$EVWUDFW,Q WKLV SDSHU ZH SURSRVHG WKH LVRODWHG PXOWLOHYHO
LQYHUWHU XVLQJ SKDVH WUDQVIRUPHUV ,W PDNHV SRVVLEOH WR XVH D
VLQJOH '& SRZHU VRXUFH GXH WR HPSOR\LQJ ORZ IUHTXHQF\
WUDQVIRUPHUV ,QWKLV LQYHUWHU WKH QXPEHU RI WUDQVIRUPHU FRXOG
EHUHGXFHGFRPSDUHZLWKDQH[LVWLQJSKDVHPXOWLOHYHOLQYHUWHU
XVLQJ VLQJOH SKDVH WUDQVIRUPHU 8VLQJ SKDVH DQJOH FRQWURO
PHWKRG ZLWK VZLWFKLQJ IUHTXHQF\ HTXDO WR RXWSXW IXQGDPHQWDO
IUHTXHQF\KDUPRQLFVFRPSRQHQWRIRXWSXWYROWDJHDQGVZLWFKLQJ
ORVV FDQ EH UHGXFHG /DVWO\ ZH WHVWHG WKH SURSRVHG SURWRW\SH
LQYHUWHU WR FODULI\ WKH SURSRVHG HOHFWULF FLUFXLW DQG
UHDVRQDEOHQHVVRIFRQWUROVLJQDOIRUWKHSURSRVHGLQYHUWHU
,QGH[ 7HUPV+%ULGJH 0XOWLOHYHO LQYHUWHU 3KDVH
WUDQVIRUPHU&+0/
,,
1752'8&7,21
5HFHQWO\LWLVEHLQJIRFXVHGRIPDNLQJWKHJUHDWHVWSRVVLEOH
UHVWUDLQDJDLQVWKDUPRQLF FRPSRVLWLRQV JHQHUDWHG E\ LQYHUWHU
LWVHOI WR GHFUHDVH WKH KDUPRQLF FRPSRVLWLRQV RI RXWSXW ,Q
VRPH RI WKRVH UHVHDUFKHV PXOWLOHYHO LQYHUWHU LV D
UHSUHVHQWDWLYH RQH 7KH KDUPRQLF FRPSRVLWLRQV FDQ EH
GHFUHDVHG ZKHQ VZLWFKHV ZRUN RQ ORZ IUHTXHQF\ DQG KLJK
YROWDJH FDQ EH PDGH LI WKH PXOWLOHYHO LQYHUWHU LV XVHG ,W LV
ZLGHO\XVHGLQPDQXIDFWXUHIDFWRU\DQGJRWSXEOLFUHFRJQLWLRQ
LQWKHSRZHUFRQYHUWHULQGXVWULDOEHFDXVHLWFDQRYHUFRPHWKH
GLVDGYDQWDJHV RI H[LVWLQJ 3:0 FRQWURO LQYHUWHU
>@>@
2UGLQDULO\ ORZYROWDJH VZLWFKLQJ HOHPHQWV DUH FRQQHFWHG LQ
VHULHVGULYHQE\FRQWLQXRXVVZLWFKLQJVLJQDOVWRJHQHUDWHVWHS
ZDYHIRUPZKLFKDUHWKHKLJKYROWDJHRXWSXWLQWKHVHFLUFXLWV
:KHQ )&& W\SH PXOWLOHYHO LQYHUWHU LV XVHG UHODWLYHO\ WKH
FLUFXLW FDQ EH FRQVLVW RI OHVV HOHPHQWV EXW WKH YROXPH RI
V\VWHPLVHQODUJHGIRUQHFHVVDU\RIPRUHFDSDFLWRUV
>@
:KHQ
'&& W\SH PXOWLOHYHO LQYHUWHU LV XVHG WKH FRPSOH[ 3:0
FRQWURO QHHG WR EH XVHG EHFDXVH PRUH FDSDFLWRUV DQG GLRGHV
DUHQHFHVVDU\IRUJHQHUDWLQJOHYHOYROWDJHVDQGWKHEDODQFHRI
HDFK '& OLQN YROWDJH RI FDSDFLWRU QHHG WR EH
FRQWUROOHG
>@>@>@
,QWKH,+&W\SHPXOWLOHYHOLQYHUWHUWKHORZ
YROWDJH +%ULGJH PRGXOHV DUH FRQQHFWHG LQ VHULHV VR LW LV
SRVVLEOH WR XVH PRGXOH WKDW FRQVLVW GHSHQGHQW '&OLQN FHOOV
EXWLWLVWKHGLVDGYDQWDJHWKDWWKHGHSHQGHQWYROWDJHQHHGWREH
SURYLGHGWRHDFK+%ULGJHVHSDUDWHO\
>@>@
,Q WKLV SDSHU D QRYHO YROWDJHSLOLQJ SKDVH 7UDQVIRUPHU
6RQJ 6XQJ*HXQ<X7DR3DUN 6XQJ-XQDUH ZLWK HOHFWULFDOHQJLQHHULQJ
GHSDUWPHQWRI&KRQQDP1DWLRQDO8QLYHUVLW\.RUHD(PDLO\XWDR#QDYHUFRP
/LP -RXQJ0LQ &KHDQJ (XL+HDQJ -XQJ .ZHQ6XQJ DQG 0RRQ &KDH
-RR DUH ZLWK 'HSDUWPHQW RI (OHFWULFDO (QJLQHHULQJ 0RNSR 1DWLRQDO
8QLYHUVLW\.RUHD(PDLOOMP#SDUDQFRP
,VRODWHG +%ULGJH 0XOWLOHYHO ,QYHUWHU ,+&0/ ,VRODWHG +
%ULGJH &DVFDGH 0XOWL /HYHO ZKLFK XVH D VLJQDO '& VRXUFH
DQGLVRODWHGSKDVHORZIUHTXHQF\WUDQVIRUPHUVLVSURSRVHG
,Q WKH SURSRVHG WRSRORJ\ E\ XVLQJ WKH SKDVH WUDQVIRUPHUV
WKHQXPEHURIWUDQVIRUPHUVFDQEHUHGXFHGFRPSDUHGZLWKWKH
H[LVWLQJ PHWKRG WKDW XVH VLQJOHSKDVH WUDQVIRUPHU DQG WKH
HFRQRPLFDODQGHIILFLHQWLQYHUWHULVSRVVLEOHWREHFRQVWUXFWHG
7KHVZLWFKLQJIUHTXHQF\RIHDFK+%ULGJHLQYHUWHULVXQLIRUP
ZLWKWKH RXWSXW EDVH ZDYH IUHTXHQF\ DQG WKHUHOD\ DQJOHVRI
HDFK VZLWFK LV FDOFXODWHG E\ 1HZWRQ5DSVRQ PHWKRG RQ WKH
EDVLV RI WKHLU DUHD WR HOLPLQDWH WKH ORZ KDUPRQLFV
FRPSRVLWLRQV IHOLFLWRXVO\ 6R DOO UHOD\ DQJOHV FDQ EH GHFLGHG
E\XVLQJWKHOLEHUDOL]DWLRQPHWKRGLQHDFKDUHD)RUFODULI\LQJ
WKH SURSRVHG ,+&0/ WRSRORJ\ WKH VLPXODWLRQ ZDV GRQH LQ
0DWODEDQGWKHLQYHUWHUZDVPDGHDQGWHVWHG
,,
3$+6(
7
5$16)250(5
,
62/$7('
+
%5,'*(
0
8/7,
/(9(/
,
19(57(5
$6WUXFWXUHRI+%ULGJHW\SHPXOWLOHYHOLQYHUWHU
,QPXOWLOHYHOLQYHUWHUVWKH+%0/LQYHUWHULVRIWHQDSSOLHG
7KHFRQILJXUDWLRQDQGSULQFLSOHRI+%0/PXOWLOHYHOLQYHUWHU
FRQVLVWLQJRI+EULGJHLQYHUWHUVSDUDOOHOWKDQFDQJHQHUDWH
OHYHOVRXWSXWLVVKRZQDVILJXUH+%0/LQYHUWHULVWKHSLOH
RI ORZ YROWDJH +EULGJHV FRQQHFWHG SDUDOOHO DQG FRQVLVWV RI
WKHVH LQGHSHQGHQW GFOLQN XQLW FHOOV $FFRUGLQJ WR WKH
VZLWFKLQJIXQFWLRQ]HURYROWDJHSRVLWLYHYROWDJHDQGQHJDWLYH
YROWDJHDUHDOOFDQEHPDGH7KHRXWSXWYROWDJH
R
9 LVWKHVXP
RI WKH DOO RXWSXW YROWDJHV RI +EULGJHV FRQQHFWHG SDUDOOHO
2XWSXW YROWDJH RI HDFK EULGJH DQG ILQDO RXWSXW YROWDJH ZLWK
SDUDOOHO FRQQHFWHG VKRZQ DV ILJXUH ZKHQ RUGLQDU\ IXQFWLRQ
PHWKRGLVXVHG,WLVNQRZQIURPILJXUHWKDWWKHFRQWUROOHGNH\
RI RXWSXW YROWDJH LV WKH VZLWFKLQJ DQJOH RI HDFK XQLW
α
α
α
α %XW LQ WKLV FRQILJXUDWLRQ WKHUH LV D
GLVDGYDQWDJH RI QHFHVVDU\ RI WKH VDPH QXPEHUV LQGHSHQGHQW
'&VRXUFHVDVWKHQXPEHUVRIWKH+EULGJHV
,W LV LPSRVVLEOH WKDW WKH SHDN YDOXH RI RXWSXW YROWDJH
H[FHHGVWKHYDOXHWKDWLVWLPHVRIVRXUFHYROWDJHZKHQXVLQJ
WKH+%0/FRQVLVWLQJRIKDOIEULGJHLQYHUWHUVLQILJXUH,Q
WKLV FRQGLWLRQ DQRWKHU YROWDJHERRVWLQJ GHYLFHV DUHQHFHVVDU\
ZKHQLQSXWYROWDJHLVORZDQGRXWSXWYROWDJHLVQHHGHGWREH
KLJK
,VRODWHG0XOWLOHYHO,QYHUWHU8VLQJ
3KDVH7UDQVIRUPHUV
6RQJ6XQJ*HXQ<X7DR 3DUN6XQJ-XQ
/LP-RXQJ0LQ&KHDQJ(XL+HDQJ-XQJ.ZHQ6XQJ0RRQ&KDH-RR
1037
978-981-05-9423-7 c
2007 RPS
W
W
W
9
'&
W
9
9
9
9
9R
W
α
1
α
2
α
3
α
4
9
'&
9
'&
9
'&
9
'&
9
'&
9
'&
9
'&
DE
)LJ7KHFRQILJXUDWLRQRIOHYHO+%0/LQYHUWHU RXWSXWYROWDJH
D&RQILJXUDWLRQRI+%0/LQYHUWHU
E7KHRSHUDWLRQSULQFLSOHRI+%0/LQYHUWHU
'&VRXUFHLQSXWVDUHFRQQHFWHGLQSDUDOOHODVKDOIEULGJH
PRGXOHV DQG WUDQVIRUPHUV DUH FRQQHFWHG LQ VHULHV LQ
VHFRQGDU\ VLGH VKRZQ DV ILJXUH 7KHQ RXWSXW YROWDJH RI
LQYHUWHU FDQ EH GHFLGHG E\ WKH YROWDJH RI WKH YROWDJH RI '&
VRXUFH DQG WKH WXUQ UDWLR RI WUDQVIRUPHU %HFDXVH RI EHLQJ
FRPELQHGZLWKWUDQVIRUPHUVWKHPXOWLOHYHOLQYHUWHUVKRZQLQ
ILJXUH KDV WKH DGYDQWDJH RI LVRODWLRQ EHWZHHQ WKH VRXUFH
YROWDJH DQG WKH RXWSXW YROWDJH FRPSDUHG ZLWK WKH H[LWLQJ
+%0/ LQYHUWHU %XW ZKHQ SKDVH PXOWLOHYHO LQYHUWHU
FRQVLVWVRIWUDQVIRUPHUW\SHPXOWLOHYHOLQYHUWHUDERYHWKHUHLV
VKRUWFRPLQJRIQHFHVVDU\IRUPRUHWUDQVIRUPHUVEHFDXVHVDPH
WUDQVIRUPHUVQHHGWREHXVHGLQHDFKSKDVH
+EULGJH&HOO
'&
9
D
6
D
6
D
6
D
6
D
6
D
6
D
6
D
6
D
6
D
6
D
6
D
6
D
6
D
6
D
6
D
6
7
7
7
7
9R
,QY
,QY
,QY
,QY
)LJ7KHFRQILJXUDWLRQRIERRVWW\SH
+%0/LQYHUWHUXVLQJWUDQVIRUPHUV
%SKDVH,+&0/LQYHUWHU
&RQILJXUDWLRQRISKDVH,+&0/LQYHUWHU
,Q SURSRVHG FRQILJXUDWLRQ RI WKLV SDSHU SKDVH ,+&0/
LQYHUWHU FRQVLVWV RI RQH '& VRXUFH DQG ORZ IUHTXHQF\
WUDQVIRUPHUV SLOLQJ YROWDJHV VKRZQ DV ILJXUH ,Q SURSRVHG
LQYHUWHU IRU XVLQJ SKDVH WUDQVIRUPHUV WKH QXPEHU RI
WUDQVIRUPHUVDQGWKHYROXPHRIV\VWHPFDQEHUHGXFHGDQGWKH
SULFH RI V\VWHP LV GHVHUYHGO\ GRZQ ,Q SULPDU\ VLGH RI
WUDQVIRUPHUV HDFK SKDVH FRQQHFWHG E\ +%ULGJHV ZKLFK FDQ
JHQHUDWH YROWDJHV
'&
9
DQG
'&
9
−
LQ VHFRQGDU\ VLGH HDFK
SKDVH LV FRQQHFWHG LQ SDUDOOHO IRU SLOLQJ YROWDJHV $QG IRU
UHVWUDLQLQJ WKH WKLUG KDUPRQLF FRPSRVLWLRQ RI SKDVH
WUDQVIRUPHUVHDFKSKDVHLVFRQQHFWHGLQ
Δ
,QILJXUHWKHRXWSXWRIWKHILJXUHLVSUHGLJHVWHGZKHQ
WUDQVIRUPHUV DUH XVHG $V ILJXUH ZH FDQ NQRZ WKDW RQO\ RQH
SKDVHRIRXWSXWVLVVKRZQZKHQSKDVHLVLQSXWWHGDQGIRU
SLOLQJWKHYROWDJHVWKHRXWSXWVDUHFRQQHFWHGLQSDUDOOHO,QWKLV
FRQILJXUDWLRQ HDFK SKDVH FDQ EH LQGHSHQGHQWO\ SUHVHQWHG ,Q
ILJXUHYROWDJHV
DN
9
EN
9
FN
9 DUHWKHRXWSXWYROWDJHRINWK+
%ULGJHDQG YROWDJHV
$N
9
%N
9
&N
9 DUH WKH RXWSXW YROWDJHV RI
HDFK SKDVH RI WUDQVIRUPHUV 7KHUHIRUH WKH UHODWLRQ EHWZHHQ
LQSXW YROWDJH DQG RXWSXW YROWDJH RI SKDVH WUDQVIRUPHU LV
VKRZQDVEHORZ
+EULGJH&HOO
37UDQFH
7U
7U
N
/RDG
1
$
%
&
9
'&
&
9
$
9
%
9
&
9
$N
9
%N
9
&N
9
DN
9
EN
9
FN
9
D
9
E
9
F
)LJ3URSRVHGRIWKH3KDVH,+&0/,QYHUWHU
9
&$
9
$%
9
%&
9
$6
9
$
9
$
9
$
9
D
9
E
9
F
9
D
9
E
9
F
9
D
9
E
9
F
9
$6
9
%6
9
&6
,+&0/
,+&0/
,+&0/
)LJ6LPSOLILHGVWUXFWXUHRI3KDVH,+&0/LQYHUWHU
»
»
»
¼
º
«
«
«
¬
ª
»
»
»
¼
º
«
«
«
¬
ª
−
−
−
−
−
−
=
»
»
»
¼
º
«
«
«
¬
ª
FN
EN
DN
&N
%N
$N
9
9
9
7
9
9
9
,Q WKH DERYH IRUPXOD 7 LV WKH WUDQVIRUP UDWLR
Q
Q
EHWZHHQWKHVWVLGHDQGWKHHGVLGHRIWKHWUDQVIRUPHU,IWKH
LQSXW YROWDJH LV EDODQFHG LQ WKUHH SKDVHV WKH VXP RI DOO
YROWDJHVRIHDFKSKDVHLVDVVKRZQEHORZ
=
+
+
FN
EN
DN
9
9
9
)URPIRUPXODDQGWKHRXWSXWYROWDJHFDQH[SUHVVHG
DVEHORZ
»
»
»
¼
º
«
«
«
¬
ª
=
»
»
»
¼
º
«
«
«
¬
ª
FN
EN
DN
&N
%N
$N
9
9
9
7
9
9
9
7KHQ WKH SKDVH RXWSXW YROWDJH RI WUDQVIRUPHU FDQ EH
H[SUHVVHGE\WKHSURGXFWRIWKHLQSXWYROWDJHDQGWKHWXUQUDWLR
RI WUDQVIRUPHU %XW ZKHQ ,+&0/ LQYHUWHU LV XVHG EHFDXVH
YROWDJHV
DN
9
EN
9
FN
9 RI VW VLGH RI WUDQVIRUPHUDUH JHQHUDWHG
E\ LQGHSHQGHQW +%ULGJH EULQJLQJ YROWDJH OHYHOV
'&
9
'&
9
−
WKUHH SKDVHV DUH RIWHQ QRW EDODQFHG 6R LQVWHDG RI
IRUPXODXVXDOO\IRUPXODLVXVHG7KHRXWSXWYROWDJHRI
,+&0/ LQYHUWHULV JHQHUDWHG E\ WKH YROWDJHV RI WUDQVIRUPHUV
FRQQHFWHG LQ VHULHV WKH OLQH YROWDJH
$%
9
%&
9
&$
9 FDQ EH
1038
The 8
th
International Power Engineering Conference (IPEC 2007)
H[SUHVVHGE\IRUPXOD
»
»
»
¼
º
«
«
«
¬
ª
+
+
+
+
+
+
+
+
+
=
»
»
»
¼
º
«
«
«
¬
ª
=
»
»
»
¼
º
«
«
«
¬
ª
&N
&
&
%N
%
%
$N
$
$
&6
%6
$6
&$
%&
$%
9
9
9
9
9
9
9
9
9
9
9
9
9
9
9
"
"
"
$V VKRZQ LQ DERYH IRUPXOD WKH OLQH YROWDJH RI SKDVH
,+&0/ PD\ EH H[SUHVVHG E\ WKH VXP RI RXWSXW YROWDJHV RI
HDFKWUDQVIRUPHU,WLVSUHGLJHVWHGDVEHORZ
¦
=
=
N
L
$L
$6
9
9
¦
=
=
N
L
%L
%6
9
9
¦
=
=
N
L
&L
&6
9
9
2XWSXWRISKDVH,+&0/LQYHUWHU
7KHLQSXWYROWDJHRINWKSKDVHWUDQVIRUPHUDQGWKHRXWSXW
YROWDJH RI $ SKDVH DUH VKRZQ LQ ILJXUH ,W FDQ EH NQRZQ
IURP ILJXUH WKDW WKH LQSXW YROWDJH RI WUDQVIRUPHU LV WKH
UHFWDQJXODUZDYHDQGLWVIUHTXHQF\LVDVVDPHDVWKHIUHTXHQF\
RI LQSXW YROWDJH LQ +%ULGJH 7KH VZLWFKLQJ VLJQDOV LQ WKH
E SKDVHDQG F SKDVHLVDKHDGRUEHKLQGRIWKH D SKDVH V7KH
FRQWURO NH\ LV WKH VZLWFKLQJ DQJOH
N
α :KHQ N WUDQVIRUPHUV
DUHXVHGWKHFRQWURONH\LVWKHVZLWFKLQJDQJOHV
α
α «
N
α
DQGWKHRXWSXWYROWDJHFDQEHDGMXVWHGE\DSWO\UHJXODWLQJWKH
VZLWFKLQJ DQJOHV
>@
([WLQFWLRQ DQJOH DQG ILULQJ DQJOH DUH
V\PPHWULFDO RQ EDVH RI
π
VR WKH H[WLQFWLRQ DQJOH FDQ EH
PDGH DV
α
π −
α
π − «
N
α
π − :KHQ WKH FRQWUROUDQJH
RIVZLWFKLQJDQJOHLV
π
α ≤
≤
N
DQGLQSXWVRIWUDQVIRUPHUV
DUH QRW EDODQFHG LQ SKDVHV WKH RXWSXW YROWDJH RI SKDVH
WUDQVIRUPHUZLOOEHGHFLGHGE\WKHFRPELQDWLRQRIYROWDJHVRI
WKH D E F SKDVH7KHUHDUHWKUHHSRVVLELOLWLHVLQWKHRXWSXW
YROWDJH RI WUDQVIRUPHUDFFRUGLQJWR WKH VZLWFKLQJ DQJOH 7KH
UDQJH RI VZLWFKLQJ DQJOH
N
α LV
π
α ≤
≤
N
DV ILJXUH D
π
α
π
≤
≤
N
DV E DQG
π
α
π
≤
≤
N
DV F 7KH
VZLWFKLQJSDWWHUQVRIHDFKSKDVHDQGRXWSXWYROWDJHRISKDVH
WUDQVIRUPHUDUHVKRZQDVILJXUHZKHQWKHWXUQUDWLRLVVHWWR
,Q HDFK UDQJH RXWSXW YROWDJH RI $ SKDVH
$N
9 LV V\PPHWULFDO
DQGWKH)RXULHUSURJUHVVLRQRIRGGIXQFWLRQFDQEHZULWWHQDV
¦
∞
=
=
VLQ
Q
QN
$N
Q
E
9
θ
7KH FRQVWDQW
QN
E DERYH FDQ EH VKRZQ DV EHORZ DFFRUGLQJ
WRWKHVZLWFKLQJDQJOHV
&DVH
π
α ≤
≤
N
»
¼
º
«
¬
ª
+
+
=
³
³
³
+
+
−
−
VLQ
VLQ
VLQ
π
α
π
α
π
α
π
α
π
α
θ
θ
θ
θ
θ
θ
π
N
N
N
N
N
G
Q
G
Q
G
Q
9
E
'&
QN
FRV
N
'&
QN
Q
Q
9
E
α
π
=
&DVH
π
α
π
≤
≤
N
»
»
¼
º
«
«
¬
ª
+
+
=
³
³
³
−
−
−
VLQ
VLQ
VLQ
π
α
π
α
π
α
α
α
π
θ
θ
θ
θ
θ
θ
π
N
N
N
N
N
G
Q
G
Q
G
Q
9
E
'&
QN
FRV
N
'&
QN
Q
Q
9
E
α
π
=
&DVH
π
α
π
≤
≤
N
»
¼
º
«
¬
ª
+
=
³
³
−
−
VLQ
VLQ
π
α
α
π
π
α
θ
θ
θ
θ
π
N
N
N
G
Q
G
Q
9
E
'&
QN
FRV
N
'&
QN
Q
Q
9
E
α
π
=
+HUH
O
O
Q
−
⋅⋅
⋅
=
N
α
π −
N
α
N
α
π
+
9
DN
9
EN
9
FN
9
$N
9
'&
9
'&
9
'&
N
α
π −
N
α
D&DVH
N
α
π
−
N
α
N
α
π
−
9
DN
9
EN
9
FN
9
$N
9
'&
9
'&
9
'&
N
α
N
α
π
−
E&DVH
π
α
−
N
N
α
π
−
N
α
9
DN
9
EN
9
FN
9
$N
9
'&
9
'&
N
α
N
α
π
−
F&DVH
)LJ:DYHIRUPVRIWUDQVIRUPHURQVZLWFKDQJOH
,WFDQEHNQRZQWKDWWKHUHVXOWVRIWKH)RXULHUSURJUHVVLRQ
LQHDFKUDQJHDUHDOOVDPHDQG
QN
E LVXQLIRUPLQWKHUDQJHRI
π
α ≤
≤
N
7KH H[SUHVVLRQV EHORZ DUH WHQDEOH E\ XVLQJ
IRUPXOD7KH)RXULHUWUDQVIRUPRIWUDQVIRUPHU¶VSULPDU\
YROWDJH
DN
9
EN
9
FN
9 LVVKRZQDV
θ
θ G
Q
E
9
Q
QN
DN
¦
∞
=
=
VLQ
θ
π
θ
G
Q
Q
E
9
Q
QN
EN
¦
∞
=
−
=
VLQ
θ
π
θ
G
Q
Q
E
9
Q
QN
FN
¦
∞
=
+
=
VLQ
+HUH
O
O
Q
−
⋅⋅
⋅
=
,Q WKH IRUPXOD DERYH WKH FRHIILFLHQW
QN
E DQG
DN
9 LV KDOI
ZDYHV\PPHWU\7KHRGGIXQFWLRQLV
FRV
N
'&
QN
Q
Q
9
E
α
π
=
%\ XVLQJ IRUPXOD DQG WKH RXWSXW YROWDJH RI
The 8
th
International Power Engineering Conference (IPEC 2007)
1039
$
SKDVH
DN
9 FDQH[SUHVVHGDV
¦
¦
∞
=
∞
=
¸
¹
·
¨
©
§
+
−
=
FRV
VLQ
VLQ
VLQ
Q
Q
Q
Q
$N
Q
Q
Q
E
Q
E
9
π
θ
θ
θ
,I
O
O
Q
−
⋅⋅
⋅
=
=
$N
9
,I
O
O
Q
−
⋅⋅
⋅
=
¦
∞
=
=
VLQ
Q
Q
$N
Q
E
9
θ
7KHUHIRUHWKHRXWSXWYROWDJH
$N
9 RINWKWUDQVIRUPHULVH[LVW
RQO\ ZKHQ
O
O
Q
−
⋅⋅
⋅
=
,W LV NQRZQ WKDW WKH UG
KDUPRQLFFRPSRVLWLRQLVQRWH[LWLQSKDVHLQYHUWHU
*HQHUDWLQJRIVZLWFKLQJVLJQDO
,Q,+&0/LQYHUWHUEHFDXVHWKHRXWSXWVRIWUDQVIRUPHUVDUH
FRQQHFWHGLQVHULHVE\SKDVHWKHRXWSXWYROWDJHRILQYHUWHUFDQ
EH H[SUHVVHG E\ WKH VXP RI RXWSXW YROWDJHV RI HDFK
WUDQVIRUPHU 7KH RXWSXW YROWDJH RI HDFK WUDQVIRUPHU LV
LQGHSHQGHQW RI WKH VZLWFKLQJ DQJOH LQ WKH UDQJH
RI
π
α ≤
≤
N
7KH RXWSXW YROWDJH FDQ EH H[SUHVVHG DV
EHORZ ZKHQ WKUHH SKDVH WUDQVIRUPHUV DUH XVHG LQ WKH
,+&0/LQYHUWHU
(
)
FRV
FRV
FRV
α
α
α
π
Q
Q
Q
Q
9
9
'&
$6
+
+
=
+HUH
π
α
α
α
≤
≤
≤
≤
,WFDQEHNQRZQWKDWLIWKHRXWSXWYROWDJHLVFRQWUROOHGE\
WKH VZLWFKLQJ DQJOHV
α
α
α WKH EDVLF FRPSRVLWLRQ LV
JHQHUDWHG ZKLOH WKH VSHFLDO KDUPRQLF FRPSRVLWLRQV DUH
UHGXFHG ,Q IRUPXOD DERYH E\ FRQWUROOLQJ VZLWFKLQJ DQJOHV
WKH EDVLF FRPSRVLWLRQ FDQ EH JHQHUDWHG ZKLOH KDUPRQLF
FRPSRVLWLRQV FDQ EH UHGXFHG ,W KDV EHHQ NQRZQ WKDW UG
KDUPRQLFFRPSRVLWLRQLVQRWH[LWVRWKHWKDQGWKKDUPRQLF
FRPSRVLWLRQVDUHWULHGWREHUHGXFHGLQWKLVSDSHU7KHIRUPXOD
ZKHUHWKHWKDQGWKKDUPRQLFFRPSRVLWLRQVFDQEHUHGXFHG
LVVKRZQDV
FRV
FRV
FRV
π
α
α
α
P
=
+
+
FRV
FRV
FRV
=
+
+
α
α
α
FRV
FRV
FRV
=
+
+
α
α
α
+HUH P LVWKHPRGXODWLRQLQGH[
,WLVDQRQOLQHDUHTXDWLRQWKDWFDQEHVROYHGE\WKHLWHUDWLYH
PHWKRGVXFKDV1HZWRQ5DSVRQPHWKRGDQGLVLPSRVVLEOHWR
EH VROYHG RQOLQH ,Q WKLV SDSHU WKH LQGH[ PRGXODWLRQ LV VHW
IURP WR JURXSV VZLWFKLQJ DQJOH YDOXHV DUH
FDOFXODWHG SUHYLRXVO\ SHU XQLW DQG WKH VZLWFKLQJ DQJOH LV
JRWE\XVLQJWKHILUVWIXQFWLRQ
,,,6
,08/$7,216$1'5(68/76
%\XVLQJ1HZWRQ5DSVRQPHWKRGWKHLQGH[PRGXODWLRQLV
VHW IURP WR FDOFXODWHG VZLWFKLQJDQJOH YDOXHV SHU
XQLWDUHVKRZQDVWDEOH
:KHQFDOFXODWHGVZLWFKLQJDQJOHYDOXHVLQWDEOHDUHXVHG
WKHLQGH[PRGXODWLRQLVVHWWR'&YROWDJHLVVHWWR9
WUDQVIRUPHUUDWLRLVVHWWRVLPXODWLRQUHVXOWVRIWKHRXWSXWRI
$ SKDVH DQG $ SKDVH RXWSXWV RI HDFK WUDQVIRUPHU LQ 0DWODE
DUH VKRZQ DV ILJXUH ,Q WKH ILUVW WUDQVIRUPHU WKH VZLWFKLQJ
DQJOH
α LVDQGWKHH[WLQFWLRQDQJOHLVDVVKRZQ
LQILJXUHELQVHFRQGWUDQVIRUPHUWKHVZLWFKLQJDQJOH
α
LVWKHH[WLQFWLRQDQJOHLVDVVKRZQLQILJXUHF
LQ WKLUG WUDQVIRUPHU WKH VZLWFKLQJ DQJOH
α LV WKH
H[WLQFWLRQ DQJOH LV DV VKRZQ LQ ILJXUH G +HUH
$
9
$
9
$
9 DUHWKH$SKDVHRXWSXWYROWDJHVRIHDFKWUDQVIRUPHU
$6
9
LV WKH RXWSXW YROWDJH RI VHFRQGDU\ WUDQVIRUPHU VLGH
FRQQHFWHGLQVHULHVDQG
UHI
$
9
B
LVWKHUHIHUHQFHYROWDJH
7LPHV
9
$
9
$
9
$
9
$BUHI
9
$6
9RO
WDJH
)LJ6LPXODWLRQUHVXOWRQPRGXODWLRQ
7DEOH6ZLWFKLQJDQJOHVIRUPRGXODWLRQLQGH[
:KHQ WKH LQGH[ PRGXODWLRQ LV FKDQJHG IURP WR
VZLWFKLQJDQJOHV RI HDFK +%ULGJH E\ XVLQJ 1HZWRQ5DSVRQ
PHWKRG DQG VZLWFKLQJ DQJOHV FDOFXODWHG E\ WKH ILUVW
OLQHDUL]DWLRQ PHWKRG E\ XVLQJ FDOFXODWHG VZLWFKLQJ DQJOH
YDOXHVVKRZQLQWDEOHLQHDFKDUHDDUHVKRZQDVILJXUH,W
LVFOHDUWKDWWKHUHLVQRWJUHDWGLIIHUHQFHEHWZHHQWKHP
$
Q
JO
H
GH
J
0RGXODWLRQP
7U
7U
7U
3URSRVHGPHWKRG
)LJ7KHRXWSXWYROWDJH7+'DQG')IRUGLIIHUHQWPRGXODWLRQ
1040
The 8
th
International Power Engineering Conference (IPEC 2007)
7+
'
'
)
0RGXODWLRQP
')
3URSRVHGPHWKRG
7+'
)LJ2XWSXWYROWDJH7+'DQG')IRUGLIIHUHQWPRGXODWLRQ
)LJ3URWRW\SH3KDVH,+&0/LQYHUWHU
7KHFRPSDULVRQRI7+'DQG')RIRXWSXWYROWDJHLQDFWXDO
VZLWFKLQJDQJOHDQGFDOFXODWHGRQHVLVVKRZQDVILJXUH,WLV
VKRZQ WKDW WKHUH LV VRPH GLIIHUHQFH QHDU LQGH[ PRGXODWLRQ
SRLQWDQGE\DGMXVWLQJWKLVYDOXHWKHSUREOHPDUHVROYHG
D
E
F
)LJ:DYHIRUPVRILQYHUWHUUHIHUHQFHYROWDJHRXWSXWYROWDJHDQG))7
DPRGXODWLRQEPRGXODWLRQDQGFPRGXODWLRQ
7KH SURSRVHG SURWRW\SH LQYHUWHU LV PDGH DQG WHVWHG WR
FODULI\ WKH UHDVRQDEOHQHVV RI WKH SURSRVHG SKDVH ,+&0/
LQYHUWHU E\ XVLQJ WKUHH SKDVH WUDQVIRUPHUV DQG VL[ ,30 LQ
WKH /DE 7KH SURFHVVRU LV '63 DQG WKH ODWFK FLUFXLW LV
XVHGIRUVXLWDEOHWRPRVWVZLWFKLQJFRQWURO
:KHQWKHLQGH[PRGXODWLRQLVDQGWKHUHIHUHQFH
YROWDJHRXWSXWYROWDJHDQG))7RIRXWSXWYROWDJHDUHVKRZQ
DV ILJXUH $V NQRZQ IURP WDEOH ZKHQ WKH LQGH[
PRGXODWLRQ LV WKUHH +EULGJH LQYHUWHUV ZRUN XQGHU
VZLWFKLQJ DQJOH FRQWURO WKXV WKH EDVLF FRPSRVLWLRQ DQG WK
WK KDUPRQLF FRPSRVLWLRQV FDQ EH UHGXFHG :KHQ WKH LQGH[
PRGXODWLRQLVWZRRIWKUHH+EULGJHLQYHUWHUVZRUNXQGHU
VZLWFKLQJ DQJOH FRQWURO WKXV WKH EDVLF FRPSRVLWLRQ DQG WK
KDUPRQLF FRPSRVLWLRQV FDQ EH UHGXFHG :KHQ WKH LQGH[
PRGXODWLRQLVRQH+EULGJHLQYHUWHUZRUNXQGHUVZLWFKLQJ
DQJOH FRQWURO WKXV RQO\ WKH EDVLF FRPSRVLWLRQ FDQ EH
FRQWUROOHG
,W FDQ EH NQRZQ WKDW WK DQG WK KDUPRQLF FRPSRVLWLRQV
FDQ EH UHGXFHG ZKHQ WKH LQGH[ PRGXODWLRQ LV LQ ILJXUH
D WK KDUPRQLF FRPSRVLWLRQ FDQ EH UHGXFHG ZKHQ WKH
LQGH[PRGXODWLRQLVLQILJXUHEWKDQGWKKDUPRQLF
FRPSRVLWLRQV DOO FDQ EH QRW UHGXFHG ZKHQ WKH LQGH[
PRGXODWLRQ LV LQ ILJXUH F ,W LV FOHDU WKDW E\ XVLQJ
SURSRVHGPXOWLOHYHOLQYHUWHUFRQILJXUDWLRQWKHRXWSXWYROWDJH
RI HDFK WUDQVIRUPHU GR QRW LQFOXGH WKH UG KDUPRQLF
FRPSRVLWLRQ ZKHQ
Δ
FRQQHFWLRQ LV XVHG LQGHSHQGHQW RI WKH
LQGH[ PRGXODWLRQ ,I WKH PHWKRG WKDW FDQ UHGXFH WKH VSHFLDO
KDUPRQLF FRPSRVLWLRQV XVLQJ 1HZWRQ5DSVRQ PHWKRG LV
DSSOLHG WKH 7+' RI RXWSXW YROWDJH DQG WKH TXDOLW\ RI WKH
RXWSXW YROWDJH DUH ERWK LPSURYHG ZLWK WKH LQFUHDVH RI WKH
RXWSXWYROWDJH
:KHQWKHLQGH[PRGXODWLRQLVWKHRXWSXWYROWDJHRI$
SKDVH DQG WKH VZLWFKLQJ VLJQDOV RI HDFK SKDVH DUH VKRZQ DV
ILJXUHDQGLWFDQEHNQRZQWKDWWKHIUHTXHQF\RIVZLWFKLQJ
VLJQDOVLVVDPHDVWKHEDVLFFRPSRVLWLRQ
:KHQ WKH LQGH[ PRGXODWLRQ LV WKH RXWSXW YROWDJH RI
LQYHUWHU SKDVHWRQHXWUDO YROWDJH RI ORDG XVLQJ <FRQQHFWLRQ
DQGWKH))7UHVXOWDUHVKRZQDVILJXUH
9
$6
9
D
9
D
9
D
)LJ2XWSXWYROWDJHVRILQYHUWHUDQGHDFKDUP
9
$6
9
$1
))7UHVXOWRI9
$1
)LJ2XWSXWYROWDJHRILQYHUWHUDQGSKDVHWRQHXWUDOYROWDJHRIORDG
The 8
th
International Power Engineering Conference (IPEC 2007)
1041
,9&
21&/86,21
,QWKLVSDSHUDQRYHOORZIUHTXHQF\SKDVHLVRODWHGPXOWL
OHYHO LQYHUWHU XVLQJ SKDVH WUDQVIRUPHUV LV SURSRVHG 7KH
SURSRVHG SURWRW\SH LQYHUWHU LV WHVWHG WR FODULI\ WKH SURSRVHG
HOHFWULF FLUFXLW DQG UHDVRQDEOHQHVV RI FRQWURO VLJQDO IRU WKH
SURSRVHGLQYHUWHU$OOUHOD\DQJOHVFDQEHGHFLGHGE\XVLQJWKH
OLEHUDOL]DWLRQPHWKRGLQHDFKDUHDRQEDVHRI1HZWRQ5DSVRQ
PHWKRG 7KH DGYDQWDJHV RI FRQILJXUDWLRQ DQG VZLWFKLQJ
PHWKRGLQWKHSURSRVHGLQYHUWHUDUHVKRZQVLPSO\DVEHORZ
(IILFLHQWDQGHFRQRPLFDOE\XVLQJRQHWUDQVIRUPHU
,QFUHDVH RI XWLOL]DWLRQ UDWH DQG GHFUHDVH RI YROXPH E\
XVLQJSKDVHWUDQVIRUPHU
3RVVLELOLW\ RI XVLQJ VLQJOH '& VRXUFH E\ XVLQJ LVRODWHG
WUDQVIRUPHU
/LWWOHWUDQVLWLRQORVVRIVZLWFKIRUORZIUHTXHQF\VXLWDEOH
IRUJUHDWFDSDFLW\
/LWWOH (0, ZKHQ JHQHUDWLQJ KLJK YROWDJH IRU SLOLQJ
YROWDJHPHWKRG
5HPRYLQJWKHKLJKHUKDUPRQLFFRPSRVLWLRQE\XVLQJWKH
OLEHUDOL]DWLRQ UHOD\ DQJOH FRQWURO LQ HDFK DUHD RQ EDVH RI
1HZWRQ5DSVRQPHWKRG
$QG LQ WKH SURSRVHG WUDQVIRUPHU LVRODWHG PXOWLOHYHO
LQYHUWHU XVLQJ VLJQDO '& VRXUFH WKH IUHTXHQF\ RI RXWSXW
YROWDJHLVVDPHDVWKHVZLWFKLQJIUHTXHQF\VRLWLVLPSRVVLEOH
WRDSSO\LQWKHH[LVWLQJVZLWFKLQJPHWKRG
95
()(5(1&(6
3HULRGLFDOV
>@ 7ROEHUW /0 )DQJ =KHQJ 3HQJ DQG +DEHWOHU 7* ³0XOWLOHYHO
FRQYHUWHUV IRU ODUJH HOHFWULF GULYHV´ ,QGXVWU\ $SSOLFDWLRQV ,(((
7UDQVDFWLRQV9ROSS
>@ )X6DQ6K\XDQG<HQ6KLQ/DL³9LUWXDO6WDJH3XOVH:LGWK0RGXODWLRQ
7HFKQLTXH IRU 0XOWLOHYHO ,QYHUWHU&RQYHUWHU´ 3RZHU (OHFWURQLFV ,(((
7UDQVDFWLRQV9ROSS
>@ )X6DQ 6K\X <HQ6KLQ /DL 9LUWXDO 6WDJH 3XOVH:LGWK 0RGXODWLRQ
7HFKQLTXH IRU 0XOWLOHYHO ,QYHUWHU&RQYHUWHU ,((( 7UDQV 9RO 1R
0D\
>@ 6-3DUN6*6RQJ<XWDR6+/HH6(&KR&-0RRQ&8.LP³1RYHO
0XOWL/HYHO 3:0 ,QYHUWHU 8VLQJ 7KH &RPPRQ $UP´ $SULO
9ROXPH1XPEHUSS.,((
%RRNV
>@ 1 0RKDQ 7 0 8QGHODQG DQG : 3 5REELQV 3RZHU (OHFWURQLFV
FRQYHUWHUVDSSOLFDWLRQVDQGGHVLJQ-RKQ:LOH\ 6RQV,QF
>@ % . %RVH 3RZHU (OHFWURQLFV DQG 9DULDEOH )UHTXHQF\ 'ULYHV
7HFKQRORJ\DQG$SSOLFDWLRQV,(((3UHVV
>@ 7LPRWK\O 6 ³7+( 32:(5 (/(&7521,&6 +$1'%22. ,QGXVWULDO
(OHFWURQLFV6HULHV&KDS
3DSHUVIURP&RQIHUHQFH3URFHHGLQJV3XEOLVKHG
>@ .$ &RU]LQH 0: :LHOHEVNL )= 3HQJ DQG - :DQJ ³&RQWURO RI
&DVFDGHG 0XOWL/HYHO ,QYHUWHUV (OHFWULF 0DFKLQHV DQG 'ULYHV
&RQIHUHQFH9ROSS
9,%
,2*5$3+,(6
6RQJ6XQJ*HXQ
ZDVERUQLQ*ZDQJ-X.RUHD+H
UHFHLYHG WKH %6 DQG 06 GHJUHHV LQ HOHFWULFDO
HQJLQHHULQJ IURP &KRQQDP 1DWLRQDO 8QLYHUVLW\ LQ
DQGUHVSHFWLYHO\)URPWRKH
ZDVD5HVHDUFK 6FLHQWLVWDW 352&20 V\VWHP /WG
)URP WR KH ZDV D 5HVHDUFK 6FLHQWLVW DW
6(2 (/(&7521,&6 &2 /7' &XUUHQWO\ KH LV
ZRUNLQJ WRZDUG WKH 3K' GHJUHH LQ HOHFWULFDO
HQJLQHHULQJDW&KRQQDP1DWLRQDO8QLYHUVLW\
+LVILHOGVRILQWHUHVWDUHSRZHUHOHFWURQLFVPRWRU
GQYHVGLJLWDOVLJQDOSURFHVVLQJWUDFWLRQVDQGWKHOUFRQWUROV\VWHP
<X 7DR
ZDVERUQ LQ/LQWDR&KLQD+HUHFHLYHGWKH
%6GHJUHHIURP4LQJGDR8QLYHUVLW\4LQJGDR&KLQD
LQ DQG 06 GHJUHH IURP 0RNSR 1DWLRQDO
8QLYHUVLW\0RNSR.RUHDLQ+HLVFXUUHQWO\LQ
FRXUVH RI 3K' LQ &KRQQDP 1DWLRQDO 8QLYHUVLW\
*ZDQJMX.RUHD
)URP WR KH ZDV D WHDFKHU RI 4LQJGDR
+XD;LD +LJK 6FKRRO 4LQJGDR &KLQD +LV UHVHDUFK
LQWHUHVWV LQFOXGH UHQHZDEOH HQHUJ\ V\VWHP PXOWLOHYHO
LQYHUWHUDQGPRWRUGULYHV
0U<XLVDPHPEHURIWKH.RUHDQ,QVWLWXWHRI3RZHU
(OHFWURQLFV.,3(
6XQJ-XQ 3DUN
UHFHLYHG WKH %6 06 DQG 3K'
GHJUHHV LQ HOHFWULFDO HQJLQHHULQJ DQG WKH 3K'
GHJUHH LQ PHFKDQLFDO HQJLQHHULQJ IURP 3XVDQ
1DWLRQDO 8QLYHUVLW\ %XVDQ .RUHD LQ
DQGUHVSHFWLYHO\
)URP WR KH ZDV DQ $VVLVWDQW 3URIHVVRU
ZLWKWKH'HSDUWPHQWRI(OHFWULFDO(QJLQHHULQJ.RMH
&ROOHJH.RMH.RUHD)URPWRKHZDVDQ
$VVLVWDQW3URIHVVRUZLWKWKH'HSDUWPHQWRI(OHFWULFDO
(QJLQHHULQJ 7RQJ0\RQJ &ROOHJH %XVDQ 6LQFH
KH KDV EHHQ DQ $VVLVWDQW 3URIHVVRU ZLWK WKH
'HSDUWPHQW RI (OHFWULFDO (QJLQHHULQJ &KRQQDP 1DWLRQDO 8QLYHUVLW\
*ZDQJMX .RUHD +LV UHVHDUFK LQWHUHVWV LQFOXGH SRZHU HOHFWURQLFV PRWRU
FRQWUROPHFKDWURQLFVPLFURPDFKLQHDXWRPDWLRQDQGURERWLFV
'U3DUNLVDPHPEHURIWKH.RUHDQ,QVWLWXWHRI(OHFWULFDO(QJLQHHUV.,((
DQGWKH.RUHDQ,QVWLWXWHRI3RZHU(OHFWURQLFV.,3(
/LP -RXQJ0LQ
UHFHLYHG WKH %6 06 GHJUHHV LQ
(OHFWULFDO (QJLQHHULQJ IURP 0RNSR 1DWLRQDO
8QLYHUVLW\ 0RNSR .RUHD LQ
UHVSHFWLYHO\ +H LV FXUUHQWO\ LQ FRXUVH RI 3K' LQ
0RNSR1DWLRQDO8QLYHUVLW\0RNSR.RUHD
&KHDQJ(XL+HDQJ
UHFHLYHGWKH%6GHJUHHVLQ
(OHFWULFDO(QJLQHHULQJIURP0RNSR1DWLRQDO
8QLYHUVLW\0RNSR.RUHDLQ+HLVFXUUHQWO\
LQFRXUVHRI06LQ0RNSR1DWLRQDO8QLYHUVLW\
0RNSR
.ZHQ6XQJ -XQJ
UHFHLYHG WKH %6 GHJUHHV LQ
(OHFWULFDO (QJLQHHULQJ IURP 0RNSR 1DWLRQDO
8QLYHUVLW\0RNSR.RUHDLQ+HLVFXUUHQWO\
LQ FRXUVH RI 06 LQ 0RNSR 1DWLRQDO 8QLYHUVLW\
0RNSR.RUHD
0RRQ &KDH-RR
UHFHLYHGWKH%606DQG3K'
GHJUHHV LQ ,QVWUXPHQWDWLRQ DQG &RQWURO IRUP
&KRQQDP QDWLRQDO 8QLYHUVLW\ .ZDQJMX .RUHDLQ
DQGUHVSHFWLYHO\+HZRUNHGIRU
WKH .RUHD3RZHU(QJLQHHULQJ&RDVD 5HVHDUFKHU
IRUPWR+HLV FXUUHQWO\DQG $VVRFLDWH
3URIHVVRU RI WKH 'HSDUWPHQW RI HOHFWULFDO
(QJLQHHULQJ 0RNSR 1DWLRQDO 8QLYHUVLW\ .RUHD
+HLVDOVRDGLUHFWRURIWKHUHVHDUFK&HQWHUIRU1HZ
5HQHZDEOH (QHUJ\ 7HFKQRORJ\ +LV PDLQ
UHVHDUFK LQWHUHVWV LQFOXGH SRZHU SODQW GHVLJQ DQG
DQDO\VLVXVLQJPRGHOLQJDQGVLPXODWLRQWRROV
1042
The 8
th
International Power Engineering Conference (IPEC 2007)