ECE566_Week5_LectureSlides_Cale.pdf Theory
- 1. Control of Wind Turbine Generators James Cale – Guest Lecturer EE 566, Fall Semester 2014 Colorado State University
- 2. Review from Day 1
- 3. Review • Lasttime, westarted withbasicconcepts from physicssuch asmagnetic fields, flux, and inductancetodefineterms andderivemagnetic equivalent circuits(MECs) for different devices. • Weexamined somebasicstationary devicesand introduced arotating member—giving riseto the concept ofinductancethat isposition dependent. • Wethen looked atcylindricaldevicesand introduced the conceptof sinusoidal winding distributions. • Weshowed how balanced three phasecurrents insinusoidalwindingsgiveriseto arotating mmf.
- 4. Review (continued) • Wesawhow rotating mmfsgiverisetotorque in electrical machines: o Inthe inductionmachine, the rotating mmfon the stator inducesanmmf onthe rotor. The rotor seekstoalignwith thestator mmf which causesatorque. o Inthe permanent magnet machine, there are magnetic polesalready onthe rotor—these polesseekto alignwiththe stator mmf giving risetotorque.
- 5. Why is EM Torque Produced? Considerthedeviceshownbelow, wheretherotorpositionis initiallyfixedataposition and Whathappenswhenthewindingisenergized?Canweprove whatwillhappen? 𝑣 𝑖 + − 𝜃𝑟(0) 𝜃𝑟 0 𝑖 = 0. 𝑇𝑒 𝑇𝐿
- 7. Torque and Co-Energy Forthissimplemachine, Wecanderivethefollowingequationfromfundamental energyrelations: 𝑇𝑒(𝑖, 𝜃𝑟) = 𝜕𝑊 𝑐(𝑖, 𝜃𝑟) 𝜕𝜃𝑟 ⇒ 𝑇𝑒= − 1 2 𝐿2𝑖2sin𝜃𝑟 𝐿 𝜃𝑟 = 𝐿1 + 𝐿2 cos 𝜃𝑟 𝑊 𝑐 = 1 2 𝐿(𝜃𝑟)𝑖2
- 8. Torque vs. Position Wecanseethatwiththetorquerelationthatwasderived, therewillbeanelectromagnetictorquethatpullstherotorin thenegative directionuntil at 𝑇𝐿 = 0 𝜃𝑟 𝑇𝑒 = 𝑇𝐿 = 0 𝜃𝑟 = 0. starting point
- 10. Review of Induction Machines Summary Notes: • Operates(produces torque) atspeeds other than synchronous speed. • Sincetorque-speed curvehas large slopenear s = 0,oncemachineisinsteady-state, rotor speed will notvary much. It islikea“constant” speed machine. • For steady-stateanalysis, use theequivalent T circuit; for transientanalysis, must usefull time domain equations, typicallyin qd0variables.
- 11. Induction Machines (Review) Torque-Speed Curve 𝑇𝐿 = 𝑇𝑒
- 12. Permanent Magnet Synchronous Generators (Review) 𝜙𝑠 𝜙𝑟 𝜃𝑟 as’ as bs’ bs cs cs’
- 13. PMSG Machine Review Summary Notes: • Inthe PMSG,the frequency of the rotor currents isthe sameasthe frequency of thestator currents (not true inIM machine) –hencethe word “synchronous” inthetitle. • Another view–bycontrolling the frequency of the stator currents (e.g., through power electronics) wecancontrol the rotor speed. • We’ll seethat bycontrol of thevoltage phase angle, cangenerate uniquetorque-speed curves.
- 15. Four Types of Wind Turbine Generators Type1 Type2 Type3 Type4
- 16. Type 1 Topology Squirrel-cage induction machine
- 17. (a) Squirrel cage induction motor; (b) conductors in rotor; (c) photograph of squirrel cage induction motor; (d) views of Smokin’ Buckey motor: rotor, stator, and cross section of stator (Courtesy: David H. Koether Photography) Squirrel Cage Induction Machine
- 18. Type 1 Topology Advantages: • Rugged electrical machineand simple (inexpensive) design—nopower electronics. Disadvantages: • Can’tcontrol rotor speed—singletorque-speed relation determinesspeed. • Lackofrotor speed control meansweare (generally) notat theoptimal tip-speed ratio. • Variationsinrotor speed fromwindcancouple directlyonto electrical grid. • Requirescap bankfor improved power quality.
- 19. Induction Machines Torque-Speed CurvewithWindTorqueLoad Curves Different torque loads (from wind) result in different rotor speeds. But generally not at the optimal tip-speed ratio.
- 20. Type 1 Topology Other Notes: • Firstgeneration ofwind turbine designs—many turbine manufacturers still usethis design. • Rotor speed varieswith slip(0-2%), mostrated at1%,withmax slipat2%. • Connected tothe turbine shaft viaagear box. • It alwaysabsorbs reactivepower—in generator andmotoring mode(thus requiring VAR compensation). • Minimum absolute valueoftorque isreachedat xxxxx(i.e., synchronous speed). 𝑠 = 0
- 21. Type 2 Topology Wound-rotor induction machine
- 22. Type 2 Topology Advantages: • Allows for somedegreeof rotor speedcontrol through theuse ofvariablerotor resistance. Disadvantages: • Speed control limitedbyrange ofacceptable slip values—typically 0-10%.Notoptimal for wind turbine design. • Efficiencypoor athigh valuesof slip,sincemore power isbeinglost inthe rotor resistance. From (3.1)ofAliprantis’ notes: 𝑃𝑎𝑔 = 1 − 𝑠 𝑃𝑚
- 23. Type 2 Topology Disadvantages(continued): • Brushes aremechanical—require maintenance. • Lackofrefined rotor speedcontrol meanswestill may not beatthe optimal tip-speed ratio. • Windvariabilitystill coupled togrid. • Still havepower factor correcting cap bank. Other Notes: • Connected tothe turbine shaft viaagear box. • It alwaysabsorbs reactivepower—in generator andmotoring mode(thus requiring VAR compensation).
- 24. Wound-Rotor Induction Machines Steady-State EquivalentT Circuit –Wound Rotor 𝑟𝑠 𝑋𝑠 𝑋𝑟 𝑟𝑟 + 𝑅𝑒 /s ′ ′ 𝐼𝑠 𝐼𝑟 ′ 𝑉 𝑠 − + 𝑋𝑀 𝑟𝑀 s = 𝜔𝑒 − 𝜔𝑟 𝜔𝑒 = 1 − 𝜔𝑟 𝜔𝑒 ′
- 25. Induction Machines Usingrotor resistance tochange torque-speed curve—to help achieveoptimal tip-speedratio.
- 27. Varying Resistance using PE Togenerateafamilyoftoquespeedcurves,youcouldconnect abankofpowerresistorstotherotorthroughbrushes.You couldthenobtainadiscretenumberofresistorvaluesby seriesorparallelcombinationsoftheresistors, usingpower electronicswitches. Anotheridea:couldyouusepowerelectronicstogetalinearly varyingrotorresistance?
- 28. Varying Resistance using PE 𝑅0 𝑅1 𝑅𝑒𝑞? 𝑅0 ≫ 𝑅1 Whenswitch off: Whenswitch on: 𝑅𝑒𝑞 = 𝑅0 𝑅𝑒𝑞 ≅ 𝑅1 Switch
- 29. Defining the “Fast-Average” 𝑓𝑎𝑣𝑔(𝑡) = 1 𝑇 𝑓 𝜏 𝑑𝜏 𝑡+𝑇/2 𝑡−𝑇/2 𝑡 𝑇 Thefast (“moving”) averagegenerally tracksthe waveform more closely than thesimpleaverage. Fast Avg Simple Avg 𝑓
- 30. Varying Resistance using PE 𝑅𝑒𝑞 = 1 𝑇𝑠𝑤 𝑅𝑒𝑞 𝜏 𝑑𝜏 𝑡0+𝑇𝑠𝑤 𝑡0 𝑡 𝑅0 𝑅1 𝑇𝑠𝑤 𝐷 = 𝐷𝑅1 + (𝑇𝑠𝑤 − 𝐷)𝑅0 𝑇𝑠𝑤 = 𝐷 𝑇𝑠𝑤 𝑅1 − 𝑅0 + 𝑅0 𝑡0
- 31. Varying Resistance using PE 𝑅𝑒𝑞 = 𝐷 𝑇𝑠𝑤 𝑅1 − 𝑅0 + 𝑅0 𝐷 𝑅0 𝑅1 𝑇𝑠𝑤 𝑅𝑒𝑞 When𝐷 = 0, 𝑅𝑒𝑞 = 𝑅0 When𝐷 = 𝑇𝑠𝑤, 𝑅𝑒𝑞 = 𝑅1 Howisthisuseful?(a)Givesawidevariationineffectiverotor resistancewithtworesistors,(b)Canobtainadesiredtorque- speedrelationthroughclosed-loopcontrolof𝐷 –thiscorrects fortemperatureeffectsonresistanceand/orbrushcorrosion.
- 32. Variable Speed Wind Turbines Power Converter Generator P, Q PF or V Q-Controller PF* or V* Q* UTILITY Rotor speed – pitch angle P-Controller P* wm wm b wm P* P* = k wm 3 w m_rated
- 33. Type 3 Topology Wound-rotor, doubly-fed induction generator (DFIG)
- 34. Type 3 Topology • Usesawound-rotor inductionmachine, but now the rotor isconnected tothe gridthrough an ac- dc-acpower electronic link. • Thepower electronic linkiscomposed of two bi- directional converters, connected through adc link(capacitor). • These convertersarereferred toasthe rotor-side converter (connects the rotor circuitstothe dc link) andthe grid-sideconverter (connects the dc linktothe grid).
- 35. Rotor-Side Converter • Controls the frequency of therotor currents to maintainsynchronism between therotor and stator rotating mmfs. • Controls the magnitude andphaseof the rotor currents—which controls the real and reactive power deliveredtothe grid. Grid-Side Converter • Maintains thedclinkvoltage, whichprovidesthe dcvoltage for the rotor-sideconverter.
- 36. AC-DC-AC Power Electronic Link 𝐿𝑑𝑐 𝒗𝑎𝑏𝑐 𝐿𝑐 𝑣𝑑𝑐 𝒊𝑎𝑏𝑐 𝑃 * 𝑺 Control How can we use power electronics to generate arbitrary currents, with phase angle referenced from utility voltage? 𝒗𝑎𝑏𝑐 𝐿𝑙𝑟 𝑄 * Example AC-DC-AC Converter
- 37. AC-DC-AC Power Electronic Link Power Electronics; Converters, Applications and Design, 3rd Edition, by N. Mohan, T.M. Undeland and W.P. Robins; John Wiley & Sons 𝑖𝑎
- 38. Induction Machines-Doubly Fed Induction Machine EquivalentT Circuit 𝑟𝑠 𝑋𝑙𝑠 𝑋𝑙𝑟 𝑟𝑟/s ′ ′ 𝐼𝑠 𝐼𝑎𝑟 ′ 𝑉 𝑠 − + 𝑋𝑀 𝑟𝑀 s = 𝜔𝑒 − 𝜔𝑟 𝜔𝑒 = 1 − 𝜔𝑟 𝜔𝑒 𝑉 𝑟 𝑠 − + ′
- 39. Rotor-Side Converter Fromthevoltageequationsderivedfromthesteady-state equivalentcircuit,youcanderive(seeAliprantis’notes,page 30): • For𝑠 > 0(“sub-synchronousoperation”),therotorside powerhasoppositesignofstatorsidepower.Forgenerator action𝑃 𝑠 < 0,therotorisabsorbingpower. • For𝑠 < 0,(“super-synchronousoperation”),therotorside powerhasthesamesignasstatorsidepower.For generatoraction𝑃 𝑠 < 0,therotorisgeneratingpower. 𝑃𝑟 ≈ −𝑠𝑃𝑠 𝑃𝑎𝑔 = 𝑃𝑚 (1 − 𝑠)
- 40. Note on Terminology 𝑠 = 𝜔𝑒 − 𝜔𝑟 𝜔𝑟 > 0 ⇒ 𝜔𝑒 − 𝜔𝑟 > 0 ⇒ 𝜔𝑟 < 𝜔𝑒 Fromthedefinitionofslip: Sointhiscase,therotorspeedislessthanthesynchronous speed,hencetheterm“sub-synchronous.”Theoppositeistrue inthesuper-synchronouscase.
- 41. Type 3 Wind Turbine Generator
- 42. Rotor-Side Converter OtherNotes: • PowerthatwaslostintheresistoroftheType2turbinecan berecoveredusingpowerelectronics.Canoperateefficiently atlargeslips(±30%istypical). • Since forlowvaluesofslip,thestatorcarriesthebulkofthe power.Sorotorsidepowerelectronicsareratedforlower powerlevels(whichmeansthey’relessexpensive!). |𝑃𝑠| ≈ 𝑃𝑟 𝑠
- 43. Control of 𝑷 and 𝑸 FromtheequivalentTcircuit wherewe’vedefined𝑋𝑠= 𝑋0 + 𝑋1.Nowif𝑅1 ≪ 𝑋𝑠, Usingtheseexpressionstocomputecomplexpower𝑆𝑠= 3𝑉 𝑠𝐼𝑠 where𝐼𝑟 = 𝐼𝑟 𝜃𝑖𝑟 = 𝐼𝑟𝑎 + 𝑗𝐼𝑟𝑏 𝑉 𝑠 = 𝑅1 + 𝑗𝑋𝑠 𝐼𝑠 + 𝑗𝑋0𝐼𝑟 𝐼𝑠 ≈ 𝑉 𝑠 − 𝑗𝑋0𝐼𝑟 𝑗𝑋𝑠 𝑃𝑠 ≈ −3 𝑋0 𝑋𝑠 𝑉 𝑠𝐼𝑟𝑎 𝑄𝑠 ≈ 3𝑉 𝑠 𝑉 𝑠 + 𝑋0𝐼𝑟𝑏 𝑋𝑠 ′ ′ ′ ′ ′ ′ ′ ′
- 44. A Simple PLL 𝑲𝑠 = 2 3 cos 𝜃 cos 𝜃 − 2𝜋 3 cos 𝜃 + 2𝜋 3 sin 𝜃 sin 𝜃 − 2𝜋 3 sin 𝜃 + 2𝜋 3 1 2 1 2 1 2 ⇒ 𝒗𝑞𝑑0 = 𝑲𝑠 𝒗𝑎𝑏𝑐 = 2𝑉 𝑠 𝟎 𝟎 𝒗𝑎𝑏𝑐 = 2𝑉 𝑠 cos 𝜃 cos 𝜃 − 2𝜋 3 cos 𝜃 + 2𝜋 3 Firstnotethatfor Keypoints:(a)wetransformtothe𝑞𝑑0referenceframesothat sinusoidallyvarying quantitiesbecomedcquantities,(b)note thatinthiscase,𝑣𝑑 shouldbezero.
- 45. A Simple PLL 𝜃𝑒 = 𝜔𝑒 𝜏 𝑑𝜏 𝑡 0 + 𝜃𝑒(0) 𝑣𝑑 𝐾𝑝 + 1 𝑠 𝐾𝑖 0 𝜔𝑒 𝒗𝑞𝑑0 = 𝑲𝑠𝒗𝑎𝑏𝑐 Σ − +
- 46. A Simple PLL Line frequency jumps from 60 to 62 Hz
- 47. Type 3 Topology Summary Notes: • Variablespeed (±30slip,or 70%<speed<130%) • Variablefrequency 3-phase, currentregulated PWMinverter isfed tothe rotor winding. • Cancontrol real andreactivepower bycontrol of the rotor magnitudeand phase. • Lowpower absorbed/generated byrotor results inlessexpenserotor converter. • Induction generator always absorbsreactive power (still needreactive power compensation) • Currently dominatesthe global market.
- 48. Type 4 Topology Permanent Magnetic Synchronous Generator (PMSG)
- 49. Type 4 Topology • Usesapermanent magnetic synchronous machinewith stator connected tothe grid through anac-dc-acpower electronic link. • Thepower electronic linkiscomposed of two bi- directional converters, connected through adc link(capacitor). • These convertersarereferred toasthe stator- sideconverter (connects the stator circuitstothe dclink) andthe grid-sideconverter (connects the dclinktothe grid).
- 50. Type 4 Topology • VariableSpeed –variablefrequency atgenerator sideandfixedfrequency (60Hz)atthe utility side • Latest generation ofwindturbines. • Rotor speed variesinavery largerange—so connected tothe turbine shaft viagear boxor directdrive(no gear box). • Absorbs/supplies reactivepower (+ 95%power factor) sonocap bankneeded. • Always usepower converter toconvert generator power andto return the power tothe utility supply (ac-dc-ac) • Power converter sizedto carryrated power.
- 51. Type 4 Topology • Outputpower(realpower,activepower)–adjustableat anyspeed(withindesignlimit). • Reactivepower(non-revenuerelated)–adjustableatany speed(withindesignlimit). • Realandreactivepowerarecontrollableindependently. • Outputelectricalpoweriscontrollableindependentof inputmechanicalpowerandspeed,however,itisnormally controlledtofollow: • Real power as a cube function of rotor rpm to optimize the aerodynamic energy capture - real power = Kw wm 3 • Reactive power is controlled to control constant voltage at the output of the generator or power factor.
- 52. Type 4 Topology StatorSideConverter • Current magnitude is adjustable by controlling the power converter • Starting current and starting torque is adjustable • Max Const. Pitch Operation: Real power = Kw wm 3 GridSideConverter • Output power factor adjustable (normally between 0.95 pf-lagging to 0.95 pf-leading. • Real power is adjusted to keep the DC bus voltage constant Havingcapabilitytoadjustthepowerfactormeansthatthe generatoroutputterminalvoltagecanbeadjustedbycontrolling theoutputreactivepower.
- 53. Stator-Side Converter • Controls the frequency of thestator currents to maintainsynchronism between therotor and stator rotating mmfs. • Controls the magnitude andphaseof the stator currents tocontrol electromagnetic torque—in order toobtainthe optimal tip-speed ratio.
- 54. Determining 𝑷 and 𝑸 From theequivalent steady-state circuit: Realpower Reactive power 𝑆𝑠 ≈ 3 𝐸𝑝𝑚 − 𝑗𝜔𝑟𝐿𝑞𝐼𝑠 𝐼𝑠 ≈ 3 2 𝜔𝑟 𝜆𝑝𝑚 − 𝐿𝑑 − 𝐿𝑞 𝐼𝑑𝑠 𝐼𝑞𝑠 + j 3 2 𝜔𝑟 𝜆𝑝𝑚𝐼𝑑𝑠 − 𝐿𝑑𝐼𝑑𝑠 − 𝐿𝑞𝐼𝑞𝑠 * 2 2
- 55. Torque 𝑇𝑒 = 3 2 𝑃 2 𝜆𝑝𝑚 − 𝐿𝑑 − 𝐿𝑞 𝐼𝑑𝑠 𝐼𝑞𝑠 𝐸 = 𝑃𝑠𝑑𝑡 = 𝑇𝑒𝑑𝜃 Energy, torque, and power arerelated by: where𝜔𝑟𝑚 = 2 𝑃 𝜔𝑟 (here 𝑃 isthe number of machine poles, not power!) For anon-salient machine,𝐿𝑑 = 𝐿𝑞, inwhichcase ⇒ 𝑃𝑠= 𝑇𝑒 𝑑𝜃 𝑑𝑡 = 𝑇𝑒𝜔𝑟𝑚 𝑇𝑒 = 3 2 𝑃 2 𝜆𝑝𝑚𝐼𝑞𝑠
- 56. Current Regulated Speed Control 𝜔𝑟𝑚 𝑇𝑒 2 3 2 𝑃 1 𝜆𝑝𝑚 𝐾 1 + 1 𝑠𝜏 Current Reg Plant 𝑃 2 𝜔𝑟𝑚 𝑆 𝜃𝑟 𝒊𝑎𝑏𝑐𝑠 𝑣𝑑𝑐 ∗ ∗ 𝑟* 𝑖𝑞𝑠 𝑟* 𝑖𝑑𝑠
- 57. Maximum Torque Per Amp