MODELING AND POWER MANAGEMENT OF A HYBRID WIND-MICROTURBINE POWER GENERATION SYSTEM by Sreedhar Reddy Guda A thesis submitted in partial fulfillment of the requirements for the degree of Master of Science in Electrical Engineering MONTANA STATE UNIVERSITY Bozeman, Montana July 2005 COPYRIGHT by Sreedhar Reddy Guda 2005 All Rights Reserved ii APPROVALof a thesis submitted by Sreedhar Reddy Guda This thesis has been read by each member of the thesis committee and has been found to be satisfactory regarding content, English usage, format, citations, bibliographic style, and consistency, and is ready for submission to the College of Graduate Studies. Dr. Hashem Nehrir Approved for the Department of Electrical and Computer Engineering Dr. James Peterson Approved for the College of Graduate Studies Dr. Joseph Fedock iii STATEMENT OF PERMISSION TO USE Inpresentingthisthesisinpartialfulfillmentoftherequirementsforamasters degreeatMontanaStateUniversity,IagreethattheLibraryshallmakeitavailableto borrowers under rules of the Library. IfIhaveindicatedmyintentiontocopyrightthisthesisbyincludingacopyright notice page, copyingisallowable onlyfor scholarly purposes, consistent withfair use as prescribed in the U.S. Copyright Law. Requests for permission for extended quotation fromorreproductionofthisthesisinwholeorinpartsmaybegrantedonlybythe copyright holder. Sreedhar Reddy Guda July 2005 iv ACKNOWLEDGEMENTS I am grateful to acknowledge and thank all of those who assisted me in my graduate program at Montana State University.First, I wouldlike to thank Dr. M. H. Nehrir,my academicadvisorhereatMSU.Theguidance,support,patienceandpersonaltimehe invested throughout myyears as a graduate student havebeen truly appreciated. Special thanksareextendedtomyothergraduatecommitteemembers,Dr.H.GaoandDr.R. Gunderson. Mr. C.Wang,myfellow student andcolleague, deserves deepest thanksfor his time and the clarifying conversations that were so useful to my understanding of this thesisand othermatters. Mostimportantly, I wouldlike to thankmyfamily andfriends for their support throughout all the years. v TABLE OF CONTENTS 1. INTRODUCTION.......................................................................................................1 Background .................................................................................................................1 Hybrid Generation System...........................................................................................2 Literature Review........................................................................................................5 Literature Review on Wind Energy Conversion System...........................................6 Literature Review on Wind Turbines....................................................................7 Literature Review on Self-excited Induction Generator ........................................8 Literature Review on Microturbine Generation System..........................................13 Objective of this Thesis and Organization of Remaining Chapters .............................15 References.................................................................................................................17 2. WIND ENERGY CONVERSION SYSTEM WIND TURBINE MODELING ....................................................................................20 Introduction...............................................................................................................20 Functional Structure of Wind Turbines ......................................................................21 Wind Turbine Modeling ............................................................................................22 Inputs and Outputs of a Wind Turbine ...................................................................23 Power Extraction from the Air stream....................................................................24 Tip Speed Ratio .....................................................................................................26 Typical Wind Turbine Operating Systems..............................................................27 Variable Speed Wind Turbine System....................................................................30 Pitch Angle Controller .......................................................................................32 Performance Curves...............................................................................................33 Simulation Results.....................................................................................................34 Conclusion.........................................................................................................42 References.................................................................................................................44 3. WIND ENERGY CONVERSION SYSTEM -SELF-EXCITED INDUCTION GENERATOR (SEIG) MODELING...........................45 Introduction...............................................................................................................45 Induction Machine.....................................................................................................46 Equivalent Electrical Circuit of Induction Machine ................................................47 Self-Excited Induction Generator (SEIG)...................................................................48 Methods of Analysis ..................................................................................................50 Steady-state Model ................................................................................................50 Steady-state and Transient Model (abc-dq0 transformation)...................................54 abc-dq0 Transformation. ....................................................................................54 Voltage Equations in Arbitrary Reference-Frame Variables ...............................56 vi TABLE OF CONTENTS - CONTINUED Torque Equations...............................................................................................59 Stationary Reference Frame ...............................................................................60 SEIG Model.......................................................................................................61 Simulation Results.....................................................................................................65 Saturation Curve ................................................................................................66 Process of Self-excitation...................................................................................67 Conclusion.........................................................................................................78 References.................................................................................................................80 4. MICROTURBINE GENERATION SYSTEM...........................................................82 Introduction...............................................................................................................82 Microturbine Generation (MTG) System...................................................................83 Types of Microturbine Systems..........................................................................84 Basic Process and Components of a MTG System. ................................................85 Mathematical Representation of a Microturbine .....................................................87 Speed and Acceleration Control .........................................................................88 Fuel System. ......................................................................................................89 Compressor-Turbine ..........................................................................................90 Temperature Control ..........................................................................................91 Permanent Magnet Synchronous Generator (PMSG)..............................................93 Permanent Magnet Materials..............................................................................93 Operating Region of a PMSM............................................................................95 dq Axis Representation of a PMSM...................................................................96 Simulation Results.....................................................................................................99 Conclusion.......................................................................................................105 References...............................................................................................................106 5. HYBRID WIND-MICROTURBINE GENERATION SYSTEM.............................108 Introduction.............................................................................................................108 Hybrid Wind-Microturbine System..........................................................................109 Description of the System....................................................................................110 Power Electronics Interface..................................................................................111 Control Principle..............................................................................................113 3-Phase Voltage Source Inverter ......................................................................114 Current Controller ............................................................................................115 Voltage Controller ...........................................................................................117 Simulation Results...................................................................................................118 Case 1. (Rise in wind input Constant load) .........................................................120 Case 2. (Drop in wind input-Constant load) .........................................................130 vii TABLE OF CONTENTS - CONTINUED Case 3. (Rise in load demand-Constant wind) ......................................................134 Case 4. (Rise in load demand-Constant wind) ......................................................138 Conclusion.......................................................................................................142 References...........................................................................................................143 6. CONCLUSION OF THE THESIS AND FUTURE WORK.....................................144 Conclusion of the Thesis..........................................................................................144 Future Work ............................................................................................................145 APPENDIX A: SIMULATION DIAGRAMS .............................................................147 viii LIST OF TABLES Table Page 2.1Comparison of Fixed and Variable Speed wind turbine systems. .............................29 3. 1: Induction Machine Parameters...............................................................................65 5.1Parameters of the controllers for 3-phase VSI. ......................................................117 ix LIST OF FIGURES Figure Page 1.1A typical wind-microturbine hybrid generation system. ............................................4 2.1.Power transfer in a wind energy converter..............................................................21 2.2Typical curves for a constant speed, stall-controlled (dotted)and variable speed pitch controlled (solid) wind turbine. ........................................28 2.3Typical pitch-regulated variable-speed wind turbine. ..............................................30 2.4Variable Speed pitch controlled wind turbine operation. .........................................32 2.5Pitch Angle Controller. ...........................................................................................33 2.6Simulated model of the variable speed pitch-regulated wind turbine. ......................35 2.7 Cp characteristics (blade pitch angleas the parameter)....................................36 2.8Output power of the wind turbine for different wind velocities................................37 2.9Wind turbine rotor speed (referred to generator side) variations with wind. .............38 2.10Tip speed ratio of the wind turbine. .......................................................................39 2.11Variation of power coefficient with wind. .............................................................40 2.12Pitch angle controller response to the wind speed change. .....................................40 2.13Wind turbine output power variation with change in wind speed. ..........................41 2.14Wind turbine torque variation with wind. ..............................................................42 3.1Per-phase equivalent circuit of the induction machine referred to the stator.............47 3.2Self-excited induction generator with external capacitor. ........................................48 3.3Determination of stable operation of self-excited induction generator. ....................49 3.4Equivalent circuit of self-excited induction generator with R-L Load. .....................51 x LIST OF FIGURES - CONTINUED Figure Page 3.5Transformation for stationary circuits portrayed by trigonometric relationships. .....55 3. 6 Two-pole, 3-phase, wye connected symmetrical induction machine ........................56 3.7Arbitrary reference-frame equivalent circuits for a 3-phase, symmetrical induction machine. ............................................................................59 3.8dq model of SEIG in stationary reference frame (All values referred to stator). .......62 3.9Variation of magnetizing inductance with magnetizing current. ..............................66 3.10Voltage build up in a self-excited induction generator. ..........................................68 3.11Variation of magnetizing current with voltage buildup. .........................................69 3.12Variation of magnetizing inductance with voltage buildup. ...................................70 3.13Failed excitation due to heavy load. ......................................................................70 3. 14Generator speed (For failed excitation case). ........................................................71 3.15SEIG phase voltage variations with load. ..............................................................72 3.16Magnetizing current variations with load...............................................................73 3.17Magnetizing inductance variations with load.........................................................74 3.18Rotor speed variations with load. ..........................................................................74 3.19Stator current variations with load.........................................................................75 3.20Load current variations with load. .........................................................................76 3.21Variation of torques with load. ..............................................................................77 3.22Output power produced by wind turbine and SEIG. ..............................................77 4.1Microturbine based CHP system (Single-Shaft Design)...........................................85 xi LIST OF FIGURES - CONTINUED Figure Page 4.2Block diagram of a microturbine. ............................................................................87 4.3Speed controller for the microturbine. .....................................................................89 4.4Block diagram of the fuel system. ...........................................................................90 4.5Compressor-Turbine package of a microturbine. .....................................................91 4.6Temperature controller............................................................................................92 4.7Hysteresis loop in the form of magnetization Band magnetic field strength H.................................................................................94 4.8Permanent magnet machine operating points on B-H curve. ....................................95 4.9Synchronously rotating frame equivalent circuits of a PMSM. ................................97 4.10Block diagram of the simulated MTG system......................................................100 4.11Power output from the MTG system. ..................................................................102 4.12Fuel demand signal of the microturbine...............................................................102 4.13Variation of shaft torque and electric torque generated. .......................................103 4.14Rotor speed variations with load. ........................................................................104 4.15Voltage across the stator terminals of PMSG.......................................................104 5.1Block diagram of the hybrid generation system. ....................................................110 5.2Block diagram of the power electronics interfacing. ..............................................112 5. 3 Power flow between two points.............................................................................113 5.4Three-phase DC/AC voltage source inverter. ........................................................115 5.5Block diagram of the current control loop for the inverter. ....................................116 5.6Block diagram of the voltage control loop for the inverter.....................................117 xii LIST OF FIGURES - CONTINUED Figure Page 5.7Wind input to the hybrid generation system. .........................................................120 5.8MTG system real power output variations with wind. ...........................................121 5.9WECS real power output variations with wind. .....................................................121 5.10MTG system output reactive power variations with wind. ...................................123 5.11WECS output reactive power variations with wind..............................................124 5.12Fuel demand signal of the microturbine...............................................................124 5.13Microturbine rotor speed variations.....................................................................125 5.14SEIG rotor speed variations. ...............................................................................126 5.15Variation of DC bus voltage on the MTG side.....................................................127 5.16Variation of the DC bus voltage on the WECS side. ............................................127 5.17 MTG side inverter output voltage.........................................................................128 5.18WECS side inverter output voltage. ....................................................................129 5. 19Wind input to the hybrid generation system. ......................................................130 5. 20MTG system real power output variations with wind. ........................................131 5. 21WECS real power output variations with wind. ..................................................131 5. 22MTG system reactive power variations with wind. .............................................132 5. 23WECS reactive power variations with wind. ......................................................133 5. 24Voltage at the load terminals. .............................................................................133 5. 25Load demand of thehybrid generation system...................................................134 5. 26MTG system real power output variations with load...........................................135 5. 27WECS real power output variations with load. ...................................................135 xiii LIST OF FIGURES - CONTINUED Figure Page 5. 28MTG system reactive power variations with load. ..............................................136 5. 29WECS reactive power variations with load. .......................................................137 5. 30Voltage at the load terminals. .............................................................................137 5. 31Load demand of the hybrid generation system....................................................138 5. 32MTG system real power output variations with load...........................................139 5. 33WECS real power output variations with load. ...................................................139 5. 34MTG system reactive power variations with load. ..............................................140 5. 35WECS reactive power variations with load. .......................................................141 5. 36Voltage at the load terminals. .............................................................................141 xiv ABSTRACT The goal of this thesisis to evaluate the performance of ahybrid wind-microturbine energysystemthroughcomputersimulationstudies.Theprimaryfocusofthisstudyis the development of dynamic models for a standalone wind energy conversion system and amicroturbinegenerationsystem.Thesystemmodeldevelopedissuitableforpower management in distributed generation studies. Thedevelopedmodelofthewindenergyconversionsystemconsistsofdynamic models for a wind turbine as well as an electric generator. A detailed model of the wind turbine based on a set of nonlinear curves is presented. The electric generator, driven by the wind turbine, is a self-excited asynchronous (induction) generator suitable for isolated andgrid-connectedoperations.Modelingoftheelectricgenerator,completewith saturation characteristic, is done using dq-axis theory. Also, the importance of excitation-capacitors during isolated mode of operation is explained. Adynamicmodelforthemicroturbinegenerationsystemisachievedbyintegrating models of a microturbine and an electric generator driven by it. The model illustrates the dynamicsofthemicroturbineanditscontrolsystems.Asetofmathematicalequations areusedtomodelapermanentmagnetsynchronousmachineactingastheelectric generatorofthemicroturbinegenerationsystem.Thedevelopedsystemiscapableof simulating the dynamics of the microturbine generation system, demonstrating its ability to meet load power requirements. Thedynamicmodelsofthewindenergyconversionsystemandthemicroturbine generationsystemareintegratedusingpowerelectronicsinterfacingandsimulatedin MATLAB/Simulink. Simulation results indicate the suitability of the developed model to studythedynamicbehaviorofthehybridgenerationsystemunderdifferentload conditions. 1 CHAPTER 1 INTRODUCTION Background Thisthesisisconcernedwiththedevelopmentofacomputersimulationmodelto evaluate the performance of a stand-alone hybrid generation system comprising of a wind energyconversionsystemandamicroturbinegenerationsystem.Modelsrepresenting each system components are developed, integrated and used to observe the overall system behavior. Theeverincreasingenergydemands,dwindlingsourcesoffossilfuelsandconcern aboutpollutionlevelsintheenvironmenthasbeenthedrivingforcebehindelectricity generationusingrenewableenergysources.Tappingtheenergyavailablefromthe renewableresourcesallowstheattainmentofnotablereductionsinthepollutionlevels andworryingclimatechanges.Ontheotherhand,theavailabilityofenergyfrom renewable sources like wind energy, solar energy, etc. is unpredictable and is affected by factorsbeyondhumancontrol.Therefore,suchrenewableenergysystemsshouldbe backed up by conventional sources of energy or energy storage devices in order to ensure continuityoftheenergysupply.Thisleadsustothetopicofhybridgenerationunits comprising conventional or unconventional sources of energy or both, where two or more individualgenerationsystemsoperateinparallelsupplementingeachother.Atypical 2 hybridgenerationsystemreliesonpowerelectronicinterfacingforfunctioningand interfacing between different generating units and with the distribution network (in grid-connected operation). In remote andisolated areasfarfrom the grid,itmaynot be an economicallyviable option to supply electric power from the grid. This is due to the high cost of transmission linesandhighertransmissionlossesthataccompanydistributionofcentrallygenerated power to remote areas. The deregulation of electricity market has made it possible for the hybrid systems to beinstalled asisolated units or grid-connected units (not discussedin thisthesis)actingasdistributedgenerations(DG)sources.Itiswelldocumentedinthe literaturethatDGscouldhavepositiveimpactsontheoperationofpowersystemsto which they are connected. DGs come in different forms such as on-site gas or diesel fired turbines,reciprocatingengines,microturbines,smallhydroinductiongenerators,wind turbinesandfuelcells.DGtechnologypromisestobeanefficient,environmentally friendlyandreliablepowersource.PropermodelingoftheseDGs,whichconstitute hybridgenerationsystems,isneededinordertostudytheiroperationandimpacton power systems. Hybrid Generation System Hybrid generation systems usually combine renewable sources like wind power with conventional sources of energy like gas turbines (or microturbines) to from an equivalent ofaminiature(orvirtual)grid.Suchaconfigurationaddressestwoimportantissues 3 namely, higher emissions because of conventional generation techniques and high cost of energy capture from renewable sources. For wind energysystems, the renewablesource of energy considered in this thesis, the emissions are nil but it has relatively high capital costs.Withmodernmicroturbinesystems,theothergeneratingsysteminthehybrid generationsystem,theenergycostsarerelativelylowerandtheemissionsofundesired gases is also low. In this thesis, these two systems models are integrated to form a model of the hybrid generation system as explained in the following paragraphs. Ahybridsystemcouldbedesignedtooperateeitherinisolatedmodeoringrid-connectedmode,throughpowerelectronicinterface.Thepowerelectronicinterface should have the ability to maintain the hybrid generation system parameters like voltage, frequency etc., at prescribed (acceptable)levels. It is essential to have a good control of the power angle and the voltage level by means of an inverter which is the main block of thepowerelectronicinterface.Controloftheinvertersoutputvoltageandthepower anglecontrolstheflowofrealpowerandreactivepower.Atypicalwind-microturbine hybrid generationsystem, along withits power electronicsinterface,is showninFigure 1.1. 4 AC loadWind turbineMicroturbineGeneratorPower electronicsinterfacePower electronicsinterfaceGeneratorWind energy systemMicroturbine systemStorage Figure 1.1A typical wind-microturbine hybrid generation system. Thehybridsystempresentedinthisthesiscomprisesofawindenergyconversion system (WECS) acting as the renewable source of energy and amicroturbine generation (MTG) system serving as the conventional source of energy. In general, it also includes a storage unit which helps to increase the overall system efficiency (Figure 1.1). However, astheemphasisisonMTGandWECSsystems,thehybridsystemconsideredinthis thesis doesnt have a storage device. Electricity generation by wind promises to be the best source of renewable energy, as rapidadvancesinwindturbinetechnologyhavemadeutilizationofwindenergyfor electricity generation possible. Moreover, the economic aspects of these technologies are now sufficiently promising to justify their use.5 Theothercomponentoftheproposedhybridgenerationsystem(Figure1.1),which triestooffsetthehighinstallationcostsinvolvedwiththewindenergysystem,isthe microturbinesystem.Withthecombinationofhighreliabilityandlowinstallationcosts microturbinesareseenasoneofthekeycomponentsinthedistributedgeneration.The emission levels of microturbines are low and they are capable of working on a variety of fuels like natural gas, sour gas, propane etc. Literature Review Thissectionoffersabriefreviewofsomeofthepublishedworkonthehybrid generating systems. The work referred in the following sections is focused mostly on the modelingofindividualcomponentsofthehybridsystem.However, thissectiondoesnt offer any review on the modeling of power electronics interface, as it is beyond the scope of this thesis. Reference[1.1]presentsahybridconfigurationcomprisingofawinddieselsystem originallydevelopedbytheHydro-Quebec,aimedatreducingthecostofelectricity supplyin remote areas. The two mainblocks of thesystem presented are, diesel- driven synchronousgeneratorandthewindturbinedrivenbytheasynchronous(induction) generator.Thewindturbineblockusesa2-dimensionallookuptabletocomputethe turbine torque output as a function of wind speed and turbine speed. At low wind speeds both the induction generator and the diesel-driven synchronous generator are required to feed the load. When the wind power exceeds the load demand, it is possible to shut down 6 thediesel-generator.Inthisall-windmode,thesynchronousmachineisusedasa synchronous condenser andits excitation systemcontrols the gridvoltage at its nominal value.A secondaryloadbankis used to regulate the systemfrequencyby absorbing the wind power exceeding consumer demand. Reference [1.2] presents a hybrid generation system referred as a virtual power plant. Thesystemconsistsofawindfarmandagasturbinedrivensynchronousgenerator whoseoutputsarecombinedbeforeconnectingtothegrid.Inthispaper,theauthors developeddynamicmodelsforthesynchronousgeneratorandinductiongeneratorand, the dynamicmodel of a wind turbineisscaled appropriately to represent the output of a windfarm.Thevoltageandtheoutputpowerarecontrolledviathegasturbineandthe synchronous generator model with the help of an automatic voltage regulator (AVR) and a power system stabilizer (PSS) attached to the synchronous generator. Literature Review on Wind Energy Conversion System Wind energy conversionsystems (WECS) are the devices which are used to convert thewindenergytoelectricalenergy.Thereexistsalargecollectionofliteratureonthe modelingofwindenergyconversionsystemsmorespecificallyonthemodelingof individualsystemcomponentsofawindenergyconversionsystem.Awindenergy conversionsystemismainlycomprisedoftwosubsystems,namelyawindturbinepart and an electric generator part. Detailed descriptions of these concepts can be found in text 7 booksonwindenergy[1.3]-[1.5].Asummaryofthetypicalwindturbinemodelsand their control strategies is presented in [1.4]. LiteratureReviewonWindTurbines.Intheliterature,mostofthemodelsusedto representawindturbinearebasedonanonlinearrelationshipbetweenrotorpower coefficient and linear tip speed of the rotor blade [1.3]-[1.9]. MuljadiandButterfield[1.6]mentiontheadvantagesofemployingavariablespeed windturbineandpresentamodelofitwithpitchcontrol.Inthismodel,duringlowto medium windspeeds, the generator and the power converter control the wind turbine to maximize the energy capture by maintaining the rotor speed at a predetermined optimum value.Forhighwindspeedsthewindturbineiscontrolledtomaintaintheaerodynamic power produced by the wind turbine either by pitch control or by generator load control. However, generator load control in the high wind regions, in some cases suffers from the disadvantage of exceeding the rated current values of the stator windings of the generator. Care should be taken not to exceed the rated values of the current. References[1.7]and[1.8]proposeadetailedmodelofthevariablespeedpitch controlledwindturbinesuitableforstudyingthetransientstabilityofmulti-megawatt sized wind turbines. The simulated model is based on a set of non linear curves depicting therelationbetweenthebladetipspeed,rotorpowercoefficientandpitchangleofthe windturbine.Thereferencesalsoconsideradetailedmodelforthewindinputwhich includes the effects of gust, noise added to the base value of wind input. Reference [1.7] 8 uses transfer-functions to represent the dynamics of the electrical generator driven by the wind turbine, while [1.8] uses dq-axis representation for the synchronous machine acting as an electrical generator. A proportional integral (PI) controller is used to implement the pitchanglecontrollertolimitthewindturbineoutputinthehighwindspeedregimes. Simulationresultsobtainedforthesemodelsindicateagoodapproximationofthe dynamicperformanceofalargewindturbinegeneratorsubjectedtoturbulentwind conditions. As an extension to this work done in [1.7] and [1.8], Slootweg et al [1.9] presented a generalmodelthatcanbeusedtorepresentalltypesofvariablespeedwindturbinesin powersystemdynamicsimulations.Themodelingofthewindturbinegivenbythe authors retains the pitch anglecontroller, which reduces wind turbine rotor efficiency at highwindspeeds,asgivenin[1.7]and[1.8].Thewindturbinedynamicsare approximatedusingnonlinearcurves,whicharenumericalapproximations,toestimate thevalueofwindturbinerotorefficiencyforgivenvaluesofrotortipspeedandpitch angle of the blade. The authors offer a comparison between the per-unit power curves of two commercial wind turbines and the one obtained theoretically by using the numerical approximation.Theresultsindicatethatageneralnumericalapproximationcanbeused to simulate different types of wind turbines. Literature Review on Self-excited Induction Generator. The conversion of mechanical power of the wind turbine into the electrical power can be accomplished by an electrical generator which can be a DC machine, a synchronous machine, or an Induction machine. 9 DC machine was used widely until 1980s, in smaller power installations below 100 kW, becauseofitsextremelyeasyspeedcontrol[1.3].ThepresenceofcommutatorsinDC machineshaslowreliabilityandhighmaintenancecosts.Thesecondkindofelectric generators are synchronous generators, suitable for constant speed systems. Requirement ofDCfieldcurrentandreducedwindenergycaptureofconstantspeedsystems, compared to variable speed systems, are discouraging factors in their use in wind systems [1.3].AnotherchoicefortheelectricgeneratorinaWECSisapermanentmagnet synchronousgenerator.Reference[1.10]presentsamodelofthevariablespeedwind turbineconnectedtoapermanentmagnetsynchronousgenerator(PMSG).ButPMSGs suffer from uncontrollable magnetic field decaying over a period of time, their generated voltagetendstofallsteeplywithloadandisnotidealforisolatedoperation[1.11]. Inductiongenerators,ontheotherhand,havemanyadvantagesoverconventional synchronousgeneratorsduetotheirruggedness,noneedforDCfiledcurrent,low maintenance requirements and low cost [1.3]. References [1.12] and [1.13] give amodel of theWECS using doublyfedinduction generator (DFIG). DFIGs allow one to produce power both from the stator and the rotor of a (wound rotor) induction generator. However increase in the power output comes with increased cost of power electronics, and their control, for the rotor circuit. One advantage of this configuration is its suitability for grid-connected operations where reactive power is supplied by the grid. 10 One of theearlyworks done on the process of self-excitationininductionmachines wasbyBassetandPotter[1.14].Inthispapertheauthorshowsthattheinduction machine,drivenbyaprimemover,canbeself-excitedusingabankofcapacitors connectedacrossitsstator terminals.Thisfacilitates theoperationofinductionmachine asanisolatedgeneratorbyusingexcitationcapacitorstoaddressthereactivepower needsofthemachine,whilestillenjoyingthebasicadvantagesofusinginduction machinesforelectricitygeneration.Additionalbenefitsincludeaself-protection mechanismagainstshortcircuits.Theauthorsalsodiscusstheimportanceofthe saturationcurveandtheexcitationcapacitancereactance.Theauthordrawsconclusion that induction generator can be made to handle any type of load, provided that the loads are compensated to present unity power factor characteristics to the generator. As a continuation to this work Wagner [1.15] proposed a method to predetermine the inductionmachinecharacteristicswhenoperatingasself-excitedinductiongenerator (SEIG).Hisanalysisisbasedonequatingthereactivepowerofthewholeinduction generator system to zero. He points out that the value to which the terminal voltage of the SEIG will rise due to self-excitation is dependent upon the speed of the rotor, value of the capacitor, and the load. In a capacitor-excited generator used as an isolated power source, both the terminal voltage and the frequency are unknown and have to be computed for a givenspeed,capacitanceandload.Theanalysisiscomplicatedowingtothemagnetic saturation in the machine. Murthy et al [1.16] proposed an analytical technique using the Newton-Raphsonmethodtoidentifythesaturatedparameters,andthegenerated 11 frequencyforgivenoperatingconditions(speed,loadandcapacitancevalue).This methodusesasteady-stateequivalentcircuittoestimatethe(steady-state)parameters usingthevaluesobtainedfromtheanalyticalanalysis.Although,themethodissuitable for computer simulations, it is efficient for steady-state analysis only. In[1.17],Elderetalexaminethephenomenonofself-excitationininduction machinesbyofferingaphysicalinterpretationoftheprocess.Theauthorscomparethe initiationofthemachineexcitationwiththeresponseofaresonantcircuit(induction machine with capacitors), caused by the action of remnant magnetism present in the rotor circuitofthemachine.Theyrightlyacknowledge theimportanceofresidualmagnetism forself-excitationto occur,inadditionto theparametersidentifiedintheearlierworks. Asacontinuationofthiswork,theauthors[1.18]examinetheuseofaself-excited inductionmachineaslow-coststand-alonegenerator,usingdq-axisrepresentation, addressing the problem of guaranteed excitation in the case of loss of residual magnetism. In this paper theauthors also examine thebehavior of the generator underbalanced and unbalanced conditions. The results obtained are used to evaluate the static VAR sources availabletocontrolthemachineexcitation.Theauthorsconcludethattheexcitation problem is minimal if added capacitance or increased machine speed are allowed. Granthametal[1.19]haveproposedamethodforpredictingtheminimumand maximumvaluesofcapacitancenecessarytoinitiateself-excitationinastand-alone induction generator. Themaximum capacitanceis usuallysolarge to have anypractical significance.Subsequently,theirmethodhasbeenextendedtopredictthetransient 12 voltage build-up initial stages of self-excitation. Also, steady-state voltage and frequency areobtainedtheoreticallyaswellasbypracticalmeans,takingintoaccounttherotor parametervariationswithfrequency.Theanalysiswasdoneusingdqaxistheory.In [1.20] theauthorscontinuedtheirworkbysimulatingawindenergyconversionsystem (WECS) obtained by integrating the dq-axis SEIG model with a wind turbine model. The windturbinemodelismodeledusingthetorque-speedcharacteristicofawindturbine. Theeffectsofmagnetizinginductanceonself-excitationandtheloadinganalysisof induction generator are studied theoretically as well as in a laboratory set up. Inaworkrelatedtoestimatetheminimumvalueofexcitationcapacitanceforself-excitation to occur, Al-Jabri andAlolah [1.21] presented amethod to estimate the value of capacitance when inductive load is connected. This was done by solving two nonlinear equations which are obtained by applying loop-impedance method on the steady-state per phase equivalent circuit of the induction generator. Also, using this method it is possible to predict the (rotor) speed threshold below which self-excitation fails to occur. InasimilarworkMalikandAl-Baharani[1.22]haveexaminedtheeffectofthe exciting capacitors on the steady-state performance of anisolated SEIG with abalanced three-phaseload.Theyconcludethattheterminalvoltageisindependentoftheload power factor and depends only on the magnitude of the load impedance. LiwangandJian-YiSu[1.23],intheirpapershowedandcomparedthedynamic performanceofanisolatedSEIGunderdifferentpowerfactorloadingconditions,using 13 bothsimulationsandlaboratoryexperiments.Similarto[1.19],theyemployeddq-axis theoryfortheanalysisandsimulatedthesaturationcharacteristicoftheSEIGasa function of magnetizing reactance and magnetizing component of the current. Fromtheabovementionedreferences,itisclearthattheanalysisusingthesteady-stateper-phaseequivalentcircuitoftheinductionmachineismostlyusedtopredictthe steady-state operatingparametersofthemachine,andtheexcitationcapacitanceneeded for initiation of the self-excitation. The other method used [1.18], [1.19], [1.23] is, the dq-axis model based on the machine theory, to study the transient as well as the steady-state response of the induction machine. Literature Review on Microturbine Generation System Amicroturbinegeneration(MTG)systemcomprisesofamicroturbinedrivingan electrical generator. Thefollowing paragraphs give abriefsummary on the earlier work doneonthemicroturbinepartoftheMTGsystemaswellasabriefreviewofits electrical generator part. Microturbines are small high-speed versions of conventional heavy-duty gas turbines. Hencethedynamicmodelofaconventionalgasturbine,withrelativelysmall thermodynamicconstants,canbeadopted tostudytheimpactsofamicroturbineonthe overallsystem.Rowen[1.24]wasamongthefirstoneswhopresentedamodelofa heavy-dutygasturbinesuitableforuseindynamicpowerstudiesandinanalysesof connected equipment. The author gave a mathematical model of a single-shaft gas turbine 14 intermsofp.u.values.Thecontrolsystemsofthegivenmodelincludespeedcontrol, accelerationcontrol,andfuelsystem.Also,thedevelopedmodelissuitableforboth isolated and parallel operation. HannettandAfzalKhan[1.25],incontinuationtoRowenswork,validatedthegas turbinemodelbycomparingitsdynamicperformancewiththatofanoperatinggas turbinegenerationsystem.TheauthorsconcludethatthemodelproposedbyRowenis adequate for the representation of a gas turbine. In[1.26], theauthorsusedthevalidatedmodelofthegasturbine[1.25]tosimulate theresponseofacombinedcycleplant.Theirsystemcomprisesofagasturbinemodel and a steam turbine model which uses the waste heat from the gas turbine through a heat recovery system. This simulated (combined cycle) model can be used for system dynamic performance studies. In an extension to this work, Jurado et al [1.27] studied the influence of microturbines on distributionnetworks stability. They also examined the transient and voltage stability ofthesystem.Theauthorsconcludethatthemicroturbines,actingasdistributed resources,arecapableofprovidingeffectiveloadfollowingserviceinadistribution system. In [1.28] the authors utilize the proposed model of the microturbine to develop a controlsystemwithanadaptivecontrollerforafuelcell-microturbinehybridpower plant.Thedevelopedadaptivecontrollerhastheabilitytostabilizethesystemfor differentdisturbancesaffectingtheplantlikeloadpowervariationorachangeinthe 15 plantmodelparameterssuchasgascomposition.Continuingtheirworkin[1.29],the authorsusedautoregressionwithexogenoussignal(ARX)identificationalgorithmto arrive at the transfer-function of a microturbine model. These transfer-functions have the samedynamicresponseastheoriginaldynamicmodelofthemicroturbine,withthe added advantage of significant reduction in the model order. AmerAl-HinaiandAliFeliachi[1.30]presentedacompletemodeloftheMTG system,usedasadistributedgenerator,bymakinguseofthemicroturbinemodel discussedintheearlierparagraphs.Itincludesthepowerelectronicinterfacingandis suitablefortransientanalysisaswellassimulationofunbalancedthree-phasepower system. This paper also presents the simulation results obtained in MATLAB/Simulink. The electric generator used in a modern MTG system is usually a permanent magnet synchronous generator (PMSG). The equations to model a PMSG are can be found in any standard textbook on electric machines e.g. [1.11]. Objective of this Thesis and Organization of Remaining Chapters Theobjectiveofthisthesisistodevelopandintegratesimulationmodelofvarious componentsofahybridgenerationsystem.Achievingthisobjective,involves performanceevaluationofallthesystemcomponents(MTGandWECS)and demonstratingitspowermanagementabilitywiththehelpofsimulationresults.The simulationmodelissuitabletostudytheimpactsofDGsonthepowersystemsbesides 16 being able to simulate the behavior of the overall hybrid system under different operating conditions. The remaining part of this thesis is organized in to four chapters. Chapter 2 introduces avariablespeedWECSandgivesdetailedmodelingofthewindturbinepartofit. Dynamicmodelingoftheelectricgeneratorpartisexplainedinchapter3.Chapter4 presentsmodeling of the MTG systemfollowedby the overallhybrid generation system completewithpowerelectronicsinterfacinggiven,inchapter5.Chapter6givesthe conclusionofthisthesisandaspectsworthyoffuturework.Simulationresultsobtained inMATLAB/Simulinkaregivenattheendofeachchapterandsimulationmodelsare given in the appendix at the end of this thesis. 17 REFERENCES 1.1MATLAB/SimulinkSimPowerSystemsDocumentation.Available: http://www.mathworks.com 1.2M.F.GillieandW.E.LeitheadOperationandregulationofawindandgasvirtual power plant, in 17th intl. conf. Electricity Dist., Barcelona, May 20003. 1.3 Mukund. R. Patel, Wind Power Systems, CRC Press, 1999, ch. 4-6. 1.4J.F.Manwell,J.G.McGowanandA.L.Rogers,WindenergyExplainedTheory, Design and application, John Wiley& Sons, 2002, ch. 7. 1.5TonyBurton,Davidsharpe,NickJenkinsandErvinBossanyi,WindEnergy handbook, John Wiley& Sons, 2001, ch. 4. 1.6EduardMuljadiandC.P.Butterfield,Pitch-controlledvariable-speedwindturbine generation,IEEETransactionsonIndustryApplications,vol.37,no.1,pp.240-246, Jan/Feb 2001. 1.7 P.M.Anderson and Anjan Bose, Stability simulation of wind turbine systems, IEEE Trans. on Power and Apparatus and Systems, vol. PAS-102, no. 12, pp. 3791-3795, Dec. 1983. 1.8O.Wasynczuk,D.T.ManandJ.P.Sullivan,Dynamicbehaviorofaclassofwind turbinegeneratorsduringrandomwindfluctuations,IEEETransactionsonPowerand Apparatus and Systems, vol. PAS-100, no. 6, pp. 2837-2845, June 1981. 1.9J.G.Slootweg,S.W.H.deHaan,H.PolinderandW.L.Kling,Generalmodelfor representing variable speed wind turbines in power system dynamics simulations, IEEE Transactions on Power Systems, vol. 18, no. 1, pp. 144-151 , Feb. 2003. 1.10AntoniosE.Haniotis;KonstantinosS.Soutis,AntoniosG.Kladas,andJohnA. Tegopoulos,Gridconnectedvariablespeedwindturbinemodeling,dynamic performanceandcontrol,inIEEEPESPowerSyst.Conf.Expos.,vol.2,pp.759-764, Oct 10-13 2004, New York, NY, United States. 1.11 Bimal K.Bose, Modern Power Electronics and AC Drives, Pearson Education, 2003. 1.12AncaD.Hansen,FlorinIov,PoulSorensen,andFredeBlaabjerg,Overallcontrol strategy ofvariablespeed doubly-fedinduction generator wind turbine,in 2004 Nordic Wind Power Conference, Chalmers University of Technology, Sweden. 18 1.13RajibDattaandV.T.Ranganathan,Variable-speedwindpowergenerationusing doublyfedwoundrotorinductionmachineAcomparisonwithalternativeschemes, IEEE Transactions on Energy Conversion, vol. 17, no. 3, pp. 414-420, Sept. 2002. 1.14E.D.BassetandF.M.Potter,Capacitiveexcitationofinductiongenerators, Trans. Amer. Inst. Elect. Eng, vol. 54, no.5, pp. 540-545, May 1935. 1.15 C. F. Wagner,Self-excitation ofinductionmotors, Trans. Amer. Inst. Elect. Eng, vol. 58, pp. 47-51, Feb. 1939. 1.16S.S.Murthy,O.P.MalikandA.K.Tandon,Analysisofselfexcitedinduction generators, Proceedings, IEE, pt. C, vol. 129, no. 6, pp. 260-265, Nov.1982. 1.17J.M.Elder,J.T.BoysandJ.L.Woodward,Theprocessofselfexcitationin induction generators, Proceedings, IEE, pt. B, vol. 130, no. 2, pp. 103-108, Mar. 1983. 1.18J.M.Elder,J.T.BoysandJ.L.Woodward,Self-excitedinductionmachineasa small low-cost generator, Proceedings IEE, pt. C, vol. 131, no. 2, pp. 33-41, Mar. 1984. 1.19C.Grantham,D.SutantoandB.Mismail,Steady-stateandtransientanalysisof self-excitedinductiongenerators,Proceedings,IEE,pt.B,vol.136,no.2,pp.61-68, Mar. 1989. 1.20 Dawit Seyoum, Colin Grantham and M. F. Rahman, The dynamic characteristics of anisolatedself-excitedinductiongeneratordrivenbyawindturbine,IEEETrans. Industry Applications, vol.39, no. 4, pp.936-944, July/August 2003. 1.21 A.K.Al Jabri andA.I. Alolah,Capacitance requirementsforisolated self-excited induction generator, Proceedings IEE, pt. B, vol. 137, no. 3, pp. 154-159, May 1990. 1.22N.H.MalikandA.H.Al-Bahrani,Influenceoftheterminalcapacitoronthe performance characterstics of a self-excited induction generator, Proceedings IEE, pt. C, vol. 137, no. 2, pp. 168-173, Mar. 1990. 1.23LiWangandJian-YiSu,Dynamicperformanceofanisolatedself-excited inductiongeneratorundervariousloadingconditions,IEEETransactionsonEnergy Conversion, vol. 14, no. 1, pp.93-100, Mar. 1999. 1.24 W. I. Rowen, Simplified mathematical representations of heavy duty gas turbines, Journal of Engineering for Power, Transactions ASME, vol. 105, no. 4, pp. 865-869, Oct, 1983. 1.25 L. N. Hannet and Afzal Khan, Combustion turbine dynamic model validation from tests, IEEE Transactions on Power Systems, vol. 8, no. 1, pp. 152-158, Feb. 1993. 19 1.26WorkingGrouponPrimeMoverandEnergySupplyModelsforSystemDynamic PerformanceStudies,Dynamicmodelsforcombinedcycleplantsinpowersystem studies,IEEETransactionsonPowerSystems,vol.9,no.3,pp.1698-1708,August 1994. 1.27A.Cano,F.JuradoandJ.Carpio,Influenceofmicro-turbinesondistribution networks stability,in Proceedings, IEEE PES General Meeting,vol. 4, pp. 2153-2158, Jul. 2003, Toronto, Canada. 1.28 F. Jurado and A. Cano, Use of ARX algorithms for modeling micro-turbines on the distributionfeeder,inProceedings,IEE:GenerationTransmissionandDistribution, vol. 151, no. 2, pp. 232-238, Mar. 2004. 1.29FranciscoJuradoandJoseRamonSaenz,Adaptivecontrolofafuelcell-microturbinehybridpowerplant,IEEETransactionsonEnergyConversion,vol.18 no.2, pp. 342-347, June 2003. 1.30AmerAl-HinaiandAliFeliachi,Dynamicmodelofamicroturbineusedasa distributedgenerator,inProceedings,34thSoutheasternSymposiumonSystemTheory, Huntsville, pp.209-213, Alabama, March 2002. 20 CHAPTER 2 WIND ENERGY CONVERSION SYSTEM WIND TURBINE MODELING Introduction Onewayofaddressingtherisingenergydemandsandgrowingenvironmental concerns,is to harness greensources of power. Among these, tapping wind energy with wind turbines appears to be the most promising source of renewable energy. Wind energy conversionsystemsareusedtocapture theenergyavailableinthewindtoconvertinto electrical energy. Inthischapter,afunctionalstructureofawindenergyconversionsystemis introduced, before making a comparison between the two typical wind turbine operating schemesinoperation,namelyconstant-speedwindturbineandvariable-speedwind turbine. In addition, the modeling and dynamic behavior of a variable speed wind turbine with pitch control capability is explained in detail. Theaveragecommercialturbinesizeofthewindinstallationswas300kWuntilthe mid ninetys [2.1]. Newer machines of larger capacity (up to 5MW) have been developed andarebeinginstalled.Wind,whenavailable,isaninfinitesourceofenergy.Other environmental impacts of wind power are limited as well.Aschematicdiagramofawindenergyconversionsystemispresentedinthenext sectionalongwithadetaileddescriptionofwindturbineanditsmodeling.The 21 functionalityofothersystemcomponentsisalsodiscussedbriefly.Inthelastsection, simulationresults,obtainedforthevariablespeedwindturbine,arepresentedtogivea better understanding of the wind turbine dynamics. Functional Structure of Wind Turbines Thefunctionalstructureofatypicalwindenergyconversionsystemisasshownin Figure 2.1: Wind SpeedMechanicalDri veUnitGeneratorAC PowerOutputRotor BladesAir flowWi nd EnergyConversi onTorque and SpeedconversionMechani cal-ElectricalEnergy ConversionKineti c Energy Mechanical Energy ElectricalEnergyControlandSupervision Figure 2.1.Power transfer in a wind energy converter. Awindenergyconversionsystemisacomplexsysteminwhichknowledgefroma widearrayoffieldscomprisingofaerodynamics,mechanical,civilandelectrical engineeringcometogether.Theprinciplecomponentsofamodernwindturbinearethe tower, the rotor and thenacelle, which accommodates the transmissionmechanismsand the generator. The wind turbine captures the winds kinetic energy in the rotor consisting oftwoormorebladesmechanicallycoupledtoanelectricalgenerator.Themain 22 componentofthemechanicalassemblyisthegearbox,whichtransformstheslower rotationalspeedsofthewindturbinetohigherrotationalspeedsontheelectrical generator side. The rotation of the electrical generators shaft driven by the wind turbine generateselectricity,whoseoutputismaintainedasperspecifications,byemploying suitable control and supervising techniques. Besides monitoring the output, these control systems also include protection systems to protect the overall system. Inthisthesisself-excitedinductiongenerator(SEIG)isusedasthegeneratorfor electricalpowergeneration,whosedynamicsaresimulatedinthenextchapter.The developedSEIGmodelissuitableforbothsteady-stateandtransientoperations.Italso includestheeffectsofsaturationofmagnetizinginductance,whichisveryimportantin the process of self-excitation. Twodistinctlydifferentdesignconfigurationsareavailableforawindturbine,the horizontalaxisconfigurationandtheverticalaxisconfiguration.Theverticalaxis machinehastheshapeofaneggbeater,andisoftencalledtheDarrieusrotorafterits inventor. However, most modern turbines use horizontal axis design [2.1]. In this chapter thedynamicmodelofahorizontalaxisturbineisdevelopedandsimulatedinthe MATLAB/Simulink, based on the turbine performance curves. Wind Turbine ModelingAsnotedabove,aWECSisacomplexsystemconvertingwindenergyto rotational energyandthentoelectricalenergy.Theoutputpowerortorqueofawindturbineis 23 determinedbyseveralfactorslikewindvelocity,sizeandshapeoftheturbine,etc.A dynamicmodel of the wind turbine,involving these parameters, is needed to understand the behavior of a wind turbine over its region of operation. By studying its modeling, it is possibletocontrolawindturbinesperformancetomeetadesiredoperational characteristic. In the following pages we will look at different performance characteristics and variables that play an important role in wind power generation, by deriving the speed and power relations. The control principles of the wind turbine are also discussed in this section. Inputs and Outputs of a Wind Turbine The inputs and output variables of wind turbine can be broken into the following: 1.Theindependentinputquantitywindspeed,determinestheenergyinputtothe wind turbine. 2.Machine-specificinputquantities,arisingparticularlyfromrotorgeometryand arrangement(i.e.,differentconfigurationslikehorizontalaxisorverticalaxis turbines, area of the blades, etc.). 3.Turbinespeed,rotorbladetilt,androtorbladepitchangle,arisingfromthe transmission system of the wind energy conversion system. 4.Turbineoutputquantities,namelyPowerorDrivetorque,whichmaybe controlled by varying the above three input quantities. 24 Power Extraction from the Air stream Withtheidentificationofthewindturbinesinputandoutputvariables,nowitis possibletoderiveanexpressionrelatingthesetwovalues.Therelationbetweenthe power and wind speed is derived as follows [2.1]: The kinetic energy in air of mass m moving with speed V is given by the following: Kinetic energy = 21.m.V2 Joules (2.1) The power in moving air flow is the flow rate of kinetic energy per second. Power = 21.(mass flow rate per second).V2 (2.2) The actual power extracted by the rotor blades is the difference between the upstream and the down stream wind powers. Therefore, equation (2.2) results in 21P = .(mass flow rate per second). ( )2o2V V (2.3) Where: P is the mechanical power extracted by the rotor in watts. V is the upstream wind velocity at the entrance of the rotor blades in m/s.Vo is the downstream wind velocity at the exit of the rotor blades in m/s. 25 Letbe the air density in (kg/m3) and A is the area swept by the rotor blades in (m2); then, the mass flow rate of air through the rotating blades is given by multiplying the air density with the average velocity. mass flow rate = 2V V. A . o+(2.4) From (2.3) and (2.4), the mechanical power extracted by the rotor is given by: ( )2o2 oV V .2) V (V. A . .21P ((

+= (2.5) After algebraic rearrangement of the terms, we have: p3C . V . A . 21P = (2.6) Where: 2VV1VV1C2o op||.|

\||.|

\| |.|

\|+= isthefractionoftheupstreamwindpower,whichis capturedbytherotorbladesandhasatheoreticalmaximumvalueof0.59.Itisalso referred as the power coefficient of the rotor or the rotor efficiency. In practical designs, themaximumachievableCpisbetween0.4and0.5forhigh-speed,two-bladeturbines and between 0.2 and 0.4 for slow-speed turbines with more blades [2.1]. 26 From (2.6), we see that the power absorption and operating conditions of a turbine are determinedbytheeffectiveareaoftherotorblades,windspeed,andwindflow conditionsat therotor.Thus, theoutputpower of theturbinecanbevariedbyeffective areaandbychangingtheflowconditionsattherotorsystem,whichformsthebasisof control of WECS. Tip Speed Ratio The tip speed ratio , defined as the ratio of the linear speed at the tip of the blade to the free stream wind speed and is given by the following expression [2.1-2.4]: TSR = = VR(2.7) Where: R is the rotor blade radius in meters. is the rotor angular speed in rad/sec. TSR is related to the wind turbine operating point for extracting maximum power. The maximumrotorefficiencyCpisachievedataparticularTSR,whichisspecifictothe aerodynamicdesignofagiventurbine.Therotormustturnathigh-speedathighwind, and at low-speed at low wind, to keep TSR constant at the optimum level at all times. The larger the TSR, the faster is the rotation of the wind turbine rotor at a given windspeed. High(rotational)speedturbinesarepreferredforefficientelectricitygeneration.From 27 (2.7), for a particular value of wind speed V, turbines withlargeblade radius R resultin low rotational speed , and vice versa. For operation over a wide range of wind speeds, wind turbines with high tip speed ratios are preferred [2.3]. Typical Wind Turbine Operating Systems Therearemainlytwokindsofwindenergyconversionsystemsinoperation;fixed-speedorconstantspeedwindturbineswhichoperateatanearlyconstantspeed, predeterminedbythegeneratordesignandgearboxratio,andvariablespeedwind turbines. The overall operating strategy determines how the various components are controlled. For example, as part of the overall control strategy, the rotor torque can be controlled to maximize energy capture, or pitch angle control can help control the power output at high windspeeds.Fixed-speedstall-regulatedturbineshavenooptionsforcontrolinput.In these turbines the turbine blades are designed with fixed pitch to operate near the optimal TSR at a specific wind speed. As wind speedincreases, so, too does the angle ofattack, andanincreasinglylargepartoftheblade,startingatthebladeroot,entersthestall regionresultinginthereducedrotorefficiencyandlimitationofthepoweroutput.A variation of the stall regulated concept involves operating the wind turbine at two distinct, constantoperatingspeeds,byeitherchangingthenumberofpolesoftheelectrical generatororchangingthegearratio.Theprincipaladvantageofstallcontrolisits simplicity,buttherearesignificantdisadvantages;forinstance,thestallregulatedwind 28 turbinewillnotbeabletocapturewindenergyinanefficientmanneratwindspeeds other than that it is designed for. Fixed-speedpitch-regulatedturbinestypicallyusepitchregulationforstart-upand, andafterstart-uponlytocontrolthepowerabovetheratedwindspeedoftheturbine. Variablespeedwindturbinestypicallyusegeneratortorquecontrolforoptimizationof power output. They use pitch control to control the output power, only above their rated windspeed.Withvariablespeed,therewillbe20-30%increaseintheenergycapture compared to the fixed-speed operation [2.1-2.5]. Typicalcurvesfor a constant speed and variable speed wind turbine are asshownin the Figure 2.2 [2.2]. NogenerationCut-inwind SpeedRated/NominalWind SpeedCut-outWind SpeedNogenerationActive Power(p.u)25 20 15 10 51.01.20.80.60.40.2(0,0)Wind Speed (m/s)Nogeneration Figure 2.2Typical curves for a constant speed, stall-controlled (dotted) and variable speed pitch controlled (solid) wind turbine. Inaconstantspeed,stall-controlledwindturbinetheturbineoutputpowerpeaks somewhathigherthantheratedlimit,thendecreasesuntilthecut-outspeedisreached. 29 Thisfeatureprovidesanelementofpassivepoweroutputregulation,ensuringthatthe generator isnot overloaded as the wind speed reaches abovenominalvalues [2.5]. With variablespeed operation although the energy captureismore, the cost ofvariable speed control is added to the overall system cost. This tradeoff between the energy increase and cost increase has to be optimized in the system design. The advantages and disadvantages of the variable and fixed-speed operations can be summarized in the following table [2.1, 2.2]. Table 2.1Comparison of Fixed and Variable Speed wind turbine systems. Constant SpeedVariable Speed Simple and robustLess mechanical stress Inexpensive electrical systemHigher energy capture Electrically efficient Aerodynamically efficient Fewer parts, hence high reliabilityLow transient torque No frequency conversion, hence, no current harmonics Mechanical damping system not needed, the electrical system could provide the damping Advantages Lower capital cost No synchronization problems. Stiff electrical controls can reduce voltage sags Aerodynamically less efficientElectrically less efficient Mechanical stressExpensive Disadvantages Noisy Sometimes, involves complex control strategies 30 Variable Speed Wind Turbine System A typical variable speed pitch-regulated wind turbine is as shown in Figure 2.3. Many parameters that characterize a variable-speed wind turbine are linked [2.6]. For example: 1.The turbine power coefficient curve, the nominal rotor speed, and the rotor diameter determine the nominal wind speedfor a wind turbine of a given nominal power 2.Theallowableamountofrotoroverspeedingandtheratedpower determines the parameters of the pitch controller. 3.The rotor inertia determines the turbine cut-in wind speed. PitchMechani smPitch AngleControllerNominal rpm- +Speed-PowerRelati onshiprpmTorqueControllerkWPower ref Figure 2.3Typical pitch-regulated variable-speed wind turbine. 31 Variablespeedpitch-regulatedwindturbineshavetwomethodsforaffectingthe turbineoperation,namelyspeedchangesandbladepitchchanges.Inotherterms,the controlstrategiesemployedintheoperationofvariablespeedwindturbinesystemare [2.7]: 1.Poweroptimizationstrategy,employedwhenthespeedisbelowtheratedwind speed, to optimize the energy capture by maintaining the optimum tip speed ratio. Thiscanbeachievedbymaintainingaconstantspeedcorrespondingtothe optimum tip speed ratio. If the speed is changed by controlling the electrical load, the generator willbe overloadedfor wind speedsabovenominalvalue. To avoid such scenario, methods like generator torque control are used to control the speed. 2.Power limitation strategy, used above the rated wind speed of the turbine to limit theoutputpowertotheratedpowerbychangingthebladepitchtoreducethe aerodynamicefficiency,therebyreducingthewindturbinepowertoacceptable levels. Theregionsoftheabovementionedcontrolstrategiesofavariablespeedwind turbine system are as shown in the Figure 2.4: 32 NogenerationCut-inwind SpeedRated/Nomi nalWind SpeedCut-outWind SpeedNogenerationActive Power(p.u)25 20 15 10 51.01.20.80.60.40.2(0,0)Wind Speed (m/s)NogenerationPowerOptimization(Constant Cp)PowerLimitation(ConstantPower) Figure 2.4Variable Speed pitch controlled wind turbine operation. PitchAngleController.Asmentionedintheprevioussubsection,pitchcontroller controlsthewindflowaroundthewindturbineblade,therebycontrollingthetoque exertedontheturbineshaft.Ifthewindspeedislessthantheratedwindspeedofthe wind turbine, the pitch angle is kept constant at its optimum value. It should be noted that the pitch angle can change at a finite rate, which may be quite low due to the size of the rotorblades.Themaximumrateofchangeofthepitchangleisintheorderof3to10 degrees/second.Inthiscontrolleraslightover-speedingoftherotoraboveitsnominal value can be allowed without causing problems for the wind turbine structure [2.6, 2.8]. The pitch angle controller used in this thesis, employs a PI controller as shown below [2.7, 2.9-2.11]: 33 P-IControl-+P measuredp.uP refp.uerror signalPitch AngleMaxPitch AngleOptimumPitch Angl eRate Limi terPitchAngle Figure 2.5Pitch Angle Controller. Aslong as the wind turbine output power islower than the rated power of the wind turbine, the error signal is negative and pitch angle is kept at its optimum value. But once thewindturbineoutputpowerexceedstheratedpowerPref,theerrorsignalispositive and the pitch angle changes to a new value, at a finite rate, thereby reducing the effective area of the blade resulting in the reduced power output. Inputs to the PI controller are in per-unit and the parameters for the controller are obtained form reference [2.11]. Performance Curves The performance of variable speed pitch-regulated wind turbines is determined by the characteristiccurvesrelatingthepowercoefficientCp,tipspeedratioTSRandpitch angle . Groups of Cpcurves obtainedbymeasurement or by computation can also be approximated in closed form by non linear functions [2.3], which can be shown as: ) ( C5x4 3 2 1 pi 6e ) C C C (C C C = (2.8) Where: is the pitch angle andis the tip speed ratio. 34 The values chosen for C1-C5 and iin this thesis are: 1 0.035 0.08 113i++=C1 = 0.5 C2 = i116C3 = 0.4C4 = 0C5 = 5 C6 = i21 According to the characteristics chosen, the coefficients C1-C5 should be modified to obtainaclosesimulationofthemachineinconsideration.Thedifferencesbetweenthe curvesofvariouswindturbinesaresmallandcanbeneglectedindynamicsimulations [2.3].In[2.6],acomparisonwasmadebetweenthepowercurvesoftwocommercial wind turbines using the general numerical approximation similar to (2.8).Simulation Results Inthissection,thesimulationsresultsofavariablespeedpitchcontrolledwind turbinemodelarepresented.Allthesimulationswerecarriedoutusing MATLAB/Simulink.Thedynamicsofthewindturbinemodelcanberepresentedwith the help of a flow chart, as shown in the Figure 2.6 followed by a brief description of the simulated model. 35 Power Coeff. CpTip Speed RatioGearbox turbinePitch AngleControllerwindRadiusPerformance CurvesP wind(Watts)Air densityPrefT wind (n-m)T drive (n-m)To SEIGgenfrom SEIG Figure 2.6Simulation model of the variable speed pitch-regulated wind turbine. The inputs for the wind turbine model are, wind speed, air density, radius of the wind turbine,mechanicalspeedoftherotorreferredtothewindturbinesideandpower reference for the pitch angle controller. The output is the drive torque Tdrive which drives theelectricalgenerator.Thewindturbinecalculatesthetipspeedratiofromtheinput valuesandestimatesthevalueofpowercoefficientfromtheperformancecurves.The pitchanglecontrollermaintainsthevalueofthebladepitchatoptimumvalueuntilthe power output of the wind turbine exceeds the reference power input. The performance curves used in this thesis (from (2.8)) are as shown below: 36 0 2 4 6 8 10 12 14 16 18 20-0.100.10.20.30.4Cp-TSR CurvesTip Speed RatioPower Coefficient, Cp3 deg0 deg1 deg2 deg4 deg5 deg15 deg25 deg35 deg45 deg Figure 2.7 Cp characteristics (blade pitch angleas the parameter). Fromtheabovesetofcurves(Figure2.7),wecanobservethatwhenpitchangleis equal to 2 degrees, the tip speed ratio has a wide range and a maximum Cp value of 0.35, suitable for wind turbines designed to operate over a wide range of wind speeds. With an increase in the pitch angle, the range of TSR and the maximum value of power coefficient decrease considerably. The parameters used for the simulation are as follows: Rated power of the wind turbine = 370 kW. 37 Radius of the wind turbine blade = 20 m. Gearbox turns ratio = 1:20. Air density = 1 kg/ m3. Figure 2.8 shows the wind turbine output power of the simulated model for different wind velocities. It can be observed that the output power is kept constant at higher wind velocities,eventhoughthewindturbinehasthepotentialtoproducemorepower;this powerlimitisusedandtopreventtheoverspeedingoftherotorandtoprotectthe electrical system. 0 5 10 15 20 250100200300400Wind turbine power outputWind velocity in m/sPower output (kW) Figure 2.8Output power of the wind turbine for different wind velocities. Forthefollowingsimulationresults,thewindturbinestartswithaninitialwind velocityof11m/satno-load,andloadwasappliedonthemachineatt=10seconds.At t=15 seconds there was a step input change in the wind velocity reaching a final value of 38 14m/s. Inboth cases the power reference remained the same (370 kW). Thesimulation results obtained for the above mentioned conditions are as follows: 0 5 10 15 20 25100012001400160018002000Time (seconds)RPMWind turbine speed variations No Load@11m/sPref=370kW@11m/sPref=370kW@14m/s Figure 2.9Wind turbine rotor speed (referred to generator side) variations with wind. FromFigures2.9and2.10wecanseethechangesinthetipspeedratio correspondingtothechangesintherotorspeedfordifferentwindandloadconditions. Duringno-loadoperation,thewindturbineisnotconnectedtotheloadandtherefore rotatesfreelyundertheinfluenceofwindattaininghighangularvelocities.From(2.7), whichgivestherelationbetweenthetipspeedratioandangularvelocityofthewind turbine, it can be concluded that higher angular velocities result in higher tip speed ratios. InthiscaseasTSRreachesavaluegraterthan18,thevalueofthepowercoefficient obtainedfromthesetofperformancecurvesisalmostzero.Astherotorpower coefficient valueis zero, the energy captured by the rotor bladesis also zero. Therefore, the torque exerted on the generator shaft also equals to zero. 39 0 5 10 15 20 258101214161820Time (seconds)TSRTip speed ratioNoload@11m/sPref=370kW@11m/sPref=370kW@14m/s Figure 2.10Tip speed ratio of the wind turbine. Asloadis applied on the wind energy conversion system, the speed of the electrical generator (to be discussed in the next chapter) drops which reduces the speed of the wind turbine (as they are coupled through a gear box, Figure 2.9). This drop in angular speed ofthewindturbinereducesthevalueofTSRresultinginahighervalueofthepower coefficient as can be observed from the power coefficient curves (Figure 2.7). Since rotor powercoefficientisnowapositive,non-zero,therotorbladesextractenergyformthe wind resulting in some output power. Figure 2.11 shows the changes in the power coefficient with changes in the tip speed ratio. From Figure 2.7 it can be seen that, on the right hand side (after reaching the peak value) of the Cp Vscurves, with increase in the value of TSR the value of Cp decreases. Figure 2.11 shows that lower wind velocities (higher TSR, see (2.7)) result in high power 40 coefficient,andhigherwindvelocities(lowerTSR)resultinlowerpowercoefficient values, so that the wind turbine output does not exceed its rated power. 0 5 10 15 20 2500.050.10.150.20.250.30.350.4Time (seconds)CpPower coefficientPref=370kW@14 m/sPref=370kW@11m/sNoload @11m/s Figure 2.11Variation of power coefficient with wind. 0 5 10 15 20 2522.533.544.5Time (seconds)Pitch angle (degrees)Pitch angleNo load@11m/sPref=370kW@11m/sPref=370kW@14 m/s Figure 2.12Pitch angle controller response to the wind speed change. 41 Observethatthepitchangleiskeptconstantbythepitchcontrolleratanoptimal valueof2degrees(Figure2.12)untilthewindturbinereachesabovethenominalwind speed (13.5 m/s), where it has the capability to produce more power than the rated power ofthesystem.Inthisregionpitchcontrolaltersthepitchoftheblade,atafiniterate, therebychangingtheairflowaroundthebladesresultinginthereducedefficiencyof wind turbine rotor. Also, from Figure 2.7 we see that with increase in the pitch angle the range of TSR which produces a positive value for rotor power coefficient reduces sharply. 0 5 10 15 20 25012345x 105Time (seconds)Power output (watts)Wind turbine output power varationsPref=370kW@14m/sPref=370kW@11m/sNoload@11m/s Figure 2.13Wind turbine output power variation with change in wind speed. FromFigures2.12and2.13weseethat theoutput ofthewindturbineisabout220 kW at 11 m/s andhas the ability to supplymore than rated power of 370 kW at 14 m/s. Asexplainedabove,thewindturbineoutputpowerislimitedto theratedpowerbythe pitch controller. 42 0 5 10 15 20 250500100015002000250030003500Time (seconds)Torque (Nm)Wind turine torquePref=370kW@11m/sPref=370kW@14m/sNoload@11m/s Figure 2.14Wind turbine torque variation with wind. ThedrivingtorqueproducedbythewindturbineasobservedinFigure2.14,varies based on the input (wind) and load conditions. When the system is not loaded the driving torque produced the wind turbineis zero, since the energy captured by the rotor is zero. Whenloadisappliedatt=10seconds,wecanseeariseinthevalueofthetorque producedbythewindturbine.Withastepincreaseinwindvelocity(to14m/s),the torqueincreasesfromitspreviousvalue,anddeliversahighertoquetotheelectrical generator. Torque seen here is obtained by dividing the power extracted from the wind by the angular velocity of the rotor and then referring it on to the generator side. Conclusion. In this chapter a variable speed wind energy conversion system has been presented.Emphasishasbeenlaidonthewindturbinepartofthetotalsystem.A comparison was made between the two typical existing wind turbine systems after a brief introductionofeachsystem.Avariablespeedwindturbinemodelwassimulatedbased 43 on the power coefficient curves. The response of the simulated model was observed with dynamicloadandchangingwindconditions.Itwasobservedwiththehelpofthe simulationresults,thatthepowerlimitationstrategycanbesuccessfullyenforcedby usingapitchcontroller.Thischapteralsosetsthegroundforthenextchapter,wherea detailed analysis of the electrical generator part of the wind energy conversion system is carried out. 44 REFERENCES 2.1 Mukund. R. Patel, Wind Power Systems, CRC Press, 1999, ch. 4-6. 2.2 J.G. Slootweg, Wind power: modeling and impact on power system dynamics, PhD dissertation, Dept. Elect. Eng., Delft University of Technology, Delft, Netherlands, 2003. 2.3 Siegfried Heier, Grid Integration of Wind energy Conversion Systems, JohnWiley& Sons, 1998, ch. 1-2. 2.4J.F.Manwell,J.G.McGowanandA.L.Rogers,WindenergyExplainedTheory, Design and Application, John Wiley& Sons, 2002, ch. 7. 2.5TonyBurton,Davidsharpe,NickJenkinsandErvinBossanyi,WindEnergy Handbook, John Wiley& Sons, 2001, ch. 4. 2.6J.G.Slootweg,S.W.H.deHaan,H.PolinderandW.L.Kling,Generalmodelfor representing variable speed wind turbines in power system dynamics simulations, IEEE Transactions on Power Systems, vol. 18, no. 1, pp. 144-151 , Feb. 2003. 2.7AncaD.Hansen,FlorinIov,PoulSorensen,andFredeBlaabjerg,Overallcontrol strategy ofvariablespeed doubly-fedinduction generator wind turbine,in 2004 Nordic Wind Power Conference, Chalmers University of Technology, Sweden. 2.8 Eduard Muljadiand C. P. Butterfield., Pitch-controlled variable-speed wind turbine generation,IEEETransactionsonIndustryApplications,vol.37,no.1,pp.240-246, Jan/Feb 2001 2.9P.M.AndersonandAnjanBose.,Stabilitysimulationofwindturbinesystems, IEEE Trans. on Power and Apparatus and Systems, vol. PAS-102, no. 12, pp. 3791-3795, Dec. 1983. 2.10 O. Wasynczuk, D.T. Man and J. P. Sullivan, Dynamic Behavior of a class of wind turbinegeneratorsduringrandomwindfluctuations,IEEETransactionsonPowerand Apparatus and Systems, vol. PAS-100, no. 6, pp. 2837-2845, June 1981. 2.11 MATLAB/Simulink Documentation. Available: http://www.mathworks.com 45 CHAPTER 3 WIND ENERGY CONVERSION SYSTEM - SELF-EXCITED INDUCTION GENERATOR (SEIG) MODELING Introduction Induction machine is used in a wide variety of applications as a means of converting electric power to mechanical work. The primary advantage of the induction machine is its rugged brushless construction and no need for separate DC field power. These machines areveryeconomical,reliable,andareavailableintherangesoffractionalhorsepower (FHP)tomultimegawattcapacity.Also,unlikesynchronousmachines,induction machinescanbeoperatedatvariablespeeds.Foreconomyandreliabilitymanywind power systems useinductionmachines, drivenby a wind turbine through a gearbox, as anelectricalgenerator.Theneedforgearboxarisesfromthefactthatlowerrotational speeds on the wind turbine side should be converted to high rotor speeds, on the electrical generator side, for electrical energy production.Therearetwotypesofinductionmachinebasedontherotorconstructionnamely, squirrelcagetypeandwoundrotortype.Squirrelcagerotorconstructionispopular because of its ruggedness, lower cost and simplicity of construction and is widely used in stand-alonewindpowergenerationschemes.Woundrotormachinecanproducehigh startingtorqueandisthepreferredchoiceingrid-connectedwindgenerationscheme. 46 Another advantage with wound rotor is its ability to extract rotor power at the added cost of power electronics in the rotor circuit. Thischapterfocusesontheelectricalgenerationpartofawindenergyconversion system. After a brief introduction of the induction machine, the electrical generator used in this thesis, a detailed analysis of theinductionmachine operated instand-alonemode is presented. As a generator, induction machines have the drawback of requiring reactive powerforexcitation.Thisnecessitatestheuseofshuntcapacitorsinthecircuit.The effectofmagnetizationinductanceonself-excitationoftheinductiongeneratoris discussed. Also, this chapter presents the two existing methods to analyze the process of self-excitation in induction machine and the role of excitation-capacitors in its initiation. Simulation results of the self-excited induction generator driven by the variable speed wind turbine are presented in the last section of this chapter. The process of voltage build up and the effect of saturation characteristics are also explained in the same section. Induction Machine IntheelectromagneticstructureoftheInductionmachine,thestatorismadeof numerous coils with three groups (phases), and is supplied with three phase current. The threecoilsarephysicallyspreadaroundthestatorperiphery(space-phase),andcarry currentswhichareoutoftime-phase.Thiscombinationproducesarotatingmagnetic field, which is a key feature of the working of the induction machine. Induction machines areasynchronousspeedmachines,operatingbelowsynchronousspeedwhenmotoring 47 and above synchronous speed when generating. The presence of negative resistance (i.e., whenslipisnegative),impliesthatduringthegeneratingmode,powerflowsfromthe rotor to the stator in the induction machine. Equivalent Electrical Circuit of Induction Machine Thetheoryofoperationofinductionmachineisrepresentedbytheperphase equivalent circuit shown in Figure. 3.1 [3.1-3.3]. RmXmX2R2(1-s)/sR1X1IoI2I1VsR2 Figure 3.1Per-phase equivalent circuit of the induction machine referred to the stator. Intheabovefigure,RandXrefertotheresistanceandinductivereactance respectively. Subscripts 1, 2 and m represent stator, rotor values referred to the stator side and magnetizing components, respectively. Induction machine needs AC excitation current for its running. The machine is either self-excited or externally excited. Since the excitation current is mainly reactive, a stand-alonesystemisself-excitedbyshuntcapacitors.Ingrid-connectedoperation,itdraws excitationpowerfromthenetwork,anditsoutputfrequencyandvoltagevaluesare 48 dictated by the grid.Where the grid capacity ofsupplying the reactive powerislimited, local capacitors can be used to partly supply the needed reactive power [3.3]. Self-Excited Induction Generator (SEIG) Self-excitedinductiongenerator(SEIG)worksjustlikeaninductionmachineinthe saturationregionexceptthefactthatithasexcitationcapacitorsconnectedacrossits stator terminals. These machines are ideal choice for electricity generation in stand-alone variable speed wind energy systems, where reactive power from the grid is not available. The induction generator will self-excite, using the external capacitor, only if the rotor has anadequateremnantmagneticfield.Intheself-excitedmode,thegeneratoroutput frequencyandvoltageareaffectedbythespeed,theload,andthecapacitancevaluein farads[3.3].Thesteady-stateper-phaseequivalentcircuitofaself-excitedinduction generator is shown in the Figure 3.2. RmXmX1+X2R2(1-s)/sIoI 1V1R1+R2I2XcLoadIm Figure 3.2Self-excited induction generator with external capacitor. Theprocessofself-excitationininductionmachineshasbeenknownformany decades [3.4]. When capacitors are connected across the stator terminals of aninduction 49 machine, driven by an external prime mover, voltage will be induced at its terminals. The inducedelectromotiveforce(EMF)andcurrentinthestatorwindingswillcontinueto riseuntilthesteady-stateconditionisreached,influencedbythemagneticsaturationof themachine.Atthisoperatingpointthevoltageandthecurrentwillbestabilizedata given peak value and frequency. In order for the self-excitation to occur, for a particular capacitance value there is a corresponding minimum speed [3.5]-[3.8]. So, in stand-alone modeofoperation,itisnecessaryfortheinductiongeneratortobeoperatedinthe saturationregion.Thisguaranteesoneandonlyoneintersectionbetweenthe magnetizationcurveandthecapacitorreactanceline,aswellasoutputvoltagestability under load as seen in the Figure 3.3: V1V1 andImXcMagneti zing current ImImXcOperati ng poi nt|.|

\|C1tan1 Figure 3.3Determination of stable operation of self-excited induction generator. Atno-load,thecapacitorcurrent c 1 c/X V I = mustbeequaltothemagnetizing currentm 1 m/X V I = . The voltage V1 is a function of Im, linearly rising until the saturation 50 point of the magnetic core is reached. The output frequency of the self-excited generator is,) CX /(2 1 fm=and f 2 = where C is self-exciting capacitance. Methods of AnalysisThere are two fundamental circuit models employed for examining the characteristics ofaSEIG.Oneistheper-phaseequivalentcircuitwhichincludestheloop-impedance methodadoptedbyMurthyetal[3.9]andMalikandAl-Bahrani[3.10],andthenodal admittancemethodproposedbyOuazeneandMcpherson[3.11]andChan[3.12].This methodissuitableforstudyingthemachinessteady-statecharacteristics.Theother method is the dq-axis model based on the generalized machine theory proposed by Elder et al [3.6] and Grantham et al [3.7], andis employed to analyze themachines transient state as well as steady-state. Steady-state ModelSteady-stateanalysisofinductiongeneratorsisofinterestbothfromthedesignand operationalpointsofview.Byknowingtheparametersofthemachine,itispossibleto determinetheperformanceofthemachineatagivenspeed,capacitanceandload conditions. LoopimpedanceandnodaladmittancemethodsusedfortheanalysisofSEIGare both based on per-phase steady-state equivalent circuit of theinductionmachine (Figure 3.4), modified for the self-excitation case. They make use of the principle of conservation 51 ofactiveandreactivepowers,bywritingloopequations[3.9],[3.10],[3.13]ornodal equations[3.11],[3.12],fortheequivalentcircuit.Thesemethodsareveryeffectivein calculating theminimumvalue of capacitanceneeded for guaranteeing self-excitation of theinductiongenerator.Forstableoperation,excitationcapacitancemustbeslightly higherthantheminimumvalue.Alsothereisaspeedthreshold,belowwhichno excitationispossible,calledasthecutoffspeedofthemachine.Inthefollowing paragraph, of loop impedance method is given for better understanding. The per-unit per-phase steady-state circuit of a self-excited induction generator under RL load is shown in Figure 3.4 [3.9], [3.11]. R / fXmXlrRr/(f-v)Rs/fXlsIIV0/fXXc / f^2Vg/ f Figure 3.4Equivalent circuit of self-excited induction generator with R-L Load. Where: Rs, Rr, R : p.u. per-phase stator, rotor (referred to stator) and load resistance respectively. Xls, Xlr, X, Xm:p.u.per-phasestatorleakage,rotorleakage(referredtostator),loadand magnetizing reactances (at base frequency), respectively. 52 Xsmax : p.u. maximum saturated magnetizing reactance. C : per-phase terminal-excitation capacitance. Xc:p.u.per-phasecapacitivereactance(atbasefrequency)oftheterminalexcitation capacitor. f, v : p.u.frequency and speed, respectively. N : base speed in rev/min Zb : per-phase base impedance fb : base frequency Vg, V0 : per-phase air gap and output voltages, respectively. In the analysis of SEIG the following assumptions were made [3.9]: 1.OnlythemagnetizingreactanceXmisassumedtobeaffectedbymagnetic saturation,andallotherparametersoftheequivalentcircuitareassumedtobe constant. Self-excitation results in the saturation of the main flux and the value of Xm reflect themagnitude of themainflux. Leakage flux passesmainlyin the air, and thus thesefluxes arenot affected to anylarge extent by thesaturation of the main flux.53 2.Statorandrotorleakagereactances,inper-unitaretakentobeequal.This assumption is normally valid in induction machine analysis. 3.Core loss in the machine is neglected. For thecircuitshowninFigure3.4, theloopequationforthecurrentcanbewritten as: I Z = 0 (3.1) where Z is the net loop impedance given by||.|

\|||.|

\|++ + +||.|

\|+||.|

\|= jXfRfjXjXfRjX jXv fRZ2clssm lrr(3.2) Sinceat steady-state excitation 0 I ,itfollowsfrom (3.1) that 0 Z = , whichimplies that both the real and imaginary parts of Z are zeros. These two equations can be solved simultaneouslyforanytwounknowns(usuallyvoltageandfrequency).Forsuccessful voltage-buildup, theload-capacitance combination and the rotor speed should resultina valuesuchthatXm=Xsmax,whichyieldstheminimumvalueofexcitationcapacitance below which the SEIG fails to self-excite. 54 Steady-state and Transient Model (abc-dq0 transformation) Theprocessofself-excitationisatransientphenomenonandisbetterunderstoodif analyzed using a transient model. To arrive at transient model of an induction generator, abc-dq0 transformation is used. abc-dq0Transformation.Theabc-dq0transformationtransfersanabc(inany referenceframe)systemtoarotatingdq0system.Krauseetal.[3.1]noted that,alltime varyinginductancescanbeeliminatedbyreferringthestatorandrotorvariablestoa frameofreferencerotatingatanyangularvelocityorremainingstationary.All transformationsarethenobtainedbyassigningtheappropriatespeedofrotationtothis (arbitrary)referenceframe.Also,ifthesystemisbalancedthezerocomponentwillbe equal to zero [3.1]. A change ofvariables whichformulates a transformation of the 3-phasevariables of stationary circuit elements to the arbitrary reference frame may be expressed as [3.1]: abcs s qdosf K f = (3.3) Where: ((((

=s 0dsqss 0 qdffff ;((((

=csbsasabcsffff ;((((((((

|.|

\|+ |.|

\||.|

\|+ |.|

\|=2121213 2 sin3 2 sin sin3 2 cos3 2 cos cos32Ks; (0) d () t0+ =;55 is the dummy variable of integration.For the inverses transformation: ((((((((

|.|

\|+ |.|

\|+|.|

\| |.|

\| =13 2 sin3 2 cos13 2 sin3 2 cos1 sin cos) (K1s In(3.3),fcanrepresentvoltage,current,fluxlinkage,orelectriccharge.The subscriptsindicatesthevariables,parametersandtransformationassociatedwith stationarycircuits.Thisabovetransformationcouldalsobeusedtotransformthetime-varyingrotorwindingsoftheinductionmachine.Itisconvenienttovisualizethe transformationequationsastrigonometricrelationshipsbetweenvariablesasshownin Figure 3.5. asfbsfcsfdsfqsf090 Figure 3.5Transformation for stationary circuits portrayed by trigonometric relationships. 56 Theequationsoftransformationmaybethoughtofasifthefqsandfdsvariablesare directedalongaxesorthogonaltoeachotherandrotatingatanangularvelocityof, whereuponfas, fbs,and fcs (instantaneousquantitieswhichmaybeanyfunctionoftime), considered as variables directed along stationary paths each displaced by 1200. Although the waveforms of the qs and ds voltages, currents and flux linkages, and electric charges aredependentupontheangularvelocityoftheframeofreference,thewaveformofthe total power is same regardless of the reference frame in which it is evaluated [3.1]. VoltageEquationsinArbitraryReference-FrameVariables.Thewinding arrangementfora2-pole,3-phase,wye-connected,symmetricalinductionmachineis shown in Figure 3.6. RsNsRsNsRsNsicsibsias+++Vbs VcsVasRrNrRrNrRrNribricriar++VcrVarVbrNeutral Neutral+ Figure 3. 6 Two-pole, 3-phase, wye connected symmetrical induction machine Thestatorwindingsareidenticalsinusoidallydistributedwindings,displaced1200, withNsequivalentturnsandresistancers.Therotorisconsistsofthreeidentical 57 sinusoidallydistributedwindings,withNrequivalentturnsandresistancerr.Notethat positive a, b, c sequence is used in both in Figures 3.5 and 3.6. The voltage equations in machine variables can be expressed as [3.1]: abcs abcs s abcsp i r V + = (3.4) abcr abcr r abcrp i r V + = (3.5) Where: Subscript s denotes parameters and variables associated with the stator. Subscript r denotes parameters and variables associated with the rotor. Vabcs, Vabcr are phase voltages. Iabcs, Iabcr are phase currents. abcs , abcrare the flux linkages and p = d/dt. Byusingtheabc-dq0transformationandexpressingfluxlinkagesasproductof currentsandwindinginductances,weobtainthefollowingexpressionsforvoltagein arbitrary reference frame [3.1]: qdos dqs qdos s qdosp i r V + + = (3.6) 'qdor'dqr r'qdor'rqdor'p ) ( i r V + + =(3.7) 58 Where: is the electrical angular velocity of the arbitrary reference frame. r is the electrical angular velocity of the rotor. ] [ ) ( 0qs dsTdqs = ;] [ ) (' ' '0qr drTdqr = . denotes rotor values referred to the stator side. Using the relations between the flux linkages and currents in the arbitrary reference frame andsubstitutingthemin(3.6)&(3.7),thevoltageandfluxequationsareexpressedas follows: qs ds qs s qsp i r V + + = (3.8) ds qs ds s dsp i r V + = (3.9) 'qr'dr r'qr'rqr'p ) ( i r V + + = (3.10) 'dr'qr r'dr'rdr'p ) ( i r V + = (3.11) ) i (i L i L 'qr qs m qs ls qs+ + = (3.12) ) i (i L i L 'dr ds m ds ls ds+ + = (3.13) ) i (i L i L 'qr qs m'qr'lrqr'+ + = (3.14) 59 ) i (i L i L 'dr ds m'dr'lrdr'+ + = (3.15) Where: Lls and Lms are leakage and magnetizing inductances of the stator respectively. Llr and Lm