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S , ( ( # ( * ( # ' # * # ( * * # ( ( # ( QCR * ' # QF D E JR , QKR ( ( , C C * , E is Ls Rs is + Ls Rs + + us iL - us uL - - C C * * , + %$ - %$ % * * - . PS . . ( C F , D K I D O C F D ic0= i0 ic0= i0 ib0= i0 i0 i a0= i0 3i 0 ia0= i 0 ib0= i0 C F , J ! * ( * ' * . , ( QGR . ( K * . CC . L ( C D ( . CC ( 3C C4 * C C 34 OQ34 C J34 G34 T CC34 J C T CD CD34 R G CC 3C C4 O K C5 O C F D 3C F4 ! . L i1+ i2 i1 i2 Cargas iguales C D , * . K 2.5 i1 2 i2 i1+i2 1.5 Corriente [A] 1 0.5 0 −0.5 −1 −1.5 −2 −2.5 0 0.005 0.01 0.015 0.02 0.025 Tiempo [s] 0.03 0.035 0.04 C E ( CF 34 OQ3 DL4 C J3 DL4 C G3 DL4 J G 3C D4 C C T CC CC3 DL4 T CD CD3 DL4 R > * . 3C D4 DL 3C C4 ) CC DL ( DL C G 34 O Q3 DL4 T C J3 DL4 T G3 DL4 J 3C E4 C C CD3 DL4 T R T CC CC3 DL4 T CD 2 3C D4 3C E4 ( 3C F4 ( , ( # CF C ( CF , C E ' T O * G ( * ( ( . * 9 . * . -- # QGR / ( * ( ( ( # * ! ( . 34 34 3 4 O L 3 4 * * # # O C 3C J4 , ( K ( ( ( CJ , ( . 34 O Q34 C G34 T C CC34 T C CD34 T R G is CC iF CD i C J , ( 3C K4 H 1.5 is i −iF 1 Corriente [A] 0.5 0 −0.5 −1 −1.5 0 0.005 0.01 0.015 0.02 0.025 Tiempo [s] 0.03 0.035 0.04 C K J ( K * ( C K 0 * ( ' " * ( > * * ( , C G34 ( ( * , ( * C G34 ( ( * 3C G4 0 O O 00T00 3C G4 I is(t) Ls Lf i(t) Ish Vh Zsh Z fh u(t) Ih Cf C G ( ( * ( O 0 0 T 0 3C H4 3C G4 0 O C 3C H4 ( 2 ( * 0 O L * O L , * * C H , ( 3C G4 ( O C O LCD O J > ( 0 0 O L * * * ( 0 O 0 , . ( * CL 5 4.5 4 3.5 L =0.12 p.u s Ls=0.1 p.u 2.5 h Z [p.u] 3 2 1.5 Resonancia paralelo 1 Resonancia serie 0.5 0 2 3 4 5 f [p.u] 6 7 8 C H * , ( ( ( *# . , ( - QF D H IR ( ( * . ( . . QF D CLR , ( ( * QCL CCR , C I ( * CC is iF i C I ( , C I ( * ( * ( * * * . . ( # ( ( QCLR & $'' ( )* " ' $ "" , ( . ! . * , ( ' ( . , ( * ! CF %( ( , * # ( 2 * & ( * & ( 2 * . * ' ( ( . + : . ( . + "!,,! ' $ ',% ( # ( ! 2 ( ( ! , # # . ( 2 ( . CD ! 2 ( ( + # ( 34 ( . ! 2 # * ( 2 ( * # ( ! 2 ( * ( . 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( ( * * 9 . # ( # , # ))) 3) ) ) 4 QCGR , . # . * . # " * " +, - # FC uF PCC_a PCC_b Ls iF + Carga No lineal us Red eléctrica F D ,( * "'( !!& $ '% , ( ( # 3"'(. "/ '& ( 4 % ( . 5* ( QFLR 2 . ( F D &+ !, ' # ' , -$! + # ( # ( * # ( * 3) - ) , 4 F E345 # ( * 3) ) , 4 F E34 ! # ' ( # ( * QFCR , * FF + Cdc Udc - + a b c Idc Ldc a b c + F E ) ( # ( * # . QFFR ( * @ 2 163 31 6 3 4 ( 163 # F E34 . ( * ( * ( # D ( , ( # * ( !& () * + # * * * ( . ( ( , * FD a a n n . F J ( * ( ( ( @ ' $% , ( * * ( QFD FER 2 F J ( +$0) ( ( ) F J34 +$0) ( # % ! * . ( # * F E34 QCCR 2 ( K +$0) ( / , 012+ FE a b c n a b c n + F K ( * n a b c F G +( * 2 * ( F K345 ( F K34 ( * F G * 3 ( 4 ! # * * * , # FJ - QFJ FKR &. !$ ' , -$! #!$ $ "' / !' $ !, ' # ( ( ( ( F H ( # , * ( * ' ( ' 3)'.- )- '- 4 ' ( * is iL PCC iF u , iL + U dc Control de tensión Control de corriente Generación de la referencia F H ( FK !, * ( 2 # # * (# 34 O 34 34 3F C4 ( * ( , " ' * * # * - ( # * QCC FG FH FI DLR ! * ( ( * * 34 O 34 34 3F F4 ! * * QDC DF DDR QFJ DE DJ DKR ( QDG DHR QDIR , * QFGR .. L # .$.7 * .. * 3 & 4 '5) 3 & %4 '5() FG , * # .$.7 ( - * !A QECR 3F D4 .. .$.7 4 3344 O F 3 D 34 34 3 CFL4 3 T CFL4 34 34 3F D4 3 CFL4 3 T CFL4 34 9 3F D4 ' * C F 34 T 3 CFL4 T 3 T CFL4 D F D 3F 4 3F T CFL4 3F CFL4 T OC OD FT F T F F 3F4 3F T CFL4 3F CFL4 F T OL 34 O D F T F F 34 O L 34 O 3F E4 3F E4 * ( .$.7 * .$.7 * 3' '.*. 4 QEF EDR , ' * ' QEER , # J ( * .. ' + * * + FH . * * !,! ) ) 2 ( # 2 ( * ! 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( 3) QFK JI KL KC KF KDR u aN + 2Udc Udc + Udc 0.5 Udc - a N 0 + 0.5 Udc - -Udc + Udc -2Udc - 0 5 + * D F +( E ( $ DG ( * ,. # +& " ' !$ ' !'! " ' #/ ),$ ) ! , ( ' * ' ' * * * ( ( &! ) % * %) -./0 3'8! ' 8 ! 4 ( QKCR * , ( * ( ' ' * * ' '8! 36.'8!. '8! 4 ( D D , ' * ' Señal de referencia Señal PWM + Señal portadora Comparador D D & ( * DH ' * ' ' ' 3)'8! ) ' 8 ! 4 3D C4 ' * # ' # # , )'8! ( C O # # 3D C4 1 $% , ' * ' ' * ( ' ( ' 3OC4 ( 3OL4 ' * ( ! * D C34 ' ( C $ C $ F $ D $ E ! ' ( L $ D $ E $ C $ F Tensión [p.u] 1 Referencia Portadora 0.5 0 −0.5 −1 Componente fundamental Señal de salida Tensión [p.u] 1 0.5 0 −0.5 −1 0 0.01 Tiempo [s] 0.02 D E & * O LH O CJ DI 1 0.9 0.8 Tensión [p.u] 0.7 0.6 0.5 0.4 0.3 0.2 0.1 50 650 750 850 1350 1450 1550 1650 Frecuencia [Hz] D J , ' * O LH O CJ , (# * 34 O % &' O C % &' O L 3D F4 , D E ' * # O LH * O JL " ' ' # O C * O O CJ O C 2 ( * ' ' * , D J ( QKLR . 3D D4 O * O O L F E K O C D J G 3D D4 3D E4 * . D K 1 $% 9 ( * ' * EL 2ft - fRef ft+ 2fRef ft-2fRef 2ft- 3fRef fRef ft- 4fRef ft ft +4fRef 2ft - 5fRef 2ft + fRef 2ft+ 3fRef 2ft+ 5fRef Frecuencia [Hz] D K , # ' * O LH O CJ ) D C , ( * ' ) D C ' ( T L , D G ( ' ( T L ( L ( ' * * * ' , ( ( D H ( ' > * ' ( 3D D4 O C D J G 3D J4 EC Tensión [p.u] ut uRef 1 0.5 0 −0.5 −uRef −1 Componente fundamental Tensión [p.u] 1 Señal sintetizada 0.5 0 −0.5 −1 0 0.01 Tiempo [s] 0.02 D G & * O LH O CJ 2ft-fRef 2ft - 3fRef fRef 2ft-5fRef 2ft +fRef 2ft + 3fRef 2ft+5fRef Frecuencia [Hz] D H , # ' * O LH O CJ 2 ) % 2 ( D C3 4 ' * * ' * D I34 ' ' EF Referencia a Referencia b Portadora Referencia c 1 (a) 0 −1 (b) 0.5 0 −0.5 (c) 0.5 0 −0.5 (d) 0.5 0 −0.5 (e) 1 0 −1 1 (f) 0 −1 1 (g) 0 −1 0 0.01 0.02 Tiempo [s] D I , !M& * 34 ' * 5 34 5 4 5 4 5 4 5 *4 5 4 * # ( ' * * # ' * ' * ' $ C $ E , ' $ C ' $ E # - !M& * D I3434 * # ( L # * D CL # * ED 2ft- fRef ft + 2fRef ft-2fRef 2ft + fRef 2ft+3fRef 2ft - 3fRef fRef ft+4fRef ft- 4fRef Frecuencia [Hz] D CL , # ' * O LH O CJ &!! ) 1 ( : 0 A CIHH QKER ! * * , ( QJLR ( * ( F 34 O D Q T T R O 34 T ( 34 1 SA a 0 Udc 2 1 N SB b 0 1 Udc 2 SC c 0 D CC +( * 3D K4 EE ) D F ) ( , 2 C C L L L C L C 20 L C C C L L L C 2 L L L C C C L C L KL CFL CHL CFL KL L L C CFL D CC ( * D CC H ) D F ) D F D CF34 ( KL ( 3 4 2 D CF34 ! ( # ( ( C & O C ½ ! & T C ½ ¾ ½ !! & T C ½ ¾ " !! " !!! & 3D G4 9 3D G4 O ! T !! T " !! " !!! O 3D H4 ( EJ III II Región 2 II Región 1 Región 3 * VII IV I VIII II Región 4 Región 6 I VII I V VI Región 5 " 6 + D CF ) & ( O ) D F D CF34 3D H4 F C F 3KL 4 3)4 O T D L D 3KL4 3)4 ) ( + O F 3)4 3D I4 3D CL4 O F 3KL )4 3D CC4 * - ' * ) D D EK ) D D 2 ( 2 ÎÁÁ Á ÁÁ ÎÁÁÁ ÁÁ Á ÎÁÁ ¼ ¼ ¼ ) ( ( , . ( . ( E , CK ( ( * QFKR QKJR ( . ( * ( ( , * * .. ( L - ( QJL JD KC KE KK KG KH KIR ++ " ' !$ ' !'! " ' #/ ),$ !!' ' * 2 . (# EG yRef e + u Regulador inversor + Sistema eléctrico y - D CD , . . ( ( D CD ' % * ' * * ' * ( ' , 3!+4 3)- 4 3 4 QCG JFR ( , ( . && 2 , ' ' * ( ' 2 # * ( . QCGR O 3* *4 3* *4 + 3D CF4 D CE , ( * EH yRef u error + - -h h y D CE i 5 +h Ref 4 Corriente [A] iRef−h 3 2 u/K 1 0 −1 0 0.001 0.002 0.003 0.004 0.005 0.006 Tiempo [s] 0.007 0.008 0.009 0.01 D CJ , O LJ (# , D CJ * , * ' ( * , ' * *# ,. * & 3& ! 4 6-.6- ( D CK ( O L QJD JF GLR 2 % , L % + L EI fsw yRef + u error y Muestreador bloqueador de orden cero D CK & &&! .%' -.0 , ' ( * - ( . !M& QJD EHR 34 O %34 T %34& 3D CD4 QGC GFR ( , * , # * ( D CG !+ ' ' ' ( , # 2 ' * D CH34 D CH34 > * ( ! ( JL Kp yRef + u error Ki y D CG , !+ e(t) u(t) 1 3Kp Acción PI 2Kp Sólo Proporcional Kp t / Ti 2T i t 7 D CH !+ &&& % + ' % ) - 0 , ' 2 ( # # TC QGDR D CI 2 QC T - T - T - R*34 O Q! T ! - T !- T T !$ -$ R34 3D CE4 - 2 * . ' JC yRef error + - u y D CI , * . O Q*34 * 34R 3D CJ4 ! . # /. O L /34 ' * 3D CK4 ( 3D CK4 % & %& /. O FQ*34 * 34R /*34 O L /34 /34 O L 3D CG4 2 ( * # ' ' * ( D FL 9 3D CE4 *34 O *3 C4 *3 4 T ! 34 T T !$ 3 4 3D CH4 * *34 O * 34 . ' C 34 O Q* T *3 C4T T *3 4 ! 3 C4 !$ 3 4R 3D CI4 ! > 3D CI4 ! !$ 5 ( ' * ( ' QCGR JF y y Ref Error( k-1) Error( k-2) y k-2 k-1 k D FL ,( OF , ( * QJF GE GJR ( * +. !$ ' $ !'! ' , -$! ' 2 #!$ $ ! * ( ' * 2 D CD ( . D FC ( ( * * ( # # # F ( * # , ( ( * JD U dc 2 iRef error + - L Control lineal PCC o iF(t) No lineal us(t) iF -Udc 2 D FC ,( * ( . , ! . 3!4 ! 34 ( ' 34 ( D FF ( 34 & 34 O ' 34 34 & 3D FL4 . ( . &, ) -0 , & 3&4 O L * , ( ( , . & 34 O 34 & 3D FC4 JE + Udc 2 - L PCC N Udc 2 + uinv (t) iF(t) us(t) - D FF * ( ( ! # ( T 34 O O T U T 3 4 3 T 4 34 O U 3D FF4 3D FD4 U > 3D FF4 # ( ( ( ( D FD ! ( ! ( ( ( # * : ( ( * ' ( ' JJ iF iF t1 t 1+tsw t t1 + t 1+tsw t + D FD ,( ( & * ! ( ' &,! . , ( ( * ( # ' . * * ! D FE ( * !+ * ( ' 3D FE4 ' O 3 4 T 3 4& 3D FE4 , !+ ' ( ( JK Señal PWM iRef error + - Udc 2 PI uinv + -Udc 2 iF Comparador Señal portadora D FE !+ ( &,& , ' ' ( # 3D FL4 . 34 O 3' 34 3 34 3D FJ4 3D FJ4 * QGKR O ( ½ ( ½ ' 3 T C4 O F Q 3 T C4 34R 34 T 3 T C4 T 34 ' 3D FK4 3D CG4 3 T C4 O 3 T C4 3D FG4 ( ' 3 T C4 O F Q 3 T C4 34R 34 T 3 T C4 T 34 ' 3D FH4 2 ! T C 3 T C4 34 , ( 3!M&4 D FJ ( V' 34 JG Tensión (V) tup uinv (k) tk tk+1 t Tsw D FJ ( ( T C ' 34 O V' 34 O ' 3 T C4 3D FH4 V' 34 O Q 34 34R T 34 3D FI4 9 . ( * * , * ( # ' , & 0 6 &00 , ( ( D FJ ( V' 34 O 3 4 O 3F 4 F 3D DL4 3D FI4 3D DL4 ( O Q R T T F 3D DC4 JH iF iF iRef k tup iRef Error k+1 T sw 6 . k k+1 T sw 62.2 D FK 2 * , D FK * * D FK34 D FK34 , ( &00 , * # +0 ",'" %#!" , * )* ( ( D FF , )* , 2 * * JL " # ( FDL : JI * FDL 34 O F 3CLL04 : D 3D DF4 , ( * ! QFCR D D 3D DD4 EHG I : 3D DE4 F ( 2 O JLL : , + & , . # . ( & U O C T F F 9 3D DJ4 ( 3D DJ4 U O EDGH 3D DK4 3D DK4 * * D FG 2 ( * ( 3 4 ( * ( , ( FL " KL fsw=5 kHz f =10 kHz 7 sw f =15 kHz sw 6 f =20 kHz 5 F sw F i (t+T )−i (t) [A] sw 4 3 2 1 0 0 0.005 0.01 0.015 0.02 L [H] 0.025 0.03 0.035 0.04 D FG ,* ( ( * * &3 4 % 2 * * 4 *% * IL , * ( ( * * 34 O EJ 3CLL0 IL4 3D DG4 4 *% $ * J G * * 34 O J3CLL04 G3CLL04 3D DH4 KC $ ! ( * . 3D DI4 . * U34 O 34 34 3D DI4 , ( ' * 3D EL4 C U O Q 34 34R & 3D EL4 &3! ) *% + ' * ' 3D DG4 * CL A" ( D FH & > . # ( # D FH ! . U$) O FFH ( U O LIK - ( ( * FL A" D FI ! ( . U$) O CCEH ( U O LEHD ( . JL W * CL A" KF Tensión [V] 200 uinv usa iF iRef 0 −200 Corriente [A] 5 0 −5 0 0.002 0.004 0.006 0.008 0.01 0.012 Tiempo [s] 0.014 0.016 0.018 0.02 D FH % & * O CL A" Tensión [V] 200 uinv usa iF iRef 0 −200 Corriente [A] 5 0 −5 0 0.002 0.004 0.006 0.008 0.01 0.012 Tiempo [s] 0.014 0.016 0.018 0.02 D FI % & * O FL A" *% $ ! * 3D DH4 * FL A" KD Tensión [V] 200 uinv usa iF iRef 0 −200 Corriente [A] 4 2 0 −2 −4 0 0.002 0.004 0.006 0.008 0.01 0.012 Tiempo [s] 0.014 0.016 0.018 0.02 D DL % & * O FL A" * ' * ( D DL , . U$) O CCF ( U O LEE &3& ) ) . * QEHR C . ' ( ! ( O LLLLK !+ ( ' ' * CL A" KE Tensión [V] 200 uinv usa iF iRef 0 −200 Corriente [A] 5 0 −5 0 0.002 0.004 0.006 0.008 0.01 0.012 Tiempo [s] 0.014 0.016 0.018 0.02 D DC % !+ * O C O LLLLK O CL A" *% , ( ' * & * FL A" ( D DC , . ( U$) O LH ( U O LFDFG , D DF ( ( > & ! * *% $ , ( * D DD !+ ' * ( * > KJ 6 6 iRef iF 4 4 2 2 Corriente [A] Corriente [A] iF 0 0 −2 −2 −4 −4 −6 0 0.002 0.004 0.006 0.008 0.01 0.012 Tiempo [s] 0.014 0.016 8 ( 8 ! 0.018 0.02 iRef −6 0 0.002 0.004 0.006 0.008 0.01 0.012 Tiempo [s] 0.014 0.016 0.018 0.02 8 ( 8 ! D DF % !+ ( uinv Tensión [V] 200 usa 0 Corriente [A] −200 iF 2 iRef 0 −2 0 0.002 0.004 0.006 0.008 0.01 0.012 Tiempo [s] 0.014 0.016 0.018 0.02 D DD % !+ * O C O LLLLK O CL A" * & FL A" ! . U$) O LHJIJ ( U O LFKLC KK &3, -0 ) +$0) 3D DC4 * CL A" *% D DE * * * CL A" & FL A" !+ CL A" ( ) D E ! . U$) O LDJ ( U O LCKH , . * ( ! * ( u Tensión [V] u inv 200 sa 0 −200 Corriente [A] 5 i F i Ref 0 −5 0 0.002 0.004 0.006 0.008 0.01 0.012 Tiempo [s] 0.014 0.016 0.018 0.02 D DE % * O CL A" KG ) D E ( * * !$) "#$ % % & ! "#$ % ' (% Tensión [V] 200 uinv usa iF iRef 0 Corriente [A] −200 2 0 −2 0 0.002 0.004 0.006 0.008 0.01 0.012 Tiempo [s] 0.014 0.016 0.018 0.02 D DJ % * O CL A" *% $ * ' * * ( D DJ ) ) D J & !+ D DK ( ' * , O DL CJ ( ' O KL * * KH ) D J ( * * !$) "#$ %&)& (' ! "#$ ( )% 8 iF i 6 Ref Corriente [A] 4 2 0 −2 −4 −6 −8 0 0.01 0.02 0.03 0.04 Tiempo [s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ed eléctrica pp pp +pq Carga perturbadora pq Compensador E C 0 ! ( ( ( , ( # # * ( 34 O 34 T 34 3E C4 ( ( ( ( 34 O 34 3E F4 E C - * , *# ( ( ( " : GJ * # * * # * .& %# " )"' $" !1" ' !(4 5 ,66$4 ( # )!7 , # ( * ( , ( ,! "45 , # * * QHER ( V34 34 O 34 3E D4 ( ( ( > 3E D4 ( 9 ( 2 ( 34 O 3E E4 ( , 2 O 34 O 34 O 34 34 3E J4 ( GK ,!! $ "45 %' ' )**5 , * . * 0 QHJ ILR CIJL 0 ( ( ( ' 3E K4 ( 3E G4 3E H4 , ( ( F # 34 O 34 O & 34 5 34 O 34 O & 34 & & C & O 34& O & C & O 34& O ¼ ¼ ¼ 3E K4 3E G4 ¼ & 3E H4 # 3 * PLS * ( ! ( 34 O & & 34& 34 O 34 34 3E I4 ( ( ( ( C O ¼ ¼ 34& 3E CL4 - ( ( ( ( ( . # ( ( * ' , ( * *& 34 O 34 O 2 34 & & 3E CC4 GG * * ( . 34 O 34 O 2 34 34 O 34 34 O 34 34 3E CF4 3E CD4 * 34 ( ( ( ( QHJR ( O 2 3E CE4 ,!& % "45')**5' %6 -"0 A QHJ IL ICR 0 CIKF , 3E CF4 ( 2 4 ( 34 O 3344 34 O 434 34 3E CJ4 0 * * & O *& T '*& T ' '+ *& O *& T *& ' + ' + 3E CK4 ( ( ( # * ( < *& ( *& ( '*& GH ( , 3E I4 34 O & & 34 34 O & & & & & 34*& 34 34*& 34 O L 3E CG4 3E CH4 , ( ' 0 A ( * ( ( ( : 34 O 34 34 O ' 34 T 34 3E CI4 ( ( ,!, ) $ - 2 E F34 ( 34 O F 34 : 34 O F 3 CFL4 : 34 O F 3 T CFL4 : O F0 O JL " 3E FL4 GI 2 2 ub(t) u (t) a u (t) c 1.5 1.5 1 1 i (t) i (t) Corriente [A] Tensión [V] 0.5 0 −0.5 0.5 0 −0.5 −1 −1 −1.5 −1.5 −2 0.02 0.022 0.024 0.026 0.028 0.03 0.032 0.034 0.036 0.038 0.04 iLc(t) Lb La −2 0.02 0.022 0.024 0.026 Tiempo [s] 0.028 0.03 0.032 0.034 0.036 0.038 0.04 Tiempo [s] + E F ) ( ( JL " * ( O C FJ DL X . 3E FL4 3E FC4 E F34 34 O L H F 3 DL4 34 O L H F 3 CJL4 34 O L H F 3 T IL4 3E FC4 2 ( ( * ) * ( ( # * ( E D > E D34 ( * * * ' , * ( * , , E D34 * HL 1.5 a iLa(t) 2.5 Potencia instantánea [W] 1 Magnitud [V,A] 3 u (t) i (t) 0.5 sa 0 −0.5 −1 ps(t)=pL(t) 2 1.5 1 0.5 p (t) C 0 −0.5 −1.5 0.02 0.022 0.024 0.026 0.028 0.03 0.032 0.034 0.036 0.038 0.04 −1 0.02 0.022 0.024 Tiempo [s] + 0.026 0.028 0.03 0.032 0.034 0.036 0.038 0.04 Tiempo [s] % E D % ( 2 ( * * CFL # $ - 5 ! * * . 3E FL4 E E 3E FF4 D 34 O 34 O F 34 O L F 3 DL4 3E FF4 2 ( * E J34 ! E J34 HC 1.5 1 iLa(t) iLc(t) Corriente [A] 0.5 0 i (t) Lb −0.5 −1 −1.5 0.02 0.022 0.024 0.026 0.028 0.03 0.032 Tiempo [s] 0.034 0.036 0.038 0.04 E E * 1.5 5 i (t) isc(t) sa Potencia instantánea [W] 1 Corriente [A] isba(t) 0.5 0 −0.5 −1 −1.5 0.02 0.022 0.024 0.026 0.028 0.03 0.032 0.034 0.036 0.038 0.04 4 3 ps(t)=pL(t) 2 1 pC(t) 0 −1 0.02 0.022 0.024 Tiempo [s] 0.026 0.028 0.03 0.032 0.034 0.036 0.038 0.04 Tiempo (s) % E J % ! ( E K 0 # * * > * , ( HF 0.8 5 i (t) Corriente [A] i (t) i (t) sa 0.4 Potencia instantánea [W] 0.6 sc sb 0.2 0 −0.2 −0.4 pL(t) 3 p (t) s 2 1 0 p (t) C −1 −0.6 −0.8 0.02 4 0.022 0.024 0.026 0.028 0.03 0.032 0.034 0.036 0.038 −2 0.02 0.04 0.022 0.024 0.026 Tiempo [s] 0.028 0.03 0.032 0.034 0.036 0.038 0.04 Tiempo [s] % E K % ( $ - 5 , ' * * FJL " E G . # 3E FD4 i (t) i (t) La iLc(t) Lb 1 Corriente [A] 0.5 0 −0.5 −1 0.02 0.022 0.024 0.026 0.028 0.03 0.032 Tiempo [s] 0.034 0.036 0.038 0.04 E G * 34 O FQL H 3 DL4 T L LH 3J T DL4R 34 O FQL H 3 CJL4 T L LH 3J T CJL4R 34 O FQL H 3 T IL4 T L LH 3J IL4R 3E FD4 HD 1.5 2.5 1 Potencia instantánea [W] ua(t) i (t) Magnitud [V, A] La 0.5 i (t) sa 0 −0.5 −1 −1.5 0.02 0.022 0.024 0.026 0.028 0.03 0.032 0.034 0.036 0.038 2 1 0.5 p (t) C 0 −0.5 0.02 0.04 ps(t)=pL(t) 1.5 0.022 0.024 0.026 Tiempo [s] 0.028 0.03 0.032 0.034 0.036 0.038 0.04 Tiempo [s] E H % 1.5 3 Magnitud [V,A] 1 iLa(t) i (t) sa 0.5 pL(t) 2.5 Potencia instantánea [W] ua(t) 0 −0.5 −1 ps(t) 2 1.5 1 pC(t) 0.5 0 −0.5 −1.5 0.02 0.022 0.024 0.026 0.028 0.03 0.032 0.034 0.036 0.038 0.04 −1 0.02 0.022 0.024 0.026 Tiempo [s] 0.028 0.03 0.032 0.034 0.036 0.038 0.04 Tiempo [s] E I % ( E H ( E I ( * ( ( * , E I34 ( * ( * HE * ' * . , E I34 @ , ( ( $ - 5 E CL 3E FE4 3E FL4 " % 7 7 ( 7 % & 7 $ # " % & 7 7 % 7 % & 7 & $ # " % 7 ) 7 ( 7 % & ) $ # 8 > 3E FE4 * JL " ( JL " FJL " 1.5 i (t) i (t) La Lb 1 Corriente [A] 0.5 iLc(t) 0 −0.5 −1 −1.5 0.02 0.022 0.024 0.026 0.028 0.03 0.032 Tiempo [s] 0.034 0.036 0.038 0.04 E CL * HJ 3 1.5 isb(t) sa Corriente [A] 1 ps(t) p (t) L isc(t) 2.5 Potencia instantánea [W] i (t) 0.5 0 −0.5 −1 2 1.5 1 p (t) C 0.5 0 −0.5 −1.5 0.02 0.022 0.024 0.026 0.028 0.03 0.032 0.034 0.036 0.038 0.04 Tiempo [s] −1 0.02 0.022 0.024 0.026 0.028 0.03 0.032 0.034 0.036 0.038 0.04 Tiempo [s] % E CC % ! ( E CC ( * ' ( * $ ! ( * * ' ( E CF , ' ( * * ' ' ' ' 3E FJ4 3E FK4 " 7 7 7 % & 7 % $ 9 " 7 7 & 7 % & ( $ 9 " 7 7 ) 7 % & 7 ( $ 9 8& HK 1.5 1.5 1 1 u (t) u (t) u (t) b i (t) c Corriente [A] Tensión [V] a 0.5 0 −0.5 i (t) i (t) La 0.5 Lc Lb 0 −0.5 −1 −1 −1.5 0.02 0.022 0.024 0.026 0.028 0.03 0.032 0.034 0.036 0.038 0.04 Tiempo [s] −1.5 0.02 0.022 0.024 0.026 0.028 0.03 0.032 0.034 0.036 0.038 0.04 Tiempo [s] + E CF ) " % 7 % 7 & 7 ) 7 & ' $ # " % & 7 % 7 7 & 7 ) 7 & ' $ # " % 7 ) 7 % 7 & ) 7 & ' 7 $ # 8( O F0 O JL " ! * E CD34 ( E CD34 , # ' * 2 ( ( # * * ' QFG IF IDR HG 1.5 1.5 1 1 i (t) sa 0.5 sc Corriente [A] Corriente [A] i (t) i (t) sb 0 −0.5 i (t) isc(t) sb 0 −0.5 −1 −1.5 0.02 isa(t) 0.5 −1 0.022 0.024 0.026 0.028 0.03 0.032 0.034 0.036 0.038 0.04 −1.5 0.02 Tiempo [s] 0.022 0.024 0.026 0.028 0.03 0.032 0.034 0.036 0.038 0.04 Tiempo [s] E CD % .+ %# " )"' $ !1 ' $ #/ ! " # * ( * * A CIED .. L ( ( QELR * A CICH QIER * A * ( ( ( , * A ' 3E FG4 ' 34 O F 34 D 34 34 34 C L 34 3E FG4 2 * F O D C L 3E FH4 HH < ( ( 3E FH4 F C O D L 3E FI4 , # ( C ( 3E FG4 O O 3E DL4 T T O T T 3E DC4 ! 3E DL4 * , O T T O T T 3E DF4 , 3E DF4 . # ( $ * A N8 > CIHD QEJ IJR ( + * * * * * , # $ ( E CE O 3E DD4 HI u xi u i Plano real i u u xi E CE ( ( . *# 2 O T 3E DF4 * $ ( +( 3E DD4 * O 3E DE4 O T 3E DJ4 ( ( < ( ( O O T T 5 O 5 O T 3E DK4 3E DG4 T IL Red eléctrica p,q ps =p qs =0 i ,i is , is Carga iC , iC p c =0 q c =q u ,u i ,i Compensador E CJ 0 # $ , 3E DK4 3E DG4 * O T O T T T T T T T 3E DH4 , 3E DH4 3E DD4 $ * $ ! 3( E CJ4 O O TC O T L 3E DI4 3E EL4 ,& % * % ! * A QEJ IJR * # . IC + O . . 3E DD4 ( O L L L L O C T L ¾ ¾ ¼ L L L 2 * , 3E EC4 3E EF4 , O T O T T 3E ED4 ! O C T L ¾ ¾ ¼ L L L T O L 3E EE4 3E EJ4 # O O O O 3E EK4 C 3 T 4 T C O 3 T 4 T 3E EG4 3E EE4 ( 3E EG4 O O IF 3E EG4 ( * * O , L T 3E EH4 3E EH4 2 . ( ( 9 M QHGR5 > >A )8 QHHR 3E EH4 . # $ QHHR # $ # $ ,&! + , CIIJ > >A )8 QHHR * ( # $ * , ( # , O L L L 3E EI4 0 QIJR * ( ID C Q3 T 4 R T T C O Q T 3 T 4 R T T C O Q T 3 T 4 R T T O 3E JL4 ( 34 O 34 T,3T4 34 ¼ 3E JC4 3E JL4 ( ¼ 34 ( * ( ,34 2 ( 3E JL4 3E EG4 * # $ * O L # $ * , 3E JC4 3E JF4 34 O 34 T T 34 ¼ 3E JF4 ( * ( - 3E JF4 * ( 9 QIC IDR ,&& 7 % )# # $ ( E F E IE ua isa iLa La Ra ub isb iLb Lb Rb isc iLc Lc Rc uc iLn isn iCa iCb iCc iCn Carga Compensador E CK , # $ # $ Y , 3E EH4Y $ Y, 3E JC4Y , * QIJR * * ( E CK ' 3E JD4 3E JE4 * * 34 O CCJ F 34 : 34 O CCJ F 3 CFL4 : 34 O IF F 3 T CFL4 : 3E JD4 O CLK X O O CDF X O DDK " O O EFL " 3E JE4 ! ' * E CG , ( . E CG34 E CG34 2 E CG34 ( IJ 200 usa(t) u (t) sb 150 u (t) isa(t) sc 150 i (t) i (t) sc sb 100 u (t) Corriente [A] Tensión [V] 100 0 50 0 −50 50 isn(t) 0 −50 −100 −100 −150 −200 0.02 0.025 0.03 0.035 0.04 0.045 0.05 0.055 −150 0.02 0.06 0.025 0.03 Tiempo [s] 0.035 0.04 0.045 0.05 0.055 0.06 Tiempo [s] + E CG ) * 150 150 Corriente [A] isb 50 100 isc Corriente [A] isa 100 isn 0 −50 −100 −150 0.02 isa isb isc isn 50 0 −50 −100 0.025 0.03 0.035 0.04 0.045 0.05 0.055 0.06 Tiempo [s] −150 0.02 0.025 0.03 0.035 0.04 0.045 0.05 0.055 0.06 Tiempo [s] ; ; % % # E CH # E CH ( * # . ( E CI , * # , # A * QIJR IK 6 a b c 4 Corriente [A] 2 0 −2 −4 −6 0.02 0.025 0.03 0.035 0.04 Tiempo [s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ed eléctrica is PCC iL Carga no lineal iF Filtro activo J C , ( . * * 3 * 4 * * * ! , ( ( * * ' , ( * * * ' , ( ( * ( * * * ( * C , * ( * , * * ' F ( ' CLJ u(t) 1. Sistema Adaptativo . Filtrado de la tensión . + uf (t) 2. Sistema de estimación de potencia . iRef (t) 3. Estimación de la corriente de referencia . iL(t) J F , D , * ( * ( ( J F 2 ( ( ( , ( ' . * * 2 ( * * * ! ! ' ( 2 * * ( * * ' * * # 0+ " % '#8 $! ' 9$% ! "/ ' (5 ( CLK # ( , ( ( QCFER ! ( N +( * ' * * * ( ! N ' * * * , - # , ' * * . , N ' , ( J D , ( N % ( ( * ' ( , * * ' Filtro de Kalman Resonante f, x d y(t) x'=Ax+ Bu y =Cx+Du Entrada Filtro resonante x(t) Filtro de Kalman J D , N % Salida CLG 3& 8 ' *34 . * *34 O # "'3 T 5 4 T 6 34 3J C4 # 5 * * ( , 6 $ ( 7' ' 34 ' * * * # * ' * 34 O # Q T 5 R 3J F4 < * 34 O # Q T 5 R 34 O # Q T 5 CFLR 34 O # Q T 5 T CFLR 3J D4 3&! ) + , * ( J E 34 & 34 O 34 T &34 T C & 3J E4 34 O 634 O C 334 T T 3J J4 ( 9 * 3J E4 * , * 3J J4 ( O O C ( . O O C * L ( J J CLH L R C + u i J E % Y [p.u] 1 0.5 0 100 Fase [º] 50 0 −50 −100 0 1 2 3 4 5 f [p.u] J J % * * 3J K4 * J K O O 3J K4 ! * ( ( LGLG C 3J G4 3J H4 C * O C T F FC 3J G4 CLI 1 0.9 0.8 0.7 Y [p.u] 0.6 Q=1 0.5 0.4 Q=2 0.3 Q=3 Q=4 0.2 Q=5 0.1 Q=6 0 0 1 2 3 f [p.u] 4 5 6 J K +@ * O O 3J H4 > * * * * * O FC CF 3J I4 * ( O C O C 2 ( J G ( * ( * ( ' . * * F 3J K4 ( . ( - ( CCL 1 Q> Q=1 k =1 L 0.6 Imaginario 0.4 0.2 Q=6 kL=0.166 kL< 0.8 Q=0.6 k =1.66 L Q=0.5 k =2 L 0 −0.2 −0.4 Q=0.6 −0.6 Q=1 −0.8 Q=6 −1 −1 −0.8 −0.6 −0.4 −0.2 0 Real 0.2 0.4 0.6 0.8 1 J G ! 34 * ( O C O C ( ( O 3J CL4 F F , * & > & , ' ( , ( ( ' 5 ( ( . $) ( # $ ! $ ( , ( ( ( ( ' N ' . 3J J4 * 3 O * * O ! T ! - T - T - ( ½ ( ½ 4 3J CC4 CCC ! O F F ! O E T F T O 3J CF4 O F H O E F T C # 3&& " 9 % 8 : , N ( N ' 5 - ( ( C T C QCFJR N ! * QCFE CFKR + +Z O + 3J CD4 CCF ( O 3J CE4 $ N 734 O 348 34Q834348 34 T *34R /34 +Z 34 O +Z 34 T 734Q/34 834Z+34R 3J CJ4 3J CK4 ( 34 O Q 734834R34 3J CG4 ! ! +Z 3 T C4 O %3Z+344 3J CH4 ! ( 3 T C4 O 3434 34 T 934 3J CI4 3J CD4 3J CI4 N 3J FL4 3J FC4 +3 T C4 O :34+34 T ;34 /34 O 834+34 T 34 3J FL4 3J FC4 +3 TC4 ( TC5 :34 +3 T C4 +345 834 ( 5 ;34 ( ( ( CCD J H ! N 34 ( , ( 3J FF4 , ( ( J H 8 QR 8 Q66 R 8 Q R 8 Q6 R O O O O 8 Q6R O L 3J FF4 L % 3J CH4 3J CI4 ( : 3J FL4 . N , ,. N % 3J CH4 CCE T C 3J CI4 O //%3+4 & 3J FD4 - * 2 < $% , ' * . 3J F4 N , ( ' , , , . N 9 3J F4 & T 3& T 4 O # 3 3& T 4 T 5 4 3J FE4 O # 3 & T 5 4 3 4 # 3 & T 5 4 3 4 > 3J FE4 3& T 4 * ' ' & , ' * ( ( 3& 4 O # 3 & T 5 4 3J FJ4 3& 4 O # 3 & T 5 4 3J FJ4 CCJ 9 3J FJ4 3J FJ4 . ( * # O 3& 4 T 3& 4 3J FK4 3 & T 5 4 O 33& 44 3J FK4 & - ( . 3J FG4 O 3 4 3 4 3 4 3 4 :34 3 T C4 3 T C4 34 34 3J FG4 :34 O 3 4 3 4 3J FH4 3 4 3 4 ! ' & ! /34 O C L " 34 34 T ( 34 3J FI4 2 * ( 3 T C4 O 34 3 34 4 34 3 34 4 3 T C4 O 34 334 4 T 34 3 34 4 3J DL4 3 T C4 O 3C 94 34 -34 O 34 T 634 34 , 9 9 L 3# 9 C4 QCFJ CFGR 3J DL4 T C , N CCK * . N * % #$ '$ 3 4 3 4 ( % % O $ 3 4 T 3 4 $ & 3C 94 ) 3J DC4 / ) : O : O 3 4 : O : O 3 4 : O 3 3 4 T 3 44 : O 3 3 4 3 44 : O : O L : O 3C 94 8 ! 8O C L L " 3J DF4 3J DD4 2 < % $ $ ' ' * QIER ' * . * ( ( - 34 O 34 T 34 T 34 34 O 34 T 34 T 34 34 O 34 T 34 T 34 3J DE4 O 3 4 T 3 4 T 34 O 3 4 T 3 CFL4 T 3 T CFL4 O 3 4 T 3 T CFL4 T 3 CFL4 3J DJ4 3J DE4 * 3J DJ4 CCG O T ) ( * 2 O 34 O 34 O 34 O 34 3J DK4 34 34 34 34 34 34 C L C L /34 O O 3J DG4 34 34 T 34 34 34 ( ( / * O O O O T T 9 3J DG4 # 34 34 O L D 3 4 34 T 34 D 34 3J DH4 D L 34 3J DI4 ) * * 3J FG4 CCH 3 T C4 3 T C4 : O 3 T C4 L 3 T C4 3 4 L 34 : 34 3J EL4 34 : 3J FH4 * . N #$ '$ $$ 3 4 3 4 $$ $% 3 4 T 3 4 $( % O $ 3 4 3 4 $ $$ 3 4 T 3 4 $$ $& $) 3C 94 8O L D L D L L ( 3J EC4 3J EF4 3&, " 9 % 8 : ! ( . ' ! * J D F N , * 3J K4 ( ' * ( ( ' ( . ' ' 2 ( N ' CCI . N 3& 4 O # %. 3J ED4 # ; * ' . ! 3J ED4 3J EE4 3& T 4 O # %. %. O 3& 4%. 3J EE4 3J EE4 * 3J DC4 3J EC4 * * ( 3J DD4 3J EF4 ! 8O C L L C 8O L " L C D L D L C 3J EJ4 3J EK4 - ( ( J I 2 ( . ( ! ( # ( CFL kL-max k L-min t xd umbral t td J I : * * (( . ( U 2 # ( ( ' ( U ( ( * 3&3 7 % + 9 , N 3N%4 * ' &?2A 2 N% * > ( CFC ( C , ' F ,. * ' D ,. * ' E ,. * * ' * ) J C ! $ 3J K4 O K FH , ( # ) J C ! N $ $) ; Q R CLL< JL KLLLL J L LF 1$ $ < $ ' ' 3J EG4 34 O O F0 O JC " 34 L + LJ LJ 34 LJ C 3J EG4 , * * , J CL ( * # ' * ' , # 3J FK4 CFF 2 55 f u A 54 f 1.5 53 52 Frecuencia [Hz] Tensión [p.u] 1 0.5 0 51 50 49 48 −0.5 47 −1 46 −1.5 0 0.5 Tiempo [s] 1 45 0 0.5 Tiempo [s] 1 J CL % C % , ' * (# F " * JL " JC " J CC 52 festimada f 51.5 real Frecuencia [Hz] 51 50.5 50 49.5 49 48.5 48 1 1.5 2 2.5 Tiempo [s] 3 3.5 4 J CC % * (# F " CFD ( F * JL " # ( * JC " , ( . L CF " O F EIGJ , ( 1+ $ %$ < ! . * ' ' * 3J EH4 #$ % # 34 O $ & # L++ 3J EH4 ++ # ' ( O FL C LJ J CF 1.5 Modo normal Modo acelerado 1 Tensión [p.u] 0.5 0 −0.5 −1 −1.5 0.4 0.45 0.5 0.55 0.6 0.65 Tiempo [s] J CF % * CFE 1.5 Señal filtrada Estado detector Señal cuadrada 1 Tensión [p.u] 0.5 0 −0.5 −1 −1.5 0.4 0.45 0.5 0.55 0.6 0.65 Tiempo [s] J CD ,( ' JLL F * ' ( ( , D ( ! J CD ( , LLF * 2 ( ( ( . 1+ $ %$ < , - , ' . # ' 34 O L L + LC F 3 4 T LC F 3J T CHL4 T ,34 LC 3J EI4 O F0 O JL " , 34 ' ( 7' O LLC CFJ 2 1.5 Tensión [p.u] 1 0.5 0 −0.5 −1 −1.5 −2 0.1 0.12 0.14 0.16 0.18 0.2 0.22 0.24 0.26 0.28 0.3 Tiempo [s] J CE 2' D 3J EI4 * * 5 * J 5 ' ( J CE Modo normal Modo acelerado 1.5 1 Tensión [p.u] 0.5 0 −0.5 −1 −1.5 0.1 0.12 0.14 0.16 0.18 0.2 0.22 0.24 0.26 0.28 0.3 Tiempo [s] J CJ % ' D CFK J CJ > O LC ' * , ( * ' 1+ $ 5 % %, $ < % 5 - , ' * * 34 O FQ3 4 T LEJ 3 T FL4 T LF 3J T CHL4R 34 O FQ3 CFL4 T LEJ 3 T CEL4 T LF 3J KL4R 3J JL4 34 O FQ3 T CFL4 T LEJ 3 CLL4 T LF 3J T KL4R O F0 O JL " 3J JL4 * * ( * * ( J 2.5 ua ub uc 2 1.5 Tensión [p.u] 1 0.5 0 −0.5 −1 −1.5 −2 −2.5 0.08 0.1 0.12 0.14 0.16 0.18 0.2 Tiempo [s] J CK 2' * E CFG ua 1.5 ub uc 1 Tensión [p.u] 0.5 0 −0.5 −1 −1.5 0.08 0.1 0.12 0.14 0.16 0.18 0.2 Tiempo [s] J CG 2' E 3 4 ' 3J JL4 LC ( J CK ( ' J CG * * 0. " % ' "% ' $ # 8 !! #% ' ! : ! - ( ' * * ( ( J CH ! * # ( QGIR , # ( 0 * ( ( 34 34 O 34 34 O 2 34 3J JC4 34 34 ( * F ( 34 2 ( CFH u(t) 1. Sistema Adaptativo . Filtrado de la tensión . + uf (t) 2. Sistema de estimación de potencia . 3. Estimación de la corriente de referencia . i L(t) + iRef (t) - + ipf (t) iL(t) J CH , ! ( * ' ( * C O Q 34 34 T 3434 T 3434R & 3J JF4 > 3J JC4 34 2 * ( * # # , 3J JC4 * ( 34 ( ' * * 34 O 34 34 O 2 34 3J JD4 34 ( * * 34 F ( 34 34 O 3* 4 T 3* 4 T 3* 4 O * 3J JE4 * 34 * 34 * 34 ' F ( ( ( ( # * * CFI Filtro de Kalman resonante + u+af _ x'=Ax+ Bu y =Cx+Du FR + FK _ 2 + x u+bf uf u+af u+bf x u+cf u+cf Ge x x x x x x PL p x x _+ i La iLb iLc _+ _ + ua ub uc iLa iLb iLc i Ref- a iRef-b i Ref- c J CI , * ( * * ( 34 O 34 34 34 3J JJ4 & 3J JJ4 ( ( ( , C O Q3* 4 T 3* 4 T 3* 4 R Q3* 4 T3* 4 T3* 4R O L 3J JK4 ( 3J JK4 ( ( ( - * ( J CI CDL ( * ( 3, 7 % ) ' % * % , ' 3J JG4 J FL ' " 7 7 7 % & 7 % $ 9 " 7 7 & 7 % & ( $ 9 " 7 7 ) 7 % & 7 ( $ 9 " % 7 % 7 & 7 ) 7 & ' $ # " % & 7 % 7 7 & 7 ) 7 & ' $ # " % 7 ) 7 % 7 & ) 7 & ' 7 $ # &8&' 1.5 1.5 1 1 u (t) ub(t) uc(t) Corriente [A] Tensión [V] a 0.5 0 −0.5 iLa(t) 0.5 iLc(t) iLb(t) 0 −0.5 −1 −1 −1.5 0.02 0.022 0.024 0.026 0.028 0.03 0.032 0.034 0.036 0.038 0.04 Tiempo [s] −1.5 0.02 0.022 0.024 0.026 0.028 0.03 0.032 0.034 0.036 0.038 0.04 Tiempo [s] + J FL ) CDC % & - $ J FC * * ( 1.5 0.8 isa(t) isb(t) isc(t) 1 iRef−a(t) iRef−c(t) 0.6 iRef−b(t) Corriente [A] Corriente [A] 0.4 0.5 0 −0.5 0.2 0 −0.2 −0.4 −1 −0.6 −1.5 0.02 0.022 0.024 0.026 0.028 0.03 0.032 0.034 0.036 0.038 −0.8 0.02 0.04 0.022 0.024 0.026 Time [s] 0.028 0.03 0.032 0.034 0.036 0.038 0.04 Tiempo [s] # J FC % * ( 3 u (t) af+ Magnitud [V,A] 2 1 i (t) sa 0 −1 −2 −3 0.02 0.022 0.024 0.026 0.028 0.03 0.032 Tiempo [s] 0.034 0.036 0.038 0.04 J FF % ' * * CDF 4 3.5 p (t) L Potencia instantánea [W] 3 p (t) s 2.5 2 1.5 1 0.5 p (t) F 0 −0.5 −1 0.02 0.022 0.024 0.026 0.028 0.03 0.032 Tiempo [s] 0.034 0.036 0.038 0.04 J FD ! * 34 34 ( 34 2 ( J FC34 * ! J FF * * JL " ' ( * , J FD * ( * , ( * ( 3,! 7 % ) ' % * % , ( # E * QIJR 2 < , CDD 200 usa(t) u (t) sb 150 u (t) isa(t) sc 150 i (t) i (t) sc sb 100 u (t) Corriente [A] Tensión [V] 100 0 50 0 −50 50 isn(t) 0 −50 −100 −100 −150 −200 0.02 0.025 0.03 0.035 0.04 0.045 0.05 0.055 0.06 −150 0.02 0.025 0.03 0.035 Tiempo [s] 0.04 0.045 0.05 0.055 0.06 Tiempo [s] + J FE ) 3J JH4 34 O CCJ F 34 : 3J JH4 34 O CCJ F 3 CFL4 : 34 O IF F 3 T CFL4 : < ( 3J JI4 O CLK X O O CDF X O DDK " O O EFL " 3J JI4 ' J FE > J FE34 J FE34 . % & - $ , * , ( CDE 100 i 80 Ref−a 80 60 i (t) i (t) sb sa Corriente [A] Corriente [A] 40 i (t) sc 20 0 −20 i (t) sn i Ref−b 60 iRef−c 40 20 i Ref−n 0 −20 −40 −40 −60 −60 −80 −80 0.02 0.022 0.024 0.026 0.028 0.03 0.032 0.034 0.036 0.038 −100 0.02 0.04 0.022 0.024 0.026 Tiempo [s] 0.028 0.03 0.032 0.034 0.036 0.038 0.04 Tiempo [s] # J FJ % * ( 200 150 uaf+(t) 100 Magnitud [V,A] isa(t) 50 0 −50 −100 −150 −200 0.02 0.022 0.024 0.026 0.028 0.03 0.032 Tiempo [s] 0.034 0.036 0.038 0.04 J FK % ' * * ( ( J FJ J FK * * JL " ' CDJ 20000 pL(t) ps(t) Potencia instantánea [W] 15000 10000 5000 p (t) F 0 −5000 0.02 0.022 0.024 0.026 0.028 0.03 0.032 Tiempo [s] 0.034 0.036 0.038 0.04 J FG ! * 34 34 ( 34 * ! * ( J FG > ( * ( @ ( 00 1 "" , # ' ( * ( . 2 ( ( ( ( * 2 * *# * * 2 ( CDK , * ( ' * , ( ( * # ( 2 ( ( ( N % ( , ( ' , . * ' , . * * ' * , ! * * > !' * , ( ( QCFH CFI CDLR % & ' ! + / , - - - $ 0 - / , , 9 + / , - CDI 3 !', ! ' . ( ( **# K C , * * ( . , ( ( * @. * ( ! * Fuente de alimentación Filtro activo de potencia Carga no lineal K C *# ( . 3& "!# ' $ #!# - ( * & & CEL ! ;! 4 ) % = 2 2!, CCLE QCDCR * ( K F K F ) 2CCLE ( ) . !+ ! !8 ! KLD ? FJL &" 2! 3)&2DFLFEL4 ( ' !M& H ? CL: E CK . ( F < E CF ( HLL' 2 ( * 2A QCDFR D +$0) 2N& JL $0 CFD +$0) ) &. CFLL : . DL CEC A CCLL ?HLL : F FFLL ? ELL : , ( ) 3(4 2N"+FF &. * JL A" , K D34 ( **# ( = = > 2 K D ( CEF ! K E 0 . ( > + & 2 ( ( CL " FL " K E $ 2 * "! KHDE * * K J "! KHDE CED Rab =150 ua L AC PCC Rectificador trifásico 950 W ub uc 230-V, 50Hz LF + 250-V - LF =30mH (0.17 p.u) LAC =40mH (0.23 p.u) (230-V, 50Hz ,1-kVA base) K K * * * EJ A: ( . DLL : * K J * * ( IJL M # FDL : * JL " , ( * ( CJL X , * ( ( ( ( K K , * # D ( JLL : ?5 < 2CCLE CEE ! ' 3* 4 ( 3* 4 * 3* 4 ! ' * " ' ( CL : , ,& * :FJ! * DJL :CL : , * FJ>! * CF CL : , K G ( ' K H ' ! M(% KLDLDJL &" K G & ( ' ,$::??? CEJ K H & ' ;!! <)) 2 )* 3'& ) 32 4 2 )* 2CCLE , * * , "!++ * * "! KHDE , )* 2 # ( !2 ,&)! )* ! CEK ! K I , )* 2!, 3%)+CCLE4 Control de tensión Control de corriente en el inversor Corriente de referencia K CL , )* CEG K CC : * ! 2!, 2 . ( 2CCLE , K I 2 2CCLE 3%)+ ; 3 1 CCLE4 K CL )* ( ?1 - 2!, CCLE * )* * )* ; 3 8* ( 2!, ! * ( ( )* K CC $ - $ ! * * "! KHDE & ++. +-- +, ++ CEH ! K CF : ++ * * $!+0 , * CLFE QCDDR , K CF ( * * * CLFE ' ;!& 4 ) * )* # % # F F E F +$0) ( # D D E D CEI * & # J 2!, * CL A" 2 C ) * * * F ) * * * D ) * * E ) * * J ) * * 3+ " ' $% !:" ;,$)!' ","'$ ' :! , " * "! KHDE * * JL " # FDL : ;& <) . 3!4 * * K CD 2 * * * CFL * ( CJL ! Tensi ó n de la fase -a Corriente de la fase -a K CD ) * 4 3.5 0.5 Magnitud [A] Magnitud [A] 3 2.5 2 1.5 0.4 0.3 0.2 1 0.1 0.5 0 0 50 250 350 550 650 850 Frecuencia [Hz] 950 1150 1250 " 0 0 50 250 350 550 650 850 Frecuencia [Hz] 950 1150 1250 . K CE , * 3 K CE4 ( . K C ( ( # K CJ ! * ( 2 ( * FAP (OFF) CJC FAP (ON) K CJ ! ' ' * , ( +$0) - * ! K CK , K CG 3 ' 4 > ' * * * ! * 3)" 3 % 4 * ) K C ( ! CJ CF W J C W ! * CJF ! K CK * ! Tensi ón de la fase -a Corriente de la fase -a K CG ) 3* 4 , K CH ( * ( ( CJD ) K C ) * 3 4 @ A 34 3 4 34 @ A B@C(" B@''' ' +$0) ( * ) ( 3 Corriente de referencia 2 Corriente inyectada por el filtro Señal de disparo 1 0 −1 −2 −3 0.124 0.126 0.128 0.13 0.132 0.134 Tiempo [s] 0.136 0.138 0.14 0.142 K CH 2 * ;&! <) ! ( ( CJL X * * # * * , * JL " ( * * CJE ! Tensi ón de la fase -a K CI Tensi ón de la fase -a K FL CJJ , ( ( K CI ' * ( * . * ' K FL ! ( * * ( , ( * * FE W LHG W * 3. " ' $% !:" '"!/ " ( ;,$)!' * * "! KHDE 2 +, KCLLLFE QCDER . F H W ) K F * * * * * K FC * * ) K F " & 3 W4 BB ( "@C A 34 B CB B [ CJK ! 200 u (t) a 150 h=1 100 Tensión [V] h=5 h=7 50 0 −50 −100 −150 −200 0.02 0.022 0.024 0.026 0.028 0.03 0.032 Tiempo [s] 0.034 0.036 0.038 0.04 K FC ' 3* 4 ;, <) ) K F K FF Tensi ón de la fase -a Corriente de la fase -a K FF ) * CJG Tensi ón de la fase -a Corriente de la fase -a K FD ) * ! ( ( K FD > * ( * K FD * * * * ' ( CJ LE W J F W ( * ( ( ;,! <) ! ( ! CJL X * K FE K FJ CJH ! Tensi ó n de la fase -a K FE ) 3* 4 * Tensi ó n de la fase -a K FJ ) 3* 4 * CJI * * * 30 " ' $% !:" '"!/ " ( ' " ;,$)!' ! ! # * "! KHDE , ( H X , ( K FK R=8 Fuente HP-6834A PCC Carga no lineal desequilibrada R=8 R=8 Filtro activo K FK , * "! KHDE # ! * ! K FG K FH ( , K FG ' ! # * * # > * . , CKL ! 150 100 uPCCa(t) uPCCb(t) u (t) PCCc Tensión [V] 50 0 −50 −100 −150 0 0.01 Tiempo [s] 0.02 K FG ) ! 2' 3# 4 * * 3# 4 Tensió ón de la fase - a Tensi corriente de la fase -a K FH . FEH W * 5 ( * * DH W , K FH CKC Tensió ón de la fase - a Tensi corriente de la fase -a K FI ) ! 3* 4 ( * * CHF W . CFE W * K FI ( * ( EG W ( * * LFJ W * ! ( * 33 1 "" 2 ( . ( , * * ' CKF ! ! ( * . * , * ( J W ( * C W * . * ( # ( . ( * + ' . , - $ / " # CKJ < )" ! " ( $," " ( # ( , ' ! ( * . ( ! - %$ + & , ( . * # # # # ! * ( . , ( * ( ! & ( ( 3!+4 ! % $ # ( * > CKK $ * ! ( , ( $$ +$ 2 ' ( . ( , * ( "') '& ) 3) 2 <& #! " ( . * * ! * * * ' ! * ' * * , # ( * ( 2 ' ( ( * * ' * , N * * ( * " # CKG * ( * 2 ( * # ' ' * * N % 2 * # ( * 2 * *# * * ( * , ( , * ( ' * <+ ,,!" ' "!!$$" 2 # , C , ( ( F ! ( ( D , # # 3 ( T (4 E & N % 2 ( # ! CKH $ J ! * ( ( . <. ,)$ " ( #!( " ' "= C / ! $ % " # P * * ( 8 ( S 1+++ 3 '& . , )!M%LLLKHFLLK 3 4 F ( / ! " # P& S %( & , > DJH >( FLLE DHEJ 0 ,' D " # $ % ( / ! P %( ,#S ' DL > CHF >(? FLLE CDECDG &,' E / ! " # $ % P ( 9 !S %( & , DGG FLLK ! EEEH 0 ,' C / ! $ % " # P! ( * ( S ' 1+++ ) ' '&3 <'& =7>? 2 ! / FLLJ F / ! " # $ % P * ( (* S ' @> '& ) <')=7>? \ 0 FLLJ D / ! $ % " # P ( A S ' A11 ) + 1 1 . <)+1=7>? 2,' 2 FLLJ CCH[CFD " # CKI E / ! " # $ % P * ( ( S ' 1+++ '+) 3 +2 <'+) 3 =7>B7C? )1 -2 & FLLK KID[KIH 1 += , & , ,' ,>,FLLJLIDGJLDLD : +( + ( -( +++ & 3& / FLLK4 ,%! 31 .", . & & , 4 +# , , -( $8 , ( C / ! " # $ % , P$ * ( S ' 1+++ @D 1 % ( '& <1%('=7C? ! 9 FLLK F / ! / , 9 , $ % " # P" & * 2S ' 1+++ '&3 <'& =7E? 28 C J / FLLG - ! C ,>,FLLJLIDGJLDLD ( ( ! DC?CF?FLLJDC?CF?FLLH , & , ,' +( " # F !+FLLELKIELLFLC ( 3>,94 ! CD?CF?FLLECF?CF?FLLJ , & , ,' +( $ % ($" ($" QCR ,>9% . ->,,> JLCKL FLLC QFR / > M '& ) % F / M ] 2 FLLE QDR , & & '& ) % FLLC / M ] 2 QER % & & " M 0 + '& ) ( & $8" CIIK QJR / > M 2 '& ) ( C / M ] 2 FLLL QKR ! P" S 1+++ 1 !- CH[FE /? FLLC QGR ! '& , ! & +,,, !%,22 CIIJ QHR / P!( [ S 1+++ 3 1 ( EL FDF[FEC / ? FLLE QIR / ! P S ) &# -( + 2 FLLL CGE QCLR " A P ( S '- 1+++ ( ID CF FCFH[FCEC FLLJ QCCR 0 2 N " P (8 * ( 8 * 8 (S 1+++ 3 1 + ( EK J IKL[IGC 9 CIII QCFR " 2A ) & P 8 S 1+++ 3 '& ) ( IL J FLLI[FLCI CIGC QCDR P" ( S 1+++ 3 '& ) ( IJ F EEC[EEI CIGK QCER $ , 2 P ( 8 S ' 1+++.1) - <1)=EC? CIGK JFI[JDJ QCJR > & " ! M $ % * / / : P ( * S ' 1+++.'+) 8 !. - EE7DC.F >8 <A / CIGG C[G QCKR " % A / . & P( 8S 1+++ '& +- !- ( C J DF[EL 2 ?9 FLLD QCGR $ $ 8 '& $ - & . , C N8B 8 8 FLLL QCHR 9 , P& * 8 !2?,&)S 1+++ 3 '& , ( CG C FKK[FGF / FLLF QCIR ! " A > P 8 8 * ( ( S 1+++ 3 1 ( FK K IHD[IIL >( ? CIIL QFLR " " A P) 8 * ( S 1+++ 3 '& + ( CD F DCJ[DFF & CIIH % CGJ QFCR 0 2 2 2 P * ( ( .S 1+++ 3 '& ) ( CE F KEF[KEG & CIII QFFR & % & 2 " ) P * ( ( 8 S 1+++ 3 '& + ( FF F KDK[KED & FLLG QFDR ) ^ P2 ( 8 * S 1+++ 3 '& + ( CL D FKD[FGF & CIIJ QFER ( P2 * S 1+++ 3 1 ( DL F ELK[ECF & ? CIIE QFJR ; > & P ( * *8 8 S ' ), '& + +2 <'+=GD? CIIF HFI[HDK QFKR / % / !5 P&( ( ( * S 1+++ 3 1 + ( EI E GFE[GDH FLLF QFGR ) $ / &A P * ( 8 S 1++ '. + '& ( CJF F DKI[DHC & FLLJ QFHR $ ) 2 P ( * ( 8 * S ' 1+++ '& +-- ) ) ! - ( F / FLLF CLCG[CLFC QFIR & / "=* N " P) *8 ( S 1+++ 3 '& + ( CF F DCC[DCH & CIIG QDLR & 2 & M P * * * ( S +3+' ( I C J[CK / ? CIII CGK QDCR 2 & %* P9 * ( S 1+++ 3 '& + ( CG E JKE[JGD / FLLF QDFR > $ N P( 8 * 8 ( 8 * 8A S 1+++ 3 '& , ( CE E CFIH[CDLD CIII QDDR < 1 < P ( 8 S ' 1+++ DF 1 + ) <1+4#=7D? ( C >( FLLF KDD[KDG QDER ; > & " & P *8 ( ( *8 S ' +- '& + +2 <'+=GH? & CIID HEC[HEK QDJR & >8 ^ " P2 * * * ( S 1+++ 3 1 ( DH K CJIC[CJII >( ? 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