts, as well as preparation for this body of work. Nevertheless, to overcome obstacles and the stumbling blocks I have faced, one needs guidance, support and encouragement. Thus, I am grateful to my advisor Dr. Abdel Latif Elshafei, for his supervision throughout this thesis and for the valuable knowledge that he shared with me. I learned valuable lessons from him personality and his vision. The support from the German-Egyptian Research Fund (GERF) project STDF 599 is appreciated. I am indebted to my mother, brothers and sisters who have motivated me constantly. They have proven the importance of having strong family bonds when I was faced with a problem during my graduate studies. My family has taken a genuine interest in my research and has provided continual encouragement throughout this process. Last, but not least, I would like to thank my fiancé for her love, support, encouragement, and proof reading skills.
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List of Tables Table 1.1 Development of wind energy in Egypt……………………………..3 Table 3.1 List of symbols of induction generator model……………………36 Table 3-2 Parameters of the WECS Simulink model [11]…………………..40 Table 3-3 Values of the state vector of WECS at two operating points……..41 Table 4.1 Cluster centers by FCM method…………………………………..70 Table 4.2 TSK Fuzzy model parameters…………………………………….72 Table 5.1 Rule base for fuzzy PI controller (using 3 membership functions).88 Table 5.2 Rule base for fuzzy PI controller (using 5 membership functions).89 Table 5.3 Rule base for fuzzy PI controller (using 7 membership functions).89
6
List of Figures 1.1
Potential of wind energy in Egypt [29]…………………………………..2
1.2
Power coefficient vs. TSR at pitch angle = 0……………………………6
2.1
Example of Darrieus and Savonius vertical-axis WT [3]……………....11
2.2
Three blades horizontal-axis wind turbine (HAWT)……………….......12
2.3
Horizontal-axis wind turbine components [5]………………………….14
2.4
The upwind and downwind configurations [6]…………………………15
2.5
Directly coupled squirrel-cage induction generator……………………18
2.6
A typical fixed speed wind turbine configuration [8]…………………..20
2.7
Permanent-magnet synchronous generator with PWM converter [8]….21
2.8
Doubly fed wound rotor induction wind turbine [1]…………………...22
2.9
Stator controlled squirrel cage induction generator [1]………………...23
2.10 WECS control levels [2]……………………………………………......25 3.1
Wind energy conversion scheme…………………………………….....27
3.2
Ideal power curve [1]…………………………………………………...29
3.3
Power density vs. wind speed [1]……………………………………....30
3.4
versus
and
[5]………………………………………………..32
3.5
Power coefficient vs. TSR at pitch angle = 0…………………………..32
3.6
Wind turbine model (air density: 1.1 kpa)……………………………...32
3.7
Output mechanical power of turbine vs. the turbine speed…………….33
3.8
Output mechanical torque of turbine vs. the turbine speed…………….33
7
3.9
Equivalent circuit of the induction machine in d-q reference frame…...34
3.10 The approximated relationship between
and
……..……………..35
3.11 Current-flow directions in the exciting capacitors……….……………..37 3.12 MATLAB Simulink WECS model……………………………………..41 3.13 Input mechanical torque (Tm ) and rectifier firing angle (
)…………42
3.14 DC link current response (IDC)………………………………………….42 4.1
Linguistic fuzzy model as a fuzzy graph……………………………….46
4.2
TSK identification algorithm…………………………………………...49
4.3
Flow diagram of the FCM algorithm [15]……………………..…….....53
4.4
Flow diagram of the subtractive clustering algorithm………………….62
4.5
Steady state power curves [5]…………………………………………..65
4.6
Turbine power curves…………………………………………………..66
4.7
Implemented fuzzy system……………………………………………..66
4.8
Wind speed observations profile…………………………….………....68
4.9
Maximum power estimated by the fuzzy model and effective maximum extractable power (FCM)…………………………………...71
4.10 Rotor speed related to wind speed profile (FCM)……………………..71 4.11
Maximum power estimated by the fuzzy model and effective maximum extractable power (Subtractive clustering)…………………72
4.12
Rotor speed related to wind speed profile (Subtractive clustering)……73
5.1
Multi rate control scheme [11]…………………………………………..75
5.2
Control system configuration [11]……………………………………....76 8
5.3
MATLAB Simulink model with PI controller………………………….77
5.4
DC link current error and the control signal (PI controller)……………77
5.5
The DC reference current and its response (PI controller)……………..77
5.6
The control signal and the response of the DC link current (PI failure)………..………………………………………………………....78
5.7
Fuzzy controller architecture…………………………………………...81
5.8
Typical membership functions…………………………………………81
5.9
PI-like fuzzy logic controller behavior………………………………...87
5.10 The overall control scheme of WECS with fuzzy controller…………..87 5.11 Input membership functions…………………………………………....87 5.12 MATLAB Simulink WECS model with fuzzy controller……………..89 5.13 The inside of Simulink fuzzy controller block…………………………89 5.14 Seven rules for each subsystem………………………………………...90 5.15 The control signal and the DC current response (test 1 using 3 membership functions)………………………………………………….91 5.16. The control signal and the DC current response (test 1 using 5 membership functions)………………………………………………….91 5.17 The control signal and the DC current response (test 1 using 7 membership functions)………………………………………………….91 5.18 DC link current error and the control signal (Fuzzy controller test 2)....92 5.19 DC link current reference and response (Fuzzy controller test 2)……...92 5.20 Fuzzy controller for WECS with scaling gains go, g1, and h…………...94
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5.21 The control signal and the current response at go=1, g1=0.1 and h=1………………………………………………………..…………….94 5.22 The control signal and the current response at go=2, g1=0.1, and h=1……………………………………………………………………..95 5.23 The control signal and the current response at go=2, g1=0.1 and h=5……………………………………………………………………..95 5.24 The Control Surface at go= 1, g1= 0.1, and h=1………………………...96 5 25 The Control Surface at go= 2, g1= 0.1, and h=1………………………...96 5.26 The Control Surface at go= 2, g1= 0.1, and h=5………………………...97
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List of Symbols Tm
Turbine mechanical torque
Pm
Turbine mechanical power
Ρ
Air density
Β
Pitch angle
R
Blade radius
Vw
Wind speed
Ct
Torque coefficient
Cp
Power coefficient
λ(TSR)
Tip speed ratio
Wr
Rotor speed
M
Mass of the air
P
Power in the wind
ids,iqs
Peak stator d&q axes currents
idr,iqr
Peak rotor d&q axes currents
λds,λqs
Peak stator d&q axes flux linkages
λdr,λqr
Peak rotor d&q axes flux linkages Peak stator d&q axes voltage
Ls
Stator inductance
Lr
Rotor inductance
Lls,Llr
Stator and rotor leakage inductance
im
Peak magnetizing current
11
vg
Peak magnitude of air-gap voltage
Lm
Magnetizing inductance
rs
Stator resistance
rr
Rotor resistance
We
Electrical frequency(rad/sec)
N
Number of poles
B
Net friction of the rotating parts of the system.
J
Net inertia of the rotating parts of the system. Peak d&q axes capacitor currents.
idl, iql
Peak d&q axes currents flowing into the converter.
C
Self-excitation capacitance. Peak magnitude of a.c line current flowing into the converter. DC link inductance and resistance. Converter and inverter d.c voltage. Maximum converter and inverter d.c voltage. Rectifier firing angle
.
Inverter firing angle P
.
Differential operator d/dt
12
Abbreviations WECS
Wind Energy Conversion System
TSK
Takagi, Sugeno and Kang
ANFIS
Adaptive-Network-Based Fuzzy Inference System
MPPT
Maximum Power Point Tracking
FCM
Fuzzy C-Means
VAWT
Variable-Axis Wind Turbine
HAWT
Horizontal-Axis Wind Turbine
SCIG
Squirrel-Cage Induction Generator
WFSG
Wound Field Synchronous Generator
PWM
Pulse Width Modulation
PMSG
Permanent Magnet Synchronous Generator
DFIG
Doubly Fed Induction Generator
FLC
Fuzzy Logic Control
FLM
Fuzzy Linguistic Model
FFM
Fuzzy Functional Model
DOF
Degree Of Firing
HCS
Hill Climb Search
RLS
Recursive Least Square
COA
Center Of Area
MOM
Mean Of Maximum
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Abstract Wind energy systems are being closely studied because of its benefits as an environmentally friendly and renewable source of energy. Because of its unpredictable availability, power management concepts are essential to extract as much power as possible from the wind when it becomes available. The purpose of this thesis is to presents a TSK fuzzy model, which represent the turbine characteristic, for maximum power point tracking (MPPT) in wind energy conversion systems. The proposed TSK fuzzy model allows the generator to track the optimal operation points of the wind turbine system under fluctuating wind conditions and the tracking process speeds up over time. This model does not require the knowledge of the wind speed. The TSK fuzzy model is applied on the WECS model. The results are obvious and illustrate the benefits of this model in maximum power point tracking (MPPT). The TSK fuzzy model identification was based on the clustering method as Fuzzy CMeans (FCM) and subtractive clustering. Then, the TSK fuzzy model parameters are tuned using back propagation and ANFIS learning techniques. Also, the rotor speed regulation is made once by PI controller and another time by fuzzy logic controller. The fuzzy controller gives better results (stable and faster response). In this thesis the Wind Energy Conversion System (WECS) model is developed. It consists of wind turbine, induction generator, and the DC link converter which is the interface with the power grid. The model is tested and validated. Then, the PI controller and fuzzy controller are designed and applied on the WECS. Also, the TSK fuzzy model is designed to achieve the maximum power point tracking. The results make sure that the proposed controller and model are successful in achieving our objectives.
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Table of Contents Acknowledgement……………………………………………………………...ii List of Tables…………………………………..…………………………........iii List of Figures………………………………………………………………….iv List of Symbols………………………………………………………………viii Abbreviations…………………………………………………………………...x Abstract………………………………………..……………………………….xi
Chapter 1
Introduction
1.1 Motivation……………………………………………………………….1 1.2 Wind Energy in Egypt…………………………………………………..2 1.3 Literature Survey………………………………………………………..4 1.4 Thesis Objectives………………………………………………………..7 1.5 Thesis Outline…………………………………………………………...8 Chapter 2
Wind Energy Conversion System (WECS)
2.1 Introduction…………………………………………………………….10 2.2 Types of Wind Turbine………………………………………...............11 2.2.1 Vertical-Axis Wind Turbine (VAWT)…………………………..11 2.2.2 Horizontal-Axis Wind Turbine (HAWT)……………...………...11 2.3 Types of Horizontal-Axis Wind Turbine………………………………14 2.4 Rotor Power Control…………………………………………...............15
15
2.5 Fixed and Variable Speed Wind Turbine……………………………...17 2.5.1 Fixed Speed Wind Turbine (Danish Concept) ………………….17 2.5.2 Variable Speed Wind Turbine…………………………………...17 2.6 Configurations of Variable Speed Wind Turbine……………………..19 2.6.1 Synchronous Generators………………………………………....19 2.6.2 Induction Generator……………………………………………...21 2.7 Wind Turbine Control………………………………………………….23 2.7 Conclusion…..…………………………………………………………25 Chapter 3
WECS Modeling and Validation
3.1 Introduction……………………………………………………………27 3.2 Wind Turbine Model…………………………………………………..27 3.2.1 Energy and Power in the Wind…………………………………..28 3.2.2 Power and Torque of Wind Turbine..………. …………………..29 3.2.3 Simulink Wind Turbine Model…………………………………..32 3.3 Self Excited Induction Generator Model………………...…………….33 3.4 Self Excitation Capacitor Model………………………………………36 3.5 DC Link Converter Model……………………………………………..37 3.6 WECS Full Model……………………………………………………..38 3.7 Model Validation………………………………………………………39 3.8 Conclusion……………………………………………..………………42 Chapter 4
Maximum Power Point Tracking Using Fuzzy Modeling
4.1 Introduction…………………………………………………………….44 16
4.2 Fuzzy Modeling...……………………………………………………...45 4.2.1 Fuzzy Linguistic Models (FLM)……………………………...…45 4.2.2 Fuzzy Functional Models (FFM)………………………………...48 4.3 Fuzzy Model Identification Based on Clustering and Learning Methods……………………………………………………….……….50 4.3.1 Fuzzy C-Means Method (FCM)…..……………………………..50 4.3.2 Model Identification Based on FCM………………………….…52 4.3.3 Mountain Clustering Method ………………………………...….55 4.3.4 Learning the Cluster Centers via Back-Propagation Method……57 4.3.5 Subtractive Clustering Method ………………...………………..59 4.3.6 Model Identification Based on Subtractive Clustering Method…63 4.4 Maximum Power Point Tracking (MPPT) Methodology………..…….64 4.5 MPPT Using Fuzzy Modeling…………………………………………66 4.6 Simulation and Results………………………………………………...68 4.6.1 MPPT Fuzzy Model Using Fuzzy C-Means Clustering Method..68 4.6.2 MPPT TSK Fuzzy Model Using Subtractive Clustering Method.70 4.7 Conclusion…………………………………………………………......73 Chapter 5
Fuzzy PI Controller for WECS
5.1 Introduction…………………………………………………………….75 5.2 Conventional PI Controller for WECS………………………………...75 5.3 PI Controller Failure……………………………………………….......79 5.4 Fuzzy Logic Control (FLC)……………………………………………79 17
5.4.1 Fuzzy Logic Controller: Basic Concept…………………………80 5.4.2 Reasoning with an FLC………………………………………….83 5.4.3 Illustration of the basic reasoning algorithm…………………….85 5.4.4 The FLC relation to The Conventional PI control……………….86 5.5 Fuzzy PI Controller Design for WECS………………………………..86 5.6 Simulation and Results………………………………………………...90 5.6.1 Applying the Designed Fuzzy PI Controller on WECS…………91 5.6 2 Tuning via Scaling Universes of Discourse…………………..…94 5.7 Conclusion………………………………………..……………………98 Chapter 6
Conclusion…………………...…………….99
References…………………………………………………………………...101 Appendix………………………………………………………………...…..104 ………………………………………………………………………الملخص...105
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Chapter 1 Introduction 1.1 Motivation There are various sources of power and there are very few that are renewable but then the use of energy has increased manifold and consequently the demand. Therefore, we need some such sources of energy that are renewable so that we can cope with the imminent energy crisis that is coming. Wind energy, solar energy, and Hydropower are examples of renewable energy which can be recycled and reused again and again. These power sources do not create pollution neither is there a scope of these energy sources of being exhausted. Sun’s rays heat the atmosphere of the earth in different degrees. There are parts of the earth that get more heat, consequently the air in those parts also gets warm and rises whereas in the other places which do not get enough heat, the air remains cold and remains close to the surface. But that one section of air, which is heated and rises, creates a void and the cold air blows to fill in the vacuum. This creates the movement of air and that is what we call wind. Now when this wind is used to get power it is called wind power. The importance of wind power was recognized quite in early period. Over 5000 years ago, the ancient Egyptians used wind power to sail their ships over the Nile River. Later people built windmills to grind grain. The earliest known windmills looked like large paddle wheels. Centuries later, the Dutch improved the windmill. They thought of propeller shape blades and made it so it could be turned to face the wind. Windmills helped the Holland to become the world's most industrialized countries by the 17th century. American colonists used windmills to grind wheat and corn, to pump water and to cut wood at sawmills. In the last century, people use windmills to generate electricity in rural areas in the 1930's; the electric windmills were used less and less.
19
In the 1970s, oil shortages pushed the development of alternative energy sources. In the 1990s, the push came from a renewed concern for the environment in response to scientific studies indicating potential changes to the global climate if the use of fossil fuels continues to increase. Wind energy is an economical power resource in many areas of the country. Wind is a clean fuel; wind farms produce no air or water pollution because no fuel is burned. Growing concern about emissions from fossil fuel generation, increased government support, and higher costs for fossil fuels (especially natural gas and coal) have helped wind power capacity in the world grow substantially over the last 10 years.
1.2 Wind Energy in Egypt Figure 1.1 shows the potential of wind energy in Egypt.
Figure 1.1. Potential of wind energy in Egypt [29]. 20
Egypt enjoys an excellent wind regime, particularly in the Suez Gulf where the wind speed exceeds 10 m/sec. In March 2003, a detailed wind atlas for the Suez Gulf Coast was issued in cooperation with Denmark. The Atlas was expanded to cover the whole country and the final version was issued in Dec. 2005. The Atlas indicates that the wind energy resource is available in a large region of the Western Desert and parts of Sinai [29]. Several pilot and demonstration projects have been installed to gain and accumulate the necessary experience since 1988.The first commercial wind farm (5 MW) was established and interconnected with the local grid of Hurghada in 1993 generating about 9 GWh/year. The farm includes 42 WT of different types and sizes. Besides, the Zafarana site on the red sea coast which has been selected to host the 1st large wind park. The site has been specified as one of the best all over the world, with excellent wind characteristics (stable profile, relatively small variations). The farm is producing annually about 850,000 MWh. Currently, the recent developments and prospects in Egypt to satisfy 3% of the electric energy demand from renewable energy resources, mainly wind & solar, by the year 2010 (See Table 1.1). Table 1.1. Development of wind energy in Egypt [29]. Year
2007/2008
2008/2009
2009/2010
2010/2011
Power (MW)
80
120
200
220
Total (MW)
310
430
630
850
Added Wind
In April, 2007 the Long-Term Plan for Wind Energy has been announced by the Supreme Council of Energy, SCE, as a comprehensive plan to increase share of wind energy to reach 20% of the total electric energy demand in by year 2020 [29]. In the long term planning, it is anticipated to have an installed 21
capacity of around 12650 MW wind farms by the year 2020/2021. According to the new plan and within a few years, Egypt will be considered among the leading countries in the world in terms of wind installed capacity. The statistics show wind energy will continue to grow globally through unrelenting research efforts and strong political support for clean renewable energy production. Research in wind energy conversion continues to grow due to the advances in power electronics used to aid in the conversion of a highly variable generator output voltage. Power electronics have made grid connection for wind turbines extremely viable. Their ability to stabilize the generated voltage through control algorithms, keeps the voltage at grid connection constant. Variable speed turbines are preferred since they allow for increased power efficiency and energy extraction from the variable wind source. There exists an optimum generator speed for every wind speed that seizes maximum electrical power from the wind passing through the turbine. As the wind speed changes it is important to have a speed controller that reacts to the changes in wind speed and controls the generator speed to match optimum points. Many power electronic devices have been used in various different combinations, some allowing for greater control and some achieving a low cost implementation.
1.3 Literature Survey Wind energy systems cover a wide range of power levels, with the large scale designs now reaching approximately 5 MW. Small scale turbines, designed for residential and commercial use, are of the low kilowatt power range. Typically, wind energy systems consist of a turbine, generator and an electronic converter. Various generators have been used including synchronous generators, induction generators, permanent magnet synchronous generators, and more recently doubly-fed induction machines. Early research invoked the use of a diode rectifier along with a thyristor rectifier and a reactive power compensator for power conversion [7].
22
Normal wind energy conversion is relatively straightforward process, but in order to capture the maximum power from the wind, the process is much more involved. The maximum of the power curve, for a particular wind speed, occurs at a particular rotor speed. Due to the aerodynamic characteristics of a wind turbine, a small variation from the optimum rotor speed will cause a significant decrease in the power extracted from the wind. Turbines do not naturally operate at the optimum wind speed for any given wind velocity because its rotor speed is dependent on the generator loading as well as the wind speed fluctuations. Because of this, non-optimized conversion strategies lead to a large percentage of wasted wind power. The more energy extracted from the wind, the more cost effective the wind energy becomes. The mechanical torque
and the captured mechanical power
of a wind
turbine can be expressed in terms of the air density ρ, the blade pitch angle β, the blade radius R and the wind velocity
as follows: (1.1) (1.2)
Where
is power extracted from the wind [Watt],
of the rotor [Nm],
is air density [kg/
], R is rotor radius [m],
coefficient (maximum value Betz’s limit 59.3 %) [10], blades [deg],
is aerodynamic torque
is aerodynamic coefficient.
and
is power
is pitch angle of rotor are nonlinear functions
with respect to the tip speed ratio (TSR)
and the pitch angle . Where the
torque and the power coefficients,
respectively, relates to each other
and
as: (1.3) λ is called the tip-speed ratio (TSR) since it is defined as the ratio of the rotational speed
of the turbine at the tip of the blade to the wind velocity: (1.4) 23
where
is rotor speed [rad/s],
is effective wind speed [m/s].
Now in order to calculate the captured power we must define the power coefficient (
. Figure 1.2 shows the relationship between power coefficient
) and TSR ( ) at
.
0.5
Power Coff.(Cp)
0.4
0.3
0.2
0.1
0
0
2
4
6 8 TIp Speed Ratio(Lambda)
10
12
14
Figure 1.2. Power coefficient vs. TSR at pitch angle = 0. From Figure 1.2, we can observe that
at
. This means
that, there is a certain turbine speed for a certain wind speed. Therefore to extract the maximum power from the wind turbine, the wind turbine speed must be regulated. Consequently, to extract the available power at any wind velocity, the control system should adjust the rotational speed in order to force
. If, on the contrary, extracting a power lower than the available
in the wind was desirable, the power coefficient should be reduced i.e. [2] [4] [5] [9]. Different algorithms have been used to track the maximum power line. In [5] an adaptive controller was developed to maximize the energy capture by regulating the rotor speed. A neural network controller was designed in [26] in order to maximize the energy capture and reduce the mechanical loads. Also in [27] an intelligent algorithm was used using the intelligent memory method with an on-line training process. An intelligent algorithm, by using a modified version of Hill Climb Search (HCS) and intelligent memory, was used in [4]. A 24
TSK fuzzy model was developed using fuzzy clustering and recursive leastsquares (RLS) optimization in [28].
1.4 Thesis Objectives In this thesis, two levels of control are designed. The high control level is responsible for producing the maximum power which should capture from the wind turbine without measuring the wind speed. This level is based on TSK fuzzy model identification. In TSK fuzzy model, the inputs are the measured rotor speed and the output power of WECS (Wind Energy Conversion System), on the one hand, and the output is the maximum turbine power, on the other hand. We use the clustering methods to produce the initial cluster centers for the TSK fuzzy model rules (structure identification). Then, we use the back propagation and ANFIS methods to tune the TSK fuzzy model parameter (parameter identification). The used TSK fuzzy model expresses about the turbine power curve characteristics. Which means at any wind speed there is optimum rotor speed at which the power capture can be maximized. The results illustrate that, we succeed by this control methodology in achieving the maximum output power at any wind speed in the range of 5 m/s to 15 m/s. The output of this control level is the reference input to the low control level. The low control level is responsible for regulating the rotor speed to achieve the optimum tip speed ratio (TSR). Consequently, achieving the maximum power coefficient (Cpmax) which maximizes the WECS output power. This can be done by controlling the DC link converter. The output power is regulated indirectly by controlling the DC link current using the rectifier firing angle. By controlling the rectifier firing angle, we can change the rotor speed to become optimum speed. The low level control is designed using once the conventional PI controller which works perfectly at predefined operating points. At this operating point the PI controller will track the reference current. But, if the operating point is changed, the PI controller may fail to track the reference value. So, the fuzzy logic controller is used as alternative to the PI controller. 25
Because that fuzzy logic controller is a nonlinear controller, it will track the reference current successfully at any operating point. Another advantage in fuzzy logic, we can tune its gains factor to give better results. The tuning process can be done using any optimization technique as Genetic Algorithm (GA) or Particle Swarm.
1.5 Thesis Outline The organization of this thesis is outlined as follows: Chapter 1 provides the introduction and the motivations for wind energy utilization. The features and the advantages of the wind energy are introduced. The wind energy and its progress in Egypt are presented. Also, a literature survey about the modern control methodology and the basic idea behind maximum wind power extraction are introduced. Finally, the main objectives and types of control technique of this thesis are introduced. Chapter 2 gives an overview of wind turbine technology and wind energy conversion system configurations. The advantages and disadvantages of the different types of wind turbines and the two main kinds of wind energy systems are discussed. Finally the WECS control is illustrated. Chapter 3 the MATLAB Simulink wind turbine model is modified. A nonlinear model of induction generator is developed by using the d-q model. The interface between the generator and the grid includes subsystems like capacitor, converter, DC link, and inverter. The objective of the modeling excludes the self-excitation process of the induction generator. It focuses on the behavior after self-excitation. The full model of the WECS is collected to be tested and validated. Finally, the proposed WECS model is tested and validated using MATLAB Simulink at a certain operating points. Chapter 4 presents the two types of fuzzy model. Then it presents the TSK fuzzy model identification based on clustering methods. The back propagation and the ANFIS techniques are used to tune the TSK fuzzy model parameters. 26
The maximum power point tracking (MPPT) methodology is presented. The TSK fuzzy model is used to achieve the maximum power point tracking (MPPT) based on FCM and subtractive clustering methods. Chapter 5 uses the WECS model, which has been developed and tested in Chapter 3 in order to design a suitable controller to regulate the power flow with minimum reactive power burden on the induction generator. A PI controller is applied on WECS and the closed loop system is simulated. But at different operating points the PI controller fails to track the set point. An introduction to fuzzy logic control is introduced. A fuzzy PI controller is applied in place of the PI controller. The gain factors of fuzzy controller are tuned. Finally, the summary and conclusion are presented. Chapter 6 summarizes all the features and contributions of the proposed maximum power point tracking fuzzy model. It also provides suggestions on the future work that can be done.
27
Chapter 2 Wind Energy Conversion System (WECS) 2.1 Introduction In this chapter we will describe the wind turbines, its components, types of the wind turbines depending on rotor position and rotor type, types of generator and how the connection with the power grid could be. Finally the WECS control will be explained. The wind is characterized by its speed and direction, which is affected by several factors, e.g. geographic location, climate characteristics, height above ground, and surface topography [1]. Wind turbines are mechanical devices specifically designed to convert part of the kinetic energy of the wind into useful mechanical energy. This mechanical energy is converted to electricity by using a generator [1]. Wind turbine operates in a simple principle. The energy in the wind turns two or three propeller-like blades around a rotor. The rotor is connected to the main shaft which spins a generator to generate electricity. Wind turbine can be used to produce electricity for a single home or building or they can be connected to an electricity grid for more widespread electricity distribution [2]. Section 2.2 shows the types of wind turbine depending on the rotor position and the main components of the horizontal-axis wind turbine. Section2.3 presents the types of horizontal-axis wind turbine. Section 2.4 illustrates limiting power control methods. Section 2.5 points out the difference between fixed speed and variable speed wind turbines. Section 2.6 shows the different configurations of variable speed wind turbine. Methodologies of control will be shown in section 3.7. Finally the conclusion of this chapter is presented in section 2.8.
28
2.2 Types of Wind Turbine There are two main types of wind turbines, the horizontal-axis and vertical-axis turbines depending on the rotor axis position.
2.2.1 Vertical-Axis Wind Turbine (VAWT) Vertical-axis wind turbine spins like a top with an axis of rotation perpendicular to the ground. The most popular types are Darrieus and Savonius [3] (See Figure 2.1). Although it has high torque, it has low speed. Therefore, it has low energy conversion efficiency. Its generator and transmission devices are located at the ground [1]. So it is easy in installation and maintenance. Another advantage of vertical-axis wind turbine is that its operation is independent on wind direction, but it is not self-starting [4].
Figure 2.1. Example of Darrieus and Savonius vertical-axis WT [3].
2.2.2 Horizontal-Axis Wind Turbine (HAWT) Horizontal-axis turbines (see Figure 2.2) are primarily composed of a two or three blades and a nacelle mounted on top of a tower where the gear box and the generator are located in the nacelle. The rotor is located at the top of a 29
tower where the winds have more energy and are less turbulent [1]. Three blades wind turbine are operated “upwind” with the blades facing the wind. The other common wind turbine type is the two blades which are usually operated “downwind”. It has a high wind energy conversion efficiency, selfstarting capability, and access to stronger winds due to its elevation from the tower. On the other hand, it includes high installation cost. Besides, it needs a strong tower to support the nacelle and rotor blades. Moreover, it has longer cables to connect the top of the tower to the ground [4]. Horizontal-axis wind turbines are the most common type used today. Horizontal-Axis Wind Turbine Main Components: The main components of the horizontal-axis wind turbine shown in Figure 2.3 can be described as follow [2]: Anemometer: It measures the wind speed and transmits wind speed data to the controller. Blades: Most turbines have either two or three blades. Wind blowing over the blades causes the blades to lift and rotate.
Figure 2.2. Three blades horizontal-axis wind turbine (HAWT). 30
Brake: A disc brake can be applied mechanically, electrically or hydraulically is to stop the rotor in emergencies. Controller: The controller starts up the machine at wind speeds of about 4 to 6 meter per second (m/s) and shuts off the machine at about 25 m/s. Turbines can’t operate at wind speeds above about 25 m/s because their generators could overheat and mechanical loading requires costly structures. Gear box: Gears connect the low-speed shaft to the high-speed shaft and increase the rotational speeds from about 30 to 60 rpm to about 1200 to 1500 rpm (the rotational speed required by most generators to produce electricity). The gear box is a costly and heavy part of the wind turbine. Engineers are exploring direct drive generator that operates at lower rotational speeds and doesn’t need gear boxes. Generator: It is usually an induction generator that produces 50/60 cycle/sec AC electricity. High-speed shaft: Drives the generator. Low-speed shaft: The rotor turns the low-speed shaft at about 30 to 60 rotations per minute. Nacelle: The rotor is attached to the nacelle, which is put on top of the tower and includes the gear box, low and high-speed shafts, generator, controller and brake. There is a cover protecting the components inside the nacelle. Some nacelles are large enough for a technician to stand inside while working. Pitch: Blades are turned, or pitched out of wind to keep the rotor from turning in winds that are too high or too low to produce electricity. Rotor: The blades and the hub together are called the rotor. Tower: Towers are made from tubular steel or steel lattice. Because wind speed increases with height, taller towers enable turbines to capture more energy and generate more electricity. 31
Wind direction: Figure 2.3 shows the so-called upwind turbine, it operates facing into the wind. Other turbines are designed to run downwind facing away from the wind. Wind vane: It measures wind direction and communicates with the yaw drive to orient the turbines properly with respect to the wind. Yaw drive: The yaw drive is used to keep the rotor facing into the wind as the wind direction changes. Downwind turbines don’t require a yaw drive; the wind blows the rotor downwind. Yaw motor: It is the yaw drive.
Figure 2.3. Horizontal-axis wind turbine components [5].
2.3 Types of Horizontal-Axis Wind Turbine. The rotor in a horizontal-axis wind turbine may be either upwind or downwind of the tower, as shown in Figure 2.4. In a downwind wind turbine, the rotor allows the turbine to have free yaw which is simpler to implement than active 32
yaw. Moreover, it is possible to reduce the blade flap wise bending loads in a downwind wind turbine using coned blades. Wind speed decreases behind the tower due to the tower obstruction in downwind wind turbines. This previous phenomenon, which causes torque variations, is called tower shadow or tower wake effect. The tower shadow effect is a source of periodic mechanical loads which may cause fatigue damage to the blades. Moreover, it produces pulsation on the aerodynamic torque which may deteriorate the output power quality. Upwind wind turbines have the rotor facing the wind in front of the tower. The basic advantage of upwind designs is that one avoids the wind shade behind the tower. The vast majority of wind turbines have this design. There is also some wind shade in front of the tower due to tower structure. Therefore, the wind turbine power slightly drops each time the rotor passes the tower.
Upwind
Downwind
Figure 2.4. The upwind and downwind configurations [6].
2.4 Rotor Power Control Wind turbines are designed to produce electricity as cheap as possible. Since wind speeds rarely exceed 15 m/s, wind turbine are generally designed to yield maximum output (rated power) at a speed around 10 -15 m/s (rated wind speed). The captured wind power should be limited as wind speed passes the rated wind speed of the turbine. To avoid damage to the generator and excessive mechanical stresses, the wind turbine is shut off when reaching a predetermined speed which is normally about 25 m/s [6]. In practice, different 33
methods may be used to control the power of a wind turbine (explained in the following sections).
a) Stalled Controlled Wind Turbine The rotor blades of a stall controlled wind turbine are bolted onto the hub at a fixed angle. The blades are aerodynamically designed to slow down the blades when winds are too strong. The stall phenomenon caused by turbulence on rotor blades prevents the lifting force to act on the rotor. The rotor blades are twisted slightly along the longitudinal axis so that the rotor blade stalls gradually rather than suddenly when the wind reaches the turbines’ critical value [4].
b) Active Stall Controlled Wind Turbine Active stall turbine is very similar to the pitch controlled turbine because it operates the same way at low wind speeds. However, once the machine reaches its rated power, active stall turbine will turn its blades in the opposite direction from what a pitch controlled machine would. By doing this, the blades induce stall on its rotor blades and consequently waste the excess energy in the wind to prevent the generator from being overloaded. This mechanism is usually either realized by hydraulic systems or electric stepper motors. [4]
c) Pitched Controlled Wind Turbine Pitch controlled wind turbine changes the orientation of the rotor blades along its longitudinal axis to control the output power. This turbine has a controller to check the output power several times per second. When the output power reaches a maximum threshold, an order is sent to the blade hydraulic pitch mechanism of the turbine to pitch the rotor slightly out of wind to slow down the turbine. Conversely, when the wind slows down, then the blades are turned (or also known as pitched) back into the wind. During this operation, the blades are pitched a few degrees with each change in wind to keep the rotor blades at the optimum angle to maximum power capture. [4] 34
2.5 Fixed and Variable Speed Wind Turbine There are two main types of WECSs, the fixed speed WECS and variablespeed WECS. The rotor speed of a fixed-speed WECS, known as the Danish concept, is fixed to a particular speed. The other type is the variable-speed WECS where the rotor is allowed to rotate freely. The variable-speed WECS uses power maximization techniques and algorithms to extract as much power as possible from the wind [4].
2.5.1 Fixed Speed Wind Turbine (Danish Concept) In this scheme, the asynchronous electric machine is directly coupled to the power grid (See Figure 2.5). The generator speed is locked to the power line frequency [1]. Squirrel-cage induction generators (SCIG) are used in fixed speed systems. Its advantages are well established, simple, robust, reliable, cheap, and maintenance-free [4]. Because the turbine rotates at a fixed speed, maximum wind energy conversion efficiency can be only achieved at one particular wind speed. This is because there is a particular rotor speed for each wind speed that will produce the optimal TSR (Tip Speed Ratio). The optimal TSR gives the maximum Cp (Power Coefficient) value [4]. Because the wind turbine has to operate at constant speed; it requires a stiff power grid to enable stable operation. Besides, it implies more expensive mechanical construction in order to be capable of absorbing high mechanical stress. Therefore, their performance is rather poor. Actually, no active control action can be done to alleviate mechanical loads and improve power quality. Furthermore, conversion efficiency is far from optimal [1].
2.5.2 Variable Speed Wind Turbine The variable-speed alternative to fixed-speed has become popular in commercial wind turbines, particularly for operation in low wind speeds [1]. The turbine is not directly connected to the utility grid. Instead of this a power electronic interface is placed between the generator and the grid to provide 35
decoupling and control of the system [4]. So we can adjust the generator speed to fit wind speed to get Cpmax. They are capable of achieving maximum aerodynamic efficiency. Therefore, at any wind speed we can adjust the turbine speed to achieve the TSR for maximum power capture. The disadvantages of the variable speed system include the additional cost of power converters and the complexity of the control algorithms [4]. The benefits commonly ascribed to variable-speed operation are larger energy capture, dynamic loads alleviation and power quality enhancement [1]. Power Grid
SCIG 1:ns
Figure 2.5. Directly coupled squirrel-cage induction generator. In this thesis, an adaptive fuzzy controller will be developed to track the maximum power at any wind speed. When the wind speed is above rated wind speed, the pitch controller is used to limit the wind power by reducing the power coefficient Cp. So, their use can offer a number of important advantages such as [2]: 1. Improving the dynamic behavior of the turbines, thereby alleviating the stresses of the mechanical construction. The turbine can thus be made lighter and therefore cheaper. 2. A variable speed system transforms the fluctuating power of the wind mainly into changes of the rotational speed of the turbine and not into
36
fluctuating torque on the electric generator’s shaft. The result is that the electric power contains fewer fluctuations. 3. Variable speed operation permits an increase of the captured energy as well as a reduction of the aerodynamic acoustic noise level.
2.6 Configurations of Variable Speed Wind Turbine Large and small scale wind turbines may be connected to a variety of electrical generators to convert the created mechanical energy to electrical power. The most common generators used are the induction generator, synchronous generator and doubly fed induction generator. While these machines are highly used in large scale systems, the permanent magnet synchronous generator is commonly used in small scale grid connected systems [7].
2.6.1 Synchronous Generators The stator of the synchronous generators holds the set of three-phase windings that supply the external load, where the rotor is the source of the machine’s magnetic field. The magnetic field is either supplied by a direct current (DC) flowing in a wound field or a permanent magnet. A. Wound Field Synchronous Generator (WFSG) Figure 2.6 illustrates a typical setup of a wind turbine with a wound field synchronous generator (WFSG) connected to the grid through power electronic converters. The WFSG has high machine efficiency. The power electronic converters allow direct control over the power factor. However, because of the winding circuit is in the rotor, the size of the WFSG can be rather large. Another drawback of the configuration in Figure 2.6 is that in order to regulate the active and the reactive power, the power electronic converter must be sized typically 1.2 times the rated power. Thus, the use of the WFSG leads to a bulky system. [8]
37
PWM Converters
Power Grid
Rectifier
Figure 2.6. A typical Variable speed wind turbine configuration [8]. In Figure 2.6, the stator of the turbine is connected to the utility grid through two back-to-back pulse width modulator (PWM) converters. The main task of the stator side converters is to control the electromagnetic torque of the turbine. By adjusting the electromagnetic torque, the turbine can be forced to extract maximum power. The rectifier connects the rotor and the utility. It converts the alternating current (AC) from the utility grid into a direct current into the rotor windings. DC current flows through the rotor windings and supplies the generator with the necessary magnetic field for operation. B. Permanent Magnet Synchronous Generators (PMSG) Permanent magnet synchronous generators (PMSG) are common in low power variable speed wind energy conversion systems [4]. The advantages of using PMSGs are its high efficiency and small size. However, the cost of the permanent magnet and the demagnetization of the permanent magnet material should be considered [8] (See Figure 2.7). In Figure 2.7 the stator windings of the PMSG wind turbine are connected to the grid through two back-to-back PWM power converters. Maximum power point tracking algorithms are usually be implemented in the utility side converter, but can generally implemented in either converter. The PWM modulation used in this configuration reduces the current harmonic component in the input and output of the system. 38
PWM Converters
Power Grid
Figure 2.7. Permanent-magnet synchronous generator with PWM converter [8]. By using PWM converters, there is also reduced torque pulsation on the generator and the output power quality is improved [4].
2.6.2 Induction Generators Asides from synchronous generators, induction generators are widely used in wind turbines [4]. Induction generators are advantageous since they are relatively inexpensive, robust and require low maintenance. The nature of induction generators is unlike that of synchronous generators. Induction generators need bi-directional power flow in the generator-side converter since they require external reactive power support from the grid [7]. In order to receive reactive power from the grid, the power electronic converter must allow bi-directional power flow. Specifically, the generator side converter must be a controllable rectifier, or a diode rectifier with capacitive bank to provide the reactive power needed [7]. A. Doubly Fed Wound Rotor Induction Generator (DFIG) The doubly fed induction generator (DFIG) has recently received a great deal of attention in wind energy conversion. In this case, a wound rotor induction generator is used which makes it possible to control the generator by accessing the rotor terminals. Wound rotor induction generators require extra 39
maintenance due to the wear associated with their brushes and slip rings. However, it is able to transfer maximum power over a wide speed range in both sub- and super-synchronous modes. These generators are excellent for high power applications in the MW power range. More importantly, the converter power rating is reduced since it is connected to the rotor, whilst the majority of the power flows through the stator [7].
Figure 2.8. Doubly fed wound rotor induction wind turbine [1]. In Figure 2.8 the stator is connected to the utility grid to provide the necessary magnetization for the machine’s operation. The rotor, on the other hand, is connected to the grid through two back-to-back PWM power converters. The rotor side converter regulates the electromagnetic torque and supplies some of the reactive power. To enable regulation of the electromagnetic torque, algorithms for extracting maximum power are implemented in the rotor side converter stage. The controller of the utility side converter regulates the voltage across the DC link for power transmission to the grid [4]. B. Stator Controlled Squirrel Cage Induction Generator (SCIG) In Figure 2.9 the stator is connected to grid through DC-link converter. The stator side converter regulates the electromagnetic torque and supplies the necessary reactive power to magnetize the machine. The grid side converter, on the other hand, controls the power quality generated power to the grid. It 40
accomplishes this task by regulating the active and the reactive power delivered to the grid while regulating the (direct current) DC link voltage [4]. The squirrel cage induction machine is very rugged, brushless, reliable, and cost effective. However, the drawback of using the SCIG is that the stator side converter must be oversized by 30-50% of machine’s rated power in order to be able to satisfy the machine’s magnetizing requirement [8].
Figure 2.9. Stator controlled squirrel cage induction generator [1].
2.7 WECS Control Control plays a very important role in modern wind energy conversion systems (WECS). Actually, wind turbine control enables a better use of the turbine capacity as well as the alleviation of aerodynamic and mechanical loads that reduce the useful life of the installation. Furthermore, with individual largescale wind facilities approaching the output rating of conventional power plants, control of the power quality is required to reduce the adverse effects on their integration into the network. Thus, active control has an immediate impact on the cost of wind energy. Moreover, high performance and reliable controllers are essential to enhance the competitiveness of wind technology [1]. They include some mechanism to limit the captured power in high wind speeds to prevent from overloading. One of the methods of power limitation is pitch control which reduces the blades lift as the captured power approximates its rated value.
41
WECS schemes with the electric generator directly connected to grid have predominated for a long time. In these WECS, the rotational speed is imposed by the grid frequency. Although reliable and low-cost, these fixed-speed configurations are too rigid to adapt to wind variations. Since, since maximum power capture is achieved at the so-called optimum tip-speed-ratio, fixed-speed WECS operates with optimum conversion efficiency only at a single wind speed. In order to make a better use of the turbine, variable-speed WECS were subsequently developed. They incorporate electronic converters as an interface between the generator and AC grid, thereby, decoupling the rotational speed from the grid frequency [1]. Usually, there are several levels of control system operation. On the uppermost level, a supervisory controller monitors the turbine and wind resource to determine when the wind speed is sufficient to start up the turbine and when, due to high winds, the turbine must be shut down for safety. This type of control is the discrete if-then variety. On the middle level there is a turbine control which includes generator torque control, blade pitch control, and yaw control. This level is responsible for determining the reference power or the reference speed at any wind speed. Generator torque control, performed using the power electronics, determines how much torque is extracted from the turbine, specifically, the high-speed shaft. The extracted torque opposes the aerodynamic torque provided by the wind and, thus, indirectly regulates the turbine speed. Depending on the pitch actuators and type of generator and power electronics, blade pitch control and generator torque control can operate quickly relative to the rotor-speed time constant. Yaw control, which rotates the nacelle to point into the wind, is slower than generator torque control and blade pitch control. Due to its slowness, yaw control is of less interest to control engineers than generator torque control and blade pitch angle control. On the lowest control level there is the separate dynamic control. This level contains the internal generator, power electronics, and pitch actuator controllers which operate at higher rates than the turbine-level control. These low-level controllers operate as black boxes from the perspective of the turbine-level 42
control. For example, the generator and power electronics controllers regulate the generator and power electronics variables to achieve the desired generator torque, as determined by the turbine-level control. The low-level controllers depend on the types of generator and power electronics, but the turbine-level control does not [5]. Figure 2.10 shows WECS control levels.
Start up
Shut Down
Braking
down Uppermost level
Supervisory Controller
Speed Ref. Middle level
Current Ref.
Turbine Control
Speed Control Lowest level
Power Ref.
Power Control
Current Control
Separate Dynamic Control
Figure 2.10. WECS control levels [2].
2.8 Conclusion In this thesis, we will use a three blades horizontal-axis variable-speed wind turbine and stator controlled squirrel - cage induction generator (direct drive) connected to a diode rectifier, reactor, and inverter which is connected to the power grid. 43
We will consider the middle level (Turbine Control) using TSK fuzzy model to determine the maximum reference power at every wind speed by measuring the rotor speed and the output power. From maximum reference power, we determine the reference current for the lowest level where the power electronics are controlled to achieve this current. So, the maximum power transfer is achieved. By these techniques we could get the maximum power point tracking (MPPT) for WECS.
44
Chapter 3 WECS Modeling and Validation 3.1 Introduction A variable speed wind energy conversion system is typically composed of a wind turbine coupled to a synchronous or asynchronous electric generator which is connected to the power grid by means of modern converter system. The converter itself may consist of a rectifier, a DC interconnected circuit, and line commutated inverter. This allows the turbine rotating speed to be decoupled from the grid frequency. In this chapter, the MATLAB Simulink wind turbine model is modified. A nonlinear model of the induction generator is developed by using the d-q model. The interface between the generator and the grid includes subsystems like capacitor, converter, DC link, and inverter (Section 3.2 to 3.5). The objective of the modeling excludes the self-excitation process of the induction generator. It focuses on the behavior after self-excitation. In Section 3.6, the full model of the WECS is presented to be tested and validated. In Section 3.7, the proposed WECS model is tested and validated using MATLAB Simulink at a certain operating points. Section 3.8 presents the conclusion for this chapter. Figure 3.1 illustrates the complete WECS model which consists of a horizontalaxis wind turbine, an induction generator, and a DC-link converter which contains a rectifier, a DC-link, and an inverter connected to the power grid.
3.2 Wind Turbine Model The power extraction of wind turbine is a function of three main factors: the wind power available, the power curve of the generator, and the ability of the generator to respond to wind fluctuation [9].
45
DC Link
Gear Box
1:n
Wind Turbine
Induction Generator
Rectifier
Inverter A.C Grid
Capacitors
Figure 3.1. Wind energy conversion scheme.
3.2.1 Energy and Power in the Wind The kinetic energy in the wind is equal to half the mass (m) of the air times the square of its velocity (
) (3.1)
Where
is in Kg and
is in m/s. (3.2)
where ρ is the air density in Kg/m3 and A is the swept area in m2 . By substituting from (3.2) in (3.1): Kinetic energy per second =
(joules per second)
However, energy per unit of time is equal to power, so this is also the expression for the power in the wind: (3.3) The main relationship that is apparent from the above calculations is that the power in the wind is proportional to: (a) The area through which the wind is passing. (b) The cube of the wind velocity.
46
The power contained in the wind is not the amount of the power that can be extracted by a wind turbine. This is because losses are incurred in the energy conversion process.
3.2.2 Power and Torque of Wind Turbine The power output of a rotor turbine varies with wind speed. Every wind turbine has a characteristic power manufacture curve. With such a curve it is possible to predict the energy production of a wind turbine without considering the technical details of its various components [2]. The power curve gives the electrical output power as a function of the hub height wind speed. Figure 3.2 presents an example of an idealized power curve for wind turbines and Figure 3.3 shows the power density versus wind speed. The performance of a given wind turbine generator can be related to three key points on the wind speed scale: Cut-in wind speed (Vmin): the minimum wind speed at which the machine will deliver useful power (Practically around 5 m/s). Rated wind speed (VN): the wind speed at which the rated power (generally the maximum output power) is reached (about 10 – 15 m/s). Cut-out or shut down wind speed (Vmax): the maximum wind speed at which the turbine is allowed to deliver power (usually limited by engineering design and safety constrain) (around 25 m/s).
Figure 3.2. Ideal power curve [1]. 47
Figure 3.3. Power density vs. wind speed [1]. The mechanical torque
and the captured mechanical power
of a wind
turbine can be expressed in terms of the air density ρ, the blade pitch angle β, the blade radius R and the wind velocity
as follows: (3.4) (3.5)
Where
is power extracted from the wind [Watt],
of the rotor [Nm],
is air density [kg/
], R is rotor radius [m],
coefficient (maximum value Betz’s limit 59.3 %) [10], blades [deg],
is aerodynamic torque
is aerodynamic coefficient.
and
is power
is pitch angle of rotor are nonlinear functions
with respect to the tip speed ratio (TSR)
and the pitch angle . Where the
torque and the power coefficients,
respectively, relates to each other
and
as: (3.6) λ is called the tip-speed ratio (TSR) since it is defined as the ratio of the rotational speed
of the turbine at the tip of the blade to the wind velocity: (3.7)
Where
is rotor speed [rad/s],
is effective wind speed [m/s]
Now in order to calculate the captured power we must define the power coefficient
.We will use the MATLAB Simulink model [10]. The non-linear, 48
dimensionless
characteristic given by Simulink is represented by the (3.8)
and (3.9) [10]: (3.8) (3.9) Where
,
,
,
and
We will modify the Simulink wind turbine model, the wind turbine model was changed from a per unit system to a real value system in order to make the turbine model compatible with the real value components of the WECS [4] .We will use three blade horizontal-axis wind turbine with 6 meter blade radius and 30 gear ratio. From the substitution of (3.9) into (3.8) and modifications we can derive the new power coefficient equation:
(3.10) For
the power coefficient equation will be: (3.11)
Figure 3.4 illustrate the power coefficient at various shows the power coefficient at
values and Figure 3.5
.
From Figure 3.5 we can observe that at
and
. This
means that, there is a certain turbine speed for a certain wind speed. Therefore to extract the maximum power from the wind turbine, the wind turbine speed must be regulated. Consequently, to extract the available power at any wind velocity, the control system should adjust the rotational speed in order to force
. If, on the contrary, extracting a power lower than the available
in the wind was desirable, the power coefficient should be reduced i.e. .
49
Figure 3.4.
versus
and
[5].
0.5
Power Coff.(Cp)
0.4
0.3
0.2
0.1
0
0
2
4
6 8 TIp Speed Ratio(Lambda)
10
12
14
Figure 3.5. Power coefficient vs. TSR at pitch angle (β) = 0.
3.2.3 Simulink Wind Turbine Model Figure 3.6 is the wind turbine model built in Simulink by implementing equation (3.4), (3.5) and (3.10) 1.1 wind _speed ^3 Avoid division by zero
1 Generator speed
Vw^3
u(1)^3
2 Wind speed (m/s)
1/4
Product
3 Lambda
Turbine Speed Wm /Vw
Product
1
p
pi *1 A=pi *R^2
0.5
2 Pm
Cp
lambda
lambda
cp beta
R 3 Pitch Angle (B)
4 Cp
Turbine Mechanical character istics
1 Tm Avoid division by zero
Figure 3.6. Wind turbine model (air density: 1.1 kpa). 50
Where the inputs are wind speed, generator speed and the pitch angle. The outputs are the mechanical torque and the mechanical power. This model has been tested and the curves of the power and torque have been introduced as shown in Figure 3.7 and Figure 3.8. 3
15 m/s
Turbine Power Pm (KW)
2.5
Vw
2
12.5 m/s 1.5
1
0.5
0
5 m/s 0
100
200
300
400
500
600
700
800
900
Rotor Speed Wr (rad/sec)
Figure 3.7. Output mechanical power of turbine vs. the turbine speed. 30
25
15 m/s
Turbine Torque Tm (Nm)
Vw 20
12 m/s
15
10
5
0
6.5 m/s
0
100
200
300
400
500
600
700
800
900
Rotor Speed Wr (rad/sec)
Figure 3.8. Output mechanical torque of turbine vs. the turbine speed.
3.3 Self Excited Induction Generator Model The equivalent circuit in the d-q reference frame of the induction generator is shown in Figure 3.9. The dynamics of the self-excited induction machine when generating is described by the following electromechanical equations [11]: 51
(3.12) (3.13) (3.14)
(3.15) (3.16) Where
p (differential operator) = d/dt.
rs
Llr
+ Lls
0
+ iqs
-
+
rr
λdr(We-Wr)
λdsWe
vqs
Lm
iqr
rs + ids
-
+ 0
Llr
Lls
+ rr
-
λqr(We-Wr)
λqsWe
vds
Lm
idr
-
Figure 3.9. Equivalent circuit of the induction machine in d-q reference frame. These equations are derived assuming that the initial orientation of the d-q synchronously rotating reference frame is such that the d-axis is aligned with the stator terminal voltage phasor [11] (i.e.
52
).
In self-excited induction generators, the magnitude of the generator air-gap voltage in the steady state is given by: (3.17) Where It should be noted that current
is not a constant but a function of the magnetizing
[11] given as: (3.18)
The functional dependency of the magnetizing inductance
on
is
experimentally determined and expressed by a piece-wise linear approximation given by [11]:
Figure 3.9 shows the relation between
in Amperes and
in Henries
.Table 3.1 shows the list of the used symbols in the previous equations. 0.9 0.8 0.7
Lm (H)
0.6 0.5 0.4 0.3 0.2 0.1 0
0
5
10
15
20
25
30
Im (A)
Figure 3.10. The approximated relationship between 53
and
.
Table 3.1. List of symbols of induction generator model. ids,iqs idr,iqr λds,λqs
λdr,λqr
Peak stator d&q axes
Ls
Stator inductance
Peak rotor d&q axes currents
Lr
Rotor inductance
Peak stator d&q axes flux
Lls,L Stator and rotor leakage
linkages
lr
inductance
im
Peak magnetizing current
currents
Peak rotor d&q axes flux linkages
Peak magnitude of air-gap
Peak stator d&q axes voltage
vg
Wr
Shaft speed(rad/sec)
Lm
Magnetizing inductance
We
Electrical frequency(rad/sec)
rs
Stator resistance
N
Number of poles
rr
Rotor resistance
B
Net friction of the rotating parts of the system.
J
voltage
Net inertia of the rotating parts of the system.
3.4 Self Excitation Capacitor Model The self excitation capacitor introduces the following state equations: (3.19) (3.20) Where the capacitor currents
flow as shown in Figure 3.11. As
, the above equations can be reduced to: (3.21) (3.22) 54
Where, : Peak d&q axes capacitor currents. idl, iql: Peak d&q axes currents flowing into the converter. C: Self-excitation capacitance. iql, idl
+
+
iqs, ids
iqc, idc
vqs, vds C
-
-
Figure 3.11. Current-flow directions in the exciting capacitors.
3.5 DC Link Converter Model The DC link converter scheme used in this thesis consists of a controlled rectifier, a DC link reactor and a controlled line commutated inverter [2]. Assuming that the converter is lossless, the instantaneous power balance equation is written as [11], (with
) (3.23)
The a.c and d.c currents of the converter are related by: (3.24) The assumption of lossless converter implies that the power factor of the converter is given by
. Hence we can deduce that: (3.25) (3.26)
Thus from (3.23) we have, 55
(3.27) The dynamics introduced by the d.c link is expressed as: (3.28) The inverter is assumed to be lossless. Thus its d.c voltage inverter delay angle
in terms of the
is given by: (3.29)
Where,
is the maximum inverter DC voltage and:
: Peak magnitude of a.c line current flowing into the converter. : DC link inductance and resistance. : Converter and inverter d.c voltage. : Maximum converter and inverter d.c voltage. : Rectifier firing angle
.
: Inverter firing angle
.
The next task is to interface the equations of the various subsystems. The interfacing equations are given by: (3.30) (3.31)
3.6 Wind Energy Conversion System Full Model Using equations (3.30) and (3.31) in (3.21) and (3.22) and using equations (3.25) and (3.26), the variables
,
,
,
and
can be eliminated
from the equations (3.12) to (3.16), (3.19) and (3.28). The resultant set of equations along with (7) constitutes the unified model of the conversion system [11]. Hence, the overall system has a seventh order nonlinear model. After 56
manipulation, the state equations of the WECS (Induction Generator, SelfExcitation Capacitor and DC Link Converter) can be stated as [2]:
Where:
The seven states namely
denoting
respectively and the control action are denoting
3.7 Model Validation In [11], the proposed model was successfully validated using a laboratory system. A separately excited d.c motor is used as the prime mover for the induction generator. The parameters for the complete experiment system are given in [11] and listed in Table 3.2.
57
In [11], the inverter was replaced with a resistive load. Two operating points were chosen: one is at a rectifier angle 50
ο
and the other is at 25ο .The
operating points at these two firing angles are given in [11] .The responses of the DC link current (IDC) for these steps are recorded and compared with the results of simulation using the nonlinear model. Table 3-2. Parameters of the WECS Simulink model [11]. J
0.09354 Kg.m2
B
0.011 Nm/rad/sec
Lls= Llr
2.17 mH
N
4 poles
rs = r r
0.56 Ω
C
338 µ farads
RDC
4Ω
LDC
400 mH
In order to represent the WECS model in MATLAB Simulink, we need initial states values for the model. This can be calculated by FSOLVE function in MATLAB. This function solves the nonlinear model at certain operating points. In MATLAB FSOLVE function, we will use the inverter firing angle = 90ο (resistive load) as in [11]. For operating point 1: iDC = 2.5, αR = u1 = 50ο and αI = u2 = 90ο. And for Operating point 2: iDC = 3.2, αR = u1 = 25ο and αI = u2 = 90ο. The values of the state vector and the mechanical torque of WECS Simulink model are listed in Table 3-3. In order to simulate the same test as in [11], the initial values of the integrators used in The Simulink WECS model shown in Figure 3.12 is chosen to be equal to the resulting values from the FSOLVE solver at the operating point 1 (Table 3-3).
58
In this test, Tm and
are set as shown in Figure 3.13.The response of the DC
link current for these steps is plotted in Figure 3.14 and this is the same result as in [11]. Table 3-3. Values of the state vector of WECS at two operating points. State name
Operating point 1
Operating point 2
X1 = iqs
12.4991 A
11.1276 A
X2 = ids
1.7719 A
3.1979 A
X3 = iqr
-0.1639 A
-0.3026 A
X4 = idr
-2.4623 A
-3.8599 A
X5 = ωr
288.1739 rad/sec
275.9937 rad/sec
X6 = Vds
151.435 V
137.4764 V
X7 = iDC
2.5 A
3.2 A
Tm
5.343 Nm
7.204 Nm
Rect. angle
U1 IDC
IDc
Rect. angle Idl
U2 Mech. Torque
Tm
-CConstant
Tm
aR
out
DC Link Converter
Idl
Induction generator
NB***Tm is calculated for two values for IDC
aR
In1
(2.5 and 3.2)
Figure 3.12. MATLAB Simulink WECS model. 59
Subsystem
This test shows that the nonlinear WECS model is stable model and it can respond the input torque variation that means wind speed variation, and the changes in the rectifier firing angle
. Now the WECS model is ready to apply
the different control schemes on it to achieve the control objectives and that will be shown in the next chapter. 55
7.5
50
Rectifier firing angle (degree)
Mechanical Torque (Tm)
7
6.5
6
45
40
35
30
5.5 25
5
0
1
2
3
4
5 time (sec)
6
7
8
9
20
10
0
1
2
3
4
5 time (sec)
6
7
8
Figure 3.13. Input mechanical torque (Tm ) and rectifier firing angle (
9
10
)
3.4
DC Link Current (A)
3.2
3
2.8
2.6
2.4
2.2
0
1
2
3
4
5 time (sec)
6
7
8
9
10
Figure 3.14. DC link current response (IDC).
3.8 Conclusion We have composed the nonlinear WECS model from its typical components (wind turbine, induction generator, self excitation capacitor, and DC link converter) in details. The power and torque curves characteristics of this
60
turbine have been plotted related to rotor speed at certain wind speeds. Also the power coefficient curve has been plotted to illustrate the relation between the wind power and the turbine power. The full model is composed from seven state space equations. This model has been tested and validated using MATLAB Simulink. From the results, we can deduce that: this model work properly and now the controllers can be applied in order to achieve our objectives. In the next chapter, the TSK fuzzy model will be designed to estimate the maximum power which should be captured from the wind turbine at any wind speed without measuring this wind speed.
61
Chapter 4 Maximum Power Point Tracking Using TSK Fuzzy Model 4.1 Introduction A model of a system is a tool that can be used to study and improve the behavior of the physical mechanism in the system. The purpose of the model is to build a global functional mathematical model of the dynamic system. The construction of a model is a process of using connectives or operators that combine or make some relation between variables and parameter within a system. For a well defined system, a good mathematical model can be obtained based on the use of algebraic operations, such as addition, subtraction, and differentiation. This mathematical model can also be obtained by parameter estimation of the dynamic model [15]. However in some cases, the physical mechanisms of the process are not well defined in which the complexity of the system has increased tremendously with the number of stages of integration. In addition ambiguity of the operating points in the local linear interval of some dynamic system could have introduced uncertainty to the system. There are also uncertainties due to external environment such that temperature and location. A well-defined global functional structure that can be used to identify a good model based on conventional method is not easy to obtain. Currently, fuzzy sets have indicated that it is capable of modeling uncertain situations and can be instrumental in the formulation of interpolative reasoning. There are at least two major advantages that can be immediately addressed in such approach. First, similarity-based reasoning can be a benefit from fuzzy sets, since similarity is usually a matter of degree. Second, fuzzy sets can represent incomplete information [15]. The concept of building models that exploit fuzzy sets is called logical models or knowledge-based models. This class of model is
62
based on the use of logical-type connectives, such as “and” , ”or” , and “ifthen”. In this chapter, section 4.2 explains the two fuzzy modeling methods, fuzzy linguistic model and fuzzy functional model. Section 4.3 shows the fuzzy model identification based on clustering methods, structure identification. Then, using back propagation and ANFIS, we can tune the fuzzy model parameters, parameter identification. Section 4.4 explains the maximum power point tracking methodology for WECS. Section 4.5 shows how we can achieve the maximum power point tracking (MPPT) using fuzzy modeling. The result in section 4.6 show that, the TSK fuzzy model based on the subtractive clustering method is successfully achieving the MPPT with high accuracy. Finally the conclusion is shown in section 4.7.
4.2 Fuzzy Modeling Fuzzy system models basically fall into two categories which differ fundamentally in their ability to represent different types of information. These models are fuzzy linguistic models (FLM) and fuzzy functional models (FFM) or TSK fuzzy model.
4.2.1 Fuzzy Linguistic Models (FLM) The concept of fuzzy linguistic model (FLM) was originally initiated by Zadeh and first applied by Mamdani [15] by trying to extract the fuzzy model directly from the expert’s knowledge. In this modeling the system is first described linguistically using terms from natural language and the translated into the formal structure of a fuzzy system model with the aid of the representational power of the theory of approximate reasoning [16]. The linguistic description is constructed subjectively on the basis of the a priori knowledge about the system. Generally, this model describes the system by means of a set of “if…then” rules in linguistic terms and can be expressed in the form as follows: 63
Where
means the k-th rule,
variables,
and
,
(j = 1,2,…,n) are the input and the output
are fuzzy subsets of the k-th rule. Membership function
of fuzzy sets Aj and Bj are denoted by Aj(x) and Bj(x) respectively. Usually the rule antecedents and consequents are defined by the fuzzy sets which are fully linguistic in description. The structure does not assume any dependence between the input and the output relationship. It is simply a collection of rules, each defining a point in the product space of model inputs and outputs. The union of these fuzzy points forms a fuzzy graph. An example of a single-input single-output (SISO) fuzzy linguistic model is shown in Figure 4.1. This model describes a type of non-linearity where universes of the input and output are partitioned by using the linguistic label [15]. According to Figure 4.1, x is the input variable with four membership functions: A1 = small, A2 = medium, A3 = high, A4 = very high, and y is the output variable with two membership functions: B1 = small, B2 = high. This model can be represented with four rules as follows: R1 :
If x is A1, then y is B1
R2 :
If x is A2 then y is B2
R3 :
If x is A3 then y is B1
R4 :
If x is A4 then y is B2
Each rule defines a typical feature of the system behavior, i.e., an "important" point in the input-output space. According to the theory of approximate reasoning, each rule of the model above; If x is A then y is B; can be translated into a canonical proposition of the form (x,y) is R. Where R is a fuzzy relationship defined on the Cartesian product of the universe XxY. Given a fuzzy input value x is A, one can obtain the relationship (x,y) on U, where U=A∩R is a fuzzy set defined on the Cartesian product universe XxY with membership function. 64
U(x,y) = A(x) ^ R(x,y) y R2
B2
R1
R3
B1 A1
R4
A2
A3
A4
x
Figure 4.1. Linguistic fuzzy model as a fuzzy graph. Applying the projection principle to get a value F as a fuzzy subset of Y, F = Projy U Such that the membership function of the projection of fuzzy set U onto the output space Y is: F(y) = max(A(x) min R(x,y)) This is known as the max-min rule of inference [15]. Even though this model is relatively easy to understand according to their expression and structure, obtaining a linguistic fuzzy model in a small number of rules from the inputoutput data sets is not a simple task [15]. This is due to the structure of data itself that does not fit well in the form of natural linguistic rules. The fuzzy linguistic modeling also called direct approach as in [16] and this direct approach to fuzzy modeling, based solely upon the use of expert’s description of the functioning of the system, has some inherent limitations. In the direct approach quantitative observations of the functioning of the system are not specifically used for the determination of the structure or parameters of
65
the model. If the expert knowledge about the system is faulty we can obtain a bad model [16] and that is disadvantage.
4.2.2 Fuzzy Functional Models (FFM) Fuzzy Functional Models (FFM) are also called TSK model introduced by Takagi, Sugeno and Kang (1985). The TSK reasoning method is associated with a rule-base of a special format that is different from FLM discussed before. Because of the nature of consequences, TSK fuzzy model is less readable but better approximator than FLM one, being a good choice in the accuracy oriented fuzzy modeling [21]. This format characterizes and provides an effective way to represent non-linear systems by combining a rule-based description with local functional description, i.e., a form of linearization [16]. The rules of this model are in the form: Rk :
If x1 is A lk and... and xn is Ank then y1 = c0k+c1k x1+…+cnk xn
Where Rk means the k-th rule, xj (j= 1, 2, .... n) in the conditional sentence are the input variables, Ajk is a fuzzy subset, yk is the output from the k-th rule, and the coefficient cjk of the linear equation is a consequent parameter. In this case, each rule represents a locally linearized model with the interval concept over the fuzzy regions defined by the rule premises. The identification of a fuzzy model using input-output data consists of two parts: Structure identification and parameter identification [16]. The structure identification consists of premise structure identification and consequent structure identification. The parameter identification also consists of premise parameters identification and consequent parameter identification. The identification process of TSK fuzzy model is shown in Figure 4.2. Structure identification: Premise structure identification: can be approached as the problem of partitioning the input space x1,…,xk into the minimum number of fuzzy subspaces that are needed to form a fuzzy model. 66
Input x
Output y Real System + Fuzzy Model
y*
Parameter
Error
Identification
Structure Identification
Figure 4.2. TSK identification algorithm. The process of selecting fuzzy subspaces is based on the unbiasedness criterion using the Group Method of Data Handling (GMDH) [15]. Consequent structure identification: can be approach as the problem of finding which input variables x1,…,xk that are necessary should appear in the consequent to form a linear combination. Parameter identification: Premise parameter identification: can be approached as the problem of determining the optimum membership functions A1,…, Ak of the fuzzy sets in the premise. The optimization process is according to the bases of the membership function. Consequent parameter identification: can be approached as the problem of determining the optimum parameters c1,....,ck to rninimize a performance index (the root mean square of the output error). The TSK model is a nonlinear model consisting of a number of rule-based linear models and membership functions that will determine the characteristic of the system. It works well with linear techniques (e.g., PID control), and is 67
better suited to mathematical analysis. However, it has a drawback; namely, it is an iterative model which means that the fuzzy partition of a data space, the membership function and the consequent are interdependent sub problems. That makes it difficult to obtain a convincing model that can be used in the practical problem [15]. To overcome this difficulty, fuzzy clustering is chosen as alternative technique for model identification. Fuzzy clustering technique and its application will be presented in the following section.
4.3 Fuzzy Model Identification Based on Clustering Methods In the literature, various algorithms are proposed for mining. These algorithms commonly utilize fuzzy clustering in structure identification. Basically, there are three different approaches in which one can utilize fuzzy clustering; the first one is based on input space clustering, the second one considers clustering realized in the output space, while the third one is concerned with clustering realized in the combined input–output space [23]. In these methods, we eliminate the presumption of existence of expert information. We just have the input-output data set. This formulation is accomplished by a two-step procedure. The first step is the generation of the rules. The output of this step is a collection of rules, including the antecedent and consequent templates, which can be seen as rough estimates of the final rule base. We can call this first step as structure identification. The second step consists of an adjustment of the templates of initial rough rules to give us the final rule-base [16] [19] [20]. The tuning can be accomplished by some of the learning methods will be described in the next section. In this section we will introduce three clustering methods: Fuzzy C-Means, Mountain-Clustering and Subtractive-Clustering method.
4.3.1 Fuzzy C-Means Method (FCM) The concept of clustering allows the partitioning of collected data points from a large data set. These points have system behavior which is interrelated, thus forming a group of clusters. The characteristic of each cluster can be used as the properties to identify their members from the members of the other clusters. 68
Fuzzy C-Means clustering (FCM) is a combination of conventional clustering method and fuzzy set theory. It is a data clustering technique, where each data point belongs to a cluster to a degree specified by a membership grade. The clusters are functions assigning to each data point a degree of membership grade between zero and one. The sum of the membership of each data point to all the clusters is one. The algorithm starts with a desired number of clusters and an initial prediction for each cluster center, assuming that these cluster centers are very inaccurately placed. In addition, every data point has a membership grade for each cluster. By iteratively updating the cluster centers as well as the membership grade of each data point, the algorithm can guide the cluster centers to the optimal location in the data space. This iteration is based on minimizing an objective function that represents the distance from any given data point to a cluster center weighted by that data point's membership grade [15] [17]. The concept of this algorithm can be presented in the mathematical way as follows: Let X={x1, x2 .... xn}, xk
Rn be a finite data set. Define
as the
degree of membership of the k-th data vector in the i cluster, where (4.1) (4.2) Let vi denote a vector representing the center of fuzzy cluster i, vi = (v1, v2,..,vc). The FCM algorithm results from trying to minimize the objective function [15]: (4.3) Where
represents the norm which is the distance measure between
the data point xk and cluster center
. The constant m is a weighting exponent
on each membership or the "amount of fuzziness". This constant can be selected as any value in the open interval of [1,∞). The higher the value of m used, the less those data whose membership values are low contribute to the objective function. Usually the value of m is chosen to be equal to 2. Thus, the 69
FCM objective function J is a weighted sum-of-squared error functional, with the square of distance error between data points and cluster centers weighted by the m-th power of the membership grade. In order to minimize the objective function, the cluster centers and membership functions are chosen so that the closer a data point is to the cluster center, the higher its membership grade is for that cluster. The general algorithm can be stated as follow: Step 1: For every (i.k), and an initial guess of the centers vi, find the membership values as follow: (4.4)
Step 2: Determine cluster centers vi (Fuzzy Centroid) for each cluster as follows: (4.5) Step 3: Repeat steps 1 and 2 until change is less than a given tolerance. If is the specified tolerance, then the algorithm is repeated until: (4.6) Other stopping criteria such as the matrix norm of the membership functions can be used. The flow diagram of the procedure described above is shown in Figure 4.3.
4.3.2 Model Identification Based on FCM In this section, we show how the clustering method, Fuzzy C-Means, can be used in a procedure for obtaining the structure and initial estimates of the parameter of the rule-base of a fuzzy system model. We will apply these methods to a fuzzy linguistic model (FLM).
70
Start
Guess at Initial Centers
Determine Memberships
Calculate New Centers
Is Change
Gray Region
( P k / P1 )
( Pk / P1) > Below thr.
Below threshold
Reject zk as a cluster center
Calculate
Reject zk as a cluster center
dmin
Is
Yes
Stop ?
No Reject zk Pk = 0 Select Next Max. Pk
Figure 4.4. Flow diagram of subtractive clustering algorithm. 80
If the potential falls in the gray region, we check if the data point provides a good trade-off between having a sufficient potential and being sufficiently far from existing clusters centers. 4.3.6 Model Identification Based on Subtractive Clustering Method In order to extract a rule Ri from cluster center
in the form of the first order
TSK fuzzy model as a linear function of input variables (two inputs one output system):
Then let
where C is a constant matrix and D is a column vector
and let: (4.27) So, the final output will be: (4.28)
(4.29)
Given a collection of n input data points, the model output is given by:
(4.30)
(4.31) 81
Where B is the matrix of output values, A is a constant matrix, and X is a matrix of parameter to be estimated. The process continues by optimizing the parameters in the consequent with respect to the training data, i.e., choose the a i ’ s and b i ’ s in some optimal fashion. As pointed out by Takagi and Sugino (1985), given a set of rules with fixed premises, optimizing the parameters with respect to training data reduces to a linear least squares estimation problem. Such problems can be solved easily and the solution is always globally optimal [15]. Based on the least square formulation, the parameters a i ’ s and b i ’ s are to be chosen such that the extracted outputs, given by equation (4.28), at the input points xi yield the smallest least squares errors as compared to the actual output yi , i.e., (4.32) Let
and
be the least squares estimates, then, the function can be modeled
as: (4.33) The subtractive clustering method and the rule extraction will be used in fuzzy modeling in the next sections.
4.4 Maximum Power Point Tracking (MPPT) Methodology Variable-speed wind turbines have three main regions of operation. A stopped turbine or a turbine that is just starting up is considered to be operating in region 1. Region 2 is an operational mode with the objective of maximizing wind energy capture. In region 3, which encompasses high wind speeds, the turbine must limit the captured wind power so that safe electrical and mechanical loads are not exceeded. For each region, the solid curve in Figure 82
4.5 illustrates the desired power-versus-wind-speed relationship for a variable speed wind turbine.
6
5
Power (kw)
High Wind Cutout
Wind Power Cp=1
4
Turbine Power
3
Region 3 2
Region 2 1
Cp=0.49 Region 1 0
0
5
10
15
20
25
Wind Speed (m/sec)
Figure 4.5. Steady state power curves [5]. In this thesis, we focus on region 2. So, the generation objective in this region is to extract all the available power in the wind using maximum power point tracking (MPPT) at any wind speed in the range of (5-15 m/s). Figure 4.6 shows the relationship between the wind speed and the rotor speed on the one hand, and the mechanical power of the wind turbine, on the other hand. This Figure also shows the maximum power line which should be tracked by the controller. The controller job is to find the optimum rotor speed, at which the maximum power can achieved, for every wind speed. Different algorithms have been used to track the maximum power line (See Figure 4.6). In [5] an adaptive controller was developed to maximize the energy capture by regulating the rotor speed. A neural network controller was designed in [26] in order to maximize the energy capture and reduce the mechanical loads. Also in [27] an intelligent algorithm was used using the intelligent memory method with an on-line training process. An intelligent algorithm, by using a modified version of Hill Climb Search (HCS) and
83
intelligent memory, was used in [4]. A TSK fuzzy model was developed using fuzzy clustering and recursive least-squares (LS) optimization in [28].
Maximum Power Line
3
Turbine Power (kw)
2.5
B
2
A
1.5
1
0.5
0 0
15
10 100
200
300
400
500
600
700
800
5
Wind Speed (m/sec)
Rotor Speed Wr (rad/sec)
Figure 4.6. Turbine power curves.
4.5 MPPT Using Fuzzy Modeling Now, we will design the middle control level which its output is the reference power for the lowest control level. Consequently, this reference power produces the reference current. A fuzzy model is designed to produce the reference maximum power without measuring the wind speed. The inputs to the fuzzy model are the rotor speed and the output power, while the output is the estimated maximum power, and that is the maximum power that can be generated from the wind turbine. Therefore, the fuzzy system, by acquiring and processing at each sample instant the inputs, is able to calculate the maximum power that may be generated by the wind generator, as shown in Figure 4.7. Referring to Figure 4.6, we can explain the proposed TSK fuzzy system. Assuming that the wind turbine operates initially at point A, the fuzzy control system from measured rotor speed ωA and turbine power PA can derive the 84
corresponding optimum operating point B, giving the desired rotor speed reference ωB. Therefore, the generator speed will be controlled in order to reach the speed ωB allowing the extraction of the maximum power PB from the turbine. The proposed fuzzy control, therefore, represents a sensorless approach since it is not necessary to measure the wind velocity.
Measured Rotor Speed TSK Fuzzy Measured Turbine Power
Reference Maximum Power
System
Figure 4.7. Implemented TSK fuzzy system. In order to compose the fuzzy model, we follow these steps: Step1: Collecting the input-output data set using the turbine curves (See Figure 4.6). The power curves allow to obtain for an assigned time varying wind velocity profile, a data set of samples (one for every time steps) consisting of two inputs (measured rotor speed and generated power) and the corresponding output (maximum extractable power). Step 2: Partitioning the input–output space. In order to perform partitioning of the input–output space, various approaches can be used. Amongst them, pattern recognition methods of fuzzy clustering, such as fuzzy c-means (FCM), are suitable tools for the partitioning process. Besides, the mountain clustering method and the subtractive clustering methods can be used. Step 3: The produced cluster centers are tuned using back propagation and the ANFIS learning techniques. Step 4: After producing and learning the cluster centers, the TSK fuzzy model is based on a set of fuzzy IF–THEN rules is designed and tested.
85
4.6 Simulation and Results In the first step we use the wind turbine model, which has been discussed in chapter 3 (See Figure 3.6), to produce the turbine curves as shown in Figure 4.6 From these curves we collect the input-output data set to be used in clustering methods. In the second step we use the clustering methods to produce the cluster centers. In this thesis, we use the Fuzzy C-Means (FCM) method and the subtractive clustering method. The results of both are compared. Then, in the third step we tune the cluster centers using back propagation and the ANFIS techniques. In the forth step, the fuzzy model is composed using the tuned cluster centers. Where, the cluster centers represent the antecedents and the consequents parts of the fuzzy system rules. By this, we make the structure and parameters identification. After that, we simulate the complete model with the designed fuzzy model. At any wind speed, the fuzzy model gives the reference maximum. The designed fuzzy model maximizes the produced power in the range wind speed from 5 m/s to 15 m/s. We simulate the fuzzy model in two cases of clustering, Fuzzy C-Means clustering and subtractive clustering. In our simulations, the wind data acquired from the Royal Netherlands Meteorological Institute and the Koninklijk Nederland’s Meteorological Institute [30] are used: wind speed time histories consist of 50,000 observations within a 2000 sec interval, with a sampling rate of 25 Hz. The used wind data set is shown in Figure 4.8. 4.6.1 MPPT Fuzzy Model Using Fuzzy C-Means Clustering Method Fuzzy c-means (FCM) is a data clustering technique where in each data point belongs to a cluster to some degree that is specified by a membership grade. This technique was originally introduced by Jim Bezdek in 1981[1] as an improvement on earlier clustering methods. It provides a method that shows 86
how to group data points that populate some multidimensional space into a specific number of different clusters [10].
14
Wind Speed (m/s)
12
10
8
6
4
0
200
400
600
800
1000
1200
1400
1600
1800
2000
time (sec)
Figure 4.8. Wind speed observations profile. This clustering technique needs the number of cluster centers. In this model, we use eleven cluster centers. That means eleven membership functions for the input and output. Consequently that means 11x11 rules in the rule base. Using MATLAB m-file, we programmed the FCM, then, the fuzzy model is composed using the cluster centers and spread radius (σ). The general fuzzy rule is:
Where
is the first input which is the measured rotor speed in rad/sec,
the second input which is the measured output power in watt, and fuzzy model output which is the reference maximum power in watt. the fuzzy sets of the first input and
is is the are
are the fuzzy sets of the second input.
We use eleven Gaussian membership functions for each input and eleven singleton membership function for the output. The produced cluster centers from clustering method are used as the centers of the membership functions. Also, we use the center of area (COA) method in the defuzzification process.
87
The fuzzy model is programmed using the Embedded MATLAB Editor-Block in Simulink editor. We get the cluster centers values as in Table 4.1 Table 4.1. Cluster centers by FCM method. Wr (Rotor Speed)
Pout (Output Power)
Pmax (Maximum
Rad/sec
Watt
Power) Watt
478.9
2359.8
2598.9
279.2
384
629.2
163.7
72.4
240
630.6
4.2
259.6
478.1
1003
23261
720
47
1791.6
433.7
1671.4
1932.6
142.2
110.1
2498.3
119.4
96.2
1406.4
373.4
991.6
1231.9
653.2
20.5
858.3
And the objective function reduces to 0.4653. Using the wind data set as in Figure 4.8 in MATLAB Simulink to test the fuzzy model, we get the estimated maximum power curve as shown in figure 4.9. Also, the effective maximum power curve is drawn in the same curve to be compared. From figure 4.9 the fuzzy model approximates with a little accuracy the maximum power extractable from wind energy conversion system. The rotor speed related to the wind speed profile is shown in Figure 4.10. Let us use the subtractive clustering with the least square methods and see the result.
4.6.2 MPPT TSK Fuzzy Model Using Subtractive Clustering Method If we do not have a clear idea how many clusters there should be for a given set of data, Subtractive clustering [10], is a fast, one-pass algorithm for estimating the number of clusters and the cluster centers in a set of data.
88
In this method, we just give the input/output data and the radius ra to the subtractive clustering method to give us the cluster centers. 2.5
2
Power (KW)
1.5
1
0.5
0 Fuzzy model estimated power Maximum power -0.5
0
200
400
600
800
1000 time (sec)
1200
1400
1600
1800
2000
Figure 4.9. Maximum power estimated by the fuzzy model and effective maximum extractable power (FCM). 400
Rotor Speed (rad/sec)
350
300
250
200
150
100
0
200
400
600
800
1000
time (sec)
1200
1400
1600
1800
2000
Figure 4.10. Rotor speed related to wind speed profile (FCM). Using MATLAB toolbox command, we build the TSK fuzzy model, then, we train the TSK fuzzy model using ANFIS technique. Using ra=0.5, clustering radius, we get six rules with Root Mean Square Error (RMSE) = 0.5386 as shown in Table 4.2.
89
Table 4.2. TSK Fuzzy model parameters. TSK
Wr (Rotor
Fuzzy
Speed)
Model
Rad/sec
Pout (Output Power)Watt
Pmax (Maximum Power) Watt
Rule 1
563.2
0
-15.81*Wr+1.722*Pout+6737
Rule 2
151.2
202.1
28.62*Wr+2.487*Pout-32380
Rule 3
744.1
0
-12.17*Wr+3.439*Pout+12910
Rule 4
319.2
1284
-8.316*Wr+0.5059*Pout+3963
Rule 5
84
42.25
44.83*Wr+26.18*Pout+22560
Rule 6
520.8
2126
1.818*Wr+0.02389*Pout+1711
The TSK fuzzy model is tested using the same wind speed data set which is used previously with Fuzzy C-Means clustering method. Figure 4.11 shows the estimated power curve and the effective power curve.
2
Power (KW)
1.5
1
0.5
0 TSK estimated maximum power Maximum power -0.5
0
250
500
750
1000
1250
1500
1750
2000
time (sec)
Figure 4.11. Maximum power estimated by the fuzzy model and effective maximum extractable power (Subtractive clustering). From Figure 4.11 we can observe that, the proposed TSK fuzzy model is successful to some extent in achieving the maximum power point tracking (MPPT) with small tolerance. Also this is better than the previous fuzzy model. 90
The rotor speed related to the wind speed profile in case of subtractive clustering method is shown in Figure 4.12 500 450
Rotor Speed (rad/sec)
400 350 300 250 200 150 100 50
0
200
400
600
800
1000
time (sec)
1200
1400
1600
1800
2000
Figure 4.12 Rotor speed related to wind speed profile (Subtractive clustering). Since the cluster radius indicates the range of influence of a cluster, a small cluster radius will usually lead to finding many small clusters in the data which result in many rules. On the other hand, a large cluster radius will usually lead to finding a few large clusters in the data which result in fewer rules.
4.7 Conclusion Sensorless peak power tracking control methods allow to overcome problems linked to the inaccuracy of measuring wind speed and to the effect of system parameters variation with time and varied environment. Nevertheless traditional sensorless peak power tracking control methods exhibit, generally, time-consuming computation, loss of accuracy or high memory occupancy. Therefore, a methodology for designing a sensorless maximum power point tracking TSK fuzzy system for variable speed wind generators has been proposed and tested in this thesis. The proposed adaptive fuzzy controller, thanks to its adaptive characteristic based on real data and without the need of an accurate model of the system to be controlled, can continuously optimize its internal parameters in order to 91
compensate for all the non-linearities and time variances of the system under control, thus adapting them to the system dynamic behavior. The TSK fuzzy system is characterized by low memory occupancy, fault tolerance and learning capability allowing overcoming some disadvantages of classical sensorless peak power tracking control methods and well adapts to be implemented on microcontroller.
92
Chapter 5
Fuzzy PI Controller for WECS 5.1 Introduction In this chapter, we will use the WECS model, which has been developed and tested in Chapter 3, in order to design a suitable controller to regulate the power flow with minimum reactive power burden on the induction generator. As discussed in chapter 3, the open loop wind energy conversion system after self-excitation exhibits a stable characteristic. Here, we seek to regulate the power flow indirectly by choosing the DC link current as the output signal of regulation. We apply a PI controller as in [11]. At a certain operating point, the controller works properly. But, if the operating point is changed the controller will fail to track the set point. This is because that the WECS model is nonlinear. So, we use a fuzzy logic controller as a nonlinear controller in place of the PI controller to track the set points at various reference DC currents. In Section 5.2, the PI controller is applied to WECS and the closed loop system is simulated. Section 5.3 shows that, at different operating points the PI controller fails to track the set point. In Section 5.4, fuzzy logic control is introduced. A fuzzy PI controller is applied to the WECS in section 5.5. Summary and conclusion are presented in section5.6.
5.2 Conventional PI Controller for WECS The objective of the controller design in [11] is to regulate the power flow with minimum reactive power burden on the induction generator. The overall control scheme proposed in [11] is shown in Figure 5.1 is required to regulate the power flow indirectly by choosing the DC link current as the output signal of regulation. For fixed reference value
, the DC link current can be maintained at a chosen
by manipulating
. In order to reduce the reactive 93
Induction Generator
DC Link
Rectifier
Inverter
IDC
Wind Turbine
ZOH
ZOH
PI
PI
Capacitors
-
Iref
+
A.C Grid
+
T1
T2
Figure 5.1. Multi rate control scheme [11]. power consumption by the converter, it is necessary to keep value
close to zero. To maintain
at
be manipulated. With suitable choice of
and
at
at a threshold ,
should also
, the power transfer through the DC
link can be maximized. The overall control scheme proposed in [11] is shown in Figure 5.2. In the first PI loop which regulates
through
, the error (
is
sampled at faster rate every T1 seconds. In the second PI loop which regulates through
, the error (
is sampled at a slower rate every T2
seconds. The choice of the sampling period T1 is bounded on the upper side by the dominant time constants of the open loop system and the desired speed of closed loop system response and on the lower side by the computer processing time. It is also affected by the PI gain values responsible for the finite word length of the digital computer. The philosophy in selecting T2 is that the T1 loop should damp out the transients in the link current well within one sampling interval T2. In [11], T1 and T2 are selected at 10 ms and 500 ms respectively. 94
In [11], PI controllers were designed using standard frequency domain optimization (Wiener-Hopf) procedures on the small signal linearized models. The PI gains Kp and Ki are so chosen as to minimize a performance index:
Where
and
are frequency dependent weighting functions. Figure 5.2
depicts the control system configuration considered for the optimization procedures. Plant
Controller R(S)
U(S)
E(S)
Gp(S)
Y(S)
+ -
Figure 5.2. Control system configuration [11]. In this test, the system response with only T1 loop operating is considered. This test was executed in [11]. The objective of this test was to show the response of the closed loop system to a step change in the input reference current During these tests,
.
is kept fixed at 168o. The Simulink model is built for this
test is shown in Figure 5.3. The gains of the PI controller used in this test were Kp = -0.16 and Ki = -10.5. The reference current changed from 2.2 A to 3 A under the assumption that this current is available from the wind turbine at certain wind speeds. In order to do this test in MATLAB Simulink, we need initial conditions to the state variables. So, we use the FSOLVE function to solve the WECS model at 2.2 A and at 3 A.
values corresponding to this values are given in [11] as
28o and 12o.
95
Figure 5.4 and Figure 5.5 show the simulation results for this test. The same results are obtained compared to the same test in [11]. Figure 5.4 shows the DC link current error and the rectifier firing angle (control signal). Figure 5.5 shows the step reference current and the dynamic response of the closed loop WECS to a step change in the input reference current.
e
Iref
aR
aR
Iref
IDC
PI Controller WECS Model
IDC
Figure 5.3. MATLAB Simulink model with PI controller. 30 28
0.6
26 Rectifier Firing Angle (degree)
1 0.8
Current error (A)
0.4 0.2 0 -0.2 -0.4
24 22 20 18 16
-0.6
14
-0.8
12
-1
0
1
2
3
4
5 time (sec)
6
7
8
9
10
10
0
1
2
3
4
5 time (sec)
6
7
8
9
10
Figure 5.4. DC link current error and the control signal (PI controller). 3.1
3
3
2.9
2.9
2.8
2.8
2.7
2.7
DC Current(A)
DC Reference Curent (A)
3.1
2.6 2.5
2.6 2.5
2.4
2.4
2.3
2.3
2.2 2.1
2.2
0
1
2
3
4
5 time (sec)
6
7
8
9
2.1
10
0
1
2
3
4
5 time(sec)
6
7
8
9
Figure 5.5. The DC reference current and its response (PI controller).
96
10
5.3 PI Controller Failure In the previous section, a PI controller is designed to maintain the DC link current at certain values at a certain predefined operating point, but if we change the reference current to different values, the designed controller may fail to maintain the stability of the closed loop WECS. This is because of changing the operating point. In this test, a step change in
from 1A to 3 A is applied using the same
designed PI controller gains in section 5.2. Figure 5.6 shows the control signal and the response of the closed loop WECS for this reference step change. We observe that this control signal is unpractical and cannot be implemented. What has happened in this test is because the WECS model is a nonlinear model and the PI controller is a linear controller. So, we need a nonlinear controller to maintain the DC link current at various operating points. One of these controllers is a fuzzy logic controller that will be explained briefly in the next section.
200
4
2
-200 DC Current Responce (A)
Rectifier Firing Angle (degree)
0
-400
-600
0
-2
-4
-800 -6
-1000
-1200
-8
0
1
2
3
4
5 times (sec)
6
7
8
9
10
0
1
2
3
4
5 time (sec)
6
7
8
9
10
Figure 5.6. The control signal and the response of the DC link current (PI failure).
5.4 Fuzzy Logic Control (FLC) Conventional control has provided numerous methods for constructing controllers for dynamic systems. Basically, these conventional approaches to 97
control system design offer a variety of ways to utilize information from mathematical models on how to do good control. Sometimes they do not take into account certain heuristic information early in the design process, but use heuristics when the controller is implemented to tune it (tuning is invariably needed since the model used for the controller development is not perfectly accurate). Unfortunately, when using some approaches to conventional control, some engineers become somewhat removed from the control problem (e.g., when they do not fully understand the plant and just take the mathematical model as given), and sometimes this leads to the development of unrealistic control laws. Sometimes in conventional control, useful heuristics are ignored because they do not fit into the proper mathematical framework, consequently, this can cause problems [12]. In the last few years the applications of artificial intelligence techniques have been used to convert human experience into a form understandable by computers. Advanced control based on artificial intelligence techniques is called intelligent control. Intelligent systems are usually described by analogies with biological systems by, for example, looking at how human beings perform control tasks, recognize patterns, or make decisions. There exists a mismatch between humans and machines: human’s reason in uncertain, imprecise, fuzzy ways while machines and the computers that run them are based on binary reasoning. Fuzzy logic is a way to make machines more intelligent enabling them to reason in a fuzzy manner like humans. Fuzzy logic, proposed by Lotfy Zadeh in 1965, emerged as a tool to deal with uncertain, imprecise, or qualitative decision-making problems. Controllers that combine intelligent and conventional techniques are commonly used in the intelligent control of complex dynamic systems. Therefore, embedded fuzzy controllers automate what has traditionally been a human control activity [13].
5.4.1 Fuzzy Logic Controller: Basic Concept By a fuzzy logic controller (FLC), we mean a control law that is described by a knowledge-based system consisting of IF ... THEN rules with vague predicates 98
and a fuzzy logic inference mechanism. Figure 5.7 shows the structure of fuzzy controller. A typical FLC describes the relationship between the change of the control Δu(k ) = u(k ) − u(k −1), on the one hand and the error e(k ) and its change Δe(k ) = e(k ) − e(k −1), on the other hand. Such a control law can be formalized as [16]: Δu(k ) = F(e(k ),Δe(k ))
(5.1)
Where F is a mapping from the inputs e(k ) and Δe(k ) to the output Δu(k ) and k is the discrete sampling index. The actual output of the controller u(k ) is obtained from the previous value of control u(k −1) that is updated by Δu(k ): u(k ) = u(k −1) + Δu(k )
(5.2)
This type of FLC was suggested by Mamdani and Assilian in 1975 [16] and is called the Mamdani-type FLC. A prototypical rule-base of a simple FLC that realizes the control law (5.1) is: 1- IF e(k ) is P AND Δe(k ) is Z THEN Δu(k ) is P 2- IF e(k ) is N AND Δe(k ) is Z THEN Δu(k ) is N 3- IF e(k ) is Z AND Δe(k ) is Z THEN Δu(k ) is Z 4- IF e(k ) is Z AND Δe(k ) is P THEN Δu(k ) is P 5- IF e(k ) is Z AND Δe(k ) is N THEN Δu(k ) is N where P, Z, and N stand for positive, zero, and negative. Each rule is characterized by an IF part called the antecedent and a THEN part called the consequent. The antecedent of a rule contains a set of conditions; the consequent contains a conclusion. Each rule works in the following way: If the conditions of the antecedent are satisfied, then the conclusions of the consequent apply.
99
We can look at the FLC as a system that has its inputs the variables that are included in the antecedents of the rules, and as an output, the variable that is
Inference mechanism
Defuzzification
Reference I/P r(t)
Fuzzification
Fuzzy controller
Rule-base
u(t)
y(t) Process
Figure 5.7. Fuzzy controller architecture. included in the consequents. We shall call the error e(k ) and its change Δe(k ) the inputs, and the change of the control signal Δu(k ) the output of the FLC as in equation (5.1). The linguistic labels (such as e(k ) is Z) are represented by fuzzy sets. The set of linguistic labels of one variable forms a term set as shown in Figure 5.8.
Figure 5.8. Typical membership functions. In Figure 5.8, the universe of discourse is assumed to be [−1, 1]. We can define the term sets of Δe and Δu analogously. The following comments explain the logic behind the rule-base:
100
1. The first two rules ensure fast approach to the set-point. If the error is positive, it means that r(k ) − y(k ) > 0 . So, an increase in the control action, u(k ), would increase the output, y(k ), such that it approaches the reference, r(k ). On the other hand, if the error is negative, a decrease in u(k )results in a decrease in y(k ) so that it approaches r(k ). 2. Rule 3 is self explanatory. 3. Rule 4 describes the control strategy when y(k ) is close to r(k ). If Δe > 0, it means e(k ) − e(k −1) > 0 . This leads to: (r(k ) − y(k ))−(r(k −1) − y(k −1))> 0.
(5.3)
Assuming slow changes in (r ) k , we can conclude that y(k −1) − y(k) > 0. Since y(k ) is decreasing below y(k −1), increasing u(k ) will push y(k ) towards y(k −1) which is closer to r(k ). 4. Rule 4 is opposite to Rule 5. It is possible to show that y(k −1) − y(k) < 0. In this case y(k ) is increasing above y(k −1). Decreasing u(k ) will pull y(k ) down to y(k −1). 5. The FLC can be improved if we consider more detailed logical statements. As an example the term set of each variable can be extended to {NL, NM, NS, Z, PS, PM, PL} where NL, NM, NS, Z, PS, PM, PL stand for negative large, negative medium, negative small, zero, positive small, positive medium, and positive large, respectively.
5.4.2 Reasoning with an FLC The term reasoning is used to indicate the process in which we are given the values of the inputs, the antecedent variables, and we use them in conjunction with our knowledge base to obtain the value of the output consequent. Formally, we can represent the rule-base of an FLC in the following format: IF U1 is B11 and U2 is B12 THEN V is D1. 101
ALSO ... ALSO IF U1 is Bm1 and U2 is Bm2 THEN V is Dm . U1 and U2 are input variables and V is the output variable. Bi1, Bi2 , and Di are linguistic values represented as fuzzy subsets of the respective universes of discourse X1, X2 , and Y . The membership functions of these linguistic values are denoted Bi1( x1), Bi2 (x2), and Di (y). If the inputs to the FLC are the values
and
,
the objective is to determine the appropriate value of the output V. A procedure to obtain the fuzzy output is: 1. Find the firing level of each of the rules. 2. Find the output of each of the rules. 3. Aggregate the individual rule outputs to obtain the overall system output. 4. Calculate the defuzzified centroid of the output fuzzy set. Given the FLC rule-base for some values of the input variables U1 and U2: The first step is to determine the level of firing,
, of the rules according to: (5.4)
hence, the degree of firing (DOF) of a rule is obtained as the minimum over the degree of matching of a rule's antecedent fuzzy sets with its appropriate input value. The second step is called fuzzy implication. In this step, the membership functions of the consequent fuzzy sets are cut up to the respective DOF. The fuzzy sets (the Fi's inferred by individual rules) are obtained from: (5.5)
102
The third step is called rule aggregation. The individual outputs from the rules are aggregated according to the following formula: (5.6) The fourth step is the process of defuzzification. This is done using the center of area (COA) or the mean of maximum (MOM) method as defined below [16]. Center of Area (COA) formula: The COA method defines the defuzzified value of a fuzzy set F as its fuzzy centroid: (5.7) The calculation of the COA defuzzified value is simplified if we consider finite universe of discourse Y and thus a discrete membership function F(y): (5.8) Mean of Maximum (MOM) formula: The MOM method determines the defuzzified value, as a mean of all values of the universe of discourse, having maximal membership grades: (5.9) Where
is the set of elements of the universe Y which attain the maximum
value of F(y) and q is the cardinality of
.
5.4.3 Illustration of the basic reasoning algorithm The main steps of the procedures described earlier for firing the rules, fuzzy implication, aggregation, and defuzzification, are summarized in the following reasoning algorithm [16]: 1- Calculate the DOF of the rules
for crisp inputs by (5.4).
103
2- Find the membership function of the output fuzzy set Fi, inferred by the ith rule according to expression (5.5). 3- Form the membership function of the output fuzzy set F using (5.6), inferred by the rule-base of FLC by aggregation the Fi. 4- Calculate the crisp output y* of the FLC using the COA (5.7) or (5.8) or MOM (5.9).
5.4.4 The FLC relation to The Conventional PI control The FLC describes with the aid of fuzzy if-then rules the relationship between the change of the control Δu(k ) = u(k ) - u(k −1) on one hand, and the error e(k) and its change Δe(k )=e(k ) - e(k −1) on the other hand: Δu(k ) = F(e(k ),Δe(k )) The internal mechanism of the FLC translates it into a mapping: Δu(k ) = f (e(k ),Δe(k )) We can see the similarity between the Mamdani-type FLC and the well known incremental algorithm of the PI controller that expressed by: Δu(k ) = Kp Δe(k ) +Ki e(k ) Where Kp and Ki are the parameters of the PI controller. Both control laws provide a relationship between variables e(k ) and Δe(k ) in one hand and Δu(k ) on the other hand. So the Mamdani-type FLC can be regarded as a PI-like fuzzy logic control algorithm. The difference is in the type of the relationship is linear, while in FLC it is nonlinear.
5.5 Fuzzy PI Controller Design for WECS By using the definitions in the previous section, we design a fuzzy PI controller on WECS to manipulate the problems of the conventional PI controller.
104
Firstly, we use the error, between the reference current and the DC link current, and the error derivative as inputs to the fuzzy controller. The output is the control signal derivative, where the rectifier firing angle
is the control
signal. Figure 5.9 shows the relationship between the error and the error derivative, on the one hand, and the control signal derivative, on the other hand. The complete control scheme of WECS with fuzzy logic controller is shown in Figure 5.10. We normalize the universe of discourse to be over the interval [-1, 1] for each input and the output. Besides, we use a singleton membership function for the output with the same number and name of the inputs membership functions. Consequently, we use scaling factor to tune the membership functions of the inputs and the output. Firstly, we use three Gaussian membership functions (N, Z, P). Then, we use five membership functions (NB, NS, Z, PS, PB). And finally we use seven Gaussian membership functions distributed over the universe of discourse for each input (NB, NM, NS, Z, PS, PM, PB). Figure 5.11 shows seven Gaussian membership functions distributed on the universe of discourse. The general rule is: RN: If e (error) is Ai and e_dot (error derivative) is Bi, Then u_dot is yi . Where N is the number of the rules, Ai is the fuzzy sets for the input 1(error signal), Bi is the fuzzy sets for the input 2 (error derivative signal), and yi is the fuzzy sets of the output (control signal derivative). Note that, we use “NB” as an abbreviation for “Negative Big”, “NM” for “Negative Medium”, ”NS” for “Negative Small”, “N” for “Negative”, “Z” for “Zero”, “P” for “Positive”, “PS” for “Positive Small”, “PM” for “Positive Medium”, and “PB” for “Positive Big”. Depending on Figure 5.9, the rule base for the PI like fuzzy controller in the three cases is produced as shown in Table 5.1, Table 5.2, and Table 5.3.
105
e_dot
u_dot < 0
e
u_dot > 0
Figure 5.9. PI-like Fuzzy logic controller behavior. r
e
u
Fuzzy
y WECS Model
+
Controller
-
Figure 5.10. The overall control scheme of WECS with fuzzy controller.
Figure 5.11. Input membership functions. Table 5.1. Rule base for fuzzy PI controller (9 rules). e e. N
N
Z
P
P
P
Z
Z
P
Z
N
P
Z
N
N
106
Table 5.2. Rule base for fuzzy PI controller (25 rules). e e.
NB
NS
Z
PS
PB
NB
PB
PB
PS
PS
Z
NS
PB
PS
PS
Z
NS
Z
PS
PS
Z
NS
NS
PS
PS
Z
NS
NS
NB
PB
Z
NS
NS
NB
NB
Table 5.3. Rule base for fuzzy PI controller (49 rules). e e.
NB
NM
NS
Z
PS
PM
PB
NB
PB
PB
PM
PM
PS
PS
Z
NM
PB
PM
PM
PS
PS
Z
NS
NS
PM
PM
PS
PS
Z
NS
NS
Z
PM
PS
PS
Z
NS
NS
NM
PS
PS
PS
Z
NS
NS
NM
NM
PM
PS
Z
NS
NS
NM
NM
NB
PB
Z
NS
NS
NM
NM
NB
NB
In defuzzification process, we use “COA” method which calculated by:
107
is denoted the firing strength of the ith rule.
where
is the
consequent center of the ith rule and y is the defuzzified output of the fuzzy controller.
5.6 Simulation and Results The fuzzy PI controller is designed using MATLAB Simulink and the full model is shown in Figure 5.12. Moreover, Figure 5.13 shows what is inside the Simulink fuzzy block in case of using seven membership functions, where each subsystem in the fuzzy block represents seven rules as shown in Figure 5.14.
g
Iref
e
h
U dot
Iref e dot
g1
FLC
z
aR
IDC
z-1 Discrete-Time Integrator
1
aR
K Ts
Zero-Order Hold
WECS Model
Unit Delay
IDC
Figure 5.12. MATLAB Simulink WECS model with fuzzy controller. 1 e
2
e
Out1
e_dot
Out2
e dot
Subsystem e
Out1
e_dot
Out2
Subsystem1 e
Out1
e_dot
Out2
Subsystem2 e
Out1
e_dot
Out2
1 Divide
U dot
Subsystem3 e
Out1
e_dot
Out2
Subsystem4 e
Out1
e_dot
Out2
Subsystem5 e
Out1
e_dot
Out2
Subsystem6
Figure 5.13. The inside of Simulink fuzzy controller block.
108
1 e 1
Gaussian MF
Constant Gaussian MF7
Product5
Product 1 Constant1
Gaussian MF10
Product6
Product1
1 Constant2
Gaussian MF9 2 e_dot
Product7
Product2
0.66 1
Constant3 Gaussian MF8
Product3
0.66
Out1
Product8
Constant4 Gaussian MF11
Product4
0.33
Product9
Constant5 Gaussian MF12
Product12
Product10 0 Constant6
Gaussian MF13
Product13
Product11
2 Out2
Figure 5.14. Seven rules for each subsystem in MATLAB fuzzy block. The fuzzy controller is programmed once by Simulink blocks and another by Embedded MATLAB Editor-Block. Both of them produce the same result.
5.6.1 Applying the Designed Fuzzy PI Controller on WECS In this test, we apply the three fuzzy controllers, using three membership functions, five membership functions, and seven membership functions. We apply a DC reference current as a step change from 2.2 A to 3A which has been applied previously in case of the conventional PI controller. Figure 5.15, 5.16, and 5.17 show the control signal and the DC current response for the three cases of fuzzy controller. From this Figures, we observe that the fuzzy controllers have been succeed to achieve the reference current. Also we observe that the desired DC link current using fuzzy logic controllers is achieved at firing angle larger than that in using
109
3.1
30
3
2.8
DC current response (A)
Rectifier firing angle (degree)
2.9
25
20
2.7 2.6 2.5 2.4 2.3 2.2
15
2.1 0
1
2
3
4
5 time (sec)
6
7
8
9
10
0
1
2
3
4
5 time (sec)
6
7
8
9
10
Figure 5.15. The control signal and the DC current response (test 1 using 9 rules). 30
3.1 3
2.8
25
DC current response
Rectifier firing angle (degree)
2.9
20
2.7 2.6 2.5 2.4 2.3 2.2
15
0
1
2
3
4
5 time (sec)
6
7
8
9
2.1
10
0
1
2
3
4
5 time (sec)
6
7
8
9
10
Figure 5.16. The control signal and the DC current response (test 1 using 25 rules). 30
3.1 3
DC current response (A)
Rectifier firing angle (degree)
2.9
25
20
2.8 2.7 2.6 2.5 2.4 2.3 2.2
15
0
1
2
3
4
5 time (sec)
6
7
8
9
2.1
10
0
1
2
3
4
5 time (sec)
6
7
8
9
10
Figure 5.17. The control signal and the DC current response (test1 using 49 rules).
110
of the conventional PI controller for the same value of the desired current. So we can capture more power in case of using the fuzzy logic controller. Also with increasing the membership functions number, the accuracy increase and the fuzzy controller gives better response. The previous result was typically produced by the conventional PI controller. But here, if we change the operating point, the fuzzy controller will maintain the stability of the closed loop system without changing the controller parameters. For example, if we apply the same step changes from 1 A to 3 A, which the conventional controller has failed to track it. The fuzzy controller has managed to track the step changes without any oscillations and good accuracy. The error signal and the control signal are shown in Figure 5.18. The DC link current and the response are shown in Figure 5.19. 60
2
55
1.5
50 Rectifier firing angle (degree)
1
Error (A)
0.5
0
-0.5
-1
45
40
35
30
-1.5
25
-2 0
1
2
3
4
5 time (sec)
6
7
8
9
20
10
0
1
2
3
4
5 time (sec)
6
7
8
9
10
Figure 5.18. DC link current error and the control signal (Fuzzy controller test 2). 3
3 2.8 2.6
DC current response (A)
DC Reference Current (A)
2.5 2.4 2.2 2 1.8 1.6
2
1.5
1.4 1.2
1 1 0
1
2
3
4
5 time (sec)
6
7
8
9
10
0
1
2
3
4
5 time (sec)
6
7
8
9
10
Figure 5.19. DC link current reference and response (Fuzzy controller test 2). 111
We observe that, the previous control signal is a practical signal and the fuzzy logic controller can maintain the stability for different operating points. But what is better also is that, we can tune the scaling of the membership function (g, g1, h) for more response stability and smoothing. The next section will discuss this point.
5.6.2 Tuning via Scaling Universes of Discourse After the membership functions and the rule-base of the FLC are setup, the next problem related to its implementation is the FLC tuning. There is no general method for tuning the FLC. Most successful results are based on the combination of good expert about the controlled object and the use of the analogies between the FLC and PID controllers [16]. The scaling factors (go, g1, h) are the main parameters used for tuning the FLC. This is because that changing the scaling factors (scaling gains) changes the normalized universes of discourse of the membership functions of the fuzzy values of input/output variables of the FLC. We can observe that the scaling changes all rules in the rule-base of the FLC. The changes in the scaling factors can produce changing in rise time, overshoot, integral square error, etc. There are some rules for tuning, derived by Mamdani, are listed below: 1- High values of go lead to low steady-state error and rise time, but they lead to poor stability (large overshoot), on contrary, low values of go lead to a poor response. 2- Fastest convergence is bounded by high values of go and g1, and relatively low values of g1. 3- Low values of h increase the rise time and the integral square error. Figure 5.20 shows the complete system, the WECS model with the fuzzy PI controller with scaling factors. The complete system is simulated at different values for scaling factors for the same previous operating point.
112
r
e
+
y WECS Model
h
Controller
g1
-
u
Fuzzy
go
Figure 5.20. Fuzzy controller for WECS with scaling gains go, g1, and h. In the first test, we choose go=1, g1= 0.1, and h=1. To see the effect of this gain change, see Figure 5.21, where we see that the output current reacts much faster and the control signal is smoother. 60 3 55
2.5 Current Response (A)
Control Signal (degree)
50
45
40 35
2
1.5 30
25 1 20
0
1
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5 time (sec)
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Figure 4.21. The control signal and the current response at go=1, g1=0.1 and h=1. As we notice, the response is slow. So we can make it faster by increasing the proportional gain go (often raising the “loop-gain” can speed up the system). Therefore, in the next test, we choose go=2, g1=0.1, and h=1, that is we double the proportional gain. Figure 5.22 shows the resulting behavior of the fuzzy control system, the control signal and the current response, where we see that the response is made significantly faster than in Figure 5.20. Actually, a similar effect to increasing the proportional gain can be achieved by increasing the output gain h.
113
60
3 55
2.5 Current Response (A)
Control signal (degree)
50
45
40
35
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1.5 30
25
1 20
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6
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10
Figure 5.22. The control signal and the current response at go=2, g1=0.1, and h=1. In the last test, we choose go=2, g1=0.1, and h=5 (See Figure 5.23). From Figure 5.23 we see that the response is made even faster than in Figure 5.22. The control surfaces for every tuning are shown in Figures 5.24, Figure 5.25, and Figure 5.26. We observe that, the last control surface is more smoothly and more fast than the previous surface. As this is just a simulation study, we can increase h further and get even faster balancing provided that we simulate the system properly by having a small enough integration step size.
60
3
55
2.5
45
Current Response (A)
Control signal (degree)
50
40 35 30
2
1.5
25 20 15
1 0
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6
7
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9
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Figure 5.23. The control signal and the current response at go=2, g1=0.1 and h=5. 114
Further increases in h will generally result in faster balancing at the expense of a large control input. For a big enough h the input may be larger than what is allowed in the physical system. At that point the simulation would not reflect reality. Accordingly, if the controller was actually implemented, the plant input will saturate and the proper balancing behavior may not be achieved. We can see that the change in the scaling gains at the input and output of the fuzzy controller can have a significant impact on the performance of the resulting fuzzy control system, and hence they are often a convenient parameter for tuning.
Figure 5.24. The control surface at go= 1, g1= 0.1, and h=1.
Figure 5.25. The control surface at go= 2, g1= 0.1, and h=1. 115
Figure 5.26. The control surface at go= 2, g1= 0.1, and h=5.
5.7 Conclusion Assuming that, we have to control a plant. If we know exactly how this plant works and how it reacts to different controls, if we know exactly what we want from the control, and if the corresponding equations are not extremely complicated, then methods of traditional control theories usually provide us with an optimal (or at least reasonably good) control strategy [14]. In many real-life situations, we do not have complete knowledge of the plant. In such situations, we cannot apply the traditional control methodology. But we have the experience of human operators who successfully control this plant. We would like to make an automated controller that uses their experience. Fuzzy control is a methodology that translates these natural-language rules (experiences) into an automated control strategy. Additionally, fuzzy logic controller is nonlinear controller, so, it can be used easily with the nonlinear systems like WECS model as we have showed in the previous sections where the fuzzy logic can operate at any operating point with stable operation. Furthermore, by changing the scaling gains (factors) of the membership functions, we can tune the FLC. By this tuning; we have got a better response (faster and stable).
116
Chapter 6 Conclusion Concerns of rising energy prices, depletion of natural resources and pollution, environmentally friendly energy resources like wind energy are becoming more prominent. Wind energy is inexhaustible, safe, has no harmful by products and is capable of supplying substantial amounts of power. The unpredictable availability of wind however, only allows it to become a secondary source of power. In order to harness as much power from the wind as possible while it is available,
intelligent
control
strategies
must
be
implemented.
With
technological advancements in wind turbine aerodynamics and power electronic interfaces, wind energy can be considered to be an excellent renewable supplementary energy source. Power electronic interfaces and intelligent control strategies make wind energy viable and attractive despite its intermittent availability. This thesis provides extensive background knowledge on the wind energy conversion system progress in the world and especially in Egypt, turbine technology, and energy conversion. The main purpose of this thesis is to design and develop TSK fuzzy model to enable maximum power transfer under fluctuating wind conditions. Various algorithms and control schemes that attempt to extract the maximum power from the wind were studied and presented. In this thesis, we have designed two levels of control. The high control level has been responsible for producing the maximum power which should capture from the wind turbine without measuring the wind speed. This level has been based on fuzzy model identification. We have used the clustering methods to produce the initial cluster centers for the TSK fuzzy model rules (structure identification). Then, we have used the back propagation and ANFIS methods for tuning the TSK fuzzy model parameter (parameter identification). The used TSK fuzzy model expresses about the turbine power curve characteristics. The results illustrate that, we succeed by this control methodology in achieving the 117
maximum output power at any wind speed in the range of 5 m/s to 15 m/s. The output of this control level has been the input to the low control level. The low control level has been responsible for regulating the rotor speed to achieve the optimum tip speed ratio (TSR). Then, achieving the maximum power coefficient (Cpmax) which maximizes the WECS output power. This could be done by controlling the DC link converter. We have regulated the output power indirectly by controlling the DC link current using the rectifier firing angle. The low level control is designed using once the conventional PI controller which works perfectly at predefined operating points. At this operating point the PI controller could track the reference current. But, if the operating point is changed, the PI controller may fail to track the reference value. So, we have used the fuzzy logic controller as alternative to the PI controller. Because that fuzzy logic controller is a nonlinear controller, it can track the reference current successfully at any operating point. Besides, we have tuned its gains factor to give better results. Several research directions and points can be proposed to extend the work presented in this thesis. For example: 1- Fuzzy control gain factors can be tuned and optimized using any optimization technique as Genetic Algorithm (GA) or Particle Swarm. 2- We have designed the TSK fuzzy model at offline mode. The online TSK fuzzy model identification can be designed to get adaptive model.
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References [1] Fernando D. Bianchi, De Battista and Ricardo J. Mantz,”Wind Turbine Control System, Principles, Modeling and Gain Scheduling Design”, Springer, 2007. [2] A.H.T.Besheer, “A Linear Matrix Inequality Approach for Model Based Fuzzy Control of Wind Energy Conversion System”, Ph.D. Thesis, Faculty of Engineering, Cairo University, August 2006. [3] Gary L. Johnson and Manhattan, KS,”WIND ENERGY SYSTEMS” January 1994. [4] Joanne Hui, “An Adaptive Control Algorithm for Maximum Power Point Tracking for Wind Energy Conversion Systems” , Master of Science thesis, Queen’s University Kingston, Ontario, Canada December 2008. [5] K.E. Johnson, Lucy Y. Pao, M.J. Balas, and J. Fingersh,” Control of Variable-Speed Wind Turbine”, IEEE Control Systems Magazine, June 2006. [6] Roohollah Fadaeinedjad, “An Integrated Modeling Method for Wind Turbines “, Ph.D. Thesis, University of Western Ontario London, Ontario, Canada, 2008. [7] Jamal Ahmed Baroudi, “Operation of a Grid Connected Variable Wind Turbine with a Flyback Converter”, Master of Science thesis, University of Alberta, fall, 2007. [8] J. Marques, H. Pinheiro, H. Grundling, J. Pinheiro, and H. Hey, “A survey on variable-speed wind turbine system,” Proceedings of Brazilian conference of electronics of power, vol. 1, pp. 732 – 738, 2003. [9] Xinfang ZHANG, Daping XU, Yibing LIU, “Intelligent control for largescale variable speed variable pitch wind turbines”, Journal of Control Theory and Applications, Vol. 3, pp. 305- 311, 2004.
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[10] “Wind Turbine Model “, MATLAB 2007b. [11] K.Natarajan, A.M.Sharaf, S.Sivakumar, S.Naganathan,” Modeling And Control Design For Wind Energy Power Conversion Scheme Using SelfExcited Induction Generator”, IEEE Transactions on Energy Conversion, Vol.EC-2, No. 3, September 1987. [12] Kevin M. Passino, Stephen Yurkovich,” Fuzzy Control”, Addison Wesley Longman, Inc, 1998. [13] Marcelo Godoy Simoes,” Introduction to Fuzzy Control”, Colorado School of Mines Engineering Division, 1999. [14] Hung T. Nguyen, Vladik Kreinovich, Ongard Sirisaengtaksin, “Fuzzy Control as a Universal Control Tool”, New Mexico State University, 1994. [15] Eric Minh Nguyen,”Model Identification Using Fuzzy Clustering and Application” , Ph.D. thesis, New Mexico State University, May 1998. [16] R.R. Yager and D.P. Filev,” Essentials of Fuzzy Modeling and Control” , John Wiley and Sons, Inc. 1994. [17] S.G. Ram,” Fuzzy C-Means Self-Organizing Controllers” ,M.Sc. Thesis, Utah State University, 1993. [18] Stephen L. Chiu, “Fuzzy Model Identification Based on Clustering Estimation”, Journal of Intelligent and Fuzzy Systems, Vol. 2, pp. 267-278, 1994. [19] M. Delgado, A.F. Gomez-Skarmeta, F. Martin, “A methodology to model fuzzy systems using fuzzy clustering in a rapid-prototyping approach” , Fuzzy Sets and System, Vol. 97, pp. 287-301, 1998. [20] A.F. Grmez-Skarmeta, M. Delgado, M.A. Vila, “About the use of fuzzy clustering techniques for fuzzy model identification”, Fuzzy Sets and Systems Vol. 106, pp.179-188, 1999.
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[21] Na Wang, Yupu Yang, “A fuzzy modeling method via Enhanced Objective Cluster Analysis for designing TSK model”, Expert Systems with Applications, 2009. [22] Liang Zhao , YupuYang, YongZeng, “Eliciting compact T–S fuzzy models using subtractive clustering and coevolutionary particle swarm optimization”, Neurocomputing, Vol. 72, pp. 2569–2575, 2009. [23] Kemal Kilic, Ozge Uncu , I. Burhan Turksen, “Comparison of different strategies of utilizing fuzzy clustering in structure identification” , Information Sciences, Vol. 177, pp. 5153–5162, 2007. [24] Plamen P. Angelov and Dimitar P. Filev, “An Approach to Online Identification of TS Fuzzy Models”, IEEE Transaction on System, Man, and Cybernetics-Part B: Cybernetics, Vol. 34, No. 1, pp.2134-2145, February 2004. [25] Wen Yu and Xiaoou Li, “Online fuzzy modeling with structure and parameter learning”, Expert Systems with Applications, Vol. 36, pp. 7484– 7492, 2009. [26] R. Chedid, F. Mrad, and M. Basma, “Intelligent Control of a Class of Wind Energy Conversion Systems”, IEEE Transactions on Energy Conversion, Vol. 14, No. 4, 1597-1604, December 1999. [27] Quincy Wang, and Liuchen Chang, “An Intelligent Maximum Power Extraction Algorithm for Inverter-Based Variable Speed Wind Turbine Systems”, IEEE Transaction on Power Electronics, Vol. 19, No. 5, 1242-1249, September 2004. [28] V. Calderaro, V. Galdi, A. Piccolo, P. Siano, “A fuzzy controller for maximum energy extraction from variable speed wind power generation systems”, Electric Power Systems Research, Vol. 78, pp. 1109–1118, 2008. [29] Fathy Ameen Mohammad, ”Financing Wind Park Project Experience from Egypt” , New and Renewable Energy Authority, NREA, Egypt, 2005. [30] http://www.knmi.nl/samenw/hydra, Version November 2006. 121
Appendix Table 3-2. Parameters of the WECS Simulink model [11]. J
0.09354 Kg.m2
B
0.011 Nm/rad/sec
Lls= Llr
2.17 mH
N
4 poles
rs = r r
0.56 Ω
C
338 µ farads
RDC
4Ω
LDC
400 mH
122
الملخص تعتبر الطاقة المتجددة من اهم المصادر المستخدمة النتاج الكهرباء وذلك نظ اًر لتوافرها فى اماكن كثيرة فى انحاء العالم وايضاً النها طاقة نظيفة ومتجددة وغير مكلفة بالمقارنة بمحطات التوليد التقليدية.
لذا نهتم فى هذا البحث باحدى صور هذه الطاقة المتجددة أال وهى طاقة الرياح .وحقيقة يرجع الفضل فى اتساع استخدامها الى اساليب التحكم المتقدمة الذكية المستخدمة لتوليد اقصى قدرة كهربية ممكنة من تربينة
الرياح.
ومن
امثلة
هذه
االنظمة
الشبكات
العصبية
و
المتحكم
المتدرج.
ونستخدم فى هذا البحث نموذج لتربينة رياح من النوع االفقى ذات الثالثة ريش والتى تقوم بتحويل طاقة الرياح الى طاقة ميكانيكية .هذه التربينة متصلة بمولد الحث الذاتى الذى يقوم بتحويل الطاقة الميكانيكية الى طاقة كهربائية .ويتم توصيل مولد الحث الذاتى بشبكة الكهرباء من خالل المحول االلكترونى وهو يعمل كحلقة وصل بين منظومة تحويل طاقة الرياح من ناحية وشبكة الكهرباء من ناحية اخري .وعن طريقه يتم ضبط التردد والجهد الناتج ليتوافق مع جهد وتردد شبكة الكهرباء. ولما كانت عملية توليد اقصى قدرة كهربية ممكنة من تربينة الرياح هى هدفنا االساسى فى هذا البحث .لذا لجانا الى استخدام نموذج المتحكم المنطقى المتدرج والذى يمثل مستوى التحكم االعلى. حيث انه يقوم بمعالجة دخول ومخارج المنظومة ليمكننا من الحصول على اقصى كهربية ممكنة بدون الحاجة الى قياس سرعة الرياح .حيث ان الدخل لهذا النموذج عبارة عن سرعة المولد المقاسة والطاقة الكهربية الناتجة .وقيمة الخرج تعبر عن اقصى قدرة متاحة فى تربينة الرياح.
ومن ثم
يقوم المتحكم المتدرج فى مستوى التحكم االدنى بعمل تنظيم لسرعة المولد لتصل للسرعة المطلوب النتاج اقصى قدرة ممكنة عند اى سرعة للرياح.
123
توليد أقصى قدرة كهربية ممكنة من منظومة تحويل طاقة الرياح بإستخدام نموذج وحاكم منطقى متدرج إعداد م/أيمن ندير فرنسيس عياد رسالة مقدمة الى كلية الهندسة ،جامعة القاهرة كجزء من متطلبات الحصول على
درجة الماجستير فى هندسة القوى واألالت الكهربية يعتمد من لجنة الممتحنين: األستاذ الدكتور/عبد اللطيف محمد رجائى الشافعى
(مشرف الرسالة)
قسم هندسة القوى واألالت الكهربية ،كلية الهندسة ،جامعة القاهرة. (عضــــو)
األستاذ الدكتور/عـــادل ضياء الدين شلتوت قسم هندسة القوى واألالت الكهربية ،كلية الهندسة ،جامعة القاهرة.
(عضــــو)
األستاذ الدكتور/فهمى متولى احمد بنــدارى قسم هندسة القوى واألالت الكهربية ،كلية الهندسة ،جامعة بنها.
كلية الهندسة ،جامعة القاهرة الجيزة ،جمهورية مصر العربية اكتوبر 9002 124
توليد أقصى قدرة كهربية ممكنة من منظومة تحويل طاقة الرياح بإستخدام نموذج وحاكم منطقى متدرج إعداد م/أيمن ندير فرنسيس عياد رسالة مقدمة الى كلية الهندسة ،جامعة القاهرة كجزء من متطلبات الحصول على
درجة الماجستير فى هندسة القوى واألالت الكهربية تحت إشراف: أالستاذ الدكتور/عبد اللطيف محمد رجائى الشافعى
كلية الهندسة ،جامعة القاهرة الجيزة ،جمهورية مصر العربية اكتوبر 9002 125
توليد أقصى قدرة كهربية ممكنة من منظومة تحويل طاقة الرياح بإستخدام نموذج وحاكم منطقى متدرج إعداد م/أيمن ندير فرنسيس عياد رسالة مقدمة الى كلية الهندسة ،جامعة القاهرة كجزء من متطلبات الحصول على
درجة الماجستير فى هندسة القوى واألالت الكهربية
كلية الهندسة ،جامعة القاهرة الجيزة ،جمهورية مصر العربية اكتوبر 9002 126
