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Reduction of current/torque ripple in low power grid-tie PMSG wind turbines Ksiazek, Peter F. 2014

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Reduction of Current/TorqueRipple in Low Power Grid-TiePMSG Wind TurbinesbyPeter F. KsiazekB.Eng., University of Victoria, 2012A THESIS SUBMITTED IN PARTIAL FULFILLMENT OFTHE REQUIREMENTS FOR THE DEGREE OFMASTER OF APPLIED SCIENCEinThe Faculty of Graduate and Postdoctoral Studies(Electrical & Computer Engineering)THE UNIVERSITY OF BRITISH COLUMBIA(Vancouver)August 2014c© Peter F. Ksiazek 2014AbstractSmall-scale Wind Energy Conversion Systems (WECS) are becoming an attractive option fordistributed and renewable energy generation. In order to be affordable, WECS must havelow capital and maintenance costs. This leads to the increasing penetration of PermanentMagnet Synchronous Generators (PMSG) operating at variable frequency with connectionsto the power grid through a rectifier, and grid-tie inverter. Because PMSGs lack brushesand can be directly coupled to wind turbines, the capital and maintenance costs are greatlyreduced. A direct connection to the grid further reduces system costs by removing therequirement of large battery banks.The loading produced by grid-tie inverters on the DC bus is different than more typicalconstant-current or constant-power loads. They are characterized by large input ripple cur-rents at twice the inverter’s grid frequency. These ripple currents are reflected through theDC bus into the PMSG causing increased heating in the stator, and ripple torques whichlead to premature bearing failure and increased maintenance costs. To mitigate this problem,manufacturers typically add large amounts of capacitance on the DC bus to partially absorbthese ripples at the expense of system size, cost, and reliability.In this work, the effects of the grid-tie inverter load are explored using system behaviouralmodels which provide insight into the low frequency behaviour of the PMSG, rectifier, DCbus, and inverter. The swinging bus concept is presented and analysed in the time andfrequency domains. A control philosophy is developed which allows the DC bus to swing,thus removing the effects of the grid-tie inverter on the PMSG while keeping the DC busiiAbstractcapacitor small. A solution consisting of a Moving Average Filter (MAF) is presented as anintegral part of the control strategy.Full simulations of a complete system are developed and investigated to verify the rippletorque reduction technique. Finally, a prototype is developed and experimental results arepresented for a 2.5kW PMSG turbine generator. The simulation and experimental resultsare compared to a traditional controller showing tangible improvements in ripple current andtorque in the PMSG, while improving the dynamic response of the system.iiiPrefaceThis work is based on research performed at the Electrical and Computer Engineering de-partment of the University of British Columbia by Peter F. Ksiazek, under the supervisionof Dr. Martin Ordonez. Some experimental work was completed in collaboration with Dr.Rafael Pen˜a-Alzola.An extended version of chapter 3 has been published in IEEE Transactions in PowerElectronics [22].As first author of the above-mentioned publications, the author of this thesis developedthe theoretical concepts and wrote the manuscripts, receiving advice and technical supportfrom Dr. Martin Ordonez. The author developed simulation and experimental platforms,receiving contributions from Dr. Ordonez’s research team.ivTable of ContentsAbstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iiPreface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ivTable of Contents . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . vList of Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . viiiList of Figures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ixAcknowledgements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xiiDedication . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xiii1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.1 Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.2 Literature Review . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31.2.1 Rectifier Topologies for PMSG . . . . . . . . . . . . . . . . . . . . . 31.2.2 Current Ripple . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41.3 Contribution of the Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51.4 Thesis Outline . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72 Permanent Magnet Synchronous Generator (PMSG) Modeling: A LowFrequency Behavioural Model and Ripple Current Effect . . . . . . . . . 8vTable of Contents2.1 Basic Model of a Wind Turbine . . . . . . . . . . . . . . . . . . . . . . . . . 92.2 Basic PMSG Rotor Reference Frame Model . . . . . . . . . . . . . . . . . . 102.3 Low Frequency Behavioural Model . . . . . . . . . . . . . . . . . . . . . . . 122.4 Single Phase Inverter Model . . . . . . . . . . . . . . . . . . . . . . . . . . . 172.5 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 193 Inverter Ripple Current and the Moving Average Filter (MAF) . . . . 213.1 Swinging Bus Behaviour . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 223.1.1 Swinging Bus Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . 223.1.2 Time Domain Behaviour . . . . . . . . . . . . . . . . . . . . . . . . 243.1.3 Frequency Domain Behaviour . . . . . . . . . . . . . . . . . . . . . . 263.2 Moving Average Filter (MAF) . . . . . . . . . . . . . . . . . . . . . . . . . 273.3 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 324 System Simulation and Experimental Results . . . . . . . . . . . . . . . . 334.1 System Simulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 334.2 Experimental Platform and Results . . . . . . . . . . . . . . . . . . . . . . . 394.2.1 Linear Load at fe = 65Hz . . . . . . . . . . . . . . . . . . . . . . . . 434.2.2 CF = 2.3 Load at fe = 65Hz . . . . . . . . . . . . . . . . . . . . . . 434.2.3 Increased Linear Load at fe = 95Hz . . . . . . . . . . . . . . . . . . 454.2.4 CF = 2.3 Load at fe = 95Hz . . . . . . . . . . . . . . . . . . . . . . 454.2.5 Linear Load Transient . . . . . . . . . . . . . . . . . . . . . . . . . . 484.2.6 High CF Load Transient . . . . . . . . . . . . . . . . . . . . . . . . . 514.3 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 515 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 535.1 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53viTable of Contents5.2 Future Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55viiList of Tables4.1 Simulated PMSG Parameters . . . . . . . . . . . . . . . . . . . . . . . . . . 354.2 Simulation Control Parameters . . . . . . . . . . . . . . . . . . . . . . . . . 354.3 PMSG Parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 394.4 Six-switch, three-phase power stage (Beaver) components . . . . . . . . . . . 42viiiList of Figures1.1 Small-scale WECS block diagram . . . . . . . . . . . . . . . . . . . . . . . . 31.2 Conceptual representation of ripple torque elimination before and after appli-cation of proposed solution . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62.1 Typical Cp(λ, β) curves for different blade pitch angles β. . . . . . . . . . . . 92.2 Typical internal construction of a PMSG . . . . . . . . . . . . . . . . . . . . 112.3 Typical PMSG WECS block diagram . . . . . . . . . . . . . . . . . . . . . . 132.4 Low frequency model for PMSG conversion system . . . . . . . . . . . . . . 142.5 Ideal rectifier output current frequency components . . . . . . . . . . . . . . 152.6 Issues in PMSG rectifier performance with fast (blue) and slow (red) voltageloops: a) a fast loop provides a better dynamic regulation at the expense ofunacceptable current ripple; b) a slow loop reduces ripple but the dynamicregulation is very poor. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 162.7 Typical full bridge grid-tie inverter . . . . . . . . . . . . . . . . . . . . . . . 182.8 Low frequency model of a single-phase inverter: The inverter produces detri-mental ripple current reflection in the machine. . . . . . . . . . . . . . . . . 182.9 Issues in DC bus reflected current ripple with inverter type loading and varyingbus capacitance: a) large capacitance (25.31% ripple), b) medium capacitance(195.0% ripple), and c) small capacitance (207.8% ripple). . . . . . . . . . . 193.1 Swinging bus operation: The capacitor charge balance principle . . . . . . . 23ixList of Figures3.2 Swinging bus operation under linear, pulsating, and non-linear loading condi-tions: a) swinging bus voltage behaviour, b) bus currents (output io and icap),c) swinging bus spectrum, and d) MAF filtered swinging bus spectrum[22] . 253.3 Proposed control scheme block diagram with MAF . . . . . . . . . . . . . . 263.4 Moving Averaging Filter for 60-point and Fs = 3.6kHz: a) magnitude in linearscale, and b) phase in radians. . . . . . . . . . . . . . . . . . . . . . . . . . . 283.5 Control scheme: MAF and loop gain frequency response . . . . . . . . . . . 303.6 Output Voltage and MAF Filtered Voltage with CF =√(2) (top) and CF =2.3 (bottom). Output voltage FFT (F1 and M1) and filtered voltage FFT (F2and M2) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 314.1 Simulated System Diagram . . . . . . . . . . . . . . . . . . . . . . . . . . . . 344.2 Simulation Results with and without MAF filter (CF =√2) . . . . . . . . . 364.3 Simulation Results with and without MAF filter (CF = 2.3) . . . . . . . . . 374.4 PMSG simulation results with variable speed . . . . . . . . . . . . . . . . . . 384.5 Experimental setup (top) and power stage (bottom) . . . . . . . . . . . . . . 404.6 DC machine prime mover (Mavilor MS450) . . . . . . . . . . . . . . . . . . . 414.7 Permanent Magnet Synchronous Machine (Fanuc 10S) . . . . . . . . . . . . 414.8 Steady state operation without MAF (top) and with MAF (bottom) at 65Hzmachine frequency and linear load: Load current (blue, 2A/div), machinetorque (orange, 2Nm/div), phase A current (red, 5A/div), and DC voltage(yellow, 10V/div, AC coupled). . . . . . . . . . . . . . . . . . . . . . . . . . 444.9 Steady state operation without MAF (top) and with MAF (bottom) at 65Hzmachine frequency and high CF load: Load current (blue, 2A/div), machinetorque (orange, 2Nm/div), phase A current (red, 5A/div), and DC voltage(yellow, 10V/div, AC coupled). . . . . . . . . . . . . . . . . . . . . . . . . . 46xList of Figures4.10 Steady state operation without MAF (top) and with MAF (bottom) at 95Hzmachine frequency and linear load: Load current (blue, 2A/div), machinetorque (orange, 2Nm/div), phase A current (red, 5A/div), and DC voltage(yellow, 10V/div, AC coupled). . . . . . . . . . . . . . . . . . . . . . . . . . 474.11 Steady state operation without MAF (top) and with MAF (bottom) at 95Hzmachine frequency and high CF load: Load current (blue, 2A/div), machinetorque (orange, 2Nm/div), phase A current (red, 5A/div), and DC voltage(yellow, 10V/div, AC coupled). . . . . . . . . . . . . . . . . . . . . . . . . . 494.12 Load transient operation (370W to 740W ) without MAF (top) and with MAF(bottom) at 95Hz machine frequency and linear load: Load current (blue,2A/div), machine torque (orange, 2Nm/div), phase A current (red, 5A/div),and DC voltage (yellow, 10V/div, AC coupled). . . . . . . . . . . . . . . . . 504.13 Load transient operation (370W to 740W ) without MAF (top) and with MAF(bottom) at 95Hz machine frequency and high CF load: Load current (blue,2A/div), machine torque (orange, 2Nm/div), phase A current (red, 5A/div),and DC voltage (yellow, 10V/div, AC coupled). . . . . . . . . . . . . . . . . 52xiAcknowledgementsI would like to thank my supervisor Dr. Martin Ordonez for selecting me as part of hisresearch team. His knowledge, support, dedication and valuable technical advice during myMaster’s program have been greatly appreciated.I would also like to acknowledge my colleagues in the lab, including: Matias Anun,Robert Cove, Jason Forbes, Juan Galvez, Dr. David Campos Gaona, Dr. Ion Isbasescu,Federico Luchino, Francisco Paz, Dr. Rafael Pen˜a-Alzola, Navid Shafiei, and Ignacio GalianoZurbriggen for providing their wealth of experience and knowledge, and for creating a funand enjoyable work environment.I must also acknowledge the professors who guided me through the courses I took as partof my program; I learned a great deal under their tutelage. The staff of the Electrical andComputer Engineering Department of the University of British Columbia also contributed tomy success. I would like to thank the University of British Columbia, the Natural Sciences andEngineering Research Council of Canada (NSERC) and the Kaiser Foundation for fundingthis research.Furthermore, I must express my deepest gratitude to my fiance´e Jennifer Graham; to mymother Zofia Ksiazek; to my brothers and sisters Richard, John-Paul, and Maria; and to mydear friend Dustin Grue. They have provided constant support and encouragement withoutwhich I would not have been successful.Finally, without the encouragement of my uncle Jozef Prozniak, I would never havereturned and completed my education. For this I am grateful.xiiTo those who believed in mexiiiChapter 1Introduction1.1 MotivationThe demand for renewable energy sources is increasing due to economic factors, including theescalating cost of fossil fuels; and environmental factors, like the effects of climate change.Renewable energy sources offer a large number of challenges due to their decentralized andintermittent nature. Furthermore, most renewable sources provide power which is incompat-ible with the AC power grid, thus creating a new class of power converters which must notonly perform basic power conversion, but also maximize power extraction while isolating therenewable energy source from the effects of the power grid.Small-scale wind turbines (of approximately 10kW) are becoming an attractive optionfor energy generation. Wind Energy Conversion Systems (WECS) may be installed on evena modest-size property, and due to their simplicity, are highly cost effective for installationby small businesses, farmers and ranchers, and remote property owners. Because WECSharness the power in the wind, the input fuel cost is essentially zero. In order to decreasecapital and maintenance costs, small-scale wind turbines generally operate without variablepitch blades or transmissions and, therefore, rotate at variable speed depending on windconditions. Variations in speed pose an interesting challenge when connecting to the fixedfrequency grid. The typical lifespan of a turbine must be approximately 20 years with littleor no maintenance, such that the owner may recoup the capital cost.Due to the variable operating speed, DC machines, or Permanent Magnet Synchronous11.1. MotivationGenerators (PMSG) with a passive rectifier, have been used to generate DC voltage andcurrent which is then used either to charge a large battery bank, or connected directly to thegrid through a grid-tie inverter. In the case of the large battery bank, the system may operatesimilarly to an Uninterruptable Power Supply (UPS), where power can still be provided inthe event of a grid fault. Battery banks also serve to insulate the machine from the effectsof the power grid; however, battery banks are large, heavy, expensive, and generally requiresome maintenance. Large capacitors are also used on the DC bus to absorb the pulsatingcurrents drawn by the grid-tie inverter. These also add to system size and cost, and decreasereliability.PMSGs are becoming dominant in this application as they have the advantages of highefficiency and reliability due to their lack of brushes and self-excitation, along with a signifi-cantly lower mass, which decreases tower cost. Challenges with PMSGs include the variablespeed nature of this AC generator, which complicates grid connections as well as the har-monic current content that tends to be generated by traditional diode bridge rectifiers. It iswell known that these harmonic currents increase the losses in the PMSG, causing increasedheating and reduced energy extraction; furthermore, ripple torque is also created, whichdamages bearings and increases the size and cost of towers. A solution must be found whicheliminates not only the ripple torque associated with the rectification process, but also theripple torque caused by a grid tie inverter. In order to be widely implemented on small-scaleWECS, the solution must have minimal cost and have a positive impact on the system’soverall reliability.Figure 1.1 illustrates a typical small-scale WECS system which will form the basis of thediscussion in this work. The system consists of a PMSG machine controlled by an activerectifier and interfaced to the power grid through an inverter. Due to the low power ratingalong with the possibility of remote installation a single-phase inverter is often used. Theactive rectifier is responsible for maintaining high quality phase currents out of the PMSG,21.2. Literature ReviewvDCiinCiDCPMSGTeActiveRectifierSinglePhaseInvertervphiphFigure 1.1: Small-scale WECS block diagramwhile the inverter provides sinusoidal output current to the grid.1.2 Literature Review1.2.1 Rectifier Topologies for PMSGCurrently, most commercially available rectifiers for PMSG WECS systems consist of simplepassive diode bridges with more complicated topologies such as six-switch, two-level VoltageSource Converters (VSC) occasionally used for higher power levels [1–3]. Where voltage reg-ulation or boosting or bucking the output voltage is required, simple single-switch topologiesare common [5–7]. In [4] a semi-controlled rectifier was used to shape only the positive halfcycle currents at a lower cost than a fully controlled rectifier. Research has followed industryin this case, and a significant amount of work has been performed with regards to traditionalsimple three-phase topologies, including the single-switch boost and interleaved topologies.The Vienna rectifier [9] is a well-known topology with high efficiency and the ability to pro-vide Power Factor Correction (PFC), which has great potential for use with PMSG. However,licensing costs have restricted its use in industry, and limited research has been performedwith the Vienna topology and a PMSG [10]. Freitas et al presented an interesting three-phasetopology based on three SEPIC converters [11]. However the output stage and its effect on thepower extraction was not analysed. The use of Discontinuous Conduction Mode (DCM) in31.2. Literature Reviewsingle-switch boost converters was common in the papers reviewed [3, 7, 11–13], as it reducesthe complexity of the control at the expense of increased losses and higher Electro MagneticInterference (EMI). These topologies cannot properly shape the input current when operatedin Continuous Conduction Mode (CCM), therefore their effectiveness at higher power levelsis greatly reduced. Irrespective of the topology used, the waveform and harmonic contents(ripple) of the current extracted from the wind turbine defines the extraction efficiency andpulsating ripple torque.1.2.2 Current RippleWhile the negative effects of current ripple on the PMSG is well known and many techniqueshave been developed to reduce the harmonics introduced by passive rectifiers and other powerconverters, the detailed study of detrimental ripple reflection remains a research opportunityin this field. Quantitative analysis of the effect inverter load-induced ripple currents have israrely performed rigorously in the literature. In general, most analysis has been performedwith a load consisting of a constant resistance connected to the DC bus of the converter[5–8, 14–17]. This type of loading is not consistent with an inverter-type load which wouldtypically be used to connect a WECS system to the power grid. Nor does it correctly modelDC/DC converters operating in constant-current, or constant-power modes operating as anintermediate power stage or, finally, the charging of batteries. Therefore, this work dealswith the analysis of rectified sinusoidal currents at twice the line frequency encountered inreal applications. The study includes passive diode rectifiers and active rectification (PWM)as an input stage of the converter. High crest factor sinusoidal currents typically foundwith non-linear loads connected to an inverter are also included in the study to characterizethe problem. In [18] an Energy Storage System (ESS) with a bi-directional converter wasproposed to help protect the grid from power oscillations. However, the concept of the ESScould be extended to stiffen the control of the DC bus and absorb the ripple current caused41.3. Contribution of the Workby the inverter. Many different control techniques could be applied to this problem. Ortegaet al proposed a novel inverter control strategy to reduce the ripple current [19]. However,this technique can only be applied when the PMSG is operating at or near the grid frequency,which is not the case with variable frequency wind turbines.1.3 Contribution of the WorkThis work introduces valuable theoretical and practical concepts to the field of energy ex-traction for renewable energy systems:• The first concept includes the characterization of the effect inverter ripple current has onthe stator currents and electric torque of a PMSG. A low frequency model is presentedto simplify the system and provide improved understanding for these line frequencyeffects.• Second, this thesis presents a digital filtering technique which removes the influence ofthe inverter ripple current from the control of the PMSG’s power converter. In Figure1.2 the effect of the inverter load on a PMSG can be clearly seen. On the left, undertypical operating conditions, the PMSG electric torque has a ripple at twice the linefrequency of the inverter and significant distortion of the PMSG phase currents occurs.After application of the digital filter the torque ripple is completely eliminated andthe phase current becomes a perfect sinusoid leading to lower mechanical stress andlosses in the PMSG. This technique, while applied here to a six-switch active rectifiertopology, can be utilized with most traditionally employed power converters and comesat little or no added cost to the overall system.A simple model is developed, and a simulation of the effects of the fixed frequecy in-verter ripple current on the variable frequency PSMG stator currents and electric torque51.3. Contribution of the WorkiDCTeiΔTe(nom)Traditional operation(large torque ripple)Proposed operation(no torque ripple)1iΔ 2iaFigure 1.2: Conceptual representation of ripple torque elimination before and after applica-tion of proposed solutionis performed. The simulation results are confirmed experimentally, utilizing a three-phase,six-switch power electronics prototype connected to a PMSG driven by a prime mover. Tra-ditional control of the power electronics prototype is employed. This consists of a sensorlessvector control with inside current and outside voltage loops. solution consisting of a digitalMoving Average Filter (MAF) is presented as a low cost digital filtering technique, whichproves to be an effective technique for removing the effect of the inverter ripple current fromthe PMSG. The effect of the MAF is confirmed in simulations and experimentally.61.4. Thesis Outline1.4 Thesis OutlineThis work is organized in the following manner:• In Chapter 2, low frequency behavioural models are developed. A model for a PMSGis developed which allows for an improved understanding of the effects ripple currentloads have on a Permanent Magnet Synchronous Generation (PMSG). Then, a lowfrequency model of a grid-tie inverter and the input ripple currents is presented. Thesemodels form the building blocks for the system.• In Chapter 3, the effects of a grid-tie inverter on the DC bus of a power converterare explained. The swinging bus concept is presented as a means of injecting constantcurrent into the DC bus while non-constant current is extracted, thereby creating avoltage swing. The swinging bus is first analysed in the time domain, and then thefrequency domain in order to develop an effective control strategy, with the MovingAverage Filter (MAF) as a key component.• in Chapter 4, the control strategy is validated. System simulations of the PMSG,rectifier, swinging bus, and grid-tie inverter are developed. Simulation studies are thenperformed to confirm proper operation. Finally, the control strategy is validated usingan experimental prototype.• in Chapter 5, conclusions and potential future work are presented.7Chapter 2Permanent Magnet SynchronousGenerator (PMSG) Modeling: A LowFrequency Behavioural Model andRipple Current EffectWhile many models have been proposed for wind turbines and PMSGs, the focus has generallybeen to improve the fidelity of the simulation. This involves working with higher frequencies,smaller step sizes, and increased complexity. The objective of this chapter is to develop amodel that shows the detrimental ripple current effect on the machine torque. The studiedmodel shows the low frequency behaviour of the system and provides the necessary tool tocharacterize undesired effects in low power grid-tie systems. In this chapter, a basic modelof a wind turbine is presented along with the commonly used rotor reference model of aPMSG coupled with the power electronics intraphase. As an alternative, a low frequency,simple model of the PMSG and power electronic converter is then presented, which allowsfor a clearer understanding of the effects of a power converter’s voltage control loop on themachine’s currents and developed torque. Finally, a low frequency model of a single-phaseinverter is presented, which better demonstrates the effects a single-phase inverter load hason a small scale WECS.82.1. Basic Model of a Wind TurbineTip Speed Ratio λPower Coeficient Cp0 5 10 15β = 0°β = 5°β = 10°β = 15°Figure 2.1: Typical Cp(λ, β) curves for different blade pitch angles β.2.1 Basic Model of a Wind TurbineA wind turbine is a device which utilizes the kinetic energy in the wind to rotate a shaftto perform useful work. The turbine may be directly connected to either a mechanical load(such as a pump or grinder) or, more commonly, coupled to a generator to produce electricity.Mathematically, a wind turbine may be described by:P = 12Cp(λ, β)ρAv3 (2.1)where P is the power produced by the wind turbine, Cp(λ, β) is the performance coefficientof the turbine, λ is the ratio of the turbine tip speed to the wind speed, β is the blade angle,ρ is the density of the air, A is the swept area of the turbine, and v is the wind velocity[20].A turbine’s Cp(λ, β) characteristic is a function of airfoil construction and determined bythe manufacturer through empirical testing or modeling. A typical Cp(λ, β) is provided hereas Figure 2.1. Note that for a given β there is a maximum Cp which occurs at only one tip92.2. Basic PMSG Rotor Reference Frame Modelspeed ratio. Therefore, in order to extract the maximum power available, one must eitheroperate the machine at variable speed, as the wind speed changes, or utilize variable pitchturbine blades. Variable pitch turbines are mechanically complex, expensive and increasethe failure rate of the turbine. Therefore, for small-scale WECS, fixed pitch turbines are thepreferable solution. This limits the selection of the generator and power converter topologyfor connection to the power grid.2.2 Basic PMSG Rotor Reference Frame ModelA common machine choice for small scale WECS is the PMSG. A PMSG is a three-phase ACmachine consisting of a permanent magnet rotor with multiple poles and three-phase statorwindings that are sinusoidally distributed (Figure 2.2). In the cutaway figure, the North andSouth poles of the magnets on the rotor are red and blue respectively, the rotor bearings green,and the sinusoidal stator windings are indicated in brown. Unlike traditional synchronousmachines, which have a coil mounted on the rotor, there is no electrical connection betweenthe stator and the rotor; therefore, no brushes are required, resulting in lower maintenancecosts. Furthermore, a multi-pole PMSG can be directly coupled to a wind turbine, eliminatingthe gearbox and thus further reducing maintenance costs.Like a traditional synchronous machine, the PMSG generates sinusoidal voltages andcurrents. However, in the PMSG, the amplitude of the voltage is proportional to machinefrequency. This is due to the constant flux generated by the permanent magnet. Therefore,any power converter used to extract power from a PMSG is required to operate at variablefrequency and variable voltage.Most common models for PMSGs utilize the rotor reference frame:vd = Ldi˙d + Rid + Lqpωriq (2.2)102.2. Basic PMSG Rotor Reference Frame ModelFigure 2.2: Typical internal construction of a PMSGvq = Lq i˙q +Riq + Ldpωrid + λpωr (2.3)Te =32p(λiq + (Ld − Lq)idiq) (2.4)where vd and vq are the direct and quadrature stator voltages, Ld and Lq are the direct andquadrature stator inductances, R is the stator resistance, p is the number of pole pairs, ωr isthe rotor angular velocity, λ is the rotor flux, id and iq are the direct and quadrature current,and Te is the electric torque of the machine[21].Looking at equation 2.4, we find that in the round rotor case (Ld and Lq equal) onlythe quadrature current iq contributes to torque production. Furthermore, in order to reducestator conduction losses, in most cases the power converter ensures id = 0. This simplifiesthe equations to:vd = Lqpωriq (2.5)vq = Lq i˙q + Riq + λpωr (2.6)112.3. Low Frequency Behavioural ModelTe =32pλiq (2.7)In equations 2.5 and 2.6 the relationship between stator voltage and machine speed canbe clearly seen. In equation 2.7 the electric torque is proportional to quadrature current.Therefore, any ripple in the stator current will lead to a ripple in electric torque.2.3 Low Frequency Behavioural ModelIn order to better understand the low frequency effects and to allow for fast running simu-lations of longer time periods, it is advantageous to combine a simple model of the powerelectronic converter with the simplified equations developed in the previous section. In gen-eral, two different types of power converters can be used with PMSG, the Voltage SourceConverter (VSC) or the Current Source Converter (CSC). Within these broad classes manydifferent topologies may be chosen, including the common six-switch inverter/rectifier, theVienna rectifier, or other semi-controlled rectifiers. However, in terms of their low frequencybehaviour, all of them operate in the same manner.Every power converter for use with PMSG will have a control strategy such as an inner,fast current loop that is used to shape the current. The set point of the current loop ismodified by an outer control loop which can be a torque controller, voltage controller, orspeed controller. Regardless of the type of outer controller, the bandwidth of the innercurrent loop must be high in order to properly shape the current – similar to a Power FactorCorrection (PFC) application. A typical system level block diagram is provided in Figure2.3.Because the power converter’s current loop is significantly faster than the other con-trollers, we may assume that the commanded set point provided by the outer loop is followedaccurately. This assumption introduces significant error into the model at higher frequencies.122.3. Low Frequency Behavioural ModelGvvDCioCiDCPMSGIaIbIcVcaVabVbcPLLdqabcVabVbcVcaφωφIaIbIcIdIqv*DCvDCGiId    Iq∗ ∗IdIqModulatorTeFigure 2.3: Typical PMSG WECS block diagramHowever at lower frequencies this is a reasonable assumption. With this simplification we re-place the power converter with the phase currents represented by controlled current sources.The current is then passed through an ideal rectifier into the DC bus capacitor (Figure 2.4).With this model we can better understand the effects of the outer voltage loop on the phasecurrent in the PMSG. A simple analytic model also allows for simulation on longer timescales in shorter periods of time, further aiding in the development of low frequency controlstrategies such as Maximum Power Point Tracking (MPPT) algorithms.Using the low frequency model, the relationship between the phase currents and the DCcurrent after the rectifier can be determined by the following:idc =[1 1 1]positiveiaibic(2.8)132.3. Low Frequency Behavioural ModelGvvDCioCiDCIaV*ovDCId    Iq∗ ∗∗Ib∗Ic∗abcdqφIaIb∗∗Ic∗IdealRectifierFigure 2.4: Low frequency model for PMSG conversion systemConverting the phase currents to the rotor reference frame we have:idc =[1 1 1]positivecos(φ) −sin(φ)cos(φ− 2pi3 ) −sin(φ−2pi3 )cos(φ + 2pi3 ) −sin(φ+2pi3 )idiq(2.9)where φ is the rotor position. Because id is controlled to be 0, we can further simplify:idc = positive{−iq[sin(φ) + sin(φ−2pi3) + sin(φ+ 2pi3)]}(2.10)The resulting DC current, which forms the input current to the DC link capacitor, will varywith id and iq, and also the rotor position φ.By performing frequency analysis with the low frequency model rotating at 60Hz with aconstant current load on the DC bus clearly reveals the output current harmonics introducedby the ideal rectifier. In Figure 2.5 the 6th and 12th harmonics of the machine frequencyare −25dB and −36dB respectively. Additional 6k harmonics (where k = 1, 2, 3...) are notshown. These harmonic currents are very small with respect to the DC component and142.3. Low Frequency Behavioural Model0 100 200 300 400 500 600 700−100−90−80−70−60−50−40−30−20−100Frequency (Hz)|i       (f)| (dB)DC6k harmonics induced by ideal rectificationDC ComponentNo componentsFigure 2.5: Ideal rectifier output current frequency componentsneglecting them will not have a significant impact on the torque ripple of the machine.Looking at Figure 2.5 one must conclude that in order to maintain sinusoidal inputcurrents, and, therefore constant torque in the PMSG, near constant DC current must beinjected by the rectifier into the DC bus. Unfortunately, because the set point of the currentloop is not constant, the outside, slow control loop will have an effect on the quality of thephase current and, therefore, on the PMSG electric torque. Any perturbation at a frequencywithin the bandwidth of the slow control loop will appear as a perturbation on the innercontrol loop’s set point. Under steady-state conditions with a constant current or resistivetype loading on the DC bus this is generally not an issue, as the load current is constant.To demonstrate the effect the outer voltage loop has on PMSG torque a short simulationstudy was performed using the low frequency model with a simple PI voltage loop. In152.3. Low Frequency Behavioural Model0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2−2000200Va (V)0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2−505Ia (A)0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2051015PhaseCurrent THD (%)0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2376378380Bus Voltage (V)0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2−12−10−8Torque (Nm)Significant undershoot caused bypoor dynamic responseLarge torque rippleTime (s)Figure 2.6: Issues in PMSG rectifier performance with fast (blue) and slow (red) voltageloops: a) a fast loop provides a better dynamic regulation at the expense of unacceptablecurrent ripple; b) a slow loop reduces ripple but the dynamic regulation is very poor.Figure 2.6 a slow PI controller (Kp = −0.5, Ki = 40) and fast PI controller (Kp = −2,Ki = 100) were implemented with a DC load of 3A with a transient to 4A occurring at 0.1s.In the figure the increased THD with the faster control loop is clearly seen (4% versus 1%).The increased torque ripple is observable. However, with the slow controller, the dynamicregulation is greatly decreased causing sluggish responses to transients characterized by thelarge undershoot indicated.The previous studies were performed with constant DC current loads. As will be demon-strated in the next section, single-phase inverter type loading conditions have significant162.4. Single Phase Inverter Modelcurrent ripple[22]. Traditionally, a large DC bus capacitor is used to help smooth the ripplecurrent caused by the inverter. However, this increases system cost and decreases reliability.2.4 Single Phase Inverter ModelAs identified in the literature review, most recent work utilizes loads modelled as simpleresistive or constant current loads. While this assumption is reasonably accurate for DCloads, or in some cases battery charging type loads, it is not a reasonable way to modelsingle-phase inverters. Because a large number of small-scale WECS are installed in grid-tieapplications without battery banks, further characterization is required.In grid-tie applications current mode inverters are generally employed. An inverter con-verts the DC voltage and current into AC voltage and current in phase with the line voltage.Figure 2.7 details a typical single-phase full bridge inverter. The inverter generates the sinu-soidal currents required by modulating switches S1 through S4. The output inductors andcapacitor act as an EMI filter to reject the switching frequency components of the outputcurrent from the line. The only other significant storage element is the input DC bus ca-pacitor, which is responsible for rejecting the switching frequency components of the inputcurrent. Because all of the high frequency components are contained within the inverter, onemay simplify the inverter to generate a low frequency model that (as in the case with thePMSG model) leads to a better understanding of the behaviour of an inverter load.Because a single phase inverter outputs current as a sinusoid in phase with the line voltage,the input current (which consists of a rectified sinusoid) has significant ripple. This rippleis characterized by a fundamental component at twice the line frequency (typically 120Hzor 100Hz) with harmonics that depend on the Crest Factor (CF) of the inverter’s outputcurrent. At low frequency an inverter type load can be modeled as a current which is equalto the instantaneous output power (vo · io) scaled by the DC bus voltage at the input to the172.4. Single Phase Inverter ModelVphS3S4S1S2VDC IphVlineiiniDCiphFigure 2.7: Typical full bridge grid-tie inverterInverterTlineiiniVDCiiniDCoutTlineioutHighCFFigure 2.8: Low frequency model of a single-phase inverter: The inverter produces detrimen-tal ripple current reflection in the machine.inverter (Figure 2.8)[23]. If the output current of the inverter is not sinusoidal, as in the casewith high CF loads such as rectifiers, then the input current also reflects nonlinearities. TheDC bus capacitor will help absorb some of this ripple. However, the amount of capacitancerequired to limit the ripple is very large, adding to the size and cost of the overall system. Theeffects of different sized bus capacitors with a constant inverter load is detailed in Figure 2.9.A very large DC bus capacitor of approximately 10mF is required to bring the ripple downto a reasonable level. Capacitors of this size or larger are not feasible from the prospectiveof cost, system size, or reliability.182.5. Summary0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.101230 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.101230 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.101230 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.10123Current (A)i        (A)500uF Capacitor1mF CapacitorDC10mF Capacitori        (A)DCi        (A)DCi      (A)inTime (s)207.8%195.0%25.31%Figure 2.9: Issues in DC bus reflected current ripple with inverter type loading and vary-ing bus capacitance: a) large capacitance (25.31% ripple), b) medium capacitance (195.0%ripple), and c) small capacitance (207.8% ripple).2.5 SummaryThis chapter proposed a simple, low frequency model for a wind driven PMSG. The relation-ship between input phase current, machine torque, and rectified output current was derived.An inverter load model was presented. The models allow for a greater understanding of non-constant current loads and their effects on the PMSG power converter. The two loop controlstrategy typically employed for PMSG power converters was presented, and the effects ofthe outer, slow control loop on the inner, fast control explained. The proposed models allowfor rapid simulation of longer time frames, improving simulations of MPPT techniques and192.5. Summaryfrequency response analysis.20Chapter 3Inverter Ripple Current and theMoving Average Filter (MAF)In the previous chapter a low frequency model of a PMSG power converter and an inverterload was proposed to better understand a PMSG’s response to low frequency effects. Wemust now examine the effect of low frequency ripple currents on the DC bus capacitor andthe DC bus voltage. The aim of this chapter is to explain the swinging bus concept andpresent the Moving Average Filter (MAF) as a key component in reducing current ripple.The concept of a swinging bus was used succesfully in other applications such as fuel cellgrid-tie [22, 23] and PFC [24] applications. This chapter employs a swinging bus concept toa three-phase WECS turbine connected to a single-phase grid-tie inverter.The swinging bus is a concept whereby a DC bus is not tightly regulated. Instead, avoltage ripple is allowed to exist on top of the DC bus similar to a PFC application. Themagnitude of the voltage ripple is generally much smaller than the nominal DC value. Thecontrol system is designed such that the frequency components of the required voltage rippleare eliminated from the controller, thus allowing for effective regulation of the average DCvoltage with an improved transient response.213.1. Swinging Bus Behaviour3.1 Swinging Bus BehaviourThe swinging bus is a method which is employed to reject the double line frequency ripplecurrents generated by the inverter load presented in the preceding chapter. Eliminating theeffects of this ripple current on the PMSG has the benefit of reducing the torque ripple inthe machine which, in turn, increases energy extraction efficiency and reduces wear on themachine’s bearings.3.1.1 Swinging Bus AnalysisWith the aid of Figure 3.1, the swinging bus operating principle is illustrated in terms ofcapacitor charge balance. In the first half of Figure 3.1, the bus is operated with a traditional,stiff bus, control strategy. In order to maintain the average DC bus voltage, the PMSGrectifier is forced to deliver current with ripple at double the inverter output frequency intothe DC bus capacitor (Figure 3.1b), thereby maintaining the instantaneous charge balance.The ripple current waveform is reflected into the PMSG as additional harmonics on the PMSGfundamental current (Figure 3.1 c). Note that these ripple currents are significant and contain120Hz fundamental and harmonics, producing significant ripple torque in the PMSG (Figure3.1a). Further compounding the problem, beat frequencies are created between the twice linefrequency component caused by the inverter and the PMSG frequency. In order to reduce thewear on mechanical components and limit the harmonic losses in the PMSG, the operatingmode is changed to constant (DC) current extraction (right side of 3.1). In this case, thequadrature current (iq) is held constant regardless of the inverter ripple current, resulting inconstant Te. The capacitor voltage is not affected and the magnitude of the voltage swing isthe same. The relationship between the size of the capacitor and the maximum output powerof the inverter determines the scale of the voltage swing. As in most PFC-type applications,the capacitor must be selected for the inverter operating range, and lifespan.223.1. Swinging Bus BehaviouriDCTeiΔTe(nom)+ δTe(nom)- δTe(nom)Traditional operation(large torque ripple)Swinging bus operation(no torque ripple)1iΔ 2a)b)iac)Figure 3.1: Swinging bus operation: The capacitor charge balance principleIn this section, the bus voltage is characterized in both the time and frequency domainsutilizing sinusoidal (linear), non-linear, and rectified types of loads. The results obtained willbe used to develop a control strategy .233.1. Swinging Bus Behaviour3.1.2 Time Domain BehaviourFigure 3.2 shows an example of a typical single-phase inverter input bus with DC bus capac-itor C = 680µF , nominal bus voltage 220V, and output load current 9.6Apeak (1.5kW outputpower). In Figure 3.2(a)(top) the system is analyzed with an applied linear load. In thiscase, the bus voltage swings at a frequency of twice the inverter operating frequency alongwith harmonics thereof. The inverter input current io is illustrated in Figure 3.2(b)(top) witha solid line, which is, as mentioned in the previous chapter in essence, equal to the instanta-neous output power (vo · io) scaled by the DC bus voltage at the input to the inverter (Figure2.8)[23]. Note that only the low frequency ripple current at the inverter operating frequencyis shown as the switching frequency components only produce small high frequency ripple inthe capacitor. The DC bus input capacitor current is also shown, note that for every 1/120seconds the DC bus capacitor maintains a net zero charge balance. This is a result of thesubtraction of the constant input current supplied by the PMSG rectifier and the inverter’spulsating input current. For the linear case, the voltage peak-to-peak ripple is approximately10%.In the next case, a phase-controlled rectifier type load is examined. Figure 3.2(a)(center)describes the DC bus voltage indicating two intervals: 1) DC voltage ramp due to constantcurrent charge, during this period the capacitor current consists entirely of the DC inputcurrent supplied by the PMSG rectifier, and 2) a sinusoidal discharge when the conductionphase angle is reached. Although the inverter current is smaller than the first case thevoltage peak-to-peak ripple is 25% larger as indicated in Figure 3.2(b)(center) with a 90◦phase conduction angle. As in the previous case, the bus voltage ripple still consists of afundamental at double the inverter operating frequency, with additional harmonic distortionthen the previous case. Furthermore, the difference between the DC input current producedby the PMSG rectifier and the inverter input pulsating current has an average of zero.243.1. Swinging Bus Behaviour−1001020   0 5 10 15 20 25 30200210220230240ms -0.400.40.81.2 Hamming, L=600-0.400.40.81.2 -0.400.40.81.2|V(f)| (pu)     Hamming, L=600Hamming, L=600210220230240210220230240 vDCvDCvDC−1001020−1001020ioicapioicapioicap0 5 10 15 20 25 30ms50 200 350 f|V(f)| (pu)|V(f)| (pu)-0.400.40.81.2-0.400.40.81.2-0.400.40.81.2|V(f)| (pu)|V(f)| (pu) |V(f)| (pu)50 200 350 flinearpulsatingnon-linearFigure 3.2: Swinging bus operation under linear, pulsating, and non-linear loading conditions:a) swinging bus voltage behaviour, b) bus currents (output io and icap), c) swinging busspectrum, and d) MAF filtered swinging bus spectrum[22]In the third, and final case, a non-linear load with a crest factor of CF = 2.3 which is typ-ical for a passive, full-wave rectifier with an input inductive filter and large output capacitoris applied as a load. Figure 3.2(a)(bottom) indicates the DC bus voltage, again consistingof two distinct intervals: First, a voltage ramp up caused by the DC input current from thePMSG rectifier with zero inverter current. Secondly, a voltage ramp down when capacitorcharge is transferred to the inverter. The bus voltage resembles a triangular waveform withdiffering slopes (approximately a saw-tooth), which contains both even and odd harmonics.The voltage peak-to-peak ripple is the largest (87.5% larger than the linear case) of all threecases analyzed. Figure 3.2(b)(bottom) describes the capacitor input current and the inverterinput current. As in the two previous cases, the difference between the DC input currentsupplied by the PMSG rectifier and the inverter input current maintains an average chargebalance of zero and the average DC bus voltage is maintained at 220V.253.1. Swinging Bus BehaviourGvV*DCvDCGiId    Iq∗ ∗IdIqModulatorMAFg1-6Figure 3.3: Proposed control scheme block diagram with MAF3.1.3 Frequency Domain BehaviourThe time domain analysis presented previously allows for a better understanding of theswinging bus behavior and the voltage ripple under different types of loading conditions.However, it is necessary to perform analysis in the frequency domain to explore the harmoniccontent present in the swinging bus voltage. This analysis will allow for the development ofthe control signal processing required to form the feedback portion of the control loop. Thefrequency contents of the swinging bus voltage waveforms are presented in Figure 3.2(c) usingthe Discrete Fourier Transform (DFT) with a hamming window. The spectrum with linearload is presented first in Figure 3.2(c)(top). The components at DC, 120Hz, 240Hz, and 360Hzare clearly visible in the figure, with double the inverter operating frequency (120Hz) beingthe primary component (neglecting the DC component). With the DC bus voltage underphase-controlled rectifier and non-linear CF = 2.3 loading conditions (Figure 3.2, center andbottom), the fundamental component at twice the inverter operating frequency (120Hz) isalso present. However, in these non-linear cases the additional harmonic components (240Hz,360Hz, etc) become a larger proportion of the spectral content.The frequency components contained in the DC bus voltage signal can be considered aperturbation to the q- and d-axis current loops in the power converter which controls theaverage bus voltage. This is explained by the proposed control scheme block diagram inFigure 3.3. In order to maintain the reference to the inner current loops constant (constant263.2. Moving Average Filter (MAF)in the dq reference frame is equivalent to sinusoidal in abc), then the undesirable 120Hzand harmonics thereof must be eliminated by the feedback signal processing (MAF ) orthe voltage compensator (Gv). The traditional solution is to set the voltage compensator’sbandwidth low enough that the voltage compensator does not respond to the 120Hz signal(typically less than 10Hz). This results in a sluggish power converter with poor dynamicresponse. The swinging bus control scheme allows the voltage compensator’s bandwidth tobe increased providing improved dynamic response. In figure 3.2(d) the resulting DC busvoltage signal after signal processing is presented, the undesirable frequency components havebeen eliminated from the control loop. thus allowing the control bandwidth of the systemto be increased. The proposed digital filter (MAF) with frequency notching characteristicsis examined and characterized in the next section. The MAF is inserted in the voltagefeedback path (MAF ) and eliminates the undesired frequency components in the DC busvoltage signal. The MAF requires only minimal hardware processing in terms of samplingfrequency, memory, and processing. Because the MAF is only inserted into the DC busvoltage feedback path, traditional control techniques may be applied to design and validatethe compensators.3.2 Moving Average Filter (MAF)The core of the swinging bus control technique is a digital filter inserted into the DC voltagefeedback path that eliminates the voltage ripple components of the DC bus voltage withoutaffecting the voltage controllers phase margin. The highly efficient, digital Moving AveragingFilter (MAF) is selected for this application because it provides an optimal solution, as itremoves both the 120Hz and harmonics. In this section the characteristics of the MAF arepresented in detail and the effectiveness of the filter is validated through experimental resultsusing linear, and high CF loading.273.2. Moving Average Filter (MAF)0 0.1 0.2 0.3 0.4 0.5 0.600.51ω|H(ω)|0 0.1 0.2 0.3 0.4 0.5 0.6−3−2−10ω<H(ω)0 360 720 1080 1440 1800 2160(a)(b)Figure 3.4: Moving Averaging Filter for 60-point and Fs = 3.6kHz: a) magnitude in linearscale, and b) phase in radians.A MAF has optimal performance in the time domain and limited performance in thefrequency domain[25]. Nevertheless, since a MAF completely attenuates at the frequencies ofinterest (120Hz and harmonics, Figure 3.4)[26], the overall result is superior in both domainscompared to other possible filters for this application. The advantages of the MAF can besummarized as follows: since the number of samples within the step edge is equal to the filterkernel size, the filter has the fastest step response; it is easy to implement and has efficientcomputation time that requires only three algebraic operations and two index operations,making implementation possible on even the least expensive micro-controllers; it reducesrandom noise by a factor equal to the square-root of the kernel size; and by careful designcan eliminate 120Hz frequency components and harmonics.283.2. Moving Average Filter (MAF)The filter is mathematically described by:v¯bus[n] =1MM−1∑k=0vbus[n+ k] (3.1)where M is the length of the kernel or number of averaging points. The equation consists ofconvolving the signal with a rectangular, unit kernel (all elements equal 1). The MAF canalso be performed using a simple recursive algorithm as follows:v¯bus[n] = v¯bus[n− 1] + vbus[n + p]− vbus[n+ p + 1] (3.2)where,p = (M − 1)2Because the algorithm consists of only simple summations and subtractions it can be easilyimplemented in a fixed-point, low-cost DSP. This is critical as it allows for implementationwithout any additional system cost as it may by integrated in the existing power converterssystem controller. In order for the MAF to operate correctly, M values must be stored andused to perform the calculation (e.g., M = 60). The voltage signal is sampled at the samplingfrequency (e.g., Fs = 3.6kHz) and the MAF calculated. This reduces the delay introducedin the discretization and, hence, in the phase lag.The analytical expression of the MAF in the discrete frequency domain (DFT) is,H(ω) = 1Msin(ωM/2)sin(ω/2)(3.3)which is the result of transforming a rectangular series of impulses (rectangular window) usingthe DFT. From this expression the elimination of the 2pi/M frequency components can beclearly seen. Fig. 3.4(a) shows the DFT of the MAF depicted in linear scale where M = 60.293.2. Moving Average Filter (MAF)  −60−40−2002040MAF 60−PointLoop gain101 102 103 104−150−100−500ω| H ( ω ) |< H ( ω )Figure 3.5: Control scheme: MAF and loop gain frequency responseThe horizontal scale is presented in discrete angular frequency (top) and continuous angularfrequency mapping for Fs = 3.6kHz (bottom). Graphically, the figure clearly describes thefrequency elimination of the MAF filter along with the unity gain at DC. Figure 3.4(b) showsthe MAF has linear phase with pi jumps in the phase corresponding to the locations of thediscrete zeroes in the unit circle at the notching frequency.In digital signal processing linear scales are typically used to design filters, whereas incontrol system design frequency analysis is traditionally performed in log-frequency and dBmagnitude scales. Because the MAF forms an integral part of the control loop gain, the filtermust be represented in log scale. Figure 3.5 shows the MAF magnitude in dB and phase inlogarithmic scales for the case of M = 60, Fs = 3.6kHz). For comparison purposes, Fig. 3.5also presents the loop gain magnitude and phase of a typical inner current loop controller.303.2. Moving Average Filter (MAF)M2M1F1F2FFT(C1)2.50V/div42.0 Hz/divF1 FFT(C2)100mV/div42.0 Hz/divF22.50V/div42.0 Hz/divM12.50V/div42.0 Hz/divM220.0ms/div25.000kS/sTbase      0.0 ms5 kSStopTriggerEdgeLinePositive120Hz 240Hz320HzFigure 3.6: Output Voltage and MAF Filtered Voltage with CF =√(2) (top) and CF = 2.3(bottom). Output voltage FFT (F1 and M1) and filtered voltage FFT (F2 and M2)In order to confirm the proper operation of the MAF filter in the voltage feedback path,the sampled output voltage reading in the DSP was output through a DAC and, using anoscilloscope, compared to the actual output voltage ripple in the time domain. The verticalscales were adjusted such that the amplitude of the DAC waveform perfectly matched theoutput voltage. The MAF was then enabled and the spectrum captured using a Discrete FFT.Figure 3.6 shows the ability of the MAF to remove the 120Hz and harmonic components fromthe feedback loop.313.3. Summary3.3 SummaryThis chapter investigated the effect of the inverter load ripple current on the DC bus and therectifiers output voltage control loop. A solution was proposed to reduce the ripple currentreflected in the rectifier and PMSG and, therefore, on the ripple torque. The solution reliesupon a digital MAF inserted in the control loop to eliminate the perturbations caused by theripple current. The MAF filter was fully explored and characterized. In the next chapter,complete system simulations will be presented to validate the proposed solution.32Chapter 4System Simulation and ExperimentalResultsIn order to verify the proper operation of the proposed torque ripple reduction technique afull system simulation was constructed. Simulation studies with and without the MAF filterare presented; clearly demonstrating the benefits of the MAF filter in the feedback path.Finally, in order to validate the technique a power stage was constructed and experimentalresults are provided.4.1 System SimulationThe full system simulation was developed using MATLAB Simulink (R2012b) with SimScapemodels to simulate the PMSG and six-switch power converter. Figure 4.1 details the simu-lated system consisting of the PMSG, input inductors (L = 5mH), phase voltage and currentmeasurements (Vab, Vbc, Vca, Ia, Ib, and Ic), switches with gate signals (g1 to g6) and outputcapacitor (C = 1mF ). The output load current (io) consists of the typical single phaseinverter-type load current described in Section 2.4. The inverter is operating at 230VRMSand 60Hz. The inverter’s load current is 5ARMS resulting in a loading of 1.15kW . Becauseof the large inertia typical of even a small-scale wind turbine the PMSG was simulated usinga speed input. The parameters for the PMSG are provided in Table 4.1. Instead of utilizingan encoder to measure the rotor speed and position a Type-I Phase Locked Loop (PLL)334.1. System SimulationGvvDCioCPMSGIaIbIcVcaVabVbcPLLdqabcVabVbcVcaφωφIaIbIcIdIqv*DCvDCGiId  Iq∗ ∗IdIqSVMLLLg1g2g3g4g5g6MAFφg1g2g3g4g5g6iDCFigure 4.1: Simulated System Diagramwas implemented to estimate these quantities, helping to reduce the overall system cost andincrease reliability. The switching frequency was selected to be 25kHz.The voltage (Gv) and current loops (Gi) consisted of digital PI controllers sampling atthe switching frequency with the parameters in Table 4.2; Space Vector Modulation (SVM)was selected as the modulation scheme. The MAF filter was implemented with a samplingfrequency at 7.2kHz and a kernel size of M = 60. The filter will therefore eliminate frequencycomponents of:f = FsM= 7.2kHz60= 120Hz (4.1)344.1. System SimulationTable 4.1: Simulated PMSG ParametersParameter ValueRotor Type Round RotorNumber of Pole Pairs 4Flux Linkage 182.7mV · sVoltage Constant 132.5mV/rpmTorque Constant 1.096N ·m/AStator Resistance 959mΩArmature Inductance 525µHTable 4.2: Simulation Control ParametersParameter ValueVoltage Kp −0.5Voltage Ki 40d-axis Current Kp 500d-axis Current Ki 500q-axis Current Kp 350q-axis Current Ki 500and harmonics thereof.The simulations were performed with 5ARMS, 230VRMS inverter type loads (1.15kw) ofboth linear (CF =√2) and non-linear (CF=2.3) loading conditions with the PMSG spinningat a constant −350rad/s. For the first half of the simulation time (from t = 0s to t = 0.05s)the MAF was active and filtering the output voltage (vo). At t = 0.05s the MAF was disabledfor comparison purposes. For the linear loading case (Figure 4.2) the effect of the MAF isclear. With the MAF enabled, there is no ripple torque caused by the inverter impartedon the machine. Furthermore, the THD of the phase current is very small and the currentappears sinusoidal with no significant harmonics present. When the MAF is disabled theeffect on the phase current, and therefore the torque is apparent. A significant amount of the354.1. System Simulation0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.1−5000500Vab (V)0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.1−505Ia (A)0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.105Load current (A)0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.1246Torque (Nm)0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.1545550555Bus Voltage (V)With MAF Filter Without MAF Filter3NmTime (s)Figure 4.2: Simulation Results with and without MAF filter (CF =√2)inverter ripple current is reflected on the phase current which causes the ripple in the torqueat twice the inverter’s line frequency (120Hz). The torque ripple is observed to be 3N ·mfor this loading condition resulting in a ripple factor of:%Ripple = 3N ·m3.4N ·m· 100% = 88% (4.2)When the inverter load becomes non-linear, the effect becomes even more apparent (Fig-ure 4.3). As for the linear case, for the first half of the simulation time (from t = 0s tot = 0.05s) the MAF was active and filtering the output voltage (vo); at t = 0.05s the MAFwas disabled. With the MAF enabled the torque ripple is again non-existant and the phase364.1. System Simulation0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.1−5000500Vab (V)0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.1−505Ia (A)0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.105Load current (A)0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.1246Torque (Nm)0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.1545550555Bus Voltage (V)With MAF Filter Without MAF Filter3.5NmTime (s)Figure 4.3: Simulation Results with and without MAF filter (CF = 2.3)current is a very high quality sinusoid. When the MAF is disabled the phase current isdistorted even more than the linear case and the torque ripple increases as well (3.5N ·m).For this loading condition the resulting ripple factor is:%Ripple = 3.5N ·m3.4N ·m· 100% = 103% (4.3)Because a PMSG wind turbine must function under variable rotor speeds, a simulationwas performed where the rotor speed decreases from −350rad/s to −300rad/s in 0.1s (Figure4.4). The inertia of the wind turbine would almost certainly limit any changes in rotor speedto well below this rate, even under very rapid changes in wind speed.374.1. System Simulation0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.1−5000500Vab (V)0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.1−505Ia (A)0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.105Load current (A)0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.133.544.5Torque (Nm)0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.1−340−320−300wr (rad/s)0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.1545550555Bus Voltage (V)Time (s)Figure 4.4: PMSG simulation results with variable speedIn Figure 4.4, we can see that the torque remains ripple free as the machine slows down.As expected the PLL tracks the rotor speed and position well and the power converterincreases the phase currents, and thereby the machine torque, to compensate for the lowerphase voltages in order to maintain the output bus voltage.384.2. Experimental Platform and ResultsTable 4.3: PMSG ParametersParameter ValueRotor Type Round RotorNumber of Pole Pairs 4Voltage Constant 176.1mV · s/radRotor Inertia 9.97mN ·m/s2Stator Resistance 693mΩDirect Axis Inductance 1.195mHQuadrature Axis Inductance 1.299mHStall Torque 12N ·mStall Current 9.6A4.2 Experimental Platform and ResultsIn order to validate the control strategy, an experimental setup was constructed (Figure 4.5)consisting of prime mover (DC machine – Mavilor MS450.040.0099.E7 – Figure 4.6), whichsimulates a wind turbine, coupled to a PMSG (Fanuc 10S A06B-0315-B063 – Figure 4.7)controlled by a six-switch, three-phase power stage developed for this work (Beaver board).A three-phase sensing and signal conditioning board was also developed (Hawk board), andthe control system developed on a dSpace real time controller (DS1103). The inverter loadswere simulated using an electronic load controlled by a Texas Instruments Delfino DSP(TMS28F335). The DC machine was powered by a constant voltage power supply (Chroma62024P-100-50). The PMSG was characterized prior to implementation of the power stage(Table 4.3).The Beaver board was constructed using the power devices in Table 4.4. To drive theIGBTs Micrel drivers (MIC4421) and TI digital isolators (TI ISO721) were used. A customlow noise/coupling isolated gate drive power supplies were also designed and constructed inorder to provide power to the high side switches.394.2. Experimental Platform and Results3-Phase Power Board (Beaver)Signal conditioning (Hawk)Input InductorsAuxillary SuppliesInverter Load ControllerFigure 4.5: Experimental setup (top) and power stage (bottom)404.2. Experimental Platform and ResultsFigure 4.6: DC machine prime mover (Mavilor MS450)Figure 4.7: Permanent Magnet Synchronous Machine (Fanuc 10S)414.2. Experimental Platform and ResultsTable 4.4: Six-switch, three-phase power stage (Beaver) componentsParameter ValueSwitches STGW50H60 IGBT (600V , 100A)Input inductors 3mH Amorphous coreInput filter 1.5µF , 1kV polypropylene with 2Ω damping resistorsDC Bus Capacitor 820µF , 400V electrolyticThe same control philosophy simulated earlier (4.1) was implemented in the dSpace.SVM was used for the switches and the current and voltage loops were tuned based uponthe commonly used technical-optimum and symmetrical-optimum methods, respectively[27].Due to limitations in the dSpace platform the switching speed was reduced from 25kHz to15kHz. Furthermore, because all sampling in the dSpace must occur synchronously the MAFfilter was implemented with a sampling rate of 15kHz and a kernel size of M = 125 resultingin a filter which eliminates frequency components of:f = FsM= 15kHz125= 120Hz (4.4)and harmonics thereof. For comparison purposes, MAF and non-MAF control code wasimplemented with the same controller parameters for both cases.The electric torque (Te) generated by the PMSG was indirectly measured by outputingthe quadrature current (Iq) from the dSpace using a Digital-to-Analog Converter (DAC) andscaling it to match the steady state torque measured on a torque sensor (Magtrol TM307/011)under constant current load. The resulting signal could then be displayed on an oscilloscope.The torque sensor could not be used to measure the ripple torque directly as the bandwidthof the sensor and it’s signal conditioning amplifier is limited (≈ 10Hz).In order to protect the prototype from extreme operating conditions, hardware Over-Voltage Protection (OVP) and Over-Current Protection (OCP) was implemented through424.2. Experimental Platform and Resultsa custom interface board (Armadillo) attached to the dSpace unit. In the event of a largephase current or voltage (positive or negative) the dSpace unit is disconnected from theBeaver board and the switches are forced off.Experiments were performed at various loading conditions and machine speeds.4.2.1 Linear Load at fe = 65HzIn the first test the machine is rotating at fe = 65Hz and a linear load of 370W (1.54Arms at240Vrms). In the non-MAF case (Figure 4.8 top) the torque signal (yellow) has a significanttorque ripple at twice the line frequency. The distortion caused by the inverter load canalso be seen on the phase current (red). The magnitude of the ripple in this case is 1.2Nmresulting in a ripple factor of:%Ripple = 1.2N ·m2.15N ·m· 100% = 55.8% (4.5)Looking at the same loading conditions with the MAF enabled (Figure 4.8 bottom), wefind the ripple has been completely eliminated from the torque signal (yellow) and only thesteady state value remains. The distortion of the phase current is also completely eliminated.4.2.2 CF = 2.3 Load at fe = 65HzIn the next test the machine is still rotating at fe = 65Hz, however a high CF load (CF = 2.3)of similar power is applied instead of the linear load. In the non-MAF case (Figure 4.9 top)the torque signal (yellow) has an even larger torque ripple at twice the line frequency. Thedistortion caused by the inverter load on the phase current (red) is also increased. A sub-harmonic oscillation is also observed. The magnitude of the ripple in this case is 2.0Nmresulting in a ripple factor of:434.2. Experimental Platform and ResultsV  (V)I  (A)T (Nm)I     (A)loadeadcV  (V)I  (A)T (Nm)I     (A)loadeadc1.2Nm1.3A5.0A4V1.3A5.0A4VFigure 4.8: Steady state operation without MAF (top) and with MAF (bottom) at 65Hzmachine frequency and linear load: Load current (blue, 2A/div), machine torque (orange,2Nm/div), phase A current (red, 5A/div), and DC voltage (yellow, 10V/div, AC coupled).444.2. Experimental Platform and Results%Ripple = 2.0N ·m1.9N ·m· 100% = 105% (4.6)As in the previous case, looking at the same loading conditions with the MAF enabled(Figure 4.9 bottom), we find the ripple has been completely eliminated from the torque signal(yellow) and only the steady state value remains. The distortion of the phase current is alsocompletely eliminated. As expected the ripple on the DC bus voltage increases and changesfrom sinusoidal in the linear to sawtooth-like in the non-linear case.4.2.3 Increased Linear Load at fe = 95HzNext to simulate an increase in the wind speed the machine is rotating at fe = 95Hz anda linear load of 590W (2.46Arms at 240Vrms) is applied. In the non-MAF case (Figure 4.10top) the torque signal (yellow) still has a significant torque ripple at twice the line frequency.The distortion caused by the inverter load continues to be present on the phase current (red).The magnitude of the ripple in this case is 1.6Nm resulting in a ripple factor of:%Ripple = 1.6N ·m2.77N ·m· 100% = 57.8% (4.7)As in the previous cases, with the MAF enabled (Figure 4.10 bottom), we find the ripplehas been completely eliminated from the torque signal (yellow) and only the steady statevalue remains. The distortion of the phase current is also completely eliminated.4.2.4 CF = 2.3 Load at fe = 95HzIn the next test the machine is still rotating at fe = 95Hz, however a high CF load (CF = 2.3)of similar power is applied instead of the linear load. In the non-MAF case (Figure 4.11 top)the torque signal (yellow) has an even larger torque ripple at twice the line frequency. The454.2. Experimental Platform and ResultsV  (V)I  (A)T (Nm)I     (A)loadeadcV  (V)I  (A)T (Nm)I     (A)loadeadc2.0Nm2.5A7.0A6V2.5A4.0A6VFigure 4.9: Steady state operation without MAF (top) and with MAF (bottom) at 65Hzmachine frequency and high CF load: Load current (blue, 2A/div), machine torque (orange,2Nm/div), phase A current (red, 5A/div), and DC voltage (yellow, 10V/div, AC coupled).464.2. Experimental Platform and ResultsV  (V)I  (A)T (Nm)I     (A)loadeadcV  (V)I  (A)T (Nm)I     (A)loadeadc1.6Nm2.2A6V2.2A6.0A6V6.0AFigure 4.10: Steady state operation without MAF (top) and with MAF (bottom) at 95Hzmachine frequency and linear load: Load current (blue, 2A/div), machine torque (orange,2Nm/div), phase A current (red, 5A/div), and DC voltage (yellow, 10V/div, AC coupled).474.2. Experimental Platform and Resultsdistortion caused by the inverter load on the phase current (red) is also increased. A sub-harmonic oscilliation is also observed. The magnitude of the ripple in this case is 2.4Nmresulting in a ripple factor of:%Ripple = 2.4N ·m2.4N ·m· 100% = 100% (4.8)As in the previous case, looking at the same loading conditions with the MAF enabled(Figure 4.11 bottom), we find the ripple has been completely eliminated from the torquesignal (yellow) and only the steady state value remains. The distortion of the phase currentis also completely eliminated. As expected the ripple on the DC bus voltage increases andchanges from sinusoidal in the linear to sawtooth-like in the non-linear case.In the previous four cases, under different load and machine speed conditions the rippletorque was completely eliminated. The MAF was effective on both linear and non-linear loadsand was effective regardless of the machine speed. Next, we will evaluate the performance ofthe MAF under transient conditions.4.2.5 Linear Load TransientIn order to prove the effectiveness of the MAF filter during transients the machine was drivenat fe = 95Hz and a linear inverter load of 370W was applied and the system was allowedto reach steady-state. The load was then doubled to 740W . The test was performed withand without the MAF. Without the MAF (Figure 4.12 top) the ripple in the torque (yellow)can be clearly seen (as in the steady-state case) and the settling time after the transient wasdetermined to be approximately 68ms. With the MAF enabled (Figure 4.12 bottom), theripple is eliminated and the settling time is also reduced to approximately 52ms. The phasecurrent (red) is also not distorted during the transition.484.2. Experimental Platform and ResultsV  (V)I  (A)T (Nm)I     (A)loadeadcV  (V)I  (A)T (Nm)I     (A)loadeadc2.4Nm5A12V5.0A5.0A9V8.0AFigure 4.11: Steady state operation without MAF (top) and with MAF (bottom) at 95Hzmachine frequency and high CF load: Load current (blue, 2A/div), machine torque (orange,2Nm/div), phase A current (red, 5A/div), and DC voltage (yellow, 10V/div, AC coupled).494.2. Experimental Platform and ResultsV  (V)I  (A)T (Nm)I     (A)loadeadcV  (V)I  (A)T (Nm)I     (A)loadeadc-1.4Nm52ms-2.8Nm68ms-1.4Nm-2.8NmFigure 4.12: Load transient operation (370W to 740W ) without MAF (top) and with MAF(bottom) at 95Hz machine frequency and linear load: Load current (blue, 2A/div), machinetorque (orange, 2Nm/div), phase A current (red, 5A/div), and DC voltage (yellow, 10V/div,AC coupled).504.3. Summary4.2.6 High CF Load TransientNext, with the machine still driven at fe = 95Hz a CF = 2.3 inverter load of 370W wasapplied and the system was allowed to reach steady-state. As in the previous case, the loadwas then doubled to 740W . Without the MAF (Figure 4.13 top) the ripple in the torque(yellow) can be clearly seen (as in the steady-state case) and the settling time was identicalto the previous case (68ms). With the MAF enabled (Figure 4.13 bottom), the ripple iseliminated and as before, the settling time is also reduced (52ms). The phase current (red)is also not distorted during the transition.In all cases, the MAF filter offers extremely effective ripple torque elimination without anyadditional component or material cost. It is possible to remove the ripple torque by slowingthe voltage loop significantly, however this will negatively impact the transient response ofthe control loop.4.3 SummaryIn this chapter system simulations and experimental testing of a ripple torque reduction tech-nique using the MAF filter presented in the previous chapter was performed. The simulationsshowed excellent rejection of the ripple torque by filtering the DC bus voltage prior to thecontrol loop. Validation of the technique trough experimentation proved the effectiveness ofthe MAF filter in the removal of the ripple torque from the PMSG. The technique was effec-tive with linear and non-linear inverter loading conditions and worked with different machinespeeds. In the final chapter, a summary of the proposed ripple torque reduction technique ispresented, along with areas of future work.514.3. Summary-3.5NmV  (V)I  (A)T (Nm)I     (A)loadeadcV  (V)I  (A)T (Nm)I     (A)loadeadc-1.8Nm52ms68ms-1.8Nm -3.5NmFigure 4.13: Load transient operation (370W to 740W ) without MAF (top) and with MAF(bottom) at 95Hz machine frequency and high CF load: Load current (blue, 2A/div), ma-chine torque (orange, 2Nm/div), phase A current (red, 5A/div), and DC voltage (yellow,10V/div, AC coupled).52Chapter 5Conclusions5.1 SummaryThis thesis introduced a method of reducing the stator ripple current in a PMSG WECScaused by a grid-tie inverter type loading. By reducing the stator ripple current the rippletorque experienced on the shaft of the machine is reduced, leading to longer bearing lifeand reduced stress on the shaft, drivetrain, and tower; thereby, reducing the capital andmaintenance costs.The low frequency loading effect caused by a grid-tie inverter was presented and thedifference between an inverter-type load and a constant resistance or constant current loadexplained.A low frequency model of a PMSG based WECS system was developed in this work.The model, derived by simplifying the rotor reference frame model, allows for improvedunderstanding of the effect ripple current loads have on a PMSGs stator currents and electrictorque. The model was then used to determine how to control the stator current to minimizethe ripple torque induced by an inverter type loading.Using the knowledge gained from the low frequency model, a control strategy was de-veloped using a MAF to eliminate the ripple currents and torque in the PMSG. Therebyimproving the energy extraction and reducing the wear on the PMSG.The theoretical concepts presented in this thesis were supported by mathematical deriva-tions, and then validated through simulation and experimental results. The contribution of535.2. Future Workthe work to the field of renewable energy extraction is proven through publication in [22].5.2 Future WorkThe concepts introduced in this work are an extension of previous work done in [22, 23] forgrid-tie fuel cell systems. The work could be extended to work with other popular three-phase topologies, such as the Vienna rectifier. Future contributions may also include digitalcompensators to further improve the phase response of the MAF, which is currently underdevelopment by the research team.54Bibliography[1] Z. Chen, J.M. Guerrero, F. Blaabjerg, “A Review of the State of the Art of PowerElectronics for Wind Turbines,” Power Electronics, IEEE Transactions on, vol.24, no.8,pp. 1859-1875, Aug. 2009.[2] J.W. Kolar, T. 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