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

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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

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