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1 D'& iue.3 &+ G<= & K ^ E 39 3 ; <= ;5 N?4@ J 76 VT' #J ; 8-AQ M ' DEE? 5 P 3 -Q Y $+" a ; ;E b.e ) EQ / G A> - &/ J hoseinpour.majid@gmail.com ; ;E b.e ) EQ / G A> - Y!" D" mohamadian@modares.ac.ir 3 ; ;E b.e ) EQ / G A> - & (39/9/ :H9 [i ge 39//3 :H9.+ ge) yazdian@modares.ac.ir &+ D&/ [ ^ K+ E K G<= H9? :D8 &H 3 ;3 < H&/ 9<@ E &4 K E D&/.3.. < 9<@ E /D&/ c&4 d G<= K ;8 DN@.3 K E ;E c49e D&/ &H 3 9<@ 4K-E /D&/ ;3 & D'& D'& iue E c&4. KJ 3 `Q &+ D&/ 9<@ K o&./? E &H K ^ E? Y> ;E c49e. ; c&4 d G<= KJ `Q &+ D&/ E K K ^ E :Dc5-E =- D'& > ; iue s K \@7 >,B G&GH AJE ;+K,+ 3E qe E d G<=? / &H A& = D'&?. GE ;3 E D& E.4 & F ; H ^ E.iC 9&4? re E.4 ^ E..[] = :^ K D'& ( HE K & A( / ( HE ;3 HE = KGE D'& K+. 49 ( Hp. C<3 <~. ( HE ;3 D9& K K+ E 3 &- <~ E 4E ;K K \ K ^ K+ E / ; ^ K+ E &- <~ E 4E K+ E >. E 4E K+ E.4 c&4 </ ; CK.<>. H J3.<> ;3 Journal of Nonlinear Systems in Elect. Eng., Vol., No, Fall 3 39
2 77 D'& iue.3 &+ G<= & K ^ E 3 ; <= ;5 N?4@ J.4 c&4 3 H 'E. 3 CI 4 \ K / ^.. 9 / ^ E J ;K E :3 G &/ _ 'E E J ;K K+ E G.[3] [] ' E 4E K+ E ^ E </ 8. ( :^ / ~ me HE) \@7 > ~ c ; dc FH J ;K? &H c49e 3? K+ &H E33=?^ qre K C<3. J ;K &H v3= = (D'& ;3 G D&/ &H / D'& /D&/. b4@ O K43 D&/ : K 3 J ;K E E ;I ( HE ;3 = 3?.. G? <.3 [4] `K&4 cj@ Du K X( K ;K wb& E &H v3=?. dc FH &H D'E := = GH@ dc FH &H ~/@ &G^/ K+ &H F J ;K ^ E.C 5 & ( 5 E ^ E.3? K / dc FH &H ZN E m &H F ^ E = (EMC) 48u &GH CK A7G \ K &H.[5] J ;K ^ E.4 &H d Z< K & ;E /. E7G ^ E? K me 4 K t `/+ ;3 &H / ^ E / ; ^ E 6? ;O ~ c 4 J ;K E / H@. & // \@7 > ~ c ;3 (NB? ;E.[] & // 5^ m xn t ;E m& ;E / E KK K.&+C > 3E 4 A> &H s E K DNE & ) 'E 5E A>,+ ;E.+y,+ ; b& ;,+ ;8.<> ;4G A E? ;3 c49e \ &+C \ K DNE &4 / <4 /P X ; <&B H&/ [. 'E ue i X' (E.+y ; droop ) &+ [ b D 6. c49e </ 6 E? le 6 \ K / &+C A A> G c/@ E Q ω P./ &+ NB K &+ D&/ :. c4 le = /. (method X' Et ;8.<> [? & <5 CK A=78 K +( H&/ [? GJO K...>? 5HN E 3 `Q K )&4 / ic g \ ' / H@. J & i </ c4> ^ ;E / \5H c49e [ : 6. `/+ &H ; ;E c49e (3C: Circular Chain Control) JK 9<@ D&/ (Master-Slave) -<( D&/ / D&/ : c49e.[7] m& ;3 c49e [ ;3 c49e [.C c49e D'+ ;E c49e D'+ ;3 c49e <( C E D'+ c49e [ / l K [? / ^. (@ d 3 &H ;tc {5( ;3 c49e NB D'+ ;E c49e [. [K = D&/ 9<@ ;3 A=78 K s &4 8E 8E l K &?. C & <5 /D&/ &/ &/ ;E A=78 D'+ Hp ;^ 3?. Cm& m G F D)? K /./ F? :J & [? G ;E c49e [ qe &/ &/ ;E 5 G [?.&4 &+ [ & D&/ FGE G ^ iue [ Journal of Nonlinear Systems in Elect. Eng., Vol., No, Fall 3 39
3 D'& iue.3 &+ G<= & K ^ E 3 ; <= ;5 N?4@ J 78 ;E {5( c49e 8E l `Q ;KE :=.4@ &H ;tc ;E c49e 5HN E7G D&/ [.[8]. e d'? s+ <&B [ '& A995E / / G g G? <(+ / xn. K E D&/ wi3 [ K ^ A7G 3 &+.K 8E l K & ;G E /. ;3 D'E := K;3 <&B [ ;/E K+ E KK s3 w> E K &.. & J ;K ^ K+ E K F K+ E K O [].. [9] E &H.~ HE Hp (SRF)-PI H)& -E / D&/ ; HE ;3 K43.. E 3 &H.~ HE (SRF)-PI /D&/ sje &/ ;E K `/+ &+ [ F [4].. [3] D < [] [] K D < ;E <( Hp E c D&/ 7= /. K+ D& (Q-V) &/ ;E K &H.+ (P-f) -.H? E E c (Q-H) G. K G Q O-.H &+ 5 F K & &/ &/.~ HE ;3 HE K &/ ;E b &+ [ F [5]./ nb <5 G G / Q O. &H d4@ &/ ;E `/+ d4@ &/ ;E D& &+ sje E /. m &H [ F [7].. - D&/ [ &- <~ E 4E N& K+ UPS KK [6].. J ;K ^ K+ E K K &+ KK C :J / t / ) K+ E KK K :J ^ K+ E KK Y95E? K X :J ;/E ^ K+ E. E.+y m D'& H /? ƒ+ H9? :/ d' E KK K [ 3E ^ K E D&/ &+ D&/ [ K 4 8E l K & c K E 3E > <(+ /D&/ ;3 < 9<@ E /D&/ ^ K+ E d K G<=.3.. H9? &H 3 9<@ 4K-E ; H5 5- :. K Y <5E m<&b ;E. ; N& E KGE D' () G S = P + jq () :K E= 99@ ;E / EV P = sinφ X EV cosφ V Q = X ( 3) Journal of Nonlinear Systems in Elect. Eng., Vol., No, Fall 3 39
4 79 D'& iue.3 &+ G<= & K ^ E 3 ; <= ;5 N?4@ J N& E KGE D' : G E K G<= D' : G `Q dh < Hp H t'. ; & N& < 3 `Q E () G ƒ+? &H. &+C \ < A( E 3 `Q E 3 &<+ `&/ l,b?.[8]. &+C \ <- A( E 3 `Q At9. &+ Hp b A> G Z<&B E? c49e /. &+C A> c&4 E K &+ D&/ : K G<= :?.C A( K E / D&/ φ K+ K ue 99@ ;E D&/ \.. qp.. \+( E 3 `Q.4> K E K.3 ( E Q ) &/ ;E d4@ &H (ω P ) &/ ;E d4@ `/+ E &/ ;E. nb (3) () / ).. & E Q &/ ;E E &H K (@ ω K `/+ :[8] Z'E K Y &+ m ((3) G Y ) ω = ω mp E = E nq ( 4) (5)? 5HN &4?.,/ &H c\e.> GH@ ;E c49e G<= J &+ dm,+.i A( &? E Q ω P &+ ANB :3 G `/+ &+ D&/ /. D At9 &H c\e c49e Y> D&/ E3 [ &H -[9] O <3 K KJ & 9 `Q K & ( E P ) &/ ;E d4@ &H (ω Q ) &/ ;E d4@.[] Journal of Nonlinear Systems in Elect. Eng., Vol., No, Fall 3 39
5 D'& iue.3 &+ G<= & K ^ E 3 ; <= ;5 N?4@ J 8 F" 8$ -3 - &+C \ G? K G<=.3 ^ K+ E. ; c&4 G (4) G &H? re c&4? H&/ X. ( D'& ;E D9& m F Y8 K K E. \ ^ E K</. E? G D'& ;3 ;4G c49e d.. :J Carrier-Based ;t [ K D&/ C K ^ E :4 G ' E `'-4 &+C > 'H ^ E F G<= & K ^ E d G<= &.3.. ;O D&/ :Kt -E --4 ic g & H ;3 4 K H&/ &?. ; &H D&/ 9<@ F & (5) G O + X E (6) G Y 9<@ ^ H&/ c&4.k G V C V C &H D&/ 9<@ :5 G V C +_ Voltage Controller I +_ Current Controller plant V C I ;3 < 9<@ 9<@ ^ D&/ :6 G Journal of Nonlinear Systems in Elect. Eng., Vol., No, Fall 3 39
6 8 D'& iue.3 &+ G<= & K ^ E 3 ; <= ;5 N?4@ J > K+. E /D&/? ^C././ E /D&/ F K & ;3 < D&/ 9<@ C?C K & ^ C K+. K;3 \./ J c&4 G<= `/+ \@7 / D&/ K C.H@ dm &.3 H9?. i w&3 &H 3 D&/ 9<@ K &H /D&/ 9<@ ^ /D&/?M.[]. &?/ s3 w> 4K-E C &<+ K 4K A K,9 ;3 < /D&/? K./ KJE E 3 "5 ( 5 E =---4 &+C \ ;3 9<@ u& ;= (I ) Z< ;3 A> Ed.y@ & 4K ; K \ E 3 &H ) V i. ; E /D&/ ;3 9<@ G (7) G.[]. :. K Y c&4 E se. \+( I o [& K /. c&4 E se I (s)/v i (s) I s sc = + Vi s s C :O. K Y &4 9<@ E se + K. 4K ; ƒ' K / / / ; M +. Z< ;3 s3 ;G I s sk GC = I s + sk GC + s C c c I (6) (7) + D dm G ;3 /D&/ dm K c (8) G. (@ 4K A & ;3 /D&/ dm,+ A( &4 9<@ E se. X8 / 8 c&4 &+ K c.4 /. ; K c Z<&B 9 : K?BE K Y 3 + I s sc I s + sk GC :C (9) G.. +?BE? K 3 ;3 9<@ K K+ 3E > 9 / JO K.. K+ K K 3 ) / ; < ;3 9<@ &4 9<@ E se Bode c (8) I I ( s) k c V ( s) i I I \ c&4 ;3 < 9<@ :7 G Journal of Nonlinear Systems in Elect. Eng., Vol., No, Fall 3 39
7 D'& iue.3 &+ G<= & K ^ E 3 ; <= ;5 N?4@ J 8 6 Root ocus Imaginary Axis System: Gi 4 Gain:.4 Pole: -5e+3 Damping: Overshoot (%): Frequency (rad/sec): 5e Real Axis ;3 9<@ ;G :8 G Bode Diagram Magnitude (db) Phase (deg) I I ( s) ( s) Frequency (rad/sec) E se bode :C :9 G $ C-' 5 J c95 =--3-4 (PI) H)& E /D&/ K & / \ (9) G Y < ;3 9<@ dm se 3E G J d3 t dc dm 3.. &4 9<@ dc dm?^ / D&/ &H ;E t K [ K &4.H@ d / d G<= 9 &.3?. ;t +. & PI /D&/ D& [ V C s I ( s) K I iωcut s sc KP + s + ωcut s + ω + KcGsC I I I o sc V C <( Hp 4K-E /D&/ : G K.5 H.. ; ω cut ; 4K-E /D&/ 3 &H 9<@ & () G s> `/+ 9E 4K /D&/ () G.[3].4 <= / 4K /D&/ K & ) 9E 8?I () G. ( I ) ;3 < /D&/ s3 ;= &H /D&/ 3 Journal of Nonlinear Systems in Elect. Eng., Vol., No, Fall 3 39
8 83 D'& iue.3 &+ G<= & K ^ E 3 ; <= ;5 N?4@ J K \+(. w45 [& ;= (I o ) ;3 GH@ s> `/+ dee. nb ((8) Y ) ;3 9<@ E se (9) Y &H 3 9<@ NB H' [& { ω } { ω ω } ω s K GC + s + K + K GC + s + K + K + K GC + + K = ( 9) 3 c p cut c c i cut c p ω ω cut 4K-E /D&/ 4K dm E dm dee K i K p +. nb () Y.4E K <( Hp `/+ 4K-E /D&/ K i K p 9 :E K c&4 O 3 D & 7= ue _ ; /D&/ &.. i ;G <( Hp K i > K >?G 9 :E K `/+ C.H@ g & K.. & &4 /D&/? H9 \ X &.3. K+ /D&/ KGE D' F () G. =. D'& m D'& m 7= p ( + K p ) ( K GCω ) s : K GC + K + K ω + K GCω 3 c c i cut c s : + K + ω K GC ω + K p cut c p ωcut c s : ( + Kc + Ki ) ωcut + + K p + ωcut KcGC s : ω () 5 P r) E-4-4 F K 3E > <( F 7= 3 &H K4G. 3 &H ;3 & Aq Xi@ E () G H&/ &. c& cj : \ &H 3 9<@ c& cj : Hp 4K J /D&/ () G Y 7ω 5ω 3ω ω `/+ `K H 4K-E /D&/.. &+C. : () Y &H / D&/ E se.. d G K ω s K ω s K ω s K ω s Gv ( s) = K s s s s i cut i3 cut3 i5 cut 5 i7 cut 7 + ωcut + ( ω ) + ωcut 3 + ( ω ) + ωcut 5 + ( ω ) + ωcut 7 + ( ω ) 7ω 5ω 3ω ω p d& `K dm dee K i7 K i5 K i3 K i E.q dm K p + /D&/ 4K dm K. 8 4/+ Hp cj : G Hp C.H@ (K i7 K i5 s> `/+ ω cut 7 ω cut5 ω cut3 ω cut?m K i3 ) c& cj : dh `/+ 4K K &? I 4.4E K & /D&/? <5E./ nb c&? 9,+.. d /D&/ ƒ+ ( K i7 K i5 K i3 G K.. :J Bode oe / H@,/ c& cj F Hp (c& cj : F `/+ 4 db K &C K) K = K = K = Ω - /D&/ / dm?,+ &H. G Hp () G Y C.H@ dm i3 i5 i7 6 K../.+? ( F K &/ C.H@.. &+i :J G `/+ 4K Bode :C K &?. K43 E &H 9<@ &.3 ;O 3 D= 4K-E /D&/ &H () G.. D= [] lead-lag Journal of Nonlinear Systems in Elect. Eng., Vol., No, Fall 3 39
9 D'& iue.3 &+ G<= & K ^ E 3 ; <= ;5 N?4@ J 84 / ƒ+ E 6 K ;3 /D&/. E Z< ;3 D&/ 9<@ F?&+C \ c&4 G g K c = G T : 5 (7) Y E dm /D&/ 3. ; K T D dm G E K+ 3 `&/ +. (@ ^ E s3 K+ &H E +M 3 ;K &H ;3 () V C Kiωcut s KP + s + ωcut s + ω + sτ α + sτ β I V C Kiωcut s KP + s + ωcut s + ω ω Ki cut s KP + s + ωcut s + ω Kiωcut s KP + s + ωcut s + ω G <( Hp 4K-E /D&/ : G Bode Diagram Magnitude (db) Ki3=Ki5=Ki7= Ki3=Ki5=Ki7= Ki3=Ki5=Ki7=4 Ki3=Ki5=Ki7=6 d/e. Phase (deg) K i7 K i5 K i3 Z<&B 9 &H 9<@ Bode :C : G E 3 ;K s3 &H V c Frequency (rad/sec) : ; (3) () 3E ;E /D&/,B /E V = V V G s s I K G i c c v c E 3 ;K &H : (@ (4) V = G s V Z s I c c o o V c lead-lag K43 E se I = Io + scvc ( s) (3) / ic3 (3) () m :&4 ; > K m Y / E 3 `Q E se D&/ E se dee Z o (s) G(s) / (4) Journal of Nonlinear Systems in Elect. Eng., Vol., No, Fall 3 39
10 85 D'& iue.3 &+ G<= & K ^ E 3 ; <= ;5 N?4@ J G s Gv ( s) ( s) kcg = + r + k G Cs + Cs + G s s k G c v c (5) Z o ( s) r + kcg + s = + r + k G Cs + Cs + G s s k G c v c : (7) Y &H 9<@ K 9<@ E se. &H 9<@ &4 9<@ E se G(s) (5) G op ( s) Gv ( s) ( s) kcg ( r k G) Cs Cs = c (6) (7) ' 8-AQ-5 &H / 5 ;4G A( E 3 D'& ;3 c49e H&/ X H9? ;E 5 & ^ E K G<=,B?. & 3 3 &H HE ;O K ` K+ 99@ ;E &+ NB `Q &+C > K+ 99@.. &+C > KJ 3 `Q 9<@ K & s3 ; 5 ' M--5 &H. K?BE K CK D) me E =J me HE 99@ ;E - & K Y 99@ \5H ;E?'E.3 P = V I i Q i c o I o c o E =J 3 ;3 ( 9 ) = V I ;E K+.. \5H ;E ) c F ;O s> `/+ /. & ic? &<+ K?.O. K+ 99@ ;E 9 6J K ;E ( B Hp Q i P i V c E 3 ;K : (8) Q i \5H 99@ ;E P i + / Hp Xi@.3.. K.. &+C \ G `/+ ; 5 ' ; %& --5 Q 3ph P 3ph ) K+ 99@ ;E 9 _ ;E KGE 9 5 ic? &<+ K & H 99@ ;E 9 K & K+ s3 &H K `/ @ ;E.~ Hp ) E? K. :. 5 > K Y Q 3ph P 3ph m = 3ph = a + b + c E E np E n P P P ref = + mq3 ph = + m Qa + Qb + Qc ω ω ω (9) `/+ E K+ &H s3 9 dee ω E &/ &/ ;E &+ dm dee m n + sm & 9? / E &H K K+ K?'E J &+ ANB +. E.[7] /? E.H@ ^ ;3 / Xi@.3 D'E Journal of Nonlinear Systems in Elect. Eng., Vol., No, Fall 3 39
11 D'& iue.3 &+ G<= & K ^ E 3 ; <= ;5 N?4@ J 86 a 5= J5 sx =- D, RJ c95 9 '-3-5 : (@ K m b K+ s3 &H >,B K HE (ω ref ) `/+ ( E m ) &H K K & sin ( ω ) ( ω ) ( ω ) V Em ref t RD Ioa ca V E t R I V cc E t + R I cb = m sin ref D ob m sin ref D oc (). KJ & 9 3 `Q ) R D + c&4 :C <. 4K-E D&/ b ^ E &H D&/ 9<@ :C < ) (3) G.. ; (4) G E s3 &H HE.3 &+ [ & ^ K E D&/ V C I V i V C ω 3ω 5ω 7ω &+ [ & D&/ c&4 :C < :3 G I V C V ca V cb V cc I oa I ob I oc P a P b P c Q a Q b Q c P 3 ph Q 3 ph n m E ω E m ω ref RDIoa RDIob RDIoc V ca V cb V cc &+ [ & D&/ c&4 :C < :4 G M) _-6 m5 K ^ E G<= c&4 G<=.5( \. 3 () D3 E H&/ & A> &.. K Matlab\Simulink N& E =J F q / E ( K K c&4 G G<=.3 &+ D&/ / H9? H= &+ D&/ c&4 G<= M D D'& F q / \5H ;E d4@ `/+ &+ D& c&4 ( E P ) o& K ^ K+ E &+ D& c&4 ( E Q ) &/ ;E d4@ &H (ω Q ) &/ ;E d4@ `/+ &/ ;E d4@ &H (ω P ) &/. 49 c c&4 ;3 c49e 3 G / ). ; K E =J me HE K+ &H (5) G. K+ A( HE &H D'& Journal of Nonlinear Systems in Elect. Eng., Vol., No, Fall 3 39
12 87 D'& iue.3 &+ G<= & K ^ E 3 ; <= ;5 N?4@ J Voltage (v) Time (sec) 9 38v 5 khz / mh / Ω µ F 8 v /8 Ω /5 Ω /8 Ω 6 Ω 6 Ω 6 Ω 3 /4 rad / sec 94 /3 rad / sec 57 /8 rad / sec 9 /9 rad / sec 8 µ sec 5 µ sec /8-3 rad/sec/var /8 - V/W 3 /5 Ω K ^ E 3 &H :5 G H&/ & A> 9 : D3 K & (V o ) 3 m &H (f) K</ `/+ () K+ 3 Z< (R) K (C) K+ 3 ;K DC FH &H (k c ) ;3 < 9<@ E /D&/ dm (k p ) &H 9<@ /D&/ E dm (k i ) <( Hp 4K /D&/ dm (k i3 ) : F 4K /D&/ dm (k i5 ) cj F 4K /D&/ dm (k i7 ) c& F 4K /D&/ dm ( ω cut ) <( Hp 4K /D&/ s> `/+ (ω cut3 ) : F 4K /D&/ s> `/+ (ω cut5 ) cj F 4K /D&/ s> `/+ ( ω cut7 ) c& F 4K /D&/ s> `/+ (τ α ) ) (τ β lead-lag /D&/.q dm lead-lag /D&/.q dm (n) 99@ ;E &+ dm (m) ;E &+ dm (R D ) KJ & 9 `Q Journal of Nonlinear Systems in Elect. Eng., Vol., No, Fall 3 39
13 D'& iue.3 &+ G<= & K ^ E 3 ; <= ;5 N?4@ J 88 F q / \5H. nb G / ).. ; me / ;3 (6) G / \5H d G G<= iue d G<= 7= K G K.. +M D'& Current (A) K ^ E 3 D'& K+ ;3 :6 G.. > q Time (sec) 4 3 oad Current Inv Current Inv Current Currant (A) =J K / / K+ ;3 ;4G.+y K E K :/ K+ F ;3 :7 G.. ; K+ K G =J K / / ;3 E K :/ 3 ;3 (7) G - G? K.&4 Y c c 7 / E 3 ;3 E.+y 3E G? - ;3 (8) G. 3 E? ^ ;3 _ / = = H&/ c&4 /.+C J& ;E ) G? /. ; ~ c ;3 (9) G. ; E K :/ 3 K+ K G<= ( E Q ) Time (sec). E? ;3 c49e H&/ c&4 Y> G<= (ω P ) D& &+ c&4 KJ `Q & &+ D&/ c&4 G<= 49 &+ D&/ c&4.5e ;E c49e 5 ) () G / &+C > D& &+ D&/ ^ E A\5H J E? 9> ;3 c49e H&/ c&4?. nb G / ). D&? / c ' E ;3 E F.~ ;3 ( 3 / ( K =.3. E? ^ ;3 3 ) Journal of Nonlinear Systems in Elect. Eng., Vol., No, Fall 3 39
14 89 D'& iue.3 &+ G<= & K ^ E 3 ; <= ;5 N?4@ J Na-7?.. K ^ K+ E H9? < 9<@ E /D&/ c&4 d G<= & <@ <@ /D&/ & &H 3 9<@ 4K-E /D&/ ;3 KK.3 3 & 9 KJ `Q K & &+ D&/ [ K <(+ 3 ƒ+? Y> ;3 c49e & D'& D'& iue E c&4.. & E - ; c&4 d G<= K o&./? E &H K E. 5 Current (A) Time (sec) (ZH) 5 Current (A) Time (sec) (w) (w ZH) K E K+ ;3 :8 G Journal of Nonlinear Systems in Elect. Eng., Vol., No, Fall 3 39
15 D'& iue.3 &+ G<= & K ^ E 3 ; <= ;5 N?4@ J 9 3 Neutral current (A) Time (sec) ~ c ;3 :9 G 4 3 oad Current Inv Current inv Current Current (A) Time (sec) D&/ c&4.5e =J K / / K+ ;3 ;4G.+y K E K :/ K+ F ;3 : G D& &+ RJ-8 [] Eyyup Demirkutlu, Suileyman Qetinkaya, Ahmet M. Hava, Output Voltage Control of A Four-eg Inverter Based Three-Phase UPS by Means of Stationary Frame Resonant Filter Banks, European Conference on Power Electronics and Applications, pp. -, 7. [] Comparison Transformerless to Transformer-based UPS Design, EMERSON Network Power. [3] M. Prodanovi c and T.C. Green, Control and filter design of three-phase inverters for high power quality grid connection, IEEE Trans. Power Electron., vol. 8, no., pp , 3. [4] P. Verdelho and G. D. Marques, Four-wire current-regulated PWM voltage converter, IEEE Trans. Ind. Electron., vol. 45, no. 5, pp , Oct [5] Jun iang, Tim C. Green, Chunmei Feng, George Weiss, Increasing Voltage Utilization in Split-ink, Four-Wire Inverters, IEEE Trans. Ind. Electron. vol. 4, no. 6, pp , June 9. [6] J. De Kooning, B. Meersman, T. Vandoorn, B. Renders,. Vandevelde, Comparison of Three-Phase Four-Wire Converters for Distributed Generation, 45th International Universities Power Engineering Conference (UPEC), pp. -6,. [7] J.M. Guerrero, J. Matas, uis Garcia de Vicuna, M. Castilla, J. Miret, Decentralized Control for Parallel Operation of Distributed Generation Inverters Using Resistive Output Impedance, IEEE Trans. Ind. Electron., vol. 54. No., 7. Journal of Nonlinear Systems in Elect. Eng., Vol., No, Fall 3 39
16 9 D'& iue.3 &+ G<= & K ^ E 3 ; <= ;5 N?4@ J [8] Josep M. Guerrero, ijun Hang, Javier Uceda, Control of Distributed Uninterruptible Power Supply Systems, IEEE Trans. Ind. Electron., vol. 55, no. 8, pp , 8. [9] M. Illindala and G. Venkataramanan, Control of distributed generation systems to mitigate load and line imbalances, in Proc. 33rd Annu. IEEE PESC,, pp [] P. Hsu and M. Behnke, A three-phase synchronous frame controller for unbalanced load, in Proc. 9th Annu. IEEE PESC, 998, pp [] Y. i, D. M. Vilathgamuwa, and. P. Chiang, Microgrid power quality enhancement using a three-phase four-wire grid-interfacing compensator, IEEE Trans. Ind. Appl., vol. 4, no. 6, pp , Nov./Dec. 5. [] H. S. Song and K. H. Nam, Dual current control scheme for PWM converter under unbalanced input voltage conditions, IEEE Trans. Ind. Electron., vol. 46, no. 5, pp , Oct [3] W. C. ee, T. K. ee, and D. S. Hyun, A three-phase parallel active power filter operating with PCC voltage compensation with consideration for an unbalanced load, IEEE Trans. Power Electron., vol. 7, no. 5, pp , Sep.. [4] Tzung-in ee, Po-Tai Cheng, Design of a New Cooperative Harmonic Filtering Strategy for Distributed Generation Interface Converters in an Islanding Network, IEEE Trans. Power Electron., vol., no. 5, pp , 7. [5] Po-Tai Cheng, Chien-An Chen, Tzung-in ee, Shen-Yuan Kuo, A Cooperative Imbalance Compensation Method for Distributed-Generation Interface Converters, IEEE Trans. Ind. App., vol. 45, no., 9. [6] S.M. Dehghan, A. Ale Ahmad, R. ourakzadegan, M. Fazeli, M. Mohamadian, A. Abrishamifar, A High Performance Controller for Parallel Operation of three-phase UPSs Powering Unbalanced and Nonlinear oads, Power Electronics, Drive Systems and Technologies Conference (PEDSTC), pp ,. [7] Dipankar De and Venkataramanan Ramanarayanan, Decentralized Parallel Operation of Inverters Sharing Unbalanced and Nonlinear oads, IEEE Trans. Power Electron., vol. 5, no., pp , Dec.. [8] J. M. Guerrero, J. Matas,. García de Vicuña, M. Castilla, and J. Miret, Decentralized control for parallel operation of distributed-generation inverters using resistive output impedance, IEEE Trans. Ind. Electron., vol. 54, no., pp , Apr. 7. [9] J.C. Vasquez, J.M. Guerrero, M. Savaghebi, J. Eloy-Garcia, R. Teodorescu, Modeling, Analysis, and Design of Stationary-Reference-Frame Droop-Controlled Parallel Three- Phase Voltage Source Inverters, IEEE Trans. Ind. Electron., vol. 6, no. 4, pp. 7-8, Apr. 3. [] J.M. Guerrero, M. Chandorkar, T. ee, P.C. oh, Advanced Control Architectures for Intelligent Microgrids Part I: Decentralized and Hierarchical Control, IEEE Trans. Ind. Electron., vol. 6, no. 4, pp. 54-6, Apr. 3. [] Dipankar De and Venkataramanan Ramanarayanan, A Proportional + Multiresonant Controller for Three-Phase Four-Wire High-Frequency ink Inverter, IEEE Trans. Power Electron., vol. 5, no. 4, pp , April. [] Y. W. i, Control and resonance damping of voltage-source and current source converters with C filters, IEEE Trans. Ind. Electron., vol. 56, no. 5, pp. 5 5, May 9. Journal of Nonlinear Systems in Elect. Eng., Vol., No, Fall 3 39
17 D'& iue.3 &+ G<= & K ^ E 3 ; <= ;5 N?4@ J [3] Y. W. i, F. Blaabjerg, D. M. Vilathgamuwa, and P. C. oh, Design and comparison of high performance stationary-frame controllers for DVR implementation, IEEE Trans. Power Electron., vol., no., pp. 6 6, Mar Journal of Nonlinear Systems in Elect. Eng., Vol., No, Fall 3 39
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