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0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
0
500
1000
1500
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Carga residencial (W)
500
400
300
200
100
0
0
5
10
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15
20
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!
400
300
200
100
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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
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<#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$/0-5 /5.H0 .-.'36/0./
33/0-5) I%'04- :'A B'3.' 4/ 8-./01#'3 /23#1- 5/ '1.#E' 3' 8#3' 4/ 1-6=%5.#=3/ 8'&' 4'& 3'
8-./01#' ='5/ A 3'5 ='./&G'5 8&-8-&1#-0'0 3-5 8#1-5 4/ 8-./01#')
!
PE (W)
400
200
0
0
20
40
60
80
100
120
140
160
180
200
0
20
40
60
80
100
120
140
160
180
200
0
20
40
60
80
100
120
140
160
180
200
0
20
40
60
80
100
Tiempo (h)
120
140
160
180
200
PFC (W)
200
100
2000
1000
P
B,ch
(W)
0
0
PB,dis (W)
400
200
0
"#$%&' () * +,-,&,./#'0 1, 230 1#0430#5#630 1,2 0#05,7'
!
!"! #$%&$'(')*+, -, .'/0'1
"#$# $%&'()%$ %&*#& '+*,-,.#/,'0%& &% 1# 2*,(,.# (# 1%$$#-,%0*# 34"56789 (# /2#( +%$-,*%
$%&'()%$ +$':(%-#& /'0 )#('$%& /'0*,02'&9 %0*%$'& ; <% *,+' :''(%#0'= "#$# %&*# #+(,/#/,>0 1#
&,<' 0%/%&#$,' %( 2&' <% )#$,#:(%& :''(%#0#& +#$# ?2% ,0<,?2% %0 ?2% -'-%0*' %&*@ %0/%0<,<'
/#<# <,&+'&,*,)' ; #&A %),*#$ (# $%/,$/2(#/,>0 <% ('& B2C'& <% %0%$DA#9 /'-' %( /#&' %0 %( ?2%
%&*E +$'<2/,%0<' (# +,(# <% /'-:2&*,:(% ; (# :#*%$A# %&*E #(-#/%0#0<' %&# %0%$DA# +$'<2/,<#=
6&*# 1%$$#-,%0*# $%&2%()% +$':(%-#& <%( &,D2,%0*% *,+'F
Minimizar/Maximizar
sujeto a
x′ · H · x + f ′ · x
A · x ≤=≥ b
LB ≤ x ≤ U B
"#$# %( 0,)%( <% <,-%0&,'0#-,%0*' ; <% '+%$#/,>0 &% )#0 # 2*,(,.#$ (#& -,&-#& $%&*$,//,G
'0%&9 (' H0,/' ?2% )#$,#$@ <% 20 +$':(%-# # '*$' &%$@ (# I20/,>0 ':C%*,)' ; (#& )#$,#:(%& #
/#(/2(#$= 60 ('& <'& 0,)%(%& &% <%&%#0 ':*%0%$ (#& $%I%$%0/,#& <% ('& <,&+'&,*,)'& +#$# ?2%
&#*,&I#D#0 (# <%-#0<# $%&,<%0/,#( %0 *'<' -'-%0*'= J<%-@& %0 %( +$,-%$ 0,)%( &% /#(/2(#0
('& )#('$%& -@K,-'& <% ('& <,&+'&,*,)'& -,0,-,.#0<' %( /'&*% D(':#( <% (# ,0&*#(#/,>0 ?2%
&%$@0 2*,(,.#<'& /'-' <#*'& %0 %( &%D20<' 0,)%(=
!"#$%&&%'(!" )! *'#!(&%+ , !(!$-.+
5# $%&*$,//,>0 +#$# ?2% %0 *'<' -'-%0*' &% &#*,&I#D# (# <%-#0<# $%&,<%0/,#( &% I'$-2(#
%0 L=MN
(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
!"#$%
0 . . . ]′
}
f = [ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 . . . ]′
|
{z
}
!"#&%
!"'(%
18·t
)*+* ,-., /01,2 .34*43- 5/ 1*23+ 065*2 * 7,+3 ,/ .383 434,/.3 9*+*
Paux :
;* <5, /3-
0/.,+,-* 804,/-03/*+ 23- ,<5093- 8, .*2 4*/,+* <5, /3 /,7,-0.,43- *93+., *5=020*+ 8, ,/,+6>*"
)3+ ?2.043 -, 45,-.+*/ 93+ 9*/.*22* 23- +,-52.*83- 3@.,/083-"
!
!"#$ %# &'#()*!+,
"#$% &'(%) #% %&*+%&$,- .,/0,-1-2/ %& %) -,*3'(/ 45'(%) /.%,-*'/&6176 8) %9%*+$-,)/ #%
,%-)':-; %& .,'1%, )+0-,; +&- )%*$+,- 2% )-# .,%('#'/&%# 2%) ('%&$/6 8 */&$'&+-*'<& #% 2%=&%
%) 3/,':/&$% 2% .,%2'**'<&; >+% 2%?'2/ - )'1'$-*'/&%# 2%) @AB"C #%,D 2% EE .%,'/2/# 2% EF
3/,-#6 "& *-2- .%,'/2/ #% *-)*+)-,D& )-# ,%G%,%&*'-# 2% *-2- 2'#./#'$'(/ 2% 1-&%,- >+% #%
1'&'1'*%; 2%?'%&2/ #%, &+)/ #' %) 2'1%&#'/&-1'%&$/ %# */,,%*$/; %) -./,$% 2% %&%,0H- 2% )G+%&$% -+I')'-,6
B- G+&*'<& /?9%$'(/ */&#'#$% %& 1'&'1':-, %) -./,$% 2% %&%,0H- 2%#2% )- G+%&$% -+I')'-, J
1-I'1':-, )- %&%,0H- -*+1+)-2- %& )/# 2%.<#'$/# 2% 3'2,<0%&/ J %& )-# ?-$%,H-#6 B- G+&*'<&
/?9%$'(/ #% ,%.,%#%&$- %& )- #'0+'%&$% %*+-*'<&K
F=
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