ADAPTABLE SLIDING MODE CONTROL FOR WIND ENERGY APPLICATION

Transcription

1 Rev Roum Sc Techn Électotechn et Éneg Vol 61 3 pp Bucaest 2016 ADAPTABLE SLIDING MODE CONTROL FOR WIND ENERGY APPLICATION ADEL ABERBOUR KASSA IDJDARENE ZOUBIR BOUDRIES 111 Key wos: Vecto contol Slng moe contol Chatteng Aaptable gans Autonomous nucton geneato Magnetc satuaton Ths pape poposes an aaptable slng moe contol (A-SMC scheme fo an autonomous nucton geneato wokng wth vaable spee an loa The thee-phase nucton geneato (IG s excte usng a PWM nvete connecte to a sngle capacto on the c e It s moelle though a phase appoach base on the applcaton of the Pak tansfom The magnetc satuaton phenomenon s nclue n the IG moel The contol stategy shoul keep the c voltage acoss the capacto constant an equal to the efeence value The contol takes a cascae confguaton fou SMCs n all The oute contol loops use aaptable gans an a tangent hypebolc functon to ensue bette pefomances n tems of esponse tme chatteng an obustness Fnally smulaton esults show the effectveness of the popose contol stategy 1 INTRODUCTION As envonmental polluton an clmate change s nceasngly event evelopng enewable enegy souces has become the majo subject of toay s enegy evoluton especally wn enegy [1 2] Wn enegy systems attacte the attenton of eseaches ue to ts non-pollutng natue abunance an elatvely nteestng cost The capablty of the uel-cage nucton geneato to excte wthout an extenal powe supply allowe ts applcaton n stan alone powe geneaton systems Futhemoe the uel-cage nucton geneato has many avantages ove othe types of electc geneatos such as obustness less cost an mantenance fee opeaton whch makes of t a pefect canate fo ths type of opeatons Inuctons geneatos ae usually excte by thee ac capactos (capacto bank connecte acoss ts stato temnals an ae known as self-excte nucton geneatos (SEIGs But ths metho has some mpotant awbacks The magntue an fequency of the stato voltage ae vey senstve to the vaatons of the otaton spee an the loa value Thus ths nees an appopate voltage egulatng scheme to mantan a constant voltage level egaless of loa an/o spee by contollng the eactve powe tansmtte to the geneato [3] To acheve ths pupose many schemes have been suggeste The wely use soluton conssts n connectng the stato wnngs of the nucton geneato ectly to a ectfe/nvete system In ths case the evce must be contolle To each ths goal a ect toque contol (DTC s use [4] Ths appoach s qute effectve an oes not eque an accuate knowlege of the machne moel but t uses a hysteess-ban contolle whch nceases the losses In aton as ths appoach s senstve to the stato esstance value the accuacy of the flux estmaton can be euce at low voltage Anothe altenatve to the DTC s vecto contol [3 5] Most of the SEIG vecto contol systems epote n lteatue use classcal popotonal ntegal (PI contolles fo voltage an/o flux contol Bees PI-contolle s vey nteestng ue to ts hgh mathematcal accuacy but t s senstve to the system paamete vaatons an can eject extenal stubances naequately Moe avance contolles such as fuzzy logc contol (FLC [6] o slng moe contol (SMC [7] have also been conee n SEIG contol systems It s epote that such contolles bng coneable pefomances n tems of esponse tme settlng tme an obustness In ths pape SMC base on vecto contol concepts s use to contol an autonomous IG Instea of the conventonal PI contolles the SMC s employe fo each nne an oute contol loops The Lyapunov ect metho s use to ensue the eachng an sustanng of the slng moe The contol stategy takes a cascae stuctue; the efeences of the cuent components ae geneate by the extenal SMCs whch use a hypebolc tangent functon nstea of conventonal sgn functon an aaptable gans nstea of constant ones So the tansent of the httng contol wll be smoothe an the chatteng phenomenon s allevate wthout loosng the system obustness 2 STUDIED SYSTEM The stue system shown n Fg 1 s consttute of a uel cage thee-phase nucton geneato (IG connecte mechancally to a wn tubne though a gea box an electcally to a PWM ectfe/nvete The c e of the latte s connecte to a capacto a battey to stat up the system f no emnant voltage s avalable an a oe whch ecouples the battey fom the ectfe/nvete as soon as the c voltage geneate s hghe than the one of the battey The loa R s equvalent to the global loa seen fom the c e The block agam of the contol scheme s also shown on the same fgue 3 MATHEMATICAL MODEL OF THE INDUCTION MACHINE Dynamc nucton machne moels ae use as the bass fo the esgn an mplementaton of contol algothms Relable an goo contol pefomance eques moe etale moels The paametes of the machne vay ue to the vaaton of opeatng pont flux an fequency At low flux values the nuctances eman constant but as the flux nceases the machne stats to satuate an the nuctances ecease Hence the accuacy of the moel pecton an Unvesté e Bejaa Faculté e Technologe Laboatoe e Technologe Inustelle et e l Infomaton (LTII Algée E-mal: abebouael@yahoof jaene@yahoof zboues@yahoof 1

2 2 Contol of solate nucton geneato usng slng moe 259 the contol pefomance can be mpove by nclung the magnetc satuaton phenomenon nto account Ths s one va a vaable magnetsng nuctance though the estmaton of the magnetsng cuent The nucton machne moel can be wtten n the synchonous efeence fame as follows [3]: V Rs ωs ls 0 ωs Lm V ωs ls Rs ωs Lm 0 = 0 R ω l R ω ( l Lm m 0 l R ( l Lm R ω ω mq 2 ' ' m m mq ls 0 Lm Lm Lm m m 2 ' m mq ' mq 0 ls Lm L m L m m m 2 ' ' m m mq m l 0 l Lm Lm Lm m m 2 mq ' m mq ' mq 0 l Lm l Lm Lm m m whee R s l s R an l ae the stato an oto phase esstances an leakage nuctances espectvely L m an L m ae the magnetsng nuctance an ts evatve wth espect to magnetsng cuent an ω s an ω ae the stato an oto electcal fequences espectvely Bees V V an ae the -q stato voltages an cuents espectvely m an mq ae the magnetsng cuents along the an q axs gven by: Fg 1 System an contol scheme (1 m = mq = q an m = 2 2 m mq (2 To expess L m wth espect to m seveal appoaches can be use whose smplest one s the polynomal appoxmaton L = m f m = n a j j= 0 j m (3 The wavefom of the magnetsng nuctance s obtane though tests at no loa fo ffeent voltage magntues In Fg 1 above we show a compason between measuements an appoxmate values of a magnetsng nuctance L m vesus m 4 CONTROL STRATEGY Geneally n vecto contol algothms the flux s kept constant at ts ate value Thus the toque can be ajuste accong to the actve powe eman In fact as the flux s contolle to be constant ts vaaton aoun the opeatng ponts s neglgble Thus the nuctances can also be conee constant (L m = L mq = M = H [3] Theefoe the moel of the IG use fo the contol s smplfe an can be conee as a lnea one In the case of the pesent wok the oentaton of the -q fame s chosen such as Ф = Ф an Ф q = 0 Theefoe the state equaton of the stato cuents can be e-wtten as:

3 260 Ael Abebou Kassa Ijaene Zoub Boues 3 1 M Φ = R ω σ s s Ls V t σ L (4 s 1 M = Rs ωs σ Ls ωs Φ V t σ L (5 s whee: σ =1 M 2 /(L s L s the leakage flux coeffcent L s = l s M an L = l M ae the stato an oto self nuctances The oto flux electomagnetc toque an the synchonous fequency can be estmate as follows [3]: M M M Φ = Tem = p Φ an ω = pω s (6 1 τs τφ whee s s the tme evatve opeato τ = L /R s oto tme constant Ω s the mechancal spee of the machne whch s measue contnuously an p s the pole pa numbe 41 SLIDING MODE CONTROL DESIGN Accong to the slng moe theoy the fst esgnng step conssts n efnng the swtchng functons (slng sufaces In the case of ths pape fou slng sufaces elate to contol objectves ae efne as follows: S S S S ( = = = Vc Vc = Φ Φ ( ( Vc ( Φ The suffcency contons fo the exstence an sustanng of the slng moe s gven as follows: S ( x sgn( S ( x η (7 (8 wth η s a postve constant If we keep ffeent sgns fo the slng suface an ts evatve the contolle vaable wll be attacte towa t whch means the exstence of a slng moton on the slng suface S(x In othe wos the vefcaton of the conton (8 mples stablty of the system In the followng we wll esgn the coesponng contol law fo each slng suface 411 SLIDING MODE CURRENTS CONTROL DESIGN (INTERNAL LOOP The slng moe contol laws of the an q-axs cuent components ae gven as follows: M Φ V = Rs ωs σ Ls σ Ls K sgn ( S( M V = Rs ωs σ Ls ωs Φ σ Ls K sgn q ( S( (9 (10 As t can be seen fom (9 an (10 thee ae two tems n the contol law a contnuous an a scontnuous one The contnuous tem eflects knowlege of the system ynamcs t s the so-calle equvalent contol whose man ule s to mantan the contolle vaable on the slng suface but t s not ntene to attact t towas t Ths task s evote to the scontnuous contol acton whch ensues the slng to occu Howeve ths contolle leas to lmte pefomance ue to the hgh contol actvty esultng n chatteng To euce the latte we wll ntouce a hypebolc tangent functon nstea of sgn functon It esults n a smooth contol sgnal Then the contol laws (9 an (10 become: M Φ V = Rs ωs σ Ls σ Ls S( K tanh ε M V = Rs s Ls s Ls ω σ ω Φ σ S ( Kqtanh ε whee ε efnes the thckness of the bounay laye (11 ( ROTOR FLUX AND DC-VOLTAGE SLIDING MODE CONTROL DESIGN (EXTERNAL LOOP The oto flux an the c voltage state equatons ae gven as follow: Φ V c M 1 = Φ τ τ (13 L c Vc c = = C C R C C whee C s the c lnk capactance an R s the esstve loa Bees L an c ae the loa cuent an the c cuent espectvely The SMC law of the oto flux s gven as: τ Φ M = S( Φ Φ K Φ tanh ε τ By assumng the followng: (14 P = V = T Ω (15 c c c em Theefoe the SMC law of the c voltage contol loop s obtane: = L Vc S( Vc KV tanh p Ω M Φ ε L (16 The gans of the oute contol loops ae self-ajustable fo pefomance mpovement an ae gven as follows: α KΦ = λφ S( Φ wth 0 α 1 α KV = λv S( Vc (17 whee: λ ( = Ф V s a postve ntege Note that the fact of usng a sgn functon n the oute loop wll lea to a hamful chatteng manly ue to the cascae

4 4 Contol of solate nucton geneato usng slng moe 261 confguaton of the contolle; the output sgnals of the extenal loop ae nputs of the ntenal loop These sgnals wll swtch fom a gven maxmal value to a mnmal one Hence the wavefoms of the stato cuents wll be affecte an completely stote Howeve n the case of the pesent wok the poblem of chatteng s lagely allevate thanks to the aaptable gan an to the hypebolc tangent functon whch smoothes the tansent of the httng contol wthout loosng the system obustness whle keepng a goo behavou of the stato cuents 5 SIMULATION RESULTS The logc contol sgnals of the PWM convete ae calculate by usng the space vecto moulaton (SVM technque The etals about ts mplementaton can be foun n [8] The moel of the nucton geneato use n ths smulaton s the one gven n equaton (1 whch takes the satuaton effect nto account The nomnal paametes of the nucton machne ae lste n the appenx The c voltage efeence value s put equal to V c = 600 V The efeence oto flux s put equal to the ate value Φ = 07 Wb The value of the loa esstance R s ntally equal to 70 Ω whch s the value that allows the machne to geneate a sgnfcant powe elate to the opeatng contons At t = 2 s the esstance s ncease to R = 140 Ω then t s ecease to ts ntal value at t = 4 s Fo ths test an acceleate anom oto spee wth we ange of vaaton s mpose ts wavefom aoun the synchonous value (Ω = 750 pm s gven n Fg 2 stubance nuces c voltage pples whle the popose stategy manages to elmnate them It can be obseve that the esponse of the c voltage obtane by the SMC s nsenstve to the apple step change n the loa esstance Concenng the stategy wth PI contolles we can obseve an oveshoot of about 10% cause by nceasng the esstance value at t = 2 s an an uneshoot wth almost the same magntue ue to the estoaton of the loa esstance to ts ntal value at t = 4 s The obtane esults confm the avantages of the stue contol stategy ove the usually use PI contolles n tems of obustness aganst loa an spee stubances Fo both cases (Fgs 5 an 6 the oto flux s well contolle an establshe to a constant value wth faste esponse concenng the SMC contolle (Fg 5 Fg 3 Dc voltage SMC metho Fg 2 Roto spee Note that the oto spee tme wavefom whch s mpose (Fg 2 s not encountee n eal wn powe conveson systems ue to the lmte ynamcs of commonly use pme moves The spee stubances ae ntentonally exaggeate to hghlght the avantage of the evelope contol stategy ove the conventonal use PI contolles n tems of obustness to spee vaatons The paametes of the PI contolles ae chosen optmally by obsevng the behavou of the contolle vaables fo ffeent combnatons of the popotonal an the ntegal gans base on the ctea of fast esponse small oveshoot an obustness Fgues 3 an 4 show that the popose contol stategy (Fg 3 exhbts moe obust esponse to the mpose spee an loa stubances compae to the PI contolle (Fg 4 Moe specfcally n the case of the latte the spee Fg 4 Dc voltage PI contolle Fg 5 Roto flux SMC metho

5 262 Ael Abebou Kassa Ijaene Zoub Boues 5 Fg 6 Roto flux PI contolle As can be obseve on the behavou of the q-axs stato cuent component as well as the zooms of stato cuents (Fg 7 the popose stategy exhbts hgh ynamc tanston when the step changes n the loa esstance occu then pemts to compensate quckly these stubances Thus the c voltage s not affecte as confme n Fg 3 On the othe e the obtane q-axs stato cuent component wth PI contolle (Fg 8 has a low ynamc tanston when the loa esstance s vae Hence the petubaton s not compensate aequately as confme n Fg 4 6 CONCLUSION In ths pape vecto contol wth an A-SMC an SMC of an nucton geneato use n an autonomous vaable spee wn system s stue An analytcal moel of the autonomous nucton geneato takng the satuaton effects nto account by the means of a vaable magnetsng nuctance has been pesente The contol leas us to fee the loa wth voltage of constant effectve value whateve the spee of the tubne an the loa The smulaton esults show that the popose contol scheme has hgh pefomance ynamc chaactestcs an shows vey stong obustness compae to the usually use PI contolle The chatteng poblem encountee n SMC s lagely allevate wthout loosng the system obustness thanks to the aaptable gans an to the hypebolc tangent functon Smple an obust the popose metho s qute elevant fo an solate wn enegy conveson system base on a uel cage nucton geneato APPENDIX Paametes of the nucton machne: P N = 55 kw U N = 230/400 V I N = 238/137 A 50 Hz Ω N = 690 pm J = 0230 kg m 2 = N m/as -1 R s = Ω R = Ω p = 4 Receve on Septembe REFERENCES Fg 7 Stato cuents SMC metho Fg 8 Stato cuents PI contolle 1 M Ajouj M Ab A Assaou Y Raman H Bounoua Slng moe contol of a oubly fe nucton geneato fo wn tubnes Rev Roum Sc Techn Électotechn et Éneg 56 1 pp ( M Doum A Assaou A Tahou M Ab Commane aaptatve un système éolen Rev Roum Sc Techn Électotechn et Éneg 60 1 pp ( K Ijaene D Rekoua T Rekoua A Tounz Vecto contol of autonomous nucton geneato takng satuaton effect nto account Enegy Conveson an Management 49 pp ( S Hamma N Hou L Sbta A DTC SEIG ve scheme fo an solate wn tubne buck system Intenatonal Confeence on Contol Decson an Infomaton Technologes (CoDIT 13 pp ( E Lev YW Lao Roto flux oente nucton machne as a DC powe geneato The 8 th Euopean Confeence on Powe Electoncs an Applcatons (EPE 99 pp 1 8 ( M Bašć D Vukanovć M Polć Fuzzy DC-voltage contolle fo a vecto contolle stan-alone nucton geneato Intenatonal Jounal of Ccuts Systems an Sgnal Pocessng 7 3 pp ( L Louze AL Memmou A Khezza M Bouchema Input-output lneazng an slng moe contol schemes fo a self-excte nucton geneato 35 th Annual Confeence of IEEE Inustal Electoncs (IECON 09 pp ( TJ Fu WF Xe A novel slng-moe contol of nucton moto usng space vecto moulaton technque ISA tansactons 44 pp (2005