Aalborg Universitet. Published in: I E E E Transactions on Smart Grid. DOI (link to publication from Publisher): /TSG.2015.
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1 Abg U D-D f k A/D Mg M-F A D-D Zhg Hgg; Zh Jg; S Qy; G J M; M Dzhg bh : E E E Sm G DO k b fm bh: /SG b : 7 Dm V A h m w Lk b fm Abg Uy f bh AA: Zhg H Zh J S Q G J M & M D 7 D-D f k A/D Mg M-F A D-D E E E Sm G 7-7 DO: /SG G gh ygh m gh f h b m b h b by h h / h ygh w f g b h g b by h g qm wh h gh? U my w y f y b fm h b f h f y h? Y my fh b h m f y f-mkg y mm g? Y my fy b h URL fyg h b h b? k w y f y b h h m bh ygh b@bk g w w m h wk mmy g y m Dw fm bk : mb 7
2 EEE RANSAONS ON SMAR GRD VOL XX NO XX XXX XX D-D f k A/D Mg M-F A D-D Hgg Zhg Fw EEE Jg Zh Qy S Mmb EEE J M G Fw EEE Dzhg M Ab h g h w hg f k / mg A gy h kg z w hg bw mg h gy my w : h my - - mh g wh y ; h - - m-f g Ug h hm h kg j k h hh DG w h h by g h m g fqy M h g f h y b / /O mm b h m y m h ym by b g by h Ly mh h ym h g h Sm xm g fy h w hg gy x m k mg kg w hg - - m-f NOMENLAURE ω Sy fqy g h my L w f h mg h m f k L w f h mg h m f k Sy g g h my η hh f h ω Nm fqy f h mg ω k+ Rf fqy f h U f h wk w by h N N S F f h G G 7 by h Fm Rh F f h U G N by A Fm Rh F G ZX by h Dm j f Ky Lby f Lg H Zhg wh h Sh f fm S Egg Nh Uy Shyg h H wh h Ky Lby f g Am f y Nh Uy f h N E My Shyg h m: hgzhg@g J Zh Q S D M wh h Sh f fm S Egg Nh Uy Shyg h -m: JgZhNEU@gmm; qy@; mzhg@ J M G wh h Dm f Egy hgy Abg Uy Abg Dmk -m: jz@k V Nm g f h mg V k+ Rf g f h ω V Λ σ h g fqy f h mg h g g f h mg U f f h ff wh h w f h mg Λ k U f f h ff wh h w f h mg ω k+ M m fqy h m f k+ σ k D ff f h wh h w f h mg k k D ff f h wh h w f h mg ϕ A w h h b h by h mg ϕ A w h h b h by h mg D-k f h f F f h Ukw f h ym y Ukw f h ym f Ukw f f h ym b A f f f h D-k f h k mb ff f h mg k mb ff f h mg k ω h g g f h y fqy k V h g g f h y g k ω h g f h y fqy k V h g f h y g L f F f h K A w f by h h m f k R f F f h b Ag whg g f h V k+ M mg g h h m f k+ V D-k g f h b A g f f f h NRODUON
3 EEE RANSAONS ON SMAR GRD VOL XX NO XX XXX XX DUE h f f f b g DG w ym mgg h w f ff DG h g h bm mg mg hf f mg h gw y wh h h [] [] mg [] by y hm []-[] w qy mm [7]-[] w hg []-[] h M m m b mg hw DG my wh mg Efg mg by kg w mg gy f w wk h f b y m bf h g y by m b [] Am mf hm f h hyb mg w [] [] x [7] [] by gg gy g ym h mg Ah hm w fw [] f b w fw bw h mg [] hh f m - f bw b w h hg D h g m b m wbk f h mh b f h mjy f h xg hq gy mhm m h hq g fy wh ffg m Uy ym b [] [] wy x -b mg ff b h m Ahgh b [] [] b- [] wk [] -b h b f w m hg x mhm m y ym h b kw f g f b b- Wh h g fm g b h m f h h b kw w hg g fqy g b h h m m kg [] [] b w g b w hg bw w mg b h y O h h h [] [7] [] kg b w hy whh m h kg g fqy g Ahgh y hm h b h fqy g h m h f fqy g h b h f h k mg h []-[] hf w hm h b fh f kg h m b Obg h ym m fm h gh y ff h m k mg ym m m mgf k g f h g m f h by h ym b h g ffy h D- m-f DDMFA q y m fm f h h q fm b h by g h / /O f g gf k g f h h mx ym y f h f m g gy h - DD f kg k hyb mg O m h w y h - MFA mh g h f h h k h m g f h b h ffy h h b f hg q fm h hm my - m-f g DDMFAV f f b g kg - wh y f w hg bw mg f fqy g g h g m-f MFA h h b Fy MFA q mhm m fm m y f h b y / /O mm [7] whh m h g b g y f kg Sy h D bh f MFA my b h f h m y f h ym hf MFA hm h g b whh h ky qm f kg Fy DD MFA h b fy mm m f []-[] B h fm wy g - MFA hm f h kg A - h h m ky mmz : h w f w hg b b h mg ff y f mg b wy k m g f wh h gg h g b z by j yg h - DG wh h mg w y y h f kg Emh h b qy g h kg M mx y-m h b wh h k mg h g m h f m g h h y b h g m g mxmm m w y hy h y h h w b h fqy g g whh xmy m f h b f h k mg hf y gf w h kg g h fqy g Sm hm h b []-[] Hw w hg g fqy g b h h m m by g h mh kg [] [] b w
4 EEE RANSAONS ON SMAR GRD VOL XX NO XX XXX XX g b w hg bw w mg b h y O h h h [] [7] [] kg b w whh m h kg g fqy g h mh h bm wg h kg g h g fqy g wh kg w hg h m b f h b mmz fw: A - m-f g DDMFAV hm f kg k hyb mg h m y ym m ym q h hm Dym - hm h w hg bw mg h hm g wh h g b w hg g/fqy g z my k DG mg A y gy f h k mg whh ff fm h f DG mg h m f h fw h k hyb mg S h hm S Sm xm S V S V y fy w S V SYSEM SRUURE AND MODELNG OF NERLNKNG ONVERER A Sym S O M h k mg hw Fg whh kg z k h mg gh Eh mg h w g h kg bw h w mg b w f g gg g f h mg h fm k mg b h y g hgh fm SS b gy [] h g- m h gy w [] fm h m y g jg bbg w fm h y g b h m y g y m h f h m y g h b gy w bm b whh g bf h by f h m y g h kg bh g- m w b w f w hg bw h w mg by g h - S h h gh m f gy m h m h h mxmm m w y bh g- m h h m f h kg fw D D D G S S b E g y R V L? m g Fg L L V m y g k g L f b f A xm f k / mg m g b L L R f b L A D D G M-: f h m w g m h h V h h kg w bb h w fm h mg h j h mg h kg fm h -k j DG h m M-: f h m w m h h ω h h kg w j h w h g mg h kg k h m f DG h h mg h m M-: h w b w f by h kg wh bh h mg - m f f h - f g fqy h hh B Dym Lz D M f Uy g VS b f h kg A m fg hw Fg f fm g h -k g ym gg g f h whg h h m g whg ym f h kg b g by V = / / V b b b = R f /L f b + /L f V b b b = / f b b wh b b b b f f g f f g whg g f h kg y V -k g y L f R f f h f f f -k y W h V b h ym wh h kg m- m- y b h ym h h ym f g mm b x -m
5 EEE RANSAONS ON SMAR GRD VOL XX NO XX XXX XX m wh h H = / b k + =f b k b k y b k b k V k + =f V k V k y b k b k wh b = [ b ] b = [ b ] L V = b V = V = b f = f h h ym b x V k + =f V k V k y k k = wh y h kw f kw f A m h y ym m ym b wy x h k mg ff b h kw f f hf --b fm ym z FDL b h b b h b h q ym z m f ym h mm f h - MFA mh y b w m: h f wh ; Sym gz Lhz h m m h ym b b fm w Am y f ym g f g ym Am m h f hg f h ym by h hg f h Fm h gy f w h gy hg ym g fy f h hg f h gy f Ag h m hm [7] f h ym h m b m Φ k = Jb mx JM ym b fm h fwg FDL wh Uk : V k + = Φ k Uk = wh h b g Ax A ROOSED ONROL SHEME A D-D M-F A Vg B h FDL ym h DDMFAV f h kg b g h fwg Bf gg h b m h m Φ k JM h b h w f Φ k g by ˆV k + = ˆV k + ˆΦ k Uk + K Ṽ k ˆΦ k + = ˆΦ k + Γ k Ṽ k + F Ṽ k Uk L wh h b g Ax A U h m Φ k m h DDMFAV b g [ ] k = k + ˆΦ k α + ˆΦ k ˆΦ [ ] k V k + ˆV k K Ṽ k f Uk δ k = k + δ g kf Uk > δ wh α = g α α α α = α V k h f j h by f h DDMFAV - ym b g by g h Ly-b by hy D f b f [] whwh mk h h h g g k h b [] [] b b mm y y by g - hgh h - hy Mhm m q h g f h h w q y x g g y g m mm y fxby wh m m b b mx g- ym y f h k mg h f h f ff m h m h fy y fm h h - MFA b y x fm hg m f O h h h h g b mm fxby ff m h m by h - h fwg b Ay wh h g g mx fm b B D-D w hg y h h DG h mg g q b b g by mmg h h h w g f mg y ff qy h w bk- wh h mg b by f h mg b w g g by D h w-gz g mg w hg mg m mg gh hgh h kg b h by h mh g h m S h w hg bw h k mg g / fqy g my j k DG mg ym - hm wh w mgm b h h - h f h kg f w hg w Fg h mhm g { ω k ω mx / σk k = V 7 k V mx / kk
6 * Ñ = + ω ω ω k EEE RANSAONS ON SMAR GRD VOL XX NO XX XXX XX k m x V m x = V m w j m g m x = m = ñ k k * k m x w j m g Fg h - h f h kg V V V ω k V k + k + k + k q m g q m g k g Fg f w hg z wh h mg wh σ k k k h ff h - h f by yg h x [7] F h w fw g y b m y ff hh h b f h fq g gh wh h mg - UL m- NL OL m f w Ug h - h kg w h h m f S y j m y wh h mg f xm w h m m f mg f f fqy g mg Hw h w mm f h kg h m by h w mgm b m Uyg f h w hm b b by fg h xm w Fg h fg h w h f gh f g h mz f h mg g ω = ω k V = V k wh k k ff Wh h kg f m h kg w kw h g f h w mg by mg h m fq g F hy y ω V y g h bk hw Fg Ag hg w hg bw h mg m mg ω = V = ξ g h h hz w Fg hf q b b ω + k = V k wh h m w b f hgh h kg f w hg = b w = V ω k + k U hg h y w hg bw ff y f mg h kg b ym b z h m x ω = V = ξ f h Af h wh h h mg hg h w mm w b g h fwg q k k+ = k L k +k } {{} ϕ + k k +k L }{{} ϕ = k +k Vk+ ω k+ k wh k h w b f by h kg wh hg h m = k L L h w f h mg h m = k+ y ϕ ϕ h w h h b h by h mg y ω k+ V k+ h m m fqy g h m = k+ g h f m hh m g x f b g k = wh V k ω k ξ UL ξ mx ] [ξ m ξ OL ] k +k V k ω k h S fm q 7 h kg m h g f h mg h w mm m y g h m fqy mg g U h m w k+ f by h kg w hg bw h mg b z Hw h b h g Eq w m f h kg f y h w m w h M wh h m gh y f h kg f h w h m b mmz : h m w m mh f h w b h h ; b f h ym b ff f h m w f by h kg hf
7 j EEE RANSAONS ON SMAR GRD VOL XX NO XX XXX XX h hh f h Eq h Eq b w fw: k = k +k V k ω k V k ω k η wh h f η h hh f h b x η = f V k ω k Eq b b m y by g Fg whh h-m f fm by V ω η A hw Fg h f S ABD h b f h η = V k ω k S BEJ S FHG h - gh- f bh h mg y S EFGHJ b h m h wh w b f h m kg h b h f S BE F H g b h hh η = f V k ω k f h h h wh bh h mg g gh- S FHG - S BEJ w w b f fm mg h h η < η O h h h wh h mg g h f S EFGHJ h kg w f y w h m η < η hf f h kg b why mk h h h hh η S BE F H b fxby g g h qm f by g Fg 7 A h [] [7] [] - h h g- h xhb by h kg g fqy g - m-f g h f h kg hf ym g f h - b mkg h m f ω k+ V k+ q ξ k+ h b z by g h ff f h - g h fwg q σ k+ = Λ σ σ k k+ > k k+ = Λ k kk k+ < wh Λ σ Λ k g Ax B h g f h w mm ff Fg b h g h ym - gy 7 g wh h w mm mgm b mh h ff g hm w hg bw h mg b z by h kg w g g fqy g h kg w h w mm k+ ff σ k+ k k+ f f h fqy ω k+ f h mg / g V k+ f h mg fm h ξ k my hgg hgg hg w ξ k+ Fg # $ % & ' % & ' + - / / / 7 : ; < fh / = A - B B / 7 k m : ; < / D K L M N O Q R S U V W X Y Z [ \ ] ^ ` ] b ` [ \ [ b E F G H * J! " q w x x y y z { } ~ y z } y w z ƒ z q } { } ~ y z } y w z ˆ f h fw h f h - A f h fqy ω k+ g V k+ hg h w mm k+ ff σ k+ k k+ w b m k σ k k k y hf w f h h - my w g h f g g h w hg whh b z by g g q g h f h mg A h g z g fqy g whh b h by g q 7 W m h h m [] [] my b b f w m fm h q b y h m ff h b h h w h m w mm h f ω V f h h hw h fw h Fg Sy Dg Ahgh mh h b wy mg fqy g g h by h fm f w hg hf y hm h b h fqy g h m Ahgh my w hg hm m y h b h h wk y DG wh mg Rgg h k mg h y y - w hg f k mg h b y g by h h h - mh my y hm h w # $ Š
8 Ÿ œ ž œ Ÿ œ ž œ ÎÕ Ô Õ Ú Ù Õ Ø Î Ó ï EEE RANSAONS ON SMAR GRD VOL XX NO XX XXX XX 7 š œ K J K JR H Q O NMH LMH K J G H ¹ ³ ¹ µ Ñ Ð Ò Ö Ð Í Î Š Œ Œ Ž Ž Ž Ì Ì Ç È É Ê Ë x y z { } ~ { ~ ƒ ˆ ˆ Ð Ï Â Ã Ä Å Æ ÑÒÓ ò ó ô õ ö ø ù þ ú û ü ý Ü ã Ý Þ ß à Þ á â ä å î æ ç è é ç ê ë ç ì í! " # $ % & # ' % & # ' % ª «ª ± ª ² ««* / - w ] ^ ` b S U V W X Y Z [ \ f g f h j < = > k m q 7 : A B B D E F Fg D f h y f h kg h hyb mg hg mg mg h b y hm [] whh m h g f w y f DG mg h b h h y b [] fqy g q gy whh mk h VS m h mh bh f yh mh h h VS ff yhz w m h f LL L V = V V ω = ω ω h b y f h kg b x fw: = k V V + k V V ω = k ω ω + k ω ω wh k V k ω k V k ω h m ω V h fqy g f h mg y wh h yhz h ω V h g fqy g b hgh h mm wk ω h y g h my A bk gm f h y f h kg hw Fg wh g h h wh h y f DG h mg m by h g g g by h g g g f h y D f h fw h f h g g g hw Fg hw h f h mg k by h kg h y f DG mg w b h g Ñ Ð Ò Ö Ð ÎÛ ÎÖ ÿ ð ñ fqy h m by g wh h wh m w f Wh h mg g m w f by h kg h y f DG w m wkg h f g fqy w b by wh h hg g w hg h w hg b m by g h g fqy hgh h y h f [] fqy g q gy m h mh bh f yh mh whh ff yhz w m h f LL h h VS -k b w m hf h VS h h by yhz wh h g h fqy b h h f h whh w h y b h f b f h DG h h x h yh mh hf h g fqy b h wh h h f h y h f my b ff fm h f [] F h f g mg h []h g h yhz f h mg b h f f h y Wh h h f h y f h mg h g h fqy b k b m h h g mg b y y f w y h fm w b b f h y f h y b h wh f f m Sm mh b f [] Wh h yhz bw h mg h h w g g f f h y h g fqy h m mh h whh h g b h ym m hf wh h h f h y h bw h y h - mh h g mg b y y h bf h h b y fxb h h f fqy g w b b D O Dgm h bk gm hwg h z f h - f h kg b f Fg 7 whh h y Fy h kg z by mg h fqy m g h m b mz by g h mh [] h m h w mm k+ Eq f h kg Ag h m w mm
9 ± Ÿ ª «Q U Y Z F EEE RANSAONS ON SMAR GRD VOL XX NO XX XXX XX # $ % & ' % $ * + - / :! " 7 ; < = ˆ Š œ ž Ÿ š Œ Œ ˆ ˆ Ž Š ˆ ž Ÿ Ÿ A B D E F G H J K L J M N O Y Z [ \ ] ^ ` ^ b f g h j k ƒ ƒ m q ¹ º» ¼ ² ³ µ q m w x y x w z x m z { m q w } m ~ V W X R S q j k m Q R S U V W X V Q Y w x y z { z } ~ x y { ~ z ` g b b f h j k m k k q ƒ ˆ Š Œ Ž Œ Ž š œ ž Ÿ ª «Z [ \ ] ^ ` ` b ] ] ` f ^ g h [ ± ² ³ µ ± µ ¹ º ² µ µ ±» ³ µ ¹ ¼ µ ½ ² ¹ ¹ µ ² ¾ À Á Â Ã Ä Å Æ Ç È É S U S V W X O Q R N J K L M [ \ ] ^ Ê Ë Ì Í Î Ï Í Î Ð Ñ Ò Ñ Ó Ô Õ Ö Ø Ù Ú Û Ü Ý Þ Ü Ý ß à á à â ã ä å æ ç $ % & ' ' & * + - / + * / 7 $ % & ' ' & * + - / + * 7! " # : &; ' < = ó ô õ ö ö ø ù ú û ü ý ü þ ÿ < = A? B D E F G H A B > D D E D G H D A A J K L M N O! " # $ % * / è é ê ë ì í î ï î ð ñ ò : ; Fg Fw h f h g g g f h y Fg 7 O gm f h kg k+ h m f h kg b h h g ff g g σ k+ k k+ Eq b g Sy g h - 7 g wh h w mm k+ ff g g σ k+ k k+ h f ω V w b m Fy h f w b g h - m-f g Ag h gm LL fqy f h - F h m-f g whh k h q h g b fm h fm by g h fqy fm h LL h ym /O h h DDMFA q b x y fm hg m f h b Myb h h hg wh LL y h ym w b y ff by h LL h j h fqy f h - fqy V [] [] b mmz fw m wh [] wh h - m h wh h mh g fqy - m Ay mm m b h b fm fm h mg y [] h mh w fm h f SM h g w by bh h fqy g h mh fm h f hh w h g fqy y y wh h h f h y h mg m wh [] [] w hg yhz f g b qy g hy h h fm z by h ff k + k q h z hgh q 7 h g h yhz f bh h bw h h y h mg h bh h w hg h f h g fqy b z h m g f [] h m h f y mm bw mg g y f fxb g h g f [] h h ym by h h h LL y by gg h gy m h bh f SM Hw h g f h h y g fqy wh kg w hg whh hf f h b f h ym y wh h ym h y g h wh h y f DG h mg by gg yhz f f h y hby hg h mg h g fqy h m Ah h DD mh h whh h g b V SMULAON RESULS h fm f h hm f h k / mg h k ym Fg h b m MALAB/Smk m h mg h w DG m wh - b y A x-wh - wh
10 EEE RANSAONS ON SMAR GRD VOL XX NO XX XXX XX L f g h kg f h mg m f h ym Ax fy h fby f h ff g h b Fm h y f h mg wh h Sm h fwg A h bh h mg y xg m f kw h; h m h h w mg y g gh Ag h gy g wh h q m - V = ω = f h g h fqy w k = kw f by h kg h h kg m- Fg hw h w h f h g h fqy Af = h mg kw 7 kw y h bh h mg g m h h - f h fqy g - y Ag η > η = h w f by h kg - kw whh m h kg f kw fm h mg h mg h m hg fm m- m- U hg y- h g b h m b kw h A h mg h h m mz f - V = ω = g w hg f h bw h w mg B Sm h h kw f h mg 7 kw f h mg h kg f kw fm h mg h mg h y- b h w hg A = h m f h mg hg kw kw y h mz f h fqy g hg - - y U g h mmh mz h m f h w b f by h kg kw g g h kg h w fw wh kw hf fm h mg h h ω h fqy h m f h kg hg fm m- m- w Fg hw h w h mz f h fqy h g b h h y h bw h mg h y- h g b h m b 7 kw h A h mg h h m mz f - h f bh h mg h h kw f h mg kw f h mg y h m h mg y g wh h mg g m h y h kg f kw fm h mg h mg whh A = h mg hg kw kw y whh mk bh h mg h b m by h m mz - - Ag h w b f by h kg kw whh m h kg f w h mg b f h w hg h Fg hw h w h mz f h fqy h g b h h kg by mg h w hg h g fm y m h g hg ym my b h g h ym by D h h kw f h mg kw f h mg y h m h mg y g m y h y h kg f kw fm h mg h mg g Eq A = h mg hg kw h mg m kw Ahgh h mg g m g h w b f by h kg kw k = kw h h h hh η < η whh m h kg f w h mg b f h w hg h Fg hw h w h mz f h fqy h g b h m f h - x bw h mg h h kg by mg h w hg h g fm E B h y hm h h h m h m h Fg hw h m fm whh b h h f h fqy g z g h m wh h f h y Sfy = yhz h bw h mg h f g fqy m h f V k ω k < ε = hf h
11 EEE RANSAONS ON SMAR GRD VOL XX NO XX XXX XX D 7 W W w w A A A «b E B b j f b B H ¹ J y E F å á ¹ H ω F G m m V Fg w - Fg w - Fg h hm gm f g f ha w W b - f h A w W b - f h g fqy g fqy hh W W W w w w A A A b b b ó ï ë ç k g õ ñ í ¹ å á ¹ ¹ m m m Fg w - Fg w - Fg w - A w W b - f h A w W b - f h A w W b - f h g fqy g fqy g fqy D g h mg hg h f f h y h h y f h DG mg h g fqy h m A = h mg hg kw h mg m kw h w f by h kg h h h hh η < η whh m h mg b f h w hg hf h y f h kg wk h y h mg m wkg h g h fqy mg b k h m y V E XERMENAL R ESULS F fyg h y f h hm k mg ym hw Fg w b h by mg mg mg h mg h mg hgh h kg h mg E F G H S J K U L M V N W X O Y Z Q R [ z { ª «µ : ; < = A B ¹ ± º ²» ³ ¼ } ~ ½ \ Ê Ë Ì Í Î Æ Ç È É ^ ] Ï Ð Ñ Ò Ó Ô ` b Õ! $ % & ' " * + - # w / 7 À f g h j k m Â Ã Ä Å Fg y Á ¾ x q h k mg f kw V y mwh h mg f kw V y w kw hz x W h gh m f w k mg N h g f h w mg w y h m wh h f h m m h qy fy U w hg h f h fqy
12 k f w W k g y 7 EEE RANSAONS ON SMAR GRD VOL XX NO XX XXX XX g mz wh h g w wy h m h y h xm w f g: Fy h h mg kw h h mg 7 kw whh m h w mg m h mg h f kw fm mg mg hgh h kg ; Sy h mg hg kw h mg hg kw whh m h w mg m h mg h f kw mg hgh h kg ; hy h mg hg kw h mg hg kw whh m h w mg h w hgh h kg ; Fhy h mg hg kw h mg hg kw whh m h w mg m ; b h h h hh h f w hgh h kg Fg hw h xm w wfm b h w fm mg y Fm h Fg b f h h f g h w mg h h g h h fh g h w mg y h h g Fg hw h xm w wfm b h w f by h kg Fg 7 Fg hw h - f h mg fqy mg g h g g y b y f h w hg w h h w wy h m hy b h m whwh mk h h h m b f h DDMFA hm m b y g h h mh h b wk h q h y ym h b m f h b g g q h mh h b m b D MFA mh q hy mhm kwg f h ym g whh w m m b y mm h m b h m y b y g V ONLUSON h g w hg f k mg z w hg bw mg my g - - m-f g h b fy h Fwg y hm h b wh h mg Fg W Fg Fg 7 W m g h A b y f w A g f q A g 7 m h w f h mg h mg ƒ 7 m h f w by h kg W Ð Ì È Ä Â 7 m V h g fqy g g h g h fqy h m Ug h hm h kg j k h hh DG w h h
13 g EEE RANSAONS ON SMAR GRD VOL XX NO XX XXX XX Fg V g A m h g g V by g h m g h fqy wh kg w hg M h g f h y b / /O mm b h m y m Sm xm h b g fy h w hg gy AENDX A Vb q : Uk = [ k k L + ] V k + = V k + V k k + = k + k = L [ Φ k = = [ Φ k = ψ L φ φ φ φ L φ L φ L k ψ L k φ k φ k φ k φl k φl k φl ] L k ψ k k φ k φ k φ k φl k φl k k k k k k φl k φ k φ k φ k ] φ L k φ L k φ L k Φ k > L gh f z f h -m ym Vb q : K = g k k k K = K Γ k = Γ k Γ k = g Γ kγ kγ k Γ k = Uk + µ = F = g F F F F = F Ṽ k = V k ˆV k Vb q : AENDX B Λ σ = k ξol k k k ω k+ V k+ k ξ OLk + V ωk+ σ k k = k +k Λ k = k ξm k k k ω k+ V k+ k ξ mk + V ωk+ kk ξ OLk = ξ k ξ OL ξ mk = ξ k ξ m ω k+ = ξ k ω k+ V k+ = ξ k V k+ V ωk+ = V k+ ω k+ Mxmm w mx Vg g V D ff k Sy g Mxmm w mx Mxmm w Q mx Fqy g f D ff k Sy g Fqy g Vg g AENDX ABLE SMULAON ES SYSEM ARAMEERS -mg L- Ω L- Ω Nm g V -mg L- Ω mh L- Ω mh Nm fqy Hz Nm g V L-L kg F mh F µf -k µf Ω ABLE SMULAON ARAMEERS AND RANGES -mg kw V < V < V W k V = k V = -mg kw kva Hz f Hz W k ω = k ω = kg Hz f Hz f UL Hz f Hz - f NL Hz f Hz - f - OL V V V V UL V V V - V NL V V V - V - OL L = g k k k = g m K = g α α α = g α = REFERENES [] J M G M hk -L L Lh A h f g mg- : z hh EEE E - A [] J Wg J X Y g F H h mm f hh mg EEE E - Ag
14 EEE RANSAONS ON SMAR GRD VOL XX NO XX XXX XX ABLE EXERMENAL SYSEM ARAMEERS / mg mx = kw V y w g f Q mx = kva mx = kw V : kw W : kw Vg fqy g V< V < V Hz < f < Hz D ff k = k = W Sy g k V = k V = k ω = k ω = F L-: R = Ω L-: R = Ω L = mh kg F mh F µf -k µf L = g k k k = g m K = g α α α = g α = [] N gk M G Mg y g f m f -b mg EEE w E - M 7 [] Q S Y Zhg H H D M H Zhg A gy f b by f gy EEE Sm G b bh [] N B M G Dym by f mg wh EEE w E 7- N [] S M Ahb Y A R Mhm A fxb gy f g- mg wh h by g mg bz EEE Sm G - S [7] L L hg Dg f w hm fg gy f b g f g wk EEE w E -7 S 7 [] Q- Zhg Y Zg f h m EEE w E -7 O [] J H Y W L F Bbjg Fxb mg w qy hm g hyb g EEE E 7-7 J [] Q- Zhg Rb f hg mg EEE E - A [] Q S J Zh J M G H Zhg Hyb hh/g-h mg h wh w mgm b EEE w E -77 O [] Q S R H H Zhg J Zh J M G A mgb ghm f b f b g h gy EEE Sm G - N [] J W Sm- F Df F B Syhz w hg f - mg Am - S [] U Nk Lh F Bbjg Db f k A mg wh ym w g EEE A - S [] X L Wg Lh A hyb / mg EEE Sm G 7- J [] Lh D L Y K h F Bbjg Am f hyb mg wh A D bg EEE w E - My [7] Lh D L Y K h F Bbjg Am f kg wh gy g hyb A-D mg EEE A 7- My/J [] Lh D L Y K h F Bbjg Hyb A-D mg wh gy g g gy fw g EEE w E - A [] N Egh E Fjh w mgm hyb A/D mg EEE Sm G - My [] X L JM G K S J Vqz R L Hg Hh f - f f hyb mg EEE Sm G - M [] H Zhg Q B Jg Y L O y g ghm f H fbk f kw ff -m ym EEE yb 7-7 D [] H Zhg Y Q Mg f f f ym EEE Fzzy Sy - A [] A H Em E J D R A z b gy f m-der mg- : fm EEE w D 7 - O [] Gy D E Q M f m f w EEE w E - D [] M D Y A-R Mhm Vb--b f h m VS -gy- mm g EEE w E - N [] H Zhg Q Y L N-wk-b m hm f -m wh ym g h gmmg EEE Am S Eg - J [7] Z H S J D m-f f f MMO -m ym EEE N Nw 7- D [] G Rg S N Z S f b w g wh h -f km f EEE E - N [] Q W D L D- -m m f w-g hf g b ym gmmg EEE E - N [] H Zhg Y X Zhg Y L D- b xm m kg f kw g ym g ym gmmg mh EEE N Nw - D [] D X B Jg Sh A m-f g f mb EEE E - N [] A Q Hg M L w G Hy J Zhg S J D h f wb gy y mgm ym h Egy EEE g f h EEE - J [] Q Shf Sf Dg k J Vqz J M G Rb wk hm f b y f mg EEE E -7 O [] M Ahb Y A-R Mhm N mh fmwk f g VS m w g g b yh-vs EEE w Sy -7 M [] A A A Rw Y A-R Mhm Am mg f ym hyb / b g ym EEE Sm G - S [] F G W J M Y-D Sg Db y g fqy f - b mg EEE E 7 - J
15 EEE RANSAONS ON SMAR GRD VOL XX NO XX XXX XX Hgg Zhg M -SM -F h BS g h MS g gg fm Nh D Uy f h J y h y H h hd g hm w gg m fm Sh Uy Njg h H j h Dm f Am Nh Uy Shyg h Fw f w y S h h b f H f h f E Am Sh f fm S Egg Nh Uy Shyg h H m h fzzy h ym wk b h H h h h j f x mgh - D Zhg h fw f EEE h E- h f EEE S Sy h fm h f h A Dym gmmg & Rfm Lg h mm EEE m g Sy H A E f AUOMAA EEE RANSAONS ON NEURAL NEWORKS EEE RANSAONS ON YBERNES NEUROOMUNG y H w A E f EEE RANSAONS ON FUZZY SYSEMS - H w w h Og Yh S F Aw fm h N N S F mm f h H w m h hg Kg Sh by h E My f h H f h EEE N Nwk Og Aw J M G S -M -SM -FM h BS g mm gg h MS g gg h hd g w fm h h Uy f B 7 y S h h b F f wh h Dm f Egy hgy Abg Uy Dmk wh h b f h Mg Rh gm Fm h g f h h Amy f S h Njg Uy f A A; fm h h f Shg Uy; fm h gh g f H Uy H h ff mg g w b gy-g ym hh gy mgm ym mz f mg mg f G A E f h EEE RANSAONS ON OWER ELERONS h EEE RANS- AONS ON NDUSRAL ELERONS h EEE E Mgz E f h EEE RANSAONS SMAR GRD EEE RANSAONS ENERGY ONVERSON H h b G E f h EEE RANSAONS ON OWER ELERONS S : w E f W Egy w E f Mg; h EEE RANSAONS ON NDUSRAL ELERONS S S: Ub w S ym Rwb Egy Sym Db G Mg A mm f h Km F; h EEE RANSAONS SMAR GRD S Sm D Db Sym H w h h f h Rwb Egy Sym h mm f h EEE E Sy H h b w f h EEE Egy h w w by hm R Hghy Rh h w EEE Fw f h b b w ym mg Jg Zh w b Y h 7 H h BS g m h MS g hy gg fm h Nh Uy Shyg h y H y wkg w h hd g hy gg fm h Nh Uy Shyg h H h w hh b w qy mm f mg yhz f mx/m-g wk h mg Egy Qy S M - h BS g w ym m fm h Nh D Uy f h J y h h MS g w h hd g hy gg fm h Nh Uy Shyg h 7 y S h h b F f wh h Sh f fm S Egg Nh Uy h H m h Omz Ay hgy f w Db Nwk Nwk f Db G Sym mg Egy H h h h j f x mgh - Dzhg M h BS g m h hd g hy gg fm Nh Uy Shyg h y H y L wh Nh Uy H h f g f- gy mgm ym mz f b g ym mg Egy
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More informationSAVE 9,893 SALE PRICE $12,961 * SAVE 6,354 $22,596 * SAVE 9,833 SALE PRICE $42,864 *
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More informationSymbols and dingbats. A 41 Α a 61 α À K cb ➋ à esc. Á g e7 á esc. Â e e5 â. Ã L cc ➌ ã esc ~ Ä esc : ä esc : Å esc * å esc *
Note: Although every effort ws tken to get complete nd ccurte tble, the uhtor cn not be held responsible for ny errors. Vrious sources hd to be consulted nd MIF hd to be exmined to get s much informtion
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