Fractional-Order Control and Simulation of Wind Turbines with Full-Power Converters

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1 Frciol-Order Corol d Simulio of Wid Turbies wih Full-Power Coverers R. Melício d J. P. S. Clão Dep. of Elecromechicl Egieerig Uiversiy of Beir Ierior Covilh, Porugl ruimelicio@gmil.com; clo@ubi.p V. M. F. Medes Dep. of Elecricl Egieerig d Auomio Isiuo Superior de Egehri de Lisbo Lisbo, Porugl vfmedes@isel.p Absrc This pper is o wid eergy coversio sysems wih full-power coverer d perme mge sychroous geeror. Differe opologies for he power-elecroic coverers re cosidered, mely mrix d mulilevel coverers. Also, ew frciol-order corol sregy is proposed for he vrible-speed operio of he wid urbies. Simulio sudies re crried ou i order o dequely ssess he quliy of he eergy ijeced io he elecric grid. Coclusios re duly drw. I. INTRODUCTION The geerl cosciousess of fiie d limied sources of eergy o erh, d ieriol dispues over he evirome, globl sfey, d he quliy of life, hve creed opporuiy for ew more efficie less polluig wid d hydro power pls wih dvced echologies of corol, robusess, d modulriy []. Cocerig reewble eergies, wid power is prioriy for Porugl's eergy sregy. The wid power gol foresee for ws esblished by he goverme s 5 MW. Hece, Porugl hs oe of he mos mbiious gols i erms of wid power, d i 6 ws he secod coury i Europe wih he highes wid power growh. A overview of he Poruguese echicl pproches d mehodologies followed i order o pl d ccommode he mbiious wid power gols o /3, preservig he overll quliy of he power sysem, is give i []. Power sysem sbiliy describes he biliy of power sysem o mii sychroism d mii volge whe subjeced o severe rsie disurbces [3]. As wid eergy is icresigly iegred io power sysems, he sbiliy of lredy exisig power sysems is becomig cocer of umos imporce [4]. Also, ework operors hve o esure h cosumer power quliy is o deeriored. Hece, he ol hrmoic disorio (THD) coefficie should be kep s low s possible, improvig he quliy of he eergy ijeced io he elecric grid [5]. The developme of power elecroics d heir pplicbiliy i wid eergy exrcio llowed for vriblespeed operio of he wid urbie [6]. The vrible-speed wid urbies re implemeed wih eiher doubly fed iducio geeror (DFIG) or full-power coverer. I vrible-speed wid urbie wih full-power coverer, he wid urbie is direcly coeced o he geeror, which i his pper is perme mge sychroous geeror (PMSG). Hrmoic emissios re recogized s power quliy problem for moder vrible-speed wid urbies. Udersdig he hrmoic behvior of vrible-speed wid urbies is esseil i order o lyze heir effec o he elecric grids where hey re coeced [7]. I his pper, vrible-speed wid urbie is cosidered wih PMSG d differe power-elecroic coverer opologies: mrix d mulilevel. Addiiolly, ew frciol-order corol sregy is proposed for he vriblespeed operio of wid urbies wih PMSG/full-power coverer opology. Simulio sudies re crried ou i order o dequely ssess he quliy of he eergy ijeced io he elecric grid. Hece, he hrmoic behvior of he oupu curre is compued by Discree Fourier Trsform (DFT) d THD. A compriso wih clssicl ieger-order corol sregy is lso preseed, illusrig he improvemes iroduced by he proposed frciol-order corol sregy. This pper is orgized s follows. Secio preses he modelig of he wid eergy coversio sysem (WECS). Secio 3 preses he ew frciol-order corol sregy. Secio 4 preses he power quliy evluio by DFT d THD. Secio 5 preses he simulio resuls. Filly, cocludig remrks re give i Secio 6. II. MODELING A. Wid Speed The wid speed usully vries cosiderbly d hs sochsic chrcer. The wid speed vriio c be modeled s sum of hrmoics wih he frequecy rge. Hz [8] //$6. IEEE 3

2 u = u + A si( ω, () where u is he wid speed vlue subjec o he disurbce, u is he verge wid speed, is he kid of he mechicl eigeswig excied i he roig wid urbie, A is he mgiude of he eigeswig, ω is he eigefrequecy of he eigeswig. Hece, he physicl wid urbie model is subjeced o he disurbce give by he wid speed vriio model [9]. B. Wid Turbie Durig he coversio of wid eergy io mechicl eergy, vrious forces (e.g. cerifugl, grviy d vryig erodymic forces cig o bldes, gyroscopic forces cig o he ower) produce vrious mechicl effecs [8]. The mechicl eigeswigs re mily due o he followig pheome: symmery i he urbie, vorex ower iercio, d eigeswigs i he bldes. The mechicl pr of he wid urbie model c be simplified by modelig he mechicl eigeswigs s se of hrmoic sigls dded o he power exrced from he wid. Therefore, he mechicl power of he wid urbie disurbed by he mechicl eigeswigs my be expressed by 3 P = P + A m gm ( h (, () = m= g m = si ω + ϕ m ( ' ) d' m, (3) where P is he mechicl power of he wid urbie, m is he hrmoic of he give eigeswig, g m is he disribuio bewee he hrmoics i he eigeswig, m is he ormlized mgiude of g m, h is he modulio of he eigeswig, d ϕ m is he phse of he hrmoic m i he eigeswig. The frequecy rge of he wid urbie model wih mechicl eigeswigs is from. o Hz. The vlues used for he clculio of re give i he Tble I [9]. C. Mechicl Drive Tri Model The mechicl drive ri cosidered i his pper is wo-mss model, cosisig of lrge mss d smll mss, correspodig o he wid urbie roor ieri d geeror roor ieri, respecively. The model for he dymics of he mechicl drive ri for he WECS used i his pper ws repored by he uhors i []. TABLE I. Source A Asymmery. Vorex ower iercio MECHANICAL EIGENSWIGS EXCITED IN THE WIND TURBINE.8 ω h m ϕ m m ω 3 ω 4/5 /5 π/ / / π/ 3 Bldes.5 9 π / (g +g ) D. Geeror The geeror cosidered i his pper is PMSG. The equios for modelig PMSG c be foud i he lierure []. I order o void demgeizio of perme mge i he PMSG, ull sor curre is imposed []. E. Mrix Coverer The mrix coverer is AC-AC coverer, wih ie bidireciol commded isuled ge bipolr rsisors (IGBTs) S ij. I is coeced bewee firs order filer d secod order filer. The firs order filer is coeced o PMSG, while he secod order filer is coeced o elecric ework. A swichig sregy c be chose so h he oupu volges hve erly siusoidl wveforms he desired frequecy, mgiude d phse gle, d he ipu curres re erly siusoidl he desired displceme power fcor [3]. A hree-phse cive symmericl circui i series models he elecric ework. The model for he mrix coverer used i his pper ws repored by he uhors i []. The cofigurio of he simuled WECS wih mrix coverer is show i Fig.. F. Mulilevel Coverer The mulilevel coverer is AC-DC-AC coverer, wih welve uidireciol commded IGBTs S ik used s recifier, d wih he sme umber of uidireciol commded IGBTs used s iverer. The recifier is coeced bewee he PMSG d cpcior bk. The iverer is coeced bewee his cpcior bk d secod order filer, which i ur is coeced o elecric ework. The groups of four IGBTs liked o he sme phse cosiue leg k of he coverer. A hree-phse cive symmericl circui i series models he elecric ework. The model for he mulilevel coverer used i his pper ws repored by he uhors i []. The cofigurio of he simuled WECS wih mulilevel coverer is show i Fig.. III. CONTROL STRATEGY A. Frciol-Order Corollers A ew corol sregy bsed o frciol-order PI corollers is proposed for he vrible-speed operio of wid urbies wih PMSG/full-power coverer opology. 3

3 Figure. WECS wih mrix coverer Figure. WECS wih mulilevel coverer Frciol-order corollers re bsed o frciol clculus heory, which is geerlizio of ordiry differeiio d iegrio o rbirry (o-ieger) order [4]. Recely, pplicios of frciol clculus heory i prcicl corol field hve icresed sigificly [5]. The frciol-order differeior c be deoed by geerl operor D [6], give by d, R( ) > d D =, R( ) =. (4) τ R < ( d ), ( ) The mhemicl defiiio of frciol derivives d iegrls hs bee he subjec of severl pproches. The mos frequely ecouered defiiio is clled Riem Liouville defiiio, i which he frciol-order iegrls re defied s D f ( = ( τ) f ( τ) dτ, (5) Γ( ) while he defiiio of frciol-order derivives is where D d f ( τ) f ( = τ d, (6) + Γ( ) d ( τ) Γ( x) x y e y dy, (7) is he Gmm fucio, d re he limis of he operio, d is he frciol order which c be complex umber. I his pper, is ssumed s rel umber h sisfies he resricios < <. Also, c be ke s ull vlue. The followig coveio is used: D D. The differeil equio of he frciol-order coroller is give by PI 3

4 u( = K e( + K D e(, (8) p where K p is he proporiol cos d K i is he iegrio cos. Tkig =, clssicl PI coroller is obied. I his pper, i is ssumed h =. 5. A good rdeoff, preseed i [7], bewee robusess d dymic performce is i fvor of he rge.4.6 for he order of iegrio. Usig he Lplce rsform of frciol clculus, he rsfer fucio of he frciol-order PI coroller is obied, give by i.5 G( s) = K p + Ki s, (9) B. Coverers Corol Power coverers re vrible srucure sysems, becuse of he o/off swichig of heir IGBTs. Pulse widh modulio (PWM) by spce vecor modulio (SVM) ssocied wih frciol slidig mode corol [6] is used for corollig he coverers. The slidig mode corol sregy preses rcive feures such s robusess o prmeric uceriies of he wid urbie d he geeror s well s o elecric grid disurbces [8]. Slidig mode corol is priculrly ieresig i sysems wih vrible srucure, such s swichig power coverers, gureeig he choice of he mos pproprie spce vecors. The im is o le he sysem slide log predefied slidig surfce by chgig he sysem srucure. The power semicoducors prese physicl limiios, sice hey co swich ifiie frequecy. Also, for fiie vlue of he swichig frequecy, error e αβ will exis bewee he referece vlue d he corol vlue. I order o guree h he sysem slides log he slidig surfce S( e αβ,, i hs bee prove h i is ecessry o esure h he se rjecory er he surfces verifies he sbiliy codiios [9] give by fiie legh wih N pois per cycle. Hece, Discree Fourier Trsform (DFT) is iroduced, give by N jπ k N X ( k) = e x( ) for k =,..., N, () = where x () is he ipu sigl d X (k) is he mpliude d phse of he differe siusoidl compoes of he x (). The hrmoic behvior compued by he THD is give by X H H = THD (%) = X F, (3) where X H is he roo me squre (RMS) vlue of he sigl, d X is he RMS vlue of he fudmel compoe. F V. SIMULATION RESULTS The mhemicl models for he WECS wih he mrix d mulilevel power coverer opologies were implemeed i Mlb/Simulik. The WECSs simuled i his cse sudy hve red elecric power of 9 kw. The wid speed vriio model is give by u = u + A si ( ω 4, (4) The operiol regio of he WECS ws simuled for wid speed rge from 5-5 m/s. The swichig frequecy used i he simulio resuls is 5 khz. The mechicl power of he wid urbie, he elecric power of he geeror, d he differece bewee hese wo powers, i.e., he ccelerig power, re show i Fig. 3. The hrmoic coe of he mechicl power of he urbie, compued by he DFT, is show i Fig. 4. ds( eαβ, S ( eαβ, <. () d P IV. POWER QUALITY EVALUATION The hrmoic behvior compued by he DFT is bsed o Fourier lysis. If is X (ω) coiuous periodicl sigl wih period of T d sisfies Dirichle codiio, he Fourier series is give by Power (kw) P g P P g N = jω X ( ω) = x( ) e for ω π. () I order o impleme Fourier lysis i compuer, he sigl i boh ime d frequecy domis is discree d hs Time (s) Figure 3. Mechicl, elecric d ccelerig power 33

5 Mechicl power (%) Firs compoe of he curre (%) Frciol PI corollers Clssicl PI corollers 4 8 Frequecy (Hz) Figure 4. Hrmoic coe of he mechicl power of he urbie The hrmoic coe of he elecric power of he geeror, compued by he DFT, is show i Fig. 5. The firs hrmoic of he oupu curre, compued by he DFT, for he WECS wih he mrix coverer is show i Fig. 6. The THD of he oupu curre for he WECS wih he mrix coverer is show i Fig. 7. Boh clssicl d frciol-order corollers re cosidered. The firs hrmoic of he oupu curre, compued by he DFT, for he WECS wih he mulilevel coverer is show i Fig. 8. The THD of he oupu curre for he WECS wih he mulilevel coverer is show i Fig. 9. Agi, boh clssicl d frciol-order corollers re cosidered. The presece of he eergy-sorge elemes llows he proposed WECS wih he mulilevel coverer o chieve he bes performce, i compriso wih he mrix coverer. The ew frciol-order corol sregy provides beer resuls comprively o clssicl ieger-order corol sregy, i wh regrds he hrmoic behvior compued by he DFT d he THD. Elecricl power (%) Frequecy (Hz) Figure 5. Hrmoic coe of he elecric power of he geeror Wid speed (m/s) Figure 6. Firs hrmoic of he oupu curre, mrix coverer; he firs hrmoic is expressed i percege of he fudmel compoe THD (%) Firs compoe of he curre (%) Clssicl PI corollers Frciol PI corollers Wid speed (m/s) Figure 7. THD of he oupu curre, mrix coverer Frciol PI corollers Clssicl PI corollers Wid speed (m/s) Figure 8. Firs hrmoic of he oupu curre, mulilevel coverer; he firs hrmoic is expressed i percege of he fudmel compoe 34

6 THD (%).5.5 Clssicl PI corollers Frciol PI corollers Wid speed (m/s) Figure 9. THD of he oupu curre, mulilevel coverer The THD of he oupu curre is lower h 5% limi imposed by IEEE-59 sdrd [], for boh power coverer opologies cosidered. Alhough IEEE-59 sdrd migh o be pplicble i such siuio, i is used s guidelie for compriso purposes []. VI. CONCLUSIONS The hrmoic behvior of vrible-speed wid urbies wih PMSG/full-power coverer opology is sudied i his pper. As ew coribuio o erlier sudies, ew frciol-order corol sregy is proposed i his pper, which chieves superior dymic chrcerisics d oupu power quliy. Simulio sudies reveled beer performce of he proposed WECS wih he mulilevel coverer, i compriso wih he mrix coverer. Also, he hrmoic behvior compued by he DFT d he THD reveled h he power quliy ijeced i he elecric grid is ehced usig he ew frciol-order corol sregy, i compriso wih clssicl ieger-order corol sregy, for boh power coverer opologies cosidered. REFERENCES [] T. Ahmed, K. Nishid, d M. Nkok, Advced corol of PWM coverer wih vrible-speed iducio geeror, IEEE Trs. Idusry Applicios, vol. 4, pp , July-Augus 6. [] A. Esqueiro, R. Csro, P. Flores, J. Ricrdo, M. Pio, R. Rodrigues, d J. Peçs Lopes, How o prepre power sysem for 5% wid eergy peerio: he Poruguese cse sudy, Wid Eergy, vol., pp , Jury-Februry 8. [3] Y. Coughl, P. Smih, A. Mulle, d M. O Mlley, Wid urbie modelig for power sysem sbiliy lysis - A sysem operor perspecive, IEEE Trs. Power Sysems, vol., pp , Augus 7. [4] N. R. Ullh d T. Thiriger, Vrible speed wid urbies for power sysem sbiliy ehceme, IEEE Trs. Eergy Coversio, vol., pp. 5 6, Mrch 7. [5] J. M. Crrsco, L. G. Frquelo, J. T. Bilsiewicz, E. Glv, R. C. P. Guisdo, A. M. Prs, J. I. Leo, d N. Moreo-Alfoso, Powerelecroic sysems for he grid iegrio of reewble eergy sources: A survey, IEEE Trs. Idusril Elecroics, vol. 53, pp. 6, Augus 6. [6] J. A. Broudi, V. Divhi, d A. M. Kigh, A review of power coverer opologies for wid geerors, Reewble Eergy, vol. 3, pp , November 7. [7] S. T. Tezerkis d S. A. Pphssiou, A ivesigio of he hrmoic emissios of wid urbies, IEEE Trs. Eergy Coversio, vol., pp. 5 58, Mrch 7. [8] Z. X. Xig, Q. L. Zheg, X. J. Yo, d Y. J. Jig, Iegrio of lrge doubly-fed wid power geeror sysem io grid, i: Proc. of he 8h I. Cof. Elecricl Mchies d Sysems, Njig, Chi, pp. 4, Sepember 5. [9] V. Akhmov, H. Kudse, d A. H. Nielse, Advced simulio of widmills i he elecric power supply, I. Jourl of Elecr. Power Eergy Sys., vol., pp , Augus. [] R. Melício, V. M. F. Medes, d J. P. S. Clão, Modelig d simulio of wid eergy sysem: mrix versus mulilevel coverers, i: Proc. 4h IEEE Medierre Elecroechicl Coferece, Ajccio, Frce, pp , My 8. [] C.-M. Og, Dymic Simulio of Elecric Mchiery: Usig Mlb/Simulik. NJ: Preice-Hll, 98, pp [] T. Sejyu, S. Tmki, N. Urski, d K. Uezo, Wid velociy d posiio sesorless operio for PMSG wid geeror, i: Proc. of he 5h I. Cof. o Power Elecroics d Drive Sysems, Sigpore, pp , November 3. [3] S. M. Brki, J. D. Aplevich, d M. Kzeri, Coroller desig for wid urbie sysem icludig mrix coverer, i: Proc. of he 7 IEEE Power Eg. Soc. Ge. Meeig, Tmp, FL, Jue 7. [4] I. Podluby, Frciol-order sysems d PI-lmbd-D-mucorollers, IEEE Trs. Auomic Corol, vol. 44, pp. 8 4, Jury 999. [5] W. Li d Y. Hori, Vibrio suppressio usig sigle euro-bsed PI fuzzy coroller d frciol-order disurbce observer, IEEE Trs. Id. Elecro., vol. 54, pp. 7 6, Februry 7. [6] A. J. Clderó, B. M. Vigre, d V. Feliu, Frciol order corol sregies for power elecroic buck coverers, Sigl Processig, vol. 86, pp , Mrch 6. [7] G. Mioe d P. Lio, New uig rules for frciol PI-lf corollers, Nolier Dymics, vol. 49, pp. 5 57, July 7. [8] B. Belr, T. Ahmed-Ali, d M. E. H. Bebouzid, Slidig mode power corol of vrible-speed wid eergy coversio sysems, IEEE Trs. Eergy Coversio, vol. 3, pp , Jue 8. [9] J. F. Silv d S. F. Pio, Corol mehods for swichig power coverers, i: Power Elecroics Hdbook, d ed., M. H. Rshid, Ed. NY: Acdemic Press, 7, pp [] IEEE Guide for Hrmoic Corol d Recive Compesio of Sic Power Coverers, IEEE Sdrd [] T. M. H. Nicky, K. T, d S. Islm, Miigio of hrmoics i wid urbie drive vrible speed perme mge sychroous geerors, i: Proc. of he 7h I. Power Egieerig Cof., pp , December 5. 35