Institute of Energy Technology, 9 th Semester Report. Control of a variable speed variable pitch wind turbine with full scale power converter

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1 Institute of Energy Technology, 9 th Semester Report Control of a variable speed variable pitch wind turbine with full scale power converter Conducted by group 95 PED9, Autumn 2007

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3 Synopsis: Institute of Energy Technology Pontoppidanstræde 0 Telephone Fax Title: Control of a variable speed variable pitch wind turbine with full power converter Theme of PED9: Design-oriented Analysis of Electric Machines and Power Electronic Systems Project period: 7. September - 7. December 2007 Project group number: 95 Participants: Massimo Valentini Thordur Ofeigsson Alin Raducu Supervisor: Florin Iov Number of copies: 5 Number of pages: 93 Finished: 7. December 2007 This project deals with the control of a small variable speed variable pitch wind turbine with full scale power converter. The chosen wind turbine (WT) concept is, at the moment, the second most common topology in the wind power industry. However it has the chance in the next future to become the best solution as the higher cost is balanced by the power quality, harmonic compensation and full grid support. In order to optimize the energy capture, a speed control system is required to control the induction generator (IG) rotor speed. The reference speed is obtained by implementing a Maximum Power Point Tracker (MPPT) algorithm; the Perturb and Observe method is selected and designed. The speed control of the electric generator is achieved by controlling the generator side converter using the Direct Field Oriented Control (DFOC) which is designed using a step-by-step procedure. When the available wind power exceeds the generator rated power, the wind turbine is operated in power limitation mode with variable pitch angle; the pitch control with proportional controller is designed and simulated. Moreover the switch control between the variable-speed operation and the power limitation mode is designed. The entire system is simulated using Matlab/Simulink, implemented in a dspace platform and tested with an experimental test setup. A Graphical User Interface (GUI) is built for the real-time evaluation of the control performance. Experimental results succesfully validate the control system design.

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5 Preface The present project report entitled Control of a variable speed variable pitch wind turbine with full scale power converter is documented by group PED9-95 in 9 th semester at Institute of Energy Technology, Aalborg University. The project period is from 7 th September to 7 th December Literature references are mentioned in square brackets by numbers. Detailed information about literature is presented in Bibliography. Appendices are assigned with letters and are arranged in alphabetical order. Equations are numbered in format (X.Y) and figures are numbered in format Fig.X.Y, where X is the chapter number and Y is the number of the item. The enclosed CD-ROM contains the project report in Latex and Adobe PDF formats, documentations used throughout the report and Simulink Models. Authors would like to thank the supervisor Florin Iov for the support and ideas provided throughout the project period. The report is conducted by: Massimo Valentini Thordur Ofeigsson Alin Raducu

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7 CONTENTS Contents Part I: Project Defintion Introduction 2. Background to Wind Energy Technology Speed control capability Power control capability Control Objectives Energy capture Mechanical loads Grid connection requirements Project description Project goals Part II: Modeling 9 2 Modeling 0 2. Wind model Wind turbine model Drive train model Induction machine model Back-to-back converter Modulation Part III: Control System Design 23 3 Maximum power point tracking Output filter design Selecting step size Control of the generator in variable speed operation 3 4. Introduction Rotor flux vector estimation Current model Voltage model Field Oriented Control Electromagnetic torque in the dq reference frame Control system design i

8 CONTENTS 4.4. Q-axis control loop design D-axis control loop design Simulation on the generator control in variable speed operation Case : variable wind speed and constant reference rotor speed Case 2: variable wind speed and variable reference rotor speed (with MPPT) Case 3: variable rotor reference speed and constant mean wind speed Case 4: variable reference rotor speed and variable mean wind speed Power limitation mode Pitch control Assessment of pitch controller model Transition between variable speed operation and power limitation mode Simulation in variable pitch operation Case : variable wind in power limitation mode Case 2: reference power profile in power limitation mode Case 3: transition between variable speed operation and power limitation mode 70 Part IV: Implementation and Experimental Evaluation 73 6 Experimental tests and results Experimental setup Digital implementation Limitations Experimental results Speed control of the SCIG over a short time frame Variable reference rotor speed and constant wind speed Variable wind speed and variable reference speed (with MPPT) Conclusion 86 Future Work 89 Bibliography 90 Acronyms 93 Nomenclature 94 Base Values 99 Part V: Appendix 0 A Squirrel Cage Induction Generator Parameters 02 B Simulation and implementation models 03 C Reference Frame Theory 06 ii

9 Part I: Project Defintion Part I: Project Defintion Introduction 2. Background to Wind Energy Technology Speed control capability Power control capability Control Objectives Energy capture Mechanical loads Grid connection requirements Project description Project goals

10 Chapter Introduction. Background to Wind Energy Technology The global energy consumption is rising and an increasing attention is being paid to alternative methods of electricity generation. The very low environmental impact of the renewable energies make them a very attractive solution for a growing demand. In this trend towards the diversification of the energy market, wind power is probably the most promising sustainable energy source. The progress of wind power in recent years has exceeded all expectations, with Europe leading the global market []. Recent progress in wind technology has led to cost reduction to levels comparable, in many cases, with conventional methods of electricity generation. Power electronics are nowadays used to efficiently interface renewable energy systems to the grid [2]. They are playing a very important role in modern wind energy conversion system (WECS) especially for MW-size wind turbines (WT) concentrated in large wind farms. Control of WECSs, performed by means of power electronics, allow the fulfilment of grid requirements, a better use of the turbine capacity and the allevation of aerodynamic and mechanical loads that reduce the lifetime of installation []. Furthermore, with WECSs approaching the output rating of conventional power plants, control of the power quality is required to reduce the adverse effects of their integration into the grid. Even though active control has an immediate impact on the cost of wind energy, it leads to high performance that is essential to enhance the competitiveness of wind technology... Speed control capability WECSs have to cope with the intermittent and seasonal variability of the wind. By this reason they begin to work when the wind speed is above the cut-in speed so that power is injected into the utlity grid; moreover they include some mechanisms to limit the captured power at high wind speeds to prevent overloading. Three control strategies can be used for captured power control [2] []: stall control; pitch control; active stall control. The stall control is based on a specific design of the blades so that stall occurs when the wind speed exceeds a certain level; it means that the captured power is automatically limited in the rated power range. This method is simple, robust and cheap but it has low efficiency at low wind speed. 2

11 CHAPTER. INTRODUCTION In case of pitch control, blades can be tuned away from or into the wind as the captured power becomes too high or too low; this is performed by rotating the blades, or part of them, with respect to their longitudinal axes. Below rated wind speed, blades are pitched for optimum power extraction whereas above the rated wind speed blades are pitched to small angle of attack for limiting the power. Advantages of this type of control are good power control performance, assisted start-up and emergency power reduction; the biggest disadvantage is the extra complexity due to the pitch mechanism. In case of active stall control, the stall is actively controlled by pitching blades to larger angle of attack with wind speed above the rated value...2 Power control capability Beyond the captured power controllability, another important feature is the speed controllability. Based on this, WTs are classified into two main categories [2][3]: Fixed speed WTs; Variable speed WTs. Fixed speed WTs are equipped with induction generator (squirrel cage induction generator SCIG or wound rotor induction generator WRIG) directly connected to the grid and a capacitor bank for reactive power compensation. This is a very reliable configuration because of the robust construction of the standard IG. The IG synchronous speed ω s is fixed and determined by the grid frequency regardless of the wind speed; this implies that such WTs can obtain maximum efficiency at one wind speed. As power electronics is not involved in this cofiguration, it is not possible to control neither reactive power consumption nor power quality; in fact due to its fixed speed, wind fluctuations are converted into torque fluctuations, slightly reduced by small changes in the generator slip, and transmitted as power fluctuations into the utility grid yielding voltage variations especially in weak grids. Variable speed WTs are equipped with an induction or synchronous generator connected to the grid through a power converter. The variable speed operation, made possible by means of power electronics, allows such WTs to work at the maximum conversion efficiency over a wide range of wind speeds. The most commonly used WT designs can be categorized into four categories [2][3][][4]: fixed speed WTs (FSWT); partial variable speed WTs with variable rotor resistance (PVSWT); variable speed WTs with partial-scale frequency converter, known as doubly-fed induction generator-based concept (DFIGWT); variable speed WTs with full-scale power converter (FSPCWT). Fig.. shows the structure of the above concepts. They differ in the generating system (electrical generator) and the way used to limit the captured aerodynamic power above the rated value. Fixed speed WTs are characterized by a squirrel cage induction generator (SCIG) directly connected to the grid by means of a transformer [2]. The rotor speed ω mech can be considered locked to the line frequency f s as very low slip is encountered in normal operation (typically around 2%). The reactive power absorbed by the generator is locally compensated by means of a capacitor bank following the production variation (5-25 steps)[2]. A soft-starter can be used to provide a smooth 3

12 .2. CONTROL OBJECTIVES wind Gear box SCIG G Capacitor Bank By-pass AC AC Soft-starter FSWT wind Gear box WRIG G Variable Resistance AC By-pass AC Soft-starter Capacitor Bank PVSWT DFIG SCIG WRSG / PMSG wind Gear Box G AC AC wind GearBox/ Gearless G AC AC Full Scale Power Converter Power Converter DFIGWT FSPCWT Figure.: Wind turbine concepts. grid connection. This configuration is very reliable because the robust construction of the standard SCIG and the simplicity of the power electronics [2][]. Partial variable speed WTs with variable rotor resistance use a WRIG connected to the grid by means of a transformer [2][][5]. The rotor winding of the generator is connected in series with a controlled resistance; it is used to change the torque characteristic and the operating speed in a narrow range (typically 0 0% above the synchronous speed)[2]. A capacitor bank performs the reactive power compenastion and smooth grid connection occurs by means of a soft-starter. For a DFIGWT, the stator is directly coupled to the grid while a partial scale power converter controls the rotor frequency and, thus, the rotor speed [2][][5][6]. The partial scale power converter is rated at 20% 30% of the WRIG rating so that the speed can be varied within ± 30% of the synchronous speed. The partial scale frequency converter makes such WTs attractive from the economical point of view. However, slip rings reduce the reliability and increase the maintenance. Variable speed FSPCWTs are characterized by the generator connected to the grid by means of the full-scale frequency converter [2][][5]; the converter performs the reactive power compensation and a smooth grid connection [7][8]. Synchronous generators have so far dominated the market for variable speed wind turbines; now induction generators are becoming more popular in WECS industry and also for variable speed applications [7][]..2 Control Objectives WECSs connected to the grid must be designed to minimize the cost of supplied energy ensuring safe operation, acoustic emission and grid connection requirements. Control objectives involved in WECSs are []: energy capture; mechanical load; grid connection requirements..2. Energy capture Variable-speed variable-pitch WTs are usually controlled according to the curve in Fig..2; it represents the energy capture capability of a WT in the generated power-wind speed plane. 4

13 CHAPTER. INTRODUCTION As it is shown in Fig..2, the range of operational wind speed is delimited by the cut-in V min and Power [W] fixed speed variable pitch operation 4 variable speed fixed pitch operation cut in speed (3.5m/s) rated wind speed (8m/s) cut out speed (25m/s) Wind speed [m/s] Figure.2: Ideal power regulation for a WT. cut-out V max wind speeds. The WT remains stopped beyond these limits. Below V min the available energy is too low to compensate the operational cost whereas above V max speed the WT is shut down to prevent mechanical overload. The selection of the V max is a trade-off between the following items []: constructing the WT robust enough to support high mechanical stress would be economically unconvenient; even though strong winds have large energy content, they occur seldomly so their contribution to the annual production is negligible. A good compromise is often V max = 25 m/s. The rated mean wind speed V n is the speed at which the electrical generator works at its rated power. Within the interval [V min ; V n ], the available power is lower than the rated value and so the WT is controlled to maximize the captured energy; in this case the WT will typicaly vary the speed proportionally to the wind speed and keep the pitch angle θ fixed (variable-speed fixed-pitch operation). In this operational region, the captured power is proportional to V 3, where V is the mean wind speed. In countries where the wind energy is dispatched as traditional energy, the captured power has to react based on the set-point given by the dispatched center; it follows that the captured power could be controlled to be less than the available one [2]. Above V n, the generator is controlled such that the captured power is limited to the rated value to prevent mechanical overload (fixed-speed variable-pitch operation). In this region the available power in the wind exceeds the rated power, therefore the WT must be operated with aerodynamic efficiency lower than in the previous region..2.2 Mechanical loads Mechanical loads can cause fatigue damage and thereby reduced lifetime of the WT. Since the overall cost is spread over a shorter period of time, the cost of energy will rise. Mechanical loads can be divided into static loads, which result from the interaction of the WT with the mean wind speed, and dynamic loads, which comprise variation of the aerodynamic torque that propagates down the drive-train and the mechanical structure. The control system of a WT has a very strong impact especially on the dynamic mechanical loads. The control of the electric generator affects the propagation of drive-train loads whereas the pitch control affects the structural loads []. 5

14 .3. PROJECT DESCRIPTION.2.3 Grid connection requirements The injection of large amount of wind power into a network might affect the steady state voltage especially in presence of weak grid [9]. To ensure electrical system stability, system operators in many European countries are setting grid connection requirements for wind generators also known as grid codes (GCs). For MW-size WECSs, very high technical demands are required, such as [2][0][7]: regulation of active and reactive power; frequency and voltage control; fast responses under dynamic situation; power quality; low voltage ride-through capability. WECSs must provide the power quality required to ensure the stability and reliability of the power system they are connected to and to satisfy the customers connected at the same grid. Voltage and frequency at the point of common coupling (PCC) must be kept as stable as possible []. In general, frequency is a quite stable variable. Frequency variations are always due to power unbalance between generation and consumption (e.g. generators accelerate when the supplied power exceeds the consumption, hence increasing the frequency; analogously they slow down when they can not cover the power demands, thereby frequecy decreases). However this is not the case when the WT is connected to an isolated power system or when multi-mw wind farms are connected to the power system []. Voltage variations take place as a consequence of variation of the mean wind speed; the amplitude of these variations depend on the impedance of the grid connected at the PCC, on active and reactive power flows. A way of attenuating voltage variations, without affecting power extraction, is to control the reactive power flow. In the past, when fixed speed wind turbine were the State-of-the-Art, the reactive power compensation was performed by means of capacitor bank following the production variation (5-25 steps). Nowadays the most effective way of reactive power control is based on power electronics. In the next years, the major research challange is directed towards the grid integration of large wind farms to the electrical power grid. It implies that the survival of different WT concepts is strongly connected by their ability to support the grid, to handle faults on the grid and to comply to grid requirements of the utility companies..3 Project description This project deals with the control of a variable-speed variable-pitch FSPCWT. According to [2], it is the second most common WT concept in the MW range on the market while the most common is the concept based on the DFIGWT. However, the concept FSPCWT has the chance in the next future to become the best solution as the higher cost is balanced by the power quality, harmonic compensation and full grid support by 00% reactive current injection during grid events [2][7]. The real system is represented in Fig..3 T shaft and ω gen are respectively the torque and the rotational speed at the generator shaft (high speed shaft). The SCIG is connected to the ac grid through a frequency converter, the so called back-to-back PWM-VSI; it is a bi-directional power converter consisting of two conventional PWM-VSCs (generator and grid side converters). The pitched-controlled WT and the gearbox are not available; therefore they are implemented by means 6

15 wind T, ω shaft GearBox gen SCIG Generator side converter AC DC DC link Grid side converter DC AC Transformer grid K gear Pitch contol Generator side converter contol Grid side converter contol Figure.3: Layout of the real system. of a torque-controlled permanent magnet synchronous motor (PMSM). The grid-side converter is not used as it would require its own control system; since its control is not included in this project, the grid side converter is substituted by a dc power supply directly connected at the dc link. The power produced by the WT and flowing through the generator side converter, is dissipated by a braking resistor whose current is controlled by the regenerative braking function provided by the converter. According to the above considerations, the layout of the system is modified as presented in Fig..4. The reference torque T ref is produced according to the models of the WT and the wind. T ref WT + gear box AC AC Frequency Converter AC grid PMSM T shaft, ω gen SCIG Generator side converter AC DC Generator side converter contol Braking Resistor dc power supply Figure.4: Modified layout of the system..4 Project goals In this project the control of a variable-speed variable-pitch WT is designed, simulated and implemented. Project goals are summarized below: overview of wind turbine technology; control of the WT in variable speed operation; control of the WT in power limitation mode; implementation of the overall control system in a dspace platform; experimental evaluation and validation. The control of the WT in variable speed operation is performed using the Direct Field Oriented Control (DFOC) [2][3][4]. The control system has been designed and simulated using Matlab/Simulink. The variable speed operation requires a maximum power point tracker (MPPT) which

16 provides the reference speed to the generator control such that the maximum power is captured by the WT. The perturb and observe algorithm has been used for the tracking; the maximum power point (MPP) tracker system has been designed and simulated. The control in power limitation mode is performed when the mean wind speed is above the rated value to avoid mechanical stress on the WT structure [2]. It is based on the control of the pitch angle of blades. The control system has been designed and simulated. The entire control system is finally implemented in a dspace system and validated by measurements on the experimental test setup.

17 Part II: Modeling Part II: Modeling 9 2 Modeling 0 2. Wind model Wind turbine model Drive train model Induction machine model Back-to-back converter Modulation

18 Chapter 2 Modeling This project is focused on the control of small WT. However such a wind turbine is not a part of the experimental setup and so it must be modelled. The power and torque production of the simulated WT depend on the mean wind speed; however the wind turbulence affects the control of the generator. In order to evaluate the power production and the effect of wind variations on the generator control, a model of the wind must be used. WTs are normally connected to the electric generator by means of a gearbox (optional) and a drive train [2]. They are not a part of the experimental setup and so they must be modelled. The drive train model must take into account the stiffness and damping of the shaft since they will affect the speed at the high speed shaft (generator side). The control of the SCIG in variable speed mode and in power limitation mode has been designed and simulated in the follwing chapters. Simulation models require a model of the full scale power converter which is a back-to-back frequency converter and a model of modulation method. The models are presented in this chapter. In variable speed operation, such as at mean wind speeds below the rated value, the WT is operated in order to maximize the enegy capture. This requires a control system that provides the generator reference speed ω r to the generator control system. This control system is called Maximum Power Point Tracker and it is presented in this chapter. 2. Wind model Reliability, performance and cost evaluation of WECSs requires simulation of long-term wind speed data. Winds are movements of air masses in the atmosphere mainly originated by temperature differences. Wind is characterized by its speed and direction, which are affected by several factors. In the lower layer of the atmosphere, up to 00m, winds are delayed by frictional forces and obstacles altering not only their speed but also their direction; this is the origin of turbulence flow, which causes wind speed variations over a wide range of amplitudes and frequencies [5]. An interesting characterization of winds in the lower layer is the kinetic energy distribution in the frequency domain, which is known as Van der Hoven spectrum (see Fig.2.) []. Although there are some differences, the kinetic energy distribution in the frequency domain in different sites follow the same pattern. It exhibits two peaks approximately at 4 days cycles and min. cycles which are separeted by an energy gap. The concentration of kinetic energy around two clearly separeted frequencies allows splitting the wind speed v into two components, the mean wind speed V and the turbulence v T [] v = V + v T (2.) 0

19 CHAPTER 2. MODELING Figure 2.: Van der Hoven spectrum Usually, the averaging period is chosen to lie within the energy gap, typically 0 min. to 20 min. minutes V = t p to+ tp 2 t o tp 2 v(t)dt (2.2) The knowledge of the mean wind speed expected at a specific site is crucial to determine the economical feasibility of a wind energy project. Its value can be determined from measurements collected during several years. The term v T denotes the atmospheric turbulence which includes all wind speed fluctuations with frequencies above the spectral gap; therfore it contains all components in the range from seconds to minutes. Turbulence has a minor impact on the annual energy capture, which is mainly determined by the mean wind speed. However it has a major impact on the aerodynamic loads and power quality []. In the wind model, the wind turbulence at a given point in space is stochastically described by means of its power spectrum based on the Kaimal model [][5]: where Φ(ω) = K V ( + ωt V ) 5 3 (2.3) K V = 9.36 σ 2 v L v V T V = L v V The Kaimal model is characterized by the longitudinal lenght scale L v and the turbulence intensity σ v, which is also the wind speed standard deviation; both L v and σ v are specific to the terrain and are experimentally obtained from wind speed measurements. The lenght scale takes values ranging from 00m to 330m whereas the turbulence intensity takes vales between 0. and 0.2 []. In order to fit results obtained by means of the Kaimal model with experimenal results, shaping filters are used. Real wind affects wind turbines in ways that the spectral method does not take into account. Three major effects should be consided when modeling wind turbines [6][]: rotational sampling, which is the fluctuation of the wind experienced by a rotating point; (2.4) (2.5)

20 2.2. WIND TURBINE MODEL wind shear, which is the delay of the wind in the lower layer of the atmosphere due to friction forces produced by the ground even in absence of obstacles; tower shadow, which is the effect on the airflow produced by the tower (3P effect). Those effects contribute to the turbulence in a deterministic way. The wind model takes into account tower shadow and rotational sampling. Required parameters for the wind model are: rotor diameter D; average wind speed V ; length scale L v ; turbulence intensity σ v ; sample time T s. The wind acting on the considered wind turbine (blade radius R = m) has been simulated using the following parameters: V = 8 m/s; σ v = 2%; L v = 200 m; T s = 0.05 s. Figure 2.2: Wind time series. 2.2 Wind turbine model The WT converts the wind energy to mechnical energy by means of a torque applied to a drive train. A model of the WT is necessary to evaluate the torque and power production for a given wind speed and the effect of wind speed variations on the produced torque. The torque T W T and power P W T produced by the WT within the interval [V min, V max ] are proportional to the WTs blade radius R, air pressure ρ, wind speed v and a coefficients C Q and C P [] [6]. T W T = 2 ρπr3 C Q (λ, θ)v 2 (2.6) P W T = C P (λ, θ)p V = 2 ρr2 C P (λ, θ)v 3 (2.7) 2

21 CHAPTER 2. MODELING C P is known as the power coefficient and characterizes the ability of the WT to extract energy from the wind. C Q is the torque coefficient and is related to C P according to: Here, λ is the tip-speed-ratio, C Q = C P λ (2.8) λ = ω W T R/v (2.9) where ω W T is the WT rotor speed. As seen from (2.6), (2.7) and (2.8) the T W T and P W T depend both on the coefficient C P ; which is normally provided by the manufacturer in the form of a lookup table. However, since there is no data available for a 2.2 kw WT an equation describing C P is required to calculate T W T and P W T. An alternative way to calculate C P is based on an approximation from [6] shown in (2.0). C P (λ, θ) = 0.22 ( 6 λ i 0.4θ 5 where θ is the pitch angle and λ i is described by the equation: λ i = λ θ θ 3 + ) e 2.5 λ i (2.0) (2.) As seen from (2.0), C P varies with the tip-speed ratio λ which is dependent on R. In order to create a the C P curve R has to be defined. Since there is no physical WT in the project, R can be selected. It is convenient that the generator produces the rated power for the most probable wind speed of the location; it is assumed to be V n = 8m/s. This gives a requirement for the size of the WT blades which is consequently calculated to be R = 2.235m; using this value, the generator should produce the rated power of 2.2kW at V n. Graphs for the WT power and torque are created using the approximated C P from (2.0). Fig.2.3 shows how P W T varies with rotor speed for different wind speeds. The optimum tip speed ratio curve gives the highest efficiency points for P W T. As seen from the figure; the maximum power is 2.2kW at V n. Fig.2.4 shows how P W T varies with ω W T for different θ at the rated mean wind speed V n. Maximum P W T is reached for θ = 0 but as θ is increased, P W T decreases. This is useful to prevent mechanical overloading of the WT when wind speed exceeds V n V=8m/s Optimum tip speed ratio Power [W] m/s 6m/s Power [W] m/s 500 4m/s 3m/s Wind turbine rotor speed [rpm] Wind turbine rotor speed [rpm] Figure 2.3: Power as a function of rotor speed for different wind speeds. Figure 2.4: Power as a function of rotor speed for different pitch angles at V n. 3

22 2.3. DRIVE TRAIN MODEL Fig.s 2.5 and 2.6 show similar curves as the above mentioned figures but the WT torque T W T is examined. As for P W T, T W T varies similarly with ω W T and θ V=8m/s Optimum tip speed ratio Torque [Nm] m/s 7m/s Torque [Nm] m/s 20 4m/s 3m/s Wind turbine rotor speed [rpm] Wind turbine rotor speed [rpm] Figure 2.5: Torque as a function of rotor speed. Figure 2.6: Torque as a function of rotor speed for different pitch angles at V n. 2 ω WT ω WT R v v λ λ θ θ 3 + λ i θ 5 e λ i 2.5 λi C P CP λ CQ v 3 ρπr C Q 2 T WT, a TWT AVG 5 sec θ If v = Else 0 [ V V ] min, max ; Figure 2.7: Block diagram of WT model. The block diagram of the WT model for the WT is shown in Fig.2.7. The model has the following inputs: WT speed ω W T, obtained from a speed meter; wind speed v, obtained from the wind model; pitch angle θ, obtained from the pitch controller. As seen from the block diagram the WT model takes the operational wind speed range of the WT into account; if v, averaged over 5s, hits outside [V min ; V max ], the available torque T W T,a is forced to be zero. The resulting torque T W T is the torque produce by the WT. 2.3 Drive train model A model of the drive train is required as it has influence on grid interconnectionon by producing power fluctuations. Other mechanical dynamics, such as tower and flap bending modes, are negligible from this point of view [7][8]. A two mass model on the generator side has been used; it is 4

23 CHAPTER 2. MODELING represented in Fig.2.8 where J W T and J gen are respectively the moment of inertia of the wind tur- ' T WT ' D e T shaft ' ω WT ' J WT ' K e ω g J gen Figure 2.8: Equivalent two-mass model of the wind turbine frive train on the generator side bine, referred to the generator side, and of the generator. The moment of inertia for the low speed shaft, high speed shaft and the gear box wheels can be neglected because they are small compared with J W T and J gen. Therefore the resultant model is essentially a two-mass model connected by a flexible shaft characterized by the equivalent torsional stiffness K e and the damping factor D e. The drive train converts the aerodynamic torque produced by the WT, T W T, into a torque at the high speed shaft T shaft. This conversion is mathematically described by the following differential equations [8][7]: ω k = ω g ω W T K gear (2.2) θ k = ω k (2.3) ω W T = T W T T shaft J W T (2.4) T shaft = D e (ω g ω W T K gear ) + K eθ k (2.5) where T W T is the WT torque referred at the high speed shaft, ω W T is the WT rotor speed, T shaft is the torque applied at the rotor of the generator and ω g is the generator mechanical speed. Parameters used for modeling the drive train are presented in Tab.2.. The drive train model, J W T 0.5 k g m 2 K e 30 Nm/rad D e Nms/rad K gear 7.4 ω g (0) rad/s ω W T (0) 78.8/7.4 rad/s Table 2.: Parameters of the drive train. whose parameters are listed in Tab.2., has been simulated with: constant generator speed ω gen = ω gen,n ; step variation of the WT torque from T W T = T W T,n /2 to T W T = T W T,n at t = 2 s. Simulation results are shown in Fig.s 2.9 and

24 2.4. INDUCTION MACHINE MODEL w g /K gear w WT Speed [p.u.] Figure 2.9: Speed response of the drive train [Nm] 0 T shaft T WT /K gear Figure 2.0: Torque response of the drive train. Fig.s 2.9 and 2.0 show that torque and speed oscillations are introduced by the drive train. If it was infinitely stiff, then it would be ω W T = ω g and T shaft = T W T. This makes the control of the generator more difficult as T shaft is a disturbance. 2.4 Induction machine model In this section the model of the induction machine in the rotating dq reference frame is derived. First, equations in the αβ stationary reference frame are obtained. The α-axis is aligned with the stator a-axis, as shown in Fig.2.. In such reference frame the induction machine can be represented γ axis q axis i sγ β axis i sq i sβ ω r δ axis rotora axis i sδ ϑ r ϑ r0 ϑ dq ω r i sd i sα ω dq d axis statora axis α axis Figure 2.: Stator αβ and dq equivalent windings. 6

25 CHAPTER 2. MODELING by means of space vectors as follows [9][20][2][3]: v sαβ = R s ī sαβ + d λ sαβ dt (2.6) The current ī sαβ, voltage v sαβ and stator flux linkage λ sαβ space vectors with respect to the α-axis are represented in the rotating dq reference frame as follows (see Fig.2.): v sαβ = v sdq e jθ dq (2.7) ī sαβ = ī sdq e jθ dq (2.8) λ sαβ = λ sdq e jθ dq (2.9) where θ dq is he angle between the stator α-axis and the d-axis. Substituting (2.7), (2.8) and (2.9) into (2.6) Hence v sdq e jθ dq = R s ī sdq e jθ dq + d dt λ sdq e jθ dq (2.20) v sdq = R s ī sdq + d λ sdq + jω dq λsdq (2.2) dt Using a similar approach, the rotor voltage equations in the δγ reference frame, rotating at ω r, can be obtained [3]. v rδγ = 0 = R s ī rδγ + d λ rδγ (2.22) dt Since the rotor is short circuited, v rδγ = 0. In order to obtain a model of the induction machine, both stator and rotor variables must be represented in the same reference frame. Being θ r the angle between the rotor δ-axis and the stator α-axis, it yields λ rδγ = λ sαβ e jθr (2.23) ī rδγ = ī sαβ e jθr (2.24) Substituting (2.23) and (2.24) in (2.22) and multiplying by e jθr the rotor voltage equation in the αβ reference frame is obtained v rαβ = 0 = R r ī rαβ + d λ rαβ dt jω r λrαβ (2.25) The current, voltage and flux linkage rotor space vectors with respect to the α-axis are represented in represented in the rotating dq reference frame as follows v rαβ = v rdq e jθ dq (2.26) ī rαβ = ī rdq e jθ dq (2.27) λ rαβ = λ rdq e jθ dq (2.28) where θ dq is he angle between the stator α-axis and the d-axis. Substituting (2.26), (2.27) and (2.28) into (2.25) v rdq e jθ dq = R r ī rdq e jθ dq + d dt λ rdq e jθ dq jω r λrdq e jθ dq (2.29) Hence v rdq = 0 = R r ī rdq + d dt λ rdq j(ω r ω dq ) λ rdq (2.30) 7

26 2.5. BACK-TO-BACK CONVERTER (2.2) and (2.30) can be written as function of the stator current space vector ī sdq and the rotor linkage flux space vector λ rdq. After mathematical manipulation [3] v sdq = R s ī sdq + σl s dī sdq dt + jω dq σl s ī sdq + L M L r d dt λ L M rdq + jω dq λ L rdq (2.3) r where 0 = σ r L M ī sdq + σ r λ rdq + d dt λ rdq + j(ω dq ω r ) λ rdq (2.32) λ rdq = L rī rdq + L M ī sdq (2.33) is the rotor flux linkage referred to the stator side is the dispersion factor and is the inverse of the rotor time constant T R. σ = L2 M L rl s (2.34) σ r = R r L r = T R (2.35) 2.5 Back-to-back converter A back-to-back converter consists of two voltage source converters (VSC) and a capacitor as shown in Fig.2.2. When operating in generator mode, the generator side converter operates as a rectifier and the grid side converter as an inverter. But as both converters are identical, power flow can be bi-directional [7][22]. DC Figure 2.2: Back-to-back converter. Model of the back-to-back converter is necessary in simulation to feed the generator model. But as the generator side is only considered in simulations, the model of the whole back-to-back converter is not needed. Consequently, the model of the generator side VSC is sufficient to carry out the simulations and is the only part considered in this section. The model of the VSC is an average model as the system includes a mechanical system making the time-frame of interest much longer than the switching time of the converter. Therefore, there is no need to have a switching model where the effect of switching adds little significance to the result. For a star connected generator, the generator side voltages v A0, v B0 and v C0, shown in Fig.2.3, can be calculated using (2.36)-(2.38) where v AN, v BN and v CN are the line-to-neutral voltages, 8

27 CHAPTER 2. MODELING DC A0 A A B C B0 C0 B C DC 0N Figure 2.3: Star connected generator and generator side VSC. between the specified points A, B or C and the neutral point N. As the average model is used, v AN, v BN and v CN are average voltages and s A, s B and s C are duty cycles. where v 0N is defined as [23]: v A0 = v AN v 0N = s A V DC v 0N = V DC 3 (2s A s B s C ) (2.36) v B0 = v BN v 0N = s B V DC v 0N = V DC 3 ( s A + 2s B s C ) (2.37) v C0 = v CN v 0N = s C V DC v 0N = V DC 3 ( s A s B + 2s C ) (2.38) v 0N = 3 (v AN + v BN + v CN ) = V DC 3 (s A + s B + s C ) (2.39) The dc link current i DC can be expressed as: [ i DC = ] s A s B s C i A i B i C (2.40) The model of the VSC is shown in Fig.2.4 where Gain is explained in (2.4), it is the matrix notation of (2.36)-(2.38). v A0 v B0 v C0 = V DC } {{ } Gain s A s B s C (2.4) 2.5. Modulation The VSC requires duty cycles s A, s B and s C in order to control the power flow through the converter. Space vector modulation (SVM) is chosen because it has higher utilization of the dc voltage than 9

28 2.5. BACK-TO-BACK CONVERTER V DC X [ v v v ] A0 B0 C0 Gain Product [ s s s ] A B i i i A B C C Dot product i DC Figure 2.4: Model of the VSC. the sinusoidal PWM method and does not require seperate modulators and calculation of zerosequence signals as in third harmoninc PWM [24]. SVM uses the stationary αβ reference frame where the reference voltage space vector V ref is defined as follows: V ref = 2 3 (v Aref + αv Bref + α 2 v Cref ) (2.42) where α = 2 + j 3 2 and v Aref, v Bref and v Cref are the reference voltages. The defintion of V ref depends on its location within the reference frame. In Fig.2.5, V ref is located in sector and is therefore defined by the state voltages V 00 and V 0. V 0 is the voltage produced by the state [ 0] where the upper switches in the first and middle leg of the VSC are conducting. T pwm is the switching period of the VSC and γ is the phase angle of V ref. 2 V 00 v β V 0 3 V ref V 0 V 000 γ 2t 2 V 0 T pwm V 00 = v α V 2t V 00 T pwm 4 6 V 00 V 0 5 Figure 2.5: V ref located in sector. As shown in Fig.2.6, the switching of states occurs in the following order [0 0 0], [ 0 0], [ 0], [ ] to reduce the number of switching commutations [25][26][27]. The states [0 0 0] and [ ] are referred to as zero states as no power flows through the VSC during their activity. Other 20

29 CHAPTER 2. MODELING states are referred to as active states. In SVM the zero states are symmetrical, that is [24]: t 7 = t 8 = T pwm 2 t t 2 = t 0 2 (2.43) t 0 t t 2 t 7 2 T pwm 2 T pwm V ref in sector can then be expressed as: where the state voltages are: V 00 = 2 3 V 0 = 2 3 Figure 2.6: The state sequence. V ref = V 00 t T pwm 2 + V 0 t 2 T pwm 2 ( ) α 0 V DC + α V DC 0 + α 2 V DC 0 ( ) α 0 V DC + α V DC + α 2 V DC 0 = 2 3 V DC (2.44) = 2 3 V DC (2.45) ( ) j (2.46) 2 The time durations, t and t 2, can be calculated using (2.44) by splitting to real and imaginary part, where V ref = V ref (cos γ + j sin γ): ] Re [V ref ] Im [V ref = V ref cos γ = 2 3 V DC = V ref sin γ = 2 3 V DC t T pwm 2 t 2 T pwm V DC The time durations for the states [ 0 0] and [ 0], are then [24]: t 2 T pwm 2 cos 60 (2.47) sin 60 (2.48) t = 3 V ref T pwm sin (60 γ) (2.49) V DC 2 t 2 = 3 V ref T pwm sin γ (2.50) V DC 2 Finally, the duty cycles of the output phase voltages v A0, v B0 and v C0 can be calculated for sector : s A = t + t 2 + T 0 2 T pwm 2 (2.5) 2

30 s B = t 2 + T 0 2 T pwm s C = 2 T 0 2 T pwm 2 (2.52) (2.53) The duty cycles can be obtained for other sectors in similiar fashion. Expression for time durations, valid for all sectors, can be found in [28].

31 Part III: Control System Design Part III: Control System Design 23 3 Maximum power point tracking Output filter design Selecting step size Control of the generator in variable speed operation 3 4. Introduction Rotor flux vector estimation Current model Voltage model Field Oriented Control Electromagnetic torque in the dq reference frame Control system design Q-axis control loop design D-axis control loop design Simulation on the generator control in variable speed operation Case : variable wind speed and constant reference rotor speed Case 2: variable wind speed and variable reference rotor speed (with MPPT) Case 3: variable rotor reference speed and constant mean wind speed Case 4: variable reference rotor speed and variable mean wind speed Power limitation mode Pitch control Assessment of pitch controller model Transition between variable speed operation and power limitation mode Simulation in variable pitch operation Case : variable wind in power limitation mode Case 2: reference power profile in power limitation mode Case 3: transition between variable speed operation and power limitation mode 70

32

33 CHAPTER 3. MAXIMUM POWER POINT TRACKING Chapter 3 Maximum power point tracking As seen in Fig.2.3 the output power of the WT varies with the rotor speed. While working in the variable speed region, the WTs efficiency can be considerably increased by varying the rotor speed to the maximum power point. The MPPT could be implemented by calculating the reference WT speed ωw T using the optimum tip-speed ratio λ opt and (3.) as described in [29][30][3]. ω W T = vλ opt R (3.) Block diagram of (3.) is shown in Fig.3. where K gear is the gear ratio and n p the number of poles. v λ opt R ω WT K gear ω mech np ω r Figure 3.: Block diagram of (3.). This should set the system quickly to its MPP, given that λ opt is in fact the optimum value. But because λ opt changes during the systems lifetime, it needs to be maintained at the optimum value by the use of an adaptive system [30]. This is difficult to implement and it is therefore considered a better approach to implement the MPPT using the simple perturb and observe method. This method is slower than the previously mentioned method but it does not require any parameters. The measured power and speed of the generator are fed to buffers which hold the values for one period. They are then compared to their values of next sampling period. Depending if they have increased or decreased, the generator reference speed ω r is increased or decreased by a constant step size dω r. The pertub and observe method used is based on [32] and [33] for PV panels. Similar method is described in [34] for WTs but it lacks the tracking of MPPT when ω W T has exceeded the MPP speed and needs to be reduced. The flowchart of the MPPT method is shown in Fig.3.2. The MPPT has been implemented with an S-function builder in Simulink. Fig.3.3 shows the structure of the whole system including the MPPT controller. Inputs to the MPPT controller are measured power P g which can be either the generator power or the WT mechanical power, the measured generator electrical rotor speed ω r and a user-defined step size dω r. 25

34 ΔP = P Δω = ω ( k) P( k ) ( k) ω( k ) ΔP = 0 ΔP>0 Δω > 0 Δω < 0 ω = ω dω r r r ω = ω + dω r r r ω = ω + dω r r r ω = ω dω r r r Figure 3.2: Flowchart of MPPT method. WIND MODEL V v MEAN WIND SPEED PROFILE WT MODEL T wt DRIVE TRAIN MODEL Tshaft ωr, P g SCIG MPPT v s is ω r VCI duty cycles Control Udc DC BUS P g + - Delay ω r + - Perturb and Observe S-function Filter ω r Delay dω r Step size Figure 3.3: Block diagram of system and MPPT. 26

35 CHAPTER 3. MAXIMUM POWER POINT TRACKING 3. Output filter design To minimize oscillations of the generator electrical rotor speed ω r, a filter is applied. The selection of filter is made by inspection of st order filters with different time constants τ: H(s) = [ τs +, τ = 90, 00, 200, 400 ] (3.2) Time constants for testing are chosen arbitrarily but it should be noted that the MPPT controller does not track for values higher than τ = 90 s. The system used in the simulation is shown in Fig.3.4 and is simulated with a fixed step of /F s = 0.2 ms, where F s = 5 khz. Delays are set to hold its inputs for one time step. Pitch θ Wind Speed V Power Calculation P g + - ω r Delay ω r + - ω r Perturb and Observe S-function Filter ω r Delay dω r Step size Delay This model does not take into account: Figure 3.4: Block diagram of simulation model. the WT inertia (it would limits the rate of change in speed); the wind speed turbulence (it would produces power oscillations); drive train and gear box (it is assumed ω W Y K gear = ω r /n p ; effects of the generator control (the error between ω r and ω r is neglected); The last point implies that ωr and ω r are the same, meaning that the generator aligns instantaneously with the reference speed. This does not reflect the operation of the real system but is considered enough to check the functionality of the MPPT and to examine different output filters. The model uses (2.0) and (2.7) to calculate the power produced by the WT for the measured electrical speed of the generator ω r. The pitch angle is irrelevant for the simulation and is set to 0. An additional delay is necessary between the output ω r and the input ω r to avoid algebraic loops 27