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w 9 ; +0 '#'1&/-#%<).-/ =">9 '# 1+)# 1-0$+(' +0) 2-&'01%) PE 9 ; +0 .'2?$%&- .' @%./?5'0- =H2 >9 1-0 +0) '0'/53) )#()1'0).) 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(+,3$&. @ BI 0(-3(-1& (- 2,(-0* (# 2&.0( 1( (.0&.7 ".0& .( ##(4* * 2*'& (- #* /*.( 1( 13)(.3&-*)3(-0&7 "- #* /*.( 1( &$(%*23:- .( 1('( 2&-.(6,3% +,( (# .3.0()*I (- &0%*. 2&-1323&-(. 1( 43(-0&I /,-23&-* 2&%%(20*)(-0( $*%* 2&)$%&'*% +,( (# 13)(-.3&-*)3(-0& %(*#39*1& (. 2&%%(20& = &'0(-1%()&. #*. 2&-.36-*. 1( 0&1&. #&. 13.$&.3034&.7 "# .3.0()* #& 4*)&. * %($%(.(-0*% ,.*-1& #* /&%),#*23:- 1( JK-0(%/*9 LM'%31& 1( (-(%6M*N 2&)& $&1()&. &'.(%4*% (- D367 E7! ! η η η η "#$%&' ()*+ ,-./&0'1 234&#56 5/ /-/&$3' 5/ %- 7#7./8' '#79'56 :67 ;/<.6&/7 5/ /-.&'5'= 7'9#5' > 9' 5/&#;'5' 5/ 9' /-/&$3' 5/ '98'</-'8#/-.6 ?'&' ;'&#67 ?/&#6567 5/ .#/8?67 7/ ?%/5/ 5/@-#& <686+ (t) h = !(t) = "˙ (t) = i (t) Pw h (t) Lr h A()B'C i (t) A()B4C (t) ĖH2 ĖB iT A()B<C !"#$% &' !()*+! $',") &'+ !"#$% &' !()*+! $',") &'+ !+ !(',! $',") $(t) 7/ 5/<9'&'- <686+ D5/8E7= 7#$%#/-56 9' -6.'<#F- 06&8%9'5' '-./&#6&8/-./= 9' (),-'#"$&)# # (t) > 9' #(t) $(t) (t) h = h = 1 i (t) 1/eH2 (t) 1/eB i A()GC A()*C (t) 56-5/ eH2 > eB 76- 9'7 /@<#/-<#'7 5/ '98'</-'8#/-.6 A;/& H%'5&6 ()BC= 7#/-56 /9 #-./&0'1 5/ <'&$' /9 /9/<.&69#1'56& > /9 #-./&0'1 5/ 5/7<'&$' 9' ?#9' 5/ <684%7.#49/ ?'&' 9' 9#-/' 5/9 2#5&F$/-6) I'84#J- 7/ .#/-/- /- <%/-.' 9' 5#0/&/-<#' 5/ /@<#/-<#'7 /- 9' <'&$' > /- 9' 5/7<'&$' 5/ 9'7 4'./&3'7= 64./-#/-56 9'7 7#$%#/-./7 &/9'<#6-/7+ (t) eH2 (t) eB η E = 1/ηF C η B,ch = 1/ηB,dis (t) si QH2 ≥ 0 (electrolizador) si no (pila de combustible) A()!'C (t) si QB ≥ 0 (carga de la bateria) si no (descarga de la bateria) A()!4C ! "#$%&' !()* +,-./0-.$ %/ 1'2 /1/3/04'2 %/ 1'2 2.24/3$2 567&.%'2 +1/3/04' +1/-4&'1.8$%'& 9.1$ %/ -'37#24.71/ "$&:$ %/ 7$4/&6$ ;/2-$&:$ %/ 7$4/&6$ (t) +,-./0-.$ ηE = 0,74 ηF C = 0,47 ηB,ch = 0,7 ηB,dis = 0,9 (t) (t) -'0 /1 .04/&-$37.' %/ /0/&:6$ QH2 < QB = 1$ %/&.>$%$ %/1 $13$-/0$3./04' %/ /0/&:6$ ĖH2 < (t) ĖB /?@&/2$%'2 -'3'* (t) = eH2 QH2 − eH2 (t) = eB QB − eB ĖH2 ĖB (t) (t) (t) (t) (t−1) (t−1) (t−1) QH2 (t−1) QB A!(!$B A!(!7B !"! #$%&' (& ($)&*$+,-)$&,.+ +0 /24/ 0.>/1 2/ &/$1.8$&C /1 %.3/02.'0$3./04' D@4.3' %/ 1'2 %.2@'2.4.>'2 %/1 2.24/3$ 7$E' /24#%.'( !"#$%&&%'(!" )! *'#!(&%+ , !(!$-.+ F$2 1.3.4$-.'0/2 4G-0.-$2 2/ 3'%/1$0 -'3' /0 AH()IB( J -'04.0#$-.D0 2/ />$1K$0 1'2 163.4/2 %/ 1$ @'4/0-.$ %/ 2$1.%$< 1$2 -$@$-.%$%/2 %/ 1'2 .04/&L$-/2 %/ .04/&-$37.' %/ /0/&:6$ = 1'2 163.4/2 %/1 $13$-/0$3./04' %/ /0/&:6$( (t) "'0 &/2@/-4' $ 1$ /04&$%$< 1$ @'4/0-.$ /D1.-$ Pw %/@/0%/ %/1 @'4/0-.$1 /D1.-' %.2@'0.71/ (t) $26 -'3' %/1 4$3$M' %/1 :/0/&$%'& /D1.-'( ;/,0./0%' Pew -'3' 1$ @'4/0-.$ 0'&3$1.8$%$ @&'%#-.%$ @'& #0 :/0/&$%'& /D1.-' %/ )N /0 /1 .024$04/ t< 1'2 163.4/2 %/ @'4/0-.$ /0 1$ /04&$%$ 2/&C0* h 0 i ≤ h (t) Pw 2./0%' P w /1 4$3$M' %/1 :/0/&$%'& /D1.-'( i ≤ h (t) Pew P w i A!(OB ! "# $%&'()*# +' *(&',)#-.*% $#,# '/ #/-#)'(#-*'(&% '0&1 /*-*&#+# $%, /# -12*-# $%&'()*# $',-*&*+# $%, /%0 *(&',3#)'0 +' #/-#)'(#-*'(&%4 −QF C −QB,dis ≤ (t) QH2 (t) QB QE ≤ QB,ch 567 8 +%(+' QE 9 QF C ,'$,'0'(&#( /#0 )#$#)*+#+'0 -12*-#0 $#,# '/ '/')&,%/*:#+%, 9 /# $*/# +' )%-.;0&*./' ,'0$')&*<#-'(&'= $#,# /# /*('# +' >*+,?@'(%7 A%( ,'0$')&% # /#0 .#&',B#0= QB,ch 9 QB,dis 0%( /%0 /B-*&'0 +' )#,@# 9 +' +'0)#,@#7 C0&%0 /B-*&'0 0;'/'( 0', 3;()*?( +'/ &#-#D% &%&#/ +' /#0 .#&',*#0 E B = #E;B 0' #0;-' E;' QB,ch = 0,2 E B 9 E;' QB,dis = 2 E B 7 "# -12*-# '(',@B# #/-#)'(#+# +'$'(+',1 +'/ &#-#D% +' /%0 +'$?0*&%0 +' >*+,?@'(% E H2 9 +' /#0 .#&',B#0 E B 7 F'.*+% # ,'0&,*))*%('0 &G)(*)#0= /#0 .#&',B#0 (% +'.'( '0&#, (;()# +'0)#,@#+#0 +'/ &%+% (* )#,@#+#0 &%&#/-'(&'H +'.'( '0&#, 0*'-$,' $#,)*#/-'(&' )#,@#+#07 I'(*'(+% '( );'(&# '0&#0 )%(0*+',#)*%('0 9 #0;-*'(+% ;( (*<'/ +' )#,@# 0'@;,%= /#0 ,'0&,*))*%('0 0' $;'+'( '2$,'0#, )%-%4 0 ≤ 0,2 E B (t) EH2 (t) EB ≤ E H2 0,9 E B 567J8 K%, L/&*-%= ;( ,'0&,*))*?( $#,# <',*M)#, ;( #/-#)'(#-*'(&% +' '(',@B# 0%0&'(*./'4 (0) EH2 (0) EB ≤ (N ) EH2t (N ) EB t 567N8 !"#$%" &'()*$+& "# 3;()*?( %.O'&*<% # -*(*-*:#, 0',1 /# 0*@;*'(&'4 2 2 2 F = cP w P w + cE H E H2 + cE B P B + cQ 2 FC 2 2 QF C + cQ QE 0*'(+% /%0 )%0&%0 +' /%0 +*0$%0*&*<%0 /%0 -%0&,#+%0 '( '/ );#+,% 67R E 567PQ8 !"#$%& '()* !&+,-+ $- .&+ $/+0&+/,/1&+ $- "2 +/+,-3# 456%/$& 7/+0&+/,/1& 8-%&9-2-%#$&% >.-?,%&./@#$&% A/.# $- ?&36"+,/6.7-0C+/,& $- 4/$%C9-2& E#,-%5# !&+,cP w :;() e<= cQ :;();e<= E cQ :;('Be<= FC cE H :D(D)e<=4 2 cE B :D(;Fe<=4 1 0.9 Potencia eólica normalizada 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 0 500 1000 1500 Tiempo (h) G/9"%# '(H* A&,-2?/# -C./?# 2&%3#./@#$# I$"%#2,- $&+ 3-+-+J !"#$%$!"&' #& !(&)*%$+" !&3& -. ?K.?".& $- .#+ $/3-2+/&2-+ $- .&+ -L"/0&+ -+,K 6#+#$& -2 ?&2$/?/&2-+ -+,/3#$#+ $&0-%#?/C2M ?"#2,& 3K+ 0%-?/+#+ L"- +-#2 .&+ $#,&+ ",/./@#$&+ 3K+ -N#?,&+ +-%K2 .&+ %-+".,#$&+( A#%# .# 0&,-2?/# $- -2,%#$# +- 4# ,&3#$& "2 0-%/&$& $- $&+ 3-+-+ $- 0&,-2?/# -C./?# (t) (t) 2&%3#./@#$# Pew I1-% G/9( '(HJ( >2 %-.#?/C2 ?&2 .# ?#%9# Lr M .&+ $#,&+ "+#$&+ +- 3"-+,%#2 -2 .# G/9( '('( ,&'-./*#!' #& .* !(/$0$1*%$+" O# &0,/3/@#?/C2 +- 4# %-#./@#$& 0#%# ,%-+ +/+,-3#+* 456%/$&+M +&.& ?&2 #.3#?-2#3/-2,& $4/$%C9-2& P +&.& ?&2 #.3#?-2#3/-2,& -2 6#,-%5#+( Q- 4# /30.-3-2,#$& -2 R#,.#6 "+#2$& .# ! 600 Carga residencial (W) 500 400 300 200 100 0 0 5 10 Tiempo (h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e >*CEE G@ BJCe >*B( G@ DC e >JCE G@ JEBFe >(B) *E MG8@ JBBBe >JJ)*B MG8@ CE* e P.Q.&.320$ 2',-. >-$1$?'@ (BCEe >B*EE G@ BDBe >*(E G@ C Fe >((E G@ D*B(e >JDD)F!( MG8@ 2',-. >-$1$?'@ !F*e >FD(E G@ K !JD(e JJ)!J R K K K D*D(e >JC)D(( MG8@ JEDCCe DC)ED R ! ! "#$%& '% ()%*+,#-. S3$ =.I '6-.30%' ./ %01.3,0'3$10.3-' 9<-01'T /$ '<.&$2093 '3U/03. ,. :.,-0'3$ 2'3 #3 2'3-&'/$%'& 6$,$%' .3 ./ 1'%./' %. 03-.&Q$I 856&0%' %. .3.&:5$ '6-.30%' .3 ./ $<$&-$%' $3-.&0'& V W#. 103010I$ ./ $<'&-. .X-.&3' %. .3.&:5$) 7. =$ $ ,#<'3.& W#. ,. %0,<'3. %. #3$ Q#.3-. %. .3.&:5$ $#X0/0$& W#. <&'<'&20'3$ #3$ <'-.320$ Paux ,'/' .3 /', 2$,', W#. ./ ,0,-.1$ 3' <#.%$ $6$,-.2.& /$ %.1$3%$) Y$ Q#32093 '6Z.-0=' ,.&[ /$ ,0:#0.3-.+ F= th X (t) Paux >()JJ@ t=1 ,0.3%' th ./ 8'&0I'3-. %. <&.%022093) (t) L$&$ '6-.3.& #3 &.,#/-$%' 9<-01' Paux %.6. ,.& 0:#$/ $ 2.&' .3 -'%', /', 03,-$3-., %. -0.1<') Y$, /010-$20'3., -\2302$, ,. =#./=.3 $ 1'%./$& 2'1' .3 >D)J!@T $#3W#. .3 .,-. 2$,' /$ <'-.320$ %. .3-&$%$ =.3%&[ %$%$ <'& ./ =0.3-' .3 2$%$ 03,-$3-. 2'3 /' 2#$/ 3' ,. <'%&[ $2-#$& ,'6&. .//$ V /$ <'-.320$ %. ,$/0%$ =0.3. ]Z$%$ <'& /$ %.1$3%$ &.,0%.320$/) Potencia salida baterías (W) ! 400 300 200 100 0 0 200 400 600 800 Tiempo (h) 1000 1200 1400 0 200 400 600 800 Tiempo (h) 1000 1200 1400 Potencia FC (W) 200 150 100 50 0 "#$%&' ()*+ ,-#.#/'0#12 13-#4' 56 .' 7'-6&8' 9$&:;0' <%36&#=&> ? .' "@ 9$&:;0' #2A6&#=&> 3'&' %2 <#<-64' 56 '.4'062'4#62-= B87&#5= C'< 0'3'0#5'56< 56 .=< #2-6&A'06< 56 #2-6&0'47#= 56 626&$8' ? .=< .84#-6< 56. '.4'06D 2'4#62-= 56 626&$8' <6 4=56.'2 0=4= 62 9()E> ? 9() >) !"#$%$!"&' #& !(&)*%$+" C' =3-#4#/'0#12 <6 F' ' &6'.#/'& 5%&'2-6 %2 36&#=5= 56 %2' <64'2') G'&' 0'.0%.'& .'< 3=-620#'< H%6 56762 0=2<%4#& -'2-= 6. 6.60-&=.#/'5=& 0=4= .' 7'-6&8'I ? H%6 56762 0656& .' 3#.' 56 0=47%<-#7.6 ? .' 7'-6&8'I <6 2606<#-' 6. 0=2<%4= &6<#5620#'.I 56. H%6 ?' 5#<3=264=<I ? .' 3=-620#' 61.#0' 5%&'2-6 <#6-6 5#'<) J<-' K.-#4' <6 3%656 =7<6&F'& 62 .' "#$) ()E) @=4= <#43.#;0'0#12I <6 <%3=25&: H%6 .' 3=-620#' 61.#0' 3&6F#<-' ? &6'. 0=#20#562) ,2 3=<#7.6 -&'D 7'L= A%-%&= 0=2<#<-#&: 62 0=2<#56&'& H%6 '47=< 5#<0&63'2I ? 6. 6A60-= H%6 6<-= -#626 62 6. 56<6436M= $.=7'. 56 .' #2<-'.'0#12) ! 4000 3500 Potencia eólica (W) 3000 2500 2000 1500 1000 500 0 0 20 40 60 80 100 120 Tiempo (h) 140 160 180 200 "#$%&' ()*+ ,-./01#' /23#1' 4%&'0./ %0' 5/6'0' !"#$%&'(" '! $& ()%*+*,&-*./ 7' -8.#6#9'1#20 5/ :' &/'3#9'4- 8'&' /3 5#5./6' 4/51&#.- '0./&#-&6/0./ 6/4#'0./ 5% #6; 83/6/0.'1#20 /0 <'.3'= %5'04- /3 1-6'04- >3#08&-$?) @/ :'0 -=./0#4- %0-5 &/5%3.'4-5 6%A 5'.#5B'1.-&#-5 A' C%/ /0 .-4- 6-6/0.- 3' 8-./01#' 4/ 3' B%/0./ '%D#3#'& Paux /5 #$%'3 ' 1/&A /3 5#5./6' 4#6/05#-0'4- /0 3' B'5/ '0./&#-& /5 1'8'9 4/ 5'.#5B'1/& /0 .-4- 6-6/0.- 3' 4/6'04' &/5#4/01#'3 4%&'0./ %0' 5/6'0') @/ :'0 -=./0#4- 3'5 &/B/&/01#'5 4/ 3-5 4#58-5#.#E-5 6-5.&'4'5 /0 3' "#$) () F 4-04/ 5/ 8%/4/ -=5/&E'& 1-6- /0 1-04#1#-0/5 4/ /D1/5- 4/ 8-./01#' /23#1' 5/ /01#/04/ /3 /3/1.&-3#9'4-& 8'&' '36'1/0'& 8'&./ 4/ 3' /0/&$G' 5-=&'0./ /0 B-&6' 4/ :#4&2$/0- A 3' -.&' 8'&./ 5/ '36'1/0' /0 3'5 ='./&G'5 5#/68&/ A 1%'04- 0# 3'5 ='./&G'5 0# 3-5 4/825#.-5 4/ :#4&2$/0-5 /5.H0 .-.'36/0./ 33/0-5) I%'04- :'A B'3.' 4/ 8-./01#'3 /23#1- 5/ '1.#E' 3' 8#3' 4/ 1-6=%5.#=3/ 8'&' 4'& 3' 8-./01#' ='5/ A 3'5 ='./&G'5 8&-8-&1#-0'0 3-5 8#1-5 4/ 8-./01#') ! PE (W) 400 200 0 0 20 40 60 80 100 120 140 160 180 200 0 20 40 60 80 100 120 140 160 180 200 0 20 40 60 80 100 120 140 160 180 200 0 20 40 60 80 100 Tiempo (h) 120 140 160 180 200 PFC (W) 200 100 2000 1000 P B,ch (W) 0 0 PB,dis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inimizar/Maximizar sujeto a x′ · H · x + f ′ · x A · x ≤=≥ b LB ≤ x ≤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t) (t) (t) (t) (t) Pw(t) − PE + PF C + PB,dis − PB,ch + Paux = L(t) r OL=MNP Q*$#& <'& $%&*$,//,'0%& <% ,D2#(<#< &'0 (#& $%(#/,'0#<#& /'0 %( 0,)%( <% ('& <%+>&,*'& <% 1,<$>D%0' ; /'0 %( 0,)%( <% (#& :#*%$A#&9 ('& /2#(%& &% /#(/2(#0 &%DH0 (#& &,D2,%0*%& %/2#/,'0%&F (t) EH2 (t) EB (t−1) = EH2 (t−1) = EB (t−1) + PE (t−1) 1 (t−1) ηE − PF C OL=M!#P ηF C (t−1) + PB,ch ηB,ch − PB,dis 1 ηB,dis OL=M!:P ! "#$# %&'(#$ )# $%*'$*+)#*',- .% /+012 .% %-%$34# *15%-(#.1 #-(%$'1$5%-(% 2% +(')'6#- )#2 %*+#*'1-%2 789:!; < 789:8;= (t) PE + M δE ≤ M (t) PE − (m − θ) δE ≥ θ (t) P F C + M δF C (t) PF C − (m − θ) δF C 789:!#; 789:!>; ≤ M 789:!*; ≥ θ 789:!.; (t) PB,ch + M δB,ch ≤ M (t) PB,ch − (m − θ) δB,ch ≥ θ (t) PB,dis + M δB,dis ≤ M (t) PB,dis − (m − θ) δB,dis ≥ θ (t) + M δaux ≤ M Paux (t) Paux − (m − θ) δaux ≥ θ 789:!%; 789:!?; 789:!3; 789:!@; 789:!'; 789:!0; 2'%-.1 A +- &#)1$ 5+< 3$#-.%B θ +- &#)1$ 5+< C%D+%E1 < m = −M δF C + δE ≤ 1 789:8#; δF C + δB,dis ≤ 1 789:8>; δB,ch + δF C ≤ 1 789:8*; δB,ch + δB,dis ≤ 1 789:8.; δaux + δE ≤ 1 789:8%; δaux + δF C ≤ 1 789:8?; 789:83; .1-.% δJ = [0, 1] (∀J = E, F C, Bch , Bdis , aux) '-.'*# 2' %) .'2C12'('&1 2% %-*+%-($# %-*%-.'.1 1 #C#3#.19 ! "#$ %&$'%())(*+&$ &+ ,-+)(.+ /& 0# )#1#)(/#/&$ 234(2#$ /& 0*$ /(,&%&+'&$ /($1*$('(5*$ $& 2-&$'%#+ &+ !678 Pw(t) − Pew(t) Pw,max ≤ 0 (t) 9!678#: PE − PE,max ≤ 0 9!678;: (t) 9!678): EH2 − EH2 ,max ≤ 0 (t) 9!678/: PB,ch − 0, 2 · EB,max · t ≤ 0 9!678&: PF C − PF C,max ≤ 0 (t) (t) PB,dis − 2 · EB,max · t ≤ 0 9!678,: (t) 9!678<: (t) 9!678=: EB − 0,9 · EB,max ≤ 0 EB − 0,2 · EB,max ≤ 0 !" #$ %& '$((&)*$+,& -./0123 "# $(+'#4($ 1#%# 00#2#% # 0# ,-+)(.+ &$ 0# $(<-(&+'&> x = cplexmex ( sense, H, f, A, b, CTYPE, LB, UB, VARTYPE ) $(&+/*> ? $&+$&> @+ 5#0*% A-& (+/()# $( &0 1%*;0&2# &$ /& 2(+(2(B#)(.+ 9$&+$& C 7: * 2#4(2(B#)(.+ 9$&+$& C ?7:6 ? D> @+ 5&)'*% )*0-2+# )*+ 0*$ )*&E)(&+'&$ /& 0# ,-+)(.+ *;F&'(5* )-#/%3'()#6 ? ,> @+ 5&)'*% )*0-2+# )*+ 0*$ )*&E)(&+'&$ /& 0# ,-+)(.+ *;F&'(5* 0(+&#%6 ? A> @+# 2#'%(B )*+ 0*$ )*&E)(&+'&$ /& 0#$ %&$'%())(*+&$6 ? ,> @+ 5&)'*% )*0-2+# )*+ 0*$ 'G%2(+*$ (+/&1&+/(&+'&$ /& 0#$ %&$'%())(*+&$6 ? HIJKL> @+ 5&)'*% )*0-2+# )*+'&+(&+/* &0 $&+'(/* /& )#/# %&$'%())(.+ /& 0# 2#'%(B /& %&$'%())(*+&$ 9M"N → O ≤P Q MLN → O =PQ MRN → O ≥P: ? "S> @+ 5&)'*% )*+ 0*$ 0T2('&$ (+,&%(*%&$ /& 0#$ 5#%(#;0&$6 ! " #$% #& '()*+, )+& -+. -/01*(. .23(,1+,(. 4( -5. '5,156-(.7 " 89:;<=>% #& '()*+, )+-20&5 )+&*(&1(&4+ (- *13+ 4( -5. '5,156-(. ?@AB → '5,156-( )+&*1&25C @DB → '5,156-( (&*(,5C @$B → '5,156-( 6++-(5&5E7 !"#$ %# %!&#'(!)'*&!#'+) >.*( &1'(- .( (&)2(&*,5 3,+F,5054+ (& (- 5,)G1'+ HI1'(- 410(&.1+&501(&*+70J7 9- (K()2" *5,-+ .( ,(5-1L5C (& 3,10(, -2F5,C 2&5 -()*2,5 4( -5. 3,('1.1+&(. 4(- '1(&*+7 9 )+&*1&25)1M& .( 4(N&( (- G+,1L+&*( 4( 3,(41))1M&C O2( 4(614+ 5 -101*5)1+&(. 4(- A=P>Q .(,R 4( ST 3(,1+4+. 4( U G+,5.7 >& )545 3(,1+4+ .( )5-)2-5,R& -5. 410(&.1+&(. M3*105. 4( -+. 41.3+.1*1'+. V 35,5 N&5-1L5, .( .(-())1+&5,R (- '5-+, M3*10+ 4( )545 41.3+.1*1'+ )+0+ (- 0RW10+ 4( *+4+. -+. '5-+,(.7 P5 X2&)1M& +6K(*1'+ )+&.1.*( (& 01&101L5, (- )+.*( *+*5- 4( -5 1&.*5-5)1M&C (- )25- .( ,(3,(.(&*5 (& -5 .1F21(&*( ()25)1M&% 2 2 + cE B EB F = cP w Pw2 max + cP F C PF2 Cmax + cP E PE2 max + cE H EH max 2max ?Y7SZE 2 :((.),161(&4+ -5 ()25)1M& 4( -5 X+,05 x′ · H · x + f ′ · x &+. O2(45% (1) (1) x = [ Pw(1) PE(1) PB,ch PF C (1) (1) PF Cmax {z (1) EH2 H = [ 0 0 0 0 0 0 0 0 0 0 0 cP w | {z cP E (1) | δF C (1) (1) δB,dis Pwmax (1) PEmax (1) PB,dis Paux EH2 (1) max (1) (1) (1) EB δE (1) (1) ′ δaux . . . ] } EBmax 18·t cP F C cE H 2 δB,ch cE B 18·t !"#$% 0 . . . ]′ } f = [ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 . . . ]′ | {z } !"#&% !"'(% 18·t )*+* ,-., /01,2 .34*43- 5/ 1*23+ 065*2 * 7,+3 ,/ .383 434,/.3 9*+* Paux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th X (t) (t) (t) (α · Paux − β · EH2 − γ · EB ) LM6FEN t=1 2/&2% α; β J γ #/& )/# .%#/#6 O%%#*,'?'%&2/ )- %*+-*'<& 2% )- G/,1- x′ · H · x + f ′ · x &/# >+%2-K (1) (1) x = [ Pw(1) PE(1) PB,ch PF C (1) | EB (1) δE (1) (1) δB,ch δF C {z 13·th (1) (1) (1) PB,dis Paux EH2 (1) (1) ′ δB,out δaux . . . ] } LM6FFN H = [ 0 0 0 0 0 100000 0 0 0 0 0 0 0 . . . ]′ | {z } LM6FPN f = [ 0 0 0 0 0 0 −10 −100 0 0 0 0 0 . . . ]′ | {z } LM6FQN 13·th 13·th A/, R)$'1/ #% 1+%#$,-& ./, .-&$-))- )/# ,%#+)$-2/# /?$%&'2/#6