POLITECNICO DI MILANO. Facoltà di Ingegneria dei Processi Industriali. Corso
di Laurea Specialistica in Ingegneria Elettrica. DOUBLE STAR MACHINE ...
POLITECNICO DI MILANO Facoltà di Ingegneria dei Processi Industriali
Corso di Laurea Specialistica in Ingegneria Elettrica
DOUBLE STAR MACHINE STUDIED FOR WIND GENERATION Relatore: Prof. MARCO MAURI
Tesi di Laurea Specilistica di: Rabah SERIR Matr. n. 755437 Anno Accademico 2012 – 2013
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DOUBLE STAR MACHINE FOR WIND ENERGY GENERATION
MASTER THESIS
RABAH SERIR
April 2013
Thesis Supervisor:
Prof. Marco MAURI
POLITECNICO DI MILANO Facoltà di Ingegneria dei Processi Industriali Corso di Laurea Specialistica in Ingegneria Elettrica
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Thanks
I wish to express my deep gratitude to my supervisor Mr. Mauri Marco professor at the University of Politecnico di Milano, for his assistance without reserve and valuable advice. I also want to thank members of the jury to have accepted to evaluate my work. I thank also all my friends and schoolmate of the Department of Electrical Engineering especially: Ferrucio, Massimo veneruzo Davide Cavaliere, Claudio Rosati, Erlind Dhami, Fabio De venz, Savino, Simone Barcellona, Alessandra Magni, Marilu Martelli, Francesca Rivetti, Gian Franco Taino, Fahem Ben-‐Yahia and Chérif Bouttamine for their help and presence. Finally I am very grateful to my family especially my dear mom.
Dedication
I dedicate this modest memory to my lover and friend FERRUCCIO without whom, this work couldn’t be done.
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Symbols and Abbreviations ASM ASG s, r as, bs, cs ar, br, cr Rs, Rr Ls Lr l fs , l fr Vas,Vbs,Vcs Ias,Ibs,Ics Φas ,Φbs,Φcs Var ,Vbr, ,Vcr Iar ,Ibr ,Icr Φar,Φbr,Φcr P(θ) [Vdqos] [Idqos] [Φdqos] [Vdqor] [Idqor ] [Φdqor] Ich C Cch Lch Rch ER P ωs ωr ωg Lm Im Re Im P g d, q S ns, nr Cem Mcc Uf , Ua JG DSAM DSAG
Asynchronous Machine. Asynchronous Generator. Indices corresponding to the stator and the rotor respectively . Indices corresponding to the three phases of the stator. Indices corresponding to the three phases of the rotor. Stator and rotor resistance. Inductance of a stator phase. Inductance of a rotor phase. Cyclic inductance of stator and rotor leakage. Stator three-‐phase voltages. Stator Currents. Stator specific magnetic flows. Rotor three-‐phase voltages. Rotor currents. Rotor specific magnetic flows. Park Matrix. Stator voltage vector in the coordinate system of Park. Stator voltage vector in the coordinate system of Park. Stator flows vector in the coordinate system of Park. Rotor voltage vector in the coordinate system of Park. Rotor current vector in the coordinate system of Park. Rotor flows vector in the coordinate system of Park Current inductive load connected with ASG. Drive capacity of self-‐priming. Capacity of series compensation. Load inductance. Load Resistance. Renewable energy. Number of Phases. Stator electrical pulse. Rotor electrical pulse. Electrical pulse slip. Magnetizing inductance. Magnetizing current. Real part of the impedance. Imaginary part. Active power. Slip. Axes of the direct and quadratic mark Park. Laplace operator. Rotational speed rotor and stator, Rpm. Electromagnetic torque of the generator. Continuous current machine. Supply voltage of the motor Mcc. Inertia of the rotor of the generator. Double Star Asynchronous Machine. Double Star Asynchronous generator.
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1, 2, r
a1, b1, c1 a2, b2, c2 ar, br, cr R1, R2, Rr Ll1 Ll2 Llr Llm C1, C2 Cs1, Cs2 L1, L2, Lr Lms Lmr Msr Lch2, Lch1 R1, R2 C1, C2 Cs1, Cs2 iaL1, iaL2 α qm q2 Turbine Pwind Pturbine Cp ΩTurbine ρ Caer λ EC F F(v) f(v) k C MPPT Pele f Cm Ωm β
R
indices corresponding to the star 1 star 2 and the rotor. Indices corresponding to the three phases of the stator 1. Indices corresponding to the three phases of the stator 2. indices corresponding to the three phases of the rotor. Stator and rotor resistances. Leakage inductance of the first stator winding. Leakage inductance of the second stator winding. Rotor leakage inductance. Leakage inductance mutual. Drive capacity corresponding to the star 1 star 2. Capacity compensation corresponding to the star 1 star 2. Self inductances stator and rotor. Mutual inductance between stator phases. Mutual inductance between rotor phases. Mutual inductance between stator and rotor phases. Loads inductances. Loads resistances. Bootstrap capacity. Parallel compensation capacity. Loads currents connected to the ASG. Offset angle between the two stars. Rotor position (phase ar) relative to the star 1 (phase a1). rotor position relative to the star 2.
Wind power. Turbine power. Power coefficient. Mechanical speed of the turbine. Density of the area. Torque generated by the wind turbine. Gear ratio. kinetic energy of wind. The distribution function of wind. The distribution function. The probability density. Shape parameter characterizes the distribution of wind. Scale parameter characterizes the wind speed. Maximum Power Point Tracking. Electrical power produced by the wind. The coefficient of friction of the rotor of the generator. The drive torque of the electric generator. The speed of the generator rotor. The pitch angle. The length of the blade.
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Abstract The Earth Summit in Rio de Janeiro (Brazil, 1992), which defined the outline of a "sustainable development", followed by the Kyoto Protocol (Japan, 1997) on the protection of the environment (reduction of gas to the "greenhouse effect") has catalyzed the emergence of non-polluting alternative energy resources, to meet the energy needs of today's society, it is necessary to find solutions and diversify. Currently, there are mainly two ways to act: The first is to reduce energy consumption (improving the performance of receivers, saving by changing consummation habits...) while improving productivity power, A second approach to the problem is to find and develop new energy sources. Indeed, the production of electricity from fossil fuels (coal, oil or gas) or fissile (uranium...) contributes greatly to environmental degradation and the depletion of non-renewable resources. That is why one of the steps to prepare a truly sustainable development is to increase the share of alternative resources. Researches are ongoing in the field of thermonuclear fusion, which eventually could be an energy solution of the future, but the future of this industry remains uncertain. By cons, we are currently witnessing a boom in renewable energy called RE (wind, solar, bioenergy), inexhaustible and non-polluting, which may constitute for Italia an alternative energy reserve, therefore a research innovative investing, especially in the field of Electrical Engineering (improvement of electromechanical chains conversion associated with these renewable sources). It is in this perspective of contribution to the development of renewable energy that enrolls my Master thesis. For various reasons, I am particularly interested in wind power. The study of energy conversion chain has been split into 5 chapters: Chapter I is an overview of renewables energies (interest, evolution, statistics) by focusing thereafter on the wind energy sector that interests us here (principle, technologies and equations) Chapter II is devoted to the state of art of different types of turbines used in electromechanical conversion chains wind, as we opted for a double star generators kind associated with wind turbine, Chapters III and IV deal respectively: Double star Asynchronous Generator (DSAG) in isolated operation in MATLAB; Double star Synchronous (induction) generator (DSSG) modeling. Chapter V is devoted to explain the overall (DSAG) chain under SUMILINK environment.
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INDEX
CHAPTER 1 ............................................................................................................................................................................ XI GENERALITIES ABOUT THE WIND SYSTEM .................................................................................................................... XI I.1. INTRODUCTION ............................................................................................................................................................... 1 I.2. ELECTRICAL POWER GENERATION FROM RENEWABLE ENERGY .................................................................. 2 I.3. PRINCIPLES AND ELEMENTS OF INCORPORATION OF WIND .......................................................................... 3 I.3.1. DEFINITION OF WIND ENERGY ............................................................................................................................... 3 I.3.2. THE HISTORY OF WIND ............................................................................................................................................. 3 I.3.3. NUMERICAL DATA ON THE WIND POWER .......................................................................................................... 4 I.3.3.1. EOLIC COMPETITION .............................................................................................................................................. 4 A. NEW KNOWLEDGE AND THE DEVELOPMENT OF POWER ELECTRONICS; ..................................................... 4 B. PERFORMANCE IMPROVEMENT IN AERODYNAMIC DESIGN OF WIND TURBINES; .................................... 4 C. STATE FUNDING FOR THE INSTALLATION OF NEW WIND POWER ................................................................. 4 I.3.3.2. EVOLUTION OF PRODUCTION COSTS ................................................................................................................ 7 I.3.4. CONSTITUTION OF WIND "CLASSIC" ..................................................................................................................... 9 I.3.5. SETUP MODES AND DIFFERENT TYPES OF TURBINES ................................................................................. 11 I.3.5.1. VERTICAL AXIS WIND TURBINES ..................................................................................................................... 11 I.3.5.2. HORIZONTAL AXIS WIND TURBINES .............................................................................................................. 12 I.4. OPERATION OF A WIND TURBINE BLADE ........................................................................................................... 13 I.4.1. DESCRIPTION OF A WING OR A TURBINE BLADE .......................................................................................... 13 I.4.2. TRIANGLE OF SPEEDS ON A WIND TURBINE BLADE .................................................................................... 13 I.4.3. SPEED CONTROL SYSTEMS OF WIND TURBINE .............................................................................................. 14 I.5. THEORETICAL NOTIONS ON THE TURBINE ........................................................................................................ 16 I.5.1. POWER COEFFICIENT CP ......................................................................................................................................... 16 I.5.2. TORQUE PRODUCED BY THE WIND .................................................................................................................... 16 I.5.3. SPECIFIC SPEED OF THE WIND ............................................................................................................................ 17 I.5.4. BETZ LIMIT ................................................................................................................................................................. 17 I.6. CHARACTERIZATION OF WIND ............................................................................................................................... 20 I.6.1. WIND SPEED INSTANTANEOUS DISTRIBUTION ............................................................................................. 20 I.6.2. REGIONAL DISTRIBUTION OF WIND SPEED .................................................................................................... 22 I.6.3. THE HISTOGRAM OF WIND SPEEDS ................................................................................................................... 22 I.6.4. WEIBULL DISTRIBUTION ....................................................................................................................................... 23 I.6.5. INFLUENCE OF HEIGHT ........................................................................................................................................... 23 I.7. OPTIMAL ENERGY PRODUCTION ............................................................................................................................ 25 A. THE AREA SWEPT BY THE ROTOR ........................................................................................................................... 25 B. DENSITY AIR AND THE WIND VELOCITY ............................................................................................................... 26
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I.8. INTEREST OF VARIABLE SPEED .............................................................................................................................. 27 I.9. SAFETY ANALYSIS ........................................................................................................................................................ 27 I.9.1. CASE OF HORIZONTAL AXIS WIND TURBINES ................................................................................................ 27 I.9.2. CASE OF VERTICAL AXIS WIND TURBINES ....................................................................................................... 28 I.10. SOME TURBINES USED IN WIND ENERGY GENERATION. ............................................................................. 29 I.10.1. THE TURBINE "AOC 15/50 HZ 50" ................................................................................................................... 29 I.10.2. THE TURBINE "FUHRLÄNDER -‐ FL30" ............................................................................................................. 29 I.10.3. THE TURBINE "GUAL -‐ STATOEOLIEN GSE 4" ............................................................................................... 29 I.10.4. THE TURBINE "WINDSIDE -‐ WS-‐4" ................................................................................................................... 30 I.11. RESEARCH AND DEVELOPMENT IN PROGRESS ............................................................................................... 31 A) WIND TURBINE TURBY ............................................................................................................................................... 31 B) THE WARP SYSTEM ...................................................................................................................................................... 32 C) THE MULTIROTORS WIND TURBINE SYSTEM ..................................................................................................... 32 D) THE KITEGEN SYSTEM ................................................................................................................................................ 33 I.12. SOME PROVISIONAL FIGURES: .............................................................................................................................. 33 I.13. EXAMPLE RATED VALUES ....................................................................................................................................... 33 A. WIND WHEEL DIMENSIONS ........................................................................................................................................ 34 A.1. MECHANICAL POWER REQUIRED: ........................................................................................................................ 34 A.2. POWER COEFFICIENT CP: ......................................................................................................................................... 34 A.3. BLADE LENGTH: .......................................................................................................................................................... 35 B. GENERATOR DIMENSION ............................................................................................................................................ 35 B.1. THE SPEED OF THE SHAFT OF THE WIND TURBINE Ω IN RAD/S AND NL RPM ...................................... 35 B.2. THE ROTOR SPEED OF THE GENERATOR Ω IN RAD/S, AND N IN RPM ..................................................... 35 CHAPTER 2 ........................................................................................................................................................................... 39 DIFFERENT CONVERSION CHAIN AND GENERATORS. ........................................................................................... 39 II.1. SYSTEMS USING SYNCHRONOUS MACHINE ........................................................................................................ 40 II.2. ELECTROMAGNETS SYNCHRONOUS MACHINES ............................................................................................... 40 II.2.1. PERMANENT MAGNET SYNCHRONOUS MACHINES OR "MSAP" ............................................................... 41 II.3. SYSTEMS USING ASYNCHRONOUS MACHINE ..................................................................................................... 41 II.3.1. SQUIRREL CAGE ASYNCHRONOUS MACHINE ................................................................................................. 42 II.3.2. DUAL STATOR ASYNCHRONOUS MACHINE .................................................................................................... 43 II.3.3. DOUBLE FED INDUCTION GENERATOR (DFIG) ............................................................................................. 44 III.3.3.1. DFIG TYPE "BRUSHLESS" ................................................................................................................................. 44 III.3.3.2. DFIG TYPE "WOUND ROTOR" ......................................................................................................................... 45 (A) DFIG -‐ KRAMER STRUCTURE ................................................................................................................................... 45 II.4. VARIABLE RELUCTANCE MACHINE ...................................................................................................................... 48 II.4.1. EXCITED DOUBLE SALIENCE VARIABLE RELUCTANCE MACHINE ........................................................... 48
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II.4.2. A NOT EXCITED VARIABLE RELUCTANCE MACHINE ................................................................................... 49 II.5. COMPARISON OF ELECTROMECHANICAL CONVERTERS ............................................................................... 49 CHAPTER 3 ........................................................................................................................................................................... 53 ASYNCHRONOUS GENERATOR. .......................................................................................................................................... 53 III.1. INTRODUCTION ......................................................................................................................................................... 54 III.2. DESCRIPTION OF THE DOUBLE STAR ASYNCHRONOUS GENERATOR ..................................................... 54 III.3. MODELING THE DOUBLE STAR ASYNCHRONOUS GENERATOR ................................................................. 55 III.3.1. MODEL GASDE IN THE NATURAL LANDMARK (ABC) ................................................................................. 55 III.3.1.1. EQUATIONS IN ELECTRICAL NATURAL LANDMARK (ABC) .................................................................. 55 III.3.1.2. FLOW EQUATIONS IN THE NATURAL FRAME (ABC) ............................................................................... 56 III.3.2. DSAG MODEL OF THE PARK AXES (D, Q) ........................................................................................................ 57 III.3.2.1. ELECTRICAL EQUATIONS IN "D, Q” AXES .................................................................................................... 57 III.3.2.2. MAGNETIC EQUATIONS IN THE "D,Q" REFERENCE FRAME .................................................................. 58 III.4. SIMULATION DSAG VACUUM ................................................................................................................................. 59 III.5. SIMULATION RESULTS ............................................................................................................................................ 61 III.6. DISCUSSION OF RESULTS ....................................................................................................................................... 63 CHAPTER 4 ........................................................................................................................................................................... 64 SYNCHRONOUS GENERATOR. ............................................................................................................................................. 64 IV.1. INTRODUCTION ......................................................................................................................................................... 65 IV.2. DESCRIPTION OF THE DOUBLE STAR SYNCHRONOUS GENERATOR ....................................................... 65 IV.3. MODELING THE DSSG .............................................................................................................................................. 66 A. STATOR INDUCTANCE MATRIX ................................................................................................................................... 68 B. PARK TRANSFORMATION: .......................................................................................................................................... 69 IV.4. MACHINE MODEL: ..................................................................................................................................................... 70 A. ELECTROMAGNETIC TORQUE ...................................................................................................................................... 71 IV.5. CONCLUSION .............................................................................................................................................................. 72 CHAPTER 5 ........................................................................................................................................................................... 73 STUDY AND SIMULATION OF THE DSAG IN AN ISOLATED MODE .......................................................................... 73 V.1. INTRODUCTION .......................................................................................................................................................... 74 V.2. INTRODUCTION TO SIMULINK .............................................................................................................................. 74 V.3. WIND TURBINE MODEL WITH ASYNCHRONOUS MACHINE ......................................................................... 75 V.4. SIMULATION RESULTS ............................................................................................................................................. 85 V.5. CONCLUSION ................................................................................................................................................................ 89 GENERAL CONCLUSION ........................................................................................................................................................ 90 REFERENCES ...................................................................................................................................................................... 91
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Chapter 1 Generalities about the wind system
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I.1. Introduction In the context of sustainable development and facing the global dual challenge posed by next depletion of fossil energy resources and problems regarding the respect to compliance with environment, strong incentives grow to develop renewable energy. The renewable energy sector is divided into three main categories: energy from mechanical origins (swell, wind), electrical origins (photovoltaic panels) or under heat energy (geothermal, solar thermal...), knowing that the origin of all these energies is Energy coming from the sun then transformed by the terrestrial environment. Indeed, the global energy consumption (Figure 1-1) continues to grow, posing critical questions about the greenhouse effect and the depletion of energy resources.
Figure (1-1): Primary energy consumption in the world and forecasts [45]. More than 80% of the energy is derived from fossil fuels (coal, oil, gas) or fissile nuclear energy. (Fig 1-2) shows the distribution in terms of primary energy in the world for all existing resources. These clean and virtually inexhaustible renewable energies are interesting in the current economic climate where we encode a portion of the costs by hiding some "collateral costs" (dismantling plants, pollution...).
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Figure (1-2): Distribution of primary energy in the world [46].
I.2. Electrical Power Generation from Renewable Energy The majority of traditional sources are extracted from deposits and then transported to the distributors or factories that can be remote, which affect costs. On the other side, the "extraction" of renewable energy place instead is critical to the processing location. It is this property that limits the use of renewable energy for power generation Electric. (Fig 1-3) gives an idea of the distribution of electricity between renewable sources and forecasts until 2030. [1]
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Figure (1-3): Estimation of global electricity production based on renewable [1]. I.3. Principles and Elements of Incorporation of Wind I.3.1. Definition of Wind Energy The wind energy is part of renewable energy. The turbine uses the kinetic energy of the wind to drive the shaft of the rotor: it is then converted into mechanical energy itself converted into electrical energy by a electromagnetic wind turbine coupled to the generator. This mechanical coupling can be direct if turbine and generator have speeds of the same magnitude order otherwise, achieved through a multiplier, There are several types of use of the produced electrical energy, either it is stored in batteries, or it is distributed through an electrical network or it provides isolated loads. The wind conversion system is also seat of loss: as a guide, the yield is 59% at the rotor wind turbine, 96% at the multiplier; we should take more into account the losses of the generator and any eventual conversion system [3]. I.3.2. The History of Wind Since ancient times, the "windmills" convert wind energy into mechanical energy, usually used to grind grain (Fig 1-4). Nowadays, there are still wind turbines coupled to water pumps, often used to irrigate dry areas, dry wetlands or watering livestock. The arrival of electricity gives the idea to "Poul La Cour" in 1891 to associate to the wind turbine a generator. Thus, the energy from the wind could be "rediscovered" and used again (in the 40s in Denmark, 1300 wind turbines). At the beginning of the last century, WTG have made a massive appearance (6 million of pieces produced) in the United States where they were the only way to get power in the isolated countryside. In the 60s, about 1 million wind turbines were working in the world. This technology has been somewhat neglected and eventually we had to wait the oil crisis of 1974, which boosted the studies and experiments on wind turbines.
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Figure (1-4): Photograph of two windmills [3].
I.3.3. Numerical Data on the wind power I.3.3.1. Eolic Competition The potential of renewable energy systems is underexploited. (Fig 1-5) shows that improvements in technology have encouraged the installation of wind energy that is growing exponentially, Europe is the leading global wind energy production ensures this power consumption of about 10 million people. Three factors have contributed to make the wind solution more competitive: A. New knowledge and the development of power electronics; B. Performance improvement in aerodynamic design of wind turbines; C. State funding for the installation of new Wind power
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Figure (1-5): Evolution of the installed wind power capacity in the world in GW [47]. A look back at Wind Force 10 In October of 1999, the wind industry published its first global forecast for 2020, which from that date seemed unimaginably far in the future. Coming off a very successful year for the industry in 1998 when more than 2,500 MW of wind power was installed to bring the global total to over 10,000 MW, the European Wind Energy Association, Greenpeace International, and the Forum for Energy and Development launched Wind Force 102, outlining a pathway for wind power to achieve 10% of global electricity supply by 2020. With analysis provided by Birger Madsen of BTM Consult, the blueprint was designed to show what was possible with all possible policy support. Many dismissed the analysis as pie-in-thesky, but the reality of the industry more than a decade later tells a different story. The scenario was refined and updated several times over the years until with the addition of the MESAP/PlaNet model supplied by DLR in 2006 it became the Global Wind Energy Outlook, a joint biennial publication by the Global Wind Energy Council and Greenpeace International, of which this is the fourth. But the fascinating thing is how closely the actual development of the industry since 1998 has tracked that original scenario as shown in the figure below. The original blueprint has become what we now refer to as our ‘Advanced scenario’, and although arrived at through much more scientific means, it stays basically the same in total numbers, although the regional distribution is quite different. Although the industry has developed along the lines of our Advanced scenario up until the last few years, we are now moving more towards the ‘Moderate’ scenario. We need visionary policymakers to create the conditions to get us back on the Advanced track.
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Figure (1-6A): Wind power installed the world (different scenarios) [47]. The reason for this change is the Kyoto Protocol, which commits signatory countries to reduce their emissions of greenhouse gases. This agreement has contributed to the emergence of national policies for the development of wind and other energies also because wind turbines do not emit carbon dioxide. The distribution of wind energy in Europe is given in the (Fig 1-6 A&B): Germany is the European market leader despite a slowdown in its facilities in 2003, Spain in second position, continues to intensively install wind power farms, and Denmark is in third with the development of the offshore and renewing wind turbines that have more than 10 years existence.
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Figure (1-6B): Wind power installed in Europe by end of 2011 (cumulative) [3]. I.3.3.2. Evolution of Production Costs It is estimated that the cost of installing a kW is about 1000 euros. Technological advances and increased production of wind turbines in recent years can reduce this number regularly (Fig 1-7). The cost per kWh depends on the cost of the installation of the turbine and the amount of electricity produced per year. This price varies depending on the site, and decreases with technological advances. Increasing the average power of Wind power and sales volume (18 MW in 1981 accumulated to 10 GW in 1998) led to a sharp decline in the cost of production kWh wind energy and investment returns more and more short. According to the tariffs, the return time is between 4 years (Germany) and 10 years (Canada), in France, between 6 and 7 years [12].
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Figure (1-7) Evolution of the average power per unit of machinery and lower costs per kWh (conditions: 20-year amortization, interest rate: 5% / year) [47]. The global cost of investment in one or more Wind power includes: - Studies and the design of the installation - Obtaining the necessary authorizations to build and connect to the grid. - The purchase of the generator and tower. - The purchase of equipment to safely connect the turbine and the electrical grid. Cost elements collected from manufacturers are provided in the following table
Table (1-1): Cost elements collected from manufacturers [25]
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I.3.4. Constitution of Wind "Classic" A wind turbine "classic" generally consists of three main components [3]:
Figure (1-8): Main components of a wind turbine [3]. - The mast (tower): generally a steel tube or possibly a metal lattice must be as high as possible to avoid disturbance near the ground. However, the amount of material implementation represents a significant cost and weight must be limited. - The nacelle: includes all the mechanical elements for coupling the rotor of the turbine to - The electric generator: trees slow and fast, bearings, gearbox. - The disc brake, different of the air brake, which allows the system to stop in case of overload. -The generator: which is usually a synchronous or asynchronous machine and the pitch blades system hydraulics or electrical (aerodynamic brake) and platform (necessary to keep the area swept by the wind generator perpendicular to the wind direction of a nacelle), the mass variation of a nacelle according to the rotor diameter grows exponentially as claimed in (Fig 1-9).
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Figure (1-9): variation of the nacelle’s mass based on the diameter of the rotor [36]. The rotor: formed by the blades assembled in their hub. For wind turbines aimed at electricity generation, the number of blades varies typically from 1 to 3 (three-bladed rotor). The blades are mainly characterized by their geometry that depend on the aerodynamic performance and the materials from which they are made; currently, composite materials such as fiberglass and more recently carbon fiber are widely used because they combine lightness with good mechanical strength. Increasing the rotor diameter will increase the mass of the blade as shown (Fig 1-10). [3]
Figure (1-10): variation of the mass of a wind turbine blade according to the diameter of the rotor [16].
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I.3.5. Setup Modes and Different Types of turbines Generally there are two types of installations of wind turbines: the wind that is not connected to the network "offgrid" it’s installed in isolated “individual”, the second mode concerns wind turbines grouped in wind farms installed onshore or, more and more offshore where the presence of the wind is steady. With offshore farms "we reduce noise and improves aesthetics. From a structural point of view, there are two main types of wind turbines that are: I.3.5.1.
Vertical Axis Wind Turbines Towers of vertical axis wind turbines are short, between 0.1 and 0.5 times the height of the rotor. This allow to place the entire device for converting energy (generator, gearbox etc..) At the foot of the wind turbine, thus facilitating maintenance. Add to this, it is not necessary to use a device orientation of the rotor. However, the winds are low near the ground, which leads to a lower efficiency because the turbine undergoes wind turbulence. These turbines must be driven at startup and the mast undergoes high mechanical stresses for these reasons, nowadays wind turbine manufacturers prefer the horizontal axis wind turbines. The two most prevalent structures of vertical axis wind turbines are based on principles of differential drag or cyclical variation of incidence: The Savonius rotor, whose operation is based on the principle of differential drag. The forces exerted by the wind on each side of a hollow body are of different intensities (Fig 1-11) [3]. it will result a torque causing the rotation of the assembly.
Figure (1-12): Saonius rotor schema [3]. The rotor Darrieus is based on the principle of the cyclical variation of incidence. A profile, placed in an airflow at different angles, is subjected to forces of variables intensities and directions. The resultant of these forces generates a torque motor driving the rotation of the device (Fig 1-12).
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Figure (1-12): Darrieus rotor schema [1]. I.3.5.2.
Horizontal Axis Wind Turbines The horizontal axis wind turbines are based on the principle of windmills. They consist of one to three aerodynamically profiled blades (Fig 1-12). Most often, the rotor of the wind turbine is three-bladed, because three blades are a good compromise between the power factor the cost and speed of the wind sensor and aesthetics compared to two-bladed. The horizontal axis wind turbines are the most used because their aerodynamic performance is superior to that of vertical axis wind turbines, and are less exposed to mechanical stress. There are two types of horizontal axis wind turbine (Figure 1-13): Upstream: the wind blows in front of the blades in the direction of the nacelle. The blades are rigid, and the rotor is oriented along the direction of the wind by a device. Downstream: the wind blows on the rear of the blades starting from the nacelle. The rotor is flexible, self-adjustable. The disposition upstream turbine is the most widely used because it is easier and gives better results for high power: no govern, operating efforts are less important and there is greater stability. The blades of horizontal axis wind turbines should always be oriented in the direction of the wind. For this, there are orientation devices of the nacelle according to this direction.
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Figure (1-13): Horizontal axis wind turbines types [3].
I.4. Operation of a wind turbine blade Wind turbine blade extracts kinetic energy from the wind and converts it, thanks to its connection with the rotor in rotary motion. The phenomenon of aerodynamic lift is at the heart of the operating principle.
I.4.1. Description of a wing or a turbine blade (Fig 1-14) describes a wind turbine blade and identifies the different areas with appropriate terminology
Figure (1-14) Description of a wind turbine blade [27].
I.4.2. Triangle of speeds on a wind turbine blade Let us suppose that there is no wind and the blade turns anyway. During its rotation, the blade "sees" come wind parallel to the plane of rotation. This is the same phenomenon that if you ride bike when there is no wind. You feel the wind "created" by your movement. The wind blows in your face. Now suppose that the blade does not rotate and the wind blows: the blade "sees" the wind come according to the direction of the wind. To Recapture the image of our cycling, you do not drive and the wind blows on your side. So you feel the wind in its direction. Suppose finally that the wind continues to blow in the same direction as the blade rotates in its plane of rotation. Blade "sees" now a wind that is a combination of previous two winds, namely the true wind and the wind due to the rotation. In the case of our cyclist, this means going fast with a side wind. You feel a combination of headwind and that
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aside. This combination wind is a relative wind. Figure (1 15) illustrates the concept of relative wind "seen" by the blade.
Figure (1-15): Schematic of the blade-element momentum approach: (a) threedimensional view of a wind turbine; (b) a discretized blade; and (c) cross-section airfoil element showing velocities and force vectors. [27]. Where: L: Real wind blow. D: wind due to the rotation. F: relative wind combination. F is the resultant of L and D The resulting construction forms a triangle, or the name of velocity triangle. During the movement of rotation of the blades, each point belonging to the blade moves on a circle. The radius r of the circle corresponds to the distance from the center of rotation. More the radius of the circle on which the point is big, the greater the point will go away at every turn, and therefore, the higher the tangential velocity, D is. We can write, for a plan, ω, blade rotation tangential velocity Vd is: Vd = r.ω All points of the same blade did not have the same tangential speed. As the relative wind is a combination of the tangential velocity and the wind speed each section of the blade, according to its distance from the center of rotation, does not "see" the same relative wind. Each blade’s section have a different relative wind, it is necessary that the angle of attack shall be also different if we want to have maximum lift in each section. To fulfill this condition, the blade is twisted or has a geometric warping. In many cases, the blades of small wind turbines, less than 5 kW, have no geometric distortion. The angle of attack is optimal for only a portion of the blade. Sake of simplicity of manufacture and cost can explain this choice. I.4.3.
Speed Control Systems of wind turbine (a) Aerodynamic Stall System "Pitch"
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Figure (1-16): Blade orientation system “pitch” [3]. This control system rotates the blades of a few degrees at each variation of the wind speed so the blades can be always positioned at an optimum angle relative to the wind, in order to extract the maximum power at any time (Fig. 1-16). That is to say we must vary the pitch angle of the blades to take full advantage of instantaneous wind and the power limit for wind speeds that are greater than the rated speed. (b) Aerodynamic Stall System "Stall": This type of control is used for most wind turbines because it has the advantage of requiring no moving parts and control system in the rotor. The wind turbine blades are fixed relative to the turbine hub. They are specifically designed to undergo stalls during strong winds. The stall is progressive when the wind reaches its critical speed (Fig1-17).
Figure (1-17): Airflow on blade profile "stall" [7]. (c) Aerodynamic Stall system "Active Stall" This type of control aims to use the advantages of the "stall" regulation and "Pitch" to control more precisely the production of electricity. This system is said to be active stall regulation. It is used for high power wind turbines.
15
I.5. Theoretical notions on the turbine I.5.1. Power coefficient CP The wind energy is the kinetic energy of the air that passes through a recoverable certain surface (S=pR or R=blade radius); the power is proportional to the cube of the speed V [m/s] 2
Pwind=1/2 ρπ R! V !
However, this energy can not be fully recovered, because it is necessary to evacuate the air who worked in the rotor blades. We introduce then the power coefficient CP in the calculation of the aerodynamic power [3]:
Pturbine=1/2 𝐶 ! ρπ R! V !
Where: ρ = 1.25 kg/m3 density of air, under normal conditions of temperature and pressure at sea level The coefficient CP characterizes the efficiency level of a wind turbine. It can be defined as the ratio: CP = (power available on the shaft) / (power available (Recoverable)
Figure (1-18): Power Coefficient [8]
I.5.2.
Torque Produced by the wind
1 𝑃! 2 𝐶! 𝜌𝜋𝑅! 𝑉 ! Γ= = Ω Ω
With Ω: The rotational speed of the turbine in [rad / s]
16
I.5.3.
Specific Speed of the Wind Also said setting speed or gear tip of the blade (tip-speed ratio) as the ratio of the !! blade tip speed to wind speed: 𝜆 = ! (1.5) !"#$
I.5.4.
Betz Limit
The total energy can not be captured by the wind turbine because the downstream speed of the rotor is never zero. So part of the kinetic energy of the wind has not been received. The theorem of the German physicist Betz shows that maximum recoverable energy in the wind by the rotor is equal to 16/27, or about 59% of the total energy of the wind. The notion of power coefficient Cp can now be presented. This limit is actually never reached and each turbine is defined by its own power coefficient expressed as a function of the specific speed standard λ [3].
Figure (1-19): Stream-tube of a Wind Turbine [3].
Betz theory modeled the airflow before and after the blades of the wind turbine via a tube current (Fig 1-19). With: V1: Wind speed before the wind turbine blades. V: the wind speed at the wind turbine blades, of the order of a few m/s. V2: the wind speed after removal of the energy by the wind turbine blades Where: V1 > V > V2 are parallel to the rotor axis. !
Recoverable wind power is expressed by: 𝑃 = 𝐶! 𝜌𝑆𝑉 ! (1-‐6) ! We can find the (CP) max by studying powers, knowing that: - The recoverable power of the turbine is due to the variation of kinetic energy of the wind: !
∆𝐸𝑐 = ! 𝜌 𝑆𝑉(𝑉!! − 𝑉!! ) (1.7)
Secondly, the force exerted on the wind turbine creates a power Pm; the theorem of the quantity of motion gives:
17
𝐹 = 𝜌 . 𝑠. 𝑉. (𝑉! − 𝑉! ) (1.8) Then:
𝑃! = 𝐹. 𝑉 = 𝜌 . 𝑆. 𝑉. 𝑉! − 𝑉! . 𝑉 = 𝜌. 𝑆. 𝑉 ! 𝑉! − 𝑉! (1.9)
Pm is the power absorbed by the rotor, that to say the mechanical power supplied to the wind wheel. We can determine the velocity V2 for which the power is maximum: 𝑃𝑚 = ∆𝐸 Whether: !
𝜌. 𝑆. 𝑉 ! 𝑉! − 𝑉! = ! 𝜌 𝑆𝑉(𝑉!! − 𝑉!! ) (1-‐10) By simplification:
!
𝑉. 𝑉! − 𝑉! = ! (𝑉! − 𝑉! )(𝑉! + 𝑉! ) (1-‐11)
Then:
𝑉=
!! !!!
(1-‐12)
!
By postponing the expression of V (1-12) in the expression (1-9):
𝑃𝑚 = 𝜌 . 𝑆.
!! !!! ! !
Power is maximum for V2 as: Which gives:
!! !!! !
. 𝜌. 𝑆 = 𝜌 . 𝑆. !" !"!
!
. 𝑉! ! − 𝑉! ! (1-‐13)
= 0
−3. 𝑉!! − 2𝑉! . 𝑉! + 𝑉!! = 0
Then we solve this quadratic equation, of unknown V2. We obtain two solutions: one is impossible (negative) and the other corresponds to:
𝑉! =
!! !
(1-‐14)
The maximum power is for: 𝑉! =
!! !
By postponing (1-12) and (1-14) in the expression (1-9) the maximum power P becomes:
𝑃!"#
max
= 𝜌. 𝑆. 𝑉!! . (!!) (1-‐15) !
Deducting the maximum power coefficient for a wind turbine CPmax
𝑃!"# = 𝜌. 𝑆. 𝑉!! .
8 1 = . 𝐶!"#$ . 𝜌. 𝑆. 𝑉!! 27 2
18
We find then:
𝐶! !"# =
!" !"
≃ 0,59 (1-‐16)
The power factor represents the ratio between the power of the rotor and the power available in the wind:
𝐶! =
𝑃!"#"! 𝑃!"#$
Taking into account the Betz limit, CP max is therefore:
𝐶! =
!!"#"! !!"#$
!
!"
= ! !"#"!! = !" (1-‐17) !
!.!.!
The maximum power of the rotor will be equal to: !" !
𝑃!"#$%&% = !" . ! 𝜌. 𝐴. 𝑣 ! (1-‐18) CP max Pwind
Taking into account all other yields of a wind turbine, such as generator or gearbox the overall efficiency of a machine is around 50% of the Betz limit.
! !" !
𝑃!"#$ !"#"! = ! . !" . ! 𝜌. 𝐴. 𝑣 ! (1-‐19)
To conclude, in many cases: PReal rotor = 0.3 Pwind The curves (Fig. 1-21) show the evolution of the power coefficient CP for real turbines of horizontal axis at 1, 2, 3 and 4 blades; note that its value remains well below the Betz limit (0.59). They depend almost on the blade profile. If we consider the three-bladed machines, we can say that its power factor is maximal for 𝜆 = 7, that is to say a peripheral speed at the blade tip equal to 7 times the wind speed. It’s for such a standard speed that the aerodynamic yield is maximized. At a given wind speed and diameter a double blade must have a rotational speed higher than a propeller (triblade). On an aerodynamic perspective, we can compare the different types of turbines by comparing their aerodynamic coefficients of power or torque according to the standard speed 𝜆.
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Figure (1-20): CP as a function of 𝝀 for different turbines [7].
- According to the (Fig 1-20), the curves giving the torque coefficient in the vertical axis systems indicates that evolves in an identical way. - These curves CP (𝜆) clearly show the advantage of the horizontal axes in terms of power, even if this judgment is to nuance when observing the energy output, especially in low wind locations (urban...). - CP curves (𝜆) are flatter for horizontal axes with a small number of blades (2,1) compared to the vertical axes or multi-blade. I.6.
Characterization of Wind I.6.1. Wind speed instantaneous distribution The wind blows where air shows differences in temperature and pressure and still runs from high pressure to low pressure. If the earth did not rotate, the air would move directly (straight) centers of high pressure (anticyclone) to the centers of low pressure (cyclone) but because of the rotation of the earth, the air is forced follow a curved path, slightly bent towards the low pressure (Coriolis effect). [9] The geographical choice of a wind farm is important in a project to produce wind energy. To determine the energy that can be effectively extracted from the wind power it would be necessary to determine the wind characteristics at this site. For the properties of a site, we must make measurements of wind speed and its direction, over a long period of time. The figures below show the variations of average speeds on a site Linate Airport (Milan, Italy) weather station over the course of an average year. It is based on the historical records from 1990 to 2012. Earlier records are either unavailable or unreliable.
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Figure (1-21-a): The average daily minimum (red), maximum (green), and average (black) wind speed with percentile bands (inner band from 25th to 75th percentile, outer band from 10th to 90th percentile). [39]. Over the course of the year typical wind speeds vary from 0 m/s to 4 m/s (calm to gentle breeze), rarely exceeding 7 m/s (moderate breeze). The highest average wind speed of 2 m/s (light breeze) occurs around March 29, at which time the average daily maximum wind speed is 4 m/s (gentle breeze). The lowest average wind speed of 1 m/s (light air) occurs around October 24, at which time the average daily maximum wind speed is 3 m/s (light breeze).
Figure (1-21-b): The daily low and high wind speed (light gray area) and the maximum daily wind gust speed (tiny blue dashes). [39].
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I.6.2.
Regional distribution of wind speed For a wind turbine implementation we must choose a site where the wind provide the energy required, so we must make measurements of wind speed at several sites. (Fig 1-22) shows an example of windy regions in Italy after satellite data of the (Wetherspark.com)
Figure (1-23): windy areas in Italy [26] According to data from the (Fig 1-23) indicates wind speeds for different sites located in Italia. I.6.3.
The histogram of wind speeds The histogram of wind speeds or speed duration curve of the site is an important tool in the characterization of a wind farm. The curve represents the speed in duration time during which the wind is in each range or bearing of speed values, for example, by providing a N set of measured values of the wind speed determining the histogram of the wind speed (the distribution curve of the wind).
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I.6.4.
Weibull distribution
It is recalled that the distribution function F (v) is the probability that the wind speed is below a certain value v and the probability density f (v) is derived from: !"(!) 𝑓 𝑉 = !" (1-‐20) Among the distributions used in the statistical models, the Weibull distribution has been found suitable for describing the statistical properties of the wind. Weibull distribution function with two parameters c and k can be written: 𝑓 𝑉 = 1 − exp −
! ! !
(1-‐21)
Using the relationship given by the equation (1-18), it follows the function of the probability density 𝑓 𝑉 =
!
! !
!
!
exp −
! ! !
(1-‐22)
With: - K: shape parameter characterizes the distribution of wind - C: scale parameter characterizes the wind speed (the more C is high more the energy is at high speeds) - V: wind speed "instant" (averaged over 10 min) I.6.5.
Influence of height
To define the characteristics of a wind farm, it is imperative to know the height on which the measures are taken and then adapt the results to the height of the turbine mast. Indeed, the wind speed V increases with height h. The expression (1.20) gives the calculation method and states that h is the height of the mast and hmes the height of measuring devices. 𝑉! ℎ = 𝑉! (ℎ!"# )
!" ! ! ! !" !"# !
(1.23)
Table (1-2) the roughness values 𝛼 depending on the nature of the obstacles in the environment:
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Type of ground Surface of a water plan Vacant Land with smooth surface (runway, turf maintained...) Agricultural area without barrier or fence, dotted with houses scattered over gentle rolling hills.
0.0024 0.003
Agricultural area with few houses and tall hedges (a height of eight meters maximum) spaced approximately 1250 m.
0.055
Agricultural area with few houses and tall hedges (a height of eight meters maximum) spaced approximately 500 m.
0.1
Agricultural area with many buildings, hedges or 8 meter spaced 250 m.
0.2
Larger cities with tall buildings Very large cities with tall buildings and skyscrapers.
Roughness parameter 0.002
0.8 1.6
Table (1-2): A parameter of surface roughness as a function of the environment. [1] Schema (1-3) shows an example of the evolution of the wind depending on the height in a windy region by an "orographic wind" (wind existing at a region independently of the effects of roughness).
Schema (1-3): average wind speed according to the height [25].
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I.7. Optimal Energy Production
Figure (1-26): Wind power control according to the wind speed [8]. To ensure maximum capture of the incident energy, we must adapt the regularity of the wind turbine speed to the wind speed and the angle of incidence of the blades. On the operating characteristic of the wind (Fig. 1-26) there are four main areas that are: Zone 1 where the wind speed is less than the starting speed of the wind turbine [Cut in speed] in this case, the turbine does not work. Zone 2 in which the wind speed is within the range [Cut in speed, Nominal speed] is the conversion of wind energy. The area where it is possible to optimize. Zone 3 where the power developed by the turbine is limited to the nominal power Pn. Indeed, beyond the "rated speed" Nominal speed wind, the additional sizing (generator power, strength of structures) would not be amortized by the gain in production. Zone 4 when to the wind speed exceeds the maximum speed permissible by the wind turbine [Cut out speed] in this case; the turbine is stopped by the emergency shutdown system [4]. There are three factors that determine the relationship between wind energy and mechanical energy recovered by the rotor: A. The area swept by the rotor
Directly depends on the wind and its size. Given that the area swept by the rotor increases with the square of the diameter of the rotor, doubling it will result in a
25
harvest of 22 = 2 x 2 = four times more energy. (Fig 1-27) gives an idea of the variation of the power unitary according to the diameter of the rotor swept as well as a forecast.
Figure (1- 27): Powers according to the sizes of wind turbines [8] B. Density air and the wind velocity Production capacity of a wind turbine is characterized by its power curve. This provides its production capacity (in Watt) according to its average wind speed at the hub (Fig. 1-27). This power curve depends on the mean annual temperature of the site, site altitude: the standard condition in which it is supplied with an average temperature of 15 ° C and an altitude of 0 m above sea from there the energy produced is the integration on time of the power curve of the turbine. This is expressed in terms of the power curve of a wind turbine P and the distribution V velocity by: 𝐸 = 𝑃 𝑉 𝑡 𝑑𝑡 in KWh/year
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I.8. Interest of Variable Speed In variable speed, the wind energy system is controlled so that for each wind speed, the wind turbine operates at maximum power. This is called the "Maximum Power Point Tracking" (MPPT). The maximum power is achieved at a speed of rotation of the turbine given by the feature of the wind turbine P (W). Then you can make a fixed frequency generator and variable speed. The variable speed generator can work for a wide range of winds thus recover maximum power. (Fig 1-30) shows that the position of the maximum of the power curve in function of the rotational speed changes with the speed of the wind. Typically, a speed setting within a range of 1 to 2 is needed to fully optimize the energy transfers.
Figure (1-30): Characteristic of the wind turbine [3] I.9. Safety Analysis I.9.1. Case of Horizontal Axis Wind Turbines This study is to estimate the impact of an accident on personal safety. The main risk of accident could have an impact beyond the simple ground crash of the turbine is the ejection of a blade or a piece of blade (Fig 1-31). All the analyzes do not take into account the effects of aerodynamic lift on the blades, but only gravitational effects.
27
Figure (1-31) diagram shows the reach of the blade for a horizontal axis wind turbine. [25]. I.9.2.
Case of Vertical Axis Wind Turbines The analysis was carried out for a wind turbine blade that is released. (Fig 1-32) illustrates the scope of the blade
Figure (1-32) diagram shows the dimension of a vertical turbine. [25].
28
I.10. Some Turbines Used in Wind Energy Generation. I.10.1. The Turbine "AOC 15/50 HZ 50" This is a Vertical Axis Wind Turbine 60 kW American version presented in 50 Hz (55 kW). Its design is similar to that of large wind turbines. More than 8 units are in operation around the world (USA, Europe, Africa). The manufacturing company was in liquidation before being recently acquired by Canadian investors.
Figure (1-34-a): Photograph of "AOC 15/50 HZ 50" [25]. I.10.2.
The Turbine "Fuhrländer - FL30" Reliable Wind turbine marketed for 15 years identical at technological level with large wind turbines.
Figure (1-34-b): Photograph "Fuhrländer - FL30" [25]. I.10.3.
The Turbine "GUAL - STATOEOLIEN GSE 4"
29
VAWT on integrating all types of buildings (residential, community, commercial, administrative and industrial buildings...)
Figure (1-34-c): Photograph of « GUAL - STATOEOLIEN GSE 4» [25.] I.10.4.
The Turbine "Windside - WS-4"
U.S. wind turbine vertical withstand extreme conditions (temperature, wind, humidity). Produces up to 60 m/s. Network connection and battery charging. Not noisy.
30
Figure (1-34-d): Photograph of « WINDSIDE - WS-4 » [25.]
I.11. Research and Development in Progress a) Wind turbine Turby
The University of Delft "Netherlands" has a department where several teachers working on the issue of urban wind. After theoretical studies have shown that the producible generated by certain types of Darrieus wind was amplified when it is placed on the roof of a building, the development of this type of turbine has been undertaken. It is in progress (Fig 1-35-A).
Figure (1-35 –a): Photograph of the Turby wind turbine [25].
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The wind turbine has yet to be tested in a real environment. Its technical characteristics are as follows: - Amplification efficiency compared to the normal flow: between 1.7 and 2.3; - Weight: rotor: 90 kg round: 230 kg; - Dimensions: around 5 m + 3 m rotor up to 1 m radius; - Power 2.5 kW. b) The WARP system The WARP system has been bidding for licenses manufacturing and marketing. The system consists of stackable modules as towers where the ventest amplified before operating propeller turbines. The same system is expected to use photovoltaic cells as outer material (Fig 1-35-B) [5].
Figure (1-35 –b): image of the WARP system [25].
c) The Multirotors wind turbine system The company Selsam has designed a wind turbine rotors with 7 3 blades with a diameter of 2.1 m providing a power of 6 kW. The shaft (the shaft on which are placed the rotors) is not parallel to the ground but inclined, in order to avoid disturbance of the airflow of a rotor on another (Fig 1-35-C) [5].
Figure (1-35 –c): Photograph of multirotor wind turbine [5].
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d) The KiteGen System Italian researchers have proposed wind electric generator driven by kites that go up to 2000 m and by their rotational movements are running an horizontal "windmill" and could generate a lot of power. According to its designers it will be much more profitable than the current solutions (Fig. 1-35-D).
Figure (1-35-d): Photograph of KitGen wind power [5]. I.12. Some provisional figures:
Wind-Force Report 12 (May 2004) In 2030: - The global installed power varies between 2700 and 6620 GW TWh. - Price floor is between 2.3 c € / kWh - € 0.474 / W. 2038: installed capacity varies between 3238 and 8510 GW TWh. Economic Impact and Environmental Report in 2020: wind power would provide 12% of global electricity. - Generate 2.3 million jobs. - Avoid 11 billion tons of CO2. Report European Wind Energy Association [EWEA] 2010: More than 100 GW in the world (10 GW offshore 70GW More in Europe I.13. Example Rated values Length of a blade, and the speed Synchronous Generator
33
To obtain an electric power of Pelec = 18 kilowatts power with a wind turbine of the following data: - The wind flowing through this region is a velocity V = 6.5 m / s. - The machine is three bladed and operates at a fixed speed. - The impeller of the turbine drives a generator asynchronous (with a yield of n (g) = 0.8 and a slip of g = -1%) and a speed multiplier (with a yield of n (m) = 0.9 and a multiplication coefficient K = 30). Sizing of the different elements: A. Wind wheel dimensions A.1. Mechanical power required: 𝑃!"!# = 𝑃! !! !! ⇒ 𝑃! =
𝑃!"!# 𝑛! 𝑛!
With: nm= 0.9 ng= 0.8 Pele= 18kW AN: 𝑃! = 18000 0.8𝑥0.9 = 25 𝑘𝑊
A.2. Power coefficient Cp: To determine the values of Cp and 𝜆 you can use the curves below
34
A.3. Blade length: To capture maximum power it comes to choose the maximum power coefficient Cpmax = 0.48 -‐ Mechanical power is given by: 1 𝑃! = 𝐶! 𝜌𝑆𝑉 ! ⇒ 𝑆 = 2 With: Pm= 25kW 𝜌 = 1,25kg / 𝑚! V= 6.5 m/s CP=0,48 AN: !×!"##
𝑆 = !.!"×!.!"×
!.! !
= 303.5 𝑚! 𝑅 =
! !
B. Generator dimension B.1. The speed of the shaft of the wind turbine 𝛀 in rad/s and NL rpm According to the previous figure (CP =0.48 and 𝜆=8) and from the formula: 𝑅Ω! 𝜆. 𝑉 𝜆= ⇒ Ω! = 𝑉 𝑅 With: 𝜆 = 8 V=6.5 m/s R= 10m AN: B.2. The rotor speed of the generator 𝛀 in rad/s, and N in rpm According to the formula: Ω = 𝐾Ω! With: K= 30 Ω! = 5.23 rad/s
𝑁 =
Ω 60 = 1500 𝑟𝑝𝑚 2 𝜋
AN: Ω = 157 rad/s
35
Finally, for a wind turbine that provides electrical power Pele= 150 Kw, we would use the following dimensions: Dimensions of wind wheel: - Wind speed in the area is greater than the speed V = 6.5 m / s. - The wind turbine is propeller. - The length of the blades is equal to 10 m. Dimensions of the Gear - The gear ratio of this multiplier is K = 30. - The multiplier is operated with a yield of Nm =0.9 Dimensions of the generator: The generator operates at a fixed speed greater than synchronous speed NS = 1500 rpm (negative slip g = -1%) with a yield of n(g) = 0.8 Relationship Between the necessary wind speed and the Height of the Tower To place a wind farm in an area with few houses and tall hedges (a height of eight meters maximum) spaced approximately by 500 m and wind speed measured at a height of hmes = 1m equal to Vmes = 8m/s it is necessary to choose the height of the tower which gives the necessary speed. For electric power of P = 101kW in this zone with the following data: - The wind turbine is used with a three bladed rotor diameter D = 2R = 20m - The generator works with a yield ng = 0.8 and synchronous speed Ns = 1500rpm. - The gearbox characterized by a transmission ratio K = 20 and return nm = 0.9. We will proceed in the following steps: Calculate the mechanical power needed: 𝑃!"!# = 𝑃! 𝜂! 𝜂! ⇒ 𝑃! = With:
𝑃!"!! 𝜂! 𝜂!
ng=0,8 nm=0,9 Pele=101kW. AN: 𝑃!"# = 140.3 𝑘𝑊 Calculate the maximum power coefficient CP: According to the previous curves for three bladed wind (Cp = 0.48 and = 8)
36
Calculate the required speed: 𝑃! = 𝐶!
1 2𝑃!"# 𝜌𝑆𝑉 ! ⇒ 𝑉 ! = 2 𝜌𝐶! 𝑆
With: Cp = 0, 48 r =1,25kg / m3 R= 10m, S =p .R2= 314 m2 Pmec = 140.3 Kw And: V= 11.42 m/s Calculate the height of the tower needed: From the formula of the Weibull distribution 𝑉! ℎ = 𝑉! ℎ!"#
⇒ 𝐿! ℎ 𝛼
VV (h) = 11,42 m/s hmes = 2m
= 𝑉! ℎ!"#
𝐿! ℎ 𝛼 ℎ!"#
𝐿!
𝛼
𝑉! ℎ ℎ 𝐿! !"# 𝛼 𝑉! ℎ!"#
With:
VV (hmes) = 8 m/s
𝛼 : Roughness parameter varies depending on the nature of the ground in this case 𝛼 = 0.1 NA: h= 6.63m The operating point of the wind turbine can be determined from the characteristic of the power P supplied by the turbine based on the rotational speed of the turbine LW for a given wind speed. The nominal operating point is chosen such that the power supplied by the wind is maximum; the block diagram (Figure 1-36) gives an idea about the design of a wind turbine.
37
Figure (1-36): macroscopic schema of the wind turbine generation. To optimize the active electrical power P cut into the wind, we adjust the rotation speed of the wind (Ω! ), the energy efficiency of a wind turbine varies between 0.5 and 0.6 depending on the properties of the elements that make up the wind turbine: rotor, gearbox, generator, power converter, filter, transformer etc.
38
Chapter 2 Different conversion chain and generators.
39
There are several types of electrical machines that can function generator that requires very specific characteristics. The specifications for a wind generator vary with the type and the geometrical dimensions of the wing. Some machines typically used in wind turbine construction are briefly described in this section, taking into account their specificities. II.1.
Systems Using Synchronous Machine The synchronous machines are known to provide very high torque at suitable geometric dimensions. They can be used in direct drive on wind turbines. Their proportion is steadily increasing (slightly more than 5% in 2001). The synchronous or synchronous machine (MS) can be used in the case of direct drive, that is to say when the mechanical connection between the wind turbine and the generator is direct, without using a multiplier. It must, however, this generator be necessarily connected to the network via frequency converters. Or the permanent magnet generator is, it can operate in standalone mode: II.2.
Electromagnets Synchronous Machines The coils of the electromagnets are supplied with direct current by means of a system of brushes and slip rings to the shaft of the generator. This supply can be done for example via an inverter that converts alternating current of the electrical network in direct current. There are different ways of generating the excitation: - Low power (less than 10 kW), the dominant conversion chain uses magnets a machine multipolar driven directly by the turbine (speeds relatively higher than those of great power turbines) and connected to a DC bus through a simple diode bridge (Fig. 2-1). This solution has also been extended to large systems. Associated Scanwind, ABB has already made prototypes cylindrical magnets architecture envisaged for offshore production up to 5 MW.
Figure (2-1): Network connection of a synchronous wind turbine [8].
40
- We can show the improvement of the conversion line, adding a chopper controlled possibly in MPPT (Maximum Power Point Tracking) to adjust the level of voltage and thus the rotational speed of the turbine. - The ideal structure with rectifier pulse width modulation, which absorbs sinusoidal currents and their phase control eventually to have a degree of freedom in the energy optimization and in the design of the system. There are several concepts of permanent magnet synchronous machines dedicated to wind energy applications, construction machinery standard (radial magnetization) at discoid generator (axial field) or at external rotor (Fig 2-2). [8]
Figure (2-2): Classical radial field machine and axial field discoid machine [8]. II.2.1.
Permanent magnet synchronous machines or "MSAP" Unlike electromagnet synchronous machine the excitation source of the rotor is independent of the network. This type of machine tends to be increasingly used by turbine manufacturers because it can operate in standalone mode, the electromagnets generator is however currently the most widely used II.3.
Systems Using Asynchronous Machine The term asynchronous is because the speed of these machines is different from the synchronous speed of the rotating field. Longtime, asynchronous machines have been stiff competition from synchronous machines in the fields of high power, until the advent of power electronics. It can be found today in many applications, especially in transportation (metro, trains, marine propulsion) in the industry (machine tools), the appliances ... It was originally only used as motor but always thanks to the power electronics, it is more often used as a generator. This is for example the case in the wind turbines. To run in single phase, asynchronous machines require a boot system. For power applications, beyond a few kilowatts, asynchronous motors are only powered by three-phase current systems. Most of the time, the Asynchronous Machine (MAS) is used because the
41
generator is capable of supporting small variations in speed which is a major asset for applications like wind energy where the wind can change quickly especially during bursts. These last generate high mechanical stresses to the system that are smaller with an asynchronous machine than with a synchronous one, functioning normally at fixed speed. As a guide, most machines used in wind turbines are type asynchronous with a squirrel cage (about 90% in 1997, 60% in 2001). However, the proportion tends to decrease. The wounded rotor asynchronous generators have been developed in recent years (3% of the machines in 1997, it rises to about 30% in 2001). II.3.1.
Squirrel Cage Asynchronous Machine This type of machine was invented by "Michail Ossipowitsch Doliwo-Dobrowolski" in the early 1890s. Asynchronous squirrel cage machines, standardized till powers of range of MW, have an advantage in economic applications especially those directly connected to the network. At a classic rotational speed (1 000-1 500 rpm), their specific cost is about 4-6 c € / W, it increases with the number of poles because the power must be obtained at a lower speed (superior torque and mass). These “fast” machines need to be associated to their wind turbine, much slower, through a mechanical speed multiplier. The rotors of such machines are composed of ferromagnetic laminations and conductor bars uniformly distributed around the periphery of the rotor. The bars are interconnected by two short-circuit rings (Fig 2-3). [13] The ferromagnetic laminations are used to canalize the lines of field while the bars are seat of induced currents.
Figure (2-3): Structure of a squirrel cage rotor [13]. The inclination of the bars of the cage reduces the variation of the magnetic circuit during the rotation of the rotor (or "notch effect") and thereby to reduce the torque ripple. It is this inclination notches which gives the ensemble bar plus short-circuit rings the form of a squirrel cage deformed. Below is shown a conversion line associated (Fig 2-4). [3]
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Figure (2-4): Network connection diagram of the wind turbine with squirrel cage MAS [3]. II.3.2.
Dual Stator Asynchronous Machine This configuration of wind turbine, allows an operating point at two speeds. Is carried out a double coil stator (Fig 2-5) which induces a variable number of pole pairs and hence a different speed ranges. It can impose two synchronous speeds by changing the number of poles. On the one hand, there is a low-power stator with large number of pole pairs for small wind speeds. Indeed, the power is given by: 𝑃!" = ΓΩ!
With: Pmg: the transferred power by the generator Γ the electromagnetic torque Ω! the synchronism speed 𝜔 the network pulsation and p the number of pole pairs. At low power corresponds a low speed, the speed being related to the number of pole pairs by: Ω! = 𝜔 𝑝 At low speed there is a high number of pole pair corresponding. On the other hand, it has a stator at high power corresponding to high speed and therefore a low number of pole pairs for the higher wind speeds, switches are used for network connection.
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Figure (2-5): Diagram of the network connection of the turbine with the double stator MAS [3]. II.3.3.
Double Fed Induction Generator (DFIG) The double-fed induction generator is an asynchronous machine. The stator windings are connected directly to the three-phase network. The rotor windings are connected to power converters whom are bidirectional in current. The capacitor between the two converters represents the DC bus. The step-up transformer provides the tuning to the distribution network. Unlike some synchronous machines that have converters crossed by 100% of the rated power. DFIG converters are sized to let pass 25% of the rated power only. They cost less and are less bulky. They can control the DFIG rotor by adjusting the speed of mechanical rotation. Indeed the DFIG allows generator operation in hypo synchronous and hyper synchronous; according to these converters we can achieve several types of these machines: III.3.3.1. DFIG Type "Brushless" This machine consists of two three-phase windings on the stator. One of the coils is connected directly to the network and is used to transfer power. The second winding, which conductor cross-section is lower, is used to vary the current excitation of the machine. High power stator is connected directly to the network and the converter is placed between the low-power stator and the network (Fig 2-6).
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Figure (2-6): asynchronous brushless machine connected on the network. [7]. III.3.3.2. DFIG Type "Wound Rotor" The rotor of an asynchronous machine with a wound rotor or with rings consists of three coils. Each coil is connected to a ring. The rings allow having an electrical connection with the coils of the rotor. This type of rotor is designed to allow the variation of resistance of the rotor by inserting resistors in series with the coils to achieve a rotor starting. This device was then used to speed variation with an acceptable yield through a process called ca hypo-synchronous cascade. Converters used are so dimensioned for a fraction of the rated power of the machine. For this configuration, there are three possible structures. (a) DFIG - Kramer structure
This configuration with variable speed is shown in (Fig. 2-7), the stator is connected directly to the network and the rotor is connected to a rectifier and an inverter is placed at the output of the rectifier. All rectifier-inverter is then dimensioned for a fraction of the rated power of the machine
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Figure (2-7): DFIG - Kramer structure [7]. (b) DFIG rotor energy dissipated (Fig 2-8) represents this configuration with the network directly connected to the stator and the rotor connected to a rectifier. A resistive load is then placed at the output of the rectifier via a chopper IGBT or GTO. The control of the IGBT allows to vary the energy dissipated by the toroid coil and operated either at variable speed while remaining in the stable part of the torque / speed characteristic of the asynchronous machine.
Figure (2-8): DFIG with slip control by the dissipated energy [7]. (c) DFIG-‐ "Scherbius" structure with Cycloconverter
46
When replacing the association rectifier - inverter by a cycloconverter (Figure 2-9) to allow bidirectional power flow between the rotor and the network, the assembly is then called "Scherbius structure" represented in (Fig 2-10). The range of variation of speed is doubled compared to the structure in the (Fig 2-8).
Figure (2-9): Scherbius Structure with cycloconverter [7].
(d) DFIG-‐ Scherbius structure with PWM converters This configuration (Figure 2-10) has the same characteristics as the Scherbius with cycloconverter. However, the switches used in this configuration (IGBT) may be controlled to the open and close and to their switching frequency. The use of this type of converter allows obtaining signal gaits of the output of Pulse Width Modulation whose modularity allows limiting disturbances modifying the frequency spectrum of the signal (first harmonic rejection of non-zero at high frequencies).
Figure (2-10): Scherbius structure with PWM converters [7].
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II.4. Variable Reluctance Machine II.4.1. Excited Double Salience Variable Reluctance Machine Among generators in the study, especially for direct drives machine there is a variable reluctance machines called VRM, type "pure" (without excitation) or excited. It is their economic advantage (low manufacturing cost) and robustness (without winding nor magnet rotor) that allowed their development. (Fig 2-11) shows a converter system generator with double salience variable reluctance (GDSVR). The currents being unidirectional, an asymmetric half-bridge inverter powers each phase independently.
Figure (2-11): Double salience variable reluctance generator [8]. Variable reluctance machines excited by induction coils or magnets may also be considered. In this case, it is more interesting to feed its by bidirectional currents (Fig 2.12). We used then "traditional" three-phase PWM inverters
Figure (2.12): variable reluctance generators Structure excited by Magnets (anisotropic) [15/48]
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II.4.2.
A Not Excited Variable Reluctance Machine The variable reluctance machine unexcited shown in (Fig 2-13) comprises 6 stator teeth distributed on 4 teeth of the rotor. To study this machine, we first determine the main dimensions and then optimized, with the aid of a genetic method coupled to the finite element method, the shape and dimensions of the notches.
Figure (2-13): Variable reluctance generator unexcited [3]. II.5. Comparison of Electromechanical Converters (Fig 2.14) shows a comparison of energy performance for different conversion chain on a three-bladed machine 600 kW [14]. The reference solution is controlled stall and cage induction generator speed. The most efficient is to control pitch, direct drive synchronous type. It may be noted that it is the low wind speeds obtainable gains most important energy gain. The results given in this study show that a comparison between the energy capture of the different control concepts is strongly influenced by the site conditions (annual mean wind speed, turbulence and the form of the annual wind speed distribution) as well as by design parameters (design tip speed ratio and choice of rotor profile). The dependence on the parameters is nonlinear so that it doesn’t allow any precise predictions for conditions, which have not been covered by the simulations.
49
(Passive) stall
Active stall
Pitch
Single speed
Stall controlled single speed concept 1
Active stall controlled single speed concept 3
Pitch controlled single speed concept 5
Two speed
Stall controlled two speed concept 2
Active stall controlled two speed concept 4
Pitch controlled two speed concept 6
Variable speed
Stall controlled variable speed concept 7
Active stall controlled variable speed concept
Pitch controlled variable speed concept 8
Figure (2-14): Comparing the performance of various wind chains [14].
These results depend also on the profile of the blades, wind conditions, including turbulence intensity (here 10%), of the speed of normalized basis (here 𝜆 = 6), of the inertia moment of the rotor (here 500 kg.m ²).
50
Table (2-1) summarizes the advantages and disadvantages of the three types of machines. Synchronous Asynchronous Variable reluctance * Good yield * Allows operating at * Partial or complete Advantages variable speed removal of the speed multiplier. * Low power, Autonomously. * Studies currently suitable for low * Need capacity for in course. speed but high self-‐excitation to price magnetize the Disadvantages machine. Connected to the network * Requirement to function at vicinity of synchronism. Table (2-1): Advantages and disadvantages of generators associated with wind turbines.
Comparative study between the two most commonly used machines in the wind industry: Criteria Synchronous machine Asynchronous machine * It requires a coil * The squirrel cage rotors excitation to be supplied are simple and robust. It with continuous current resulting high reliability. either by an external The asynchronous Construction source, or through auxiliary generators are engines and alternative manufactured in very high rotating diodes. series for small and middle powers. * The risk of repairs is * Maintenance is greater, especially at the minimized. Spare parts are coals, rotating diodes, coils still available through the Maintenance and spare excitement. Spare parts are widespread use of parts not always available due to asynchronous motors. limited market especially in certain areas such as developing countries. * For proper operation on * Not required. However, an interconnected network, when switching on the a synchronoscope need to network it appears a control the three current peak whose Synchronization synchronization conditions. duration depends on the * For machines of very little slip value at the time of power ( Ld). In order to verify the modeling method, a 2-D model of the machine prototype is implemented by a commercial finite-element (FE) code (ANSYS Maxwell) Fig. (4-4). Machine parameters as functions of rotor position θ (expressed in terms of electrical degrees) are then determined by a sequence of FE analyses (FEAs), taking advantage of the built-in post processing procedures. Even if the method presented in this paper applies to a generic angular displacement 2α between the two winding sets, in the example application, the displacement angle is practically constrained by the stator configuration that was initially designed for a conventional three-phase winding. Other design issues, related to the flux utilization and the mutual coupling between sets, introduce further constraints to the choice of 2α.
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Fig (4-4) Two-dimensional model adopted for the FEA[44]. A. Stator Inductance Matrix In the hypothesis of the rotor anisotropic magnetic structure, the self-inductance and mutual inductance are functions of θ. Furthermore, assuming that the geometric and electromagnetic asymmetry of the three-phase winding sets and saturation effects are negligible, the self-inductance for the i th winding (i = a1, b1, c1, a2, b2, or c2) is assumed to be expressed as: 𝐿! (𝜃) = 𝐿!" + 𝐿!! cos(2𝜃! ) (1) Where Ls0 is the average value of the self-inductance, Ls2 is the second-harmonic coefficient, and θi is the electric displacement angle of the i th winding magnetic axis from the d-axis. The constant term Ls0 is a sum of the leakage inductance Lσ and the constant self-inductance Ls0’. Similar to (1), the expressions of the mutual inductances between the two different i and j phases of the same star winding (i, j = a1, b1, c1 or i, j = a2, b2, c2 and i ≠ j) are assumed to be (Ms0 average value; Ms2 second-harmonic coefficient) 𝑀!" (𝜃) = 𝑀!" + 𝑀!! cos(𝜃! + 𝜃! ) (2) The whole 6 x 6 stator inductance matrix L(θ) consists of four 3 x 3 inductance matrices: The upper left L1(θ) and lower right L2(θ) matrices contain the Li(θ) and Mij(θ) coefficients defined by (1) and (2) and related to the first and the second winding set, respectively; the upper right matrix M12(θ) and its transpose M21(θ) =MT12(θ) in the lower left corner are related to the mutual coupling between different sets defined by: 𝑀!" (𝜃) = 𝑀!" cos(𝜃! − 𝜃! ) + 𝑀!! cos(𝛾!" ) (3) Finally, the whole inductance matrix for the stator windings can be represented as a block matrix in the form
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𝐿! (𝜃) 𝑀!" (𝜃)
𝐿 𝜃 =
𝑀!" (𝜃) (4) 𝐿! (𝜃)
As we have treated the electrical equation of the DSAG before won’t repeat it we will skip this part concerning the DSSG as long as equations are alike and we can refer to the previous chapter. B.
Park transformation:
Park’s transformation for a three-phase system with no neutral connection is defined by the 2 X 3 matrix as 𝑇! 𝛿 =
! !
!!
cos 𝛿
cos(𝛿 −
− sin 𝛿
− sin(𝛿 −
)
! !! !
cos(𝛿 +
)
!!
− sin(𝛿 +
)
! !! !
(5)
)
The transformation matrix that transforms the phase variables, for instance, the 6 x 6 L(θ) matrix, into the d–q reference frame is composed by two Park’s transformation matrices and can be expressed as: 𝑇! (𝜃 + 𝛼) 0!,! 𝑇! 𝜃 = (6) 0!,! −𝑇! (𝜃 + 𝛼) Where 0i,j is a null matrix with i rows and j columns. Applying (6) to (4), the resulting matrix LT1, related to two couples of orthogonal windings d∗ − q∗ and d∗∗ − q∗∗, is given by
𝐿 !! = 𝑇! 𝜃 𝐿 𝜃 𝑇!! 𝜃 = With:
𝐿!∗ 𝐿!"∗ = 𝐿!"∗∗ = 0
𝐿!"∗ 𝑀!"∗
𝑀!"∗ 𝐿!"∗∗
0 𝐿!∗
! ! 𝐿!∗ = 𝐿!! + !!! − 𝑀!! + 𝑀!! 𝐿!∗ = 𝐿!! − !!! − 𝑀!! − 𝑀!! !
!
𝑀!∗ = ! + (3𝑀!! + 𝑀!!) 𝑀!∗ = ! + (3𝑀!! − 𝑀!!) ( 7)
With LT1 not being a diagonal matrix, the transformed winding couples d∗ − q∗ and d∗∗− q∗∗ are mutually coupled with respect to each other. The matrix of the further transformation required to eliminate such a coupling can be found by diagonalizing LT1. With a suitable rearrangement of rows and columns, the transformation matrix T2 to the final decoupled D1 − Q1 and D2 − Q2 reference frames (also referred to as D–Q reference frames) is obtained
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1 0 0 1 𝑇! = 𝑘 0 1 −1 0 Where 𝑘 = 1
1 0 0 1 (8) 0 −1 1 0 2
is the orthonormalization coefficient to enable the power to be
invariant. From here 𝐿!! 0 0 0 0 𝐿!! 0 0 𝐿 !! = (9) 0 0 𝐿!! 0 0 0 0 𝐿!! Where the inductances are: 𝐿!! = 𝐿!∗ + 𝑀!∗ 𝐿!! = 𝐿!∗ + 𝑀!∗ 𝐿!! = 𝐿!∗ − 𝑀!∗ 𝐿!! = 𝐿!∗ − 𝑀!∗ (10) Finally, by combining (6) and (8), the whole transformation results in 𝑇! (𝜃 + 𝛼) 𝑇! (𝜃 − 𝛼) ! 𝑇! 𝜃 = ! ! ! (11) 𝑇! (𝜃 + 𝛼 + ! ) 𝑇! (𝜃 − 𝛼 − ! ) It is worth mentioning that LT2 is directly derivable by the application of T 3(θ). The proposed transformation eliminates, like Park’s one, the triplex harmonics from the transformed quantities, although they are generally not relevant in symmetric threephase systems IV.4.
Machine model:
Although the double star IPM synchronous machine outlined in Fig. (4-3) is described by six equations, there are actually only four independent variables, if the rotor electromagnetic quantities are assumed to be fixed, and augmented to five if the rotor circuit has to be taken into account. In addition to the analysis of the rotor circuit harmonics proposed in, the harmonic phase displacement is taken into account for a better matching between the measured and simulated back electromotive forces (EMFs). The rotor position-dependent inductances can be transformed accordingly by applying T 3(θ), as shown before. In the following, the voltage equations in the decoupled D1−Q1 and D2−Q2 reference frames are derived from the voltage equation set defined according to the source sign convention. 𝑢! + 𝑅! 𝑖! + 𝑝𝜙! = 0 (12) Where Rs is the phase winding resistance, p is the time derivative operator, and
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u! = [u!! u!! u!! u!! u!! u!! ]! i! = [i!! i!! i!! i!! i!! i!! ]!
𝜙!" = 𝑀!" (𝜃)𝐼! 𝜙! = [𝜙!! 𝜙!! 𝜙!! 𝜙!! 𝜙!! 𝜙!! ]! = 𝐿 𝜃 𝑖! + 𝜙!" (13) Are the arrays related to the phase voltage, current, and flux linkages at no load and load respectively. The no-load flux linkage 𝜙 PM,i of the i th winding (i = a1, b1, c1, a2, b2, or c2) caused by the PMs is expressed representing, the PMs themselves as an equivalent rotor winding supplied by a constant current If. The i th element of the Mfs(θ) array is expressed as Mfs,i = Mfs(θi) = 𝜙 PM,i / If , i.e; the mutual inductance with the i th stator winding. No-load flux harmonics are taken into account by expressing Mfs(θi) as
𝑀!" 𝜃! =
⋈ !!! 𝑀!"
cos(𝑛𝜃! + 𝜙! ) (14) By replacing the flux expressions of (13) in (12) and applying T3(θ), the resulting voltage equations in the couples of decoupled orthogonal stator windings D1−Q1 and D2−Q2 are obtained (ω = pθ) 𝑝𝑖!" = 𝐿!! (−𝑢 + 𝑒 − 𝜔𝐽𝐿 + 𝑅 𝑖 ) (15) !" !" !! ! !" !" Where LDQ = LT2, iDQ, uDQ, and eDQ arrays in the form fDQ = [fD1 fQ1 fD2 fQ2 ]T (f =i,u,e) and (being I4 a 4 x 4 identity matrix) 0 −1 0 0 1 0 0 0 𝑅! = 𝑅! 𝐼! 𝐽 = 𝑒!" = − 𝑝 + 𝜔𝐽 𝜙!",!" 0 0 0 −1 0 0 1 0 𝜙!",!" = 𝑇! 𝜃 . 𝑀!" 𝜃 I! = [𝜙!",!! , 𝜙!",!! , 𝜙!".!! , 𝜙!",!! ]! (16) Taking geometric and electromagnetic symmetry for granted, and assuming α = π/12, the fundamental wave and (12k ±1)th harmonics (k = 1, 2, 3, . . .) in the original quantities are mapped intoD1−Q1 pair quantities, resulting as constant terms and 12k th harmonics, while the (6(2k + 1) ± 1)th harmonics (k = 0, 1, 2, . . .) are mapped into D2−Q2 pair quantities, resulting as (6(2k + 1))th harmonics. Thus, the derived transformation yields decoupled D–Q reference frames with similar properties as the d–q and z1−z2 subspaces by vector space decomposition. A. Electromagnetic Torque
The equation for the electromagnetic torque is derived starting from the instantaneous power 𝑃 𝑡 = 𝑢!! 𝑖!! + 𝑢!! 𝑖!! + 𝑢!! 𝑖!! + 𝑢!! 𝑖!! (17)
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In the steady state and neglecting the resistive voltage drop, the voltage (15) yield 𝑢!" = 𝐸!" − 𝜔𝐽𝐿!" 𝑖!" . (18) Combining (17) and (18) and dividing P by the angular speed Ω = ω/np (np = number of pole pairs), the electromagnetic torque is obtained With ∗ ∗ 𝐶!" = 𝑛! 𝑖!! 𝜙!! + 𝑖!! 𝜙!! − 𝑖!! 𝜙!",!! − 𝑖!! 𝜙!",!! (19) With: ∗ 𝜙!! = 𝑖!! 𝐿!! − 𝐿!! + 𝜙!",!! ∗ 𝜙!! = 𝑖!! 𝐿!! − 𝐿!! + 𝜙!",!! (20) If PM flux harmonics are negligible but the fundamental one and LD2 = LQ2, i.e; according to (7) and (10), Mm2 = Ls2 + 2Ms2, (19) simplifies to: ∗ 𝐶!" = 𝑛! 𝜙!! 𝑖!!
(21)
Recalling the simplified expression of the electromagnetic torque of variablereluctance three-phase machines.
IV.5. Conclusion The developed methodology simplifies the analysis of the double star PM synchronous generator; converting the six-phase voltage equation set into two decoupled complex differential equations. The method takes into account the harmonic content of the no-load flux linkages (generally relevant in the actual PMSG configurations) and applies to generic angular displacements between the two winding sets. The simplification introduced by the proposed approach can be advantageous to the purpose of the power flow control. The implementation of the method in a simulation environment, applied to different operating conditions, confirms its correctness and states its effectiveness from the point of view of the calculation time.
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Chapter 5 Study and simulation of the DSAG in an isolated mode
73
V.1.
Introduction
In this chapter, we focus on the modeling of a three-bladed horizontal axis wind turbine. We will develop the model of the turbine and the asynchronous generator selfexcited under SIMULINK environment, without addressing the control strategy to study the variation in time between the power turbine and generator. V.2. Introduction to Simulink SIMULINK is software which allows to model, simulate and analyze dynamic systems. The company “The Math Works Inc.” produced this software. It is a fully integrated tool core calculation Matlab provides a modeling environment based on block diagrams. Simulink has a graphical interface that facilitates the analysis of systems in the time and frequency domain. Simulink systems are more described by Matlab code lines but simply defined by block diagrams in which all elements are pre-defined in libraries of block element that is to assemble. The block diagram of the (Fig.5-1) shows the representation of such a system [31]
Figure (5-1): Representation of a system under Simulink.
The system modeled using Simulink can receive data from the Matlab workspace or send output data. Data exchange between Simulink and Matlab workspace can be done using common variables or through MAT files. At the Simulink modeling provides: - A graphical editor in which the blocks are connected together with lines of connection. - Customizable block libraries. At the level of Simulink simulation allows:
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- Simulation of continuous time systems; discrete or hybrid; - Simulation of linear systems (defined in matrix form) and non-linear V.3. Wind turbine model with Asynchronous Machine The following figure shows the three parts to simulate:
Figure (5-2): Configuration of a wind turbine [32]. V.3.1. Aerodynamics Unit (Wind) Wind is energetically primary wind turbines. The kinetic energy of the wind is transformed partly into mechanical energy by the turbine, and then into electrical energy by the generator. This is an important variable to model for the simulation accuracy and it depends on the quality of the model. One of the principles adopted is to generate a time series of wind speed from a noise input. To do this, the wind speed will be decomposed into two components: • a turbulent wind component vT(t) is a stationary random process (does not vary with the average wind speed). • a slow component vav, which is the average wind speed varies regularly over longer periods in a given site. V (t) = vo+ vT (t) (5-1) The Aero turbine filter the high frequency fluctuations. We reconstitute for this purpose a low pass filter to the component of turbulence so that it reproduces a characteristic closer to reality whose transfer function is given [32] by: !
𝐻! = !!!.! (5-‐2)
The value of the time constant depends on the diameter of the rotor and also the turbulence intensity of the wind and the average wind speed (τ = 4s) [32].
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Fig. (5-3): Wind reconstruction synoptic
V.3.2. Mechanical unit In this part, there is the wind turbine, the speed multiplier and the rotor of the generator: the wind turbine consists of three adjustable blades; multiplier adjusts the speed of the wind turbine electric generator that runs at about 1500 (rpm). V.3.2.1 Model of Turbine The mathematical equation below shows the relationship between wind speed and mechanical power extracted. ! 𝑃!"#$ = ! 𝜌. 𝜋. 𝑅! 𝑉 ! (5-‐3) Where 𝜌 = 1.25 kg/m3 density of air, under normal conditions of temperature and pressure. V is the wind speed. As the wind turbine can retrieved only a fraction of the wind power (power coef CP) aerodynamic power occurring at the turbine rotor is then written: ! 𝑃!"#$ = ! 𝐶! . 𝜌. 𝜋. 𝑅! 𝑉 ! (5-‐4) The power coefficient Cp is the aerodynamic efficiency of the wind turbine. It depends on the characteristic of the turbine. (Fig 5-4) represents the variation of the coefficient as a function of the speed ratio 𝜆 and the angle of orientation of the blade 𝛽. The gear ratio is defined as the ratio between the linear speed of the blades and the wind speed:
𝜆=
!.!!"#$%&' !
(5-‐5)
The torque exerted by the wind on the turbine (or mechanical torque to the output of the turbine) is defined by:
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𝐶!"# =
!!"#$%&' !!
in (N.m) (5-‐6)
Numerical approximations have been developed in literature to calculate the coefficient Cp and different expressions have been proposed. We present below four types already used in four scientific articles [20], [32], [33], [34], respectively: 𝜋 𝜆 + 0.1 𝐶! 𝜆, 𝛽 = 0.5 − 0.167 𝛽 − 2 sin − 0.000184 𝜆 − 3 . (𝛽 − 2) 18.5 − 0.3 𝛽 − 2 𝐶! 𝜆, 𝛽 = 𝐶! 𝐶!
!.!!"# 1 0.003 !!! ( ) !!!.!!"! . ! ! !! + 𝐶 . 𝜆 − ! − 𝑐! . 𝛽 − 𝐶! 𝑒 ! 𝜆 + 0.08𝛽 𝛽 + 1
Where: C1=0.5109 C2= 116 C3=0.4 C4=5 C5=21 C6=0.0068 3) 𝐶! = 0.22 ×
!!" !!
− 0.4𝑥𝛽 − 5 𝑒
!!"# !!
and
! !!
=
! !!!!.! !
−
!.!"# ! ! !!
4) 𝐶! 𝜆 = 7.95633 10!! 𝜆! − 17.375 10!! 𝜆! + 9.86 10!! 𝜆! − 9.4 10!! 𝜆! + 6.38 10!! + 0.001
With: 𝛽 : Pitch angle. 𝑅 : Blade’s high Ω!"#$%&' : Turbine mechanic speed in (rad/s) For our example of wind turbine power coefficient Cp is given in reference [33] by the following equation: 𝐶! = 0.22×
!!" !!
− 0.4×𝛽 − 5 𝑒
!!"# !!
and
!
!!
=
!
!!!!.! !
−
!.!"#
! ! !!
(5-‐7)
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Figure (5-4) Wind turbine model developed in Matlab / Simulink
The (Fig.5-5) illustrates the curves of Cp (λ) for several values of β (deg) obtained by the equation (5-7).
Figure (5-6): Characteristic of the power coefficient in function of the relative velocity λ. V.3.2.2 Multiplier Model The multiplier is the connection between the turbine and the generator. It is assumed rigid and modeled by a simple gain. The multiplier elasticity and friction are neglected. Energy losses in the multiplier are considered void. The mechanical torque of the wind turbine is divided by the multiplication ratio to obtain mechanical torque on the generator shaft [4]:
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!
𝐶!"# = ! 𝐶!"# Where: K = Multiplication ratio Cmec = Mechanical torque adjusting speed of the turbine to that of the generator as well Ω!"# = 𝐾. Ω! (5-‐9) Where: Ω!"# : Generator speed (rad/s mechanic). V.3.2.3 Shaft model The differential equation that characterizes the mechanical behavior of the turbine and generator is given by: 𝑑Ω!"# 𝑗 = 𝐶! − 𝑓. Ω!"# 𝑑𝑡 Where: J = total inertia of the rotating parts (turbine + generator) (kg.m2). f = coefficient of viscous friction. CT = (Cem + CMEC) = total turbine torque (Nm). Cem = electromagnetic torque of the generator (Nm). In generator mode the Cem torque has a negative sign. The block diagram below shows the shaft model associated to the wind turbine model:
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Figure (5-7): The mechanical model developed in Matlab / Simulink.
V.3.3 Electric part The model of the asynchronous generator is derived from the machine biphasic [1] assuming that the variables are expressed in a rotating frame to the synchronous speed, the equations of the induction machine can be written as follows: 𝐿!
𝑑𝐼!" 𝑑𝐼!" + 𝐿! = −𝑅! 𝐼!" − 𝑉!" 𝑑𝑡 𝑑𝑡
𝐿! 𝐿! 𝐶 𝐶
𝑑𝐼!" 𝑑𝐼!" + 𝐿! = −𝜔𝐿! 𝐼!" + 𝑅𝐼!" − 𝜔𝐿! 𝐼!" 𝑑𝑡 𝑑𝑡 𝑑𝐼!" 𝑑𝐼!" + 𝐿! = −𝜔𝐿! 𝐼!" + 𝜔𝐿! 𝐼!" − 𝑅! 𝐼!" 𝑑𝑡 𝑑𝑡
𝑑𝑣!" = 𝑖!" 𝑑𝑡 𝑑𝑣!" = 𝑖!" 𝑑𝑡
This system can be represented as follows: 𝐿! × 𝐿1 . 𝑋 + 𝐿2 . 𝑋 = 𝐴1 . 𝑋 + 𝜔× 𝐴2 . 𝑋
+ 𝜔×𝐿! ×( 𝐴3 . 𝑋 ) 80
Where:
1 0 1 𝐿1 = 0 0 0
0 1 0 1 0 0
−𝑅𝑠 0 1 𝐴1 = 0 0 0
1 0 1 0 0 0
0 1 0 1 0 0
0 −𝑅𝑠 0 1 0 0
0 0 0 0 0 0 1 0 −𝑅𝑟 0 0 0
0 𝑙 0 0 0 0 𝑙 0 0 1 0 𝑙 𝐿2 = 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 −𝑅𝑟 0 0
0 0 0 0 0 0
0 0 0 𝑙 0 0
0 0 0 0 1 0
0 0 0 0 0 1
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 −1 0 0 𝐴2 = 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
𝑖!" 0 0 1 0 0 0 0.001 𝑖!" 0 0 0 1 0 0 0.001 𝑖 0 −1 0 −1 0 0 0.01 𝐴3 = 𝑋 = !" 𝑋! = 𝑖!" 1 0 1 1 0 0 0.01 𝑣!" 0 0 0 0 0 0 0 𝑣!" 0 0 0 0 0 0 0 Several types of equations can express the electromagnetic torque of the asynchronous machine including this one: 𝐶𝑒𝑚 = 𝑃𝐿! (𝑖!"! + 𝑖!"! )𝑖!" − (𝑖!"! + 𝑖!"! )𝑖!" The block diagram of the self-excited asynchronous generator, which is the image of the equations given above, is shown (Fig. 5-8): - The inputs are the stator and rotor currents (at t = 0), the stator tensions (at t = 0) representing the remanent field and the mechanical speed. - The outputs are the stator currents and rotor, the stator voltages and electromagnetic torque.
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Figure (5-8): Generator model developed in Matlab / Simulink.
Figure (5-9): Diagram derived from the equations of state.
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Figure (5-10): Diagram of the Park transformation.
The model of the entire system consisting of the asynchronous generator, the turbine and the wind speed multiplier, as developed in Matlab-Simulink, is as follows (Fig.5-9)
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Figure (5-11): Simulation scheme developed in Matlab-Simulink of the wind system consists of the asynchronous machine and wind turbine.
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The parameters of the whole system are collated in Tables 5-1.
Air Turbine Data Rotor Diameter Number of blades Air density The wind average speed Pitch angle Time constant value
23.2 m 3 1.23 Kg/m3 9 m/s 2° 4s
Gear Box Data Speed ration Moment of inertia Viscous friction coefficient
23.75 102.8 Kg.m2 0.0024
Asynchronous Generator Data Number of pole pair Moment of inertia Stator Resistor Rotor Resistor Leakage inductance (stator-‐ rotor) Magnetizing inductance Lm= 0.011 H
2 0.038 Kg.m2 Rs=1.9 Rr= 2.1 Ls=0.0132
V.4.
Tab 5-1: The parameters of the wind turbine system [33].
Simulation Results
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V.5. Conclusion This chapter has allowed us to describe the steps of modeling a wind turbine. As a first step, we established a model to reproduce variations of wind speed based on a sampling of the power spectral density of measured speeds at a site. These variations of wind are then applied to a model turbine using the basic equations giving the torque wind depending on the density of the air, the power coefficient of the wind turbine of the wind velocity and the length of a blade. The rotational speed of the turbine, calculated based on the inertia and viscous friction coefficient is then imposed as a reference. The results showed a good correlation between Matlab and Sumulink. We denote higher amplitudes in Sumilink regarding current peaks relating the winds.
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General conclusion To position our theme we discussed the first chapter with a brief introduction of renewable energy focusing primarily on wind energy and electrical conversion chains associated. Then different combinations of generators, power converter were discussed in the second chapter. In the third chapter, we have developed a unified model of the generator induction generator squirrel cage (SEIG: Self Excited Induction Generator) , it has focused on the modeling and analysis of a double star asynchronous generator DASG: the results of different simulations in Matlab revealed that the performance of the DSAG are strongly influenced by capacity value excitement, the drive speed and the type of load. We were able to improve performance by inserting compensation capacitors in series or in parallel (solving the problem of demagnetization of the machine). steady vacuum and charge. In particular, we showed that the stator variables were directly influenced by the variation of the rotor speed of the wind, the capacity of excitement and initial magnetization state and the type of load connected.
The fourth chapter in the latter, we performed an original model of the double star synchronous generato which was used to simulate the behavior and diet saturated, the results were validated experimentally. After we have developed an analytical study of special IPM synchronous generator, we have showed the decoupled park transformation and explained the method. In the end, the fifth and final chapter, we completed the modeling of the entire wind turbine using a self-excited generator for supplying a consumer alone. This simulation model was developed under environmental SUMULINK from bibliographic data [33]. The simulation results obtained using the two software (Matlab / Simulink) we have, in addition to the validation of the two models in generator mode, highlight the vibratory phenomenon of wind system, we have also taken into account in analyzing the behavior of the wind turbine of the continuously variable and random wind. Following these observations and results, some interesting perspectives can contribute to improve the operation of the wind turbine are possible: - The first point we look attractive for the realization of an experimental platform for testing real-time behavior of a variable speed wind generator delivering on different types of loads and validate the simulation results presented in this thesis. - It would also be interesting to develop a control system that adjusts the turbine changes the angle of attack of the blade (pitch control) changes in wind power to control the power generated.
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