QUASI-EXTREMUM SCALAR CONTROL FOR INDUCTION TRACTION MOTORS: RESULTS OF SIMULATION. Rodica Feştilă* Vasile Tulbure** Eva Dulf * Clement Feştilă*

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1 QUAI-EXEMUM CALA CONOL FO INDUCION ACION MOO: EUL OF IMULAION odia Feşilă aile ulbue Eva Dulf Cleen Feşilă Depaen of Auoai Conol, ehnial Univeiy of Cluj-Napoa, Fauly of Auoaion and Copue iene, 6-8 Baiiu, Cluj-Napoa, oania Phone: (064) 408, E-ail: Adiniaion of he oanian ailway Aba: he pape i baed on he poibiliy o edue he induion oo loe by paial load, hooing he opial lip. Fo he ailway aion appliaion, he opeaion by paial load i vey fequen and fo a long-ie peiod. he auho peen he eul of iulaion fo wo upepoed ye: peed onol ye and exeu-eahing ye wih e ignal. he advanage of he exeu-eah onol ye, ipleened in a heap and aeible veion, ae deonaed. Keywod: induion oo, ailway aion, exeu-eah onol. INODUCION he heoy and he opeaion of he induion ahine pove ha a eain ehanial powe ay be deliveed fo infiniy of pai: ao volage ao fequeny. Eah pai deeine he flux level. I i poible o define vaiou opiu ieia ( axiu effiieny ) available by he iniizaion of he ahine loe. In aod o (Feila, 005), an aive ehod of opiizaion i baed on he eleial powe eaueen fo a nown ehanial load and on he eah fo he opiu lip (Feila, 005; Koun, 00). he equaion of he oo loe a funion of he lip i a nonlinea one, wih exeu (iniu). In ode o ainain he opeaing poin of he ahine on he exeu, i i neeay o apply an exeueahing ye. If, fo all powe eleial dive oboi, ahine-ool, e. he ehanial load hange fequenly, in eleial aion ye aie opeaion a high powe and fo long ie a onan ehanial powe, vey ofen, paial load. Wih he developen of he high powe eleial invee and of he dediaed DP, i i poible o ovelap wo onol loop: a laial peed (o oque) loop and an exeu-eah onol loop. he onibuion i baed on iplified odel of he invee and of he induion ahine in ode o deeine he oo oque and he eleial powe. If a eady ae of he opeaion an be found, an exeu-eah onol ye i enabled, unil he eleial powe eahe he iniu. I i ued an exenal, peiodial e ignal iangula hape wave whih deeine he ineae o he deeae of he addiional volage onol ignal. One he exeu poin wa eahed, he ye opeae in hi new eady ae, unil a hange in he ehanial powe i deeed.. IMPLIFIED MODEL FO INDUCION MOO AND INEE Baed on he equivalen / phae iui, figue (Koun, 00; ulbue, 003), fo a pai: ao volage, ao fequeny (, ω ), he oo oque i given by he equaion ():

2 ω ~ L σ L σ I L Figue. Pe phae equivalen iui 3 = () ω ω ( Lσ Lσ ) whee (,, L σ, L σ ) ae he laial oo paaee (Feila, 005; Fanua, 986; ulbue, 003),() i he lip: ω Ω = () ω and (Ω ) i he oo ehanial angula peed. Fo he oo i uppoed one pole-pai. Ω Ω PI - Conolle Invee ω Induion Moo Figue. peed onol ye opology Load Ω andue In he peed onol loop, figue, i i ued a powe invee and a PI peed onolle. he following equaion goven he whole peed onol ye: - fo onolle: I () = P Ω() Ω() (3) - angula fequeny e-poin: - volage e poin: u ω ω = (4) ( ω ) = ω β ω (5) - oo volage and fequeny ae given by: N () = ; ω () inv - ehanial dive equaion: Ω () () () ω = (6) L = (7) J B and - he load oque i uppoed: ( ) inv = Ω (8) L L0 Hee: -( P ) and ( I ) ae he popoional and inegal oeffiien; -(ω N ) i he aed angula peed (ω N =34ad/e); -( inv ) i he invee equivalen ie-onan; -(J) i he oen of ineia and (B) i he fiion oeffiien; -( ω ; u ; β; ) ae onvenional oeffiien (Feila, 005; Koun, 00). In (Koun, 00; ulbue 003) i poved ha he equaion (5) enue a onan level fo he oo flux, a he aed value Φ = Φ aed. he equaion () (8) allow he analyi of he behavio of he onol ye unde ala aegy (/f=on=). he oo loe ae: l, I I P = (9) given by he ao oope loe, oo oope loe and oe loe. In (Kou, 00) i given he equaion: P l, ( Ω ) Ω L σ (0) he eiaion of he invee loe i a diffiul a one. Uing he eul fo (Feila, 005), ( Ω ) Pl,inv he oal eleial powe i given by he equaion: P el = Ω L σ Ω 3. EXEMUM CONOL YEM () By paial load, he induion oo loe (P l, ) a funion of he lip () exhibi an exeu (iniu) (Feila, 005; Koun, 00). Fo inane, in he ae of equaion (0), he opial lip () i given by: = () ( ) Ω L σ

3 In he ala onol aegy, he exeu-eah ue a anipulaed vaiable he volage (α ) and a e ignal he iangula volage (α ), in ode o hange he ao volage ( ): oal = M = = eul he dependene: α α Baed on he iplified equaion (Fanua, 986): a) ( ) M ~ M (3.) M M = = b) (3.) M M ( ) =. ( ) ( ) If he e ignal α () i a iangula wave wih he apliude ( ) M =α M, and he peiod ( ), he poiion of he uen opeaing poin (, o 3 in figue 3) elaive o he exeu an be deeined by he vaiaion ( P l, ) due o he e ignal (α M =( ) M ), in he fi half peiod ( /), o ha : - if ( P l, >0), he uen lip i < (poin ) - if ( P l, <0), he uen lip i > (poin3), and - if ( P l, 0), he lip i opial =. In ode o foe he induion oo o opeae loe o exeu (hooing he anipulaed vaiable a ap α =d ): - a negaive anipulaed vaiable (α ) u be added o ha = α () - α () = α () - d = α(), (4) if ( P l, >0), Pl, Pel Pel α α 3 α - Pel - a poiive anipulaed vaiable (α ) u be added o ha = α () α () = α () d = α(), (5) if ( P l, <0), - α ()=0 if ( P l, 0). I i ipoan o noe ha in hi pape i i aeped he hypohei ha funion P l, =f () and P el =f () have he ae uue ( hape ). 4. GLOBAL IMULAION CHEME he boh onol ye (peed and exeueah) whee iulaed uing IMULINK. he global ye opology i given in figue 4. he aihei uni (f ) alulae he lip (), equaion (), and he uni (f p ), alulae he oal elei powe P el, equaion (). Ω - Ω e ignal Geneao L0 ω Σ K I ω K P ω inv Induion - Moo Σ J B ω ( ) β ω ω ω N Σ α α Σ W α inv INEE Pel,i ign Σ - z - CONOL UNI Figue 4. Global ye opology W3 5. IMULAION AEGY In hi pape a vey iple iulaion aegy i peened: a. In he ie ineval (0 ): - he exeu-eah onol ye (EC) wa diabled, (α()=0); - a ap efeene Ω M () = ε wa ipoed and he ain vaiable Ω (), (), (), ω (), P el, wee egieed. b. In he ie ineval ( ): - he EC eain diabled (α()=0); - a onan efeene ΩM() = wa applied in ode o eah he eady ae. In he ie ineval ( 3 ), he boh ye ae aive. Baed on he analyi of he effe of he e ignal α (), he anipulaed vaiable α() edue he upplied eleial powe unil he diffeene ( P el, ) i aple Pel fp f Ω Ω ω P el, < hehold ; Figue 3. Piniple of opeaion of he exeu onol ye in ha oen ( ) he quai-exeu wa eahed.

4 d. In he ie ineval (3 ), he e ignal α() i diabled (by W) and he whole ye opeae wih he peviou value α(3)=. (by W3; d=0). he eleial powe i oninuouly eaued. If any ignifian hange i deeed, he ignal α() deeae in a eain ie peiod and he ahine flux ineae o he value aoiaed o he equaion (5). 6. IMULAION EUL he geneal hee in IMULINK i given in figue 5, whee: =80 p.u.; =0 p.u.; 3 =40 p.u.; P N =30N; N =0, K P =0; K i =0-3 ; inv =; K w =; β= ; K u =0.7; W n =34; J=; B=0.05; L0 =5; K =0.9; =0.08; =0.087; L σ = ; L σ = he eul of he iulaion ae given in figue 6. he evoluion of he eleial powe i given in figue 6a. he diffeene P el, = (P el, -P el,- ) ae peened in figue 6.b: P el, > 0, whih deide d<0; α = - d ; he e of he diffeene P el,, ae negaive beaue P el, deeae unil he quaiiniu value P el,in 4.6 W i eahed. he figue 6.. give he anipulaed vaiable α() and he figue 6.d, peen he evoluion of he lip (). Figue 6. iulaion eul 7. CONCLUION he aual pape deonae he uiliy of he exeu-eah onol ye. Fo inane, fo a aed oo powe of 30 W, a paial load ( 50%; 5W), he eleial powe given by he ain line ay be edued fo 5.8W o 3.9W, ainaining he oo ehanial peed paially unhanged. EFEENCE Feşilă,., ulbue,., Feila, Cl. (005). Abou he Opial Opeaion of he Invee Fed Induion Moo, In: Poeeding of he CC-5 Inenaional Confeene, Buhae, 005 Fanua A., Magueanu,. (986). Eleial Mahine and Dive, (in oanian) Buhae Koun, H. and ohe (00). Analyi of a aion Induion Moo Dive Opeaing Unde Maxiu Effiieny and Maxiu oque pe Apee Condiion, Pivae Couniaion ulbue. (003). Conibuion egading he Aynhonou Moo Conol fo ailway aion, Dooal hei (in oanian), ehnial Univeiy of Cluj-Napoa

5 Figue 5. he geneal iulaion hee

ADAPTIVE BACKSTEPPING CONTROL FOR WIND TURBINES WITH DOUBLY-FED INDUCTION GENERATOR UNDER UNKNOWN PARAMETERS

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