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Advanced incremental conductance MPPT for small wind turbines Syskakis, Tomás 2021

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Advanced IncrementalConductance MPPT forSmall Wind TurbinesbyToma´s SyskakisBASc, The University of British Columbia, 2017A THESIS SUBMITTED IN PARTIAL FULFILLMENT OFTHE REQUIREMENTS FOR THE DEGREE OFMASTER OF APPLIED SCIENCEinThe Faculty of Graduate and Postdoctoral Studies(Electrical and Computer Engineering)THE UNIVERSITY OF BRITISH COLUMBIA(Vancouver)February 2021c© Toma´s Syskakis 2021The following individuals certify that they have read, and recommend to the Faculty ofGraduate and Postdoctoral Studies for acceptance, the thesis entitled:Advanced Incremental Conductance MPPT for Small Wind Turbinessubmitted by Toma´s Syskakis in partial fulfillment of the requirements forthe degree of Master of Applied Sciencein Electrical and Computer EngineeringExamining Committee:Dr. Martin Ordonez, Electrical and Computer EngineeringSupervisorDr. William Dunford, Electrical and Computer EngineeringSupervisory Committee MemberiiAbstractSmall wind turbines (WTs) are robust and commercially viable distributed generation al-ternatives to photovoltaic (PV) generation in locations deemed unsatisfactory due to lowirradiance levels. However, small WTs are susceptible to variable environmental conditionsand require sophisticated maximum power point tracking (MPPT) algorithms to ensure thesystem operates at the maximum power point (MPP) when subjected to fluctuating windspeeds. Optimal relationship based (ORB) and hill-climbing (HC) algorithms are the tradi-tional MPPT methods for small WTs due to their simplicity, yet these strategies suffer fromseveral challenges: ORB algorithms rely on parameterized coefficients that change over time,whereas HC variants are susceptible to algorithm confusion and lack standardized frameworksfor choosing the optimal MPPT controller update frequency and perturbation magnitude.This work introduces a novel control-oriented small WT model that facilitates an intu-itive approach for analyzing the electromechanical system. This modelling technique enablesthe development of two incremental conductance (InCond) based MPPT strategies that ad-dress the aforementioned challenges.The first presented MPPT strategy tracks the optimal system operating point using anadapted mechanical InCond algorithm and suppresses power oscillations around the MPP.This results in: 1) elimination of algorithm confusion, 2) accurate tracking and detectionof the MPP and 3) improved steady state efficiency. The algorithm design requires onlyelectrical sensing, thereby making this method sensorless from a mechanical perspective.iiiAbstractThe second presented MPPT framework uses the control-oriented model and an onlineimpedance measurement technique to perform a system impedance frequency response anal-ysis. Through this analysis, a small WT equivalent circuit is derived and MPPT controller isdeveloped using a novel system identification (SysID) algorithm to perform InCond control.This methodology offers three advantages over conventional methods: 1) accurate trackingwhen subjected to erratic wind speeds, 2) optimal MPPT over the system lifetime and 3)a systematic approach for choosing the MPPT update frequency, facilitated by the systemimpedance frequency response analysis.The presented MPPT methods are supported with detailed mathematical proceduresand validated with simulation and experimental results. This thesis significantly contributesto the advancement of small WT modelling and MPPT.ivLay SummaryThe proliferation of affordable consumer distributed generation systems necessitates a closerlook at small wind turbines and their accompanying modelling and control. Small windturbines require specific control algorithms to harvest the maximum amount of energy froma wind resource. Although simple to implement, traditional small wind turbine controltechniques suffer from several methodological challenges. Specifically, perturbation-based al-gorithms are susceptible to algorithm confusion and lack standardized frameworks for tuningkey control parameters.This thesis presents a novel control-oriented modelling technique for small wind turbineswhich facilitates the development of two perturbation-based control strategies to address theaforementioned challenges. The first presented method focuses on mitigating algorithm con-fusion and improving a traditional algorithm. The second presented strategy is a comprehen-sive methodology utilizing real-time system identification and a small wind turbine equivalentcircuit to achieve dynamic control and provide a framework for tuning fundamental controlparameters.vPrefaceThis work is based on research performed at the Electrical and Computer Engineering de-partment of the University of British Columbia by Toma´s Syskakis, under the supervision ofDr. Martin Ordonez.Chapters 2 and 3 contain modified content that was presented at the IEEE 10th In-ternational Symposium on Power Electronics for Distributed Generation Systems (PEDG),2019 [1]:• T. Syskakis and M. Ordonez, “MPPT for small wind turbines: zero-oscillation sen-sorless strategy,” 2019 IEEE 10th International Symposium on Power Electronics forDistributed Generation Systems (PEDG), pp. 1060-1065, 2019.As first author of the above-mentioned publication, the author of this thesis developedthe theoretical concepts and wrote the manuscripts, receiving advice and technical supportfrom Dr. Martin Ordonez. The author developed the simulation models and experimentalplatforms, receiving contributions from Dr. Ordonez’s research team. In particular, Dr. IonIsbasescu contributed to developing the experimental platform for the work done in [1].viTable of ContentsAbstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iiiLay Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . vPreface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . viTable of Contents . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . viiList of Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xList of Figures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xiAcknowledgements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xiiiDedication . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xiv1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.1 Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.2 Literature Review . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51.2.1 Modelling Methods for Wind Turbine Control . . . . . . . . . . . . . 51.2.2 Wind Turbine Maximum Power Point Tracking . . . . . . . . . . . . 131.3 Contribution of the Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . 191.4 Thesis Outline . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21viiTable of Contents2 Control-Oriented Small Wind Turbine Modelling . . . . . . . . . . . . . . 232.1 System Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 242.1.1 Mechanical Subsystem to Electrical Equivalent Circuit . . . . . . . . 252.1.2 Electrical Subsystem Average-Value Modelling . . . . . . . . . . . . 282.1.3 Complete Control-Oriented Small WT Model . . . . . . . . . . . . . 322.2 Small Wind Turbine Characteristic Curves . . . . . . . . . . . . . . . . . . 342.2.1 Characteristic Curves Derivation . . . . . . . . . . . . . . . . . . . . 352.2.2 Traditional InCond MPPT . . . . . . . . . . . . . . . . . . . . . . . 373 Zero-Oscillation Sensorless MPPT . . . . . . . . . . . . . . . . . . . . . . . 393.1 Proposed MPPT Algorithm . . . . . . . . . . . . . . . . . . . . . . . . . . . 413.1.1 Adapted Incremental Conductance . . . . . . . . . . . . . . . . . . . 413.1.2 Power Oscillation Detection and Suppression . . . . . . . . . . . . . 453.1.3 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 473.2 Simulation Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 493.3 Experimental Validation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 523.3.1 Emulators . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 523.3.2 Turbine Emulation Platform . . . . . . . . . . . . . . . . . . . . . . 543.3.3 Experimental Validation . . . . . . . . . . . . . . . . . . . . . . . . . 573.4 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 594 System Identification MPPT . . . . . . . . . . . . . . . . . . . . . . . . . . . 604.1 Proposed MPPT Algorithm . . . . . . . . . . . . . . . . . . . . . . . . . . . 614.1.1 Lock-In Amplifier . . . . . . . . . . . . . . . . . . . . . . . . . . . . 624.1.2 System Impedance Frequency Response . . . . . . . . . . . . . . . . 664.1.3 System Identification . . . . . . . . . . . . . . . . . . . . . . . . . . 704.1.4 MPP Controller . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72viiiTable of Contents4.2 Simulation Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 734.3 Experimental Validation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 784.4 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 835 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 845.1 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 845.2 Future Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88ixList of Tables3.1 ZOS InCond Simulation System Parameters . . . . . . . . . . . . . . . . . . 494.1 SysID MPPT Simulation System Parameters . . . . . . . . . . . . . . . . . . 744.2 SysID MPPT Wind Velocity Profile Parameters . . . . . . . . . . . . . . . . 744.3 MPPT Algorithm Parameters . . . . . . . . . . . . . . . . . . . . . . . . . . 774.4 SysID MPPT Controller Parameters . . . . . . . . . . . . . . . . . . . . . . 82xList of Figures1.1 Large wind turbine use cases. . . . . . . . . . . . . . . . . . . . . . . . . . . 21.2 Small wind turbine use cases. . . . . . . . . . . . . . . . . . . . . . . . . . . 21.3 Power coefficient curves for VAWTs and HAWTs. . . . . . . . . . . . . . . . 41.4 Small wind turbine system diagram. . . . . . . . . . . . . . . . . . . . . . . . 51.5 Wind turbine power and torque modelling block diagram. . . . . . . . . . . . 81.6 Small wind turbine power electronics architectures. . . . . . . . . . . . . . . 121.7 LiDAR and cup anemometers for wind turbines. . . . . . . . . . . . . . . . . 141.8 Tip speed ratio control block diagram. . . . . . . . . . . . . . . . . . . . . . 151.9 Small wind turbine characteristic curves. . . . . . . . . . . . . . . . . . . . . 171.10 Perturbation-based MPPT algorithm behavior. . . . . . . . . . . . . . . . . . 172.1 Small wind turbine system under study. . . . . . . . . . . . . . . . . . . . . 242.2 Mechanical model to electrical equivalent circuit analogies. . . . . . . . . . . 262.3 Mechanical system translated to an electrical equivalent circuit. . . . . . . . 272.4 PMSG and 3ΦR equivalent circuit. . . . . . . . . . . . . . . . . . . . . . . . 302.5 Inverted buck DC-DC converter. . . . . . . . . . . . . . . . . . . . . . . . . . 312.6 Small wind turbine control-oriented model. . . . . . . . . . . . . . . . . . . . 332.7 Expanded small wind turbine characteristic curves. . . . . . . . . . . . . . . 363.1 Traditional InCond algorithm behavior. . . . . . . . . . . . . . . . . . . . . . 403.2 Adapted mechanical InCond MPPT algorithm flow chart. . . . . . . . . . . . 42xiList of Figures3.3 Turbine speed measurement and torque estimation. . . . . . . . . . . . . . . 443.4 Complete ZOS InCond algorithm flow chart. . . . . . . . . . . . . . . . . . . 463.5 ZOS InCond simulation waveforms. . . . . . . . . . . . . . . . . . . . . . . . 503.6 ZOS InCond vs traditional InCond. . . . . . . . . . . . . . . . . . . . . . . . 513.7 Turbine emulation platform experimental setup. . . . . . . . . . . . . . . . . 553.8 ZOS InCond experimental waveforms. . . . . . . . . . . . . . . . . . . . . . . 584.1 MAF and LIA block diagram. . . . . . . . . . . . . . . . . . . . . . . . . . . 624.2 System impedance bode plot. . . . . . . . . . . . . . . . . . . . . . . . . . . 654.3 System impedance frequency response analysis. . . . . . . . . . . . . . . . . 674.4 Small wind turbine equivalent circuit. . . . . . . . . . . . . . . . . . . . . . . 674.5 SysID MPPT algorithm block diagram. . . . . . . . . . . . . . . . . . . . . . 714.6 SysID MPPT simulation waveforms. . . . . . . . . . . . . . . . . . . . . . . 754.7 MPPT algorithm simulation comparison. . . . . . . . . . . . . . . . . . . . . 774.8 Small wind turbine test platform. . . . . . . . . . . . . . . . . . . . . . . . . 794.9 HAWT under test power coefficient curve. . . . . . . . . . . . . . . . . . . . 794.10 Small wind turbine experimental characteristic curves. . . . . . . . . . . . . 814.11 SysID MPPT experimental waveforms. . . . . . . . . . . . . . . . . . . . . . 825.1 Battery energy storage vs small wind turbine equivalent circuits. . . . . . . . 86xiiAcknowledgementsFirstly, I would like to sincerely thank my supervisor, Dr. Martin Ordonez, for his insight,encouragement and invaluable advice.I would also like to acknowledge all of my lab mates and colleagues. I have cherishedthese past years and will forever be grateful for the camaraderie and experiences we sharedwhile on the roller coaster that is academic research. In particular, I want to thank Dr.Ion (Isbi) Isbasescu for his willingness and thoroughness in designing and building exquisiteexperimental prototypes and platforms. And to Pancho and Nacho, thank you both for yourmentorship and selfless support.To my Mom and Dad, thank you for your unconditional love and encouragement. Tomy sister, Triana, thank you for keeping me grounded. To my Yiayia Niovi, thank you foryour unwavering faith and delicious meals. To my family and friends, thank you for yourenthusiasm and support.Lastly, I would like to thank you, the reader, for your interest in this work. I hope youfind answers to your questions.α´φoβαxiiiTo my Mom and Dad.xivChapter 1Introduction1.1 MotivationWith growing societal awareness and political emphasis regarding climate change, the adop-tion of renewable distributed generation systems, such as photovoltaic (PV) panels and windturbines (WTs), is paramount [2,3]. Distributed generation and energy storage technologiesoffer significant benefits to both utility companies and energy consumers such as support foroff-grid communities, energy autonomy and favorable grid-tie features (e.g. peak shaving,virtual inertia, black start, etc.) [4]. Specifically, large and small WT installations have seenrecord adoption over the last decade with significant projected growth over the next 50 years.Large utility-scale WTs, seen in Fig. 1.1, have drastically dropped in cost with technologyinnovation, improved manufacturing methods, comprehensive installation infrastructure andmature supply chains [3]. Whereas small WTs, seen in Fig. 1.2, are consumer friendly re-newable generation options with a plethora of use cases. Growing interest from individualsand communities warrants a closer look at small WTs and their accompanying modellingand control methods.Industry semantics designates the power range of small WTs to be 50W up to 50kW.To promote the proliferation of small WT systems, the levelized cost of energy (LCOE) forthese installations must be competitive with other energy generation methods. The LCOEtakes into account the amount of energy generated and the build, operating and maintenance112MW5MWFigure 1.1: Large WTs, some with diameters over 100 meters, are economical renewablegeneration options that can be deployed inland or in the ocean at locations with sufficient andconstant wind flow. These installations are the culmination of vast research and developmentefforts and represent a significant monetary investment.10kW1kWFigure 1.2: Small WTs are a versatile distributed generation alternative to PV with a plethoraof terrestrial and marine use cases. As they are subjected to highly variable wind velocityprofiles, dynamic control algorithms are required in order to maximize the harvested windenergy while still being cheap to manufacturer and implement.21.1. Motivationcosts of the system over its lifetime; therefore, to ascertain financial viability, a small WTsystem must be economical to build, robust and ensure a high conversion efficiency undervarying wind speeds [5, 6].PV and WT systems require similar control functionality in order to extract the maxi-mum amount of power from their respective natural phenomenon. PV systems utilize poweroptimizers to adjust the system operating point and extract the maximum amount of powerfrom the available solar irradiance [7, 8]. Similarly, WT control systems require sophisti-cated maximum power point tracking (MPPT) algorithms to extract the maximum amountof power from a moving body of air. Although PV and WT systems share similar trackingphilosophies, each require unique control solutions specific to system design and behavior.Regarding WTs, for a given wind velocity there exists a singular maximum power point(MPP) to which the system must be driven. This MPP is dependent on the power coefficient(Cp) curve that is unique to every wind turbine and is parameterized based on the tip speedratio (TSR, λ). This Cp(λ) curve is a measure of the turbine’s energy conversion efficiencyover its operating range. As seen in Fig. 1.3, Cp(λ) exhibits uniform concavity for bothvertical axis wind turbines (VAWTs) and horizontal axis wind turbines (HAWTs); therefore,there exists a unique MPP for a fixed wind velocity (vw). Regardless of turbine design, thetheoretical maximum conversion efficiency from aerodynamic energy to rotational mechanicalenergy is known as the Betz limit (Cp = 59.3%) - named for Albert Betz who first derivedthe limit in 1966 [9]. Utility-scale WTs, developed using sophisticated modelling techniquesand cutting edge materials engineering, achieve maximum power coefficients of 75–80% ofthe Betz limit.The intent of the MPPT algorithm is to adjust the turbine angular velocity (ωt) as vwchanges in order to maintain the optimum TSR (λopt) and ensure the system is operating atthe MPP. Large WTs utilize expensive light detection and ranging (LiDAR) equipment to31.1. MotivationHAWTVAWT2 4 6 8 10 12 140102030405060=  ( ) [%] = 59.3  BETZ LIMIT   0%Figure 1.3: Typical power coefficient curves for fixed pitch VAWTs and HAWTs.measure vw several hundred meters away from the turbine’s location. A parameterized modelof the turbine system is then used to calculate the optimum ωt and the turbine’s blade pitchis adjusted to accelerate or decelerate the WT accordingly.For small WTs, inherent financial limitations necessitate the use of alternative MPPTtechniques as wind velocity measurement equipment (LiDAR or anemometer) and bladepitch adjustment systems constitute a significant portion of the total system cost. Tradi-tional small WT MPPT control techniques, although simple to implement, suffer from severalmethodological challenges. Specifically, industry-favored perturbation-based algorithms aresusceptible to algorithm confusion and lack standardized frameworks for tuning key controlparameters. Therefore, the optimum small WT MPPT method should have the followingqualities: 1) dynamic control to maximize the harvested energy from highly variable wind ve-locity profiles, 2) purely electrical sensing and control techniques to minimize manufacturingcosts and 3) a comprehensive framework for tuning key control parameters.The work presented in this thesis encompasses two paradigms related to small WTs:modelling and MPPT control. A control-oriented model is developed that increases simula-41.2. Literature ReviewHAWTGearboxGENERATORTURBINE POWER ELECTRONICSFigure 1.4: A typical small WT system diagram.tion speed and facilitates other key systemic insights. Moreover, two novel MPPT methodolo-gies are presented that address the shortcomings of conventional perturbation-based trackingmethods. The following literature review will, therefore, discuss small WT modelling andtraditional MPPT strategies.1.2 Literature Review1.2.1 Modelling Methods for Wind Turbine ControlA typical small WT system, illustrated in Fig. 1.4, is comprised of three parts: the tur-bine, generator and power electronics. The turbine mechanical subsystem includes a fixedpitch VAWT or HAWT coupled to an electric generator via a speed increaser gearbox. Thepower electronics subsystem performs the MPPT and interfaces with the grid or, when inislanded mode, supplies power to the connected microgrid. Additional “smart” features canbe implemented to provide grid support during transient events, voltage and frequency ridethrough and real-time data streaming [10]. The following sections will discuss modellingconsiderations for the turbine, generator and power electronics subsystems.51.2. Literature ReviewTurbineThe turbine rotor is a mechanical structure that consists of a set of blades connected radiallyto a central hub and shaft. Typically, two or three blades are used; however, low power (lessthan 500W) turbine manufacturers produce rotor options with five blades. The number ofturbine blades used depends on the required aerodynamic efficiency, financial considerationsand system reliability. Turbine rotor blades, inspired by aviation airfoils, are designed togenerate a lift force perpendicular to the direction of air flow. In aeronautical wing design,the generated lift force is used to propel the craft vertically; alternatively, turbine blades aresituated such that the generated lift force causes the entire rotor structure to rotate arounda central axis [11].In practical turbine design, the aerodynamic to mechanical conversion efficiency is pa-rameterized as the Cp(λ) curve. As briefly mentioned in Section 1.1, Cp(λ) is a highly non-linear uniformly concave curve that is a function of the turbine TSR. The TSR is dependenton the turbine radius (R), turbine angular velocity (ωt) and wind velocity (vw):λ =Rωtvw. (1.1)As seen in Fig. 1.3, there exists a singular TSR (λopt) for which the WT extracts themaximum amount of power. The location of λopt and the shape of the Cp(λ) curve is depen-dent on the physical characteristics of the turbine such as the number of blades, blade pitchand airfoil design. Over time, Cp(λ) may change due to blade leading edge erosion, subsystemdegradation and geographical location surface roughness [12–15]. For large utility-scale WTsystems, it is economically viable to perform routine maintenance and site specific modellingto address these issues. However, small WT manufacturers rely on economies of scale, ratherthan large single site installations, to attain a profitable business model. As such, small WT61.2. Literature Reviewcontrol techniques cannot rely on hard coded parameterized Cp(λ) curves and expect thesystem to operate at optimum efficiencies.The mechanical power generated by the wind turbine (Pt) can be expressed as a functionof the available power in the wind (Pw):Pw =12Aρv3w (1.2)Pt = Pw · Cp(λ) = 12Aρv3w · Cp(λ), (1.3)where ρ, A, vw, Cp(λ), respectively, denote the air density, swept rotor area, wind velocityand power coefficient. Effective modelling of any wind energy conversion system, if a WTis utilized, requires the Cp(λ) curve to be accommodated. Depending on the size of theturbine and the available facilities, experimental testing can be done within a wind tunnelto parameterize the power coefficient for the specific turbine under test. Alternatively, finiteelement analysis (FEA) and computational fluid dynamics (CFD) modelling can be performedon the turbine airfoil design to derive Cp(λ). Once the curve is known, a look up table (LUT)or the parameterized function is embedded in the model. In the simulation environment, theoperating point TSR is calculated based on the input vw profile and current ωt. Using theLUT or derived function, the power coefficient is then determined and Pt can be calculatedbased on (1.3), as seen in Fig. 1.5.The lift forces generated by the turbine blades create a torque about the central rotorshaft. This turbine torque (Tt) is calculated based on the power relationship using Pt and ωt:Tt =Ptωt. (1.4)71.2. Literature Review( ) 2AρPa3LUTTFigure 1.5: Turbine mechanical power (Pt) calculation block diagram using a Cp(λ) curvelook up table (LUT).Both large and small WT systems operate over the same TSR range; consequently, as bladeradii get larger, turbine rotational speeds decrease in order to preserve the optimum TSR.Therefore, the addition of a mechanical gearbox is required to increase the rotational speedof the generator shaft closer to its rated value. If a speed increaser gearbox is included, thegenerator torque (Tg) and angular velocity (ωg) will be scaled by the gearbox ratio (Ngb)accordingly:Tg =1Ngb· Tt (1.5)ωg = Ngb · ωt. (1.6)Taking into account the turbine and generator inertia, the mechanical dynamic equation ofthe two mass system is:(JtN2gb+ Jg)· dωgdt=TtNgb− Tg −(BtN2gb+Bg)· ωg, (1.7)where T , ω, J and B, respectively, denote the torque, angular velocity, moment of inertia andmechanical damping coefficient. The subscripts t and g, respectively, represent the turbineand generator. The mechanical dynamic equation is a first order ordinary differential equation81.2. Literature Review(ODE) that can be modelled and analyzed using conventional simulation software such asSimulink. Alternatively, the mechanical dynamic equation can be translated to the electricaldomain [16, 17]. Utilizing mechanical to electrical analogies, an equivalent electrical circuitcan be constructed that proves helpful for analysing the interactions between mechanical andelectrical systems. In the electrical domain, torque is a through variable analogous to currentand angular velocity is an across variable analogous to voltage [18]. Another benefit oftranslating mechanical systems to the electrical domain is the ability to use circuit modellingsoftware such as Plexim or PowerSIM to analyze the WT electromechanical system. Anequivalent electrical model of the small WT mechanical system is developed and furtherdiscussed in Chapter 2.GeneratorEnergy harvesting efforts, whether photonic or kinetic in nature, invariably culminate ina method to generate electrical energy. Most modern gadgets, appliances and machinesrequire electrical power to operate. Every year, countries invest billions of dollars into thedevelopment and maintenance of vast electrical generation and distribution networks whichspan across and between continents. From the perspective of wind energy conversion, theaerodynamic kinetic energy of the wind is translated to rotational mechanical energy andthen must be translated, yet again, into electrical energy. A suitable electric generatormust be chosen to perform this final energy conversion. Predominately, doubly-fed inductiongenerators (DFIGs) and permanent magnet synchronous generators (PMSGs) have been usedin small WT installations [19].A DFIG is a generator design with a multi-phase wound rotor whose windings areaccessible through a slip ring assembly. The DFIG stator is connected to the grid andthe rotor windings are connected to a back-to-back power electronics converter that controlsboth the rotor and grid currents, typically using vector or direct torque control [20]. This91.2. Literature Reviewconfiguration allows the turbine rotational frequency to deviate from the grid frequency. Avariable speed WT, as opposed to a fixed speed WT, is able to utilize a wind resource moreefficiently. Compared to other variable speed generator options, converter costs for a DFIGare low as only a fraction of the generated electrical power is processed by the converter, themajority of the power is fed to the grid via the stator. For this reason, DFIGs are typicallyused in higher power systems. However, although the initial investment for a DFIG is lowercompared to PMSGs, the rotor windings and slip ring assembly require frequent maintenanceand are not easily serviceable [21–23].A PMSG uses rare-earth permanent magnets rather than a wound rotor with slip ringsto generate an excitation field. These generators are initially more expensive than DFIGs,yet offer numerous advantages such as minimal rotor maintenance, low cogging torque aswell as a higher conversion efficiency and power to weight ratio for low, medium and highspeed applications. PMSGs have become the industry standard for small WT installations asadvancements in high power switching devices have reduced converter costs and novel controlmethods increase system efficiencies [24–30]. For these reasons, the PMSG will be used inthe development of the small WT system presented and analyzed in this thesis.Typically, PMSG modelling techniques rely on simulating the generator dynamic equa-tions in the (direct-quadrature) rotor reference frame [31–34] using the Park transforma-tion [35]:vd = Lqiqωe − Lddiddt−Raid (1.8)vq = Ldidωe − Lq diqdt−Raiq + λpmωe, (1.9)where v, i and L, respectively, denote the voltage, current and inductance. The subscriptsd and q, respectively, represent the direct and quadrature axes. ωe is the generator electri-cal angular frequency and λpm is the permanent magnet flux linkage. The electromagnetic101.2. Literature Reviewgenerator torque (Tg) induced in the rotor is given by:Tg =(32)(p2)[(Lq − Ld) iqid + λpmiq], (1.10)where p is the number of generator poles. The generator torque opposes the turbine mechan-ical torque (Tt), and the difference between Tt and Tg determines the angular accelerationof the mechanical subsystem. A drawback of this modelling method is that the generatorinductance, resistance and magnetic flux linkage must be known. Manufacturers do not typ-ically include these equivalent model parameters in the generator documentation especiallyfor low power applications; moreover, specialized equipment is required to measure theseparameters accurately. Alternatively, average-value modelling of the PMSG and rectificationpower electronics can be employed to simplify the overall system, reduce simulation timeand emphasize system level control [20, 36–39]. This control-oriented modelling technique isdiscussed in Chapter 2.Power ElectronicsThe variable amplitude and frequency AC voltage generated by the PMSG cannot be directlyconnected to the utility grid. Drawing parallels to PV systems, a power optimizer and grid-tieinverter is required to condition the generator output to track the system MPP and seamlesslyinterface with the grid. Fig. 1.6 illustrates two power electronics architectures that are favoredin small WT applications using a PMSG: (a) back-to-back converter bidirectional topologyand (b) diode bridge rectifier and DC-DC converter power optimizer. Both architectures usea grid-tie inverter and DC link between the grid and generator side converters but differ intheir voltage rectification and generator side control methods [25].In architecture (a), a back-to-back converter bidirectional topology is utilized whichconsists of two voltage source converters (VSCs) connected through a DC bus [40–43]. The111.2. Literature ReviewPMSGHAWTHAWTPMSG1:1:BACK-TO-BACK CONVERTER3ΦRAC-DC DC-ACDC-DC DC-AC(a)(b)ggFigure 1.6: Favored small WT power electronics architectures: (a) back-to-back converterbidirectional topology and (b) diode bridge rectifier and DC-DC converter power optimizer.grid side VSC is responsible for DC bus regulation and grid interfacing; whereas, the generatorside VSC is responsible for MPPT and active rectification of the generator variable frequencyAC voltage output. Active rectification results in lower AC-DC conversion losses and thegenerator side VSC topology enables advanced three-phase control methods for turbine speedand torque control.In architecture (b), passive rectification using a three-phase diode bridge rectifier (3ΦR)is chosen to reduce build and maintenance costs and ensure robustness over the operatinglifetime of the system [1, 16, 44, 45]. A DC-DC converter interfaces with a stiff DC bus andperforms the direct duty-cycle MPPT. The DC bus is regulated by a VSC that interfaceswith the grid or, when in islanded mode, supplies power to the connected microgrid. Thisoption supports dynamic control algorithms while maintaining simplicity and requires fewer121.2. Literature Reviewpower switches and electrical sensors than architecture (a); therefore, this topology is utilizedin the small WT system developed, analyzed and tested throughout this thesis.1.2.2 Wind Turbine Maximum Power Point TrackingSpecific maximum power point tracking (MPPT) control algorithms are required to ensurethe WT system is operating at its maximum power point (MPP) when subjected to a chang-ing wind speed. Large WT installations use sophisticated optimal relationship based (ORB)MPPT algorithms, such as power signal feedback (PSF), optimal torque control (OTC) andtip speed ratio (TSR) control [46–51]. These methods rely on light detection and ranging(LiDAR) equipment or cup anemometer readings of the wind velocity, as seen in Fig. 1.7,and/or parameterized WT coefficients in order to determine the MPP; moreover, ORB algo-rithms operate under the assumption that the parameterized system coefficients remain validover all operating conditions and throughout the WTs service life [52]. For large utility-scaleWTs, system parameters may be updated as they change over time; however, when ORBalgorithms are implemented for small WTs, system parameters are not typically updatedresulting in decreased energy harvesting efficiency.Alternatively, hill-climbing (HC) based MPPT methods, such as perturb and observe(P&O) and incremental conductance (InCond), may be used which require few sensors, min-imal tuning of control parameters and no prior system parameterization or environmentalmeasurements [1, 45, 53–56]. Although simple to implement, a HC framework to derive theoptimal MPPT controller update frequency has yet to be developed due to the variability inmechanical system design (turbine inertia and power coefficient). Other drawbacks of tra-ditional HC algorithms include power oscillations around the MPP, slow dynamic responsedue to a fixed perturbation magnitude and controller confusion resulting from wind speedvariability. Modified HC and hybrid ORB-HC algorithms have been derived to address some131.2. Literature ReviewLiDARANEMOMETERFigure 1.7: LiDAR anemometer units located in the nose cone of the turbine rotor are ableto measure wind speeds several hundred meters down range from a turbine. This gives theMPPT controller sufficient time to adjust the system operating point to ensure maximumconversion efficiency. Cup anemometer readings are situated on the turbine nacelle andprovide real-time wind speed feedback.of these issues using adaptive step control or by perturbing advanced control variables; how-ever, these methods typically improve upon one or two shortcomings while exacerbating ornegating the others.A new subset of artificial intelligence (AI) based heuristic algorithms, such as fuzzy logicand neural network controllers, have been proposed [57–63]. However, AI, when applied toMPPT, is still in its infancy and further research is required to determine best practices [46,56]. Consequently, heuristic algorithms are omitted in the following literature review in orderto limit the scope to industry standard MPPT methods, specifically optimal relationshipbased and hill-climbing algorithms.Optimal Relationship Based AlgorithmsORB algorithms, the most widely used MPPT techniques in large WT control, rely onparameterized curves or LUTs to provide an optimum reference signal to the WT controller.PSF, a classical control approach, uses a pre-programmed optimal power versus turbine speed141.2. Literature ReviewopopCONTROLLERAC-DC DC-ACFigure 1.8: Most modern utility-scale wind turbines utilize tip speed ratio control MPPT.The optimal wind turbine speed is calculated using λopt and the measured vw.curve P optt (ωt) populated using measurements at various wind velocities. This optimal curve,as well as a turbine rotational speed measurement, is used to generate a power referencesignal to the controller which then adjusts the turbine speed accordingly. Similarly, forOTC, a variant of PSF, an optimal torque versus turbine speed curve T optt (ωt) is used tooutput a torque reference signal to the controller.Currently, most commissioned utility-scale WTs use LiDAR equipment to accuratelymeasure the wind speed and direction several hundred meters down range. These units,although accurate, are expensive and not suitable for small WT installations. Prior to LiDARanemometers, nacelle mounted cup anemometers measured the local wind speed; however,these devices are susceptible to turbulence induced by the rotating turbine blades and do notallow for down wind measurements.Another prominent ORB MPPT method is TSR control, illustrated in Fig. 1.8, where theoptimal turbine speed (ωoptt ) is calculated based on the wind velocity measurement, turbine151.2. Literature Reviewradius and optimal TSR (λopt). The obvious caveat to this method is the parameterizedCp(λ) curve and location of λopt must be known prior to turbine deployment. For multi-million dollar turbine systems, rigorous FEA and CFD modelling, advanced materials andprecision moulding are utilized to generate accurate parameterized power coefficient curves.However, there are a number of factors that may cause λopt to drift over time such as increasedblade surface roughness, leading edge erosion, subsystem degradation and location surfaceroughness [12–15]. When using TSR control, this λopt drift will affect conversion efficiencyat low wind velocities if not addressed (at high wind speeds the turbine output power iscurtailed to a nominal level).Hill-Climbing AlgorithmsHC MPPT techniques are predominately used in small WT systems due to their simplicityand adequate tracking accuracy. These methods periodically update the turbine operatingpoint in order to extract system information and search for the MPP while subjected tochanging environmental conditions. P&O and InCond, two well establish algorithms in bothPV and small WT MPPT, are derived from the power versus voltage P (V ) and currentversus voltage I(V ) characteristic curves. Utilizing power electronics architecture (B), thesmall WT characteristic curves Pg(Vg) and Ig(Vg) for a fixed vw are plotted in Fig. 1.9.The rectified generator output power (Pg) is dependent on the turbine Cp(λ) curve and,therefore, exhibits uniform concavity with a singular MPP. It is also noted that the location ofthe maximum generator current does not coincide with the MPP. This behavior is consistentwith PV cell P (V ) and I(V ) characteristic curves, and conceptual parallels can be drawnbetween the two systems.Utilizing a P&O algorithm, as seen in Fig. 1.10, the system operating point is adjustedby stepping the applied voltage to the generator (Vg) up or down. The sign of the difference160204060800123g V[ ]MPP5 15 25 35 45PMPPIMPPW[]P gA[]gIMAXFigure 1.9: Small WT system Pg(Vg) and Ig(Vg) characteristic curves for a fixed vw.MPPTPggPgPg(n-1)Pg(n)Δ gPgΔPgΔΔ gPg(n-1)Pg(n)Δ gg = +gPgΔ Pg(n) Pg(n-1)= -PgΔ >0Δ g=-Δ g NOYESFigure 1.10: An illustration of large and small voltage perturbation step sizes and its affecton steady state power oscillations and controller tracking speed (left). Perturb and observeMPPT algorithm flow diagram (right).171.2. Literature Reviewbetween the previous Pg(n − 1) and current Pg(n) power measurements determines the di-rection of the next Vg step in order to move the operating point towards the MPP. Similarly,the InCond algorithm compares the incremental conductance (gac = −dIg/dVg) to the abso-lute conductance (gDC = Ig/Vg) to determine the next Vg step direction. At the MPP, theincremental and absolute conductances are equal signalling an impedance match between thesource and load. The InCond algorithm applied to a small WT system is discussed furtherin Chapter 2.The magnitude of the voltage step as well as the controller update frequency mustbe tuned for optimal performance as these control parameters greatly affect the MPPTeffectiveness as seen in Fig. 1.10. For example, a large voltage perturbation will arriveat the MPP quickly; however, there will be a significant power oscillation due to the largeperturbation. Alternatively, a small voltage perturbation will yield smaller power oscillationsaround the MPP but the tracking speed is slower as more steps are required. Similarly, thecontroller update frequency must be chosen to effectively track the variations in wind speedbut also allow the system dynamics to settle to facilitate accurate calculations within theMPPT algorithm. Due to widespread consumer and utility PV adoption, methodologieshave been derived which quantify the minimum controller update frequency and suitableperturbation magnitude for PV HC MPPT methods [64, 65]. A similar tuning methodologyfor small WT systems has yet to be developed due to system variability.Other drawbacks of HC algorithms include power oscillations around the MPP andcontroller confusion due to changes in wind speed. Modified HC algorithms have been derivedto address some of these issues; however, these methods typically improve upon one ortwo shortcomings while exacerbating or negating the others. Adaptive step HC variantsfor P&O and InCond adjust the voltage perturbation magnitude for fast tracking whenthe system operating point is away from the MPP and facilitates a small power oscillation181.3. Contribution of the Workwhen the system is at the MPP [52, 66, 67]. However, these methods increase controllerconfusion due to the variation in perturbation step size. Hybrid ORB and HC methodshave been presented which perturb an arbitrary control variable derived from the P (V )or I(V ) characteristic curves [45, 48, 52, 68]. Parameterized characteristic curves for thespecific small WT system are required to perform this type of control. In addition, asa perturbation-based MPPT method is utilized, the voltage step magnitude and controllerupdate frequency must still be optimized. The MPPT techniques presented in Chapters 3 and4 look to address the aforementioned shortcomings of conventional small WT perturbation-based MPPT algorithms.1.3 Contribution of the WorkThe work presented in this thesis introduces contributions to both modelling and control ofsmall WT systems:• A control-oriented model of the small WT system is developed. This modelling tech-nique facilitates an intuitive approach for analyzing the small WT electromechanicalsystem, enables the derivation of novel WT characteristic curves (power vs voltage, cur-rent vs voltage and conductance vs voltage) and increases simulation speed comparedto conventional modelling methods.• Two novel small WT MPPT methodologies are presented which address the aforemen-tioned shortcomings of traditional HC strategies:1. Zero-Oscillation Sensorless (ZOS) InCond maintains the benefits of the traditionalInCond method (computational efficiency, ease of implementation and low sensorcount) and addresses its main challenges of steady state power oscillations andincorrect algorithm decisions under changing environmental conditions. The ZOS191.3. Contribution of the WorkInCond algorithm determines the optimal duty cycle and then suppresses the os-cillation around the MPP. This results in: 1) elimination of algorithm confusiondue to changing wind speeds, 2) accurate tracking and detection of the MPP and3) improved steady state efficiency. The design of the algorithm requires onlyelectrical sensing, thereby making this MPPT method sensorless from a mechan-ical perspective. Implementing the ZOS InCond strategy increases the energyharvesting efficiency by 3.4% compared to the traditional InCond algorithm.2. A real-time System Identification (SysID) based MPPT framework is developedutilizing a lock-in amplifier (LIA), a derived small WT equivalent circuit and theSysID algorithm to address all HC challenges without incurring increased hard-ware requirements. The LIA is a digital signal processing (DSP) technique thatperforms a frequency response analysis at programmable operating points. LIAshave been used in the past to identify parameters in electrochemical, electromag-netic, electromechanical and electrical systems. Using the LIA and the developedcontrol-oriented small WT model, a system impedance frequency response anal-ysis is performed and an equivalent circuit for the small WT system is derived.Using the SysID algorithm, the small WT system equivalent circuit parametersare calculated in real time and the system operating point is adjusted using anintegral controller to facilitate adaptive step functionality. This control methodlocks on to the MPP and is less susceptible to algorithm confusion compared totraditional HC MPPT methods. The SysID MPPT methodology offers three keyadvantages over conventional tracking strategies: 1) accurate tracking when sub-jected to highly variable wind speeds, 2) optimal MPPT is guaranteed over thesystem lifetime even through degradation, maintenance and retrofitting and 3)a systematic approach for choosing the MPPT update frequency, facilitated bythe system impedance frequency response analysis. When subjected to a highly201.4. Thesis Outlinevariable wind velocity profile, utilizing the SysID algorithm increases the energyharvesting efficiency by 9.5% compared to the traditional InCond algorithm.The ZOS InCond MPPT strategy, presented in Chapter 3, was developed at the begin-ning of my MASc degree. This MPPT method addresses the steady state power oscillationsand algorithm confusion drawbacks affecting traditional InCond control; however, althoughcorrective and interesting in its own right, I believe the ZOS InCond algorithm did not ap-propriately provide a framework for choosing the optimal MPPT controller update frequencyor perturbation magnitude.As such, my research shifted to develop a more comprehensive MPPT strategy. TheSysID MPPT methodology, presented in Chapter 4, addresses the conventional disadvantagesof HC methods and also presents an approach for choosing the optimal MPPT controllerupdate frequency using a novel system impedance frequency response analysis.1.4 Thesis OutlineThis work is organized and presented in the following manner:• In Chapter 2, the control-oriented small WT model is developed. The modelling frame-work for translating the mechanical WT system to the electrical domain is discussed.An average-value model of the PMSG and rectification power electronics is used tosimplify the overall system, reduce simulation time and emphasize system level control.Using the developed model, the small WT system characteristic curves are derived andthe traditional InCond control algorithm is contextualized using these curves.• In Chapter 3, the ZOS InCond MPPT strategy is presented. The traditional InCondalgorithm is translated to the mechanical domain where current and voltage are sub-stituted for turbine torque and angular velocity. A novel turbine torque estimation211.4. Thesis Outlinetechnique is developed based on the control-oriented small WT model and a purelyelectrical angular velocity measurement is utilized. Subsequently, these variables areused in the development of the ZOS InCond strategy. The theoretical analysis is sup-ported by simulation results and experimental validation is performed using a customturbine emulation platform.• In Chapter 4, the SysID MPPT methodology is presented. A real-time impedancemeasurement technique is developed using a digital LIA. Using this impedance mea-surement, a system impedance frequency response analysis is performed and an equiv-alent circuit for the small WT system is derived. Based on the small WT equivalentcircuit, a SysID algorithm is determined to enable a faster MPPT controller updatefrequency to be used. The equivalent circuit parameters are calculated in real-timeusing the SysID algorithm, and a MPPT controller is developed to facilitate adaptivestep functionality. The SysID MPPT framework is supported by simulation results andexperimental validation is performed using a small WT test platform.• Lastly, in Chapter 5, a summary of this work is presented as well as ideas for futureresearch opportunities.22Chapter 2Control-Oriented Small Wind TurbineModellingA model is a mathematical representation of a real-world system. It is an engineering tool toenhance system understanding, facilitate design optimization and develop control peripherals.The advent of convenient simulation software for complex electrical, mechanical and thermalsystems has greatly simplified the modelling process; however, models are an abstraction ofa real-world system regardless of embedded complexity. Therefore, system models must bedeveloped and contextualized within a problem scope to determine the required fidelity tothe system of interest.For example, a comprehensive parasitic model for a neutral point clamped multi-levelinverter would be required to analyze switching harmonics. Conversely, the addition of para-sitic components to a small WT DC-DC converter model would not benefit the developmentof MPPT control techniques. The mechanical system time constants are several orders ofmagnitude larger than the settling time of the power converter; therefore, the added modelcomplexity would increase simulation time to the detriment of system level algorithm de-velopment. Consequently, useful models are those that consider the ramifications for overcomplexity and implement reasonable compromises to relate model fidelity to the problemscope.232.1. System ModelHAWTPMSG1: 3ΦR DC-DC DC-ACFigure 2.1: Small wind turbine system under study.WTs have been utilized for centuries to grind grains into flour, pump water and to gen-erate electricity. Due to their utility, they have been extensively studied and modelled tobetter understand and optimize their aerodynamics and energy transfer. However, there is anopportunity to adapt current WT models to better suit small consumer-friendly WTs. Thischapter discusses the control-oriented modelling approach used to derive a suitable systemmodel for developing small WT MPPT techniques. The mechanical subsystem is translatedto an equivalent electrical circuit. For electrical engineers, mechanical-electrical analogiesfacilitate an intuitive approach for analyzing electromechanical systems within the familiarelectrical domain. An average-value model for the electrical subsystem is introduced whichemphasizes system level control. The mechanical and electrical subsystems are combined toproduce the complete control-oriented small WT model. Additionally, the system character-istic curves are derived for a fixed wind velocity and the traditional InCond MPPT algorithmis conceptualized for small WTs.2.1 System ModelThe small WT system under study, illustrated in Fig. 2.1, is comprised of three parts: theturbine, generator and power electronics. The turbine mechanical subsystem includes a fixedpitch HAWT coupled to a permanent magnet synchronous generator (PMSG) via a speed242.1. System Modelincreaser gearbox. The variable frequency AC output from the PMSG is rectified using athree-phase diode bridge rectifier (3ΦR). A DC-DC converter interfaces with a stiff DC busand performs the direct duty-cycle MPPT. A three-phase DC-AC inverter connects with thegrid or supplies local loads and regulates the DC bus. The following sections discuss anddevelop the mechanical and electrical subsystem models, culminating in a control-orientedsmall WT model specifically tailored for increased simulation speed and development ofMPPT techniques.2.1.1 Mechanical Subsystem to Electrical Equivalent CircuitMechanical-electrical analogies are used to translate the mechanical system, typically drawnusing a free body diagram, into an electrical equivalent circuit. These analogies are beneficialwhen analyzing electromechanical systems where there is an inherent connection betweenmechanical and electrical subsystems. Small WTs convert energy from the mechanical toelectrical domain and, as such, these analogies will be used as an analysis tool.There are several techniques for modelling mechanical systems with electrical compo-nents. Each approach designates one variable as a through variable (e.g. current) and an-other as an across variable (e.g. voltage). Throughout this chapter, torque is chosen as thethrough variable and angular velocity is chosen as the across variable. The core componentsof rotating mechanical systems are inertia elements, spring elements, damper elements andgearboxes. All rotational mechanical systems can be represented using these components.Each component has an electrical circuit representation as seen in Fig. 2.2.To reiterate, the dynamic equation of the small WT mechanical system with a speedincreaser gearbox is:(JtN2gb+ Jg)· dωgdt=TtNgb− Tg −(BtN2gb+Bg)· ωg, (2.1)252.1. System ModelTi Cvi dvdtC=TddtJ=JTi Rvi vR=T B=BTi LvkINERTIADAMPER GEARBOXSPRINGT dtk= ∫ i dt1= ∫vL1:Ng12T1T2 Ideal Transformer1:v1 v2i1 i2v2 v1= Ni1 i2= N2 1= NT1 = Ngg T2Figure 2.2: Component analogies used for converting the mechanical model to an electricalequivalent circuit.where T , ω, J and B, respectively, denote the torque, angular velocity, moment of inertia andmechanical damping coefficient. The subscripts t and g, respectively, represent the turbineand generator and Ngb denotes the gearbox ratio. Using the mechanical-electrical componentanalogies in Fig. 2.2, the translated equivalent circuit is illustrated in Fig. 2.3: turbine andgenerator inertia elements are converted to capacitors, damper elements are converted toresistors and the gearbox is converted to an ideal transformer. The turbine and generatorshafts are assumed to be sufficiently stiff so as to limit the complexity of the mechanicalmodel, therefore no spring elements are required. Torque is represented as a variable currentsource and angular velocity manifests as the voltage across the capacitors.262.1. System Modelggggg Ideal TransformerMECHANICAL SYSTEM1 1 g1: g1: gggELECTRICAL EQUIVALENT CIRCUITFigure 2.3: Mechanical system translated to an electrical equivalent circuit.The aerodynamic lift forces acting on the turbine blades generate a torque about theturbine rotor shaft. This turbine torque (Tt) is a model input and is calculated based on Ptand the turbine angular velocity (ωt):Tt =Ptωt=12Aρv3w · Cp (λ)ωt. (2.2)Referring to Equation 2.1, an imbalance between the turbine and generator torques willresult in an angular acceleration. This torque imbalance will occur due to wind resourceintermittency and/or daily load variation; consequently, the turbine and generator angularvelocities increase or decrease and the system will settle at a new operating point. Modellingthe electromagnetic generator torque (Tg) is discussed in the following section.272.1. System Model2.1.2 Electrical Subsystem Average-Value ModellingThe small WT electrical subsystem includes the PMSG, 3ΦR, DC-DC converter and DC-ACinverter. There are a plethora of modelling philosophies and frameworks that can be appliedto any single component or groups of components. Each method, ranging in complexity andexactness, must be considered within the context of the problem scope so as to choose a modelthat accurately describes the system while not sacrificing simulation resources unecessarily.As the small WT subsystems bridge mechanical and electrical domains, and a MPPT control-oriented model is desired, emphasis is directed towards modelling average-value behavior forthe electrical subsystems.PMSG and 3ΦRSmall WT systems typically utilize PMSGs due to their high power-to-weight ratio, robust-ness and convenience. To reduce build and maintenance costs, 3ΦRs are utilized to convertthe generator AC output to DC. An appropriate electromechanical model of the PMSG and3ΦR subsystem is required to facilitate the analysis and control of the WT system. Ideally,the model should relate the system variables - torque (Tg), angular velocity (ωg), voltage (Vg)and current (Ig) - while maintaining the fundamental subsystem macro-dynamics. Simplifi-cations, where applicable, are considered to produce an average-value model of the subsystemsuitable for MPPT algorithm development.For an ideal and unloaded PMSG, the amplitude of the generated AC line-line voltage(VˆL) is proportional to the generator electrical angular frequency (ωe) via the generatorvoltage constant (kv):VˆL = kvωe, (2.3)282.1. System Modeland ωe is related to ωg and number of generator poles (p) by:ωe =p2ωg. (2.4)Assuming the PMSG stator phase resistance (Rg) is negligible and the capacitance (C) issufficiently large so as to ensure a voltage-stiff DC bus, the well established voltage expressionfor a three-phase diode bridge rectifier with a constant current output is:Vg =3piVˆL − 3piωeLgIg, (2.5)where Lg is the PMSG stator phase inductance. Using (2.3) and (2.4), the PMSG and 3ΦRvoltage expression can be further simplified and related to system variable ωg:Vg = keωg − kxωgIg. (2.6)The generator voltage coefficient (ke) and impedance coefficient (kx) can be easily calculatedusing parameters found on the PMSG nameplate or datasheet and the following relationships:kx =3pi· p2· Lg [Ω · s/rad] (2.7)ke =3pi· p2· kv, [V · s/rad] (2.8)Equation (2.6) is only valid when Vg is sufficiently voltage-stiff as is the case in thesmall WT system. The DC-DC converter and large DC link capacitance ensures that thecommanded voltage applied to the output terminals of the 3ΦR is maintained regardless ofa changing ωg. When utilized in this manner, PMSG and 3ΦR systems have been experi-mentally verified to exhibit a linear voltage regulation curve, as described in (2.6); therefore,292.1. System ModelCgf(   )ggggggg3ΦRPMSG3ΦRggLgRgLPMSGggCFigure 2.4: PMSG and 3ΦR equivalent circuit.this relationship can be used to derive a Theve´nin equivalent circuit for the system. Thisequivalent circuit, illustrated in Fig. 2.4, is comprised of a variable voltage source and vari-able resistance in series where both are dependent on ωg. This modelling method describesthe average-value behavior of the PMSG and 3ΦR subsystem but does not consider systemlosses or efficiency - the variable resistance represents the voltage regulation slope and doesnot dissipate any power.Mechanical and electrical losses are not considered in this model as they do not provideany valuable insights into WT MPPT control. Therefore, assuming negligible losses, theoutput electrical power is equal to the mechanical input power and a function can be derivedfor the generator torque (Tg):Tg =Pgωg=VgIgωg= keIg − kxI2g . (2.9)302.1. System ModelCLPWMdgdgggFigure 2.5: Inverted buck DC-DC converter.Tg is an input to the mechanical subsystem equivalent electrical circuit developed in Section2.1.1. This electromagnetic torque opposes the aerodynamic turbine torque as described in(2.1). The derived relationship relating Tg to Ig intuitively aligns with other generator andmotor models. Torque, when discussing electric motor or generator control techniques, isoften closely affiliated with electric current.The PMSG and 3ΦR subsystem Theve´nin equivalent circuit resembles the equivalentcircuit for a brushed DC motor albeit with variable elements. This simple circuit is intuitiveto understand and appropriately describes the subsystem average-value behavior withoutincurring unnecessary model complexity.DC-DC ConverterThe DC-DC converter is responsible for ensuring the small WT is operating at its MPP.Unlike most DC-DC power converters where the controller regulates the output voltage, theinput of the DC-DC converter is regulated to adjust the WTs operating point and perform theMPPT. An inverted buck converter, seen in Fig. 2.5, is commonly used due to its simplicity.In order to use this topology, the DC link voltage (VDC) between the DC-DC converter andDC-AC inverter must be larger than the maximum generator voltage V MAXg = keωMAXg .312.1. System ModelModern power electronics benefit from high switching frequencies and advanced con-trollers executed on exceedingly fast timescales (often within microseconds). Therefore, DCbus voltages within the electrical subsystem are tightly regulated and any minor deviationor transient will not affect the average-value behavior of the small WT.Considering the turbine mechanical time constant is several orders of magnitude largerthan the DC-DC converter settling time and assuming the DC bus capacitance (C) is large,the driven voltage (Vg) of the inverted buck converter is voltage-stiff and can be simplified toa controlled voltage source as seen in Fig. 2.5. Vg is dependent on the converter duty-cycle (d)and the DC link voltage (VDC). VDC is regulated by the grid-tie inverter and is also assumedto be voltage-stiff. A model for the DC-AC grid-tie inverter is not discussed or implementedas its behavior is not pertinent to the MPPT problem scope.2.1.3 Complete Control-Oriented Small WT ModelThe complete control-oriented small WT system, seen in Fig. 2.6, includes the wind turbine(depicted in red), the developed mechanical subsystem equivalent electrical circuit (depictedin blue), the PMSG and 3ΦR average-value model (depicted in green) and the simplifiedDC-DC converter (depicted in yellow).The wind turbine is modelled using a block diagram to calculate the turbine torquebased on (2.2). When performing simulations using the control-oriented model, the systemshould be initialized to an equilibrium state. This initialization is important as there is analgebraic loop involving ωt used in the Tt calculation. Simulating systems with inherentalgebraic loops creates a circular dependency between system outputs and inputs requiringsimulation software to solve the model at each time-step, adding computational overheadand increasing simulation time. This algebraic loop is implicit to all WT modelling methods.322.1. System ModelHAWTGEARBOXg PMSGCLPWMdggggg Ideal Transformerf(   )gdg1 1  gg1: g1: g gg( )gR2Aρa3CONTROL-ORIENTED MODELPMSG & 3ΦR DC-DC CONVERTERMECHANICAL SUBSYSTEMWIND TURBINEPMSG & 3ΦR DC-DC CONVERTERMECHANICAL SUBSYSTEMWIND TURBINEFigure 2.6: Small wind turbine control-oriented model.The wind resource, arguably the most important modelling aspect of the WT system,is often overlooked when analyzing and developing MPPT algorithms. Wind velocity, airdensity and temperature measurements are taken when performing a wind site assessment togauge whether a specific geographic location is environmentally suitable for a WT installation.These assessments average wind speed data over ten minute windows. For determiningproject financial feasibility, these averaged wind speed measurements are adequate; however,understanding wind variability is paramount to the design of small WT MPPT methodologies.Smaller WTs, with inherently less wind capture potential due to their relatively small sweptrotor areas, require MPPT controllers to adapt to turbulent or gusting wind. Without aclear picture of how the wind is behaving, system control engineers will be hard pressed todesign, tune and implement adequate MPPT controllers. Therefore, for simulation purposes,wind velocity profiles should be chosen based on wind site data available from meteorological332.2. Small Wind Turbine Characteristic Curvesassociations or research institutes - such as Environment Canada and the National RenewableEnergy Laboratory (NREL). If sufficient wind data is unavailable, arbitrary wind velocityprofiles can be generated to suit the MPPT problem scope.The mechanical subsystem equivalent circuit allows conventional circuit analysis simula-tion software to be used and facilitates an intuitive approach for analyzing electromechanicalsystems for electrical engineers. Average-value electrical subsystem models focus modellingemphasis on system macro-dynamics resulting in a small WT model tailored for MPPT al-gorithm development. This modelling method also increases simulation speed compared toconventional techniques by reducing unnecessary system complexity.The developed model facilitates the derivation of the small WT characteristic curves,further explained in the following section. Moreover, using the control-oriented small WTmodel, a novel turbine torque estimation is developed in Chapter 3 and a system impedancefrequency response analysis is performed in Chapter 4.2.2 Small Wind Turbine Characteristic CurvesThe control-oriented modelling approach allows for the small WT system to be analyzedat various steady state operating points to derive the system characteristic curves - namelypower vs voltage (Pg vs Vg) and current vs voltage (Ig vs Vg). These curves can be fur-ther analyzed to produce the absolute conductance (gDC) and incremental conductance (gac)characteristic curves for a small WT system which are utilized in traditional InCond MPPTcontrol.342.2. Small Wind Turbine Characteristic Curves2.2.1 Characteristic Curves DerivationFor a small WT system subjected to a fixed vw and operating at an arbitrary λ, a HAWTwith radius R will be rotating with angular velocity:ωt =λvwR. (2.10)Using the parameterized Cp(λ) curve, the turbine power is calculated using:Pt =12(piR2)ρv3w · Cp(λ), (2.11)and the turbine torque is found using the mechanical power relationship:Tt =Ptωt. (2.12)At steady state, the generator angular velocity and torque are related to the turbine angularvelocity and torque via the gearbox ratio:ωg = Ngbωt (2.13)Tg =1NgbTt. (2.14)Using the PMSG and 3ΦR torque equation (2.9), the output DC current (Ig) is found bycalculating the roots of the quadratic function and taking the minimum:Ig = min(roots[−kxI2g + keIg − Tg = 0]). (2.15)352.2. Small Wind Turbine Characteristic Curves0204060800123g V[ ]1/[]gMPPgac5 15 25 35 45-0.3-0.2-0.100.1gMPPgac gDC>PMPPIMPPW[]P gA[]gac gDC<ggac<0IMAXggdd=gac<0ggdd=gac>0gac>0gDCFigure 2.7: Derived small WT Pg(Vg), Ig(Vg) and g(Vg) characteristic curves for a fixed vw.Finally, the output DC voltage (Vg) is found by evaluating the PMSG and 3ΦR voltageequation (2.6) at the operating angular velocity and output current:Vg = keωg − kxωgIg. (2.16)For a fixed vw, Vg and Ig are evaluated over the entire TSR operating range: 0 ≤ λ ≤λMAX . The system output power (Pg) is calculated by multiplying Vg and Ig at each operatingpoint. The small WT Pg(Vg) and Ig(Vg) characteristic curves for a fixed wind velocity areshown in Fig. 2.7. Pg(Vg) is dependent on the turbine Cp(λ) curve and, therefore, exhibitsuniform concavity with a singular maximum power point for a fixed vw. It is also noted thatthe location of the maximum current does not coincide with the location of the maximumpower. This is also observed in PV characteristic curves.362.2. Small Wind Turbine Characteristic CurvesUsing the Ig(Vg) waveform, gDC and gac are calculated as:gDC =IgVg(2.17)gac = − dIgdVg(2.18)The small WT g(Vg) characteristic curves are shown in Fig. 2.7. Interestingly, due tothe shape of Ig(Vg), gac is negative from 0 ≤ Vg < Vg(IMAX) and positive from Vg(IMAX) <Vg < VMAXg . Moreover, gac and gDC are equal at a singular point over the entire operatingregion. This phenomenon is utilized in traditional InCond control and the following sectionderives the InCond MPP criterion for small WTs.2.2.2 Traditional InCond MPPTUtilizing the small WT characteristic curves, the traditional InCond MPPT criterion can bederived. At the MPP:dPgdVg∣∣∣∣MPP= VgdIgdVg+ Ig = 0. (2.19)Rearranging (2.19), the traditional InCond relationship arises:− dIgdVg=IgVggac = gDC .(2.20)Substituting in gac and gDC yields the following relationship at the MPP:Vg = VMPP ⇒ gDC = gac. (2.21)372.2. Small Wind Turbine Characteristic CurvesFor a WT system subjected to a constant wind speed, the MPP criterion is divided into twoconditions:(a) Vg < VMPP ⇒ gac < gDC(b) Vg > VMPP ⇒ gac > gDC .(2.22)The inverted buck converter duty-cycle must be dynamically updated in order to adjustVg to satisfy the MPP criterion described in (2.22) while the system is subjected to variablewind speeds. If the system operating point satisfies condition (a), Vg must be increased; and,conversely, if the system operating point satisfies condition (b), Vg must be decreased.To evaluate (2.22), gDC and gac must be calculated. gDC is easily determined by di-viding the measured Ig and Vg. However, calculating gac requires evaluating the derivativedIg/dVg. Traditionally, gac is estimated by injecting a fixed-step perturbation into the systemand taking the difference between two adjacent operating points. This method succumbs toaforementioned methodological pitfalls, namely power oscillations around the MPP and con-troller confusion due to changes in wind velocity. These drawbacks are addressed in Chapters3 and 4.38Chapter 3Zero-Oscillation Sensorless MPPTThe traditional InCond MPPT algorithm, discussed in the previous chapter, has severalalgorithmic disadvantages, such as power oscillations around the MPP and incurred controllerconfusion due to changes in wind velocity. These disadvantages result in an overall reductionin the system energy harvesting efficiency. In this chapter, a MPPT strategy is developedthat maintains the benefits of the traditional InCond method (computational efficiency, easeof implementation and low sensor count) and addresses its main challenges of steady statepower oscillations and incorrect algorithm decisions. The Zero-Oscillation Sensorless (ZOS)InCond algorithm determines the optimal duty cycle and then suppresses the oscillationaround the MPP. This results in: 1) elimination of algorithm confusion due to change inwind velocity, 2) accurate tracking and detection of the MPP and 3) improved steady stateefficiency. The design of the algorithm requires only electrical sensing thereby making thisMPPT method sensorless from a mechanical perspective.At steady state, the traditional InCond algorithm oscillates around the system MPPwhen subjected to a constant wind speed. This power oscillation is due to the searchingnature of the MPPT algorithm. Each duty cycle step forces a perturbation in the appliedvoltage Vg which is then used to continually probe for the MPP. Power oscillations manifestas a periodic three level quantization as seen in Fig. 3.1. The ZOS InCond algorithm rec-ognizes this oscillatory behavior and stabilizes the duty cycle at the optimal value. Systemlosses are minimized when in this operating mode and the algorithm is able to identify a39Chapter 3. Zero-Oscillation Sensorless MPPTggPgg~~ ~ ~~~ ~~tPgtΔ gΔ gΔ g~~123123ΔPgIN COND STEADYSTATETOG DETECTg~~Figure 3.1: Illustration of the traditional InCond periodic power oscillation at steady state.The Pg(Vg) and Vg(Ig) planes (left) show the small WT characteristic curves and trackingprocess. The time domain Pg and Vg waveforms (right) depict the ZOS InCond behavior: theMPP is found via InCond control then the power oscillations around the MPP are detectedand suppressed to eliminate losses in steady state.change in wind speed by monitoring the turbine torque. InCond tracking is reactivated oncea significant change in environmental conditions is observed. Redundant voltage perturba-tions contaminate tracking information; therefore, the removal of these redundancies reducesalgorithm confusion resulting in a more accurate controller.In the following chapter, the ZOS InCond strategy is presented and corroborated usingsimulation results. Experimental validation is performed using a custom Turbine EmulationPlatform (TEP).403.1. Proposed MPPT Algorithm3.1 Proposed MPPT AlgorithmThe proposed ZOS InCond MPPT algorithm implements the conventional InCond control us-ing mechanical variables and further improves the traditional method by adding functionalityto detect and suppress power oscillations at steady state. The traditional InCond algorithm,which uses current and voltage measurements, is translated to the mechanical domain andtailored for small WTs. Translating the InCond algorithm to utilize mechanical variablesrelates MPPT control decisions more closely to turbine behavior and provides an indicationof environmental conditions.3.1.1 Adapted Incremental ConductanceEstablished mechanical to electrical analogies allow for the traditional InCond algorithm tobe adapted for SWT systems, as seen in Fig. 3.2, where current is substituted with torqueand voltage is substituted with angular velocity:IV= − dIdV⇒ Tω= −dTdω. (3.1)As this modified InCond is related to turbine behavior, an estimation of the turbine torqueTt and speed ωt is required to evaluate:Ttωt= −dTtdωt. (3.2)Assuming the mechanical damping coefficient is negligible and the system inertia (Jsys) isknown, Tt can be estimated using a modified version of the small WT mechanical dynamicequation:Tˆt = Ngb(Tˆg + Jsys∆ωˆg∆t), (3.3)41Δ = 0 ΔΔ= −  Δ = 0 ΔΔ> −  Δ > 0 =  =  = + Δ   = 1 = − Δ   = -1YESNONONO NOYES YESNOYESYESIN CONDΔ = −  Δ = −  ==;RETURNMPPTAfFigure 3.2: Adapted mechanical InCond MPPT algorithm flow chart.423.1. Proposed MPPT Algorithmwhere:Jsys = Jg +JtN2gb. (3.4)The estimated generator torque (Tˆg) is calculated using (2.9) which requires a single currentmeasurement for Ig, and the PMSG and 3ΦR coefficients (ke and kx) must be determinedprior to system deployment. ωg is measured by performing a zero cross detection (ZCD) onthe generator phase voltage (Va). The measured frequency (fg) of the ZCD pulse train isthen scaled by the number of generator poles:ωˆg =2p· 2pifg. (3.5)Most industry standard DSPs are capable of performing the frequency measurement by usinga dedicated hardware core or digital input and a sufficiently fast interrupt. The ZCD pulsetrain can be generated using a Schmitt Trigger comparator circuit.The ∆ωg/∆t derivative uses the ZCD speed measurement and is evaluated at the ADCsampling frequency (fs). ωˆt is related to ωˆg by the gearbox ratio:ωˆt =1Ngbωˆg. (3.6)Using the estimated turbine torque (Tˆt) and measured turbine speed (ωˆt), shown inFig. 3.3, the MPP is found by evaluating the modified InCond algorithm illustrated in Fig. 3.2.∆Tt and ∆ωt are calculated using the previous and current operating point measurements.The system variables are not monitored between perturbation steps.Ideally, the MPPT controller update frequency (fMPPT ) would be fast enough to ensurethat the system adequately responds to variations in the wind velocity; however, as men-433.1. Proposed MPPT AlgorithmSgg gΔΔ1g2 ZCD FREQCOUNTER 2 gESTIMATIONTORQUEMEASUREMENTSPEED^^^g^a2g^fFigure 3.3: Turbine speed measurement and torque estimation used in the adapted InCondalgorithm.tioned in Chapter 2, the mechanical time constant dominates the small WT system. After aperturbation, the controller must wait a sufficient amount of time for the mechanical systemdynamics to settle before re-executing the MPPT algorithm. This is to ensure the measuredand calculated system variables, essential for accurate tracking, are representative of the truesystem operating point and not contaminated with transient dynamics.With that being said, the ZOS InCond strategy is not a framework for choosing the opti-mal MPPT controller update frequency or perturbation magnitude; instead, it addresses theredundant power oscillations at steady state and algorithm confusion inherent in traditionalHC MPPT methods. Therefore, for this application, fMPPT is chosen based on the PMSGelectromechanical time constant:TMPPT = KMPPT · RgJsysk2e(3.7)fMPPT =1TMPPT, (3.8)443.1. Proposed MPPT Algorithmwhere KMPPT is a scaling constant, Rg is the generator phase resistance and ke is the gen-erator voltage constant. fs is chosen as:fs = 100 · fMPPT . (3.9)This yielded satisfactory results in both simulation and experimental validation; however,the method for choosing fMPPT is unrefined and relies on ad-hoc tuning to achieve suitableresults. Further considerations and comments can be found in Section Power Oscillation Detection and SuppressionOnce the MPP is found, a fixed number of oscillations, called toggles, about the MPP iscounted using the algorithm described in subsystem (B) Tog Detect of Fig. 3.4. On eachMPPT controller update, the current duty cycle is either incremented or decremented by afixed amount (∆d) based on the evaluated InCond algorithm. When a change in the direction(DIR) of ∆d (positive to negative or negative to positive) is registered, the toggle counter(NTOG) is incremented and the optimal duty cycle (dMPP ) is updated. If NTOG is equal toMAXTOG (a configurable parameter which determines the maximum number of oscillationsaround the MPP) then the controller enters into Steady State (SS) and the duty cycle is fixedto d = dMPP .Once in SS, seen in subsystem (C) of Fig. 3.4, the algorithm waits for an appreciablechange in Tˆt larger than the threshold T to resume searching for the MPP using the adaptedInCond algorithm. The change in torque required to resume searching is referenced to thetorque measurement when the algorithm enters SS. This ensures the SS functionality doesnot allow |∆T | to drift with a slowly changing vw.45=  =  ∙ < 0 = + 1 =  YES NOYESNOTOG DETECT|Δ | >  Δ = −  Δ = −  ==;= 1 YESNO=  = 0 = 1 =  = 0 YESNO= (Δ ) = 0 = + Δ  ∙NORETURNYESMPPTSTEADYSTATECIN ONDACB=  == 0=fFigure 3.4: The complete ZOS InCond MPPT algorithm flow chart. Toggle detection andsteady state oscillation suppression form the core contributions of the proposed MPPT strat-egy.463.1. Proposed MPPT AlgorithmThe duty cycle perturbation magnitude (∆d) can be adjusted to suit the preferredcontroller rise time. Other tunable algorithm parameters include: MAXTOG (the maximumnumber of toggles around the MPP before the controller enters into SS) and T (the changein torque threshold to register a significant wind velocity deviation).With the exception of the Tog Detect and Steady State added behavior, the ZOS InCondstrategy operates as a HC algorithm. These additions eliminate algorithm confusion whensubjected to variable wind speeds and improve steady state harvesting efficiency while notadding considerable complexity or computational overhead.3.1.3 DiscussionAlthough the proposed MPPT method addresses several important disadvantages of con-ventional P&O algorithms, the ZOS InCond strategy does not appropriately address all ofthe shortcomings and, in some ways, the controller tuning process suffers from non-trivialramifications from the added algorithm functionality. The parameters that dictate algorithmperformance (the duty cycle perturbation ∆d, MPPT update frequency fMPPT , SS torquethreshold T and maximum number of toggles MAXTOG) all require tuning to ensure adynamic and accurate MPPT strategy. However, the degree to which each parameter canaffect algorithm behavior across the entire system operating range is often overlooked.For example, T should be chosen such that the algorithm resumes searching for theMPP after a significant change in wind speed (∆vw). Turbine power is proportional to v3wbut for a small change in vw:Pt =12AρCp (vw + ∆vw)3 (3.10)Pt = P¯t + ∆Pt =12AρCpv3w +12AρCp(∆v3w + 3vw∆v2w + 3v2w∆vw). (3.11)473.1. Proposed MPPT AlgorithmThis shows that ∆Pt and, therefore, ∆Tt are not proportional to only ∆v3w but rather theyare dependent on a cubic function consisting of both vw and ∆vw. T may be tuned forhigher wind speeds so that a desired ∆vw will trigger the algorithm to leave SS; but, at lowerwind speeds, for the same ∆vw, the measured ∆Tt will be significantly less. This could resultin delayed tracking where the algorithm is “stuck” until ∆Tt is significant enough to exitSS which would require a larger ∆vw. Ideally, T would be dynamically updated based onvw. As HC MPPT methods do not directly measure vw, a relationship could be establishedrelating T to ωt. When operating at the MPP, ωt increases linearly with vw; therefore, ωtwould serve as a good proxy for vw.Another methodological challenge is the estimation of Tt which uses the control-orientedmodel derivation for Tg and modified mechanical dynamic equation. The InCond algorithmdoes not require a significantly accurate Tg measurement and this estimation was deemedsufficient for developing the algorithm. However, the simplified angular velocity derivative in(3.3) can artificially inflate the contribution from the angular acceleration multiplied by thesystem inertia. Derivatives taken in this quantized manner are sensitive and susceptible tomeasurement noise unless proficient signal conditioning and filtering is implemented.In regards to choosing the MPPT update frequency, although unrefined, relating fMPPTto the electromechanical time constant is an attempt to correlate controller update frequencyto system dynamics. Ultimately, this resulted in a cumbersome “guess and check” tuningmethod in order to determine the optimal KMPPT coefficient. A perturbation-based MPPTmethodology is proposed in Chapter 4 that discusses practical steps for choosing fMPPTconsidering system inertia and Cp(λ).483.2. Simulation Results3.2 Simulation ResultsSimulation results highlighting the ZOS InCond MPPT strategy behavior are presented inthis section. The small WT control-oriented model, as described in Chapter 2, is simulatedusing the Plexim Plecs blockset in Simulink and the ZOS InCond algorithm is implementedusing a Matlab function block. Simulation parameter values are detailed in Table 3.1.Simulation waveforms of a HAWT system subjected to vw step responses are shown inFig. 3.5. The wind velocity vw, duty cycle d, power coefficient Cp, turbine power Pt, turbineangular velocity ωt and turbine torque Tt are plotted. The ZOS InCond algorithm correctlysearches for and detects the MPP, suppresses duty cycle oscillations around dMPP and waitsfor a sufficient change in Tt to continue tracking. The steady state behavior facilitatesa correct tracking decision and eliminates algorithm confusion due to the change in windvelocity. The shaded red area of the Cp and Pt waveforms designates unharvested energy dueTable 3.1: ZOS InCond Simulation System ParametersParameter Value UnitsMechanical SystemJt 1 kg m2Jg 0.02275 kg m2Bt 10−6 N m s rad−1Bg 10−6 N m s rad−1Ngb 5 -Turbine SystemR 2 mA 12.56 m2ρ 1.225 kg m−3Coptp 0.48 -λopt 8.1 -Parameter Value UnitsElectrical Systemke 2.887 V s rad−1kx 0.0565 Ω s rad−1p 10 -VDC 600 V- -MPPT Algorithm∆d 0.02 -T 3 N mMAXTOG 4 -KMPPT 110 -fMPPT 3.024 Hz497911 [ %]   [] 15 20 252460 5A CORRECTDECISIONC STEADYSTATEB TRACKMPP [/ ] 2503504504080120  [] []  ^^t ]]s   Figure 3.5: Simulated waveforms of the wind velocity vw, duty cycle d, power coefficientCp, turbine power Pt, turbine angular velocity ωt and turbine torque Tt subjected to windvelocity step responses. The vw profile begins at 7m/s, at t = 5s vw steps up to 11.5m/s andthen steps down to 9m/s at t = 17s.503.2. Simulation Results [ %]  56780.50.60.7343842480.511.50.40 2 4 6 8 10 []   [/ ] POWER OSCILLATIONINCORRECT DECISIONENERGY LOSSMPPT WIND UPTrad InCondZOS InCondt ]]sCORRECT DECISIONTRACKMPPSTEADYSTATEFigure 3.6: ZOS InCond strategy versus traditional InCond MPPT.to tracking error compared to the MPP. The simulated waveforms are segregated into colorscorresponding to the ZOS InCond MPPT algorithm subsystems. Referring to the algorithmflow chart in Fig. 3.4, blue signifies the adapted InCond algorithm, orange signifies the TogDetect behavior and green signifies the algorithm is in Steady State.To emphasize the ZOS InCond improvements over the traditional InCond method, acomparative simulation is run where both MPPT methods control the same small WT systemand are subjected to the same wind velocity profile. As seen in Fig 3.6, it is evident that, fortraditional InCond, the power oscillations at steady state influence unfavorable and incorrect513.3. Experimental Validationalgorithm decisions that results in a significant deviation from the MPP. Due to the confusion,the system operating point is pushed in the wrong direction for a number of update cycles andthe tracking efficiency decreased by 6% for the situation illustrated in Fig 3.6. This trackingwind up is a characteristic flaw for all traditional HC based MPPT methods. The MPPTsimulation comparison verifies that the proposed ZOS InCond strategy addresses traditionalInCond deficiencies.3.3 Experimental ValidationExperimental validation for WT MPPT algorithms poses certain logistical and technicalchallenges. Small WT blade diameters can range from less than one meter to more thanten meters. Prior to large-scale manufacturing, prospective WT designs can be deployed attest sites with sophisticated environmental, mechanical and electrical sensors to observe theoperating behavior. However, wind resources are notoriously intermittent and uncoopera-tive; therefore, due to turbine size and wind variability, alternative validation methods arerequired. Simulation and design software are useful tools, but final system commissioningmust be done using a physical manifestation. An intermediary testing approach between sim-ulation software and a full-scale prototype are emulation platforms. This section discussesthe use of a turbine emulation platform to experimentally validate the ZOS InCond MPPTstrategy.3.3.1 EmulatorsEmulators have been used extensively in microgrid development as they are lab friendlyinfrastructure that can mimic the behavior of distributed generation sources, energy storagesystems and load elements. Emulation platforms utilize software to evaluate system modelsand a hardware layer to output system variables in real-time. As such:523.3. Experimental Validation• An emulator can represent an impressive range of possible loading and environmentalconditions• Using an emulator negates the risk of damaging costly large-scale microgrid setups• An emulator allows long time duration experiments to be run in a reduced time period• The spatial footprint associated with emulators is significantly less than their real-worldcounterpartFor these reasons, emulators are a vital tool that can be implemented to test different aspectsof system control, robustness and efficiency while reducing testing costs.An ideal emulation platform used for testing distributed generation sources, energy stor-age systems or entire microgrids would perfectly emulate the real-world system in both steadystate and dynamic response. Real-world systems can be modelled using fundamental systemvariables (e.g. voltage, current, velocity, torque, force, etc.) to describe system behavior.Emulators use a software layer to simulate the modelled system output based on user con-figurable loading and environmental conditions. At each simulated time step, the emulatorhardware layer controls the interfacing equipment to update the operating point and adjustthe system variables. This hardware layer can take the form of a power converter or electricmotor to emulate the desired real-world system.Emulation platforms have proven useful in testing microgrid energy management, powerconverter dynamic control functionality as well as high-level system control algorithms suchas MPPT. As emulators utilize circuit protection and embedded safety protocols, they avoidcostly damage to power converters and expensive real-world systems. Successive experimentscan be run with high repeatability and frequency to monitor converter control, efficiency androbustness. Hardware and software costs to implement an emulator capable of simulatinglarge-scale microgrids are typically lower than the real systems.533.3. Experimental ValidationAlthough advancements in system modelling have resulted in emulators with high accu-racy, the dynamic behavior of the emulator will not exactly mimic the real system. Systemmodelling requires approximations and linearization of high order differential equations whichin turn reduces the accuracy of the model. Moreover, communication bandwidth and hard-ware control limits will also affect the emulators ability to imitate real system transientdynamics at small time scales.3.3.2 Turbine Emulation PlatformExperimental validation of the proposed MPPT algorithm is presented using a developedturbine emulation platform (TEP). The TEP, seen in Fig. 3.7, utilizes a Magtrol torque andspeed sensor, Opal-RT hardware-in-loop (HIL) simulator and WEG CFW-11 voltage sourceinverter (VSI) to control a 5.5kW WEG induction motor (IM) which emulates the torqueprofile of a small WT.The Opal-RT HIL simulator is programmed with the small WT model. This model in-cludes the turbine power coefficient curve, power calculation and mechanical system dynamicsin order to generate a turbine torque reference. More explicitly, the HIL simulator:1. Calculates the turbine power output based on the user configured wind velocity profile2. Generates a turbine torque reference for the system operating point3. Implements inertial compensation to adjust for the discrepancy between the emulationplatform inertia and turbine system inertia4. Outputs an analog voltage torque reference signal T ∗IMThis torque reference is passed to the VSI which uses vector control to adjust the IM torque.Fundamentally, the IM will spin at the same speed as a small WT subjected to the specified543.3. Experimental ValidationMASTERCONTROLVECTORCONTROLPWMtPMSGINDUCTION MOTOR TORQUE &SPEED SENSORVOLTAGE SOURCE INVERTER WIND VELOCITY PROFILEGRID3ΦR DC-DCggIM*OPAL-RT HILGRIDIMVSIOPAL-RT HILPMSGggPMSG & 3ΦR DC-DC CONVERTERTURBINE EMULATION PLATFORMCLPWMdggIM*Figure 3.7: Turbine emulation platform experimental setup.environmental conditions. The torque and speed sensor are used to measure the systemoperating point and feed them back to the HIL model.Once properly configured, the TEP facilitates the development and testing of small WTspecific hardware and control algorithms. A Leeson 5.5kW PMSG and custom MPPT powerelectronics are connected to the TEP. Essentially, the equipment connected to the TEPwill behave as though they are connected to a small WT. An industry-standard TI C2000microcontroller is employed to perform the analog to digital conversion of the measured553.3. Experimental Validationvoltage and current, generate the PWM switching signals to drive the DC-DC converter anddigital processing to execute the ZOS InCond MPPT algorithm.Due to the discrepancy between the small WT system and TEP inertias, software basedinertial compensation must be implemented in order to ensure the correct transient behaviorand preserve the small WT mechanical dynamics. Assuming negligible damping, the TEPmechanical dynamic equation is:(JIM + Jg)dωgdt= TIM − Tg, (3.12)where JIM and TIM , respectively, are the IM inertia and torque. Similarly, once againassuming negligible damping, the small WT mechanical dynamic equation is:(JtN2gb+ Jg)dωgdt=TtNgb− Tg. (3.13)To emulate the turbine mechanical dynamics, the following relationship must be satisfied:TIM − TgJIM + Jg=dωgdt=TtNgb− TgJtN2gb+ Jg. (3.14)Rearranging the above relationship to solve for TIM yields the inertial compensated torquereference for the TEP (T ∗IM):T ∗IM =(JIM + JgJtN2gb+ Jg)· TtNgb+(1− JIM + JgJtN2gb+ Jg)· Tg. (3.15)563.3. Experimental ValidationTg is measured by the Magtrol torque sensor and used in (3.15). The measured generatorspeed and user defined wind velocity profile is used to calculate Tt based on (1.4). A blockdiagram of the Tt calculation is shown in Fig. 1.5. The IM torque is assumed to track theT ∗IM reference; however, in actuality, the VSI vector control includes internal bandwidthlimitations set by the manufacturer that cannot be overridden. Although it could not beproperly tuned for optimal performance, the TEP serves as a valid and useful tool to developand test small WT MPPT strategies.3.3.3 Experimental ValidationThe TEP is configured to use the same simulation parameters as described in Table 3.1.A duty cycle perturbation ∆d of 3.5% and update period TMPPT = 2s were found to yieldsatisfactory results. This larger update time, compared to the simulated controller, is to allowfor the TEP system dynamics to settle before evaluating the ZOS InCond algorithm. Due tothe torque and speed sensors proximity to the VSI, IM and PMSG, significant electromagneticinterference necessitated the use of digital low pass filters implemented in the HIL simulator.This heavy filtering also contributed to the reduced update frequency of the MPPT controller.Experimental results are shown in Fig. 3.8. The measured generator voltage Vg is propor-tional to the converter duty cycle and serves as an indicator for the ZOS InCond algorithm.Similar to the simulation figure, the experimental figure is segregated into colors based on theMPPT behavior. To reiterate, blue signifies the adapted InCond algorithm, orange signifiesthe Tog Detect behavior and green signifies the algorithm is in Steady State.The TEP is subjected to a wind velocity step response to illustrate the ZOS InCondbenefits and validate the strategies simulated behavior. vw begins at 3.75[m/s] and steps upto 5[m/s] at t = 70s. The experimental captures match the simulated results and the benefitsof the ZOS InCond are evidently illustrated in Fig. 3.8. The Vg and Pt waveforms exhibit573.544.553035404550200300400500[ ]gY2Y112016020040 50 60 70 80 90 10012162024 [ %]   []   [/ ]  []    []t ]]s   B TRACKMPPA CORRECTDECISIONC STEADYSTATEFigure 3.8: Experimental waveforms of the wind velocity vw, measured generator voltage Vg,power coefficient Cp, turbine power Pt, turbine speed ωt and turbine torque Tt subjected toa wind velocity step response. The vw profile begins at 3.75m/s and, at t = 70s, vw steps upto 5m/s. The waveforms are segregated into colors based on MPPT algorithm behavior.583.4. Summarythe tell-tale periodic three level quantization of perturbation-based MPPT. The ZOS InCondalgorithm determines the optimal duty cycle and then suppresses the oscillation around theMPP which facilitates the elimination of algorithm confusion due to variable wind speed andimproves steady state energy harvesting efficiency.3.4 SummaryThe theory and validation of the ZOS InCond MPPT strategy for small WT systems waspresented in this chapter. The conventional InCond algorithm was translated to the mechan-ical domain and adapted for small WT MPPT using a novel turbine torque estimation basedon the control-oriented modelling technique.To summarize, the ZOS InCond algorithm determined the optimal duty cycle using theadapted InCond algorithm and suppressed the power oscillations around the MPP. This re-sults in: 1) elimination of algorithm confusion due to change in wind velocity, 2) accuratetracking and detection of the MPP and 3) improved steady state efficiency. The algorithmdesign requires only electrical sensing thereby making this MPPT method sensorless from amechanical perspective. These additional features augment the conventional InCond algo-rithm to create a more reliable and efficient MPPT strategy.The proposed algorithm behavior was simulated and verified using the control-orientedsmall WT model discussed in Chapter 2. A turbine emulation platform was developed totest and validate the ZOS InCond strategy through experimental results.The ZOS InCond strategy was developed to learn about and incrementally improve uponHC MPPT algorithms tailored for small WTs. These insights proved incredibly helpful in thedevelopment of a comprehensive MPPT methodology, further discussed in Chapter 4, thataddresses all major disadvantages of perturbation-based MPPT strategies for small WTs.59Chapter 4System Identification MPPTIn this chapter, a novel small WT MPPT framework is developed utilizing a lock-in amplifier(LIA), small WT equivalent circuit and a real-time system identification (SysID) algorithmto address all aforementioned HC MPPT shortcomings without incurring increased hard-ware requirements. The LIA is a digital signal processing (DSP) technique that performsa frequency response analysis at programmable operating points. LIAs have been used inthe past to identify parameters in electrochemical, electromagnetic, electromechanical andelectrical systems. Using the LIA and the developed control-oriented small WT model, asystem impedance frequency response analysis is performed and an equivalent circuit for thesmall WT system is derived. Utilizing the SysID algorithm, the small WT system equivalentcircuit parameters are calculated in real-time and the system operating point is adjusted us-ing an integral controller to facilitate adaptive step functionality. This control method lockson to the MPP and is less susceptible to algorithm confusion compared to traditional HCMPPT methods.The proposed MPPT methodology offers three key advantages over conventional MPPTmethods: 1) accurate tracking when subjected to highly variable wind speeds, 2) optimalMPPT is guaranteed over the system lifetime even through degradation, maintenance andretrofitting and 3) a systematic approach for choosing the MPPT update frequency, facilitatedby a system impedance frequency response analysis. Simulation and experimental results arepresented in Sections 4.2 and 4.3 respectively.604.1. Proposed MPPT Algorithm4.1 Proposed MPPT AlgorithmTo extract more real-time information from the small WT system without using additionalmechanical or environmental sensors, a fixed frequency sinusoidal perturbation is injected viathe DC-DC converter duty-cycle. This small-signal sinusoidal perturbation is used to inferinformation about the small WT system operating point as opposed to using a fixed stepperturbation like traditional P&O and InCond algorithms.Section 4.1.1 discusses the use of two LIAs to extract the small-signal amplitude fromVg and Ig in order to estimate the system incremental impedance (Z) at the perturbationfrequency (fp). Utilizing the Z measurement, a system impedance frequency analysis ispresented in Section 4.1.2. The impedance frequency analysis forms the foundation of theSysID MPPT methodology which ensures practical steps are taken to determine fp andMPPT controller update frequency (fMPPT ).A small WT system equivalent electrical circuit is derived from the impedance bode plotanalysis and, due to the nature of the equivalent circuit, a SysID algorithm is proposed inSection 4.1.3 to increase fMPPT and facilitate dynamic tracking.To implement the MPPT controller in real time, the LIA impedance extraction methodand a SysID algorithm are utilized to estimate gac. A Moving Average Filter (MAF) isapplied to Vg and Ig to extract their average values and calculate gDC . Once the estimatedincremental conductance (gˆac) and estimated absolute conductance (gˆDC) are calculated,an integral controller is employed to ensure their difference is zero and the MPP criterion,described by (2.22), is satisfied. The utilization of the integral controller facilitates variablestep functionality and excellent dynamic control. Further details of the MPPT controller aregiven in Section Proposed MPPT Algorithmt kTsppMAFMAF22ADCLPFANALOG DIGITAL FILTERINGLIAx(k)x m)-(kxx(t)MAFA~A~dA~qxdxqFigure 4.1: Block diagram of the implemented MAF and LIA subsystems for extracting.4.1.1 Lock-In AmplifierThe sinusoidal perturbation injected into the converter duty-cycle manifests as a small-signalcomponent in Vg and Ig. The gˆac measurement utilizes the digital LIA, seen in Fig. 4.1, toextract the small-signal voltage and current amplitude at fp. To maintain generality, x(t)denotes the LIA input signal:x(t) = x¯(t) + A˜ sin(ωpt+ θ), (4.1)where x¯ is the band-limited low frequency component and A˜ is the amplitude of the small-signal component at fp (ωp = 2pifp). Applying an anti-aliasing low-pass filter (LPF) andthen sampling the signal with a period Ts, x(t) in the discrete domain, is given by:x(k) = x¯(k) + A˜ sin(ωpkTs + θ). (4.2)624.1. Proposed MPPT AlgorithmThe discretized signal x(k) is then multiplied by sine and cosine functions to produce thedirect and quadrature components (denoted by the d and q subscripts) as seen in Fig. 4.1:xd(k) = x(k) · sin(ωpkTs)= x¯(k) sin(ωpkTs)+12A˜ cos(θ)− 12A˜ cos(2ωpkTs + θ)(4.3)xq(k) = x(k) · cos(ωpkTs)= x¯(k) cos(ωpkTs)+12A˜ sin(θ) +12A˜ sin(2ωpkTs + θ).(4.4)The output of the sine and cosine multiplication has three components: a DC componentproportional to A˜ and two AC components with angular frequencies ωp and 2ωp. As xd andxq are still contaminated with AC components of known frequencies, a MAF, illustrated inFig. 4.1, is applied to extract the average value of the direct and quadrature components:xd =12A˜ cos(θ)xq =12A˜ sin(θ).(4.5)The MAF exhibits high selectivity, excellent noise immunity and can be easily implementedusing a DSP to filter out the unwanted sinusoidal contributions. After filtering the directand quadrature components using the MAF, the small-signal component amplitudes arecalculated as:A˜d = 2xd = A˜ cos(θ)A˜q = 2xq = A˜ sin(θ).(4.6)634.1. Proposed MPPT AlgorithmWith A˜d and A˜q, the total small-signal amplitude is calculated as:|A˜| =√A˜2d + A˜2q =√(A˜ cos(θ))2+(A˜ sin(θ))2, (4.7)and the phase shift is:θ = tan−1(A˜qA˜d). (4.8)The LIA is implemented to extract the small-signal amplitude and phase shift from asignal of interest with a small-signal component of a known frequency (in this particular casethat frequency is fp). The output of the LIA can be represented using vector notation asboth the direct and quadrature axes are 90◦ apart. Polar notation seen in (4.9) or Cartesiancomplex number notation seen in (4.10) can be used; however, the tan−1 operation to cal-culate the phase shift can be inconvenient to implement on a DSP, therefore the Cartesianrepresentation is preferred.~˜A(fp) = |A˜|∠θ (4.9)~˜A(fp) = A˜d + jA˜q. (4.10)Implementing two LIAs, one for Vg and one for Ig, yields two small-signal amplitude vectors:~˜Vg(fp) = V˜d + jV˜q~˜Ig(fp) = I˜d + jI˜q.(4.11)The output from the voltage and current LIAs is then used to calculate the incrementalimpedance (Z) at fp by dividing~˜Vg and~˜Ig:Z(fp) =~˜Vg(fp)~˜Ig(fp)=V˜d + jV˜qI˜d + jI˜q. (4.12)644.1. Proposed MPPT Algorithm10-3 10-2 10-1 100 101f ]]Hz-3-2-100246R]]X]]fpLOW FREQUENCY MEDIUM FREQUENCY HIGH FREQUENCYR fp( )X fp( )Figure 4.2: Re(Z) and Im(Z) bode plot of the small WT system for λ = λopt and vw = 6m/s.This vector division can be simplified to facilitate implementation on a DSP:Re(Z) = R(fp) =V˜dI˜d + V˜q I˜qI˜2d + I˜2q[Ω] (4.13)Im(Z) = X(fp) =V˜q I˜d + V˜dI˜qI˜2d + I˜2q, [Ω] (4.14)where R(fp) and X(fp) denote the resistive and reactive components of the impedance mea-sured at fp, as seen in Fig. 4.2. It is important to note that the application of the voltageperturbation results in an oscillation in the turbine angular velocity. The magnitude of theangular velocity oscillation, and the resultant oscillation in the output current, is relatedto the system operating point (λ, vw); therefore, the measured incremental impedance canbe related to the small WT characteristic curves and perform MPPT based on the InCondcriterion.654.1. Proposed MPPT AlgorithmDuring normal MPPT operation, fp remains fixed and the incremental impedance mea-surement is used to calculate gac. However, in Section 4.1.2, fp is swept across a frequencyrange to analyze the theoretical impedance frequency response.4.1.2 System Impedance Frequency ResponseUsing simulations, a theoretical impedance bode plot, seen in Fig. 4.2, is constructed for thesmall WT system by sweeping fp across a frequency range and extracting R(fp) and X(fp).As illustrated in Fig. 4.3, the impedance behavior is consistent when analyzed over the entireTSR operating region (0 ≤ λ ≤ λMAX) and across the operating wind velocities.Due to the consistent impedance behavior, a Theve´nin equivalent circuit, shown inFig. 4.4, is derived for the system based on the impedance bode plots. The equivalentimpedance contains contributions from the small WT subsystem (rT and CT seen in Fig. 4.4denoted in red) and the PMSG and 3ΦR subsystem (rG seen in Fig. 4.4 denoted in green).The parameters of the equivalent circuit (rG, rT , CT and VWT ) are all variable anddependent on the system operating point (λ, vw) necessitating the real-time aspect of theSysID further discussed in Section 4.1.3. The equivalent impedance expressed in standardform is given by:Z(jω) = (rT + rG)1 +jω(rT+rGrGrTCT)1 +jω(1rTCT), (4.15)6632106420642010-310-210-1100101f ]]HzW[ ]Pg040801201604 8 120Z ]]| |= 4 /s[ ]m= 10CTrTrG ===0.4026.525300 mFCTrTrG ===0.4836.230345 mFCTrTrG ===0.483-4.195590 mF= 8 /s[ ]m = 6= 6 /s[ ]m= 8Figure 4.3: System impedance frequency response across the entire operating region. Thesystem impedance is consistent, therefore an equivalent circuit can be deduced for the smallWT system. Interestingly, for λ < λopt, the equivalent circuit parameter rT is negative. Thisis due to the concave nature of the Pg(λ) curve.CTrTVWTrGdggSMALL WT PMSG & 3ΦR CFigure 4.4: Small WT system equivalent circuit. The consistent impedance frequency re-sponse behavior allows for an equivalent circuit to be derived.674.1. Proposed MPPT Algorithmand:Re(Z) = R(ω) =rT + rG(1 + (rTCTω)2)1 + (rTCTω)2(4.16)Im(Z) = X(ω) =−r2TCTω1 + (rTCTω)2. (4.17)The swept frequency range is divided into three distinct regions: low frequency (fL, ωL),medium frequency (fM , ωM) and high frequency (fH , ωH). As seen in Fig. 4.2, X(f) onlycontributes to the impedance magnitude within the medium frequency region; otherwise,X(fL) = X(fH) ≈ 0. Similarly, R(f) is constant in the low and high frequency regions:Z(fL) = R(fL) = rT + rG (4.18)Z(fH) = R(fH) = rG. (4.19)The inertia of the mechanical subsystem manifests as a capacitor CT in the derivedequivalent circuit. Relating the physical response of the small WT to the equivalent circuit,several interesting observations can be made about the system behavior when subjected toa sinusoidal perturbation:• At high perturbation frequencies (fp = fH), the applied voltage perturbation is unableto affect the turbine angular velocity due to the system inertia. At these frequenciesCT behaves as a short circuit and the total impedance is equal to the contribution fromthe PMSG and 3ΦR subsystem (Z = rG).• At low perturbation frequencies (fp = fL), the turbine angular velocity changes in phasewith the slow voltage perturbation. At these frequencies CT behaves as an open circuitand the total impedance is equal to the contribution from the small WT subsystemand PMSG and 3ΦR subsystem (Z = rT + rG).684.1. Proposed MPPT Algorithm• For perturbation frequencies within the medium frequency region (fp = fM), the tur-bine angular velocity oscillates due to the applied voltage perturbation; however, thereis phase delay between the voltage perturbation and turbine speed oscillation due to thesystem inertia. At these frequencies CT contributes to the total impedance accordingto (4.15).The mechanical ramifications of applying a voltage perturbation to the small WT areintuitively conceptualized by the equivalent circuit. Moreover, the impedance frequencyresponse analysis incorporates contributions from the system inertia, PMSG and 3ΦR andCp(λ) curve. All of these aspects will influence the maximum attainable fp and fMPPT for aspecific small WT system and must be considered when tuning these parameters.The practice of maximizing power transfer from an electrical source to a load is calledimpedance matching. For DC systems, such as the small WT system when analyzed using itsTheve´nin equivalent circuit, this condition is satisfied when the load resistance (rDC = Vg/Ig)is equal to the source resistance (rac = rT + rG). Fundamentally, the InCond algorithm isactively adjusting the load resistance to match the source resistance which changes dependingon λ and vw. Therefore, to evaluate the InCond MPP criterion, both rT and rG must bedetermined as:gac =1rac=1rT + rG=1R(fL). (4.20)Through the impedance frequency response analysis, rG is identified to be related to thePMSG and 3ΦR control-oriented model. Calculating kx prior to system deployment and bymeasuring the generator angular velocity (ωˆg) in real time, rG is estimated as:rˆG = kxωˆg. (4.21)694.1. Proposed MPPT AlgorithmOne method to measure R(fL) would be to set fp ≤ fL; however, this would result inan extremely slow MPPT controller update frequency. Section 4.1.3 discusses the use of aperturbation frequency within the medium frequency range and the SysID algorithm requiredto estimate R(fL) using a Z(fM) impedance measurement.4.1.3 System IdentificationTo achieve a suitable controller update frequency, the use of a fp within the medium frequencyrange is required. Using the LIA method to measure the system impedance at fp and thederived equivalent circuit from the previous section, a system of three equations can becreated to determine expressions for rT and CT :1 R(ωp) =rT + rˆG(1 + (rTCTωp)2)1 + (rTCTωp)22 X(ωp) =−r2TCTωp1 + (rTCTωp)23 rˆG = kxωˆg,(4.22)where ωp is known, R(ωp) and X(ωp) are measured and rˆG is estimated using the measuredωˆg as seen in Fig. 4.5. Similar to the ZOS InCond strategy, ωˆg is determined by performinga zero cross detection (ZCD) on the PMSG phase voltage (Va). The output of the ZCDcircuit is fed into a frequency counter (FC) where the measured frequency (fˆg) is scaled bythe number of generator poles (p) as follows:ωˆg =2p· 2pifˆg. (4.23)704.1. Proposed MPPT AlgorithmdgZCD FCgMAFLIALIASysIDMAFMAFCggDCgacSWT & PMSG 3ΦR CONVERTERfs fMPPTaI(z)SysID  MPPTZ fp( )fp^^^Gr^Figure 4.5: Block diagram of the SysID MPPT method.Solving (4.22) yields the following expressions forrˆT and CˆT :rˆT =X(ωp)2R(ωp)− rˆG +R(ωp)− rˆG (4.24)CˆT =√rˆT + rˆG −R(ωp)(R(ωp)− rˆG)(rˆTωp)2 . (4.25)The system InCond can be estimated using (4.24):gˆac = (rˆT + rˆG)−1 =(X(ωp)2R(ωp)− rˆG +R(ωp))−1. (4.26)This SysID algorithm is only valid when using a perturbation frequency within the mediumfrequency range. As this range is dependent on the particular system, an impedance frequencyanalysis must be carried out on a case-by-case basis. The maximum fp is determined as the714.1. Proposed MPPT Algorithmboundary between the medium and high frequency regions of the system impedance bodeplot. Practically, fp is chosen within the medium frequency region based on the small-signalvoltage and current amplitudes and the sensing hardware capabilities. fMPPT is chosen tobe less than or equal to fp.Using the small WT control-oriented model, a sensitivity analysis can be performedto determine how the impedance frequency response changes based on important systemparameters (system inertia, generator impedance and voltage coefficients and the turbineCp(λ) curve). Based on this sensitivity analysis, an optimal fp and fMPPT can be choseneven if the exact parameter values are unknown. The impedance frequency response analysisforms the foundation of the SysID MPPT methodology which ensures practical steps aretaken to determine fp and fMPPT .4.1.4 MPP ControllerOnce gˆac and gˆDC have been calculated, the MPPT controller adjusts the duty-cycle toregulate the difference between the conductances to zero and satisfy the MPP criterion. Theintegral controller I(z), seen in Fig. 4.5, takes the form:d¯(n+ 1) = d¯(n) +KI (gˆDC(n)− gˆac(n)) , (4.27)where d¯(n) is the discrete MPP duty-cycle at step n and KI is the integral coefficient. Asmall sinusoidal perturbation is added to d¯(n) with an amplitude D˜ and frequency fp. Theresulting duty-cycle is given by:d(k) = d¯(n) + d˜(k)= d¯(n) + D˜ sin(ωpkTs).(4.28)724.2. Simulation Resultsd¯(n) is updated at the MPPT update frequency, whereas d˜(k) is updated at the samplingfrequency (fs  fp) to ensure a smooth perturbation signal with limited harmonics. D˜ mustbe chosen to yield a significant enough perturbation in Vg and Ig to ensure the small-signalmagnitude can be extracted by the LIAs. This is dependent on the ADC resolution andsignal conditioning circuitry used. The integral coefficient KI can then be tuned to yield thedesired dynamic response and settling time.To summarize, the SysID MPPT method utilizes MAFs, LIAs and the derived SysIDalgorithm to accurately calculate the system incremental and absolute conductances. Anintegral controller I(z) facilitates adaptive step functionality with zero steady-state errorwhile ensuring dynamic control.4.2 Simulation ResultsThis section presents simulation results of the SysID MPPT strategy controlling a smallHAWT subjected to a highly variable vw profile. Furthermore, an energy efficiency compar-ison of the SysID, ZOS InCond and traditional InCond MPPT algorithms subjected to thesame variable vw profile is also presented. The comparative metrics indicate the superior gˆacestimation of the SysID algorithm is able to lock on to the system MPP more effectively thanboth the ZOS and traditional InCond methods resulting in a higher harvesting efficiency.System simulation parameter values are detailed in Table 4.1. The parameters are chosenbased on a characterized HAWT that is used in the experimental validation detailed in Section4.3. The control-oriented small WT model and the MPPT algorithms are simulated usingthe Plexim Plecs blockset and Simulink.The simulated waveforms, depicted in Fig. 4.6, include the generator power Pg, converterduty-cycle d, estimated incremental and absolute conductance (gˆac and gˆDC) and turbine734.2. Simulation ResultsTable 4.1: SysID MPPT Simulation System ParametersPARAMETER VALUE UNITSTurbine SystemCoptp 0.48 -λopt 8.1 -R 0.63 mA 1.247 m2ρ 1.225 kg m−3Mechanical SystemNgb 1 -Jt 0.0298 kg m2Bt 10−6 N m s rad−1Jg 6.16e-04 kg m2Bg 10−6 N m s rad−1PARAMETER VALUE UNITSPMSG & 3ΦRke 0.3126 V s rad−1kx 6.31e-03 Ω s rad−1p 12 -VDC 55 V- - -MPP ControllerfMPPT 0.2 Hzfp 0.5 Hzfs 32 HzKI 0.4 -D˜ 0.01 -power coefficient Cp. Typically, WTs are located in regions with consistent wind speedsthat change on seasonal, diurnal and turbulent time scales. The simulated wind profile isan extremely turbulent case chosen to emphasize the effectiveness of the presented SysIDMPPT methodology. The system is initialized to λ = 5 and subjected to the wind velocityprofile vw(t). vw(t) is an amalgam of three sinusoidal functions of varying amplitudes andfrequencies (seen in Table 4.2):vw(t) = 7 +3∑i=1Ai sin(ωit). [m/s] (4.29)Table 4.2: SysID MPPT Wind Velocity Profile Parametersi 1 2 3Ai 1.2 0.9 0.6ωi 0.1267 0.1885 0.377074gacgDC^^W[]P01002003000.30.40.5-0.6-0.20.2-0.400. 40 60 80 100 120 1400 1601/[]gdd~d_+d(t)= dΔ =KI gDC gac-( )_t ]]sPgPMPP  Figure 4.6: Simulation results utilizing the SysID MPPT method for controlling a small WTsystem subjected to a highly variable wind profile. The generator power (Pg), duty-cycle (d),incremental conductance (gac), absolute conductance (gDC) and turbine power coefficient(Cp) are plotted.754.2. Simulation ResultsTo illustrate the dynamic control nature of the proposed method, the system is subjectedto the worst case scenario at start up: the initial λ < λopt and an increasing vw will pushλ further away from the optimal TSR. The SysID algorithm takes one update period tocalculate and lock on to gˆac and gˆDC . In four update periods the controller has successfullydriven the system to the MPP. The duty-cycle is continuously updated to satisfy the MPPcriterion with zero tracking confusion even under the volatile wind velocity profile.Fig. 4.6 serves as a qualitative indicator for the compelling performance of the SysIDalgorithm. However, quantitative metrics are beneficial when comparing the performancebetween different MPPT options. Therefore, the SysID, ZOS InCond and traditional InCondalgorithms are simulated using the same HAWT system, initial conditions and wind velocityprofile described in (4.29). The energy harvesting efficiency (η) of each algorithm as wellas the average efficiency (ηAV G) over the entire simulation is plotted in Fig. 4.7. All MPPTspecific parameters are detailed in Table 4.3. The efficiency plot is calculated as η = Pg/PMPPwhere PMPP is the maximum available power. The SysID algorithm has a perturbationfrequency of 0.5Hz and a slower MPPT update frequency of fMPPT = 0.2Hz is required dueto the SysID gˆac estimation method. The ZOS and traditional InCond algorithms have aMPPT update frequency of 0.5Hz (over twice as fast as the SysID method) due to theirsimplified gˆac calculation.The average energy harvesting efficiency for the traditional InCond algorithm is ap-proximately 80%. This competent performance, and its simple implementation, is why thetraditional algorithm is still utilized for consumer small WT installations. Implementing theadapted ZOS InCond, the harvesting efficiency increased by 3.4% compared to the traditionalmethod. The SysID methodology yielded the highest harvesting efficiency of 89.5% - a 9.5%increase in efficiency compared to the traditional InCond algorithm. This comparison clearlyindicates the benefits of the SysID strategy.7610080604020002550751000255075100t ]]sηAVG= 89.5%ηAVG= 80%0255075100Efficiency%[]SysIDZOS InCondTrad InCondηAVG= 83.4%Figure 4.7: MPPT algorithm performance comparison.Table 4.3: MPPT Algorithm ParametersSysIDfMPPT 0.2 Hzfp 0.5 Hzfs 32 HzKI 0.4D˜ 0.01ZOS InCondfMPPT 0.5 HzKMPPT 110∆d 0.04T 0.1 N mMAXTOG 3Trad InCondfMPPT 0.5 Hz∆d 0.04- -- -- -774.3. Experimental Validation4.3 Experimental ValidationTo corroborate the simulated Pg(Vg), Ig(Vg) and g(Vg) curves as well as the validity of theSysID MPPT method presented in this paper, an experimental platform was constructed.This platform, seen in Fig 4.8, is comprised of five industrial fans driving a HAWT withparameters listed in Table 4.1. The Cp(λ) curve for the HAWT under test is shown inFig. 4.9. To minimize design and manufacturing costs, small WT blades are not optimallydesigned to maximize aerodynamic lift and, consequently, Coptp for small WTs is typically lessthan utility-scale WTs. Coptp for the small WT under test is calculated to be approximately21% with a λopt ≈ 7.1.Moreover, due to the inherently small rotor diameter, small WTs require a larger windvelocity to generate useful amounts of electrical power. A common marketing misconceptionused by manufacturers is to advertise their turbine with a rated power at an exceptionallyhigh wind speed. Most locations with a favorable wind resource have an average wind speedof 5− 8m/s, whereas most small WTs are advertised for a rated wind speed of 10− 14m/s.For perspective, wind speeds between 10 − 14m/s are rated a six on the Beaufort scale(an empirical metric that relates wind speed to observed conditions at sea or on land).These wind speeds will generate large white-capped waves and using an umbrella outside isextremely difficult. Needless to say, these are not average operating conditions. Comparingthe maximum turbine power at these different wind speeds yields:Pt(vw = 7 [m/s]) =12AρCoptp (7)3= 55 [W ](4.30)Pt(vw = 12 [m/s]) =12AρCoptp (12)3= 277 [W ].(4.31)78Figure 4.8: Small WT test platform. In lieu of a dedicated wind tunnel, this test platformis able to generate a constant wind velocity of 4m/s. A cup anemometer is mounted on anadjustable apparatus to monitor the wind speed at different locations. The HAWT undertest is rated for 400W at a wind velocity of 14m/s.05101520() [%]2 3 4 5 6 7 8 9 10 ( ),Figure 4.9: HAWT under test power coefficient curve. Where the optimal operating point is(λopt, Coptp ) ≈ (7.1, 21%).794.3. Experimental ValidationA 5m/s decrease in wind velocity reduces the power output by 80%. Installing a small WT ina location with a less than favorable wind resource will further decrease the potential poweroutput. For example, in locations with a daily average wind speed of 4m/s, installing thetest platform HAWT will yield an average power output of just 10W . Evidently, a locationwind site assessment is essential to investigate the effectiveness of a small WT installation.Typically, an anemometer is placed at the potential installation site for one to two years tocollect wind speed and direction data before a decision is made to install the turbine.The fan array is able to produce a constant wind speed of 4m/s. For testing purposes, ahigher wind velocity would be preferable; however, due to financial limitations and availableequipment, the fan array test platform is sufficient to validate the small WT equivalent circuitand SysID MPPT methodology. The HAWT under test includes a PMSG whose output isconnected to a 3ΦR and inverted buck DC-DC converter.Using the experimental platform subjected to a constant wind speed, the system exper-imental Pg(Vg), Ig(Vg) and g(Vg) are measured and shown in Fig. 4.10. These experimentalcurves verify the simulated curves in Fig. 2.7 where, for constant environmental conditions,there exists one maximum power point at which the incremental and absolute conductancesare equal. Notably, gˆac is measured using the sinusoidal perturbation, LIA impedance ex-traction and SysID algorithm method. Observing the g(Vg) waveform in Fig. 4.10, it isevident that gˆac = gˆDC at the MPP. This important figure validates the SysID incrementalconductance measurement technique. At the MPP for a vw of 4m/s:PMPP = 10.2W ; VMPP = 10.9V ; IMPP = 0.94A. (4.32)An industry-standard C2000 TI microcontroller is used to perform the analog to digi-tal conversion of the generator voltage and current, PWM generation to drive the DC-DC804.3. Experimental Validation02468W[]P g101/[]g-[]MPP6 8 10 12 14 16 g V[ ]gMPPgDCgacIMAXPMPPIMPPFigure 4.10: Small WT system experimental Pg(Vg), Ig(Vg) and g(Vg) curves for vw = 4m/s.converter switching signals and digital processing to execute the SysID algorithm. An ex-perimental oscilloscope capture of the working algorithm is shown in Fig. 4.11. The MPPTcontroller parameters are listed in Table 4.4.The sinusoidal perturbation can be seen in the generator voltage, current and outputpower. gˆac and gˆDC are calculated by the microcontroller and then output using a digitalto analog converter and visualized in the oscilloscope capture. The system was initializedto λ > λopt and the SysID MPPT controller successfully locks onto the MPP after sevenupdate periods. The integral controller adaptive step functionality and simple tuning allowsfor more aggressive tracking if desired.In regards to the signal conditioning circuitry, the maximum values of Vg and Ig mustbe mapped to the input voltage range of the ADCs. The current SysID MPPT architecturecalls for only two ADCs to be used (one for Vg and one for Ig). The ADC resolution mustbe large enough for the DSP to quantize the small-signal voltage and current amplitudesand extract an accurate gˆac estimation. ADC resolution becomes an issue as the Vg and Ig814.3. Experimental Validation60s16sgac^gDC^gVgIgPMPPP =10.2WMPPV =10.9VMPPI =0.94AFigure 4.11: Experimental results utilizing the small WT test platform and fan array. Thegenerator power Pg (yellow), generator voltage Vg (orange), generator current Ig (green),estimated incremental conductance gˆac (blue) and estimated absolute conductance gˆDC (red)are plotted.Table 4.4: SysID MPPT Controller ParametersPARAMETER VALUE UNITSfMPPT 0.0625 Hzfp 0.1 Hzfs 2 kHzKI 0.5 -D˜ 0.04 -operating range of a small WT can be significant. This operating range is dependent on theturbine cut in and rated wind velocities.Ideally, the voltage and current signals would be decoupled into their respective small-signal and average-value components. However, due to the low frequency perturbation, thedecoupling of these signals would be a challenge. Another potential solution would be toimplement a signal conditioning stage with variable gain based on ωg. This would utilize the824.4. SummaryADC resolution more effectively and improve the gac estimation accuracy while allowing fpand fMPPT to be increased closer to the high frequency region of the small WT impedancebode plot.4.4 SummaryA novel SysID based MPPT methodology for small WTs was presented in this chapter. Theuse of a digital LIA facilitated a system impedance frequency response analysis and thedevelopment of an equivalent circuit for the small WT system. Using the LIA impedanceextraction method and equivalent circuit, a real-time SysID algorithm was derived to increasethe MPPT controller update frequency. The implemented integral controller ensures zerosteady-state error and facilitates adaptive step functionality. The presented methodologyoffers three advantages over conventional small WT MPPT methods: 1) accurate trackingwhen subjected to highly variable wind speeds, 2) optimal MPPT is guaranteed over thesystem lifetime even through degradation, maintenance and retrofitting and 3) a systematicapproach for choosing the MPPT update frequency, facilitated by the system impedancefrequency response analysis.When subjected to a turbulent wind velocity profile, the SysID methodology yielded thehighest average energy harvesting efficiency of 89.5% when compared to the traditional In-Cond (ηAV G = 80%) and adapted ZOS InCond (ηAV G = 83.5%) algorithms. Detailed mathe-matical procedures were provided to support the proposed methodology. The aforementionedbenefits were demonstrated through simulation results and experimental validation using asmall WT test platform.83Chapter 5Conclusions5.1 SummaryThis thesis introduced a novel control-oriented modelling technique that facilitated an intu-itive approach for analyzing the small WT electromechanical system, enabled the derivationof the small WT characteristic curves and increased simulation speed compared to conven-tional modelling methods. This modelling approach proved invaluable to the development ofa small WT system impedance frequency response analysis and the subsequent derivation ofan equivalent circuit for the small WT system.Furthermore, two novel InCond-based MPPT methodologies were presented. The zerooscillation sensorless (ZOS) InCond MPPT strategy determined the system MPP using anadapted InCond algorithm and suppressed steady state power oscillations. This resulted in:1) elimination of algorithm confusion due to changing wind speeds, 2) accurate tracking anddetection of the MPP and 3) improved steady state efficiency. The algorithm design requiredonly electrical sensing thereby making this MPPT method sensorless from a mechanical per-spective. These additional features improve upon the conventional InCond algorithm tocreate a more reliable and efficient MPPT strategy while maintaining a similar implementa-tion complexity. When compared to traditional InCond, utilizing the ZOS InCond methodincreased the overall energy harvesting efficiency by 3.5%. The ZOS InCond behavior was845.2. Future Workverified using simulated results and further experimental validation was performed using acustom turbine emulation platform.The real-time system identification (SysID) based MPPT methodology was developedusing a digital lock-in amplifier (LIA), the control-oriented small WT model and a novelSysID algorithm to address all HC MPPT shortcomings. A system impedance frequencyresponse analysis was performed and an equivalent circuit for the small WT system wasderived. A MPPT controller was developed incorporating the SysID algorithm that calculatedthe small WT system equivalent circuit parameters in real-time and adjusted the systemoperating point using an integral controller. This control method locks on and successfullytracks the MPP even in erratic winds. The SysID MPPT methodology offered three keyadvantages over conventional MPPT methods: 1) accurate tracking when subjected to highlyvariable wind speeds, 2) optimal MPPT is guaranteed over the system lifetime even throughdegradation, maintenance and retrofitting and 3) the system impedance frequency responseanalysis facilitates a systematic approach for choosing the MPPT controller update frequency.When subjected to a turbulent wind velocity profile, the SysID methodology yielded anaverage energy harvesting efficiency of 89.5% - a 9.5% increase in efficiency compared to thetraditional InCond algorithm. Detailed mathematical procedures were provided to supportthe proposed methodology. The theoretical concepts were supported through simulationresults and experimental validation using a small WT test platform.A modified version of the control-oriented small WT model and ZOS InCond MPPTstrategy was presented at the IEEE 10th International Symposium on Power Electronics forDistributed Generation Systems (PEDG), 2019 [1]. The SysID MPPT methodology has beencompiled in preparation for publication in the IEEE Transactions on Industrial Electronics.855.2. Future WorkCTrTVSWTrGCprpVBrsDC-DC BMSSMALL WIND TURBINEEQUIVALENT CIRCUITBATTERY ENERGY STORAGEEQUIVALENT CIRCUITFigure 5.1: Similarities between the small WT and battery energy storage equivalent circuits.5.2 Future WorkThe real-time SysID aspect of the SysID MPPT strategy, presented in Chapter 4, has appli-cations in battery management systems (BMS) for determining equivalent circuit parametersused to monitor battery state of charge (SoC) and state of health (SoH). Coincidentally, theequivalent circuit for a battery energy storage system is the same as the equivalent circuitderived for the small WT system as seen in Fig. 5.1.Current SoC and SoH estimation techniques rely on complex Kalman filters or Coulombcounting with error correction. Kalman filters require advanced battery system modelling,open circuit voltage measurements and constant re-calibration to ensure an accurate SoC es-timation. Coulomb counting and adapted versions also require specific parameterized curvesrelating the SoC to the discharge current with frequent re-calibration necessary. Batteryimpedance measurements and spectroscopy have been used in the past to correlate the esti-mated battery impedance to a known SoC; however, these methods rely on offline measure-ments requiring the battery to be disconnected from the load.The LIA impedance extraction method and SysID algorithm could be modified to es-timate the battery equivalent circuit parameters in real-time. 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