Robust Control Design of Permanent Magnet Direct-drive Wind Power System

Transcription

1 9 A publcaton of CHEMICA ENGINEERING TRANSACTIONS VO. 59, 07 Gust Etors: Zhuo Yang, Junj Ba, Jng Pan Copyrght 07, AIDIC Srvz S.r.l. ISBN ; ISSN 8-96 Th Italan Assocaton of Chcal Engnrng Onln at DOI: 0.0/CET Robust Control Dsgn of Prannt Magnt Drct-rv Wn Powr Syst J Mng* a, Qaobo Pan a,shuang Zhao b a School of Autoaton Engnrng, Northast Danl Unvrsty, Jln 0, Chna; b Dpartnt of Mathatcs, Hlongjang Insttut of Tchnology, Harbn,5000,Chna ngjaaaa@6.co. Ang at th ffculty of rap rspons control n th syst caus by th hgh nrta of th wn turbn syst wth larg capacty, th work stu th robust control of nonlnar sp of rct-rv prannt agnt wn turbn. Aftr analyzng th charactrstcs of wn turbn as wll as th nonlnar ynac structur of prannt agnt synchronous otor, w propos a coprhnsv control stratgy cobnng Backstppng control tchnology an sturbancs attnuaton to sgn th sp rgulaton controllr of wn turbn. On th bass, th tho of loa toru fforwar copnsaton was ntrouc to for a uck-rspons control stratgy that s asy to b ralz. Sulaton shows copar wth th tratonal vctor control an th voltag fforwar couplng control, th propos control stratgy has th ffctvnss an robustnss for th uck-rspons control of wn turbn wth larg capacty.. Introucton Copar wth th tratonal oubly-f nucton wn turbn, th rct-v prannt agnt synchronous turbns lnats th sp garbox, thus splfyng th chancal transsson, provng th wn nrgy utlzaton rat an rucng th cost of opraton an antnanc. It has bn wly us n wn powr gnraton systs wth larg capacty, spcally offshor wn powr (Srra t al., 07; ao t al., 05). Prannt agnt synchronous turbn s a coplx objct wth ultvarabl, strong couplng, nonlnarty an varabl paratrs. Furthror, th hgh nrta of turbn whl wth larg capacty causs th ffculty n th uck-rspons control of th syst. It has bco a nw hot spot n wn powr control. In Rfrnc (Vrrll t al., 07), a nonlnar aaptv poston/sp trackng control for snsorlss PMSMs, wth sultanous staton of uncrtan constant loa toru an stator rsstanc.in Rfrnc (u an Pan 05), t aopts th voltag f forwar couplng currnt vctor control. Manwhl, th ral-t ynac copnsaton s prfor to stator currnt by th onln obsrvaton of loa, whch ffctvly provs th syst sp control. In Rfrnc (Vrrll, 0), f th xognous rotor poston rfrnc sgnal (whch s to b globally track wthout assung ts forknowlg) s rstrct to th class of snusoal sgnals wth uncrtan bas, apltu, fruncy an phas, a strongr rsult can b rv by rsortng to nonlnar avanc ntfcaton tchnus.it s appl to nustral PMSM sp control. In Rfrnc (X t al., 05), a ult-objctv control stratgy s propos bas on th fback lnar ol, whch achvs th MPPT blow th rat wn sp an th nu syst loss. It os not tak nto account th stuaton of hgh nrta loa n th nonlnar os an th stratgs of prannt agnt rct-rv wn turbn or PMSM, wth lttl attnton to th ynac uck rspons of th syst an th probl of robust. Th work propos a coprhnsv control stratgy cobnng Backstppng control tchnology an sturbancs attnuaton to sgn th sp rgulaton controllr of wn turbn anwhl, cobn wth th ynac copnsaton of loa toru fforwar, t ralz th uck-rspons control of larg rct-rv wn powr syst. Th sulaton shows th fasblty an ffctvnss of th propos control stratgy. Plas ct ths artcl as: J Mng, Qaobo Pan, Shuang Zhao, 07, Robust control sgn of prannt agnt rct-rv wn powr syst, Chcal Engnrng Transactons, 59, 9-4 DOI:0.0/CET759004

2 0. Th athatc ols of Prannt-agnt Drct-rvn wn powr syst Prannt-agnt Drct-rvn wn powr syst gnrally nclus wn achn, PMSM, Dual PWM rctfyng vc syst an so on, th basc structur can b sn fro Fgur Fgur : Prannt agnt rct rv wn powr syst. Faturs an ols of wn achn Th wn achn s th an part for th nrgy convrson of wn syst. Tp sp rato, ptch angl of bla an powr coffcnt ar thr portant paratrs of wn achn. Assung that th aroynac charactrstcs of th blas of wn achn ar noral, th aroynac prforanc of a non-nsonal wn achn wll pn on th tp sp rato an th ptch angl of bla (u t al., 006). P ρπr v C ( P λ, β) T l = = ω ω In ths forula, P s th output powr of th wn achn, W s th sp of bla angl, ρ s ar nsty, Mchancal output powr s proportonal to powr coffcnt CP, CP s a functon of th tp of th bla λ an th ptch angl β. Whn th ar sp V s crtan, rotor powr coffcnt C p (λ, β) trns th ablty of wn achn to absorb th wn.. ol of prannt agnt synchronous gnrator Assung that th snusoal strbuton of gas gap fl an th agntc crcut s unsaturat, gnorng th y currnt an th hystrss loss, th uaton unr th - axs PMSM stator voltag wll b as follow (Gng t al., 009; Guan t al., 04): Elctroagntc toru uaton T = pn[ ψ f ( ) ] Mchancal uaton of wn achn ω J = Tl T t Bω In ths forula, U, U,,,, ar coponnts of paxal, of stator voltag, lctrcty an nuctanc. Ψ f s th agntc chan of th prannt agnt rotor, J s th nrta of th otor rotor, B s th vscous frcton syst, ω s th rotaton sp of th otor rotor, p n s th logarthc agntc pols. Whn th otor s us as an plct PMSM, whch ans = =. Thus, th PMSM of th wn syst n th - coornat syst cos out. () () () ω Rs = pnω 0 p ω n Rs pnψ f J u 0 p + u nψ f B ω Tl J J. Robust nonlnar athatcal ol of prannt agnt synchronous (4) Whn thr s ntrfrnc n th syst, syst (4) (ω 0, 0, 0 ) s fn stat varabl s x =ω -ω 0, x = - 0, x = - 0, th ol can b scrb as:

3 B pnψ f T x = ( x+ ω0) ( x + 0) + J J J R Pnψ f u s x = pnω ( x + ω0) ( x + 0) + ( x+ ω 0) + ε Rs u x = ( x + ω0) + pnω ( x + 0) + ε Obvously, syst (5) s th robust nonlnar athatcal ol of th thr orr oubl nput. It has paratrc uncrtanty an unknown sturbanc.on ths bass, th controllng targt s: unr th uncrtanty of paratr an th unknown sturbanc of ε, ε, us u, u to control x, x, x. W aopt ntgrat control syst whch cobns ntrfrnc supprsson an Backstppng.. Dsgn of th robust controllr for prannt agnt rct rv syst Th controllng sgn tho of Backstppng s a grat robust controllng tool whch solvs th nonlnar syst that has thr-lgg structur. It can construct th yapunov functon by rcurson an gv th full analytcal soluton of controllng nput.. Th robust controllng achn s sgn whch bass on Backstppng Snc (5) s not a stanar for of ucton, w n to choos varabl y=x an ak y=0, an thn, th zro ynac scon orr ol of (5) wll b as follow: x = ax bx + c u x = x x + f + ε (6) Whr B pnψ f B T ψ Rs R P s n f a =, b=, c= ω + b, =, f =pnω ω + ω J J J J (5), Pψ = p ω 0 + n f n, w c x = k a x+ b b, W gt th pnalty sgnals of th syst (5): z=x, Th vrtual controllr was chosn. ( ) construct th coornat transforaton was as follows. = x, = x x, For of (6) as follows: = kb ak a c ca u b b b b = + x kx + f + k + ε W choos th yapunov functon V = σ, V = V + σ, Thn V = kσ bσ, γ γ σ γ = + ε = σ ε ε σ H V z k, Thr xst th controllr: γ 4 σ bσ ak a c ca u = + + kx + f + k + γ σ b b b b lt was assu that V V + σ y γ H = V + z ω =, ω = ( ε ) T ε γ σ γ γ σ γ σ ε ε σ ε ε σ =k y y γ 4 γ 4, W obtan th Euaton by rvaton. (7) (8) Controllr was slct as follows:

4 u = Rs( x + ω0) + pnω ( x + 0) + y+ y γ To fully consr th faturs of hgh-capacty achn unt s savantag lk bg rotatonal nrta an slow rspons sp, t s spcally portant to sgn rasonabl loa toru obsrvr an us th obsrv ata to ralz f-forwar copnsaton of loa toru.. Th fforwar control of loa toru Analyzng th faturs of wn achn, w can know fro (), for larg nrta wn achn, th pnuatc toru T l sp ω, nvronntal wn sp V, an ptch angl ar rctly corrlat. Gnrally spakng, larg capacty rct rv unt s low sp unt, th nvronntal wn sp s contnuously an slowly. Whn th unt s opratng unr th rat wn sp, ptch angl not chang, th toru of wn whl also changs slowly, t can b rgar as unknown constant n a lt t. W sgn ar whl pnuatc toru T F s sturbng obsrvr on ths assupton bass. ω TF = Bω + T = Tl J t An th coponnt of acclratng toru can b wrt as: ω J t J = Δn Δt As to nonsalnt pol PMSM, substtut lctroagntc toru () nto (), w can gt : T F = J Δn pnψ f Δt In th forula, lnkag of prannt agnt Ψ f an th saplng pro can b all consr as constant. Thus forula () can b splf to: T F =K + K Δn, K =(/)p n Ψ f, K =J/9.55Δt. Unr th noral opraton of th syst. Th loa toru an actual syst loa toru can b approxatly ual. Thus, w can sgn loa toru sturbng obsrv on th bass of (). Usng ts output ata as th copnsaton of sturbanc an th gvn nforaton of sgnal sp togthr to b th gvn nput of sp rgulator, whch aks th ynac rspons of th rng of rotatonal sp control prov pronntly. Th controllng structur s as Fgur. ω r ω r T F J a b c (9) (0) () () p n ω θ t θ Fgur : Ovrall structur of control syst Abov all, fback control u u can b xprss furthr as: σ bσ ak a c ca u = + + kx + f + k + + k4t γ σ b b b b F ()

5 4. Sulaton analyss To vrfy th valty of th propos nonlnar robust control stratgy, th nonlnar robust control cobng th loa toru f forwar. Th sulaton ol us MW W8 prannt agnt rct-rv wn turbn fro Wan Copany. Tabl shows th paratrs. Tabl : Th sulaton ol of th an paratrs Na Tchncal paratrs Na Tchncal paratrs rotor atr 8 for of nao REPMSG rat wn sp 0/s th statc ata of rotatonal nrta of syst 50000kg th rang of wn sp whl workng /s-5/s nubr of pol pars 60 sp ajustnt o ajust th rotor nonal voltag 690V utlzaton of wn th rct axs coponnt of th 0.45 nrgy stator wnng nuctanc 0.H rat powr 000kW stator phas wnng rsstanc 0.05 Ω Frst, w n to vrfy th vracty of loa toru sturbng obsrvr urng th obsrvaton, Assung that th ntal valu of wn sp V s 5/s, slowly changs n th sulaton t 0.5s an stabl at 0/s. through th thortcal calculaton of actual loa toru changs fro 90000N to N. Fgur s th loa toru sturbanc obsrvr output wavfor. W can know fro Fgur, th sgn loa toru sturbanc obsrvr can track th actual loa toru valu corrctly an track th changs of actual loa toru uckly an n t whn th utaton happns. It s fully vrf that th obsrvaton of th loa toru an th rotatonal nrta s corrct an ffctv urng th abov xprnt. Whn th nvronntal wn sp changs, th wn syst sp control coan sgnal changs. To ralz th MPPT of wn syst, w n to ajust PMSM. Th sulaton ol conuct sulaton xprnt n th fl of voltag fforwar couplng control an th -gan control control stratgy cobn loa toru fforwar copnsaton. Th trackng wavfor of otor sp can b sn n Fgur 4. Sulaton of wn sp valu s st as shown n fgur 4 (a).motor sp trackng wavfor as shown n fgur 4 (b), th local tals as shown n fgur 4 (c), r curv by -gan control stratgy, th blu curv for tratonal voltag fforwar couplng control stratgy. Fgur : loa toru sturbanc obsrvr output wavfor Fgurs 4 show th voltag fforwar couplng control, th actual otor sp can uckly track th gvn sp. Furthror, whn th loa toru changs abruptly, t can wll supprss th sturbanc. Th fluctuaton of th actual sp of th otor s obvously ruc, but wth th ncras of ajustnt t, not conucv to th uck rspons of th syst. rspctvly. By ajustng th -gan control an cobng th control stratgy of loa toru fforwar copnsaton, th ovrshoot an ajustnt t ar al wth goo ynac prforanc, unr th prs of accurat an uck trackng.

6 4 Fgur 4: Th sulaton of ynac curv 5. Conclusons Ang at th hgh nrta loa of th larg-capacty wn turbn as wll as th nonlnarty of th syst, th work stablsh an affn robust nonlnar ol. Morovr, a control stratgy was propos bas on th gan control an th loa toru fforwar copnsaton. In th thortcal rvaton, w objctvly ntrouc th sp ffrntal an th loa toru fforwar copnsaton. It funantally sp up th trackng of syst sp, thus gratly provng th ynac rspons sp of wn powr syst n th cas of hgh nrta loa. Du to th full consraton of th nonlnarty of th syst, th controllr coul ffctvly supprss th ntrfrnc to th stabl gnrator syst. Sulaton shows th propos control stratgy has th ffctvnss an fasblty for th uck-rspons control of wn turbn wth larg capacty. Acknowlgnts Ths work was support by th Ph.D. Rsarch Fun, Projct approval nubr 9. Rfrnc Gng H.., Yang G., Zhou W.S., 009, MPPT stratgy consrng wn turbn ynacs. Elctrc Powr Autoaton Eupnt, 9(0), 07-. Guan W.Y., Wu F., Ju P., 04, Sulaton an optz control of rct-rv prannt agnt wn powr syst. Powr Syst Protcton an Control, 4(9), ao Z.G.. H S.E., Dong X.Z., Wang B., Cao R.B., Sh S.X., J., Zhng W., 05, Rsarch on th syst protcton for nhancng th accooaton an transsson of larg scal wn powr. Powr Syst Protcton an Control, 4(), u B., Pan Q.B., 05, arg rct-rv wn powr syst to uckly rspon to control stratgy. Elctrc Machns & Control Applcaton, 4(), u Q.H., H Y.K., Zhao R.D., 006, Itaton of th charactrstc of wn turbn bas on DC otor. Procngs of th CSEE, 6(7), 4-9. Srra S.., Mank S., Ab H.S., 07, Dsgn ollng an sulaton of varabl sp axal flux prannt agnt wn gnrator, Sustanabl Enrgy Tchnologs an Assssnt, 9(), 4-4. Vrrll C.M., 0, Synchronzaton of prannt agnt lctrc otors: Nw nonlnar avanc rsults. Nonlnar Analyss: Ral Worl Applcatons, (), Vrrll C.M., To P., ornzan E., 07, Nonlnar trackng control for snsorlss prannt agnt synchronous otors wth uncrtants.control Engnrng Practc. 60, X Y., X.C., u J.C., Huang W., Huang C.X., 05, Nonlnar control stratgy of rct-rv prannt agnt wn powr syst. Elctrc Swtchgar, 5(), 5-0.