!
"!# $
!# % !
& '()
'( # $
*
+,# $%
# ) %
! - # . %
- #
) %
/, / /
!"
#
& '
( ) *(
) *(
) *(# + ) *(
,- + .
$/000 1& $.00 1&2
3400 1&
) *(
5
6
' 7$ , 4 3 8
$0 $8 ,9 ,4 ,. ,3 /9 /- /4 /.: & 7$$8 ,4 /.:
% '
7,,9/9:
7$ $8 /.: " "
%
1
7$4 $3 ,0 ,3: &
7$,:
6,
6 /
% ' ;
6 9
<
6- % '
&
!
*
5
=
%
$ 0"
5
%
>
<>
?
5
Æ
@
+
6
>?
A
>
?
+ + B
&
+
'+
>$
?
=
'
*
6
>$ $
% >$
>$ >$
% $
Ò0
Ò
Ò
'Ò(
Ø0
Ø
Ø'Ò(
Ì
#$< 6
>, >- >,/ $$
<> < >
>$ B
*
#
C
> <
>
&
<>
D
>$
> $ &
<>
'
> $
&
< <>
<> $
<>
$
B
>
>$ #
<>
0
<>>E
>
0
<> '
E
Æ
$ '
2 '
<> '
0
Æ
' 6
'
E
$
!
0$ ,
>$ F
$ ,
$
>$ $ ,
'
,, "
F
0
0
0
/
>
E
E
/
>
>
/
'
5
A
Æ
+
"
# +
'
= $
E
9
9
9
'
# ,
0 25 50 75 100 125 150 Hours
2000 3000 4000 5000 6000 7000 8000
Load
#,<
'
" D 9
$ , / 9 +
' E,
,EE
,G, =
* $9 +'
& $9
'
, 9
>$43
> $0
E/0
@
'
&
' 7-:
$G9
<
7. /$: +
@
7$$ /$:
%
% * +
=+ ' 7/0: 7/$ 6,-:
&
<
' H
7$$:
+ Æ
% $G9
# 7$8: % <>
>
<>
I<>
%
9
2 <>
E
-
E
E
<>2< + ,G/ 4
' <I .
@ , /
' %
+ 4 I
C .
$G9
>
E
J
E
E
3
>
8
E
< +,
J
>
<
+/
$0
A
& 8
$0
8
7$8 6 /4:
7,-: # $0
+
"
6 '
7$8 6
/-: 7,- ,4:
.
$G9
*
!
>
6
>
F
I
I F
F
4 !
F
<>
F
E F
!
F
"<>
"
E
"
I #
<>
#$
$#+'
F
'
$
,
%
< I $$
' %
0
<>
F
'
*
>
F
F
E
Æ
0$ +' *= Æ
<>
F
0
Æ
> 0
;
>
'
Æ
$E
%
' $
B(H*@
7$- ,,: 7$8 6/9:
.
$G9 K
L
>
9
% 7$86/.:7,-:
+
%
+ %C$
7/8:
D
%C, + & 0
E&$ $
I
E&$
+
' "
B'
+
7$86/-: 7,-,4:
% '
7$./,:<
" %
#/
'(
%
'(
' (
' (
# /< 6 % '
+ ) *(
+ $083 *
#9
,9
$43
!
1
6 # 9
+ + ,9
$ 1
. 6 3 8
$0
D 7//:
+ *
" *B;)*
+ 3 $
'
0 5000 10000 15000 20000 25000 Hours
2000 4000 6000 8000
Load
0 50 100 150 200 250 300 Hours
3000 4000 5000 6000 7000
Load
#9< C G
!
"
#
$ %#
$< D
%
' > $,9
M<>$$083
<>
$
>
E
' >$,92 M $,
' > $,9 M
# - # 4
0 200 400 600 800 1000
Days 4000
5000 6000 7000 8000
Mean Load
#-< @
#>, #>-
#
M ((
0 5 10 15 20 -2000
-1000 0 1000 2000
Category 2
0 5 10 15 20
-1000 0 1000 2000
Category 5
#4< 1 , -
@ 7/:
* 2
" ) ) $
)
/4-
.
!
1 +
*H1*
+ " Æ *
*
+ ,7*
: ,7*
:
,7*
*
:>,7*
*
:)((
*
-
*
-
*
>(
E.
(
EE.
(
(( $/
-
# >$ .
>$+ Æ (
&B 0
,7(
:>0,7(
:>
(( ,7(
(
: > 0 > / +
/
*
<>*
0 (( *H1* $/
-/*
>./(
(( (
&B0
- . -1 >$-
1-
1
.1> $E.
1E
E.
1
* *H1*+ *
'
2
2
*
>
2
(
((
6*H 1* +
*
+3 4
" 5
<> $/
$/
*
*H1*
-/N/
5
>./O/
(
(
6$0
-1 > $ -
1 N1 > $ N
1 .1 > $ EE .
1
O1>$EEO
1
C *
-/N/
$/
$
/
*
>./O/
(
6*H 1* "
3 + 4
+
,7*
* :0((2 7/:
Æ-
N
.
O
*H1*
' Æ
( Æ
C H 7/6 -:
*H1*
" /49 " $
5
<>
,
E,
E
# 5
C H !
7/3: *H1*$$ '
' Æ
5
J
-
5
>(
E
J
.
(
((
J
-
>0/-..-4 J
.
>04/88.3 (
$0$--//33 ((
*
6*H 1*$$$
0,0
$/$/
$ J
-
/
>$E J
.
/(
$9
*H1*./0$
$E J
-
E
J
-
,
E,$E J
-
,
J
-
E
E
J
-
$
E
J
-
>(
E
J
.
(
(( $-
#
## >$3
J
>
7
'
E8
' >$,9 $4
+8
9
+' #+
!" 7//:
$,
$,
+
<>
$ >#
0
M2 # >$3
& + $,
>
J
E
M2' >$,9 $.
"
' <
>
J
E
(( $3
:,9
,9 # $-
$4 $3
>
7
:,9
$8
E$E J
-
J
-
E,
,$E J
-
E, J
-
J
-
$
J
-
E
8
E(
E J
.
(
((
9
$8 +
9
>$0 # >$3
$8
$
8
# >$3 (
M
>
>$ >$
C >$
+ +
D
6 / &
>
E
B'
>
7$/,$: 7$9:
C
7$/:
' P
7,8 6 -: #
+
=
% 3
>$ 4
Q
+
>$ Q
34>
Q
<
0
>+
> ,0
+
Q
<>
Q
>$
B 4
4
$; ; '
#+'; $ 4
3 '7$/
/$:
34
>
,$
+
; 4
+
<>
E
;<>; < >
; ,,
,, 6
;
'
$
>
1 &0 <$ '
;
E$ ;
>$
&<$
<
>
,/
7,$ * ,,: & ;
' E$ '
>$
>$
'
+
<>
<>
>
*
,,
<>
>$
<>
E
;>;
< >
>
C '
'
>
>
;
'
' ;
% ' DEE''
# B;* /0 7,/:
# ) *(
> $43 > ,- > .
CR8000.30!M,30
$30 1C .43 1A CRS $0,0
#
,
% ' %C$
> $0
B(H*@> -0 B;* /0
"
" $
"
$
7
E
:
&
' + &
, $ >9000 $ >3000
$00000 ,00000 $G9
, % '
%C, C B;* /0 > $0
B(H*@>,00
$
E
+ '
#. + % '
(*+ *,+ (*+ *,+
- .$ $. -/! "# . -/-
- "! "$ -/# $-! $! -/-#
!- !- #! -/$ -"- # -/-
!- - -/- !# $$ -/
-- .- $ -/ . -# -/
-- ### .- -/-. $$"# -/-
&'(&)
012(*+ (*+ *,+
"$ - " -/-
! ! "! - -/.
- .$ $ - -/#
# #$" #$ # -/!
-.$ ! ! -/.
# -$ $- $. -/#
# !. # -/""
. $$ $# -. -/$
,<
%C, $. $.34
& KL % %C$
" K L %C, ,
" C
%C,
%C,
' %C$
+
%C, K L
-2000 0 2000 4000 6000 8000 10000
0 20 40 60 80 100 120 140 160 180
therm. generation hydro generation load
# .< & $.
-/" "$ -- ##$ ".#! ".! #/$
-/ "# !! $#! ".- !$ #!. #/-.
-/-! $ .- !! " .!"$ - #/$
-/- . ""- ""!-- "- ".$ #-$$ !-/
-/--! ." $ .!#! #!-" $!!$ -.$ ./"!
-/-- -- .# #! !" ."# "-- #"/$
/<
&
'
# 7,-:
*% '
6 9, #
>$00 >00$
+ +
<>,9 C + >$,9
(
$8
(
8
>$99 $8
H*B% AD 79: /
. "
" $
6 9, < <> , " & <>
&
P
3 > 00$
Æ
# 3
"
0 0.2 0.4 0.6 0.8 1
relative tolerance for the scenario tree 3.15·10 7
3.2·10 7 3.25·10 7 3.3·10 7 3.35·10 7 3.4·10 7
Dual optimum
0 25 50 75 100 125 150
Hours 20
40 60 80 100
# 3< @
> $
& >000$ 000- 00$ ¾
6 #$%
@ # A1A#R
& ' (
@ @ 1RB & C
A ( 6 M M P ) *(
) *(A
# PD P R * 6 &
= A #
*' C # B;* /0
M @ TU D R
+
12 %#%3/#45#) 63/#&
! & 5 #
* '*(**78*99#
1*2 :# #& ) ;6 # &
<=,><=< =?>+8>#
1+2 @! A#:# = 4#5#& )
< B!C@ D#
192 !#% :#& 45B%/%/ #
=$ $ >
)$5$% $ 5 ' (#
1,2 /E /#/#& = # A#=#
) / >#
1D2 /E /#/# )6 4#& 5 !
# A )/ > FGG ?
@ > ' (#
172 /E /#/# )6 4#& = #
*9 '( +789,#
1>2 / A# / # / :#/# 4 5#& ) 6
& ! !@#
'D(D787+#
12 /H 5#:# 5 :## :36 4 B# A .#:#& %
! #&
! ') C# ##(#F! = 7+8*+#
12 ==#4?#& I!
# 'F#
A# F ;#( % B ; ) <# 9,>
) > **8,D#
6#**#
1*2 =J3:#/ #)##& ) #
" '*( *,8,+#
1+2 =J3 :# ?!F@ B# 4? #& )
& 5 # A ?
@ ?*
#
192 =J3 :# ?!F@ B# 4?#& /
#**#
1,2 .@ )#F! F#/#& =
% # # '*(
D787*#
1D2 .)#;# )##G#$#&
#& $ % & ' '
/#4663@ 5##( 5 < 5<# *>
) < B! C@ **79 '(#
172 4# B!@ #A# 4? #)64#& !
8 5 # D '*(
D78>#
1>2 ?!F@ B# # 4? #& =
6?I ; !#& ( " (
" ) (% <= D97 <=< =?
* D87>#
12 ?!F@ B# F! F#/# B!@ #A# 4? # #& A!
% # &
$ % & ' ' /# 4663@
5##( 5 < 5<# *>) <
B! C@** +7 '(#
1*2 ?!F@ B# B!@ #A# #&
! # & "
'?#F@)#I# 4:##( ) < *D*8D9,#
1*2 # 4? #& ) #
A> *#
1**2 F! F#/#& A K
6# 9D '( ,8**#
1*+2 F! F#/#& L BI5*#M+#& 5 . A@ /BK
I6#A5) ) 4 !
+M9#
*( ' #:##(>5**#
1*,2 B!@ #A#& ) % 4 A! )
$) #A#=#
* ' (#
1*D2 B!@ #A#4?#& )% !
#
'*( *,8*7*#
1*72 B? 4# 4? #& 5 ! !
A
* #
1*>2 A5##/@# #& H
# # *, '*( 989*9#
1*2 4)#$#& )) ) " # /
#
1+2 4@ 4#$# 4#:& $ & Ä
N # # D '7>(
D8+D#
1+2 4?#)64#& & 5#&
" '? #F@)#I4 :#
#( ) < *,78,>#
1+*2 )##. #B#& #
'9(*>8+,#
1++2 )A% ) L<9#,# =5A=))
>#
1+92 )#& F!@6)?@ A
# *( ' #:# #( 7>
5*#
1+,2 $@)# :#4#% ;#& 5#
'D( 978,>#
1+D2 $@)# :#4#& % N
# 9> '*( 8>#
1+72 $@)# F@# %#)#C#&
# 9>'*(
*D>8*>#
1+>2 4& %' " &+,#/
%,#
1+2 G .#.#=#& $!
% # +'>>( 7D+877+#