$NWLYH6FKZLQJXQJVUHGXNWLRQ
',3/20$5%(,7
YRQ
+DQQHV 'RSSHOKRIHU
GXUFKJHIKUW DP
,QVWLWXW IU (OHNWURQLVFKH 0XVLN XQG $NXVWLN
9RUVWDQG 28QLY3URI 'LSO,QJ 0DJ 'UWHFKQ 5REHUW +|OGULFK
%HJXWDFKWHU XQG %HWUHXHU
28QLY3URI 'LSO,QJ 0DJ 'UWHFKQ 5REHUW +|OGULFK
([WHUQHU %HWUHXHU
'LSO,QJ 'UWHFKQ 0DUWLQ 3IOJHU $9/ /LVW *PE+ *UD]
*UD] LP 0lU] =XVDPPHQIDVVXQJ
6FKZLQJXQJHQ GLH YRQ GHQ 0RWRUODJHUQ DXI GLH .DURVVHULH EHUWUDJHQ ZHUGHQ KDEHQ ]XP
7HLO JUR‰HQ (LQIOX‰ DXI GDV ,QQHQJHUlXVFK XQG VRPLW DXFK DXI GHQ 4XDOLWlWVHLQGUXFN HLQHV
)DKU]HXJHV =LHO GHU YRUOLHJHQGHQ $UEHLW ZDU HV GLHVH 6FKZLQJXQJHQ P|JOLFKVW HIIL]LHQW ]X
PLQLPLHUHQ 'DIU ZXUGH HLQ 6\VWHP ]XU DNWLYHQ 6FKZLQJXQJVUHGXNWLRQ $FWLYH 9LEUDWLRQ
&DQFHOODWLRQ LQ HLQHU )HHGIRUZDUG 6WUXNWXU HQWZLFNHOW (LQH (LQIKUXQJ LQ JUXQGOHJHQGH
)LOWHUVWUXNWXUHQ XQG DGDSWLYH )LOWHU HUOlXWHUW GLH DOOJHPHLQH )XQNWLRQVZHLVH GLHVHV 6\VWHPV
)U GLH YHUZHQGHWH +DUG XQG 6RIWZDUH ZXUGH HLQ 1DWLRQDO ,QVWUXPHQWV 5HDO7LPH 6\VWHP
YHUZHQGHW
'DV HUVWHOOWH 6RIWZDUHSURJUDPP EHVWHKW DXV ]ZHL 7HLOHQ GHU 6\VWHPLGHQWLILNDWLRQ XQG GHU
HLJHQWOLFKHQ 5HGXNWLRQV5RXWLQH *HWHVWHW ZXUGH GDV 6\VWHP PLW HLQHP HLJHQV GDIU
NRQVWUXLHUWHQ 9HUVXFKVDXIEDX
$EVWUDFW
9LEUDWLRQV WUDQVIHUUHG IURP WKH HQJLQH PRXQWV WR WKH FDU ERG\ KDYH ODUJH LPSDFW RQ WKH
LQWHULRU VRXQG ILHOG DQG WKXV RQ WKH LPSUHVVLRQ RI WKH TXDOLW\ RI D YHKLFOH 7KH WDUJHW RI WKLV
WKHVLV ZDV WR PLQLPLVH WKHVH YLEUDWLRQV HIILFLHQWO\ 7KHUHIRUH DQ DFWLYH YLEUDWLRQ FDQFHOODWLRQ
V\VWHP ZDV GHYHORSHG LQ D IHHGIRUZDUG VWUXFWXUH $ SUHOLPLQDU\ LQWURGXFWLRQ LQ ILOWHU VWUXFWXUHV
DQG DGDSWLYH V\VWHPV H[SODLQV WKH JHQHUDO IXQFWLRQDOLW\ RI WKH V\VWHP 7KH VRIW DQG KDUGZDUH
XVHG IRU VLJQDO SURFHVVLQJ ZDV D 1DWLRQDO ,QVWUXPHQWV 5HDO7LPH V\VWHP
7KH SURJUDP FRQVLVWV RI WZR SDUWV D V\VWHP LGHQWLILFDWLRQ DQG D YLEUDWLRQ FDQFHOODWLRQ URXWLQH
7KH IXQFWLRQDOLW\ RI WKH V\VWHP ZDV WHVWHG DW D VSHFLDO EUHDGERDUG FRQVWUXFWLRQ
'DQNVDJXQJ
0HLQ 'DQN JHKW DQ DOOH GLH DP *HOLQJHQ GLHVHU $UEHLW LKUHQ $QWHLO KDWWHQ
%HVRQGHUHU 'DQN JHEKUW PHLQHP %HWUHXHU +HUUQ 'LSO,QJ 'UWHFKQ 0DUWLQ 3IOJHU IU VHLQ
LQ PLFK JHVHW]WHV 9HUWUDXHQ XQG VHLQH JUR‰DUWLJH 0RWLYDWLRQ (UVW GXUFK VHLQH ,QLWLDWLYH XQG
GLH %HUHLWVWHOOXQJ GHU (LQULFKWXQJHQ XQG *HUlWH GHU )LUPD $9/ /LVW *PE+ ZXUGH GLHVH
$UEHLW P|JOLFK
:HLWHUV P|FKWH LFK +HUUQ 28QLY3URI 'LSO,QJ 0DJ 'UWHFKQ 5REHUW +|OGULFK IU VHLQH
XQ]lKOLJHQ %HUDWXQJHQ XQG VHLQHP HQRUPHQ (LQVDW] ZlKUHQG GHV 6WXGLXPV KHU]OLFKVW GDQNHQ
0HLQ JU|‰WHU 'DQN JLOW DEHU PHLQHQ (OWHUQ GLH PLU GXUFK LKUHQ )OHL‰ XQG KDUWH $UEHLW PHLQ
6WXGLXP HUP|JOLFKW KDEHQ
,QKDOWVYHU]HLFKQLV
,QKDOWVYHU]HLFKQLV
(LQOHLWXQJ
$GDSWLYH )LOWHU XQG $OJRULWKPHQ
hEHUVLFKW
(LQIKUXQJ
$GDSWLYH )LOWHU
(LQIKUXQJ LQ GLH DGDSWLYHQ )LOWHU
.ODVVLILNDWLRQ GHU $GDSWLRQVDOJRULWKPHQ
(LJHQVFKDIWHQ DGDSWLYHU $OJRULWKPHQ
$QZHQGXQJVEHLVSLHOH
:LHQHU )LOWHU
3UREOHPVWHOOXQJ
:LHQHU ± +RSI ± *OHLFKXQJ
'LH 0HWKRGH GHV VWHLOVWHQ $EVWLHJV
6WRFKDVWLVFKH *UDGLHQWHQYHUIDKUHQ
'HU /06$OJRULWKPXV
)HKODQSDVVXQJ
)LOWHUVWUXNWXUHQ IU DNWLYH 5HGXNWLRQVV\VWHPH
hEHUVLFKW
6\VWHPLGHQWLILNDWLRQ
$GDSWLYH )HHGIRUZDUG 6WUXNWXU
)HHGIRUZDUG 6WUXNWXU PLW );/06$OJRULWKPXV
$EOHLWXQJ GHV );/06$OJRULWKPXV
$GDSWLYH )HHGEDFN 6WUXNWXU
)HHGEDFN 6WUXNWXU PLW );/06$OJRULWKPXV
+\EULG 6WUXNWXU
,QKDOWVYHU]HLFKQLV
$NWLYH 6FKZLQJXQJVUHGXNWLRQ
hEHUVLFKW
6FKPDOEDQG )HHGIRUZDUG 6WUXNWXU
(LQOHLWXQJ
$GDSWLYH 1RWFK)LOWHU
$NWLYHV (LQ]HO)UHTXHQ] 5HGXNWLRQVV\VWHP
6\VWHP ]XU DNWLYHQ 6FKZLQJXQJVUHGXNWLRQ
(LQIKUXQJ
$XVIKUXQJ
6\VWHPLGHQWLILNDWLRQ
0HKUIDFK)UHTXHQ] $9&
=XVDPPHQIDVVXQJ XQG $XVEOLFN
/LWHUDWXUYHU]HLFKQLV
$QKDQJ $
6\VWHP XQG 7HVWDXIEDX
+DUGZDUH
6RIWZDUH
$XVZHUWXQJHQ
$QKDQJ %
%(',(181*6$1/(,781*
%ORFNVFKDOWELOG XQG %HVFKUHLEXQJ
%HGLHQXQJ GHU 6RIWZDUH
6FKULWW 6\VWHPLGHQWLILNDWLRQ
6FKULWW $9& ± 5RXWLQH
6\VWHPNRPSRQHQWHQ
.DSLWHO
(LQOHLWXQJ
(LQOHLWXQJ
'LH /lUPEHOlVWLJXQJ LQ GHU ,QGXVWULH ZXFKV PLW GHU VWHLJHQGHQ 9HUZHQGXQJ YRQ WHFKQLVFKHQ
*HUlWHQ ZLH 0RWRUHQ /IWHUQ 7UDQVIRUPDWRUHQ .RPSUHVVRUHQ HWF 'LH WUDGLWLRQHOOH $UW
GHU /lUPEHNlPSIXQJ YHUZHQGHW SDVVLYH 7HFKQLNHQ ZLH $EGHFNXQJHQ .DSVHOXQJHQ RGHU
6FKDOOGlPSIHU 6ROFKH SDVVLYHQ 'lPSIXQJVPD‰QDKPHQ ZHUGHQ ZHJHQ LKUHV EUHLWEDQGLJHQ
(LQVDW]EHUHLFKV VHKU JHVFKlW]W 'LH 1DFKWHLOH OLHJHQ DEHU DP PHLVW YHUKlOWQLVPl‰LJ KRKHQ
3UHLV LKUHU *U|‰H XQG GHU UHODWLY VFKOHFKWHQ :LUNXQJ EHL WLHIHQ )UHTXHQ]HQ %HVRQGHUV EHL
*HUlXVFKHQ GLH GXUFK VWDUNH PHFKDQLVFKH 6FKZLQJXQJHQ HQWVWHKHQ VW|‰W GLH SDVVLYH
'lPSIXQJ DQ LKUH *UHQ]HQ
'LH HUVWH VFKULIWOLFKH )RUPXOLHUXQJ GHU ,GHH HLQHU DNWLYHQ /lUPEHNlPSIXQJ $FWLYH 1RLVH
&DQFHOODWLRQ DOV /lUPDXVO|VFKXQJ GXUFK JHVWHXHUWH ,QWHUIHUHQ] VLQG GLH 3DWHQWVFKULIWHQ YRQ
3 /XHJ DXV GHQ -DKUHQ XQG 6\VWHPH ]XU DNWLYHQ 6FKZLQJXQJVUHGXNWLRQ RGHU DXFK $FWLYH 9LEUDWLRQ &DQFHOODWLRQ $9&
6\VWHPH JHQDQQW VLQG GHQ $1& 6\VWHPHQ VHKU lKQOLFK 'LH 8QWHUVFKLHGH OLHJHQ KDXSWVlFKOLFK
LQ GHU 9HUZHQGXQJ XQWHUVFKLHGOLFKHU 6HQVRUHQ XQG $NWXDWRUHQ
'XUFK GHQ .|USHU XQG /XIWVFKDOO GHV 0RWRUV ZLUG GDV ,QQHQJHUlXVFK YRQ )DKU]HXJHQ VWDUN
EHHLQIOX‰W $NWLYH 6\VWHPH ]XU 6FKZLQJXQJVUHGXNWLRQ HQWKDOWHQ HOHNWURG\QDPLVFKH :DQGOHU
GLH GHQ XQJHZROOWHQ .|USHUVFKDOOHLQWUDJ GXUFK ,QWHUIHUHQ] UHGX]LHUHQ 'LH HQWVWDQGHQH
3HJHOPLQGHUXQJ LP )DKU]HXJLQQHQUDXP NDQQ GLUHNW JHPHVVHQ ZHUGHQ 'DGXUFK HUKlOW PDQ
$XIVFKOX‰ EHU GDV VFKZLQJXQJVWHFKQLVFKH 9HUEHVVHUXQJVSRWHQWLDO XQWHUVFKLHGOLFKHU
0H‰SXQNWH
$9& XQG $1& KDEHQ HLQHQ ZHLWHQ $QZHQGXQJVEHUHLFK GHU YRQ .RSIK|UHUQ IU GLH /XIWIDKUW
EHU /lUPUHGX]LHUXQJ EHL *HVFKLUUVSOHUQ ELV KLQ ]XU ,QQHQJHUlXVFKGlPSIXQJ LQ )DKU]HXJHQ
UHLFKW $XV GLHVHP +LQWHUJUXQG KHUDXV EHVWDQG GLH $XIJDEHQVWHOOXQJ HLQ PRELOHV 6\VWHP ]XU
DNWLYHQ 6FKZLQJXQJVUHGXNWLRQ ]X HQWZLFNHOQ GDV GHQ PRELOHQ (LQVDW] LP .UDIWIDKU]HXJ
HUP|JOLFKW
YJO>/XHJ @ ]LWLHUW QDFK >.XR 0RUJDQ @
6HLWH
.DSLWHO
$GDSWLYH )LOWHU
$GDSWLYH )LOWHU XQG $OJRULWKPHQ
hEHUVLFKW
'LH DGDSWLYHQ )LOWHU VLQG GLH *UXQGODJH GHU DNWLYHQ 5HGXNWLRQVV\VWHPH 8P HLQ 9HUVWlQGQLV
IU GLH )XQNWLRQ GLHVHU DNWLYHQ 6\VWHPH ]X EHNRPPHQ ZLUG LQ GLHVHP .DSLWHO HLQH (LQIKUXQJ
LQ GLH DGDSWLYHQ )LOWHU XQG GHP DP KlXILJVWHQ YHUZHQGHWHQ $GDSWLRQVDOJRULWKPXV JHJHEHQ
YJO ><DQJ @
6HLWH .DSLWHO
$GDSWLYH )LOWHU
(LQIKUXQJ
(LQ )LOWHU LVW HLQ 6\VWHP GDV (LQJDQJVVLJQDOH QDFK EHVWLPPWHQ .ULWHULHQ YHUDUEHLWHW XQG
$XVJDQJVVLJQDOH OLHIHUW 'DEHL KlQJHQ GLH .ULWHULHQ YRQ GHQ $QZHQGXQJHQ DE XQG N|QQHQ VHKU
XQWHUVFKLHGOLFK VHLQ
L
)UHTXHQ]VHOHNWLRQ 7LHISD‰ +RFKSD‰ %DQGVSHUUH
L
6W|UXQWHUGUFNXQJ (FKRV ,QWHUIHUHQ]HQ 5DXVFKHQ
L
6\VWHPLGHQWLILNDWLRQ
L
$OOHQ JHPHLQVDP LVW GDV =LHO GLH JHZQVFKWHQ ,QIRUPDWLRQHQ DXV GHQ (LQJDQJVVLJQDOHQ ]X
H[WUDKLHUHQ
(LQJDQJVVLJQDO [Q
$XVJDQJVVLJQDO \Q
)LOWHU
$EE 3ULQ]LS HLQHV )LOWHUV
7UDQVYHUVDOILOWHU
%HLP HLQHP OLQHDUHQ WUDQVYHUVDOHP )LOWHU LVW GDV $XVJDQJVVLJQDO HLQH OLQHDUH )XQNWLRQ GHV
(LQJDQJVVLJQDOV (V JLOW GDV 6XSHUSRVLWLRQVSULQ]LS
ZHQQ [Q → \Q XQG [Q → \Q LVW
GDQQ IROJW D [Q D [Q → D \Q D \Q
∀ α1D
(LQ 7UDQVYHUVDOILOWHU LVW GXUFK HLQH QLFKWUHNXUVLYH 'LIIHUHQ]HQJOHLFKXQJ
\Q D [Q D [Q D [Q1
FKDUDNWHULVLHUW
'D GLH ,PSXOVDQWZRUW HLQHV VROFKHQ )LOWHUV
K
HLQH HQGOLFKH /lQJH
L
1

D
) L) 1
L
(2.2)
VRQVW
KDW ZLUG HLQ 7UDQVYHUVDOILOWHU DXFK ),5)LOWHU HQJO )LQLWH ,PSXOVH
5HVSRQVH JHQDQQW
)U GLH 'DUVWHOOXQJ LP )UHTXHQ]EHUHLFK ZLUG GLH ]7UDQVIRUPLHUWH YHUZHQGHW %HL HLQHP
NRPSOH[HQ H[SRQHQWLHOOHQ (LQJDQJVVLJQDO GHU )RUP ] JLOW
L
\>L@
L
+]] 6HLWH .DSLWHO
$GDSWLYH )LOWHU
'LH hEHUWUDJXQJVIXQNWLRQ LVW GXUFK
+ ‘ ]’ ,
{,
L
K ]1
L
L
,
{D ]
1
L
JHJHEHQ (LQ 7UDQVYHUVDOILOWHU LVW DXIJUXQG
L
,
{, K
‘ ] V ì’
1L
b
L
L
b?
LPPHU VWDELO
(LQ 6SH]LDOIDOO GHV 7UDQVYHUVDOILOWHUV LVW GHU 3UlGLNWRU GHU DXV GHQ ELVKHULJHQ %HREDFKWXQJHQ
HLQHV 6LJQDOV VHLQHQ ]XNQIWLJHQ :HUW YRUKHU]XVDJHQ YHUVXFKW )U HLQHQ (LQVFKULWWSUlGLNWRU
JLOW ]%
[ ‘ Q0 ’ Z [Q Z [Q ± Z1 [Q ± 1 (LQ UHNXUVLYHV )LOWHU ZLUG GXUFK HLQH UHNXUVLYH 'LIIHUQ]HQJOHLFKXQJ
\Q D \Q ± D1 \Q ± 1 [Q
K IU L
EHVFKULHEHQ 'D GLH ,PSXOVDQWZRUW HLQHV VROFKHQ )LOWHUV HLQH XQHQGOLFKH /lQJH KDW L≠
→ ∞ ZLUG HLQ UHNXUVLYHV )LOWHU DXFK ,,5)LOWHU HQJO ,QILQLWH ,PSXOVH 5HVSRQVH JHQDQQW
'LH hEHUWUDJXQJVIXQNWLRQ LVW GXUFK
+ ‘ ] ’,
{, D ]
1
L
L
D
L
JHJHEHQ (LQ UHNXUVLYHV )LOWHU LVW QXU GDQQ VWDELO ZHQQ DOOH 3ROVWHOOHQ YRQ
/|VXQJHQ GHU FKDUDNWHULVWLVFKHQ *OHLFKXQJ
{, D ] , 1
L
L
L
+]
GK GLH
LQQHUKDOE GHV (LQKHLWVNUHLVHV GHU
NRPSOH[HQ ](EHQH OLHJHQ (LQ 7UDQVYHUVDOILOWHU NDQQ LQ YHUVFKLHGHQHQ 6WUXNWXUHQ UHDOLVLHUW
ZHUGHQ 'DEHL LVW GLH GLUHNWH 6WUXNWXU $EE DP EHNDQQWHVWHQ
]
Z
]
]
Z
Z
A[Q
$EE 'LUHNWH 6WUXNWXU HLQHV 3UlGLNWRUV
6HLWH .DSLWHO
$GDSWLYH )LOWHU
$GDSWLYH )LOWHU
(LQIKUXQJ LQ GLH DGDSWLYHQ )LOWHU
'LH DGDSWLYH
,GHH LVW GHP PHQVFKOLFKHQ :XQVFK QDFKHPSIXQGHQ ZHOFKHU GLH OHEHQGHQ
6\VWHPH GHU 1DWXU GLH VLFK LKUHU 8PJHEXQJ DQSDVVHQ NRQQWHQ QDFK]XELOGHQ YHUVXFKW *UR‰H
)RUVFKXQJVDUEHLW OHLVWHWH %HUQDUG :LGURZ GHU VLFK DE FD PLW DGDSWLYHQ 6\VWHPHQ
EHVFKlIWLJWH
8QWHU HLQHP DGDSWLYHQ )LOWHU YHUVWHKW PDQ HLQH $QRUGQXQJ GLH DXV HLQHP SURJUDPPLHUEDUHQ
'LJLWDOILOWHU XQG HLQHP $GDSLRQVDOJRULWKPXV EHVWHKW 'HU $GDSWLRQVDOJRULWKPXV RGHU DXFK
DGDSWLYHU $OJRULWKPXV JHQDQQW VWHOOW GLH .RHIIL]LHQWHQ GHU )LOWHUV QDFK EHVWLPPWHQ .ULWHULHQ
XQG LQ $EKlQJLJNHLW YRP (LQJDQJVVLJQDO HLQ XP HLQ JHZQVFKWHV hEHUWUDJXQJVYHUKDOWHQ ]X
HUUHLFKHQ $EE +LHUEHL LVW ]X EHDFKWHQ GD‰ GLH (LQJDQJVVLJQDOH GHV JHVDPWHQ DGDSWLYHQ
6\VWHPV DXV [Q XQG GQ EHVWHKHQ ZlKUHQG GLH 6\VWHPDXVJDQJVVLJQDOH GLH GLH JHZQVFKWHQ
,QIRUPDWLRQHQ HQWKDOWHQ MH QDFK $QZHQGXQJHQ GDV 6FKlW]VLJQDO \Q GDV )HKOHUVLJQDO HQ
GQ ± \Q RGHU GLH )LOWHUNRHIIL]LHQWHQ VHLQ N|QQHQ
(LQJDQJVVLJQDO
[Q
3URJUDPPLHUEDUHV
'LJLWDOILOWHU
6FKlW]VLJQDO
\Q
B
.RHIIL]LHQWHQ
$GDSWLRQV
DOJRULWKPXV
∑
6W|UVLJQDO
GQ
)HKOHUVLJQDO
HQ
GQ ± \Q
$EE *UXQGSULQ]LS HLQHV DGDSWLYHQ )LOWHUV
'LH DGDSWLYHQ )LOWHU KDEHQ IROJHQGH 0HUNPDOH
$GDSWLYH )LOWHU ZHUGHQ HLQJHVHW]W ZHQQ GLH VWDWLVWLVFKHQ (LJHQVFKDIWHQ GHU 6LJQDOH QLFKW
YROOVWlQGLJ EHNDQQW RGHU ]HLWLQYDULDQW VLQG
L
L
%HLP DGDSWLYHQ )LOWHU JLOW HV PHLVWHQV HLQ 2SWLPLHUXQJVSUREOHP ]X O|VHQ 'DV .ULWHULXP IU
GLH .RHIIL]LHQWHQHLQVWHOOXQJ LVW IDVW LPPHU GLH 0LQLPLHUXQJ GHV )HKOHUVLJQDOV HQ
]LWLHUW QDFK >.XR 0RUJDQ @
6HLWH .DSLWHO
L
$GDSWLYH )LOWHU
'LH )LOWHUNRHIIL]LHQWHQ ODVVHQ VLFK QLFKW D SULRUL EHVWLPPHQ 6LH KlQJHQ VHOEVW YRP
(LQJDQJVVLJQDO DE 'HPHQWVSUHFKHQG VLQG DGDSWLYH )LOWHU HLJHQWOLFK QLFKWOLQHDUH )LOWHU
7URW]GHP ZLUG KlXILJ YRQ OLQHDUHQ DGDSWLYHQ )LOWHUQ JHUHGHW ZHQQ GLH ]XJUXQGH OLHJHQGH
)LOWHUVWUXNWXU GHV SURJUDPPLHUEDUHQ 'LJLWDOILOWHUV OLQHDU LVW
.ODVVLILNDWLRQ GHU $GDSWLRQVDOJRULWKPHQ
(LQH .ODVVLILNDWLRQ GHU $GDSWLRQVDOJRULWKPHQ NDQQ $EELOGXQJ HQWQRPPHQ ZHUGHQ 'LH
2SWLPDOILOWHU GLH IU VWDWLRQlUH 6LJQDOH :LHQHU)LOWHU XQG LQ QLFKWVWDWLRQlUHQ 8PJHEXQJHQ
.DOPDQ)LOWHU KHL‰HQ VHW]HQ YRUDXV GD‰ GLH VWDWLVWLVFKHQ (LJHQVFKDIWHQ GHU 6LJQDOH
YROOVWlQGLJ EHNDQQW VLQG (LQ VR HQWZRUIHQHV )LOWHU LVW RSWLPDO LP 6LQQH GHV HUZDUWHWHQ
TXDGUDWLVFKHQ )HKOHUV
+LHUEHL NDQQ ]ZLVFKHQ GHU GLUHNWHQ XQG GHU LWHUDWLYHQ /|VXQJ GHV :LHQHU)LOWHUV XQWHUVFKLHGHQ
ZHUGHQ :lKUHQG EHLP HUVWJHQDQQWHQ GLH /|VXQJ GLUHNW EHUHFKQHW ZLUG HUPLWWHOW GHU ]ZHLWH
$QVDW] LWHUDWLY GLH /|VXQJ GD VLH YLHOOHLFKW DQDO\WLVFK QLFKW DEJHVFKORVVHQ DQJHJHEHQ ZHUGHQ
NDQQ ]% EHL QLFKWOLQHDUHQ 2SWLPLHUXQJVSUREOHPHQ RGHU GXUFK DQGHUH 8PVWlQGH ]% ]X
JUR‰HU 5HFKHQDXIZDQG XQG 6SHLFKHUEHGDUI EHL HLQHU GLUHNWHQ /|VXQJ
)LOWHUHQWZ XUIVSULQ]LSLHQ
2SWLPDOILOWHU
.DOPDQ
'DWHQILOWHU
:LHQHU
GLUHNW
R IIOLQH
LWHUDWLY
R QOLQH
%OR FN
DGDSWLY
UHNXUVLY
$EE .ODVVLILNDWLRQ GHU )LOWHUHQWZXUIVSULQ]LSLHQ
%HL GHQ 'DWHQILOWHUQ VLQG GLH VWDWLVWLVFKHQ (LJHQVFKDIWHQ GHU 6LJQDOH XQEHNDQQW RGHU QXU
6HLWH .DSLWHO
$GDSWLYH )LOWHU
WHLOZHLVH EHNDQQW 6WDWW GHVVHQ VWHKHQ 'DWHQ LQ )RUP YRQ %HREDFKWXQJHQ $EWDVWZHUWH GHU
6LJQDOH ]XU 9HUIJXQJ GLH HQWZHGHU ]XU 6FKlW]XQJ GHU 6LJQDOVWDWLVWLN RGHU GLUHNW ]XP
(QWZXUI YRQ DGDSWLYHQ )LOWHUQ YHUZHQGHW ZHUGHQ
'DEHL
VWDUWHQ GLH
RIIOLQH $OJRULWKPHQ
HUVW ZHQQ
VlPWOLFKH %HREDFKWXQJHQ
GHU 6LJQDOH
YRUOLHJHQ +LQJHJHQ VLQG GLH RQOLQH $OJRULWKPHQ GLH LP =XVDPPHQKDQJ PLW DGDSWLYHQ )LOWHUQ
DXFK DGDSWLYH $OJRULWKPHQ JHQDQQW ZHUGHQ IU (FKW]HLWYHUDUEHLWXQJ NRQ]LSLHUW +LHU OlXIW GLH
6LJQDOYHUDUEHLWXQJ SDUDOOHO ]XU 'DWHQHUIDVVXQJ 'HVKDOE HLJQHQ VLFK
EHVRQGHUV
JXW IU $QZHQGXQJHQ LQ
DGDSWLYH $OJRULWKPHQ
]HLWYDULDQWHQ 8PJHEXQJHQ $OOHUGLQJV PX‰
KLHU GLH
)LOWHUVWUXNWXU YRUKHU IHVWJHOHJW ZHUGHQ VR GD‰ D SULRUL .HQQWQLVVH QRWZHQGLJ VLQG
'LH %ORFNDOJRULWKPHQ DUEHLWHQ EORFNRULHQWLHUW 6LH VDPPHOQ HLQHQ %ORFN YRQ 'DWHQ JHKHQ YRQ
GHU $QQDKPH GHU 6WDWLRQDULWlW LQQHUKDOE HLQHV %ORFNV DXV VFKlW]HQ DXV GHQ 'DWHQ GLH
6LJQDOVWDWLVWLN XQG EHVWLPPHQ GDQQ GLH IU GLHVHQ 'DWHQEORFN RSWLPDOHQ )LOWHUNRHIIL]LHQWHQ
'DQDFK ZLUG GLH 3UR]HGXU 6DPPHOQ
± 6FKlW]HQ ± %HVWLPPHQ ZLHGHUKROW 6LH VLQG LQ GHU
9RUJHKHQVZHLVH GHQ RIIOLQH $OJRULWKPHQ YHUZDQGW
'LH UHNXUVLYHQ $OJRULWKPHQ ]HLFKQHQ VLFK GDGXUFK DXV GD‰ VLH QDFK MHGHP QHXHQ $EWDVWZHUW
GHU (LQJDQJVVLJQDOH VRIRUW GLH )LOWHUNRHIIL]LHQWHQ DNWXDOLVLHUHQ 6LH ZHUGHQ GHVKDOE DOV UHNXUVLY
EH]HLFKQHW ZHLO VLH GLH QHXHQ )LOWHUNRHIIL]LHQWHQ ]XP =HLWSXQNW Q DXV GHQ DOWHQ .RHIIL]LHQWHQ
]XP =HLWSXQNW 3
XQG GHQ DNWXHOOHQ %HREDFKWXQJHQ GHU (LQJDQJVVLJQDOH ]XP =HLWSXQNW Q
EHVWLPPW ZHUGHQ 'LH 9RUWHLOH GHU UHNXUVLYHQ %HUHFKQXQJ JHJHQEHU HLQHU EORFNRULHQWRLHUWHQ
9RUJHKHQVZHLVH OLHJHQ YRU DOOHP LQ GHU VFKQHOOHUHQ 5HDNWLRQ DXI GLH ]HLWOLFKHQ bQGHUXQJHQ GHU
lX‰HUHQ 6\VWHPXPJHEXQJ XQG LQ GHP JHULQJHUHQ 6SHLFKHUEHGDUI GD ELV DXI GLH PRPHQWDQHQ
$EWDVWZHUWH HLQH $XI]HLFKQXQJ GHU (LQJDQJVVLJQDOH QLFKW Q|WLJ LVW ,Q PHLQHU $UEHLW ZHUGHQ
NHLQH %ORFNDOJRULWKPHQ EHWUDFKWHW VR GD‰ XQWHU HLQHP DGDSWLYHQ $OJRULWKPXV DXWRPDWLVFK HLQ
UHNXUVLYHU $OJRULWKPXV ]X YHUVWHKHQ LVW
6HLWH .DSLWHO
$GDSWLYH )LOWHU
(LJHQVFKDIWHQ DGDSWLYHU $OJRULWKPHQ
'LH :DKO HLQHV DGDSWLYHQ $OJRULWKPXV KlQJW LP ZHVHQWOLFKHQ YRQ GHQ IROJHQGHQ )DNWRUHQ DE
L
.RQYHUJHQ]JHVFKZLQGLJNHLW WUDQVLHQWHV 9HUKDOWHQ
-HGHU UHNXUVLYH $OJRULWKPXV VWDUWHW PLW LUJHQGZHOFKHQ KlXILJ ZLOONUOLFK JHZlKOWHQ
$QIDQJVEHGLQJXQJHQ 'LH $Q]DKO GHU ,WHUDWLRQHQ GLH GHU $OJRULWKPXV EHQ|WLJW XP ]X HLQHU
VWDWLRQlUHQ
/|VXQJ
HLQJHVFKZXQJHQHP
=XVWDQG
]X
NRQYHUJLHUHQ
EHVFKUHLEW
GLH
.RQYHUJHQ]JHVFKZLQGLJNHLW GHV $OJRULWKPXV
L
*HQDXLJNHLW GHU 3DUDPHWHUVFKlW]XQJ
'LH $EZHLFKXQJ GHU LP HLQJHVFKZXQJHQHQ =XVWDQG JHVFKlW]WHQ 3DUDPHWHU IU VWDWLRQlUH
6LJQDOH YRQ GHQ RSWLPDOHQ .RHIIL]LHQWHQ HLQHV HQWVSUHFKHQGHQ 2SWLPDOILOWHUV LVW HLQ 0D‰ IU
GLH *HQDXLJNHLW GHU 3DUDPHWHUVFKlW]XQJ
L
$GDSWLRQVIlKLJNHLW
(LQ DGDSWLYHU $OJRULWKPXV PX‰ LQ GHU /DJH VHLQ GHQ ]HLWOLFKHQ bQGHUXQJHQ GHU 3DUDPHWHU
XQG GHU 6LJQDOVWDWLVWLN LQ QLFKWVWDWLRQlUHQ 6\VWHPXPJHEXQJHQ KLQUHLFKHQG VFKQHOO ]X IROJHQ
'LHVH (LJHQVFKDIW FKDUDNWHULVLHUW GLH $GDSWLRQVIlKLJNHLW HQJO WUDFNLQJ HLQHV $OJRULWKPXV
L
6WDELOLWlW XQG 5REXVWKHLW
'D HLQ UHNXUVLYHU $OJRULWKPXV JUXQGVlW]OLFK ]X GHU .ODVVH GHU UFNJHNRSSHOWHQ 6\VWHPH
JHK|UW LVW GLH 6WDELOLWlW GHV $OJRULWKPXV HLQ ZHVHQWOLFKHU (QWZXUIVDVSHNW $X‰HUGHP LVW HV
ZQVFKHQVZHUW GD‰ GLH /HLVWXQJVIlKLJNHLW GHV $OJRULWKPXV P|JOLFKVW XQDEKlQJLJ YRQ GHQ
(LQJDEHGDWHQ LVW ,Q GLHVHP )DOO VDJW PDQ GD‰ GHU $OJRULWKPXV UREXVW LQ %H]XJ DXI GLH
6LJQDONRQGLWLRQLHUXQJ LVW
6HLWH .DSLWHO
L
$GDSWLYH )LOWHU
5HFKHQDXIZDQG XQG 6SHLFKHUEHGDUI
'LH .RPSOH[LWlW HLQHV $OJRULWKPXV ZLUG LP ZHVHQWOLFKHQ GXUFK GHQ 5HFKHQDXIZDQG DOVR
GLH $Q]DKO GHU DXV]XIKUHQGHQ 2SHUDWLRQHQ XQG GHQ 6SHLFKHUEHGDUI EHVWLPPW 6LH
HQWVFKHLGHQ EHU GLH +DUGZDUHNRPSOH[LWlW ZHQQ GHU $OJRULWKPXV DXI HLQHP $6,&&KLS
HQJO $SSOLFDWLRQ 6SHFLILF ,QWHUJUDWHG &LUFXLW LPSOHPHQWLHUW ZHUGHQ VROO E]Z GLH
HUIRUGHUOLFKH 5HFKHQ]HLW ZHQQ GHU $OJRULWKPXV DXI HLQHP VHTXHQWLHOOHQ 5HFKQHU
SURJUDPPLHUW ZLUG
L
6WUXNWXU GHV $OJRULWKPXV
(LQ $OJRULWKPXV GHU HLQH UHJXOlUH XQG PRGXODUH 6WUXNWXU EHVLW]W XQG DXV SDUDOOHO
DXVIKUEDUHQ 2SHUDWLRQHQ EHVWHKW HLJQHW VLFK EHVRQGHUV JXW IU 9/6,5HDOLVLHUXQJ HQJO
9HU\ /DUJH 6FDOH ,QWHJUDWLRQ XQG 3DUDOOHOLPSOHPHQWLHUXQJ
L
1XPHULVFKH (LJHQVFKDIWHQ
'LH EHJUHQ]WH :RUWEUHLWH GHU 'LJLWDOUHFKQHU GLH HLQH HQGOLFKH 5HFKHQJHQDXLJNHLW
LPSOL]LHUW IKUW XQYHUPHLGOLFK ]X 4XDQWLVLHUXQJV E]Z 5XQGXQJVIHKOHUQ GLH GLH
5HFKHQHUJHEQLVVH HLQHV $OJRULWKPXV YHUIlOVFKHQ +LHU LQWHUHVVLHUW QHEHQ GHU QXPHULVFKHQ
*HQDXLJNHLW GLH YRQ GHU YHUZHQGHWHQ :RUWEUHLWH XQG GHP $OJRULWKPXV DEKlQJW EHVRQGHUV
GLH QXPHULVFKH 6WDELOLWlW GD VLFK LQ HLQHP UHNXUVLYHQ $OJRULWKPXV GLH 5XQGXQJVIHKOHU
YHUVWlUNHQG IRUWSIODQ]HQ DNNXPXOLHUHQ XQG VFKOLH‰OLFK ]XU 'LYHUJHQ] GHV $OJRULWKPXV
IKUHQ N|QQHQ %HLGH $VSHNWH GLH GLH $XVZLUNXQJHQ GHU 5XQGXQJVIHKOHU DXI GLH
$OJRULWKPHQ EHVFKUHLEHQ ZHUGHQ ]XVDPPHQIDVVHQG DOV GLH QXPHULVFKHQ (LJHQVFKDIWHQ
EH]HLFKQHW
(V LVW NDXP P|JOLFK HLQHQ $OJRULWKPXV LQ DOOHQ REHQ JHQDQQWHQ (LJHQVFKDIWHQ JOHLFK]HLWLJ
]X RSWLPLHUHQ +lXILJ ZHUGHQ JHJHQVlW]OLFKH $QIRUGHUXQJHQ EHQ|WLJW VR GD‰
.RPSURPLVVH ]X VFKOLH‰HQ VLQG (V JLEW NHLQHQ DGDSWLYHQ $OJRULWKPXV GHU DOOHQ DQGHUHQ
EHUOHJHQ LVW 'LH :DKO GHV ULFKWLJHQ $OJRULWKPXV KlQJW QLFKW ]XOHW]W YRQ GHQ
$QIRUGHUXQJHQ XQG GHQ 5DQGEHGLQJXQJHQ GHU NRQNUHWHQ $QZHQGXQJ DE XQG PX‰ YRQ )DOO
]X )DOO LQGLYLGXHOO JHWURIIHQ ZHUGHQ
6HLWH .DSLWHO
$GDSWLYH )LOWHU
$QZHQGXQJVEHLVSLHOH
7\SLVFKH $QZHQGXQJHQ YRQ DGDSWLYHQ )LOWHUQ VLQG
,QYHUVH 6\VWHPPRGHOLHUXQJ
3UlGLNWLRQ
6\VWHPLGHQWLILNDWLRQ
6W|UXQWHUGUFNXQJ
(V VLQG KLHU QXU HLQLJH %HLVSLHOH DQJHIKUW XP GLH YLHOVHLWLJHQ (LQVDW]P|JOLFKNHLWHQ GHU
DGDSWLYHQ )LOWHU DXI]X]HLJHQ )U HLQ QlKHUHV 6WXGLXP ZLUG DXI ><DQJ @ XQG >:LGURZ
6WHDUQV @
YHUZLHVHQ
,QYHUVH 6\VWHPPRGHOLHUXQJ
DGDSWLYH .DQDOHQW]HUUXQJ
%HL GHU LQYHUVHQ 6\VWHPPRGHOLHUXQJ KDW GDV DGDSWLYH )LOWHU :] GLH $XIJDEH GLH
,QYHUVH
HLQHV
XQEHNDQQWHQ
G\QDPLVFKHQ
6\VWHPV
]X
3]
PRGHOOLHUHQ
'DV
(LQJDQJVVLJQDO GQ ZLUG YRP XQEHNDQQWHQ 6\VWHP 3] JHILOWHUW XQG GLHQW JOHLFK]HLWLJ
GHU (U]HXJXQJ GHV )HKOHUVLJQDOV HQ PLW HQ
GQ ± \Q
(LQ %HLVSLHO LVW GLH DGDSWLYH
.DQDOHQW]HUUXQJ GLH GXUFK GLH 'LVSHUVLRQ GHV hEHUWUDJXQJVNDQDOV KHUYRUJHUXIHQHQ
9HU]HUUXQJHQ GHU 6LJQDOH ]X NRPSHQVLHUHQ YHUVXFKW ,Q VROFKHQ $QZHQGXQJHQ LVW PHLVW
GDV HQW]HUUWH 6LJQDO \Q GDV JHVXFKWH $XVJDQJVVLJQDO
(LQJDQJVVLJQDO 8QEHNDQQWHV
6\VWHP
GQ
[Q
6FKlW]VLJQDO
$GDSWLYHU
)LOWHU :]
\Q
)HKOHUVLJQDO
HQ
B
∑
$EE ,QYHUVH 6\VWHPPRGHOLHUXQJ
6HLWH .DSLWHO
$GDSWLYH )LOWHU
3UlGLNWLRQ
$56SHNWUDOVFKlW]XQJ
OLQHDUH SUlGLNWLYH 6LJQDOIRUPNRGLHUXQJ LQ GHU 6SUDFK XQG %LOGYHUDUEHLWXQJ /3&
DGDSWLYH 'LIIHUHQ]SXOVFRGHPRGXODWLRQ $'3&0
%HL GHU 3UlGLNWLRQ VSLHOW GDV DGDSWLYH )LOWHU GLH 5ROOH HLQHV 3UlGLNWRUV XP DXV GHQ
ELVKHULJHQ %HREDFKWXQJHQ HLQHV 6LJQDOV VHLQHQ ]XNQIWLJHQ :HUW YRUKHU]XVDJHQ +LHU
LQWHUHVVLHUHQ ZDKOZHLVH GLH 3UlGLNWRUNRHIIL]LHQWHQ RGHU GDV 6FKlW]VLJQDO
)HKOHUVLJQDO
\Q
E]Z GDV
HQ
(LQJDQJVVLJQDO
[Q
9HU]|JHUXQJ
[Q
$GDSWLYHU 6FKlW]VLJQDO
)LOWHU :]
\Q
)HKOHUVLJQDO
HQ
B
∑
GQ
$EE 3UlGLNWLRQ
6\VWHPLGHQWLILNDWLRQ
'LH 6\VWHPLGHQWLILNDWLRQ ZLUG LQ GHQ .DSLWHOQ XQG QlKHU EHKDQGHOW
6W|UXQWHUGUFNXQJ
(FKRNRPSHQVDWLRQ
5DXVFKXQWHUGUFNXQJ
DGDSWLYH $QWHQQHQJUXSSHQ
'LH 6W|UXQWHUGUFNXQJ LVW HLQH .ODVVH YLHOIlOWLJHU $QZHQGXQJHQ 'DV =LHO EHVWHKW GDULQ
DGGLWLYH 6W|UXQJHQ ZLH (FKRV ,QWHUIHUHQ]HQ XQG 5DXVFKHQ GLH GHQ (PSIDQJ HLQHV
1XW]VLJQDOV EHHLQWUlFKWLJHQ ]X XQWHUGUFNHQ ,Q GLHVHP )DOO LVW GDV YRQ GHU 6W|UXQJ
EHUHLQLJWH )HKOHUVLJQDO
HQ GDV JHZQVFKWH 6LJQDO
6HLWH .DSLWHO
$GDSWLYH )LOWHU
6LJQDO 6W|UXQJ
GQ
6W|UXQJ
$GDSWLYHV
)LOWHU
[Q
6FKlW] VLJQDO
)HKOHUVLJQDO
∑
B
HQ
\Q
$EE 6W|UXQWHUGUFNXQJ
:LHQHU )LOWHU
'DV :LHQHU )LOWHU LVW HLQ 2SWLPDOILOWHU IU VWDWLRQlUH 6LJQDOH (V LVW NHLQ DGDSWLYHV )LOWHU GRFK
HLQLJH 7HFKQLNHQ GLHVHV )LOWHUV ODVVHQ VLFK JXW DXI DGDSWLYH %ORFNDOJRULWKPHQ EHUWUDJHQ ,P
IROJHQGHP ZLUG YRQ 7UDQVYHUVDOILOWHUQ XQG UHHOOZHUWLJHQ 6LJQDOHQ DXVJHJDQJHQ
3UREOHPVWHOOXQJ
[
>[ [ [@%
VHL HLQ =XIDOOVYHNWRU GHU 'LPHQVLRQ
1
XQG
G
VHL HLQH =XIDOOVYDULDEOH
G GXUFK HLQH /LQHDUNRPELQDWLRQ GHU .RPSRQHQWHQ YRQ [
\ , Z [ 0 Z [ 0 0 Z [ , Z% [
,QWHUHVVDQW LVW GLH 6FKlW]XQJ YRQ
‡
+LHUEHL LVW
Z
RSWLPDOHQ
.RHIIL]LHQWHQYHNWRUV
>Z Z Z1@7
GHU .RHIIL]LHQWHQYHNWRU 'DV .ULWHULXP ]XU %HVWLPPXQJ GHV
LVW
GLH
0LQLPLHUXQJ
GHV
HUZDUWHWHQ TXDGUDWLVFKHQ )HKOHUV
06( HQJO 0HDQ 6TXDUHG (UURU
PLQ
Z
ˑ Z ’ , (H , ( • G 1 \ – , ( • G 1 Z7 [ –
‡
Z DXIJUXQG GHU OLQHDUHQ )LOWHUVWUXNWXU XQG GHV YHUZHQGHWHQ .ULWHULXPV HLQH NRQYH[H
TXDGUDWLVFKH )XQNWLRQ YRQ Z L
1 LVW KDW ξZ HLQ JOREDOHV XQG HLQGHXWLJHV
'D ξ
L
0LQLPXP $EELOGXQJ YHUDQVFKDXOLFKW GLH 6WUXNWXU HLQHV VROFKHQ )LOWHUV
6HLWH .DSLWHO
$GDSWLYH )LOWHU
[
Z
[
[
Z
Z
∑
G
\
∑
B
∑
H
$EE 6FKlW]XQJ YRQ G GXUFK HLQH /LQHDUNRPELQDWLRQ YRQ [ [ [
'LH 6WUXNWXU GHV 'DWHQYHNWRUV [ ZXUGH QLFKW H[SOL]LW IHVWJHOHJW ,Q NRQNUHWHQ $QZHQGXQJHQ
NDQQ [ XQWHUVFKLHGOLFKH )RUPHQ DQQHKPHQ ,Q 3UlGLNWLRQV XQG )LOWHUXQJVDQZHQGXQJHQ HQWKlOW
[ GLH OHW]WHQ 1 $EWDVWZHUWH HLQHV HLQ]LJHQ 6LJQDOV ]% LQ GHU )RUP [ >[Q [Q ± [Q
± 1 @% +LHU KDQGHOW HV VLFK XP HLQ HLQNDQDOLJHV 7UDQVYHUVDOILOWHU 1 ± WHU 2UGQXQJ
'LH IU GLHVHQ )DOO VSH]LILVFKH 6WUXNWXU YRQ [ ZLUG KlXILJ DOV 6KLIWHLJHQVFKDIW GHU 'DWHQ
EH]HLFKQHW
:LHQHU ± +RSI ± *OHLFKXQJ
'LH QRWZHQGLJH %HGLQJXQJ ]XU 0LQLPLHUXQJ YRQ
*UDGLHQWHQYHNWRUV
|
ˑ Z ’ ,
_
M
M
M Z M Z
M
M Z
ξZ
QlPOLFK GDV 1XOOVHW]HQ GHV
` ˑ Z’ , 1 ( • [ H–
%
Z IKUW ]XP 2UWKRJRQDOLWlWVSULQ]LS
• [ 0 – , _ [ ‘ G 1 [% Z ’ ` , ‡
G ± Z%[ VWHKW DOVR RUWKRJRQDO ]XP 5HJUHVVLRQVYHNWRU [
DQ GHU 6WHOOH GHV RSWLPDOHQ .RHIIL]LHQWHQYHNWRUV
'DV )HKOHUVLJQDO
H
'DUDXV HUJLEW VLFK GLH :LHQHU+RSI*OHLFKXQJ DXFK 1RUPDOJOHLFKXQJ JHQDQQW
& Z ,
PLW GHU
´
1 [ 1 ± .RUUHODWLRQVPDWUL[
& , • [ [% –
6HLWH .DSLWHO
$GDSWLYH )LOWHU
XQG PLW GHP 1 [ .UHX]NRUUHODWLRQVYHNWRU
´
, • [/
`
LVW HLQH V\PPHWULVFKH QLFKWQHJDWLY GHILQLWH 0DWUL[ PLW
% , :3/ , % , B } , / ,VW VLH QLFKW VLQJXOlU GK LQYHUWLHUEDU GDQQ JLOW VRJDU GLH SRVLWLYH 'HILQLWKHLW
, ,@
%
}, / ,Q GLHVHP )DOO LVW GHU .RHIIL]LHQWHQYHNWRU GHV :LHQHU)LOWHUV GXUFK
Z , &
´
JHJHEHQ (QWVSUHFKHQG HUJLEW VLFK GHU 06( XQWHU $XVQXW]XQJ GHV 2UWKRJRQDOLWlWVSULQ]LSV ]X
Ë PLQ , ˑ Z ’ , (H , ( _ G ‘ G 1 [% Z ’` , Ï G 1 Ï \ ZREHL
ÏG ,
( G XQG
Ï\,
( \ , Z% & Z ,
´%
Z ,
´%
´
GLH /HLVWXQJ GHV 5HIHUHQ]VLJQDOV
G XQG GHV 6FKlW]VLJQDOV \ GDUVWHOOHQ
)U GLH %HUHFKQXQJ GHV RSWLPDOHQ .RHIIL]LHQWHQYHNWRUV LVW GLH .HQQWQLV YRQ
XQG ∆ Q|WLJ
'HU 5HFKHQDXIZDQG GLHVHU %HUHFKQXQJ EHWUlJW 21
'LH 0HWKRGH GHV VWHLOVWHQ $EVWLHJV
,P OHW]WHQ $EVFKQLWW ZXUGH GLH GLUHNWH /|VXQJ GHV :LHQHU)LOWHUV JH]HLJW +LHU ZLUG HLQH
LWHUDWLYH /|VXQJ QlPOLFK GLH GHV VWHLOVWHQ $EVWLHJV YRUJHVWHOOW 'LH 0RWLYDWLRQ IU GLHVH
0HWKRGH LVW GLH 9HUPHLGXQJ GHU UHFKHQDXIZHQGLJHQ 0DWUL[LQYHUVLRQ
,GHH XQG $OJRULWKPXV
'HU 0HWKRGH GHV VWHLOVWHQ $EVWLHJV OLHJW GHU *HGDQNH ]XJUXQGH GD‰ GHU *UDGLHQWHQYHNWRU
∇ξZ
VWHWV LQ GLH 5LFKWXQJ GHV VWHLOVWHQ $EVWLHJV ]HLJW 'D QDFK GHP 0LQLPXP YRQ
JHVXFKW ZLUG LVW HV QDKHOLHJHQG DXVJHKHQG YRQ HLQHP $QIDQJVYHNWRU
1XOOYHNWRU
JHVHW]W
ZLUG
LQ
MHGHP
,WHUDWLRQVVFKULWW
GHQ
Z
ξZ
GHU KlXILJ ]XP
.RHIIL]LHQWHQYHNWRU
LQ
GLH
HQWJHJHQJHVHW]WH 5LFKWXQJ GHV DNWXHOOHQ *UDGLHQWHQYHNWRUV ]X NRUULJLHUHQ %H]HLFKQHQ ZLU
GHQ .RHIIL]LHQWHQYHNWRU GHU QWHQ ,WHUDWLRQ PLW
ZQ
VR ZLUG GHU .RHIIL]LHQWHQYHNWRU GHV
6HLWH $GDSWLYH )LOWHU
.DSLWHO
Q
WHQ ,WHUDLRQVVFKULWWHV ZLH IROJW EHUHFKQHW
+LHUEHL LVW
|
Z ‘ Q 0 ’ , Z ‘ Q’ 0
ˑ 3 ’ ,
|
ˑ Z ’b
Z , Z [3 \
—
_1
|
ˑ 3 ’ `
‡
GHU DNWXHOOH *UDGLHQWHQYHNWRU XQG — LVW HLQH
JHHLJQHW ]X
ZlKOHQGH SRVLWLYH .RQVWDQWH GLH GLH 6FKULWWZHLWH GHU ,WHUDWLRQ VWHXHUW 'HU )DNWRU ò GLHQW
OHGLJOLFK GD]X XP GHQ )DNWRU GHV *UDGLHQWHQYHNWRUV
|
ˑ 3 ’ ,1 _ [ ‘ / 1 [% Z ‘ 3 ’’ ` , 1 _
´
Z [ 3\`
]XJXQVWHQ HLQHU HLQIDFKHQ 'DUVWHOOXQJ ]X NRPSHQVLHUHQ 'DPLW HUJLEW VLFK GLH 5HNXUVLRQ ]X
Z ‘ 3 0 ’ , Z ‘ 3’ 0 a _
ZQ
'LH .RQYHUJHQ]DQDO\VH ]HLJW GD‰
´
Z [ 3\ `
H[SRQHQWLHOO JHJHQ
Z
NRQYHUJLHUW 'LH ,WHUDWLRQ ZLUG
VRODQJH ZLHGHUKROW ELV HLQ $EEUXFKVNULWHULXP ]% GLH 1RUP GHU 'LIIHUHQ] ]ZLVFKHQ
ZQ
ZQ
XQG
± NOHLQHU ZLUG DOV HLQH YRUJHJHEHQH 6FKUDQNH HUIOOW LVW 'HU 5HFKHQDXIZDQG GLHVHU
2SHUDWLRQHQ SUR ,WHUDWLRQ
'LH .RQYHUJHQ]DQDO\VH XQWHUVXFKW GLH %HGLQJXQJHQ XQG ZLH VFKQHOO ZQ ]X GHP RSWLPDOHQ
.RHIIL]LHQWHQYHNWRU Z NRQYHUJLHUW 'D]X ZLUG GLH (YROXWLRQ GHV )HKOHUYHNWRUV HQ ZQ ±
¹
Z EHWUDFKWHW hEHU GLH (LJHQZHUW]HUOHJXQJ GHU .RUUHODWLRQVPDWUL[ & , 8 & %
0HWKRGH EHWUlJW
21 'LDJRQDOPDWUL[
∑
HUJHEHQ VLFK GLH (LJHQZHUWH YRQ
∑
λ
]X
L
PLW L
PLW GHU
1 'LH QRWZHQGLJH
XQG KLQUHLFKHQGH .RQYHUJHQ]EHGLQJXQJ IU GLH 0HWKRGH GHV VWHLOVWHQ $EVWLHJV ODXWHW
ZREHL
λPD[
? ?È
PD[
—
GHQ JU|‰WHQ (LJHQZHUW YRQ & EH]HLFKQHW =XU 9HUDQVFKDXOLFKXQJ GHU 0HWKRGH
ZLUG GHU )DOO 1
EHWUDFKWHW ,Q GLHVHP )DOO VWHOOW GDV 0LQLPLHUXQJVNULWHULXP HLQ VLFK QDFK
REHQ |IIQHQGHV 3DUDERORLG GDU GHVVHQ WLHIVWHU 3XQNW GHU /|VXQJ GHU :LHQHU+RSI *OHLFKXQJ
Z
& ∆
HQWVSULFKW
'LH
+|KHQOLQLHQ
GHV
3DUDERORLGV
VLQG
NRQ]HQWULVFKH
(OOLSVHQ
'LH
$EELOGXQJ ]HLJW HLQH JHRPHWULVFKH ,QWHUSUHWDWLRQ GHU 0HWKRGH GHV VWHLOVWHQ $EVWLHJV ,Q
GLHVHP %HLVSLHO NRQYHUJLHUW GDV 6\VWHP YRQ
Z
7
QDFK
QDFK
Z IU Q
6HLWH .DSLWHO
$GDSWLYH )LOWHU
$EE 9HUDQVFKDXOLFKXQJ GHU 0HWKRGH GHV VWHLOVWHQ $EVWLHJV
YJO >:LGURZ 6WHDUQV @
=XVDPPHQIDVVXQJ GHU 0HWKRGH GHV VWHLOVWHQ $EVWLHJV
´
(LQJDQJ $XVJDQJ ZQ
3DUDPHWHU ? — ? È
PD[
6WDUWEHGLQJXQJHQ Z
)RU W 'R
Z ‘ Q’ , Z ‘ Q 1 ’ 0
—_
´
1
& Z ‘ Q 1 ’`
(QG
6HLWH .DSLWHO
$GDSWLYH )LOWHU
6WRFKDVWLVFKH *UDGLHQWHQYHUIDKUHQ
'HU /06$OJRULWKPXV
'LH 0HWKRGH GHV VWHLOVWHQ $EVWLHJV ZLUG VHOWHQ DQJHZDQGW GD GLH %HUHFKQXQJ GHV
*UDGLHQWHQYHNWRUV GLH .HQQWQLV GHU H[DNWHQ .RUUHODWLRQVPDWUL[ XQG GHV H[DNWHQ
´
.UHX]NRUUHODWLRQVYHNWRUV
YRUDXVVHW]W GLH LQ GHU 3UD[LV PHLVW QLFKW YHUIJEDU VLQG (LQ
$QVDW] ]XU 9HUPHLGXQJ GLHVHU 6FKZLHULJNHLW LVW GLH 6FKlW]XQJ GHV *UDGLHQWHQYHNWRUV DXV GHQ
%HREDFKWXQJHQ GHU 6LJQDOH
*HJHEHQ VHLHQ GLH %HREDFKWXQJHQ [Q >[Q [Q [1Q@7 XQG GQ IU W ! 'LH
$XIJDEH EHVWHKW GDULQ GQ GXUFK HLQH /LQHDUNRPELQDWLRQ DXV [LQ L 1 ]X VFKlW]HQ
/ ‘ Q’ ,
{, Z
1
L
L ‘ Q ’ [L ‘ Q ’ ,
Z% ‘ Q ’ [ ‘ Q ’
XQG GLH /HLVWXQJ GHV 6FKlW]IHKOHUV
H ‘ Q’ , G ‘ Q ’ 1 \ ‘ Q ’ , G ‘ Q ’ 1
Z% ‘ Q ’ [ ‘ Q ’
EHU GLH :DKO GHV .RHIIL]LHQWHQYHNWRUV ZQ ]X PLQLPLHUHQ 'LH 0HWKRGH GHV VWHLOVWHQ
$EVWLHJV HUPLWWHOW GHQ GDIU RSWLPDOHQ .RHIIL]LHQWHQYHNWRU
´
%
Z ‘ Q ’ , & ‘ 3 ’ ‘ 3 ’ , [ _ [ ‘ 3 ’ [ ‘ 3 ’ `\ _ [ ‘ 3 ’ / ‘ 3 ’`
GXUFK GLH IROJHQGH 5HNXUVLRQ
|
Z ‘ 3 ’ , Z ‘ 31 ’ 0 a _1 ˑ 31 ’`
'HU *UDGLHQWHQYHNWRU LVW JHJHEHQ GXUFK
|
‡
´
ˑ 31 ’ , 1 _ ‘ 3 ’ 1 ‘ 3 ’ Z ‘ 31 ’`
‡
(LQH QDKHOLHJHQGH 0|JOLFKNHLW ]XU 6FKlW]XQJ YRQ Q XQG ∆Q LVW GLH ]HLWOLFKH 0LWWHOXQJ YRQ
[Q[%Q XQG [QGQ EHU HLQ EHVWLPPWHV =HLWLQWHUYDOO %HVRQGHUV HLQIDFK VLQG MHGRFK GLH DXI
GHQ DNWXHOOHQ %HREDFKWXQJHQ EDVLHUHQGHQ PRPHQWDQHQ 6FKlW]XQJHQ
%
& ‘ Q ’ , [ ‘ Q ’ [
‘ Q’
XQG
´
‘ 3’ ,
[ ‘ 3’ / ‘ 3’
'LH HQWVSUHFKHQGH 6FKlW]XQJ GHV *UDGLHQWHQYHNWRUV LVW

 ‘ 31 ’ , 1 _ ‘ 3 ’ 1
Ë
‘ 3 ’ ‘ 31 ’ ` , 1 ‘ 3 ’ _ / ‘ 3 ’ 1
|
´

&
Z
[
‡
[ ‘ 3 ’ Z ‘ 31 ’`
%
‡
6HLWH .DSLWHO
$GDSWLYH )LOWHU
(V LVW ]X EHDFKWHQ GD‰
|
Ë ‘ 3’
ZHJHQ VHLQHU
VWRFKDVWLVFKHQ 1DWXU QLFKW XQEHGLQJW LQ GLH
JHZQVFKWH 5LFKWXQJ GHV VWHLOVWHQ $EVWLHJV ]HLJW 'D MHGRFK HLQH 5HNXUVLRQ LVW LVW HLQ
lKQOLFKHV 9HUKDOWHQ ZHJHQ GHU LQKlUHQWHQ ]HLWOLFKHQ 0LWWHOXQJ ]X HUZDUWHQ
6HW]W PDQ GLHVHQ VWRFKDVWLVFKHQ *UDGLHQWHQYHNWRU LQ GLH 5HNXUVLRQVIRUPHO HLQ HUJLEW
VLFK
Z ‘ 3 ’ , Z ‘ 31 ’ 0 — [ ‘ Q ’ _ G ‘ Q ’ 1 [% ‘ Q ’ Z ‘ Q1 ’`
, _, 1
,
— [ ‘ Q ’ [% ‘ Q ’` Z ‘ Q1 ’ 0 — [ ‘ Q ’ G ‘ Q ’
Z ‘ Q1 ’ 0 — [ ‘ Q ’ H ‘ QQ1 ’ ZREHL
H ‘ QQ1 ’ , G ‘ Q ’ 1 Z% ‘ Q1 ’ [ ‘ Q ’
GHU VRJHQDQQWH D SULRUL )HKOHU LVW GD HU GHQ 6FKlW]IHKOHU ]XP =HLWSXQNW Q XQWHU %HQXW]XQJ GHV
YRUDQJHJDQJHQHQ .RHIIL]LHQWHQYHNWRUV
ZQ ± GDUVWHOOW ,P *HJHQVDW] GD]X EH]HLFKQHW HQ
LQ GHQ EHU GHQ DNWXHOOHQ .RHIIL]LHQWHQYHNWRU
ZQ
GHILQLHUWHQ 6FKlW]IHKOHU ]XP
=HLWSXQNW Q *OHLFKXQJHQ XQG ELOGHQ ]XVDPPHQ PLW GHU :DKO GHV 6WDUWZHUWHV
/06$OJRULWKPXV HQJO /HDVW 0HDQ 6TXDUH 'LHVHU $OJRULWKPXV LVW ZHJHQ VHLQHU
(LQIDFKKHLW VHKU EHNDQQW XQG LQ GHU 3UD[LV ZHLW YHUEUHLWHW 'LH $NWXDOLVLHUXQJ GHV
.RHIIL]LHQWHQYHNWRUV EHQ|WLJW QXU 1 0XOWLSOLNDWLRQHQ XQG 1 $GGLWLRQHQ
'LH .RQYHUJHQ]DQDO\VH GHV /06$OJRULWKPXV LVW ZHJHQ VHLQHV VWRFKDVWLVFKHQ &KDUDNWHUV
ZHVHQWOLFK VFKZLHULJHU DOV EHL GHU 0HWKRGH GHV VWHLOVWHQ $EVWLHJV :lKUHQG GRUW DOOH *U|‰HQ
GHWHUPLQLVWLVFK VLQG PX‰ EHLP /06$OJRULWKPXV ZQ DOV HLQ QLFKWVWDWLRQlUHU VWRFKDVWLVFKHU
9HNWRUSUR]H‰ DXIJHID‰W ZHUGHQ GD GLH (LQJDQJVVLJQDOH [Q XQG GQ VHOEVW DOV VWRFKDVWLVFKH
3UR]HVVH PRGHOOLHUW ZHUGHQ (V ZHUGHQ GDKHU QXU GLH (UJHEQLVVH GHU .RQYHUJHQ]DQDO\VH LQ GHU
=XVDPPHQIDVVXQJ DXIJH]HLJW 'LH $EE ]HLJW HLQH JHRPHWULVFKH ,QWHUSUHWDWLRQ GHV /06
$OJRULWKPXV 6WDUWZHUW LVW ZLHGHUXP Z % XQG Q Z
GHQ
6HLWH .DSLWHO
$GDSWLYH )LOWHU
$EE 9HUDQVFKDXOLFKXQJ GHV /06$OJRULWKPXV
YJO >:LGURZ 6WHDUQV @
=XVDPPHQIDVVXQJ GHV /06$OJRULWKPXV
(LQJDQJ [Q GQ
$XVJDQJ ZQ
3DUDPHWHU ? — ?
6WDUWEHGLQJXQJHQ
)RU W
( c[ ‘ Q ’c
Z
YRUDXVJHVHW]W —
EÈ
PD[
'R
HQ Q ± ZQ
GQ ± Z%Q ± [Q
ZQ ± —[QHQQ ± (QG
6HLWH .DSLWHO
$GDSWLYH )LOWHU
)HKODQSDVVXQJ
1HEHQ GHU .RQYHUJHQ]EHGLQJXQJ LVW QRFK GHU VWDWLRQlUH =XVWDQG GHV /06$OJRULWKPXV
LQWHUHVVDQW ,Q GLHVHP $EVFKQLWW ZLUG GHU 5HVWIHKOHU ˑ’ , OLP ˑ 3’ XQG GHU *UHQ]ZHUW
3
l
(Y ‘ ’ , OLP (YL ‘ Q ’ DQJHJHEHQ )U HLQH DXVIKUOLFKH +HUOHLWXQJ GHU )HKODQSDVVXQJ ZLUG
L
DXI
Q
l
><DQJ @ YHUZLHVHQ 'HU WUDQVIRUPLHUWH 'LIIHUHQ]YHNWRU ;Q ZLUG EHU HLQH
(LJHQZHUW]HUOHJXQJ GHU 0DWUL[ HUKDOWHQ
'LH %HWUDFKWXQJ GHV *UHQ]EHUJDQJV
Q l IU -Q XQG &Q IKUW ]X
{, È ; ‘’
1
Ë ‘ ’ , Ë PLQ 0
L
L
L
;L ‘’ , ‘ 1 a È L 0 a È L ’ ;L ‘’ 0 a È L ˑ’
‡
6XPPLHUW PDQ GLH ]ZHLWH *OHLFKXQJ EHU DOOH L XQG VHW]W VLH LQ GLH HUVWH *OHLFKXQJ HLQ HUJLEW
VLFK QDFK HLQLJHQ 8PIRUPXQJHQ
ˑ’ ,
1 đ a ’
( Y ‘ ’ ,
L
ZREHL GLH )XQNWLRQ
η—
—
‘ 1
ËPLQ @ Ë PLQ —È ’
Ë ‘ ’ @ L
O GHILQLHUW LVW 'LHVHV (UJHEQLV YHUGHXWOLFKW HLQHQ ZLFKWLJHQ
8QWHUVFKLHG ]ZLVFKHQ GHU 0HWKRGH GHV VWHLOVWHQ $EVWLHJV XQG LKUHU VWRFKDVWLVFKHQ 9DULDQWH
:lKUHQG
EHLP
HUVWJHQDQQWHQ
ξQ
JHJHQ
ξPLQ
NRQYHUJLHUW
NDQQ
GHU
06(
GHV
/06
$OJRULWKPXV QLHPDOV GLHVHQ PLQLPDOHQ :HUW HUUHLFKHQ 'HU *UXQG KLHUIU LVW GLH 9HUZHQGXQJ
GHV VWRFKDVWLVFKHQ *UDGLHQWHQYHNWRUV XQG HLQHU NRQVWDQWHQ 6FKULWWZHLWH $XV VLHKW PDQ
GD‰
VLFK
EHU
GHQ
.RUUHNWXUWHUP
— [ ‘ Q ’ H ‘ QQ 1 ’
GLH
=XIlOOLJNHLW
GHU
PRPHQWDQHQ
%HREDFKWXQJHQ [Q DXI GHQ .RHIIL]LHQWHQYHNWRU ZQ EHUWUlJW 'LHV LVW GLH 8UVDFKH IU GLH
)OXNWXDWLRQ YRQ ZQ 'D — NRQVWDQW LVW EOHLEW GLH YRQ GHP .RUUHNWXUWHUP —[QHQQ
DQJHUHJWH )OXNWXDWLRQ LPPHU YRQ 1XOO YHUVFKLHGHQ
‘ ( Y L ‘ ’ @
’ ZDV VLFK LKUHUVHLWV LQ
GHP YHUJU|‰HUWHQ 5HVWIHKOHU Ë ‘ ’ @ ËPLQ DXVGUFNW 7KHRUHWLVFK LVW ]ZDU P|JOLFK GXUFK GLH
:DKO HLQHU ]HLWYDULDQWHQ JHJHQ QXOO NRQYHUJLHUHQGH 6FKULWWZHLWH —Q HLQH YHUVFKZLQGHQGH
)OXNWXDWLRQ ( YL ‘ ’ , E]Z Ë ‘ ’ , Ë PLQ ]X HU]LHOHQ :LUG DEHU GLH 6FKULWWZHLWH ]X NOHLQ
LVW GHU /06$OJRULWKPXV QLFKW PHKU DGDSWLRQVIlKLJ
6HLWH .DSLWHO
$GDSWLYH )LOWHU
$OV .RPSURPL‰ ZlKOW PDQ PHLVWHQV HLQH NOHLQH DEHU NRQVWDQWH 6FKULWWZHLWH
'LH DXI ξPLQ QRUPLHUWH $EZHLFKXQJ GHV 5HVWIHKOHUV YRQ GHP PLQLPDOHQ 06( ZLUG GLH
)HKODQSDVVXQJ HQJO PLVDGMXVWPHQW JHQDQQW
1
1
0 , ˑ’Ë1 FLPLQ , 1đ𗠒— ’ I — { ÈL IU — { ÈL E PLQ
L ,
L ,
6LH JLEW DQ XP ZLHYLHO 3UR]HQW GHU 5HVWIHKOHU GHQ PLQLPDOHQ 06( EHUVFKUHLWHW (V LVW
HLQVLFKWOLFK GD‰ IU HLQH JHULQJH )HKODQSDVVXQJ GLH 6FKULWWZHLWH — NOHLQ JHZlKOW ZHUGHQ PX‰
$XI GHU DQGHUHQ 6HLWH LVW DXV GHQ 'LVNXVVLRQHQ EHU GLH 0HWKRGH GHV VWHLOVWHQ $EVWLHJV
EHNDQQW GD‰ HLQH VFKQHOOH .RQYHUJHQ] HLQH JUR‰H 6FKULWWZHLWH YRUDXVVHW]W 'LHVH
ZLGHUVSUFKOLFKH $QIRUGHUXQJ DQ GLH :DKO GHU 6FKULWWZHLWH VWHOOW QHEHQ GHU (PSILQGOLFKNHLW
GHU .RQYHUJHQ]JHVFKZLQGLJNHLW JHJHQEHU GHU .RQGLWLRQV]DKO GHU .RUUHODWLRQVPDWUL[ HLQHQ
ZHLWHUHQ 1DFKWHLO GHV /06$OJRULWKPXV GDU
6HLWH .DSLWHO
)LOWHUVWUXNWXUHQ IU DNWLYH 5HGXNWLRQVV\VWHPH
)LOWHUVWUXNWXUHQ IU DNWLYH 5HGXNWLRQVV\VWHPH
hEHUVLFKW
,Q .DSLWHO ZHUGHQ GLH XQWHUVFKLHGOLFKHQ JUXQGOHJHQGHQ )LOWHUVWUXNWXUHQ IU DGDSWLYH
6\VWHPH
DQJHIKUW
5HIHUHQ]VHQVRU
HLQH
(V
ZHUGHQ
QXU
6HNXQGlUTXHOOH
HLQNDQDOLJH
XQG
HLQHQ
6\VWHPH
EHVFKULHEHQ
)HKOHUVHQVRU
GLH
EHVLW]HQ
QXU
HLQHQ
$XFK
GLH
6\VWHPLGHQWLILNDWLRQ ZLUG NXU] EHKDQGHOW ZREHL VLH .DSLWHO QRFKPDOV EHL GHU SUDNWLVFKHQ
5HDOLVLHUXQJ HUZlKQW ZLUG
6HLWH .DSLWHO
)LOWHUVWUXNWXUHQ IU DNWLYH 5HGXNWLRQVV\VWHPH
6\VWHPLGHQWLILNDWLRQ
(LQ DGDSWLYHU )LOWHU NDQQ ]XP 1DFKELOGHQ HLQHV SK\VLNDOLVFKHQ 6\VWHPV YHUZHQGHW ZHUGHQ (LQ
%HLVSLHO LQ GHP HLQ HLQNDQDOLJHV 6\VWHP QDFKJHELOGHW ZLUG LVW LQ $EE GDUJHVWHOOW 'DV
XQEHNDQQWH 6\VWHP 3] XQG GHU DGDSWLYH )LOWHU :] YHUZHQGHQ GDV VHOEH (LQJDQJVVLJQDO 'HU
DGDSWLYH )LOWHU YHUVXFKW VHLQ $XVJDQJVVLJQDO \Q VR HLQ]XVWHOOHQ GD‰ HV GHP $XVJDQJVVLJQDO
GQ GHV 6\VWHPV 3] HQWVSULFKW (V IROJW (] >3] ± :]@;] .RQYHUJLHUW GHU DGDSWLYH
)LOWHU VR ZLUG :] 3]
:LUG HLQ ),5)LOWHU YHUZHQGHW HUJLEW VLFK GDV )HKOHUVLJQDO ]X H ‘ Q ’ , G ‘ Q ’ 1
{, K
L
L
[ [ Q L \
PLW K DOV .RHIIL]LHQWHQ YRQ :]
8P YRU DOOHP EHL EUHLWEDQGLJHQ (LQJDQJVVLJQDOHQ HLQH JXWH 1DFKELOGXQJ ]X HUP|JOLFKHQ PX‰
GHU DGDSWLYH )LOWHU DXVUHLFKHQG YLHOH .RHIIL]LHQWHQ EHVLW]HQ
6LQG GLH 2SWLPLHUXQJVNRHIIL]LHQWHQ GHV $GDSLRQVDOJRULWKPXV ULFKWLJ JHZlKOW ZLUG HLQ
0LQLPLHUHQ GHV PLWWOHUHQ TXDGUDWLVFKHQ )HKOHUV HLQ DXVJH]HLFKQHWHV 0RGHOO OLHIHUQ ,Q GLHVHU
$QZHQGXQJ LQWHUHVVLHUHQ PHLVW GLH )LOWHUNRHIIL]LHQWHQ ]XU SDUDPHWULVFKHQ %HVFKUHLEXQJ GHV
6\VWHPV
L
(LQJDQJVVLJQDO
[Q
8QEHNDQQWHV
6\VWHP 3]
$GDSWLYHU
)LOWHU :]
$XVJDQJVVLJQDO YRQ 3]
GQ
B
∑
)HKOHUVLJQDO
HQ
$XVJDQJVVLJQDO YRQ :]
\Q
$EE 6\VWHPLGHQWLILNDWLRQ
YJO >1HOVRQ (OOLRW @
6HLWH .DSLWHO
)LOWHUVWUXNWXUHQ IU DNWLYH 5HGXNWLRQVV\VWHPH
$GDSWLYH )HHGIRUZDUG 6WUXNWXU
%HL GHQ DQJHIKUWHQ )HHGIRUZDUG 6WUXNWXUHQ KDQGHOW HV VLFK XP 6\VWHPH ]XU DNWLYHQ
5HGXNWLRQ YRQ 6W|UVLJQDOHQ (LQ 6WUXNWXUGLDJUDPP HLQHU %UHLEDQG )HHGIRUZDUG 6WUXNWXU LVW LQ
$EELOGXQJ ]X VHKHQ 'LHVH 6\VWHPH EHQ|WLJHQ HLQ 5HIHUHQ]VLJQDO [Q ZHOFKHV EHL GHU
DNWLYHQ 6FKZLQJXQJVUHGXNWLRQ ]% YRQ HLQHP %HVFKOHXQLJXQJVVHQVRU RGHU HLQHP
'UHK]DKOVHQVRU VWDPPHQ NDQQ 'HU DGDSWLYH )LOWHU YHUVXFKW PLW +LOIH YRQ [Q XQG GHP
)HKOHUVLJQDOV HQ VHLQ $XVJDQJVVLJQDO \Q 6FKlW]VLJQDO VR HLQ]XVWHOOHQ GD‰ HQ JHJHQ QXOO
JHKW 6] VWHKW LP 6WUXNWXUGLDJUDPP IU GLH 6HNXQGlUSIDGWUDQVIHUIXQNWLRQ ]ZLVFKHQ \Q XQG
HQ 'DULQ HQWKDOWHQ VLQG ]% :DQGOHU 9HUVWlUNHU 6HQVRUHQ (LQH JHQDXH %HVFKUHLEXQJ GHU
YRQ 6] EHUFNVLFKWLJWHQ (OHPHQWH IU GLH $9& $QZHQGXQJ ZLUG QRFK LQ .DSLWHO YRUJHQRPPHQ
5HIHUHQ]VLJQDO
[Q
8QEHNDQQWHV
6\VWHP 3]
$GDSWLYHU
)LOWHU :]
6W|UVLJQDO
GQ
B
)HKOHUVLJQDO
HQ
6FKlW]VLJQDO 6HNXQGlU \Q
SIDG 6] JHILOWHUWHV
\Q
6FKlW]VLJQDO
2SWLPLHUXQJV
DOJRULWKPXV
$EE 6WUXNWXUGLDJUDPP HLQHU %UHLEDQG )HHGIRUZDUG 6WUXNWXU
$XV GHP 6WUXNWXUGLDJUDPP HUNHQQW PDQ GD‰ VLFK GLH =7UDQVIRUPLHUWH GHV )HKOHUVLJQDOV DXV
(] >3] ± 6] :]@ ;]
]XVDPPHQVHW]W $OV 9HUHLQIDFKXQJ NDQQ QDFK GHP .RQYHUJLHUHQ GHV DGDSWLYHQ )LOWHUV GDV
)HKOHUVLJQDO DOV ,GHDOHUZHLVH DQJHQRPPHQ ZHUGHQ 'DUDXV IROJW GLH LGHDOH 7UDQVIHUIXQNWLRQ
:] 3] 6]
,Q :RUWHQ 'HU DGDSWLYH )LOWHU :] PX‰ GDV 6\VWHP 3] XQG JOHLFK]HLWLJ GHQ 6HNXQGlUSIDG
YJO >.XR 0RUJDQ @
6HLWH .DSLWHO
6]
)LOWHUVWUXNWXUHQ IU DNWLYH 5HGXNWLRQVV\VWHPH
LQYHUV QDFKELOGHQ 'HU JUR‰H 9RUWHLO GLHVHU 0HWKRGH LVW GD‰ PLW HLQHP H[DNWHQ 0RGHOO
GHU 5HJHOVWUHFNH GDV 6\VWHP VRIRUW DXI HLQH bQGHUXQJ GHV (LQJDQJVVLJQDOV UHDJLHUHQ NDQQ
'HP GLJLWDOHQ 6LJQDOSUR]HVVRU VWHKW GLH 9HU]|JHUXQJV]HLW YRQ
3]
]XU 9HUIJXQJ XP GDV
LGHDOH *HJHQNRSSOXQJVVLJQDO ]X EHUHFKQHQ XQG GLH XQYHUPHLGEDUH 9HU]|JHUXQJ YRQ
6]
]X
NRPSHQVLHUHQ ,VW GLHV P|JOLFK ZUGH GLH $QWZRUW GHV 3UR]HVVRUV NDXVDO VHLQ 'DPLW NDQQ GDV
$9&6\VWHP
DXFK
%UHLWEDQGHLQJDQJVVLJQDOH
DXVO|VFKHQ
$QVRQVWHQ
N|QQHQ
QXU
VFKPDOEDQGLJH RGHU SHULRGLVFKH 6LJQDOH ZLUNXQJVYROO EHNlPSIW ZHUGHQ
)HHGIRUZDUG 6WUXNWXU PLW );/06$OJRULWKPXV
:LUG DOV 2SWLPLHUXQJVDOJRULWKPXV IU GHQ DGDSWLYHQ )LOWHU GHU /06$OJRULWKPXV YHUZHQGHW
N|QQHQ OHLFKW 3UREOHPH GXUFK ,QVWDELOLWlWHQ LP 5HJHONUHLV DXIWUHWHQ GD GDV $XVO|VFKVLJQDO XQG
GDV )HKOHUVLJQDO HLQH YRQ GHU )UHTXHQ] DEKlQJLJH 9HU]|JHUXQJ GXUFK GHQ 6HNXQGlUSIDG 6]
EHVLW]HQ 8P GLHVHQ (IIHNW ]X NRPSHQVLHUHQ NDQQ HLQ LGHQWLVFKHU )LOWHU 6 ] LP
5HIHUHQ]VLJQDOSIDG SOD]LHUW ZHUGHQ XP GDPLW ]XVlW]OLFK GLH *HZLFKWH GHV /06$OJRULWKPXV
LP 9RUDXV ]X DNWXDOLVLHUHQ 'LHV HQWVSULFKW GHP VRJHQDQQWHQ JHILOWHUWHQ ;/06$OJRULWKPXV

[ \
DXFK );/06$OJRULWKPXV JHQDQQW 'HU );/06$OJRULWKPXV LVW GHU EHL $9& 6WUXNWXUHQ
DP KlXILJVWHQ YHUZHQGHWH $OJRULWKPXV (U ZXUGH YRQ :LGURZ IU DGDSWLYH
.RQWUROOVWUXNWXUHQ XQG YRQ %XUJHVV IU $1& $QZHQGXQJHQ DEJHOHLWHW 'LH 4XDOLWlW GHV
DNWLYHQ 5HGXNWLRQVV\VWHPV LVW DEHU DXFK VWDUN YRQ GHU 7UDQVIHUIXQNWLRQ GHV 6HNXQGlUSIDGV
DEKlQJLJ ZHOFKH GXUFK HLQH 6\VWHPLGHQWLILNDWLRQ EHVWLPPW ZLUG
$EELOGXQJ ]HLJW HLQ 6WUXNWXUGLDJUDPP HLQHU )HHGIRUZDUG 6WUXNWXU PLW );/06
$OJRULWKPXV
YJO >:LGURZ 6WHDUQV @
YJO >%XUJHVV @
6HLWH .DSLWHO
)LOWHUVWUXNWXUHQ IU DNWLYH 5HGXNWLRQVV\VWHPH
5HIHUHQ]VLJQD
8QEHNDQQWHV
6\VWHP 3]
[Q
6W|UVLJQDO
GQ
B
)HKOHUVLJQDO
HQ
$GDSWLYHU 6FKlW]VLJQDO 6HNXQGlU
SIDG 6] \Q
\Q
)LOWHU :]
A
6]
[Q
JHILOWHUWHV 5HIHUHQ]VLJQD /06
$EE 6WUXNWXUGLDJUDPP HLQHU )HHGIRUZDUG 6WUXNWXU PLW );/06$OJRULWKPXV
$EOHLWXQJ GHV );/06$OJRULWKPXV
'LH $EOHLWXQJ GHV );/06$OJRULWKPXV NDQQ DQKDQG $EE YHUIROJW ZHUGHQ 'DV VLFK
HUJHEHQGH )HKOHUVLJQDO NDQQ PDQ GXUFK
HQ
DXVGUFNHQ ZREHL
3
GQ ± VQ > Z%Q [Q @
GHU =HLWLQGH[ LVW VQ IU GLH ,PSXOVDQWZRUW GHV 6HNXQGlUSIDGHV 6]
VWHKW XQG HLQH OLQHDUH )DOWXQJ DQ]HLJW 'HU .RHIIL]LHQWHQYHNWRU YRQ :] LVW
ZQ ZQZ
Q@
%
XQG GHU 6LJQDOYHNWRU LVW
IU GLH )LOWHURUGQXQJ 'HU
[Q
ZQ
>ZQ
>[Q [Q [Q1@% 1 VWHKW
)LOWHU :] PX‰ YRQ DXVUHLFKHQG JUR‰HU 2UGQXQJ VHLQ XP GLH
$QWZRUW GHV SK\VLNDOLVFKHQ 6\VWHPV JHQJHQG JHQDX PRGHOOLHUHQ ]X N|QQHQ 9RUDXVJHVHW]W
ξ(Q
(>HQ@
LVW GLH PLWWOHUH TXDGUDWLVFKH .RVWHQIXQNWLRQ GDQQ PLQLPLHUW GHU DGDSWLYH
)LOWHU GHQ PRPHQWDQHQ TXDGUDWLVFKHQ )HKOHU

ˑ Q ’ , H ‘ 3 ’
PLW +LOIH GHV $OJRULWKPXV GHV VWHLOVWHQ $EVWLHJHV 'LHVHU YHUlQGHUW GHQ .RHIIL]LHQWHQYHNWRU LQ
GLH 5LFKWXQJ GHV QHJDWLYHQ *UDGLHQWHQ PLW GHU 6FKULWWZHLWH
|
Z ‘ 30 ’ , Z ‘ 3 ’ 1 a Ë ‘ 3 ’
a XQG PDQ HUKlOW
‡
(LQH $XVIKUOLFKHUH +HUOHLWXQJ ZXUGH LQ .DSLWHO YRUJHQRPPHQ
6HLWH .DSLWHO
|
ˑ 3 ’
)LOWHUVWUXNWXUHQ IU DNWLYH 5HGXNWLRQVV\VWHPH
LVW GHU
|
|
ˑ 3 ’ ,
]XU =HLW Q XQG ZLUG GXUFK
$XV
IROJW
PLW [Q
|
|
PRPHQWDQH 6FKlW]ZHUW GHV PLWWOHUHQ TXDGUDWLVFKHQ )HKOHUJUDGLHQWHQ 06(
0 ‘ 3’ , _
0 ‘ 3 ’` 0 ‘ 3 ’
DXVJHGUFNW
H ‘ Q ’ , 1 V ‘ Q ’ 2 [ ‘ Q ’ , 1 [ ‘ Q ’ >[Q [Q [Q/@% XQG [Q
VQ [Q
'HVKDOE ZLUG GLH 6FKlW]XQJ GHV *UDGLHQWHQ ]X
|
 ‘ Q ’ , 1 [ ‘ Q ’ H ‘ Q ’
Ë
‡
6HW]W PDQ LQ HLQ VR HUKlOW PDQ GHQ );/06$OJRULWKPXV
ZQ ZQ — [Q HQ
,Q GHQ SUDNWLVFKHQ $QZHQGXQJHQ LVW
6]

XQEHNDQQW XQG PX‰ GXUFK GHQ )LOWHU
6 ‘ ]’
JHVFKlW]W ZHUGHQ 'XUFKOlXIW GDV 5HIHUHQ]VLJQDO GLHVH 1lKHUXQJ GHV 6HNXQGlUSIDGHV HQWVWHKW
GDV JHILOWHUWH 5HIHUHQ]VLJQDO
[ ‘ Q ’ , V ‘ Q ’ 2 [ ‘ Q ’ V ‘ Q ’
6 ‘ ] ’ 'HU );/06$OJRULWKPXV
‡
 ‘ ]’
LVW VHKU WROHUDQW LQ %H]XJ DXI )HKOHU GLH LQ GHU 6FKlW]XQJ YRQ 6] GXUFK GHQ )LOWHU 6
PLW
DOV GLH ,PSXOVDQWZRUW GHV 6HNXQGlUSIDGILOWHUV
HU]HXJW ZHUGHQ 8QWHU GHU 9RUDXVVHW]XQJ HLQHU ODQJVDPHQ $GDSWLRQ OLHJW GLH *UHQ]H IU GLH
.RQYHUJHQ] EHL FD *UDG 3KDVHQIHKOHU ]ZLVFKHQ
RIIOLQH0RGHOOLHUXQJ
GD]X
YHUZHQGHW
ZHUGHQ
XP
6]
6]
XQG
6 ‘ ] ’
ZlKUHQG
‡
'HVKDOE NDQQ HLQH
HLQHV
YRUDXVJHKHQGHQ
7UDLQLQJV DE]XVFKlW]HQ
6HLWH .DSLWHO
)LOWHUVWUXNWXUHQ IU DNWLYH 5HGXNWLRQVV\VWHPH
$GDSWLYH )HHGEDFN 6WUXNWXU
%HL GHQ )HHGEDFN 6\VWHPHQ VWHKW QXU GDV )HKOHUVLJQDO
HQ ]XU 9HUIJXQJ XP GDV
6FKlW]VLJQDO \Q ]X HU]HXJHQ 'DV 6FKlW]VLJQDO HQWVSULFKW GHP *HJHQNRSSOXQJVVLJQDO GHV
DGDSWLYHQ )LOWHUV ,Q $EE LVW HLQ YHUHLQIDFKWHV 6WUXNWXUGLDJUDPP GDUJHVWHOOW 'DUDXV LVW ]X
HUNHQQHQ GD‰ ']
(] 6] <]
(] LVW GDEHL GDV 6LJQDO GHV )HKOHUVHQVRUV XQG <] GDV VHNXQGlUH 6LJQDO %HL GHU 9HUZHQGXQJ
GHV /06$OJRULWKPXV ]XU $GDSWLRQ GHV )LOWHUV :] ZLUG YHUVXFKW GHQ PLWWOHUHQ TXDGUDWLVFKHQ
)HKOHU (>HQ@ DXI HLQ 0LQLPXP ]X UHGX]LHUHQ 'D DXFK KLHU GHU 6HNXQGlUSIDG VWDUNHQ (LIOX‰
DXI GLH )XQNWLRQ GHV 6\VWHPV KDW NDQQ HLQ GHXWOLFKH 9HUEHVVHUXQJ GXUFK GLH ,PSOHPHQWLHUXQJ
GHV );/06$OJRULWKPXV HUUHLFKW ZHUGHQ
6W|UVLJQDO
GQ
$GDSWLYHU
)LOWHU :]
6FKlW]VLJQDO
\Q
6HNXQGlUSIDG
6]
B
∑
)HKOHUVLJQDO
HQ
$EE 9HUHLQIDFKWHV 6WUXNWXUGLDJUDPP HLQHV )HHGEDFN 6\VWHPV
)HHGEDFN 6WUXNWXU PLW );/06$OJRULWKPXV
(LQ JHVDPWHV HLQNDQDOLJHV DGDSWLYHV )HHGEDFN 6\VWHP PLW );/06$OJRULWKPXV LVW LQ $EE GDUJHVWHOOW 'LH $EELOGXQJ VROO ]XP OHLFKWHUHQ 9HUVWlQGQLV GHU )XQNWLRQ GLHQHQ 'LH
JUXQGVlW]OLFKH ,GHH LVW GDV SULPlUH 6W|UVLJQDO GQ ]X EHZHUWHQ XQG DOV 5HIHUHQ]VLJQDO [Q ]X

YHUZHQGHQ 'HU )LOWHU 6 [ ] \ LVW ZLHGHU HLQH P|JOLFKVW LGHDOH 1DFKELOGXQJ GHV UHDOHQ
6HNXQGlUSIDGHV 6] XQG GLHQW ]X GHVVHQ .RPSHQVDWLRQ
YJO >.XR 0RUJDQ @
6HLWH .DSLWHO
)LOWHUVWUXNWXUHQ IU DNWLYH 5HGXNWLRQVV\VWHPH
%HL 9HUZHQGXQJ GHU 5HIHUHQ]VLJQDOV\QWKHVH ZLUG GDV VHNXQGlUH 6LJQDO \Q GXUFK GLH

6HNXQGlUSIDGQlKHUXQJ 6 ‘ ] ’ JHILOWHUW XQG GDQDFK PLW HQ NRPELQLHUW XP GDV NQVWOLFK
HU]HXJWH 5HIHUHQ]VLJQDO G ‘ Q ’ , [ ‘ Q’ ]X JHQHULHUHQ 'DPLW LVW
 ‘ ] ’ ,( ‘ ] ’ 0 6
 ‘ ]’< ‘ ]’
; ‘ ]’ K '
‡
6W|UVLJQDO
GQ
5HIHUHQ]VLJQDO
[Q
$GDSWLYHU
)LOWHU :]
6FKlW]VLJQDO
∑
B
6HNXQGlUSIDG
)HKOHUVLJQDO
HQ
6]
\Q
A
6]
A
6]
[Q
/06
A
GQ
NQVWOLFK JHQHULHUWHV 5HIHUHQ]VLJQDO
∑
$EE $GDSWLYHV )HHGEDFN 6\VWHP PLW );/06$OJRULWKPXV
'DV 5HIHUHQ]VLJQDO [Q VHW]W VLFK ]XVDPPHQ DXV
[ ‘ Q’ , G ‘ Q ’ , H ‘ Q ’ 0

PLW
V2 P
{
2, V2 \ ‘ Q1 P’

0 DOV .RHIIL]LHQWHQ GHU )LOWHU 0WHU 2UGQXQJ 6 [ ] \
W
6HLWH .DSLWHO
)LOWHUVWUXNWXUHQ IU DNWLYH 5HGXNWLRQVV\VWHPH
+\EULG 6WUXNWXU
=XU 9HUYROOVWlQGLJXQJ ZLUG KLHU GLH +\EULG 6WUXNWXU QRFK NXU] HUZlKQW 'LHVH LVW GLH
.RPELQDWLRQ GHU )HHGIRUZDUG XQG )HHGEDFN 6WUXNWXU
'HU 5HIHUHQ]VHQVRU OLHJW P|JOLFKVW QDKH DQ GHU SULPlUHQ 6W|UTXHOOH XQG YHUVRUJW GDV
)HHGIRUZDUG 6\VWHP PLW GHP 5HIHUHQ]VLJQDO [Q 'HU )HKOHUVHQVRU ZLUG QDFKJHVFKDOWHW XQG
QLPPW GDV YHUEOHLEHQGH )HKOHUVLJQDO HQ DXI GDV ]XP (U]HXJHQ HLQHV 5HIHUHQ]VLJQDOV IU GLH
)HHGEDFNVFKOHLIH DOV DXFK IU GLH $GDSWLRQ GHU EHLGHQ DGDSWLYHQ )LOWHU GLHQW 'HU
)HHGIRUZDUG]ZHLJ O|VFKW 6W|UVLJQDODQWHLOH GLH PLW GHP 5HIHUHQ]VLJQDO NRUUHOLHUHQ DXV XQG GHU
)HHGEDFNWHLO YHUPLQGHUW GLH YRUKHUVDJEDUHQ .RPSRQHQWHQ GLH GXUFK GHQ 5HIHUHQ]VHQVRU QLFKW
EHDFKWHW ZHUGHQ
,Q $EE LVW HLQ YHUHLQIDFKWHV 6WUXNWXUGLDJUDPP HLQHV +\EULG 6\VWHPV GDUJHVWHOOW 'DV
VHNXQGlUH 6LJQDO \Q ZLUG GXUFK GLH $XVJlQJH EHLGHU )LOWHU GHP )HHGIRUZDUG )LOWHU $] XQG
GHP )HHGEDFN )LOWHU &] HU]HXJW 'HU NRPELQLHUWH .RQWUROOHU :] EHVLW]W GLH

'LH
JHILOWHUWHQ 6LJQDOH [Q XQG G ‘ Q’ ZHUGHQ ]XU .RHIIL]LHQWHQDGDSWLRQ YRQ :] XQG : ]
YHUZHQGHW (LQ 6\VWHP PLW ,PSOHPHQWLHUXQJ GHV );/06$OJRULWKPXV ]HLJW QRFK $EELOGXQJ
'LH 9RUWHLOH GLHVHU 6\VWHPH OLHJHQ LQ HLQHU QLHGULJHUHQ YHUZHQGEDUHQ )LOWHURUGQXQJ XQG
GHU EHVVHUHQ )XQNWLRQ DOV HV GLH MHZHLOV HLQ]HOQHQ 6\VWHPH KlWWHQ
5HIHUHQ]HLQJlQJH
[Q
YRP 5HIHUHQ]VHQVRU XQG GDV HUZDUWHWH 3ULPlUVLJQDO G ‘ Q ’
‡
5HIHUHQ]VLJQD
[Q
3]
GQ B
\Q
)HHGIRUZDUG
$9&
)HKOHUVLJQDO
∑
∑
HQ
6FKlW]
VLJQDO
)HHGEDFN
$9&
$EE 9HUHLQIDFKWHV 6WUXNWXUGLDJUDPP HLQHV +\EULG 6\VWHPV
YJO >.XR 0RUJDQ @
6HLWH .DSLWHO
)LOWHUVWUXNWXUHQ IU DNWLYH 5HGXNWLRQVV\VWHPH
5HIHUHQ]VLJQDO
[Q
A6]
6W|UVLJQDO
8QEHNDQQW
6\VWHP 3]
[Q
GQ
/06
: ]
B
∑
6FKlW]VLJQDO
\Q
∑
HQ
6]
)HKOHUVLJQDO
HQ
: ]
A6]
A
GQ
A
GQ
/06
NQVWO 5HIHUHQ]VLJQDO
A6]
∑
$EE +\EULG 6\VWHP PLW );/06$OJRULWKPXV
6HLWH .DSLWHO
$NWLYH 6FKZLQJXQJVUHGXNWLRQ
$NWLYH 6FKZLQJXQJVUHGXNWLRQ
hEHUVLFKW
'LH DNWLYH 6FKZLQJXQJVUHGXNWLRQ LVW HLQH SUDNWLVFKH $QZHQGXQJ GHU DGDSWLYHQ
)LOWHUVWUXNWXUHQ 'DV LP =XJH GLHVHU 'LSORPDUEHLW HQWZLFNHOWH 6\VWHP IU .UDIWIDKU]HXJH
ZXUGH LQ HLQHU 6FKPDOEDQG )HHGIRUZDUG 6WUXNWXU UHDOLVLHUW XQG LVW LQ .DSLWHO QlKHU
EHVFKULHEHQ =XYRU ZHUGHQ GLH *UXQGODJHQ GHU YHUZHQGHWHQ 6WUXNWXU GLH DGDSWLYH 1RWFK
)LOWHUXQJ HUOlXWHUW
6HLWH .DSLWHO
$NWLYH 6FKZLQJXQJVUHGXNWLRQ
6FKPDOEDQG )HHGIRUZDUG 6WUXNWXU
(LQOHLWXQJ
9LHOH 6W|UJHUlXVFKH VLQG SHULRGLVFK EHVRQGHUV MHQH YRQ 0DVFKLQHQ .RPSUHVVRUHQ 0RWRUHQ
/IWHUQ 3URSHOOHUQ 0LW +LOIH YRQ 6HQVRUHQ ZLUG HLQ HOHNWULVFKHV 5HIHUHQ]VLJQDO HU]HXJW GDV
GLH *UXQGIUHTXHQ] GHU 6W|UXQJ XQG GHUHQ +DUPRQLVFKH HQWKlOW
9RUWHLOH GHU 6FKPDOEDQG )HHGIRUZDUG $9&
8QJHZROOWH 5FNZLUNXQJHQ GHV $XVO|VFKVLJQDOV DXI GDV 5HIHUHQ]VLJQDO ZHUGHQ YHUPLHGHQ
1LFKWOLQHDULWlWHQ XQG $OWHUXQJ GHV 5HIHUHQ]VHQVRUV KDEHQ EHLQDKH NHLQHQ (LQIOX‰ DXI GDV
5HIHUHQ]VLJQDO
'XUFK GLH 3HULRGL]LWlW GHU 6W|UVLJQDOH LVW GLH .DXVDOLWlW QLFKW ]ZLQJHQG QRWZHQGLJ
(V EHVWHKW GLH 0|JOLFKNHLW MHGH +DUPRQLVFKH JHWUHQQW ]X NRQWUROOLHUHQ GD GDV
5HIHUHQ]VLJQDO GLH *UXQGVFKZLQJXQJ HQWKlOW
%HL GHU 0RGHOOLHUXQJ GHU hEHUWUDJXQJVIXQNWLRQ GHV 6HNXQGlUSIDGHV PX‰ QXU GHU
)UHTXHQ]EHUHLFK EHVWLPPW ZHUGHQ LQ GHP VLFK GLH +DUPRQLVFKHQ EHZHJHQ 'DGXUFK
N|QQHQ ),5 )LOWHU PLW UHODWLY QLHGULJHU 2UGQXQJ YHUZHQGHW ZHUGHQ
$GDSWLYH 1RWFK)LOWHU
'LH $SSOLNDWLRQ GHU DGDSWLYHQ 1RWFK)LOWHUXQJ ZXUGH YRQ =LHJOHU IU GLH SHULRGLVFKH $1&
HQWZLFNHOW 'LH 9RUWHLOH GHU DGDSWLYHQ 1RWFK)LOWHU VLQG HLQH HLQIDFKH .RQWUROOH GHU %DQGEUHLWH
XQG GLH 0|JOLFKNHLW GHU H[DNWHQ )UHTXHQ] XQG 3KDVH GHU ,QWHUIHUHQ] ]X IROJHQ $EELOGXQJ ]HLJW HLQHQ DGDSWLYHQ 1RWFK)LOWHU PLW ]ZHL *HZLFKWHQ ]XU )LOWHUXQJ HLQHU HLQ]HOQHQ )UHTXHQ]
'DV 5HIHUHQ]VLJQDO LVW HLQ .RVLQXV PLW [Q [Q &FRVωQφ ZREHL $ GLH $PSOLWXGH
XQG ω GLH )UHTXHQ] LVW 8P GLH ]ZHLWH .RPSRQHQWH [Q &VLQωQφ ]X HU]HXJHQ ZLUG
GLH 6LJQDOSKDVH XP ƒ JHGUHKW 'LH ]ZHL 5HIHUHQ]VLJQDOH [Q XQG [Q ZHUGHQ LP 1RWFK
)LOWHU GXUFK ZQ XQG ZQ JHWUHQQW JHZLFKWHW XQG GDQDFK ]XU (U]HXJXQJ GHV
YJO >.XR 0RUJHQ @
YJO>:LGURZ 6WHDUQV @
YJO >=LHJOHU @
6HLWH .DSLWHO
$NWLYH 6FKZLQJXQJVUHGXNWLRQ
$XVO|VFKVLJQDOVVXPPLHUW 'LH *HZLFKWH YRQ :] ZHUGHQ LQ GLHVHP %HLVSLHO PLWWHOV /06
$OJRULWKPXV HLQJHVWHOOW
/Q
6W|UVLJQDO
[Q
ƒ 3KDVHQ
'UHKXQJ
[Q
5HIHUHQ]
VLJQDO
:]
ZQ
∑
[Q
B
HQ
)HKOHU
VLJQDO
ZQ
\Q
∑
6FKlW]
VLJQDO
/06
$EE $GDSWLYHU 1RWFK)LOWHU PLW ]ZHL *HZLFKWHQ
'LH $GDSWLRQ GHU )LOWHUNRHIIL]LHQWHQ ZLUG GXUFK GHQ /06$OJRULWKPXV VLHKH .DSLWHO YRUJHQRPPHQ 'DUDXV IROJW
Z ‘ 30 ’ , Z ‘ Q’ 0 —H ‘ Q ’ [ ‘ Q ’
Z ‘ Q0 ’ , Z ‘ Q ’ 0 —H ‘ Q ’ [ ‘ Q ’ 
'LH GLJLWDOHQ 5HIHUHQ]VLJQDOH PLW ω
πI7 XQG GHU 6DPSOLQJIUHTXHQ] I VLQG
[ ‘ Q ’ , & FRV ‘ Q Õ 0 Ғ
[ ‘ Q ’ , & FRV ‘ Q Õ 0 Ғ 
HQ αδ QP
'DV )HKOHUVLJQDO HQ LVW
ZDV HLQHP δ−,PSXOV PLW GHU $PSOLWXGH α EHL HLQHP GLVNUHWHQ =HLWSXQNW Q
LVW GHU (LQKHLWVLPSXOV DQ GHU 6WHOOH Q
¾
HQ[Q  & FRV ‘ P Õ 0 Ғ
,
/
1Q7 3
2
1Q7 3
2
P HQWVSULFKW δQ
LVW HLQ GXUFK GDV QLFKW YHU]|JHUWH 5HIHUHQ]VLJQDO [Q LQ GHU $PSOLWXGH YHUlQGHUWH
)HKOHUVLJQDO DQ GHU 6WHOOH Q
P 'DQDFK ZLUG HLQH GLJLWDOH ,QWHJUDWLRQ PLW GHU 7UDQVIHUIXQNWLRQ
—± XQG GHU ,PSXOVDQWZRUW —XQ± GXUFKJHIKUW XQ LVW GDEHL GHU GLVNUHWH
6HLWH .DSLWHO
$NWLYH 6FKZLQJXQJVUHGXNWLRQ
(LQKHLWVVSUXQJ
XQ  IU Q
IU Q
?
D
)DOWHW PDQ —XQ ± PLW HQ[Q HUJLEW VLFK
PLW
Q
D 0
P
ZQ
—
α & FRVPω φ
:LUG GLH YHU]|JHUWH 6SUXQJIXQNWLRQ PLW
[Q
PXOWLSOL]LHUW HUJLEW VLFK GLH
$QWZRUW ]X
PLW
PLW
Q
Q
D 0
P
D 0
P
\Q
—
α &ð FRVQω φ FRVPω φ
'LH VHOEH +HUOHLWXQJ LVW LP 3ULQ]LS IU \Q JOWLJ XQG HUJLEW
\Q
—
α &ð VLQQω φ VLQPω φ
:HUGHQ GLH *OHLFKXQJHQ XQG NRPELQLHUW HUJLEW VLFK GLH $QWZRUW
GHV DGDSWLYHQ )LOWHUV ]X
\Q
—
α &ð FRV>Q ± Pω@
—
Q
IU
D 0
P
α &ð XQ ± P ± FRV>Q ± Pω@
'LH *OHLFKXQJ LVW QXU YRQ Q P DEKlQJLJ XQG VWHOOW HLQH ,PSXOVDQWZRUW GDU
'DPLW NDQQ GLH OLQHDUH 7UDQVIHUIXQNWLRQ KHUJHOHLWHW ZHUGHQ :HQQ P
JHVHW]W ZLUG IROJW
GLH ,PSXOVDQWZRUW GHV OLQHDUHQ ]HLWLQYDULDQWHQ 6LJQDOSIDGHV ]X
\Q
—&ðXQ ± FRVQ
ω
'LH ]XJHK|ULJH 7UDQVIHUIXQNWLRQ LVW GLH ]7UDQVIRUPLHUWH YRQ \Q 6LH LVW JHJHEHQ GXUFK
* ‘ ]’ ,
—&
_
] ‘ ] 1 FRV Õ ’
] 1 ] FRV Õ 0 1
`
,
—& ‘ ] FRV Õ 1 ’
] 1 ] FRV Õ 0 ‡
:LUG MHW]W GLH )HHGEDFNVFKOHLIH JHVFKORVVHQ HUJLEW VLFK GLH hEHUWUDJXQJVIXQNWLRQ +] YRP
SULPlUHQ (LQJDQJVVLJQDO GQ ]XP 6\VWHPDXVJDQJ HQ ]X
+ ‘ ]’ ,
( ‘ ]’
' ‘ ]’
,
0 * ‘ ]’
,
] 1 ] FRV Õ 0 ] 1 ‘ 1 —& ’ ] FRV Õ 0 1 —& ‡
*OHLFKXQJ ]HLJW GD‰ GLH (LQ]HO)UHTXHQ] $XVO|VFKXQJ GLH (LJHQVFKDIWHQ HLQHV 1RWFK
)LOWHUV EHL GHU 6SHUUIUHTXHQ] ω EHVLW]W 'LH 1XOOVWHOOHQ YRQ +] OLHJHQ LQ GHU ](EHQH EHL
6HLWH .DSLWHO
]
$NWLYH 6FKZLQJXQJVUHGXNWLRQ
, H6 Õ M
DOVR JHQDX DXI GHP (LQKHLWVNUHLV DQ GHQ :LQNHOQ ω UDG 'LH 3ROH OLHJHQ DXI
]
± —&ðFRVω M> ± —&ð ± ± —&ðð FRVðω@
'LH 3ROH OLHJHQ LQQHUKDOE GHV (LQKHLWVNUHLVHV EHL HLQHP 5DGLXV YRQ ± —&ð
DOVR XQJHIlKU
EHL ± —&ð YRP 0LWWHOSXQNW HQWIHUQW XQG EHL GHQ :LQNHOQ YRQ
FRV
> ± —&ð ± ± —&ð
FRVω@
)U HLQH ODQJVDPH $GDSWLRQ GK NOHLQH :HUWH YRQ —&ð KlQJHQ GLH :LQNHO YRP )DNWRU
a
‘ 1
a ’ ,
[
1 a 0 a 1 a \
—ð& —ð& DE 'D GLHVHU :HUW DEHU QXU NQDSS YRQ HLQV YHUVFKLHGHQ LVW NDQQ LQ SUDNWLVFKHQ (LQVDW]
1XOOVWHOOHQ LGHQWLVFK VLQG
:HQQ GLH 1XOOVWHOOHQ GHV )LOWHUV DXI GHP (LQKHLWVNUHLV OLHJHQ LVW GLH 7LHIH GHU .HUEH GHV
1RWFK)LOWHUV DQ GHU 6WHOOH ω = ω0 XQHQGOLFK 'LH 6FKlUIH GHV )LOWHUV ZLUG GXUFK GLH 1lKH GHU
3ROH ]X GHQ 1XOOVWHOOHQ EHVWLPPW .RUUHVSRQGLHUHQGH 3ROH XQG 1XOOVWHOOHQ VLQG XQJHIlKU GXUFK
HLQHQ $EVWDQG YRQ —&ð JHWUHQQW 'LH G% %DQGEUHLWH GHV 1RWFK)LOWHUV HUJLEW VLFK ]X
DQJHQRPPHQ ZHUGHQ GD‰ GLH :LQNHO GHU 3ROH PLW GHQ :LQNHOQ GHU
% —&ð UDG
—& Í 7 +]
7 VWHKW IU GLH 6DPSOLQJSHULRGH
:HQQ VLFK GLH )UHTXHQ] GHV 5HIHUHQ]VLJQDOV VFKQHOO lQGHUW RGHU MLWWHUW PX‰ GHU 6SHUUEHUHLFK
GHV 1RWFK)LOWHUV EUHLWHU ZHUGHQ 'DV NDQQ GXUFK HLQHQ JU|‰HUHQ $GDSWLRQVNRHIIL]LHQWHQ —
EHZLUNW ZHUGHQ 'DPLW HUJLEW VLFK VRJDU HLQ VFKQHOOHUHV .RQYHUJLHUHQ GHV )LOWHUV DEHU DXFK HLQ
JU|‰HUHU 5HVWIHKOHU
$NWLYHV (LQ]HO)UHTXHQ] 5HGXNWLRQVV\VWHP
,Q GLHVHP .DSLWHO ZLUG PLW +LOIH GHU DGDSWLYHQ 1RWFK)LOWHUXQJ HLQ DNWLYHV (LQ]HO)UHTXHQ]
5HGXNWLRQVV\VWHP JHELOGHW 'LH *HZLFKWH ZHUGHQ GXUFK GHQ YHU]|JHUWHQ /06$OJRULWKPXV
DNWXDOLVLHUW XP GDV )HKOHUVLJQDO ]X PLQLPLHUHQ 'HVKDOE LVW
6HLWH $NWLYH 6FKZLQJXQJVUHGXNWLRQ
.DSLWHO
Z5Q
ZREHL
δ
]XU
9HU]|JHUXQJ
.RPSHQVDWLRQ
Z5Q —HQ[5Q ±
δ
GHU
δ
S
6HNXQGlUSIDG7UDQVIHUIXQNWLRQ

NDQQ DXFK HLQH 6FKlW]XQJ GHV 6HNXQGlUSIDGHV
GLHQW
6 [ ]\
$OWHUQDWLY
]XU
DXV GHP );/06
$OJRULWKPXV YHUZHQGHW ZHUGHQ 'LHV ZLUG LQ $EE GDUJHVWHOOW
[Q
[Q
:]
ZQ
ZQ
[Q
ƒ
A
6]
∑
\Q
GQ
6]
∑
B
HQ
A
6]
[Q
[Q
/06
$EE $NWLYHV (LQ]HO)UHTXHQ] 5HGXNWLRQVV\VWHP PLW );/06$OJRULWKPXV
'LH DGDSWLYHQ *HZLFKWH ZHUGHQ LQ GLHVHP )DOO GXUFK
S 
DNWXDOLVLHUW ZREHL [Q XQG [Q DXV [Q XQG [Q GXUFK GLH )LOWHUXQJ PLW 6 ‘ ] ’
HQWVWHKHQ 8QWHU GHU %HGLQJXQJ HLQHU ODQJVDPHQ $GDSWLRQ ZLUG GLH 7UDQVIHUIXQNWLRQ GHV
6FKPDOEDQG $9& 6\VWHPV ]X
Z5Q
Z5Q —[5QHQ
] FRV Õ 0 ] 1 • FRV Õ 1 ¿ FRV ‘Õ 1 Ò Á ’– ] 0 1 ¿ FRV Ò Á
PLW β = 2—& & & VWHKW IU GLH $PSOLWXGH YRQ 6] XQG Ò Á , Ò 1 Ò  LVW GLH
3KDVHQGLIIHUHQ] ]ZLVFKHQ 6] XQG 6 ‘ ] ’ EHL GHU )UHTXHQ] ω )U NOHLQH β EHVLW]W +] GLH
NRQMXJLHUW NRPSOH[HQ 3ROH EHLP 5DGLXV U , 1 ¿ FRV ÒÁ 'D DOOH 7HUPH GLH VLFK PLW β
‡
HUJHEHQ SRVLWLY VLQG NDQQ GHU 5DGLXV GHU 3ROH QXU JU|‰HU HLQV ZHUGHQ ZHQQ FRV Ò Á QHJDWLY
+ ‘ ]’ ,
8
]
V
8
V
SRO
LVW 'DUDXV IROJW GLH 6WDELOLWlWVEHGLQJXQJ
FRV
ÒÁ @
4/07
1
S
? ÒÁ ?
S
6HLWH .DSLWHO
$NWLYH 6FKZLQJXQJVUHGXNWLRQ
6\VWHP ]XU DNWLYHQ 6FKZLQJXQJVUHGXNWLRQ
(LQIKUXQJ
'DV UHDOLVLHUWH 6\VWHP ]XU DNWLYHQ 6FKZLQJXQJVUHGXNWLRQ EHVWHKW DXV ]ZHL 6RIWZDUHURXWLQHQ
GHU 6\VWHPLGHQWLILNDWLRQ XQG GHU $9&5RXWLQH VRZLH DXV GHQ LQ $EE DEJHELOGHWHQ
.RPSRQHQWHQ (LQH JHQDXHUH %HVFKUHLEXQJ GHU YHUZHQGHWHQ 6RIW XQG +DUGZDUH IROJW LP
$QKDQJ +LHU VROO GLH )XQNWLRQVZHLVH GHV 6\VWHPV QlKHU HUOlXWHUW ZHUGHQ
'HU YRP 0RWRU LQGX]LHUWH .|USHUVFKDOO EHUWUlJW VLFK EHU GLH 0RWRUODJHU DXI GLH .DURVVHULH
XQG EHHLQIOX‰W VRPLW GDV ,QQHQJHUlXVFK GHV .UDIWIDKU]HXJV VWDUN $XI GHU .DURVVHULHVHLWH GHV
0RWRUODJHUV LVW GHU HOHNWURG\QDPLVFKH 6FKZLQJHUUHJHU 6KDNHU XQG GHU
%HVFKOHXQLJXQJVDXIQHKPHU PRQWLHUW 'LHVH VROOWHQ P|JOLFKVW HQJ EHLHLQDQGHUOLHJHQ GDPLW GHU
PHFKDQLVFKH :HJ XQG VRPLW GLH HQWVWHKHQGH 9HU]|JHUXQJ P|JOLFKVW JHULQJ EOHLEW 'DV
$XIILQGHQ HLQHU ]XU HIIHNWLYHQ 5HGX]LHUXQJ GHV ,QQHQJHUlXVFKHV JHHLJQHWHQ 6WHOOH DQ GHQ
0RWRUODJHUQ NDQQ GXUFK GLH $FWLYH 3DWK 7UDFNLQJ $37 0HWKRGH GLH YRQ GHU )LUPD $9/
/LVW *PE+ HQWZLFNHOW ZXUGH VWDUN EHVFKOHXQLJW ZHUGHQ 'LH %DVLV IU GLH %HUHFKQXQJHQ
GLHVHU 0HWKRGH ELOGHQ GDV 6FKDOOIHOG LP )DKU]HXJLQQHQUDXP LP )DKUEHWULHE JHPHVVHQ PLW ELV
]X 0LNURIRQHQ XQG GLH *HUlXVFKEHUWUDJXQJVIXQNWLRQHQ YRQ GHQ
$QWULHEVVWUDQJYHUELQGXQJVSXQNWHQ ]X GHQ 0LNURIRQHQ LP )DKU]HXJ JHPHVVHQ XQWHU 6KDNHU
$QUHJXQJ 'DPLW NDQQ (LQIOX‰ GHU YHUVFKLHGHQHQ /DJHU DXI GDV ,QQHQJHUlXVFK EHVWLPPW
ZHUGHQ $EE ]HLJW GLH 6NL]]H HLQHV .UDIWIDKU]HXJ PLW 0RWRU 0RWRUODJHUQ XQG
0LNURIRQHQ IU GLH 0HVVXQJ GHV 6FKDOOIHOGHV LP )DKU]HXJLQQHQUDXP
$EE $376WUXNWXUVNL]]H HLQHV )DKU]HXJHV DXV >3IOJHU 5XVW @
YJO >3IOJHU 5XVW @
6HLWH .DSLWHO
$NWLYH 6FKZLQJXQJVUHGXNWLRQ
$XVIKUXQJ
$OV 5HIHUHQ]VHQVRU GLHQW HLQ 'UHK]DKOJHEHU GHU EHL MHGHU 8PGUHKXQJ HLQHQ ,PSXOV DEJLEW
[Q 'DGXUFK HQWVWHKW HLQH ,PSXOVNHWWH PLW GHU 3HULRGHQGDXHU GLH GHP .HKUZHUW GHU
*UXQGIUHTXHQ] HQWVSULFKW 'DV IU GLH %HUHFKQXQJ QRWZHQGLJH .RVLQXVVLJQDO [Q ZLUG PLW
+LOIH GHU LQ GHU 6RIWZDUH EHVWLPPWHQ 3HULRGHQGDXHU HU]HXJW :LH LQ $EE DEJHELOGHW LVW
GHU 3ULQ]LSVNL]]H GHV JHVDPWHQ 6\VWHPV ZLUG [Q XQG [Q PLW +LOIH GHU GXUFK GLH 6RIWZDUH
EHVWLPPWHQ 3HULRGHQGDXHU DXV [Q JHQHULHUW =XYRU ZLUG GDV 'UHK]DKOVLJQDO JHILOWHUW XQG LQ
HLQ GLJLWDOHV 6LJQDO XPJHVHW]W
6W|UTXHOOH
0RWRU
'UHK]DKO
JHEHU
6W|U
VFKZLQJ
GQ
PHFKDQLVFKH 6XPPDWLRQ
DP 0RWRUODJHU
+]
$QWL$OLDVLQJ
)LOWHU
$'8PVHW]HU
5HIHUHQ]VLJQDO
3HULRGH EHVW
VLQ FRV JHQHU
[Q
[Q
[Q
$GDSWLYHU
)LOWHU :]
6FKlW]
VLJQDO
\Q
'$8PVHW]HU
/06
)HKOHU
VLJQDO
HQ
$QWL$OLDVLQJ
)LOWHU
$'8PVHW]HU
[Q
)
6]
[Q
+$]
+]
6FKZLQJ
HUUHJHU
%HVFKOHXQLJXQJV
DXIQHKPHU
6LJQDO
YHUVWlUNHU
6LJQDO
YHUVWlUNHU
UHDOHU 6HNXQGlUSIDG 3]
GLJLWDOH 6LJQDOYHUDUEHLWXQJ
$EE 3ULQ]LSVNL]]H GHV JHVDPWHQ 6\VWHPV
,Q GHU 6NL]]H HQWVSULFKW
XQG
+]
VWHOOHQ
+] GHU hEHUWUDJXQJVIXQNWLRQ YRP 0RWRU ]XP 0RWRUODJHU +8]
GLH
%HVFKOHXQLJXQJVDXIQHKPHU
DXI
hEHUWUDJXQJVIXQNWLRQHQ
GDV
0RWRUODJHU
GDU
YRP
'LH
6FKZLQJHUUHJHU
:LUNXQJVZHLVH
GHU
E]Z
GLJLWDOHQ
6LJQDOYHUDUEHLWXQJ ZXUGH LQ GHQ YRUDQJHJDQJHQHQ .DSLWHOQ EHUHLWV HUOlXWHUW 'HU YRP 0RWRU
LQGX]LHUWH XQG DXI GDV 0RWRUODJHU EHUWUDJHQH .|USHUVFKDOO HUJLEW LQ 6XPPH PLW GHP
HLQJHOHLWHWHQ $XVO|VFKVLJQDO GDV )HKOHUVLJQDO ,GHDOHUZHLVH ZUGH GDV )HKOHUVLJQDO GXUFK HLQH
6HLWH .DSLWHO
$NWLYH 6FKZLQJXQJVUHGXNWLRQ
.UDIWPHVVXQJ EHVWLPPW ZHUGHQ 'D HV GDIU DEHU IU GLHVHQ (LQVDW]]ZHFN NHLQH SDVVHQGHQ
6HQVRUHQ JLEW ZLUG GLH %HVFKOHXQLJXQJVPHVVXQJ DOV (UVDW] YHUZHQGHW 'DV
%HVFKOHXQLJXQJVVLJQDO ZLUG YHUVWlUNW JHILOWHUW XQG IU GLH 6LJQDOYHUDUEHLWXQJ LQ HLQ GLJLWDOHV
6LJQDO XPJHVHW]W 'LH (U]HXJXQJ GHU PHFKDQLVFKHQ 6FKZLQJXQJHQ DXV GHP $XVO|VFKVLJQDO
\Q 6FKlW]VLJQDO GHU 6HNXQGlUTXHOOH ZLUG YRQ HLQHP HOHNWURG\QDPLVFKHQ 6FKZLQJHUUHJHU
EHZLUNW 'DV 6FKlW]VLJQDO ZLUG ]XYRU QRFK LQ HLQ DQDORJHV 6LJQDO XPJHVHW]W XQG YHUVWlUNW
6] LVW LQ GLHVHP 3ULQ]LSVFKDOWELOG HLQ DQGHUV HLQJH]HLFKQHW DOV LQ GHQ 6WUXNWXUGLDJUDPPHQ
ELVODQJ 'D DEHU GLH NRPSOHWWH /DXI]HLW GHV .UHLVHV YRP $XVJDQJ GHV GLJLWDOHQ )LOWHUV :] ELV
]XP ZLHGHU LQV 'LJLWDOH XPJHVHW]WH 6LJQDO GQ EHWUlJW PVVHQ DOOH GD]ZLVFKHQ OLHJHQGHQ
(OHPHQWH XQG *HUlWH EHUFNVLFKWLJW ZHUGHQ
,Q GHU UHDOLVLHUWHQ $9&±5RXWLQH ZHUGHQ GLH .RHIIL]LHQWHQ GHV LQ GHU 6\VWHPLGHQWLILNDWLRQ

EHVWLPPWHQ 6HNXQGlUSIDGILOWHUV 6 [ ] \ GXUFK HLQH ]HLWGLVNUHWH )RXULHU7UDQVIRUPDWLRQ LQ
HLQHQ )UHTXHQ]EHUHLFK YRQ +] ELV ]XU KDOEHQ 6DPSOLQJIUHTXHQ] I +] WUDQVIRUPLHUW
'DV (UJHEQLV OLHJW LQ %HWUDJ XQG 3KDVH YRU GDPLW GLH 5HIHUHQ]VLJQDOH [Q XQG [Q HLQIDFK
JHILOWHUW ZHUGHQ N|QQHQ 'XUFK +LQ]XIJHQ GHU 3KDVH XQG 0XOWLSOLNDWLRQ PLW GHU $PSOLWXGH
HUJHEHQ VLFK [Q XQG [Q
8
6\VWHPLGHQWLILNDWLRQ
)U GLH 5HDOLVLHUXQJ GHV 6\VWHPV PLW +LOIH GHV );/06$OJRULWKPXV LVW HLQH YRUKHUJHKHQGH
6\VWHPLGHQWLILNDWLRQ QRWZHQGLJ ,Q $EE LVW HLQH 3ULQ]LSVNL]]H GHU HLQJHVHW]WHQ
6\VWHPLGHQWLILNDWLRQ GDUJHVWHOOW
'LH
6\VWHPLGHQWLILNDWLRQ
HQWVSULFKW
HLQHP
GLJLWDOHQ
1DFKELOGHQ
GHV
JHVDPWHQ
6LJQDOYHUDUEHLWXQJVNUHLVHV 3] GXUFK GHQ GLJLWDOHQ DGDSWLYHQ )LOWHU 'DV UHDOLVLHUWH
6RIWZDUHSURJUDPP JHQHULHUW ZHL‰HV 5DXVFKHQ GDV ]XP (LQHQ EHU GHQ $QDORJ'LJLWDO
8PVHW]HU XQG HLQHQ $XGLR9HUVWlUNHU ]XP 6FKZLQJHUUHJHU JHOHLWHW XQG EHU GHQ
%HVFKOHXQLJXQJVDXIQHKPHU /DGXQJVYHUVWlUNHU XQG '$8PVHW]HU ZLHGHU GHU %HUHFKQXQJ
]XJHIKUW ZLUG =XP $QGHUHQ ZLUG GHU GLJLWDOH 5DXVFKZHUW GLUHNW GHP GLJLWDOHQ )LOWHU
EHUJHEHQ 'DV 6FKlW]VLJQDO \Q XQG GDV LQ HLQ GLJLWDOHV 6LJQDO XPJHVHW]WH GQ ZHUGHQ
VDPSOHZHLVH PLWHLQDQGHU YHUJOLFKHQ 0LW PLW GHU EHUHFKQHWHQ 'LIIHUHQ] HQ XQG GHP DNWXHOOHQ
6DPSOH GHV ZHL‰HQ 5DXVFKHQV ZHUGHQ GLH .RHIIL]LHQWHQ YRQ :] PLWWHOV /06$OJRULWKPXV
6HLWH $NWLYH 6FKZLQJXQJVUHGXNWLRQ
.DSLWHO
DGDSWLHUW
'LH
HUKDOWHQHQ
6LJQDOYHUDUEHLWXQJVNUHLVHV
hEHUWUDJXQJVIXQNWLRQHQ
)LOWHUNRHIIL]LHQWHQ
6]
YRP
GDU
+$]
VWHOOHQ
E]Z
6FKZLQJHUUHJHU
+]
E]Z
GLH
6\VWHPDQWZRUW
HQWVSUHFKHQ
GHV
ZLHGHU
GHQ
%HVFKOHXQLJXQJVDXIQHKPHU
]XP
0RWRUODJHU
PHFKDQLVFKH 6XPPDWLRQ
DP 0RWRUODJHU
NHLQH 6W|UVFKZLQJXQJHQ
YRUKDQGHQ GD
0RWRU QLFKW LQ %HWULHE
GQ
+]
+$]
%HVFKOHXQLJXQJV
DXIQHKPHU
6FKZLQJ
HUUHJHU
6LJQDO
YHUVWlUNHU
6LJQDO
YHUVWlUNHU
$QWL$OLDVLQJ
)LOWHU
$'8PVHW]HU
ZHL‰HV
5DXVFKHQ
[Q
'$8PVHW]HU
UHDOHU 6HNXQGlUSIDG 3]
$GDSWLYHU
)LOWHU :]
\Q
6FKlW]
VLJQDO
GQ $XVJDQJVVLJQDO
YRQ 3]
HQ )HKOHU
VLJQDO
/06
$EE 3ULQ]LSVNL]]H GHU HLQJHVHW]WHQ 6\VWHPLGHQWLILNDWLRQ
6HLWH $NWLYH 6FKZLQJXQJVUHGXNWLRQ
.DSLWHO
0HKUIDFK)UHTXHQ] $9&
,Q GHQ SUDNWLVFKHQ $QZHQGXQJHQ EHVWHKHQ GLH 6W|UVLJQDOH PHLVW DXV PHKUHUHQ EHUODJHUWHQ
6FKZLQJXQJHQ GLH VLFK DXV GHU *UXQGVFKZLQJXQJ XQG GHQ ]XJHK|ULJHQ +DUPRQLVFKHQ
]XVDPPHQVHW]HQ (LQ 1RWFK)LOWHU PLW PHKUHUHQ 6SHUUIUHTXHQ]HQ LVW HLQ VHKU JXWHV ,QVWUXPHQW
]XU %HDUEHLWXQJ VROFKHU 6W|UVLJQDOH ,P $OOJHPHLQHQ EHQ|WLJHQ GLHVH )LOWHU DEHU HLQH K|KHUH
2UGQXQJ GLH ]XP %HLVSLHO GLUHNW SDUDOOHO GLUHNWSDUDOOHO RGHU NDVNDGLHUW UHDOLVLHUW ZHUGHQ
NDQQ (V ZLUG KLHU QXU HLQH NXU]H hEHUVLFKW GHU 9HUIDKUHQ JHJHEHQ *HQDXHUH (UOlXWHUXQJHQ
ILQGHQ VLFK LQ GHU DQJHJHEHQHQ /LWHUDWXU
'LUHNWH )RUP
,VW
HLQH
0HWKRGH
]XU
(OLPLQLHUXQJ
YRQ
EHUODJHUWHQ
SHULRGLVFKHQ ,QWHUIHUHQ]HQ XQG ZXUGH YRQ *ORYHU
6LQXVVFKZLQJXQJHQ
RGHU
DQGHUHQ
HQWZLFNHOW 'DV 5HIHUHQ]VLJQDO LVW HLQH
6XPPH YRQ 0 6LQXVVFKZLQJXQJHQ
[ ‘ Q’ ,
{ $2
2 ,
FRV ‘ Õ 2 Q ’
‡
$2 VWHKW IU GLH $PSOLWXGH XQG ω2 JLEW GLH )UHTXHQ] GHU PWHQ 6LQXVVFKZLQJXQJ DQ :HQQ GLH
)UHTXHQ]HQ GHU 5HIHUHQ]VFKZLQJXQJHQ QDKH EHLHLQDQGHU OLHJHQ LVW HLQ ODQJHV )LOWHU /!! 0
Q|WLJ XP HLQH UHODWLY JXWH )UHTXHQ]DXIO|VXQJ ]X HUKDOWHQ 'DV LVW MHGRFK HLQH XQHUZQVFKWH
/|VXQJ GD DGDSWLYH )LOWHU K|KHUHU 2UGQXQJ HLQ ODQJVDPHV .RQYHUJHQ]YHUKDOWHQ EHVLW]HQ (LQH
P|JOLFKH $QZHQGXQJ YRQ *ORYHUV 0HWKRGH LVW GLH $EVFKZlFKXQJ YRQ /lUP GHU GLUHNW YRQ
0DVFKLQHQ JHQHULHUW ZLUG
3DUDOOHOH )RUP
+LHU ZHUGHQ 0 )LOWHU
PLW MHZHLOV ]ZHL *HZLFKWHQ SDUDOOHO JHVFKDOWHW XP
0
YHUVFKLHGHQH
6LQXVVFKZLQJXQJHQ DXV]XO|VFKHQ GLH LP 5HIHUHQ]VLJQDO HQWKDOWHQ VLQG 'DV $XVO|VFKVLJQDO LVW
GDQQ GLH 6XPPH GHU $XVJlQJH GHU DGDSWLYHQ )LOWHU
\ ‘ Q’ ,
{
2 ,
\ 2 [ Q\
W
YJO >.XR 0RUJDQ @
YJO >*ORYHU @
6HLWH .DSLWHO
$NWLYH 6FKZLQJXQJVUHGXNWLRQ
$XVJDQJ \2Q ZLUG VR EHKDQGHOW DOV RE HV HLQH (LQ]HO)UHTXHQ] $XVO|VFKXQJ ZlUH 'D
QXU HLQ )HKOHUVHQVRU YHUZHQGHW ZLUG JLEW HV DXFK QXU HLQ )HKOHUVLJQDO HQ 'LHVHV ZLUG ]XP
$NWXDOLVLHUHQ DOOHU 0 DGDSWLYHQ )LOWHU GXUFK GHQ );/06$OJRULWKPXV YHUZHQGHW
-HGHU
'LUHNW3DUDOOHOH )RUP
6SH]LHOO ]XU 6WHLJHUXQJ GHU 4XDOLWlW YRQ $1& 6\VWHPHQ IU GHQ )DKU]HXJLQQHQUDXP ZXUGH HLQ
6\VWHP PLW PHKUHUHQ 5HIHUHQ]JHQHUDWRUHQ XQG ]XJHK|ULJHQ DGDSWLYHQ )LOWHUQ HQWZLFNHOW 'LH
,GHH LVW HV GLH 0HQJH YRQ HQJ EHLHLQDQGHU OLHJHQGHQ KDUPRQLVFKHQ 6LQXVVFKZLQJXQJHQ
DXI]XWHLOHQ XQG *UXSSHQ ]X ELOGHQ EHL GHQHQ VLFK GLH )UHTXHQ]HQ XQWHUHLQDQGHU P|JOLFKVW
VWDUN XQWHUVFKHLGHQ $OOJHPHLQ JLOW *LEW HV 0 KDUPRQLVFKH 6FKZLQJXQJHQ GLH DXVJHO|VFKW
ZHUGHQ VROOHQ XQG . .0 6LJQDOJHQHUDWRUHQ GDQQ HQWKlOW MHGHV 5HIHUHQ]VLJQDO [NQ GLH
IUHTXHQ]YHUVHW]WHQ 6LQXVVFKZLQJXQJHQ YRQ MHGHU .WHQ +DUPRQLVFKHQ N . 'LHVH
5HIHUHQ]VLJQDOH ZHUGHQ YRQ GHQ ]XJHK|ULJHQ DGDSWLYHQ )LOWHUQ YHUDUEHLWHW 'XUFK GDV
$XIWHLOHQ GHU 6LJQDONRPSRQHQWHQ NDQQ GLH *HVFKZLQGLJNHLW XQG GDV .RQYHUJHQ]YHUKDOWHQ GHU
DGDSWLYHQ )LOWHU ZLUNXQJVYROO YHUEHVVHUW ZHUGHQ ,P 9HUJOHLFK ]XU 0HWKRGH PLW GHU GLUHNWHQ
,PSOHPHQWDWLRQ JHVFKLHKW GLHV GXUFK GHQ JUR‰HQ )UHTXHQ]DEVWDQG GHQ GLH VLQXVI|UPLJHQ
.RPSRQHQWHQ YRQ [NQ XQWHUHLQDQGHU KDEHQ
.DVNDGHQIRUP
'LH 9LHOIDFK6LQXVUHIHUHQ]VLJQDOH N|QQHQ DXFK VHKU JXW LQ HLQHU .DVNDGH YRQ 0 (LQ]HO
)UHTXHQ] )LOWHUQ ]ZHLWHU 2UGQXQJ YHUDUEHLWHW ZHUGHQ 'LH JHVDPWH $QWZRUW HLQHU VROFKHQ
$QRUGQXQJ HQWVSULFKW
+ ‘ ]’ ,
:2] LVW GHU
z+
2 ,
z
2 ,
2 ‘ ] ’ , 0 6 ‘ ] ’ : ‘ ] ’
2
PWH DGDSWLYH )LOWHU ZREHL MHGHU GLHVHU )LOWHU HLQHQ 3RO EHL ω2 KDW 'DGXUFK
+] HLQHQ 6SHUUEHUHLFK EHL ω2 :HQQ HLQH 6FKlW]XQJ GHU 6HNXQGlUSIDG
7UDQVIHUIXQNWLRQ P|JOLFK LVW NDQQ HLQH 3VHXGRNDVNDGH HU]HXJW ZHUGHQ GLH LP ,GHDOIDOO ZLH
HLQH UHDOH .DVNDGH DUEHLWHW 'LHVH ZUGH DEHU PLW HLQHU 6FKlW]XQJ GHU 7UDQVIHUIXQNWLRQ
DXVNRPPHQ
EHVLW]W MHGHV
YJO ><XDQ @
YJO >0RUJDQ 7KL @
6HLWH .DSLWHO
=XVDPPHQIDVVXQJ XQG $XVEOLFN
=XVDPPHQIDVVXQJ XQG $XVEOLFN
'DV =XVDPPHQVWHOOHQ HLQHU JHHLJQHWHQ %DVLV IU HLQ PRELOHV 6\VWHP ]XU DNWLYHQ
6FKZLQJXQJVUHGXNWLRQ ZDU GHU HUVWH 6FKULWW GLHVHU 'LSORPDUEHLW 'DEHL ZXUGH YHUVXFKW GHQ
GHU]HLWLJHQ 6WDQG GHU 7HFKQLN P|JOLFKVW HIIL]LHQW DXV]XQXW]HQ ,P $QVFKOX‰ IROJWH GLH
3URJUDPPLHUXQJ XQG GLH 7HVWSKDVH 'DV HQWZLFNHOWH 3URJUDPP LVW LP 3ULQ]LS IU DOOH
$QZHQGXQJHQ JHHLJQHW GLH HLQH 6FKPDOEDQG )HHGIRUZDUG 6WUXNWXU XQWHUVWW]HQ
$NWLYH 6FKZLQJXQJVUHGXNWLRQ VWHOOW NHLQ JHQHUHOOHV 9HUIDKUHQ GDU PLW GHU DOOH /lUP XQG
6FKZLQJXQJVSUREOHPH JHO|VW ZHUGHQ N|QQHQ $EHU YRUDXVVLFKWOLFK ZLUG GXUFK GLH
ZHLWHUHQWZLFNHOWHQ $OJRULWKPHQ GLH YHUEHVVHUWH '63 +DUGZDUH XQG GHQ LPPHU JHULQJHU
ZHUGHQGHQ 3UHLVHQ GLHVHU 6\VWHPH GHU $QZHQGXQJVEHUHLFK VWHWLJ JU|‰HU ZHUGHQ
6HLWH /LWHUDWXUYHU]HLFKQLV
/LWHUDWXUYHU]HLFKQLV
>/XHJ @
3 /XHJ
3URFHVV RI VLOHQFLQJ VRXQG RVFLOODWLRQV
86 3DWHQW ]LWLHUW QDFK >.XR 0RUJDQ @
><DQJ @
%LQ <DQJ
$GDSWLYH )LOWHU
9RUOlXILJH $XVDUEHLWXQJ HLQHU 9RUOHVXQJ
5XKU8QLYHUVLWlW %RFKXP >.XR 0RUJDQ @
6HQ 0 .XR XQG 'HQQLV 5 0RUJDQ
$FWLYH 1RLVH &RQWURO $ 7XWRULDO 5HYLHZ
3URF RI WKH ,((( >:LGURZ 6WHDUQV @
% :LGURZ XQG 6 ' 6WHDUQV
$GDSWLYH 6LJQDO 3URFHVVLQJ
3UHQWLFH+DOO >1HOVRQ (OOLRW @
3 $ 1HOVRQ XQG 6 - (OOLRW
$FWLYH FRQWURO RI VRXQG DQG YLEUDWLRQ
06F FRXUVH LQ VRXQG DQG YLEUDWLRQ VWXGLHV
8QLYHUVLW\ RI 6RXWKKDPSWRQ >%XUJHVV @
- & %XUJHVV
$FWLYH DGDSWLYH VRXQG FRQWURO LQ D GXFW $ &RPSXWHU 6LPXODWLRQ
- $FRXVW 6RF $PHU YRO ]LWLHUW QDFK >.XR 0RUJDQ @
>=LHJOHU @
( =LHJOHU
6HOHFWLYH DFWLYH FDQFHOODWLRQ V\VWHP IRU UHSHWLYH SKHQRPHQD
8 6 3DWHQW ]LWLHUW QDFK >.XR 0RUJDQ @
6HLWH /LWHUDWXUYHU]HLFKQLV
>3IOJHU 5XVW @
0 3IOJHU XQG $ 5XVW $9/ /LVW *PE+
$FWLYH 3DWK 7UDFNLQJ ± $ 5DSLG 0HKRG IRU WKH ,GHQWLILFDWLRQ
RI 6WUXFWXUH %RUQH 1RLVH 3DWKV LQ 9HKLFOH &KDVVLV
%HLWUDJ IU GLH '$*$ 7DJXQJ >*ORYHU @
- 5 *ORYHU
$GDSWLYH QRLVH FDQFHOLQJ DSSOLHG WR VLQXVRLGDO LQWHUIHUHQFHV
,((( 7UDQV $FRXVW 6SHHFK 6LJQDO 3URFHVVLQJ ]LWLHUW QDFK >.XR 0RUJDQ @
><XDQ @
< <XDQ 1 6 .DSVRNDYDWKLV . &KHQ XQG 6 0 .XR
$FWLYH QRLVH FRQWURO V\VWHP
86 3DWHQW
]LWLHUW QDFK >.XR 0RUJDQ @
>0RUJDQ 7KL @
'5 0RUJDQ XQG - 7KL
$ PXOWLWRQH SVHXGRFDVFDGH ILOWHUHG; /06 DGDSWLYH QRWFK ILOWHUNRHIIL]LHQWHQ
3URF RI WKH ,((( ]LWLHUW QDFK >.XR 0RUJDQ @
6HLWH $QKDQJ $
$QKDQJ $
6\VWHP XQG 7HVWDXIEDX
L
+DUGZDUH
=XU %HUHFKQXQJ XQG 'DWHQHUIDVVXQJ ZXUGH HLQ 3;,6\VWHP GHU )LUPD 1DWLRQDO ,QVWUXPHQWV
YHUZHQGHW (V EHLQKDOWHW HLQHQ (FKW]HLW IlKLJHQ &RQWUROOHU DXI ,QWHO 3HQWLXP %DVLV XQG GLH
0H‰NDUWHQ ]XP (LQOHVHQ XQG $XVJHEHQ GHU 'DWHQ (LQ HLJHQHV *HKlXVH EHKHUEHUJW GLH
NRPSOHWWHQ 5HFKHQ XQG 'DWHQHUIDVVXQJVNRPSRQHQWHQ $X‰HUGHP EHLQKDOWHW GDV JHVDPWH
$9&6\VWHP QRFK $QVFKOX‰EO|FNH GLH PLW %1&6WHFNHUQ YHUVHKHQ VLQG =XU (U]HXJXQJ GHV
*HJHQNRSSOXQJVVLJQDOV ZXUGH HLQ HOHNWURG\QDPLVFKHU 6FKZLQJHUUHJHU YHUZHQGHW 'HU $XGLR
9HUVWlUNHU GLHQWH ]XU 6LJQDOYHUVWlUNXQJ GHU HLQIDFKHQ ,PSOHPHQWLHUXQJ HLQHU +DUGZDUH
6SDQQXQJVEHJUHQ]XQJ EHL XQJHZROOWHP $XIVFKZLQJHQ GHV $XVO|VFKDOJRULWKPXV XQG HLQHU
VFKQHOOHQ $QSDVVXQJVP|JOLFKNHLW EHL bQGHUXQJ GHU PHFKDQLVFKHQ .RPSRQHQWHQ 'DV
)HKOHUVLJQDO ZXUGH PLW HLQHP %HVFKOHXQLJXQJVDXIQHKPHU DXIJHQRPPHQ XQG PLW +LOIH HLQHV
/DGXQJVYHUVWlUNHUV XP GHQ )DNWRU HUK|KW
'DV 6\VWHP ZXUGH DXI HLQHP 9HUVXFKVDXIEDX JHWHVWHW GDU DXV HLQHP KlQJHQG JHODJHUWHP
6WDKOVWDE GHP DQUHJHQGHQ 6FKZLQJHUUHJHU XQG HLQHP )UHTXHQ]JHQHUDWRU EHVWDQG 'HU
)UHTXHQ]JHQHUDWRU VWHXHUWH EHU GHQ $XGLR9HUVWlUNHU GLH PHFKDQLVFKH $QUHJXQJ XQG GLHQWH
JOHLFK]HLWLJ DOV 'UHK]DKOVLJQDOJHEHU 9HUVRUJW ZXUGH GHU $XGLR9HUVWlUNHU GXUFK HLQH
$XWREDWWHULH
'DV 3URJUDPP OlXIW GLUHNW DOV H[HFXWDEOH)LOH DXI GHP 3;,&RQWUROOHU 'DKHU LVW HLQ 3& QXU
]XU 6WHXHUXQJV XQG 9LVXDOLVLHUXQJV]ZHFNHQ QRWZHQGLJ
6HLWH $QKDQJ $
%ORFNVFKDOWELOG GHV 7HVWDXIEDXV
3&
57 ± 6\VWHP
PLW
,26FKQLWWVWHOOHQ
287
,1
%1&
$QVFKOX‰ER[ 'lPSIXQJVJOLHG *HJHQNRSSOXQJV
VLJQDO
%1&
$QVFKOX‰ER[
'UHK]DKOVLJQDO
6WHUHR$XGLR
9HUVWlUNHU
6SDQQXQJV
YHUVRUJXQJ
*HJHQNRSSOXQJV
VLJQDO
PHFKDQLVFKH
*HJHQNRSSOXQJ
*HJHQNRSSOXQJV
6FKZLQJHUUHJHU
)UHTXHQ]
JHQHUDWRU
PHFKDQLVFKHV
)HKOHUVLJQDO
6WDKO
VWDE
)HKOHUVLJQDO
/DGXQJV
9HUVWlUNHU
HOHNWULVFKHV
)HKOHUVLJQDO
%HVFKOHXQLJXQJV
DXIQHKPHU
PHFKDQLVFKH
$QUHJXQJ
$QUHJXQJV
VLJQDO
*HJHQNRSSOXQJV
VFKZLQJHUUHJHU
$EE $ %ORFNVFKDOWELOG GHV JHVDPWHQ 7HVWDXIEDXV
$XI GHQ QlFKVWHQ 6HLWHQ VLQG LQ GHQ $EELOGXQJHQ $ ELV $ GHU 7HVWDXIEDX XQG GLH
YHUZHQGHWHQ .RPSRQHQWHQ ]X VHKHQ
6HLWH $QKDQJ $
$EE $ 7HVWDXIEDX NRPSOHWW
$EE $ /DGXQJVYHUVWlUNHU 3;,(LQKHLW XQG )UHTXHQ]JHQHUDWRU
6HLWH $QKDQJ $
$EE $ 6FKZLQJHUUHJHU ]XU $QUHJXQJ GHV $XIEDXV
$EE $ 6FKZLQJHUUHJHU IU GLH $XVO|VFKXQJ XQG %HVFKOHXQLJXQJVVHQVRU
6HLWH $QKDQJ $
L
6RIWZDUH
$OV 3URJUDPPLHUVRIWZDUH ZXUGH GLH JUDSKLVFKH (QWZLFNOXQJVXPJHEXQJ 1DWLRQDO ,QVWUXPHQWV
/DE9LHZ JHZlKOW 'DV 3URGXNW NDP DXIJUXQG HLQHU UHODWLY HLQIDFKHQ 3URJUDPPLHUXQJ XQG GHU
VFKQHOOHQ (U]HXJXQJ HLQHU JUDSKLVFKHQ %HGLHQHUREHUIOlFKH ]XP (LQVDW] /DE9LHZ ZLUG PLW
+LOIH ]ZHLHU )HQVWHU SURJUDPPLHUW 'DV 'LDJUDPPIHQVWHU LVW GLH HLJHQWOLFKH
3URJUDPPLHUREHUIOlFKH LQ GHU GLH YHUVFKLHGHQHQ 9LUWXHOOHQ ,QVWUXPHQWH HLQJHIJW XQG
YHUEXQGHQ ZHUGHQ :HLWHUV N|QQHQ GLH XQWHUVFKLHGOLFKVWHQ 5HFKHQRSHUDWLRQHQ DOV 6\PERO XQG
HLQH *UXSSH YRQ 2SHUDWLRQHQ DOV HLQ 8QWHUSURJUDPP GHILQLHUW ZHUGHQ
'DV ]ZHLWH )HQVWHU LVW GDV %HGLHQXQJVIHQVWHU (V GLHQW GHU %HGLHQXQJ XQG 9LVXDOLVLHUXQJ GHV
NRPSOHWWHQ 6\VWHPV +LHU ZHUGHQ GLH (LQ XQG $XVJDEHJHUlWH IHVWJHOHJW VRZLH GDV 3URJUDPP
JHVWDUWHW XQG JHVWRSSW $XFK 'LDJUDPPH XQG DQGHUH $Q]HLJHQ VLQG LQ GLHVHP )HQVWHU
HQWKDOWHQ *HQDXHUHV ZLUG LQ GHU %HGLHQXQJVDQOHLWXQJ EHVFKULHEHQ
$EELOGXQJ $ ]HLJW GDV %HGLHQXQJVIHQVWHU GHU 6\VWHPLGHQWLILNDWLRQ QDFK HUIROJWHU
2SWLPLHUXQJ XQG $EE $ MHQHV GHU $9&5RXWLQH ,Q $EE VLHKW PDQ LP HUURU'LDJUDPP DQ
GHU 6WHOOH D GDV )HKOHUVLJQDO GLUHNW QDFK GHP 6WDUWHQ GHU 6RIWZDUH XQG XQWHU E HLQHQ
VFKQHOOHQ 5FNJDQJ GHU 6FKZLQJXQJHQ GXUFK GDV (LQVFKDOWHQ GHU DNWLYHQ 5HGXNWLRQ %HL
QRFKPDOLJHU %HWlWLJXQJ GHV &DQFHOODWLRQ 21 .QRSIHV N|QQHQ GLH 6FKZLQJXQJHQ ZLHGHU
RKQH $XVO|VFKXQJ EHWUDFKWHW ZHUGHQ VLHKH F 1DFK GHP HUVWHQ $XVO|VFKHQ HUIROJHQ GLH
ZHLWHUHQ $GDSWLRQHQ VFKQHOOHU GD GLH .RHIIL]LHQWHQ JHVSHLFKHUW EOHLEHQ GHU VFKQHOOHUH $EIDOO
DP %HJLQQ YRQ G (LQH QHXH $GDSWLRQ LVW QXU EHL 'UHK]DKOlQGHUXQJ QRWZHQGLJ
6HLWH $QKDQJ $
$EE $ %HGLHQXQJVIHQVWHU GHU 6\VWHPLGHQWLILNDWLRQ
$EE $ %HGLHQXQJVIHQVWHU GHU $9&5RXWLQH LQ %HWULHE
6HLWH $QKDQJ $
L
$XVZHUWXQJHQ
$XI GHQ IROJHQGHQ 6HLWHQ ZLUG GHU =XVDPPHQKDQJ ]ZLVFKHQ YHUVFKLHGHQHQ
$GDSWLRQVNRHIIL]LHQWHQ GHU GDUDXV IROJHQGHQ 2SWLPLHUXQJVJHVFKZLQGLJNHLW XQG GHQ
UHVXOWLHUHQGHQ (UJHEQLVVHQ IU GLH 4XDOLWlW GHU 6\VWHPLGHQWLILNDWLRQ XQG GHU $9&5RXWLQH
JH]HLJW 'DV 9HUKDOWHQ EHL LGHDOHQ (LQVWHOOXQJHQ ZXUGH LQ GHQ $EELOGXQJHQ $ XQG $
GDUJHVWHOOW 'LH IROJHQGHQ %LOGHU ]HLJHQ GLH 5HDNWLRQHQ EHLGHU 3URJUDPPH EHL VFKOHFKW
JHZlKOWHQ $GDSWLRQVNRHIIL]LHQWHQ — 'XUFK HLQHQ NOHLQHQ 2SWLPLHUXQJVNRHIIL]LHQWHQ GDXHUW GLH
$GDSWLRQ VHKU ODQJH GD GLH 6FKULWWZHLWH GHV 2SWLPLHUXQJVDOJRULWKPXV VHKU JHULQJ ZLUG VLHKH
$EE $ 'LH 6\VWHPLGHQWLILNDWLRQ P‰WH VHKU ODQJH ODXIHQ ELV VLFK GLH DGDSWLYHQ )LOWHUZHUWH
QDKH]X LGHDO HLQJHVWHOOW KlWWHQ 7URW]GHP ZUGHQ VLFK QXU JHULQJH 4XDOLWlWVYHUEHVVHUXQJHQ
]HLJHQ *U|‰HUH $XVZLUNXQJHQ KDW HLQ ]X NOHLQHU .RHIIL]LHQW EHL GHU $9&5RXWLQH $EE $
$EE $ 6\VWHPLGHQWLILNDWLRQ PLW ]X NOHLQHP $GDSWLRQVNRHIIL]LHQWHQ
6HLWH $QKDQJ $
$EE $ $9&±5RXWLQH PLW ]X NOHLQHP $GDSWLRQVNRHIIL]LHQWHQ
'XUFK GHQ NOHLQHQ .RHIIL]LHQWHQ GDXHUW GLH $GDSWLRQ ]X ODQJH 'DUDXV HUJLEW VLFK HLQ VHKU
VFKOHFKWHV ]HLWOLFKHV 9HUKDOWHQ 6FKRQ EHL HLQHU ODQJVDPHQ bQGHUXQJ GHU 'UHK]DKO NDQQ GDV
6\VWHP NHLQH JXWH 5HGXNWLRQ GHU 6FKZLQJXQJHQ HU]LHOHQ
,Q $EELOGXQJ $ LVW HLQ $XIVFKZLQJHQ GHV )HKOHUVLJQDOV GHU 6\VWHPLGHQWLILNDWLRQ ]X VHKHQ
'D GHU $GDSWLRQVNRHIIL]LHQW ]X JUR‰ LVW ILQGHW GHU 2SWLPLHUXQJVDOJRULWKPXV GDV 0LQLPXP
QLFKW (U VSULQJW EHU GDV DEVROXWH 0LQLPD KLQZHJ XQG VFKZLQJW VLFK GDGXUFK LP
VFKOLPPVWHQ )DOO DXI 'XUFK HLQHQ 9HUJOHLFK GHV )HKOHUVLJQDOV LP %LOG HUURU VLJQDO RGHU GHU
$PSOLWXGHQ XQG 3KDVHQZHUWH QDFK GHU ]HLWGLVNUHWHQ )RXULHU7UDQVIRUPDWLRQ GHU
)LOWHUNRHIIL]LHQWHQ PLW GHQ *UDSKHQ DXV $EE$ LVW OHLFKW ]X HUNHQQHQ GD‰ VLFK GHU DGDSWLYH
)LOWHU QLFKW DXI GDV ]X RSWLPLHUHQGH 6\VWHP HLQVWHOOHQ NRQQWH
6HLWH $QKDQJ $
$EE $ 6\VWHPLGHQWLILNDWLRQ PLW ]X JUR‰HP $GDSWLRQVNRHIIL]LHQWHQ
$EE $ $9& ± 5RXWLQH PLW ]X JUR‰HP $GDSWLRQVNRHIIL]LHQWHQ
6HLWH $QKDQJ $
$EELOGXQJ $ ]HLJW GDV $9&±6\VWHP LQ %HWULHE $OOH :HUWH ZDUHQ JOHLFK HLQJHVWHOOW ZLH LP
7HVWODXI GHU LQ $EE $ JH]HLJW ZXUGH +LHU LVW ]X VHKHQ GD‰ VLFK NHLQH JXWH 5HGX]LHUXQJ GHU
6FKZLQJXQJHQ GXUFK HLQHQ ]X JUR‰HQ $GDSWLRQVNRHIIL]LHQWHQ HUJLEW ,P 7HVW GHU LQ $EE $
GDUJHVWHOOW LVW ZXUGH GHU .RHIIL]LHQW QRFKPDOV HUK|KW 'DV 9HUJU|‰HUQ KDWWH DEHU HLQH VHKU
JHIlKUOLFKH )ROJH 'DV 6\VWHP VFKZLQJW DXI
$EE $ $XIVFKZLQJHQ GHV $9&6\VWHPV
6HLWH $QKDQJ %
$QKDQJ %
%(',(181*6$1/(,781*
'DV $9& $FWLYH 9LEUDWLRQ &DQFHOODWLRQ 6\VWHP EHVWHKW DXV GHP $9& 6RIWZDUH 3DNHW
HLQHP 3& GHU 6LJQDOYHUDUEHLWXQJVHLQKHLW 6HQVRUHQ $NWXDWRUHQ XQG GHQ SDVVHQGHQ
9HUVWlUNHUQ 'DV 6\VWHP YHUVXFKW GHQ .|USHUVFKDOO GHV 0RWRUV GXUFK ,QWHUIHUHQ] P|JOLFKVW
HIIL]LHQW ]X PLQLPLHUHQ 'LH 6RIWZDUH VHW]W VLFK DXV ]ZHL 7HLOHQ ]XVDPPHQ
6\VWHPLGHQWLILNDWLRQ XQG $9&±5RXWLQH 'LH )XQNWLRQVZHLVH XQG %HGLHQXQJ EHLGHU 7HLOH ZLUG
LP IROJHQGHQ NXU] EHVFKULHEHQ 'LH +DUGZDUH.RPSRQHQWHQ PVVHQ ODXW %ORFNVFKDOWELOG
YHUEXQGHQ ZHUGHQ
%ORFNVFKDOWELOG XQG %HVFKUHLEXQJ
1RWHERRN
576\VWHP
PLW
,26FKQLWWVWHOOH
287
%1&
$QVFKOX‰ER[
$XGLR
9HUVWlUNHU
'UHK]DKOLPSXOV
JHEHU
,1
'UHK]DKO
LPSXOVH
*HJHQNRSSOXQJV
VLJQDO
)HKOHUVLJQ DO
%DWWHULH
'UHK]DKO
LPSXOVH
%1&
$QVFKOX‰ER[
/DGXQJV
9HUVWlUNHU
)HKOHUVLJQDO
*HJHQNRSSOXQJV
6FKZLQJHUUHJHU
PHFKDQLVFKH hEHUWUDJXQJ
%HVFKOHXQLJXQJV
DXIQHKPHU
$EE % %ORFNVFKDOWELOG
6HLWH $QKDQJ %
8P HLQH DNWLYH 5HGXNWLRQ YRQ 6FKZLQJXQJHQ DQ )DKU]HXJHQ YRUQHKPHQ ]X N|QQHQ PVVHQ
GLH HOHNWURG\QDPLVFKHQ 6FKZLQJHUUHJHU 6KDNHU DQ GHQ 0RWRUODJHUQ EHIHVWLJW ZHUGHQ 'LH
%HVFKOHXQLJXQJVDXIQHKPHU VROOWHQ VR QDK DOV P|JOLFK DQ GHQ 6KDNHUQ DQJHEUDFKW ZHUGHQ
GDPLW GLH PHFKDQLVFKH 6WUHFNH XQG VRPLW GLH /DXI]HLW P|JOLFKVW NOHLQ JHKDOWHQ ZLUG
$EELOGXQJ % ]HLJW GLH 0RQWDJH HLQHV PLW D EH]HLFKQHWHQ 6KDNHUV XQG E GHV ]XJHK|ULJHQ
%HVFKOHXQLJXQJVDXIQHKPHUV DQ HLQHP F 0RWRUODJHU 'DV 1RWHERRN NRPPXQL]LHUW EHU /$1
9HUELQGXQJ PLW GHU 3;,5HDO7LPH(LQKHLW XQG PX‰ EHL GHU HUVWHQ ,QEHWULHEQDKPH EHU GHQ
0HDVXUHPHQW DQG $XWRPDWLRQ ([SORUHU NRQILJXULHUW ZHUGHQ 'DV %ORFNVFKDOWELOG % JLEW
+LQZHLVH ZLH GLH +DUGZDUH.RPSRQHQWHQ YHUEXQGHQ ZHUGHQ PVVHQ
$EE % D 6KDNHU E %HVFKOHXQLJXQJVDXIQHKPHU F 0RWRUODJHU
6HLWH $QKDQJ %
%HGLHQXQJ GHU 6RIWZDUH
:LUG GDV MHZHLOLJH 3URJUDPP JHVWDUWHW VLQG DOOH )HOGHU EHUHLWV DXVJHIOOW 'LHVH :HUWH VROOWHQ
QDFK 0|JOLFKNHLW QLFKW YHUlQGHUW ZHUGHQ DX‰HU ]X 7HVW]ZHFNHQ XP GLH YHUVFKLHGHQHQ .DUWHQ
XQG )UHTXHQ]HQ PLWHLQDQGHU ]X YHUJOHLFKHQ
,P *HKlXVH GHV 3;,6\VWHPV VLQG GUHL .DUWHQ HLQJHEDXW
.DUWH LVW GLH 1, $QDORJ,Q .DUWH
.DUWH LVW GLH 1, $QDORJ2XW .DUWH
.DUWH LVW GLH 1, 0XOWL,2 .DUWH
-H QDFK 9HUVLRQ GHV 3URJUDPPV VLQG DXFK GLHVH 1XPPHUQ HQWVSUHFKHQG HLQJHWUDJHQ XQG GLH
0H‰NDUWHQ PVVHQ GHPHQWVSUHFKHQG DQJHVFKORVVHQ ZHUGHQ
.DUWH NDQQ GLUHNW PLW GHP ]XJHK|ULJHQ 0H‰JHUlW YHUEXQGHQ ZHUGHQ %HL GHQ .DUWHQ XQG
VLQG GLH %1&$QVFKOX‰EO|FNH ]X YHUZHQGHQ
L
6FKULWW 6\VWHPLGHQWLILNDWLRQ
'LH 6\VWHPLGHQWLILNDWLRQ HQWVSULFKW HLQHP GLJLWDOHQ 1DFKELOGHQ GHV JHVDPWHQ
6LJQDOYHUDUEHLWXQJVNUHLVHV GXUFK HLQHQ GLJLWDOHQ DGDSWLYHQ )LOWHU 'DV 6RIWZDUHSURJUDPP
JHQHULHUW ZHL‰HV 5DXVFKHQ GDV ]XP (LQHQ EHU GHQ $QDORJ'LJLWDO8PVHW]HU XQG HLQHQ $XGLR
9HUVWlUNHU ]XP *HJHQNRSSOXQJVVFKZLQJHUUHJHU JHOHLWHW XQG EHU GHQ
%HVFKOHXQLJXQJVDXIQHKPHU /DGXQJVYHUVWlUNHU XQG '$8PVHW]HU ZLHGHU GHU %HUHFKQXQJ
]XJHIKUW ZLUG =XP $QGHUHQ ZLUG GHU MHZHLOLJH GLJLWDOH :HUW GHV ZHL‰HQ 5DXVFKHQV GLUHNW
GHP $GDSWLRQVDOJRULWKPXV EHUJHEHQ 'RUW ZHUGHQ GLH EHLGHQ 6LJQDOH VDPSOHZHLVH YHUJOLFKHQ
XQG PLW GHU EHUHFKQHWHQ 'LIIHUHQ] HLQ GLJLWDOHU )LOWHU DGDSWLHUW 'LH HUKDOWHQHQ
)LOWHUNRHIIL]LHQWHQ VWHOOHQ GLH 6\VWHPDQWZRUW GHV 6LJQDOYHUDUEHLWXQJVNUHLVHV GDU 1DFK HLQHU
]HLWGLVNUHWHQ )RXULHU7UDQVIRUPDWLRQ GHU .RHIIL]LHQWHQ HUKlOW PDQ IU GHQ
$UEHLWVIUHTXHQ]EHUHLFK GDV 9HUKDOWHQ LQ %HWUDJ XQG 3KDVH ,Q $EE% XQWHU
)LOWHUFRHIILFLHQWV PDJQLWXGH XQG SKDVH VLQG GLHVH $XVZHUWXQJHQ JXW ]X HUNHQQHQ 'LH
(UJHEQLVVH GHU 6\VWHPLGHQWLILNDWLRQ VLQG ZLFKWLJH 9RUDXVVHW]XQJHQ IU HLQH JXW
IXQNWLRQLHUHQGH DNWLYH 6FKZLQJXQJVUHGXNWLRQ
6HLWH $QKDQJ %
(V ZHUGHQ QXQ DOOH (LQJDEHP|JOLFKNHLWHQ GHV 3URJUDPPV NXU] EHVFKULHEHQ
$,±&$5' ,VW GLH 1XPPHU GHU YHUZHQGHWHQ DQDORJHQ (LQJDQJVNDUWH
$2±&$5'
,VW GLH 1XPPHU GHU YHUZHQGHWHQ DQDORJHQ $XVJDQJVNDUWH
$QDORJ ,QSXW &KDQQHO
(QWVSULFKW GHP DQJHVFKORVVHQHQ DQDORJHQ (LQJDQJVNDQDO
$QDORJ 2XWSXW &KDQQHO (QWVSULFKW GHP DQJHVFKORVVHQHQ DQDORJHQ $XVJDQJVNDQDO
6&$1 5$7( +LHU
LVW GLH 6DPSOHUDWH HLQ]XWUDJHQ 'HU YRUHLQJHVWHOOWH :HUW
HQWVSULFKW GHU K|FKVWHQ P|JOLFKHQ 6DPSOHUDWH GHV 6\VWHPV
RSWLPL]DWLRQ FRHIILFLHQW 6WHKW IU GHQ :HUW GHV 2SWLPLHUXQJVNRHIIL]LHQWHQ
RI UXQV *LEW
GLH $Q]DKO GHU 6FKOHLIHQGXUFKOlXIH IU GLH 2SWLPLHUXQJ DQ
$XFK KLHU LVW HLQ :HUW HLQJHVWHOOW GHU LGHDO DXI GDV YRUKDQGHQH
6\VWHP DEJHVWLPPW LVW 6ROOWH GLH 2SWLPLHUXQJ ]X NXU] ODXIHQ
LVW GHU :HUW ]X HUK|KHQ
LWHUDWLRQ
'LHQW QXU DOV $Q]HLJH XQG JLEW GHQ DNWXHOOHQ )RUWVFKULWW GHU
6\VWHPLGHQWLILNDWLRQ DQ
:HLWHUV VLQG YRUKDQGHQ
6723.QRSI
IU HLQHQ VRIRUWLJHQ $EEUXFK GHU 5RXWLQH
)LOWHUNRHIIL]LHQWHQ *UDSK
(UURU*UDSK
0DJQLWXGH XQG 3KDVH*UDSK
$OOH 'LDJUDPPH GLHQHQ QXU GHU .RQWUROOH XQG JHEHQ ,QIRUPDWLRQHQ EHU GDV QDFKJHELOGHWH
6\VWHP DQ 'DV IROJHQGH %LOG ]HLJW GLH %HGLHQXQJVREHUIOlFKH GHU 6\VWHPLGHQWLILNDWLRQ
6HLWH $QKDQJ %
$EE % 6\VWHPLGHQWLILNDWLRQ LP 6WDUW]XVWDQG
L
6FKULWW $9& ± 5RXWLQH
%HL GHU $9&5RXWLQH ZLUG GDV 6W|UVLJQDO LQ GLHVHP )DOO .|USHUVFKDOO YRP
9HUEUHQQXQJVPRWRU PLWWHOV DNWLYHU *HJHQNRSSOXQJ UHGX]LHUW 'LHV ZLUG GXUFK HLQH
PHFKDQLVFKH ,QWHUIHUHQ] GHU 6FKZLQJXQJHQ GHV 0RWRUV 6W|UVLJQDO XQG HLQHV JHJHQSKDVLJHQ
$XVO|VFKVLJQDOV ZLUG YRQ HLQHP HOHNWURG\QDPLVFKHQ 6FKZLQJHUUHJHU HU]HXJW HUUHLFKW )U
GLH %HUHFKQXQJ GHV *HJHQNRSSOXQJVVLJQDOV VLQG GDV 'UHK]DKOVLJQDO XQG HLQ
%HVFKOHXQLJXQJVVLJQDO DOV (LQJDQJVSDUDPHWHU Q|WLJ
'HU $9& $OJRULWKPXV JHQHULHUW HLQ VLQXVI|UPLJHV $XVO|VFKVLJQDO GHVVHQ )UHTXHQ] DEKlQJLJ
YRQ GHU JHPHVVHQHQ 'UHK]DKO XQG GHU DXV]XO|VFKHQGHQ 0RWRURUGQXQJ LVW 'XUFK GDV YRP
%HVFKOHXQLJXQJVDXIQHKPHU JHOLHIHUWH 6LJQDO GHP (UJHEQLV GHU 6\VWHPLGHQWLILNDWLRQ XQG GHP
'UHK]DKOVLJQDO ZLUG GLH $PSOLWXGH VRZLH GLH H[DNWH 3KDVHQODJH GHV 6FKZLQJHUUHJHUV DGDSWLY
EHVWLPPW
6HLWH $QKDQJ %
1DFKGHP GLH 6\VWHPLGHQWLILNDWLRQ EHHQGHW ZXUGH NDQQ GLH $9&5RXWLQH JHVWDUWHW ZHUGHQ
'LH $9& 5RXWLQH OlXIW ELV VLH GXUFK GUFNHQ GHV 6723.QRSIHV EHHQGHW ZLUG 'XUFK GHQ
&$1&(//$7,21 21 .QRSI NDQQ GLH DNWLYH $XVO|VFKXQJ EHOLHELJ (LQ XQG $XVJHVFKDOWHW
ZHUGHQ
$,±&$5' ,VW GLH 1XPPHU GHU YHUZHQGHWHQ DQDORJHQ (LQJDQJVNDUWH
$2±&$5' ,VW GLH 1XPPHU GHU YHUZHQGHWHQ DQDORJHQ $XVJDQJVNDUWH
$QDORJ ,QSXW &KDQQHO
(QWVSULFKW GHP DQJHVFKORVVHQHQ DQDORJHQ (LQJDQJVNDQDO
$QDORJ 2XWSXW &KDQQHO
(QWVSULFKW GHP DQJHVFKORVVHQHQ DQDORJHQ $XVJDQJVNDQDO
6&$1 5$7(
+LHU LVW GLH 6DPSOHUDWH HLQ]XWUDJHQ 'HU YRUHLQJHVWHOOWH :HUW
HQWVSULFKW GHU K|FKVWHQ P|JOLFKHQ
RSWLPL]DWLRQ FRHIILFLHQW
6DPSOHUDWH GHV 6\VWHPV
6WHKW IU GHQ :HUW GHV 2SWLPLHUXQJVNRHIIL]LHQWHQ
&$1&(//$7,21 21
6WDUW .QRSI 'XUFK (LQ XQG $XVVFKDOWHQ GLHVHV .QRSIHV NDQQ
GLH (IIL]LHQ] GHV 6\VWHPV JXW EHREDFKWHW ZHUGHQ
6723
'LHQW ]XP %HHQGHQ GHV ODXIHQGHQ 3URJUDPPV
RUGHU WR FDQFHO
+LHU NDQQ IUHL HLQJHVWHOOW ZHUGHQ ZHOFKH 0RWRURUGQXQJ
DXVJHO|VFKW ZHUGHQ VROO
WKUHVKROG IRU USP
6FKZHOOZHUW IU GLH 'UHK]DKOGHWHNWLRQ GXUFK GDV
GHWHFWLRQ
'UHK]DKOLPSXOVVLJQDO 'HU :HUW LVW VR ]X ZlKOHQ GD‰ GLH
'UHK]DKODQ]HLJH HLQHQ UXKLJHQ 9HUODXI ]HLJW
:HLWHUV VLQG YRUKDQGHQ
URWDWLRQ VSHHG =HLJW GLH DNWXHOO JHIDKUHQH 'UHK]DKO DQ
(UURU*UDSK
6WHOOW GLH QRFK EULJ EOHLEHQGHQ UHVXOWLHUHQGHQ
6FKZLQJXQJHQ
DQ
GHU
6WHOOH
GHV
%HVFKOHXQLJXQJVDXIQHKPHUV
GDU
6HLWH $QKDQJ %
$EE % $9&5RXWLQH LP 6WDUW]XVWDQG
,Q $EELOGXQJ % LVW GLH $9& 5RXWLQH GLUHNW QDFK GHP 6WDUWHQ GHV 3URJUDPPV GDUJHVWHOOW +LHU
EHVWHKW GLH 0|JOLFKNHLW GLH YHUVFKLHGHQHQ (LQVWHOOXQJHQ ]X lQGHUQ
(V IROJHQ GLH %HGLHQXQJVREHUIOlFKHQ EHLGHU 3URJUDPPWHLOH LQ %HWULHE 'LH EHLGHQ $EELOGXQJHQ
GLHQHQ ]XU .RQWUROOH GHV 6\VWHPV XQG VWHOOHQ HLQHQ LGHDOHQ %HWULHEV]XVWDQG GDU
6HLWH $QKDQJ %
$EE % 6\VWHPLGHQWLILNDWLRQ QDFK $EODXI GHU 2SWLPLHUXQJ
$EE % $FWLYH 9LEUDWLRQ &DQFHOODWLRQ 5RXWLQH LQ %HWULHE
6HLWH $QKDQJ %
6\VWHPNRPSRQHQWHQ
9HUZHQGHWH 6RIW XQG +DUGZDUH
.RPSRQHQWHQ GHU )LUPD 1DWLRQDO ,QVWUXPHQWV
/DE9LHZ 5HDO7LPH &RQWUROOHU 3;, PLW 0K] 3HQWLXP 3UR]HVVRU
'\QDPLVFKH 6LJQDOHUIDVVXQJVNDUWH 1, IU 3;,
$QDORJ $XVJDQJVNDUWH 1, IU 3;, RGHU
0XOWLIXQNWLRQV ,2 .DUWH 3&, ( IU 3;,
*HKlXVH 3;,%
$QVFKOX‰EO|FNH %1&
/DE9LHZ 6RIWZDUH 9HUVLRQ 5HDO7LPH
/DGXQJVYHUVWlUNHU
$XGLR9HUVWlUNHU
6FKZLQJHUUHJHU
%HVFKOHXQLJXQJVDXIQHKPHU
'UHK]DKOVLJQDOJHEHU E]Z )UHTXHQ]JHQHUDWRU LP 7HVWDXIEDX
GLYHUVH .DEHO XQG 9HUELQGXQJHQ
1RWHERRN RGHU 3&
$FWLYH 9LEUDWLRQ &DQFHOODWLRQ 6RIWZDUHSDNHW
L
L
L
L
L
L
L
L
L
L
L
L
L
L
L
L
6HLWH 

rotec Lüftungsgitter für Rahmeneinbau > W414VA

rotec Lüftungsgitter für Rahmeneinbau > W424

W468AK/1 < rotec schalldämmende Lüftungsgitter

M-2001 Datasheet

W421 - Lüftungsgitter

W484 < rotec Lüftungsgitter für Rahmeneinbau

rotec Lüftungsgitter für Rahmeneinbau > W415

FRITZ!Box Ereignisse, Stand Dienstag, 22 313 KB

Diagnostische Referenzwerte für CT Untersuchungen an