Operation and Control of HVDC links embedded in AC systems

7+(6,6)257+('(*5((2)/,&(17,$7(2)(1*,1((5,1*

2SHUDWLRQDQG&RQWURORI+9'&OLQNVHPEHGGHGLQ$&V\VWHPV

E\

-(11<3$8/,1'(5

'HSDUWPHQWRI(OHFWULF3RZHU(QJLQHHULQJ&KDOPHUV8QLYHUVLW\RI7HFKQRORJ\

*|WHERUJ6ZHGHQ

2SHUDWLRQDQGFRQWURORI+9'&OLQNVHPEHGGHGLQ$&V\VWHPV-(11<3$8/,1'(5-(11<3$8/,1'(57HFKQLFDOUHSRUW1R/6FKRRORI(OHFWULFDO(QJLQHHULQJ&KDOPHUV8QLYHUVLW\RI7HFKQRORJ\/,6617HOHSKRQH ±)D[ ±(PDLO MHQQ\SDXOLQGHU#HOWHNQLNFKDOPHUVVH:HE ZZZHOWHNQLNFKDOPHUVVH&KDOPHUV%LEOLRWHN5HSURVHUYLFH*|WHERUJ6ZHGHQ

$EVWUDFW7KLVWKHVLVLQYHVWLJDWHVKRZGFWUDQVPLVVLRQDIIHFWVVWDELOLW\DQGYROWDJHFRQWURORIDQDFWUDQVPLVVLRQQHWZRUN6LPXODWLRQVDUHPDGHERWKLQDEXVV\VWHPEDVHGRQWKHZHOONQRZQ&LJUp1RUGLFV\VWHPDQGLQDVPDOOEXVV\VWHP(PSKDVLVLVJLYHQWRWKHXQGHUVWDQGLQJRIGLIIHUHQWFRQWURORSWLRQVIRUKYGFWUDQVPLVVLRQDQGKRZLWLVXWLOLVHG$QXPEHURIVFHQDULRVDQDO\VHGE\6YHQVND.UDIWQlWZKLFKDUHVHULRXVWRWKH6ZHGLVKWUDQVPLVVLRQV\VWHPVWDELOLW\DUHLQYHVWLJDWHG7KHVHWHVWFDVHVLQYROYHVORVVRIJHQHUDWLRQDQGWUDQVPLVVLRQFDSDFLW\DQGORDGLQFUHDVHDVZHOODVGHFUHDVH6HYHUDOFRQWUROVWUDWHJLHVKDYHEHHQWHVWHGIRUWKHKYGFOLQNV$PRQJWKHP

DUHIRUH[DPSOHFRQVWDQWSRZHUFRQWURODQGWKHXVHRIDSRZHUIORZFRQWUROOHUZLWKGHYLDWLRQLQIUHTXHQF\RUWUDQVIHUUHGDFWLYHSRZHUDVLQSXWVLJQDOV,QWKHVPDOOWHVWV\VWHPWKHLQIOXHQFHRIWKHORDGYROWDJHGHSHQGHQF\KDVDOVREHHQLQYHVWLJDWHG,WFDQEHFRQFOXGHGWKDWWKHLQIOXHQFHRIDQKYGFOLQNRQWKHVWDELOLW\RIDSRZHUV\VWHPGXULQJGLVWXUEHGFRQGLWLRQVLVVLJQLILFDQWHYHQLIWKHKYGFSDUWLVDPLQRUSDUWRIWKHDFV\VWHP,WLVDOVRREYLRXVWKDWWKHFRQWURORIWKHKYGFOLQNLVFUXFLDOWRWKHEHKDYLRXURIWKHHQWLUHQHWZRUN,QWKLVWKHVLVZHKDYHVHHQWKDWDQKYGFOLQNLQWKHULJKWORFDWLRQDQGZLWKD

SURSHUUHJXODWLRQPD\SUHYHQWDV\VWHPFROODSVHWKDWRWKHUZLVHZRXOGRFFXU7KLVRSHQVWKHSRVVLELOLW\WRLPSURYHWKHEHKDYLRXURIWKHSRZHUV\VWHPWKHDYRLGDQFHRIGLVWXUEDQFHVDQGSRVVLEO\WKHWUDQVIHUFDSDFLW\ZKLFKPD\EHPRVWLQWHUHVWLQJXQGHUVWUDLQHGFRQGLWLRQV,WLVVKRZQWKDWWKHORDGYROWDJHGHSHQGHQF\PD\KDYHDVLJQLILFDQW

LQIOXHQFHRQV\VWHPSHUIRUPDQFH,WLVVKRZQWKDWWKHYROWDJHGHSHQGHQF\LQIOXHQFHVERWKWKHDPSOLWXGHRIWKHYROWDJHVZLQJVIROORZLQJDGLVWXUEDQFHDQGWKHPD[LPXPWUDQVIHUDEOHSRZHURYHUDQKYGFOLQHGXULQJDGLVWXUEDQFH7KLVLQGLFDWHVWKDWLQVRPHVLWXDWLRQVZLWKKLJKORDGVDQGDSRZHUGHILFLWLWLVHVVHQWLDOWRKDYHNQRZOHGJHDERXWWKHORDGYROWDJHGHSHQGHQF\LQRUGHUWREHDEOHWRXWLOLVHWKHSRZHUV\VWHPHIILFLHQWO\.H\ZRUGV+YGFDFGFLQWHUDFWLRQORDGYROWDJHGHSHQGHQF\FRQWURORIKYGFFRQYHUWHUVYROWDJHLQVWDELOLW\V\VWHPRYHUORDG

$FNQRZOHGJHPHQWV,ZRXOGOLNHWRVWDUWZLWKH[SUHVVLQJP\JUDWLWXGHWRP\VXSHUYLVRUDQGH[DPLQHU3URIHVVRU-DDS'DDOGHUZLWKRXWZKRP,QHYHUZRXOGKDYHEHJXQP\3K'VWXGLHVDQGFHUWDLQO\QHYHUZRXOGKDYHDFFRPSOLVKHGWKLVWKHVLV,ZRXOGDOVROLNHWRVHQGP\WKDQNVWR3URIHVVRU0DWK%ROOHQDQG$VVLVWDQW3URIHVVRU$PEUD6DQQLQRIRUWKHLUHQFRXUDJHPHQWLGHDVDQGVXSSRUW0\VWHHULQJFRPPLWWHHFRQVLVWLQJRI*XQQDU$VSOXQGDQG3HKU+MDOPDUVVRQ$%%3RZHU7HFKQRORJLHV$%%HUQW+DQVVRQ9DWWHQIDOO9lVWQlW$%DQG8UEDQ$[HOVVRQ9DWWHQIDOO$%KDVDOVREHHQRIJUHDWKHOSWRPHDQG,WKDQN\RXIRU\RXULQWHUHVWLQP\SURMHFW3HKU+MDOPDUVVRQDQGKLVVWDIIDWWKH$%%RIILFHLQ&KDOPHUV7HNQLNSDUNKDVDOVREHHQRIJUHDWKHOSLQILQGLQJHUURUVLQWKH6LPSRZLQSXWILOHVDQGLQWHUSUHWLQJWKHVLPXODWLRQUHVXOWV7KLVSURMHFWKDVEHHQILQDQFHGE\(OIRUVNDVDQ(/(&75$SURMHFW7KLVVXSSRUWLVJUDWHIXOO\DFNQRZOHGJHG7KHVWDIIDWWKH3RZHU6\VWHP$QDO\VLV'HSDUWPHQWDW$%%KDVEHHQLQYDOXDEOHLQKHOSLQJPHWRVROYHGLIILFXOWLHVZLWKVRIWZDUHDQGVLPXODWLRQV,HVSHFLDOO\ZRXOGOLNHWRPHQWLRQ$QQ3DOHVM|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

&RQWHQWV$EVWUDFW$FNQRZOHGJHPHQWV&RQWHQWV&KDSWHU ,QWURGXFWLRQ

$EULHIKLVWRU\RIKYGF %DFNJURXQGRIWKHSURMHFW 2EMHFWLYHV 2XWOLQHRIWKHWKHVLV

&KDSWHU +9'&V\VWHPVRYHUYLHZ $GYDQWDJHVRIKYGFWUDQVPLVVLRQ

/RVVHVDQGFRVWV 5HDFWLYHSRZHUFRPSHQVDWLRQ 6WDELOLW\DQGFRQWURO (QYLURQPHQWDODVSHFWV

'UDZEDFNVDQGGLIILFXOWLHV +DUPRQLFV 5HDFWLYHSRZHUFRQVXPSWLRQ )DXOWFOHDULQJ

%DVLFSRZHUFRQYHUVLRQ )LULQJGHOD\DQGFRPPXWDWLRQ ,QYHUWHURSHUDWLRQ &RPPXWDWLRQIDLOXUH

&RQILJXUDWLRQVDQGFRPSRQHQWV %DVLFKYGFFRQILJXUDWLRQV 0DLQFRPSRQHQWVRIDKYGFV\VWHP 0XOWLWHUPLQDOKYGF

SXOVHFRQYHUWHUV +YGFZLWKYROWDJHVRXUFHFRQYHUWHUV 6WDELOLW\LPSURYHPHQWZLWKKYGF +YGFVFKHPHV±DVHOHFWLRQ

&KDQGUDSXU±3DGJKH,QGLD 3DFLILF,QWHUWLH86$ /H\WH±/X]RQ3KLOLSSLQHV

+YGFGHYHORSPHQW &DSDFLWRUFRPPXWDWHGFRQYHUWHU )LOWHUV

&KDSWHU &RQWURORIKYGFFRQYHUWHUV %DVLFSULQFLSOHV

2SHUDWLRQUHTXLUHPHQWV &RQWUROPRGHV &RQWUROFKDUDFWHULVWLFV $OWHUQDWLYHLQYHUWHUFRQWUROPRGHV $GGLWLRQDOFRQWURODVSHFWV 'DPSLQJFRQWURO

7KHFXUUHQWRUGHU &RQWUROFRRUGLQDWLRQ

6WDWLRQSROHDQGFRQYHUWHUFRQWURO %ORFNLQJDQGGHEORFNLQJ

9DOYHEORFNLQJ %ORFNLQJVHTXHQFH 'HEORFNLQJVHTXHQFH

0XOWLWHUPLQDOV\VWHPV 3DUDOOHOPXOWLWHUPLQDOV\VWHPV 6HULHVPXOWLWHUPLQDOV\VWHP

&KDSWHU 0RGHOOLQJDQGVRIWZDUH 6LPSRZLQJHQHUDO

3RZHUIORZDQDO\VLV '\QDPLFVLPXODWLRQ

$&V\VWHPPRGHO 7UDQVPLVVLRQV\VWHPHOHPHQWV /RDGV 6\QFKURQRXVPDFKLQHV 7UDQVIRUPHUV

+9'&V\VWHPPRGHO 0DLQFRPSRQHQWV &RQWURO6\VWHP

9DOLGLW\RIWKHPRGHOV *HQHUDO +9'&V\VWHPPRGHO

&KDSWHU 7KHWHVWQHWZRUN

7KHVPDOOV\VWHP %DVLFV 7HVWFDVHVDQGUHJXODWLRQ

7KHODUJHV\VWHP 2ULJLQ *HQHUDORXWOLQHRIWKHQHWZRUN

0RGLILFDWLRQV /RDGGLVWULEXWLRQ /RDGPRGHO '\QDPLFPRGHOV 1HWZRUNFKDUDFWHULVWLFV 7HVWFDVHV

&KDSWHU 6LPXODWLRQVDQGUHVXOWV 7KHILUVWKYGFPRGHO±VWDJH

&DVH &DVH &DVH &DVH &DVH &RPPHQWVWRVWDJHVLPXODWLRQV

7KHVPDOOV\VWHP±VWDJH :LWKRXWSRZHUIUHTXHQF\FRQWUROOHU :LWKSRZHUIUHTXHQF\FRQWUROOHU ,QIOXHQFHRIWKHYROWDJHGHSHQGHQF\RIWKHORDG &RPPHQWVWRVWDJHVLPXODWLRQV

7KHODUJHSRZHUV\VWHP±VWDJH 7HVWFDVHDQDO\VLV 6LPXODWLRQV±&DVHB 6LPXODWLRQV±&DVHB 6LPXODWLRQV±&DVHB &RPPHQWVWRVWDJHVLPXODWLRQV

&KDSWHU &RQFOXVLRQVDQGIXWXUHZRUN &RQFOXVLRQV )XWXUHZRUN

5HIHUHQFHV$EEUHYLDWLRQV 'HQRWDWLRQV$SSHQGL[$±0RGLILFDWLRQVRIWKH1RUGLFQHWZRUN$SSHQGL[%±&RQYHUWHUPRGHOOLQJLQ6LPSRZ$SSHQGL[&±/RDGGLVWULEXWLRQRIWKHPRGLILHG1RUGLFQHWZRUN

&KDSWHU,QWURGXFWLRQ

&KDSWHU ,QWURGXFWLRQ $EULHIKLVWRU\RIKYGF,WLVZHOONQRZQWKDWWKHILUVWHOHFWULFLW\FRPPHUFLDOO\JHQHUDWHGE\7KRPDV$OYD(GLVRQZDVGFSRZHU7KHILUVWWUDQVPLVVLRQV\VWHPVIRUHOHFWULFDOSRZHUZHUHDOVRGFV\VWHPV7KHSUREOHPZDVWKDWORZYROWDJHGFSRZHUFRXOGQRWEHWUDQVPLWWHGRYHUORQJHUGLVWDQFHVDQGWKHUHIRUHWKHVXFFHVVIRUDFV\VWHPVZDVLQHYLWDEOH+RZHYHUZKHQWKHKLJKYROWDJHYDOYHZDVGHYHORSHGLWEHFDPHSRVVLEOHWRWUDQVIHUGFSRZHURYHUORQJGLVWDQFHVDQGKLJKYROWDJHGLUHFWFXUUHQWKYGFZDVERUQ7KHILUVWKYGFYDOYHZDV+HZLWW¶VPHUFXU\YDSRXUYDOYHSUHVHQWHGLQ

EXWWKHILUVWFRPPHUFLDOKYGFWUDQVPLVVLRQZDVQRWUHDOLW\XQWLOLQZKHQWKH0:N9OLQNEHWZHHQWKH6ZHGHQPDLQODQGDQGWKHLVODQGRI*RWODQGZDVFRPPLVVLRQHG>@7KHILUVWODUJHKYGFWUDQVPLVVLRQV\VWHPWKDWZDVGHVLJQHGIRUWK\ULVWRUWHFKQRORJ\ZDVEXLOWLQ&DQDGDLQ,WLVDEDFNWREDFNDV\QFKURQRXVLQWHUFRQQHFWLRQZLWKDUDWLQJRI0:DW±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

ILHOGRIORDGDQGJHQHUDWLRQFKDUDFWHULVWLFV&RQYHUWHUYDOYHWHFKQRORJ\KDVGHYHORSHGIURPWKHPHUFXU\DUFYDOYHVYLDWK\ULVWRUVWRKLJKIUHTXHQF\VZLWFKHG,*%7VDQG*72VZLWKDFRQVWDQWO\LQFUHDVLQJSRZHUUDWLQJ7KHPDLQDGYDQWDJHZLWKWKHVHQHZYDOYHVLVWKHSRVVLELOLW\WRFRQWUROQRWRQO\WKH

&KDSWHU,QWURGXFWLRQ

ILULQJLQVWDQWEXWDOVRWKHWXUQRIILQVWDQW7KDQNVWRWKHGHYHORSPHQWRIWKHVHYDOYHVWKHYROWDJHVRXUFHFRQYHUWHUWHFKQRORJ\EHFDPHLQWHUHVWLQJIRUPHGLXPDQGKLJKSRZHUDSSOLFDWLRQV$OVRWKHGFFDEOHWHFKQRORJ\KDVPDGHSURJUHVVWKHODVWIHZ\HDUVDQGKDVPDGHDKLJKSRZHUGHQVLW\LQWKHFDEOHSRVVLEOH5HJDUGLQJORDGVDQLQFUHDVLQJSDUWRIDOOHQGXVLQJHTXLSPHQWFRQYHUWVDF

YROWDJHWRGFEHIRUHLWLVXVHG7KLVLVGXHWRWKDWHOHFWURQLFGHYLFHVVXFKDVFRPSXWHUVDQGFRQVXPHUHOHFWURQLFVWRDODUJHH[WHQWFRQVWLWXWHVWKHLQFUHDVHLQHOHFWULFLW\FRQVXPSWLRQLQWKHLQGXVWULDOFRXQWULHV$JURZLQJSDUWRIPHGLXPDQGODUJHLQGXFWLRQPDFKLQHVLVXVLQJDFGFDFFRQYHUVLRQWREHDEOHWRRSHUDWHWKHPDFKLQHZLWKYDU\LQJVSHHGDQGWKHUHE\DKLJKHIILFLHQF\,IWKHVHORDGVZHUHFRQQHFWHGWRDGFJULGWKHODVWFRQYHUVLRQVWHSFRXOGEHRPLWWHG2XUHQYLURQPHQWFDOOVIRUDVKLIWIURPIRVVLOIXHOWRUHQHZDEOHHQHUJ\

VRXUFHVIRUH[DPSOHK\GURZLQGRUVRODUSRZHU/DUJHVFDOHUHQHZDEOHVUHTXLUHSRZHUWUDQVPLVVLRQRYHUORQJGLVWDQFHV7KLV

LVQRWIHDVLEOHZLWKDFDQGGFKDVVKRZQWREHWKHEHWWHUDOWHUQDWLYH6PDOOVFDOHUHQHZDEOHVDUHE\WKHLUQDWXUHRIOLPLWHGVL]H7KH\ZLOOSURYLGH

HOHFWULFSRZHUIRUDVLQJOHKRXVHDVPDOOLQGXVWU\RUDQXUEDQTXDUWHURUDYLOODJH$VDUHVXOWRQHPD\H[SHFWDQLQFUHDVHLQGLVSHUVHGJHQHUDWLRQZKHUHERWKODUJHVFDOHSURGXFWLRQDQGPDQ\VPDOOVL]HGJHQHUDWLQJXQLWVDUHFRQQHFWHGWRWKHQHWZRUNDWGLIIHUHQWYROWDJHOHYHOV,QDGGLWLRQUHQHZDEOHVPRVWO\DUHVRXUFHVZLWKDYDU\LQJRXWSXW,WLVOLNHO\WKDWQHWZRUNWRSRORJLHVZLOOFKDQJHLQRUGHUWRFRSHZLWKDPXFKZLGHUVSDQLQORDGYDULDWLRQDQGORDGIORZGLUHFWLRQ7RGD\ZLQGSRZHULVFRQVLGHUHGWREHDVHULRXVFDQGLGDWHIRUJHQHUDWLRQRID

VXEVWDQWLDOSDUWVHYHUDOSHUFHQWDQGPRUHRIWKHHOHFWULFLW\QHHGLQVHYHUDOFRXQWULHV7KHDYHUDJHWXUELQHVL]HKDVLQDIHZ\HDUVLQFUHDVHGIURPN:WRPRUHWKDQ0:'HYHORSPHQWLVIRFXVHGRQWXUELQHVL]HVRIVHYHUDO0:7KHVHODUJHVL]HWXUELQHVXVHFRQYHUWHUVIRUFRQQHFWLRQWRWKHJULGWKHUHE\LPSURYLQJFRQWURORIDYDU\LQJLQSXWDQGUHGXFLQJWKHKDUPRQLFFRQWHQWRIWKHRXWSXW&RQQHFWLRQWRDGFJULGLIDYDLODEOHVKRXOGJLYHFKHDSHUVROXWLRQVSDUWLFXODUO\ZLWKFDEOHFRQQHFWHGRIIVKRUHZLQGIDUPV$OOWKHVHIDFWVWRJHWKHUVXJJHVWVWKDWWKHUHDUHLQFHQWLYHVWRFRQVLGHUV\VWHP

VROXWLRQVZKLFKDWOHDVWLQDWUDQVLWLRQSHULRGDUHEDVHGRQYDULRXVPL[WXUHVRIDFDQGGFJHQHUDWLRQWUDQVPLVVLRQDQGGLVWULEXWLRQV\VWHPV$QRWKHUUHDVRQIRULQYHVWLQJUHVRXUFHVLQWKLVILHOGLVJLYHQLQ(35,V

³'HVWLQDWLRQV´WKHSODQVIRUXSFRPLQJUHVHDUFKSURJUDPVZKHUHLWLVZULWWHQ³0DQ\WUDQVPLVVLRQFRPSDQLHVDUHUHYLVLWLQJWKHUROHRI+9'&DVDSRWHQWLDOWRROIRUQHWZRUNH[SDQVLRQ«)XUWKHUPRUHWKHUHLVDJURZLQJODFNRI+9'&H[SHUWLVHLQPDQ\WUDQVPLVVLRQRZQHURUJDQLVDWLRQV´>@,QRWKHUZRUGVLWLVLPSRUWDQWWRFRQWLQXHWRLQFUHDVHRXUNQRZOHGJHLQWKHILHOGRIRSHUDWLQJRIKYGFERWKLQQRUPDORSHUDWLRQDQGLQGLVWXUEHGVLWXDWLRQV

&KDSWHU,QWURGXFWLRQ

2EMHFWLYHV2QHFDQQRWH[SHFWWKDWUDGLFDOFKDQJHVZLOOKDSSHQRQDVKRUWWLPHVFDOHLQWKHSUHVHQWZD\RIJHQHUDWLQJWUDQVPLWWLQJDQGGLVWULEXWLQJHOHFWULFDOHQHUJ\/DUJHLQYHVWPHQWVORQJGHSUHFLDWLRQWLPHVDQGDORZLQFUHDVHRIHOHFWULFDOFRQVXPSWLRQDUHVRPHUHDVRQVDWOHDVWLQWKHLQGXVWULDOLVHGFRXQWULHV2QWKHRWKHUKDQGPRGHUQVRFLHW\LVKLJKO\GHSHQGHQWRQDZHOOIXQFWLRQLQJ

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

WUDQVPLVVLRQV\VWHPVDQLQFUHDVLQJSDUWRIWKHHOHFWULFSRZHUZLOOEHWUDQVPLWWHGE\KYGFOLQHV

$LPV±ORQJWHUP− ,QVLJKWLQWKHPRVWDSSURSULDWHFRPELQDWLRQVRIDFDQGGFIRUGLIIHUHQW

DSSOLFDWLRQVDQGGLIIHUHQWYROWDJHOHYHOV− .QRZOHGJHRIWHFKQLTXHVIRUGHVLJQRSHUDWLRQDQGFRQWURORIGFQHWZRUNV

DWGLIIHUHQWYROWDJHOHYHOV$LPV±VKRUWWHUP− ,QYHVWLJDWHKRZGFWUDQVPLVVLRQDIIHFWVVWDELOLW\DQGYROWDJHFRQWURORIWKH

DFWUDQVPLVVLRQQHWZRUN− .QRZOHGJHRIGLIIHUHQWFRQWURORSWLRQVIRUKYGFWUDQVPLVVLRQDQGKRZLWLV

XWLOLVHG 2XWOLQHRIWKHWKHVLV,QWURGXFWLRQ±FKDSWHU7KHLQWURGXFWLRQFKDSWHUJLYHVWKHEDFNJURXQGWKDWPRWLYDWHGWKHLQLWLDWLRQRIWKLVSURMHFWLWVWDWHVWKHREMHFWLYHVIRUWKLVWKHVLVDQGDOVRSURYLGHVDEULHIKLVWRU\RIKYGFWHFKQRORJ\

&KDSWHU,QWURGXFWLRQ

+YGFV\VWHPVRYHUYLHZ±FKDSWHU,QFKDSWHUDGHVFULSWLRQRIWKHEDVLFWKHRULHVIRUKYGFWUDQVPLVVLRQDQGSRZHUFRQYHUVLRQZLWKWK\ULVWRUFRQYHUWHUVDUHJLYHQ7KHPRVWFRPPRQO\XVHGFRQILJXUDWLRQVDQGFRPSRQHQWVDUHGHVFULEHGDQGWKHPDLQDGYDQWDJHVDQGGUDZEDFNVDUHSUHVHQWHG)LQDOO\VRPHVHOHFWHGKYGFVFKHPHVDUHPHQWLRQHGDQGDEULHIRYHUYLHZRIVWDWHRIWKHDUWWHFKQRORJ\LQWKLVDUHDLVJLYHQ&RQWURORIKYGFFRQYHUWHUV±FKDSWHU7KLVFKDSWHUGHDOVZLWKWKHFRQWUROV\VWHPRIKYGFFRQYHUWHUV7KHEDVLFSULQFLSOHVDUHGHVFULEHGDQGWKHGLIIHUHQWFRQWURORSWLRQVDYDLODEOHDUHGLVFXVVHG0XOWLWHUPLQDOVFKHPHVDQGFRQWUROFRRUGLQDWLRQLVDOVRPHQWLRQHG0RGHOOLQJDQGVRIWZDUH±FKDSWHU&KDSWHUGHVFULEHVWKHVRIWZDUHXVHGIRUWKHVLPXODWLRQVDQGWKHPRGHOVLPSOHPHQWHGLQWKLVVRIWZDUH7KHVLPXODWLRQSURJUDPXVHGLV6LPSRZDSRZHUV\VWHPVLPXODWLRQSURJUDPGHYHORSHGE\$%%7KHUHDVRQVIRUFKRRVLQJWKLVVRIWZDUHDQGWKHYDOLGLW\RIWKHPRGHOVXVHGDUHPHQWLRQHG7KHWHVWQHWZRUN±FKDSWHU,QWKLVFKDSWHUWKHWHVWQHWZRUNVXVHGLQWKHVLPXODWLRQVDUHGHVFULEHG%RWKDODUJHSRZHUV\VWHPPRGHOEDVHGRQWKH&LJUp1RUGLFQHWZRUNDQGDVPDOOEXVQHWZRUNLVXVHG7KHWHVWFDVHVXVHGDUHGLIIHUHQWVFHQDULRVWKDWPD\OHDGWRDV\VWHPFROODSVH6LPXODWLRQVDQGUHVXOWV±FKDSWHU,QFKDSWHUWKHSHUIRUPHGVLPXODWLRQVDQGWKHLUUHVXOWVDUHSUHVHQWHGDQGGLVFXVVHG7KHVLPXODWLRQVKDYHEHHQGRQHLQWKUHHVWDJHVXVLQJGLIIHUHQWREMHFWLYHV7KHODUJHWHVWV\VWHPLVXVHGLQVWDJHDQGDQGWKHVPDOOV\VWHPLQVWDJH&RQFOXVLRQVDQGIXWXUHZRUN±FKDSWHU&KDSWHUVXPVXSWKHPDLQFRQFOXVLRQVIURPWKHVLPXODWLRQVDQGJLYHVVRPHVXJJHVWLRQVIRUWKHFRQWLQXLQJZRUN0RGLILFDWLRQVRIWKH1RUGLFQHWZRUN±$SSHQGL[$,QWKLVDSSHQGL[GHWDLOVDUHJLYHQDERXWWKHPRGLILFDWLRQVPDGHLQWKH&LJUp1RUGLFQHWZRUN&RQYHUWHUPRGHOOLQJLQ6LPSRZ±$SSHQGL[%$SSHQGL[%JLYHVDGHWDLOHGGHVFULSWLRQRIWKHPRGHORIWKHFRQYHUWHUVDQGLWVFRQWUROV\VWHPLQ6LPSRZ

&KDSWHU+9'&V\VWHPVRYHUYLHZ

&KDSWHU +9'&V\VWHPVRYHUYLHZ,QWKLVFKDSWHUDJHQHUDOGHVFULSWLRQRIKYGFV\VWHPVDQGSRZHUFRQYHUVLRQZLOOEHJLYHQ7KHEDVLFSULQFLSOHVDQGFRQILJXUDWLRQVZLOOEHGLVFXVVHGDQGDQRYHUYLHZRIH[LVWLQJKYGFWUDQVPLVVLRQVZLOOEHJLYHQ $GYDQWDJHVRIKYGFWUDQVPLVVLRQ+YGFWUDQVPLVVLRQKDVEHHQLQVXFFHVVIXORSHUDWLRQLQSRZHUV\VWHPVDOORYHUWKHZRUOGIRUDERXW\HDUV7KHUHDUHVRPHZHOONQRZQDQGDFFHSWHGIDFWVWKDWMXVWLI\WKHFRQWLQXDWLRQRIKYGFGHYHORSPHQW,QWKHIROORZLQJDFRPSDULVRQLVPDGHEHWZHHQDFDQGGFWUDQVPLVVLRQ$FRPPRQZD\WRFRPSDUHWKHVHWZRWHFKQRORJLHVLVDWZRSROHGFOLQNYHUVXVDGRXEOHWKUHHSKDVHDFLQWHUFRQQHFWLRQZLWKWKHVDPH0:UDWLQJ7KHVHWZRDOWHUQDWLYHVDUHFRQVLGHUHGWRKDYHDVLPLODUUHOLDELOLW\ /RVVHVDQGFRVWV&RPSDUHGWRDQHTXLYDOHQWDFOLQHDGFWUDQVPLVVLRQFDXVHVORZHUWUDQVPLVVLRQORVVHVDQGDOVRORZHULQYHVWPHQWFRVWV%RWKWKHORVVHVDQGWKHUHTXLUHGFDSLWDOIRUWKHWHUPLQDOVDUHRQWKHRWKHUKDQGKLJKHUIRUDGFV\VWHP7KH´EUHDNHYHQ´GLVWDQFHWKDWLVWKHOHQJWKRIWKHWUDQVPLVVLRQOLQHDWZKLFKWKHWRWDOFRVWVDUHWKHVDPHIRUERWKDOWHUQDWLYHVLVKRZHYHUGHFUHDVLQJ,IWKHREMHFWLYHIRUWKHSODQQHGLQWHUFRQQHFWLRQLVWRHFRQRPLFDOO\WUDQVPLWODUJHDPRXQWVRISRZHURYHUDORQJGLVWDQFHKYGFLVWKHEHVWDOWHUQDWLYH$PDMRULW\RIWKHZRUOG¶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

7KLVFDQEHGRQHZLWKD³EDFNWREDFN´VWDWLRQZLWKRXWDWUDQVPLVVLRQOLQH


(QYLURQPHQWDODVSHFWV7KHHQYLURQPHQWDOLPSDFWRIDGFWUDQVPLVVLRQOLQHLVFRQVLGHUDEO\ORZHUWKDQIRUDQHTXLYDOHQWDFRQH8VXDOO\WKHHQYLURQPHQWDOLVVXHVDUHGLYLGHGLQWRIRXUPDLQFDWHJRULHVQRLVHHOHFWULFILHOGUDGLRLQWHUIHUHQFHDQGYLVXDOLPSDFW1RLVHLVDVXEMHFWWKDWPD\FDXVHPRUHFRPSODLQWVLQWKHFDVHRIDGFV\VWHPWKDQDQDFV\VWHP7KHPDLQFRQWULEXWRUVWRDXGLEOHQRLVHDUHWKHWUDQVIRUPHUV2WKHUVRXUFHVPD\EHWKHVPRRWKLQJUHDFWRUVILOWHUVDQGFRROLQJWRZHUV7KHQRLVHOHYHOFDQEHUHGXFHGDQGWKHEHVWZD\LVSUREDEO\WRXVHORZQRLVHFRPSRQHQWV%XWWKLVPD\EHPRUHH[SHQVLYHWKDQIRUH[DPSOHWRXVHHQFORVXUHVRUQRLVHGDPSLQJFRYHUVRUZDOOV7KHHOHFWULFILHOGXQGHUDWUDQVPLVVLRQOLQHLVSDUWO\GXHWRWKHSRWHQWLDO

GLIIHUHQFHEHWZHHQWKHFRQGXFWRUDQGHDUWKDQGSDUWO\GXHWRVSDFHFKDUJHVSURGXFHGE\FRURQDGLVFKDUJHV+RZHYHUVLQFHWKHUHLVQRVWHDG\VWDWHGLVSODFHPHQWFXUUHQWLQWKHGFFDVHWKHSUREOHPLVOHVVVHYHUHFRPSDUHGZLWKDF7KLVPHDQVWKDWDGFWUDQVPLVVLRQUHTXLUHVOHVVVSDFHOHVVULJKWRIZD\DQGDOVRORZHUWRZHUVWKDQWKHFRUUHVSRQGLQJDFOLQH,IWKHGFV\VWHPXVHVJURXQGUHWXUQWKHUHZLOOEHSRWHQWLDOGLIIHUHQFHVDORQJWKHHDUWKVXUIDFHDQGWKHDUHDDURXQGWKHHOHFWURGHVPD\KDYHWREHIHQFHGRII7KHKDUPRQLFVFDXVHGE\WKHRSHUDWLRQRIWKHKYGFFRQYHUWHUVDQGWKH

FRPPXWDWLRQSURFHVVJLYHULVHWRGLVWXUEDQFHVLQWKHN+]DQG0+]IUHTXHQF\UHJLRQ7KHVHGLVWXUEDQFHVFDQEHPLWLJDWHGWKURXJKVKLHOGLQJRIWKHYDOYHKDOO7KHUDGLRLQWHUIHUHQFHRIDKYGFOLQHLVKRZHYHUORZHUWKDQWKDWRIDFRPSDUDEOHDFOLQH>@$VPHQWLRQHGDERYHDGFWUDQVPLVVLRQUHTXLUHVOHVVVSDFHWKDQDQDF

WUDQVPLVVLRQSHU0:WREHWUDQVIHUUHG7KLVDOVRPHDQVWKDWWKHYLVXDOLPSDFWZLOOEHOHVV)XUWKHUPRUHZLWKGFWUDQVIHULWLVRIWHQSRVVLEOHWRFKRRVHDFDEOHWUDQVPLVVLRQLQVWHDGRIDQRYHUKHDGOLQHWUDQVPLVVLRQLQZKDWFDVHWKHYLVXDOLPSDFWLVFRQILGHWRWKHFRQYHUWHUVWDWLRQV

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

φWDQ⋅= 34 ZKHUHφLVWKHSKDVHGLIIHUHQFHEHWZHHQWKHIXQGDPHQWDOIUHTXHQF\YROWDJHDQGFXUUHQWFRPSRQHQWVRULQRWKHUZRUGVWKHSRZHUIDFWRURIWKHFRQYHUWHU7KHUHODWLRQVKLSEHWZHHQφDQGWKHILULQJDQJOHαWKDWLVWKHDQJOHEHWZHHQWKHQDWXUDOILULQJLQVWDQWDQGWKHDFWXDOILULQJRIWKHYDOYHFDQEHZULWWHQDV

[ ]FRVFRVFRV X++⋅= ααφ :KHUHXLVWKHFRPPXWDWLRQLQWHUYDODQJOHFRUUHVSRQGLQJWRWKHHIIHFWRIWKHDFVLGHLQGXFWDQFHPRUHDERXWWKHFRPPXWDWLRQSURFHVVLQVHFWLRQ7KHUHDFWLYHSRZHUUHTXLUHGLVSDUWO\GHOLYHUHGE\WKHKDUPRQLFILOWHUV

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


WK\ULVWRUYDOYHLVDVHULHVFRQQHFWLRQRIVHYHUDOWK\ULVWRUHOHPHQWV7KHWK\ULVWRULVFRQWUROODEOHLQWKHVHQVHWKDWLWLVSRVVLEOHWRGHFLGHZKHQWRVWDUWFRQGXFWLQJEXWWKHWXUQRIIDXWRPDWLFDOO\RFFXUVDWWKH]HURFURVVLQJRIWKHFXUUHQW7KHUHDVRQIRUWKHSRSXODULW\RIWKHWK\ULVWRULVWKDWLWFDQFDUU\YHU\KLJKFXUUHQWVVHYHUDONLORDPSHUHVDQGLWLVDOVRDEOHWREORFNKLJKYROWDJHVXSWRDURXQGN9

)LJXUH$ WKUHHSKDVH EULGJH FRQQHFWHG WR D YROWDJH VRXUFH WKURXJK DQ

LQGXFWDQFHWKDWUHSUHVHQWVV\VWHPDQGWUDQVIRUPHULPSHGDQFH7KHEDVLFSULQFLSOHRIUHFWLILFDWLRQLVWKDWWKHYDOYHVFRQGXFWLQSDLUVDQGWKHFRPPXWDWLRQEHWZHHQYDOYHVLHWKHWUDQVIHURIFXUUHQWIURPRQHYDOYHWRDQRWKHULVGHWHUPLQHGE\WKHDFSKDVHYROWDJHVRUWKHFRPPXWDWLQJYROWDJH7KLVLVFDOOHGQDWXUDORUOLQHFRPPXWDWHGFRQYHUWHUV7KHUHVXOWLQJGFYROWDJHKDVDULSSOHRIVL[WLPHVWKHV\VWHPIUHTXHQF\%\

FRQQHFWLQJDODUJHUHDFWRULQVHULHVRQWKHGFVLGHWKHFXUUHQWLVKRZHYHUVPRRWK7KHYROWDJHZDYHIRUPVFDQEHVHHQLQILJXUH,QWKHWRSJUDSKWKHSKDVHYROWDJHVX X DQGX DUHVKRZQDVGRWWHGFXUYHV7KHVROLGFXUYHVVKRZX DQGX WKHSRVLWLYHDQGQHJDWLYHSRWHQWLDOVDWSRLQWVDQGLQILJXUHUHVSHFWLYHO\,WLVDOVRLQGLFDWHGLQILJXUHWRSJUDSKZKLFKYDOYHWKDWLVFXUUHQWO\FRQGXFWLQJ7KHERWWRPJUDSKVKRZVWKHVL[SKDVHWRSKDVHYROWDJHVWRJHWKHUZLWKWKHUHVXOWLQJGFYROWDJHX X X ,IZHORRNDWDFHUWDLQLQVWDQWLQWLPHPDUNHG$LQILJXUHZKHQ

YDOYHVDQGLVFRQGXFWLQJZHKDYHX X DQGX X DQGX ZLOOIROORZWKHSKDVHSKDVHYROWDJHX X X :KHQZHDUULYHWRLQVWDQW%WKHDPSOLWXGHRIX EHFRPHVODUJHUWKDQWKHDPSOLWXGHRIX :LWKUHIHUHQFHWRILJXUHYDOYHZLOOQRZEHIRUZDUGELDVHGLHLWZLOOVWDUWFRQGXFWLQJ:KHQYDOYHVWDUWVFRQGXFWLQJWKHSRWHQWLDOX ZLOOHTXDOX LQVWHDGRIX DQGYDOYHZLOOKDYHDQHJDWLYHYROWDJHVLQFHX X DQGZLOOVWRSFRQGXFWLQJ7KHLQVWDQW%ZLOOEHFDOOHGWKHQDWXUDOILULQJLQVWDQWIRUYDOYH

α; L

X

X

8

8

8


7KHUPVYDOXHRIWKHLGHDOQRORDGYROWDJHWKDWLVWKHPD[LPXPRXWSXWYROWDJHFDQEHFDOFXODWHGE\LQWHJUDWLQJWKHLQVWDQWDQHRXVYDOXHVRYHUDQ\°SHULRG$IWHUVRPHFDOFXODWLRQVZHKDYH>@

888 ==π

ZKHUH8 LVWKHUPVYDOXHRIWKHDFSKDVHWRSKDVHYROWDJH

)LJXUH9ROWDJH ZDYHIRUPV LQ D VL[SXOVH FRQYHUWHU ZLWK QR ILULQJ DQJOH

GHOD\

0 1 2 3 4 5 6 7 8 9-2

-1

0

1

2

ua ub uc

u1

u2

Cathode potential

Anode potential

Valve 3 Valve 5 Valve 1

Valve 2 Valve 4 Valve 6 Valve 2

wt (rad)

U (p

.u)

Voltage waveforms

A B

0 1 2 3 4 5 6 7 8 9-3

-2

-1

0

1

2

3

ud

Phase-phase voltages

wt (rad)

U (p

.u)


)LULQJGHOD\DQGFRPPXWDWLRQ:KHQXVLQJWK\ULVWRUYDOYHVWKHILULQJLQVWDQWRIHDFKYDOYHFDQEHGHOD\HGZLWKUHVSHFWWRWKHQDWXUDOILULQJLQVWDQWWKDWLVZKHUHDGLRGHZRXOGVWDUWFRQGXFWLQJDQGFRQVHTXHQWO\WKHGFYROWDJHFDQEHUHGXFHGWRDGHVLUHGYDOXH$VVXPLQJWKHFRPPXWDWLRQUHDFWDQFH; WKDWLVWKHUHDFWDQFHEHWZHHQWKHFRPPXWDWLQJYROWDJHDQGWKHFRQYHUWHUYDOYHVWREH]HURWKHGFYROWDJHDFKLHYHGFDQEHH[SUHVVHGDV

αFRV 88 = :KHUH8 LVWKHPD[LPXPGFYROWDJHDWQRORDGDQGZLWKRXWILULQJDQJOHGHOD\DQGαLVWKHILULQJDQJOH([DPSOHVRIYROWDJHZDYHIRUPVZLWKDGHOD\DQJOHα °FDQEHVHHQLQILJXUH

)LJXUH ,GHDOLVHG YROWDJH ZDYHIRUPV LQ D VL[SXOVH FRQYHUWHU ZLWK ILULQJ

DQJOHGHOD\α °DQGFRPPXWDWLRQUHDFWDQFHQHJOHFWHG

0 1 2 3 4 5 6 7 8 9-2

-1

0

1

2

u1

u2

Cathode potential

Anode potential

alfa

wt (rad)

U (p

.u)

Voltage waveforms, alfa=15 deg

0 1 2 3 4 5 6 7 8 9-3

-2

-1

0

1

2

3

ud


wt (rad)

U (p

.u)


,QUHDOLW\WKHFRPPXWDWLRQUHDFWDQFHLVRIFRXUVHQRWLQVLJQLILFDQWDQGWKH

FRPPXWDWLRQZLOOQRWEHLQVWDQWDQHRXV7KHGFYROWDJHZLOOEHUHGXFHGHYHQPRUHEHFDXVHRIWKHYROWDJHGURSDFURVVWKHUHDFWDQFH>@

,;88π

α FRV −= ZKHUH, LVWKHGLUHFWFXUUHQW'XULQJWKHFRPPXWDWLRQWKHWZRYDOYHVLQYROYHGLQWKHFRPPXWDWLRQIRU

H[DPSOHYDOYHDQGYDOYHFRQGXFWVLPXOWDQHRXVO\DQGWKHSKDVHYROWDJHVLQSKDVHDDQGSKDVHEZLOOEHVKRUWFLUFXLWHGWRJHWKHUWKURXJKWKHFRPPXWDWLRQUHDFWDQFH; (YHQWXDOO\WKHFXUUHQWZLOOEHWUDQVIHUUHGIURPYDOYHWRYDOYHDQGWKHFRPPXWDWLRQZLOOEHILQLVKHG7KHWLPHWKLVWDNHVLVPHDVXUHGE\WKHFRPPXWDWLRQLQWHUYDODQJOHRURYHUODSDQJOHWKDWLVGHQRWHGX'XULQJWKHFRPPXWDWLRQLQWHUYDOKRZHYHUWKHSRVLWLYHSRWHQWLDOX ZLOOIROORZWKHYROWDJH

XXX −=! ZKHUH GWGL/X "#$&% = LVWKHYROWDJHDFURVVWKHFRPPXWDWLRQ

UHDFWDQFH,QILJXUHWKHHIIHFWRIWKHFRPPXWDWLRQUHDFWDQFHRQWKHYROWDJHZDYHIRUPVLVVKRZQDQGLQILJXUHWKHFXUUHQWWKURXJKYDOYHVDQGDQG, LVSORWWHG'XULQJWKHILUVWFRPPXWDWLRQLQWHUYDOGHQRWHGXWKHWRWDOFXUUHQW, LVVKLIWHGIURPYDOYHWRYDOYH$WHYHU\LQVWDQW, L '( L '*) DQGIRUα ωWαX FRVFRV

FRVFRV+XW,L ,-

+−−

=αα

ωα


)LJXUH 9ROWDJHZDYHIRUPVLQDVL[SXOVHFRQYHUWHUZLWKILULQJDQJOHGHOD\

α °DQGFRPPXWDWLRQUHDFWDQFHWDNHQLQWRDFFRXQW

0 1 2 3 4 5 6 7 8 9-2

-1

0

1

2

u1

u2

Cathode potential

Anode potential

alfa

u

wt (rad)

U (p

.u)

Voltage waveforms, alfa=15 deg, incl. commutation

0 1 2 3 4 5 6 7 8 9-3

-2

-1

0

1

2

3

ud


wt (rad)

U (p

.u)


)LJXUH &XUUHQWZDYHIRUPVLQDVL[SXOVHFRQYHUWHUZLWKILULQJDQJOHGHOD\

α °DQGFRPPXWDWLRQUHDFWDQFHWDNHQLQWRDFFRXQW ,QYHUWHURSHUDWLRQ,IWKHGHOD\DQJOHαLVVHWWR°RUPRUHQHJDWLYHYROWDJHSHULRGVEHJLQVWRDSSHDU7KLVLVQRWDSUREOHPVLQFHWKHVPRRWKLQJUHDFWRUVDWWKHGFVLGHRIWKHFRQYHUWHUPDLQWDLQVWKHSRVLWLYHFXUUHQWIORZDOVRZKHQWKHYROWDJHVZLWFKHVSRODULW\:KHQα °WKHSRVLWLYHDQGQHJDWLYHYROWDJHSHULRGVDUHHTXDODQGWKHUHIRUHWKHPHDQGLUHFWYROWDJHZLOOEH]HUR%H\RQG°WKHPHDQGLUHFWYROWDJHLVQHJDWLYHDQGWRPDLQWDLQRSHUDWLRQDGFSRZHUVXSSO\LVQHFHVVDU\7KLVVXSSO\ZRXOGRYHUFRPHWKHQHJDWLYHYROWDJHDQGIRUFHWKHFXUUHQWWRFRQGXFWLQWKHVDPHGLUHFWLRQ,QRWKHUZRUGVSRZHULVVXSSOLHGWRWKHDFV\VWHPDQGWKHFRQYHUWHULVLQLQYHUVLRQPRGH+RZHYHUαFDQQRWEHDVPXFKDV°6RPHH[WLQFWLRQDQJOHγPXVWEHOHIWWRUHHVWDEOLVKWKHEORFNLQJFDSDELOLW\RIWKHSUHYLRXVO\FRQGXFWLQJYDOYHRWKHUZLVHWKHYDOYH


WKDWMXVWKDVVWRSSHGFRQGXFWLQJZRXOGSLFNXSWKHFXUUHQWDJDLQDQGWKHFRPPXWDWLRQZRXOGQHYHUWDNHSODFH7KHH[WLQFWLRQDQJOHFDQEHH[SUHVVHGDVγ °αXZKHUHαLVWKHGHOD\DQJOHDQGXLVWKHFRPPXWDWLRQRYHUODSDQJOH7KHPLQLPXPH[WLQFWLRQDQJOHLVXVXDOO\VHWWR°WR°,QILJXUHLGHDOYROWDJHZDYHIRUPVWKDWLVZLWKRXWFRPPXWDWLRQUHDFWDQFHIRULQYHUWHURSHUDWLRQLVVKRZQZLWKα °1RWHWKDWX . X / DQGX 0 KDYHVKLIWHGSRODULW\FRPSDUHGWRUHFWLILHURSHUDWLRQILJXUH

)LJXUH ,GHDOLVHG YROWDJHZDYHIRUPV LQ D VL[SXOVH FRQYHUWHU LQ LQYHUVLRQ

PRGHZLWK ILULQJ DQJOH GHOD\α ° DQG FRPPXWDWLRQ UHDFWDQFHQHJOHFWHG

0 1 2 3 4 5 6 7 8 9

-2

-1

0

1

2

u2

u1

Cathode potential

Anode potential

wt (rad)

U (p

.u)

Voltage waveforms, alfa=150 deg

0 1 2 3 4 5 6 7 8 9-3

-2

-1

0

1

2

3

ud


wt (rad)

U (p

.u)

alfa gamma


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

OLQNV7KHEDFNWREDFNLQWHUFRQQHFWLRQILJXUHDFRQVLVWVRIWZRFRQYHUWHUVDWWKHVDPHVLWH7KH\DUHFRQQHFWHGGLUHFWO\WRHDFKRWKHUZLWKRXWDQ\WUDQVPLVVLRQOLQHLQEHWZHHQ7KLVRSWLRQLVXVHGZKHQWKHDLPRIWKHKYGFOLQNLVWRFRQQHFWWZRSRZHUV\VWHPVZLWKGLIIHUHQWIUHTXHQFLHVRUZLWKGLIIHUHQWFRQWUROSKLORVRSKLHV7KHPRQRSRODUVFKHPHILJXUHELQYROYHVWZRFRQYHUWHUVFRQQHFWHG

ZLWKDVLQJOHFRQGXFWRU(DUWKRUWKHVHDLVQRUPDOO\XVHGDVWKHUHWXUQFRQGXFWRUEXWDOVRDPHWDOOLFUHWXUQFRQGXFWRUFDQEHXVHG7KHELSRODUOLQNILJXUHFLVWKHPRVWZLGHO\XVHG,QWKLV

FRQILJXUDWLRQWZRPRQRSRODUV\VWHPVDUHFRPELQHGRQHLVUXQZLWKDSRVLWLYHSRODULW\YROWDJHDQGWKHRWKHUZLWKQHJDWLYHSRODULW\7KLVDOWHUQDWLYHJLYHVDKLJKHUUHOLDELOLW\WKDQWKHRWKHUFRQILJXUDWLRQVVLQFHHDFKSROHFDQRSHUDWHRQLWVRZQXVLQJJURXQGUHWXUQLIWKHRWKHUSROHWHPSRUDULO\KDVWREHWDNHQRXWRIVHUYLFH$QRWKHUDOWHUQDWLYHFRQILJXUDWLRQLVDPXOWLWHUPLQDOVFKHPHWKDWLVDKYGF

V\VWHPZLWKPRUHWKDQWZRFRQYHUWHUVWDWLRQV7KHDGGLWLRQDOVWDWLRQVFDQEHFRQQHFWHGHLWKHULQVHULHVRULQSDUDOOHO7RGD\WKHUHLVRQO\RQHODUJHVFDOHPXOWLWHUPLQDOKYGFV\VWHPLQRSHUDWLRQWKH4XHEHF±1HZ(QJODQGWUDQVPLVVLRQZLWKD0:UDWLQJDQGDGFYROWDJHOHYHORI±N9


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

1 2

354(687:9 2

1 2

3;4(6<79 2

3;4(6<79 2

1 2

1 2

D

E

F


ZLQGLQJWUDQVIRUPHUVRUHYHQVL[VLQJOHSKDVHWZRZLQGLQJWUDQVIRUPHUVFDQEHXVHG6PRRWKLQJUHDFWRUV/DUJHLQGXFWRUVZLWKDQLQGXFWDQFHXSWR+DUHFRQQHFWHGLQVHULHVRQWKHGFVLGHRIWKHFRQYHUWHU7KHVPRRWKLQJUHDFWRUVHUYHVVHYHUDOSXUSRVHV 5HGXFHVWKHKDUPRQLFFRQWHQWLQYROWDJHVDQGFXUUHQWVRQWKHGFOLQH 3UHYHQWVWKHFXUUHQWIURPEHFRPLQJGLVFRQWLQXRXVDWORZORDG 5HGXFHVWKHUDWHRIULVHRIWKHGLUHFWFXUUHQWDIWHUDGLVWXUEDQFH

7KLVLQWXUQSUHYHQWVSHUPDQHQWFRPPXWDWLRQIDLOXUHVLQWKHLQYHUWHUIROORZLQJDFYROWDJHUHGXFWLRQVDQGOLPLWVWKHSHDNFXUUHQWLQWKHUHFWLILHUGXULQJDVKRUWFLUFXLWRQWKHGFOLQH

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


&LUFXLWEUHDNHUV7KHFLUFXLWEUHDNHUVRQWKHDFVLGHRIWKHFRQYHUWHUWUDQVIRUPHUDUHXVHGWRWDNHWKHKYGFOLQNRXWRIVHUYLFHDQGIRUFOHDULQJWUDQVIRUPHUIDXOWV)RUFOHDULQJRIGFVLGHIDXOWVFRQYHUWHUFRQWUROLVXVHG

AC bus

CB

Transformers

Reactive powersource

AC filter

DC filter

Converterbridge

Ground electrode

DC smoothingreactor

DC filter

DC line

AC bus

DC line

Reactive powersource

AC filter

CB

Transformers

CB= Circuit breaker

DC smoothingreactor

)LJXUH6FKHPDWLFRIDELSRODUKYGFWUDQVPLVVLRQ 0XOWLWHUPLQDOKYGF7KHILUVWFRPPHUFLDOPXOWLWHUPLQDOKYGFV\VWHPEXLOWLVWKH6DUGLQLD&RUVLFD,WDO\VFKHPH,QDWKLUGWHUPLQDOZDVDGGHGRQ&RUVLFDWRDQH[LVWLQJKYGFOLQNEHWZHHQ6DUGLQLDDQG,WDO\7KHUHDUHWKUHHSRVVLEOHFRQILJXUDWLRQDOWHUQDWLYHVIRUDPXOWLWHUPLQDOKYGFV\VWHP>@ 7KHFRQYHUWHUVFDQEHFRQQHFWHGLQSDUDOOHODQGRSHUDWHDWDFRPPRQ

YROWDJH7KHFRQQHFWLRQEHWZHHQWKHFRQYHUWHUVWDWLRQVFDQEHHLWKHUUDGLDORUPHVKHG0RVWVWXGLHVGRQHRQPXOWLWHUPLQDOV\VWHPVKDYHSURSRVHGWKHSDUDOOHOFRQILJXUDWLRQZLWKUDGLDOFRQQHFWLRQV7KHPHVKHGDOWHUQDWLYHJLYHVKLJKHUUHGXQGDQF\EXWUHTXLUHVJUHDWHUOHQJWKRIGFFDEOHV

7KHFRQYHUWHUVFDQEHFRQQHFWHGLQVHULHVZLWKDFRPPRQGLUHFWFXUUHQW:KHQWKLVDOWHUQDWLYHKDVEHHQFRQVLGHUHGLWKDVPRVWO\FRQFHUQHGVPDOOWDSSLQJVWDWLRQVXSWRRIWKHUDWHGSRZHU,QWKHVHFDVHVLWPD\EHPRUHHFRQRPLFDOZLWKDVHULHVWDSVLQFHLWFDQEHGLPHQVLRQHGIRUDORZHUYROWDJHWKDQDSDUDOOHOWDSZKLFKKDVWRKDYHWKHIXOOYROWDJHUDWLQJ

$PL[HGFRQILJXUDWLRQZLWKERWKSDUDOOHODQGVHULHVWDSSLQJVWDWLRQVPD\DOVREHFRQFLHYDEOH

7KHSDUDOOHOFRQILJXUDWLRQLVFRQVLGHUHGWREHPRUHSUDFWLDOWKDQWKHVHULHVRQHZLWKORZHUOLQHORVVHVLVHDVLHUWRFRQWURODQGRIIHUVPRUHSRVVLELOLWLHVIRUIXWXUHH[WHQVWLRQV


SXOVHFRQYHUWHUV$VPHQWLRQHGLQVHFWLRQRQHRIWKHPRVWHIIHFWLYHZD\VWRUHGXFHWKHHPLVVLRQRIKDUPRQLFVIURPWKHFRQYHUWHULVWRLQFUHDVHWKHFRQYHUWHUSXOVHQXPEHU7KLVLVGRQHE\XVLQJWZRVL[SXOVHFRQYHUWHUVDQGFRQQHFWRQHRIWKHPWRD<<WUDQVIRUPHUDQGWKHRWKHUWRD<∆WUDQVIRUPHU7KHWZRFRQYHUWHUEULGJHVDUHFRQQHFWHGLQVHULHVRQWKHGFVLGHDQGLQSDUDOOHORQWKHDFVLGH7KHUHVXOWLQJDFFXUUHQWLQSKDVHZLOOWKHQEHWKHVXPRIWKHFXUUHQWVLQSKDVHLQWKHWZRWUDQVIRUPHUV$)RXULHUDQDO\VLVRIWKHFXUUHQWKDUPRQLFV>@VKRZVWKDWZLWKDSXOVHFRQYHUWHUWKHORZHVWDFFXUUHQWKDUPRQLFVDUHWKH = > DQGWKH = > )RUDVL[SXOVHFRQYHUWHUWKHORZHVWKDUPRQLFVDUH = > DQG = > 7KHDPSOLWXGHRIWKHKDUPRQLFVDUHLQYHUVHO\SURSRUWLRQDOWRWKHLURUGHU7KHVHULHVFRQQHFWLRQRQWKHGFVLGHJLYHVWKDWWKHWRWDOGFYROWDJHZLOOEHWKHVXPRIWKHGFYROWDJHVRIWKHWZRVL[SXOVHFRQYHUWHUV6LQFHRQHWUDQVIRUPHULVFRQQHFWHGLQ<<DQGWKHRWKHULQ<∆WKHWZRYROWDJHVZLOOEHVKLIWHG°ZLWKUHVSHFWWRHDFKRWKHU7KHWRWDOGFYROWDJHZLOOKDYHDULSSOHZLWKDIUHTXHQF\RIWLPHVWKHIXQGDPHQWDOWREHFRPSDUHGZLWKWKHSXOVHFRQILJXUDWLRQZKHUHWKHULSSOHKDVDIUHTXHQF\RIVL[WLPHVWKHIXQGDPHQWDO7KLVUHVXOWVLVKDUPRQLFVRIWKHRUGHUDQGDERYHLQWKHGFYROWDJH7KHPDJQLWXGHRIWKHGFVLGHKDUPRQLFVYDULHVZLWKILULQJDQJOHα +YGFZLWKYROWDJHVRXUFHFRQYHUWHUV:KHQKLJKVZLWFKLQJIUHTXHQF\FRPSRQHQWVOLNH,*%7V,QVXODWHG*DWH%LSRODU7UDQVLVWRURU*72V*DWH7XUQ2II7K\ULVWRUEHFDPHDYDLODEOHIRUKLJKYROWDJHDSSOLFDWLRQVYROWDJHVRXUFHFRQYHUWHUV96&VXWLOLVLQJSXOVHZLGWKPRGXODWLRQ3:0ZHUHGHYHORSHG7KHVHFRQYHUWHUVDUHDOVRUHIHUUHGWRDVVHOIFRPPXWDWHGFRQYHUWHUV%DVLFDOO\IURPDV\VWHPSRLQWRIYLHZWKLVW\SHRIFRQYHUWHUDFWVDVDPRWRURUJHQHUDWRUZLWKRXWPDVVDQGFDQFRQWURODFWLYHDQGUHDFWLYHSRZHULQGHSHQGHQWO\)RUVLPSOLFLW\WKHWHUPLQRORJ\KYGFOLJKWZLOOIURPQRZRQEHDGDSWHGIRUD96&ZLWK3:0,QWKLVVHFWLRQKYGFOLJKWZLOOUHIHUWRWKHFRQYHUWHUWHFKQRORJ\H[FOXVLYHO\DQGQRWWKHHQWLUHV\VWHPZLWKVWDWLRQPRGXOHVFDEOHVDQGDOO7KH3:0SULQFLSOHLVWRVZLWFKYHU\IDVWLQWKHN+]DUHDEHWZHHQWZR

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

OLJKWWHFKQRORJ\FDQEHVXPPDULVHGDVIROORZV>@


&ODVVLFDOKYGFZLWKOLQHFRPPXWDWHGFRQYHUWHUVLVPRVWHIIHFWLYHLQWKH

KLJKSRZHUUDQJHDERYHVD\0:+YGFOLJKWLVIHDVLEOHIURPWHQVRI0:XSWRDURXQG0:DQGWKHXSSHUOLPLWLVFRQVWDQWO\LQFUHDVLQJ

+YGFOLJKWLVELSRODUE\QDWXUHDQGGRHVQRWKDYHDFRQQHFWLRQWRJURXQGWKHUHIRUHWZRFRQGXFWRUVDUHUHTXLUHG

1RDFWUDQVIRUPHULVQHHGHGEHWZHHQWKHDFQHWZRUNDQGWKH96&$VHULHVUHDFWRULVHQRXJKWRVHSDUDWHWKHIXQGDPHQWDOIUHTXHQF\IURPWKH3:0ZDYHIRUP,IWKHGFYROWDJHOHYHOGRHVQRWPDWFKWKHDFV\VWHPYROWDJHDQRUGLQDU\DFWUDQVIRUPHUFDQEHXVHG

2QO\VPDOOILOWHUVDUHQHHGHGZLWKWKHKYGFOLJKWWHFKQRORJ\1RH[WUDUHDFWLYHSRZHUSURGXFWLRQLVUHTXLUHGDQGEHFDXVHRIWKHKLJKVZLWFKLQJIUHTXHQF\RQO\KLJKSDVVILOWHUVDUHQHFHVVDU\WRPLWLJDWHKDUPRQLFV

7RVPRRWKWKHGFFXUUHQWDGFFDSDFLWRULVXVHGLQVWHDGRIDVHULHVVPRRWKLQJUHDFWRUDQGGFILOWHUV+HQFHWKHWHUPYROWDJHVRXUFHFRQYHUWHUV

+YGFOLJKWGRHVQRWUHO\RQWKHDFV\VWHPWRNHHSWKHYROWDJHDQGIUHTXHQF\VWDEOHDQGFDQRSHUDWHDJDLQVWDSDVVLYHDFQHWZRUN

&RQYHQWLRQDOKYGFFDQFRQWUROWKHUHDFWLYHSRZHUE\VZLWFKLQJRIILOWHUVDQGVKXQWFDSDFLWRUVEXWWKLVUHTXLUHVH[WUDHTXLSPHQWDQGKHQFHJLYHVULVHWRH[WUDFRVWV:LWKWKH3:0WHFKQLTXHWKHDFWLYHDQGUHDFWLYHSRZHUFDQEHLQGHSHQGHQWO\DQGDOPRVWLQVWDQWDQHRXVO\FRQWUROOHG

$VVXPLQJWKDWWKHUDWLQJRIWKH96&VZLOOFRQWLQXHWRULVHLWZRXOGEHLQWHUHVWLQJDVDFRQWLQXDWLRQRQWKLVWKHVLVWRORRNLQWRWKLVWHFKQLTXHDVDQDOWHUQDWLYHWRWKHWHFKQLTXHLQYHVWLJDWHGVRIDU)XUWKHUUHDGLQJDERXW96&WHFKQRORJ\VHHIRUH[DPSOH>@

6WDELOLW\LPSURYHPHQWZLWKKYGF,QPRVWFDVHVWKHUHDVRQIRUEXLOGLQJDKYGFOLQNLVWKHQHHGIRUEXONSRZHUWUDQVPLVVLRQDQGRULQWHUFRQQHFWLRQRIDV\QFKURQRXVSRZHUV\VWHPV,QVRPHFDVHVKRZHYHUWKHKYGFOLQNFDQDOVRSURYLGHDQHQKDQFHGRYHUDOOV\VWHPVWDELOLW\,IWKHKYGFOLQHLVFRQQHFWHGLQSDUDOOHOZLWKDFOLQHVPRGXODWLRQRIWKH

DFWLYHSRZHURIWKHKYGFOLQNFDQGDPSRVFLOODWLRQVRQWKHDFFRQQHFWLRQV7KLVLVWKHWUDGLWLRQDOZD\RILPSURYLQJV\VWHPGDPSLQJE\PHDQVRIKYGFSRZHUPRGXODWLRQ([DPSOHVRIWKLVVWUDWHJ\FDQEHIRXQGHJLQWKH5LKDQG'HOKLDQG&KDQGUDSXU3DGJKHSURMHFWVLQ,QGLD,IRQWKHRWKHUKDQGKYGFLVXVHGWRFRQQHFWWZRDV\QFKURQRXVV\VWHPVWKH

VLWXDWLRQLVGLIIHUHQW*HQHUDOO\LQWHUDUHDRVFLOODWLRQVGRQRWH[LVWEHWZHHQWKHWZRV\VWHPVFRQQHFWHGWKURXJKWKHKYGFOLQN8QIRUWXQDWHO\ORZIUHTXHQF\RVFLOODWLRQVZLWKLQRQHRIWKHV\VWHPVFDQEHWUDQVIHUUHGRYHUWKHKYGFOLQNWRWKHRWKHUV\VWHP%XWKYGFSRZHUPRGXODWLRQFDQEHXVHIXODQ\ZD\LIDQ\RIWKHV\VWHPVFRQWDLQJURXSVRIPDFKLQHVRVFLOODWLQJWRZDUGVHDFKRWKHU7KHQPRGXODWLQJRIGFSRZHUFDQKHOSLQGDPSLQJWKHRVFLOODWLRQVRQWKHDFWLHOLQHFRQQHFWLQJWKHVHJURXSVRIPDFKLQHV+RZHIIHFWLYHWKHSRZHUPRGXODWLRQ


FDQEHGHSHQGVRQWKHORFDWLRQRIWKHKYGFFRQYHUWHUUHODWLYHWRWKHLQHUWLDRIWKHPDFKLQHVRVFLOODWLQJ>@

+YGFVFKHPHV±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±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


RSSRVLWHWKHQRUWKKDVDKLJKSRZHUGHPDQGGXHWRKHDWLQJDQGWKHVRXWKKDVDORZHUFRQVXPSWLRQ7KHLQWHUWLHKDVEHHQH[SDQGHGLQVHYHUDOVWHSVDQGWRGD\WKHKYGFSDUWRIWKHLQWHUWLHKDVDUDWLQJRI0:DW±N9>@(DFKSROHRIWKHELSRODUKYGFOLQNFRQVLVWVRIWKHWKUHHRULJLQDOSXOVH

PHUFXU\DUFFRQYHUWHUVLQVHULHVZLWKDSXOVHWK\ULVWRUFRQYHUWHUIURP,QSDUDOOHOZLWKWKHVHIRXUFRQYHUWHUVDVHFRQGFRQYHUWHUVWDWLRQIURPLVFRQQHFWHGZLWKDSXOVHWK\ULVWRUFRQYHUWHU7KLVFRQILJXUDWLRQDOORZVQXPHURXVFRQWUROPRGHDOWHUQDWLYHVVLQFHWKHWZRFRQYHUWHUVWDWLRQVDWHDFKSROHDUHRSHUDWHGZLWKLQGHSHQGHQWFRQWUROV%HVLGHVWKHQRUPDOIXQFWLRQVRIWKHFRQYHUWHUFRQWUROVLQFOXGLQJJHQHUDWLRQ

RIGHOD\DQJOHRUGHUEORFNLQJDQGGHEORFNLQJVHTXHQFHVDQGFXUUHQWYROWDJHDQGH[WLQFWLRQDQJOHJDPPDFRQWUROVWKHFRQYHUWHUFRQWURODOVRLQFOXGHVPL[HGFXUUHQWYROWDJHDQGFXUUHQWJDPPDFRQWUROV%\XVLQJWKHVHPL[HGFRQWUROVDFRPELQHGFXUUHQWPDUJLQDQGYROWDJHOLPLWLQJWHFKQLTXHLVUHDOLVHGXVLQJDSUHGHILQHG8 ? , ? VORSHDQGGFYROWDJHRIIVHWIRUUHFWLILHUDQGγ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±/X]RQ3KLOLSSLQHV7KLV0:N9PRQRSRODU+9'&OLQNVWUHWFKHVEHWZHHQDJHRWKHUPDOSODQWRQWKHLVODQGRI/H\WHWRWKHPDLQLVODQG/X]RQWRVXSSO\SRZHUWRWKH0DQLODDUHD7KHKYGFDOWHUQDWLYHZDVFKRVHQSDUWO\EHFDXVHRIWKHVHDFURVVLQJSDUWO\EHFDXVHWKHQHHGRILPSURYHGVWDELOLW\LQWKH0DQLODSRZHUV\VWHP +YGFGHYHORSPHQW(YHQWKRXJKWKH96&WHFKQRORJ\LVDGYDQFLQJUDSLGO\WKHFODVVLFDOKYGFWHFKQLTXHLVVWLOOHYROYLQJDQGZLOOSUREDEO\NHHSDSDUWRIWKHSRZHUWUDQVPLVVLRQPDUNHWLQWKHIXWXUHDVZHOO,QWKLVVHFWLRQVRPHGHYHORSPHQWWUHQGVZLOOEHPHQWLRQHG


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

FDSDFLWRUVDOVRUHGXFHWKHULVNRIFRPPXWDWLRQIDLOXUHVLQWKHFRQYHUWHU7KHFDSDFLWRUVSURYLGHDVRXUFHRIFRPPXWDWLRQYROWDJHLQDGGLWLRQWRWKHYROWDJHDWWKHDFEXV7\SLFDOO\D&&&FDQWROHUDWHDYROWDJHGURSZLWKRXWDQ\FRPPXWDWLRQIDLOXUHV>@7KHVXSSRUWLQFRPPXWDWLRQYROWDJHUHVXOWVLQDUHGXFHGRYHUODSDQJOHDVZHOOZKLFKLQWXUQZLOOJLYHULVHWRDVRPHZKDWLQFUHDVHGJHQHUDWLRQRIKDUPRQLFV7KLVFDQEHKDQGOHGE\XVLQJKLJKSHUIRUPDQFHILOWHUV7KHFRQYHUWHUVWDELOLW\LVDOVRLPSURYHGZLWKD&&&FRPSDUHGWRD

FRQYHQWLRQDOFRQYHUWHU7KHFRQWULEXWLRQWRWKHFRPPXWDWLRQYROWDJHIURPWKHFDSDFLWRUVUHVXOWVLQSRVLWLYHLPSHGDQFHFKDUDFWHULVWLFVIRUDQLQYHUWHUDWPLQLPXPFRPPXWDWLRQPDUJLQFRQWURO7KHFRQVHTXHQFHRIWKLVLVWKDWDQLQFUHDVHLQGFFXUUHQWUHVXOWVLQDQLQFUHDVHLQGFYROWDJHLQVWHDGRIDGHFUHDVHWKDWZRXOGKDYHEHHQWKHFDVHZLWKDFRQYHQWLRQDOLQYHUWHUZLWKFRPPXWDWLRQPDUJLQFRQWURO7KXVWKHG\QDPLFSHUIRUPDQFHZLOOEHVLJQLILFDQWO\LPSURYHG2WKHUHIIHFWVRIWKHFRPPXWDWLRQFDSDFLWRUVDUH 5HGXFHGYDOYHVKRUWFLUFXLWFXUUHQWVGXHWRWKHYROWDJHGURSDFURVVWKH

FDSDFLWRUYDULVWRUVWKDWDUHXVHGWRSURWHFWWKHFDSDFLWRUVIURPRYHUYROWDJHV7KLVDOVRPHDQVDKLJKHUSHDNYROWDJHDFURVVWKHYDOYHV

6LQFHWKHUHDFWLYHSRZHUIORZWKURXJKWKHFRQYHUWHUWUDQVIRUPHULVPLQLPLVHGWKHWUDQVIRUPHUUDWLQJFDQEHUHGXFHG

7KHHOLPLQDWLRQRIVZLWFKDEOHILOWHUEDQNVFRQVLGHUDEO\UHGXFHVWKHDUHDUHTXLUHGIRUWKHKYGFVWDWLRQ

)LOWHUV7RIXOO\XWLOLVHWKHEHQHILWVRIDFDSDFLWRUFRPPXWDWHGFRQYHUWHUWKHILOWHUVXVHGVKRXOGEHKLJKSHUIRUPDQFHILOWHUVVXFKDVFRQWLQXRXVO\WXQHGDFILOWHUVDQGDFWLYHGFILOWHUV7KHSULQFLSOHRIDFRQWLQXRXVO\WXQHGILOWHULVWKDWWKHUHDFWRULQGXFWDQFHLV

DGMXVWHGWRPHHWIUHTXHQF\DQGFRPSRQHQWYDULDWLRQV7KLVLVGRQHE\LQVHUWLQJDQLURQFRUHZLWKDFRQWUROZLQGLQJLQWKHILOWHUUHDFWRU$GFFXUUHQWLQWKHFRQWUROZLQGLQJDIIHFWVWKHSHUPHDELOLW\RIWKHFRUHZKLFKLQWXUQFKDQJHVWKHLQGXFWDQFHRIWKHUHDFWRU


7KHDFWLYHGFILOWHULVDZD\RIPHHWLQJWKHLQFUHDVLQJO\VWULQJHQWGHPDQGVUHJDUGLQJLQWHUIHUHQFHOHYHOVIURPGFOLQHV7KHFRQFHSWLVWRFRPELQHDQDFWLYHGFILOWHUZLWKDVPDOOSDVVLYHILOWHUEUDQFK$FXUUHQWIRUPHGRQWKHEDVLVRIWKHPHDVXUHGKDUPRQLFVRQWKHGFOLQHLVWKHQLQMHFWHGWKURXJKWKHSDVVLYHILOWHULQWRWKHGFFLUFXLWWRHOLPLQDWHWKHVHKDUPRQLFV>@

)LJXUH6LQJOHOLQHGLDJUDPRID&&&ZLWKFRQWLQXRXVO\WXQHGDFILOWHU

$&EXV<∆

&KDSWHU&RQWURORIKYGFFRQYHUWHUV

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

QHHGWROLPLWRYHUFXUUHQWDQGPLQLPLVHGDPDJHGXHWRIDXOWVDQGWRSUHYHQWWKHV\VWHPIURPFORVLQJGRZQLQWKHFDVHRIDFV\VWHPGLVWXUEDQFHV

%DVLFSULQFLSOHV7KHVLQJOHOLQHGLDJUDPLQILJXUHDVKRZVDPRQRSRODUOLQNRURQHSROHRIDELSRODUOLQN$QHTXLYDOHQWFLUFXLWDQGDYROWDJHSURILOHDUHVKRZQLQILJXUHVEDQGF7KHGLUHFWFXUUHQW, ? IORZLQJIURPWKHUHFWLILHUWRWKHLQYHUWHULV>@

GIHJGIKHLKLL555

88,−+

−=

γα FRVFRV MM DQGWKHGFYROWDJHDWWKHUHFWLILHUGFWHUPLQDOVFDQEHH[SUHVVHGDV

NOIPPNN P ,588 −= αFRVQ 8 ?RFS DQG8 ?TRUA DUHWKHQRORDGGLUHFWYROWDJHLQWKHUHFWLILHUDQGWKHLQYHUWHUUHVSHFWLYHO\5 V*S DQG5 V(A DUHWKHHTXLYDOHQWFRPPXWDWLQJUHVLVWDQFHVZKLFKDFFRXQWIRUWKHYROWDJHGURSLQWKHFRQYHUWHUVGXHWRFRPPXWDWLRQRYHUODSDQG5W LVWKHGFOLQHUHVLVWDQFH%\FRQWUROOLQJWKHLQWHUQDOYROWDJHV8 ?RFS DQG8 ?RUA WKHGFYROWDJHDWDQ\

SRLQWRQWKHOLQHDQGWKHGFFXUUHQWRUWKHGFSRZHUFDQEHFRQWUROOHG7KLVLVGRQHHLWKHUE\FRQWUROOLQJWKHUHFWLILHUYDOYHLJQLWLRQDQJOHα, (RUH[WLQFWLRQDQJOHγ, RIDQLQYHUWHURUE\FRQWURORIWKHDFYROWDJHWKURXJKWUDQVIRUPHUWDSFKDQJLQJ&RQWURORIWKHYDOYHLJQLWLRQDQJOHLVXVHGIRUUDSLGDFWLRQDQGLVWKHQIROORZHGE\WDSFKDQJLQJWRUHVWRUHWKHFRQYHUWHUTXDQWLWLHVWRWKHLUQRUPDOUDQJH


2SHUDWLRQUHTXLUHPHQWV,PSRUWDQWUHTXLUHPHQWVIRUVDWLVIDFWRU\RSHUDWLRQRIDQKYGFOLQNDUHIRUH[DPSOH>@ 7KHSUHYHQWLRQRIODUJHIOXFWXDWLRQVLQWKHGLUHFWFXUUHQW7KHOLQHDQG

FRQYHUWHUUHVLVWDQFHVDUHUHODWLYHO\VPDOOZKLFKZLWKUHIHUHQFHWRHTXDWLRQPHDQVWKDWDVPDOOFKDQJHLQWKHLQWHUQDOYROWDJH8 ?RFS RU8 ?RUA OHDGVWRDODUJHFKDQJHLQ, ? 6XFKYDULDWLRQVDUHXVXDOO\QRWDFFHSWDEOHIRUVDWLVIDFWRU\RSHUDWLRQRIWKHSRZHUV\VWHPDQGDWRRKLJKFXUUHQWPD\DOVRGDPDJHWKHYDOYHVRURWKHUHTXLSPHQW7KHUHIRUHUDSLGFRQYHUWHUFRQWUROLVHVVHQWLDOWRDYRLGWKHVHFXUUHQWIOXFWXDWLRQV

7KHGFYROWDJHVKRXOGEHNHSWDWDYDOXHQHDUWKHUDWHGYDOXH7KLVPLQLPLVHVWKHGLUHFWFXUUHQWQHHGHGWRWUDQVPLWWKHGHVLUHGSRZHUDQGWKHUHE\WKHOLQHORVVHVDUHDOVRPLQLPLVHG

7KHSRZHUIDFWRUVVKRXOGEHDVKLJKDVSRVVLEOH7KLVLVLPSRUWDQWIRUVHYHUDOUHDVRQVHJWRDYRLGH[FHVVLYHUHDFWLYHSRZHUFRQVXPSWLRQLQWKHFRQYHUWHUVWRNHHSWKHUDWHGSRZHURIWKHFRQYHUWHUDVKLJKDVSRVVLEOHWRUHGXFHYDOYHVWUHVVHVDQGWRPLQLPLVHORVVHVDQGFXUUHQWUDWLQJVRIWKHDFV\VWHPHTXLSPHQW7KHSRZHUIDFWRURIWKHFRQYHUWHUFDQDSSUR[LPDWHO\EHH[SUHVVHGDV>@

[ ]FRVFRVFRV X++≈ ααφ IRUDUHFWLILHU

[ ]FRVFRVFRV X++≈ γγφ IRUDQLQYHUWHU

ZKHUHXLVWKHFRPPXWDWLRQRYHUODSDQJOHVHH&KDSWHU)URPWKHHTXDWLRQLWLVFOHDUWKDWLQRUGHUWRNHHSWKHSRZHUIDFWRUKLJKαIRUDUHFWLILHUDQGγIRUDQLQYHUWHUPXVWEHNHSWORZ7KHVHDQJOHVFDQQRWEHNHSWWRRORZKRZHYHU)RUWKHUHFWLILHUαKDVDPLQLPXPOLPLWRIDURXQGWRPDNHVXUHWKDWWKHYDOYHVKDYHDKLJKHQRXJKYROWDJHEHIRUHILULQJ7REHDEOHWRDOORZDQLQFUHDVHGGFYROWDJHIRUUHJXODWLRQSXUSRVHVVRPHPDUJLQPXVWEHJLYHQVLQFHDQLQFUHDVHGGFYROWDJHPHDQVDGHFUHDVHGα7KHUHIRUHαLVVHOGRPJLYHQDYDOXHORZHUWKDQRU)RUWKHLQYHUWHUγ PXVWEHNHSWODUJHUWKDQDFHUWDLQYDOXHWRDYRLGFRPPXWDWLRQIDLOXUH7KHFRPPXWDWLRQPXVWEHFRPSOHWHGDQGVRPHWLPHPXVWEHJLYHQIRUGHLRQLVDWLRQEHIRUHWKHFRPPXWDWLRQYROWDJHUHYHUVHVDWα DQGγ 7\SLFDOO\WKHPLQLPXPYDOXHRIWKHH[WLQFWLRQDQJOHLVDURXQGIRUD+]V\VWHP

&RQWUROPRGHV7KHEDVLFFRQWUROV\VWHPLVDUUDQJHGLQWKHIROORZLQJZD\7KHUHFWLILHUXVHVDFXUUHQWFRQWURODQGDαOLPLWFRQWUROZKLFKLQFOXGHVDPLQLPXPαOLPLW7KHREMHFWRIWKLVPLQLPXPILULQJDQJOHOLPLWLVWRPDNHVXUHWKDWWKHUHLVHQRXJKYROWDJHDFURVVWKHYDOYHVEHIRUHWKHILULQJWDNHVSODFHRWKHUZLVHWKHFRPPXWDWLRQZLOOIDLO,QWKHFXUUHQWFRQWUROPRGH&&D


FORVHGORRSUHJXODWRUFRQWUROVWKHILULQJDQJOHDQGWKHUHE\WKHGFYROWDJHWRNHHSWKHGFFXUUHQWDWWKHGHVLUHGYDOXH,IWKHPHDVXUHGGLUHFWFXUUHQWLVVPDOOHUWKDQDUHIHUHQFHYDOXHWKHILULQJGHOD\DQJOHZLOOEHGHFUHDVHGDQGYLFHYHUVD7DSFKDQJHUFRQWURORIWKHFRQYHUWHUWUDQVIRUPHULVXVHGWRNHHSαZLWKLQWKHDOORZHGUDQJHXVXDOO\EHWZHHQDQG7KHLQYHUWHULVSURYLGHGZLWKDFRQVWDQWH[WLQFWLRQDQJOHFRQWURO&($DQG

DFXUUHQWFRQWURO,QWKH&($PRGHDFRPSURPLVHLVPDGHEHWZHHQDORZULVNRIFRPPXWDWLRQIDLOXUHVLIγLVODUJHDQGDORZUHDFWLYHSRZHUFRQVXPSWLRQLIγLVVPDOOZKLFKXVXDOO\UHVXOWVLQDYDOXHRIγRIDURXQG,QVSHFLDOFDVHVYROWDJHFRQWURODQGβFRQWUROPD\EHRILQWHUHVWVHHVHFWLRQ,QQRUPDORSHUDWLRQWKHUHFWLILHULVLQFXUUHQWFRQWUROPRGHDQGWKHLQYHUWHU

LQ&($PRGH,IWKHDFYROWDJHGHFUHDVHVWKHILULQJDQJOHLQWKHUHFWLILHUZLOODOVRGHFUHDVHWRNHHSWKHGFYROWDJHXS:KHQαKLWVWKHPLQLPXPαOLPLWWKHUHFWLILHUZLOOVZLWFKWRαOLPLWFRQWURODQGWKHLQYHUWHUZLOOWDNHRYHUWKHFXUUHQWFRQWURO&RQWUROFKDUDFWHULVWLFVDUHVKRZQLQILJXUH

)LJXUH D6FKHPDWLFGLDJUDPRIDKYGFOLQN E(TXLYDOHQWFLUFXLW F9ROWDJHSURILOH &RQWUROFKDUDFWHULVWLFV,QWKHIROORZLQJZHVLPSOLI\WKHGLVFXVVLRQE\DVVXPLQJDWZRWHUPLQDO

V\VWHP,QQRUPDORSHUDWLRQWKHUHFWLILHUNHHSVWKHFXUUHQWFRQVWDQWE\YDU\LQJαFXUUHQWFRQWUROPRGH&&EXWDVαUHDFKHVWKHPLQLPXPOLPLWQRIXUWKHUYROWDJHLQFUHDVHLVSRVVLEOHDQGWKHUHFWLILHUZLOOSDVVRYHUWRFRQVWDQWLJQLWLRQDQJOHPRGH&,$PDLQWDLQLQJα α XBY Z ,QILJXUHVHFWLRQ$%UHSUHVHQWV

, [SKDVHDFV\VWHP

SKDVHDFV\VWHP

GFOLQH

5HFWLILHU ,QYHUWHU

D

8 \I] ^ FRVα 8 [ _ 8 [ ` 8 \I] aFRVγF

5 b _ 5 c 5 b `

8 [ _ 8 [ `, d8 \I] ^ FRVα 8 \I] a FRVγ

E


WKH&&PRGHDQGVHFWLRQ)$UHSUHVHQWVWKH&,$PRGH1RUPDOO\WKHRSHUDWLRQSRLQWLVORFDWHGVRPHZKHUHEHWZHHQ$DQG%)RUQRUPDORSHUDWLRQDQGZLWKWKHLQYHUWHULQFRQVWDQWH[WLQFWLRQDQJOH

PRGH&($WKHLQYHUWHUFKDUDFWHULVWLFVLQWHUVHFWZLWKWKHUHFWLILHUFKDUDFWHULVWLFVDW(LQILJXUH+RZHYHULIWKHYROWDJHZRXOGGHFUHDVHWKHUHFWLILHU&,$FKDUDFWHULVWLFVZRXOGIROORZWKHGDVKGRWWHGOLQH)$DQGWKHWZRFKDUDFWHULVWLFVWKHUHFWLILHU&&DQGWKHLQYHUWHU&($ZRXOGQRWLQWHUVHFW7RDYRLGWKLVVFHQDULRWKHLQYHUWHUDOVRKDVDFXUUHQWFRQWUROPRGH7KHFXUUHQWRUGHULQWKHLQYHUWHULVVHWWRDORZHUYDOXHWKDQLQWKHUHFWLILHUDQGWKHUHVXOWLQJLQYHUWHU&&FKDUDFWHULVWLFVLVJLYHQE\WKHVHFWLRQ*+7KHGLIIHUHQFHEHWZHHQWKHUHFWLILHUDQGWKHLQYHUWHUFXUUHQWRUGHUVLVFDOOHG

WKHFXUUHQWPDUJLQ, X 1RUPDOO\, X LVRIWKHUDWHGFXUUHQW$WUHGXFHGYROWDJHWKHLQYHUWHUWDNHVRYHUWKHFXUUHQWFRQWUROWDVNDQGWKH

UHFWLILHUFRQWUROVWKHYROWDJH7KHQHZRSHUDWLQJSRLQWZLOOEH(1RWHWKDWWKHGLUHFWFXUUHQWIORZLQJWKURXJKWKHV\VWHPKDVEHHQUHGXFHGZLWKWKHFXUUHQWPDUJLQ

)LJXUH 6WHDG\VWDWHFKDUDFWHULVWLFVIRUFRQYHUWHUFRQWURO 7KHSULQFLSDOHIIHFWRIWKHFXUUHQWPDUJLQLVWKDWWKHGFYROWDJHLVLQFUHDVHGDVORQJDVDOOFRQYHUWHUVFDQFRQWUROWKHLUFXUUHQWV7KHPD[LPXPYROWDJHOLPLWLVGHWHUPLQHGE\WKHPLQLPXPILULQJDQJOHLQDUHFWLILHURUWKHH[WLQFWLRQDQJOHLQDQLQYHUWHU:KHQWKHPD[LPXPGFYROWDJHOLPLWLVUHDFKHGLQRQHVWDWLRQWKHVWDWLRQLVQRORQJHUDEOHWRFRQWUROLWVFXUUHQWEXWDFWVDVDVODFNIRUWKHRWKHUFXUUHQWFRQWUROOLQJVWDWLRQV,QPRVWKYGFVFKHPHVWKHFRQYHUWHUVDUHUHTXLUHGWREHDEOHWRUHYHUVHWKH

SRZHUIORZ7KDWLVERWKFRQYHUWHUVVKRXOGEHDEOHWRRSHUDWHHLWKHUDVDUHFWLILHURUDQLQYHUWHU7KLVLVDFFRPSOLVKHGE\SURYLGLQJHDFKFRQYHUWHUZLWKDFRPELQHGUHFWLILHULQYHUWHUFRQWUROFKDUDFWHULVWLF>@,QILJXUHWKHVHFRPELQHGFKDUDFWHULVWLFVDUHVKRZQ,QILJXUHDWKHSRZHUIORZGLUHFWLRQLVIURPFRQYHUWHUWRFRQYHUWHUWKDWLVFRQYHUWHUDFWVDVUHFWLILHUDQGFRQYHUWHUDVLQYHUWHU,QILJXUHEFRQYHUWHULVWKHUHFWLILHUDQGFRQYHUWHUWKHLQYHUWHU

8 e GLUHFWYROWDJH8 egf QRORDGGLUHFWYROWDJH, e GLUHFWFXUUHQW, eih FXUUHQWUHIHUHQFH&& FRQVWDQWFXUUHQWFRQWUROPRGH&,$ FRQVWDQWLJQLWLRQDQJOHFRQWURO PRGHα FRQVWDQW&($ FRQVWDQWH[WLQFWLRQDQJOH FRQWUROPRGHγ FRQVWDQW

8 j

8 jik

5HFWLILHU&&,QYHUWHU&&

,QYHUWHU&($5HFWLILHU&,$

$)

%

() $

*

+

(5HGXFHGYROWDJH


)LJXUH&RPELQHGUHFWLILHULQYHUWHUFKDUDFWHULVWLFVD3RZHUIORZGLUHFWLRQ

IURPFRQYHUWHUWRFRQYHUWHUE3RZHUIORZGLUHFWLRQIURPFRQYHUWHUWRFRQYHUWHU

$OWHUQDWLYHLQYHUWHUFRQWUROPRGHV,QVRPHVSHFLILFVLWXDWLRQVLWFDQEHSURILWDEOHWRFKRRVHDQRWKHUFRQWUROVWUDWHJ\IRUWKHLQYHUWHUWKDQWKH&($FRQWURO'&YROWDJHFRQWURO$FORVHGORRSYROWDJHFRQWUROOHUPD\EHXVHGWRNHHSWKHGLUHFWYROWDJHDWDQ\SRLQWRQWKHGFOLQHDWDFRQVWDQWYDOXH7KHFRQVWDQWYROWDJHFRQWUROKDVDIODW8,FKDUDFWHULVWLFLQFRQWUDVWWRWKHFRQVWDQWγFRQWUROFKDUDFWHULVWLFZKLFKKDVDVPDOOQHJDWLYHVORSH7KHYROWDJHFRQWUROKDVDVOLJKWO\KLJKHUYDOXHRIγZKLFKUHVXOWVLQDORZHUULVNIRUFRPPXWDWLRQIDLOXUHV

8l

&RQYHUWHU&&&RQYHUWHU&&

&RQYHUWHU&($&RQYHUWHU&,$

(

&RQYHUWHU&,$

&RQYHUWHU&($

8 l

&RQYHUWHU&&&RQYHUWHU&&

&RQYHUWHU&($&RQYHUWHU&,$

(&RQYHUWHU

&,$

&RQYHUWHU&($

D E


EFRQWURO:LWKFRQVWDQWβFRQWUROβ γXWKDWLVWKHFRPPXWDWLRQPDUJLQSOXVWKHFRPPXWDWLRQRYHUODSDQJOHWKHLQYHUWHU8,FKDUDFWHULVWLFVKDYHDSRVLWLYHVORSH,QORZORDGFRQGLWLRQVFRQVWDQWβFRQWUROJLYHVDGGLWLRQDOVHFXULW\DJDLQVWFRPPXWDWLRQIDLOXUHEXWDWKLJKHUORDGVWKHPLQLPXPγOLPLWPD\EHHQGDQJHUHG7KHUHIRUHWKLVFRQWUROPRGHLVRQO\XVHGDVDEDFNXSFRQWUROGXULQJWUDQVLHQWFRQGLWLRQV $GGLWLRQDOFRQWURODVSHFWV7DSFKDQJHUFRQWURO7KHREMHFWLYHRIWKHWDSFKDQJHUFRQWURODWWKHUHFWLILHULVWRSODFHWKHYROWDJHFHLOLQJRIWKHFRQYHUWHULHWKH8 mon VRDVWRPLQLPLVHWKHUHDFWLYHSRZHUFRQVXPSWLRQ$WWKHLQYHUWHUWKHWDSFKDQJHUFRQWUROPD\EHXVHGWRNHHSWKHGFYROWDJHZLWKLQGHVLUHGOLPLWV,IWKHFRQYHUWHUILULQJDQJOHVαIRUDUHFWLILHURUγIRUDQLQYHUWHUH[FHHGWKHJLYHQUDQJHIRUPRUHWKDQDFHUWDLQWLPHDIHZVHFRQGVWDSFKDQJHUFRQWURORIWKHFRQYHUWHUWUDQVIRUPHUVLVXVHGWRUHVWRUHWKHILULQJDQJOHWRDYDOXHZLWKLQWKHGHVLUHGUDQJH6LQFHWDSFKDQJHUVDUHUHODWLYHO\VORZLQRSHUDWLRQDWLPHGHOD\LVXVHGWR

SUHYHQWXQQHFHVVDU\WDSFKDQJLQJGXULQJWUDQVLHQWFRQGLWLRQV0LQLPXPILULQJDQJOH7KHVLJQDOVIRUFRQWUROOLQJFXUUHQWRUGHUDQGFXUUHQWPDUJLQDUHWUDQVPLWWHGIURPWKHPDVWHUFRQWUROWRWKHFRQYHUWHUVWDWLRQVE\DWHOHFRPPXQLFDWLRQOLQN,IWKLVOLQNIDLOVRULIDGFOLQHIDXOWRFFXUVLWPD\KDSSHQWKDWWKHLQYHUWHUVZLWFKHVWRUHFWLILFDWLRQPRGH7RSUHYHQWWKLVWKHLQYHUWHUKDVDPLQLPXPαOLPLWZKLFKNHHSVWKHILULQJDQJOHODUJHUWKDQ7KHUHFWLILHUKRZHYHULVDOORZHGWRVZLWFKWRLQYHUWHUPRGHαODUJHUWKDQ

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


7KHFXUUHQWRUGHU:KHQWKHGHVLUHGFXUUHQWWKHFXUUHQWRUGHUVKDOOEHHVWDEOLVKHGWKHIROORZLQJOLPLWVPXVWEHFRQVLGHUHG• 0D[LPXPFXUUHQWOLPLW±1RUPDOO\WKHPD[LPXPDOORZHGVKRUWWLPH

FXUUHQWLVUHVWULFWHGWRDURXQGWRWLPHVWKHQRUPDOIXOOORDGFXUUHQW7KHOLPLWLQJIDFWRULVXVXDOO\WKHFXUUHQWUDWLQJRIWKHYDOYHV

• 0LQLPXPFXUUHQWOLPLW±,IWKHFXUUHQWLVORZWKHLQHYLWDEOHULSSOHLQWKHGFFXUUHQWPD\FDXVHLWWREHFRPHLQWHUPLWWHQW7KLVLVQRWDFFHSWDEOHEHFDXVHRIWKHKLJKYROWDJHVWKLVZLOOLQGXFHLQWUDQVIRUPHUZLQGLQJVDQGUHDFWRUV$QRWKHUUHDVRQIRUQRWDOORZLQJWKHFXUUHQWWREHFRPHWRRORZLVWKDWDWORZFXUUHQWVWKHFRPPXWDWLRQRYHUODSEHFRPHVVPDOO,IWKHRYHUODSEHFRPHVWRRVPDOOWKHWZRYROWDJHVWHSVLQWKHEHJLQQLQJDQGLQWKHHQGRIWKHFRPPXWDWLRQPHUJHLQWRRQHODUJHYROWDJHVWHSDQGWKLVFDXVHVH[WUDVWUHVVRQWKHYDOYHV

• 9ROWDJHGHSHQGHQWFXUUHQWRUGHUOLPLW9'&2/±:KHQWKHYROWDJHLVORZLWPD\QRWEHSRVVLEOHWRPDLQWDLQWKHUDWHGFXUUHQW7KHUHDFWLYHSRZHUGHPDQGRIWKHFRQYHUWHUPD\ULVHWRDQXQDFFHSWDEOHOHYHOZKLFKOHDGVWRWKHQHFHVVLW\WRGHFUHDVHWKHFXUUHQWRUGHU7KHLQFUHDVHLQUHDFWLYHSRZHUGHPDQGLVSDUWO\GXHWRWKHKLJKαRUγQHFHVVDU\WRNHHSWKHFXUUHQWKLJKDWORZYROWDJHDQGSDUWO\GXHWRWKHGHFUHDVHLQUHDFWLYHSRZHUVXSSO\IURPILOWHUVDQGFDSDFLWRUVZKHQWKHYROWDJHGHFUHDVHV$GGLWLRQDOO\WKHUHLVDQLQFUHDVHGULVNRIFRPPXWDWLRQIDLOXUHVDQGYROWDJHLQVWDELOLW\DWORZYROWDJHV7KH9'&2/UHGXFHVWKHPD[LPXPFXUUHQWOLPLWZKHQWKHYROWDJHIDOOV

EHORZDVSHFLILHGYDOXHRULID+]FRPSRQHQWLVGHWHFWHGRQWKHGFVLGHFRPPXWDWLRQIDLOXUH7KH9'&2/FKDUDFWHULVWLFVPD\EHDIXQFWLRQHLWKHURIWKHGFYROWDJHRUWKHDFFRPPXWDWLRQYROWDJH,QILJXUHWKH8,FKDUDFWHULVWLFVLQFOXGLQJ9'&2/DUHVKRZQ7KH

LQYHUWHU9'&2/DQGUHFWLILHU9'&2/DUHLGHQWLFDOLQRUGHUWRPDLQWDLQWKHFXUUHQWPDUJLQ

)LJXUH &XUUHQWOLPLWDVDIXQFWLRQRIDFRUGFYROWDJH

,p qTr s 8SSHUOLPLW

/RZHUOLPLW

8 t 8 u 8 RU8p r v

9ROWDJHGHSHQGHQWOLPLW/LPLWV

/9VHOHFW

8 RU8p r v

, p w x y z w p

, p qTr s

, z p w z


&RQWUROFRRUGLQDWLRQ7KHFRQWUROV\VWHPRIDKYGFV\VWHPFDQEHGLYLGHGLQWRWKUHHKLHUDUFKLFDOOHYHOVEULGJHRUFRQYHUWHUFRQWUROSROHFRQWURODQGPDVWHUFRQWUROVHHILJXUH7KHFRQYHUWHUFRQWUROHVWDEOLVKHVWKHILULQJLQVWDQWVDQGGHFLGHVWKH

PLQLPXPOLPLWVIRUWKHILULQJDQJOHVαDQGγ7KHFRQYHUWHUFRQWUROKDVWKHIDVWHVWUHVSRQVHLQWKHFRQWUROKLHUDUFK\7KHSROHFRQWUROFRRUGLQDWHVWKHFRQYHUWHUFRQWUROVZLWKLQWKHVDPHSROH,W

KDQGOHVWDSFKDQJHUFRQWURODQGFRQYHUVHVWKHFXUUHQWRUGHUWRDILULQJDQJOHRUGHUWKDWLVSDVVHGRQWRWKHFRQYHUWHUFRQWURO7KHSROHFRQWURODOVRFRRUGLQDWHVVWDUWLQJXSDQGEORFNLQJRIWKHFRQYHUWHUV7KHPDVWHUFRQWUROGHWHUPLQHVWKHFXUUHQWRUGHUDQGFRRUGLQDWHVWKH

FXUUHQWRUGHUVLJQDOVWRWKHGLIIHUHQWSROHV,WSURYLGHVDOLQNEHWZHHQWKHVHSDUDWHSROHFRQWUROVDQGWKHRYHUDOOV\VWHPFRQWUROWKDWLVWKHFRQWURORIWKHHQWLUHV\VWHPQRWRQO\WKHKYGFSDUW

)LJXUH &RQWUROV\VWHPKLHUDUFK\

&RQY&RQWURO

&RQY&RQWURO

&RQY&RQWURO

&RQY&RQWURO

3ROH&RQWURO

3ROH&RQWURO

&RQYHUWHU3ROH

%LSROH

'&OLQH

2YHUDOOV\VWHPFRQWURO

0DVWHUFRQWURO

|F~ FUU g B FF oo * |F~ FUoT g U~ U


6WDWLRQSROHDQGFRQYHUWHUFRQWURO$QRYHUYLHZRIWKHFRQWUROV\VWHPLVVKRZQLQILJXUHZKHUH, m DQG8 m DUHPHDVXUHGTXDQWLWLHV(DFKFRQYHUWHUKDVDFRQYHUWHUILULQJFRQWURO&)&ZKLFKSURYLGHVWKHILULQJGHOD\DQJOHαWRWKHYDOYHV7KHLQSXWWRWKH&)&LVDQαRUGHUWKDWLVDGHVLUHGYDOXHRIα7KHαRUGHUGHQRWHGα LQILJXUHLVGHWHUPLQHGE\DFXUUHQWFRQWURODPSOLILHU&&$7KH&&$LVQRUPDOO\FRPPRQWRDOOWKHFRQYHUWHUVFRQQHFWHGLQVHULHVLQDSROH7KHLQSXWVLJQDOWRWKH&&$LVDFRQWUROHUURUIRUPHGE\WKHGLIIHUHQFHEHWZHHQWKHFXUUHQWRUGHU, mon DQGWKHPHDVXUHGGLUHFWFXUUHQW, m ,QRQHRIWKHVWDWLRQVDFXUUHQWPDUJLQ, X LVDSSOLHGVHFWLRQ&RQWUROFKDUDFWHULVWLFV7KHFXUUHQWRUGHUWKDWLVXVHGWRIRUPWKHLQSXWVLJQDOWRWKH&&$LV

REWDLQHGIURPDYROWDJHGHSHQGHQWFXUUHQWRUGHUOLPLWHU9'&2/DVH[SODLQHGLQVHFWLRQ7KH9'&2/UHGXFHVWKHFXUUHQWRUGHULIWKHGFYROWDJHGHFUHDVHVIRUH[DPSOHGXULQJDGLVWXUEDQFHVXFKDVDOLQHIDXOWRUQHWZRUNVZLWFKLQJ7KH9'&2/DOVRSOD\VDQLPSRUWDQWUROHLQIDFLOLWDWLQJWKHUHFRYHU\RIWKHSRZHUWUDQVPLVVLRQDIWHUDGLVWXUEDQFH,IWKHKYGFSROHLVRSHUDWHGZLWKFRQVWDQWFXUUHQWFRQWUROWKHUHIHUHQFH

YDOXHRIWKHFXUUHQWRUGHU, ng WKDWLVXVHGDVDQLQSXWVLJQDOWRWKHFXUUHQWRUGHUOLPLWHULVSURYLGHGIURPWKHPDVWHUFRQWURO0&WKDWFRRUGLQDWHVWKHFXUUHQWRUGHUV, n RIDOOWKHFRQYHUWHUVLQWKHVDPHSROH7KHKYGFSROHFDQDOVREHRSHUDWHGLQFRQVWDQWSRZHUFRQWUROPRGH,QWKDW

FDVHWKHFXUUHQWRUGHUUHIHUHQFHYDOXH, ng LVGHWHUPLQHGIURPDSRZHURUGHU3 n E\GLYLGLQJE\WKHGLUHFWYROWDJH8 m 7KHDELOLW\WRFRQWUROWKHDFWLYHSRZHUIORZRIDQKYGFVWDWLRQPD\EHXVHG

WRFRQWUROWKHIUHTXHQF\RIWKHDFV\VWHPRUIRUGDPSLQJRIHOHFWURPHFKDQLFDORVFLOODWLRQV,QWKHVHFDVHVWKHSRZHURUGHU3 n LVFRPSOHPHQWHGE\∆3WKHRXWSXWIURPDSRZHUIUHTXHQF\FRQWUROOHU3)&ZKLFKPD\UHVSRQGWRFKDQJHVLQWKHV\VWHPIUHTXHQF\∆IFKDQJHVLQWKHVSHHGRIDURWDWLQJPDFKLQH∆ωRUWKHWUDQVIHUUHGDFWLYHSRZHURQDQDFOLQH∆3 Y 7KH3)&FDQDOVRVXSSOHPHQWWKHFXUUHQWRUGHUGLUHFWO\E\DGGLQJD∆,LIWKHFRQYHUWHULVRSHUDWHGLQFXUUHQWFRQWUROPRGH$QLQYHUWHUZKLFKRSHUDWHVRQLWVPD[LPXPILULQJDQJOHPLQLPXP

H[WLQFWLRQDQJOHPD\EHHPSOR\HGWRFRQWUROLWVDFRUGFYROWDJH7KHFRQWUROOHUWDNLQJFDUHRIWKLVLVFDOOHGYROWDJHFRQWUROOHU9&7KHLQSXWWRWKH9&LVDFRQWUROHUURU∆8IRUPHGE\WKHGLIIHUHQFHEHWZHHQWKHGHVLUHGYROWDJHIRUDVSHFLILHGQRGHDFRUGFDQGWKHDFWXDOYROWDJHDWWKDWQRGH>@


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

Σ

3)&

0& 9'&2/

Σ

∆3

3

, o , I

&&$

&)&9&

∆8

α

α

α'&

6\VWHP

, 8

, 8

SKDVH$&

6\VWHP∆ ∆ω ∆I 3 ¡ ¢

∆Ι

,


%ORFNLQJVHTXHQFH,QFRQWUDVWWRDQDFOLQHZKHUHWKHRSHUDWLRQRIDFLUFXLWEUHDNHULPPHGLDWHO\LVRODWHVDOLQHDGFOLQNLVVKXWGRZQJUDGXDOO\E\PHDQVRIFRQYHUWHUFRQWURO7KHEORFNLQJRIDSROHLVDFKLHYHGE\UDPSLQJWKHYROWDJHDQGFXUUHQWGRZQWR]HURZLWKLQDIHZKXQGUHGPV7KHUHFWLILHULVWKHQRSHUDWHGQHDUWKHLQYHUVLRQUHJLRQODUJHαZKLFKUHPRYHVDQ\VWRUHGHQHUJ\IURPWKHGFV\VWHP$IWHUWKLVWKHE\SDVVVZLWFKHVDUHFORVHG,IRQHYDOYHJURXSLVWREHEORFNHGDQGRQHWRUHPDLQLQRSHUDWLRQWKH

ILULQJDQJOHRIWKHYDOYHJURXSWREHEORFNHGLVUDPSHGWR°7KHQWKHE\SDVVVZLWFKLVFORVHG 'HEORFNLQJVHTXHQFH$W\SLFDOVWDUWLQJVHTXHQFHPD\SURFHHGDVIROORZV 7KHFRQYHUWHUWKDWVWDUWVILUVWHLWKHUDUHFWLILHURUDQLQYHUWHUHVWDEOLVKHV

YDOYHILULQJDQGFRQGXFWLRQ7KHILULQJDQJOHLVKHOGDW°WR°ZKLFKUHVXOWVLQDORZGFYROWDJH

7KHRWKHUFRQYHUWHUDOVRHVWDEOLVKHVYDOYHILULQJ7KHORZYROWDJHDQGKLJKILULQJDQJOHLVPDLQWDLQHGDQGWKHFXUUHQWLVKHOGDWDURXQGWRSX

:KHQWKHVWDUWXSLVFRQFOXGHGWKHYROWDJHLVLQFUHDVHG:KHQWKHYROWDJHKDVUHDFKHGDVHWSRLQWRIWRRIUDWHGYDOXHWKHFXUUHQWRUGHULVUHOHDVHGWRUHDFKWKHSUHVHWYDOXH

0XOWLWHUPLQDOV\VWHPV$PXOWLWHUPLQDOKYGFV\VWHPLVXVXDOO\RSHUDWHGLQVXFKDZD\WKDWDOOFRQYHUWHUVH[FHSWRQHDUHFRQWUROOLQJWKHLUFXUUHQWVDFFRUGLQJWRDVSHFLILHGUHIHUHQFHYDOXH7KHODVWFRQYHUWHUZKLFKLVXVXDOO\DQLQYHUWHULVWKHQJLYHQWKHUHVSRQVLELOLW\WRFRQWUROWKHGFYROWDJHWRDJLYHQYDOXHRUWRNHHSWKHH[WLQFWLRQDQJOHγFRQVWDQW7KHFRQWUROSULQFLSOHVIRUDPXOWLWHUPLQDOKYGFV\VWHPDUHDJHQHUDOLVDWLRQ

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


,IWKHFRQYHUWHUVDUHFRQQHFWHGLQSDUDOOHODFRRUGLQDWLRQRIWKHFXUUHQWRUGHUVLVQHFHVVDU\VRWKDWWKHVXPRIWKHFXUUHQWRUGHUVRIDOOUHFWLILHUVHTXDOVWKHVXPRIWKRVHRIWKHLQYHUWHUVPLQXVWKHFXUUHQWPDUJLQ7KHUHDUHVRPHGUDZEDFNVZLWKDSDUDOOHOFRQQHFWHGPXOWLWHUPLQDOKYGF

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

GLIIHUHQWSDUWVRIWKHV\VWHP /RVVHVDUHKLJKHUDVFRPSDUHGWRWKHSDUDOOHOFRQQHFWHGV\VWHPGXHWR

ORZHUYROWDJHV$SHUPDQHQWOLQHIDXOWZLOOFDXVHDWRWDOV\VWHPLQWHUUXSWLRQ

&KDSWHU0RGHOOLQJDQGVRIWZDUH

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

KDQGOHGE\WKH6LPSRZSURJUDPSDFNDJHWKHPD[LPXPVL]HRIWKHSRZHUV\VWHPLVGHWHUPLQHGE\WKHDYDLODEOHFRPSXWHUFDSDFLW\0RUHLQIRUPDWLRQDERXW6LPSRZDQGLWVIHDWXUHVFDQEHIRXQGLQ>@DQG

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

KDVWREHH[DFWO\RQHVODFNEXVLQHDFKDFQHWZRUN$FWLYHDQGUHDFWLYHSRZHURIORDGVVKXQWVHWFDUHVHWWR]HUR

7KHSRZHUIORZLVVROYHGLQDG\QDPLFVLPXODWLRQZKHUHWKHSRZHURIORDGVLVLQFUHDVHGWRWKHGHVLUHGYDOXHDVDIXQFWLRQRIWLPH

7KHPD[LPXPDQGPLQLPXPOLPLWVIRUUHDFWLYHSRZHUDUHLQFUHDVHGWRDERXWWLPHVWKHYDOXHVHWE\WKHXVHU7KLVLVWRNHHSWKHYROWDJHYDULDWLRQVPDOO

7KHUHDFWLYHSRZHUOLPLWVDUHWKHQGHFUHDVHGWRZDUGVWKHGHVLUHGYDOXHVDVDIXQFWLRQRIWLPH


$IWHUDPDMRUHYHQWWKHWLPHVWHSLVGHFUHDVHGWRRQHSHUFHQWRIWKHLQLWLDOYDOXH7KLVLVHTXLYDOHQWWRDQRUGLQDU\G\QDPLFVLPXODWLRQ

,QRUGHUWRVROYHWKHSRZHUIORZZLWKWKHG\QDPLFPHWKRGWKHEDFNZDUGGLIIHUHQWLDWLRQPHWKRGLVXVHG7KHUHE\IDVWFKDQJHVDUHGDPSHGRXWZKLFKPHDQVWKDWWKHVWDWLRQDU\VROXWLRQLVUHDFKHGHDVLHU

7RVSHHGXSWKHFRPSXWDWLRQSURFHVVVRPHPLQRUHYHQWVDUHQRWKDQGOHGXQWLOWKHHQGRIWKHWLPHVWHS7KLVLVDFFHSWDEOHVLQFHWKHH[DFWWLPHIRUDQHYHQWLVQRWLPSRUWDQWLQDSRZHUIORZFDOFXODWLRQ

7KHGHULYDWLYHVRIDOOYDULDEOHVDUHFKHFNHGDQGLIWKHYDOXHVRIWKHGHULYDWLYHVDUHOHVVWKDQDVSHFLILHGYDOXHVWHDG\VWDWHLVUHDFKHGDQGWKHDFWLYHSRZHULVVHWWRLWVGHVLUHGYDOXHV7KHFRQWLQXDWLRQRIWKHVLPXODWLRQLVSHUIRUPHGZLWKQHZIDVWHUWLPHFRQVWDQWV

7KHGHULYDWLYHVRIDOOYDULDEOHVDUHFKHFNHGDJDLQDQGLIVWHDG\VWDWHLVUHDFKHGWKHWLPHFRQVWDQWVDUHVHWWR]HURDQGWKHVLPXODWLRQLVFRQWLQXHG

:KHQVWHDG\VWDWHLVUHDFKHGDJDLQZLWK]HURWLPHFRQVWDQWVWKHWROHUDQFHLVGHFUHDVHGWRWKHQRUPDOYDOXHDQG1HZWRQLWHUDWLRQVDUHSHUIRUPHGXQWLOFRQYHUJHQFHLVUHDFKHG

8QWLOQRZWKHWUDQVIRUPHUUDWLRVKDYHEHHQDVVXPHGWREHFRQWLQXRXVO\YDULDEOHLQRWKHUZRUGVWKHUDWLRPRVWVXLWHGIRUWKHFDOFXODWLRQVKDVEHHQXVHG1RZWKHUDWLRVDUHVHWWRWKHSRVLWLRQFORVHVWWRWKHRSWLPDOFDOFXODWHGYDOXHDQG1HZWRQLWHUDWLRQVDUHSHUIRUPHGDJDLQXQWLOFRQYHUJHQFHLVUHDFKHG

3XUH1HZWRQPHWKRG7KHSXUH1HZWRQPHWKRGLVDQDOWHUQDWLYHWRWKHG\QDPLFPHWKRG,WLVPRUHGLIILFXOWWRILQGDVROXWLRQZLWKWKLVPHWKRGEXWLIDVROXWLRQLVUHDFKHGLWXVHVOHVVFRPSXWDWLRQWLPHWKDQLQWKHFDVHRIWKHG\QDPLFDSSURDFK7KH1HZWRQPHWKRGLVSUHIHUDEO\XVHGZKHQLWLVNQRZQWKDWDSRZHUIORZVROXWLRQLVFORVHDWKDQGHJLIVRPHPLQRUFKDQJHVKDVEHHQPDGHLQWKHV\VWHP,IWKHV\VWHPLVYHU\ODUJHPRUHWKDQQRGHVLWPLJKWEHIHDVLEOHWRXVHWKHG\QDPLFPHWKRGIRUWKHILUVWVWHSVDQGWKHQFKDQJHWRWKH1HZWRQPHWKRG ,QLWLDOO\DOOYROWDJHVDUHVHWWRWKHGHVLUHGYROWDJHRIWKHVODFNEXVDQG

DFWLYHDQGUHDFWLYHSRZHURIORDGVHWFDUHVHWWR]HUR7KHWUDQVIRUPHUUDWLRVDUHDVVXPHGWREHFRQWLQXRXVO\YDULDEOH,QFRQWUDVWWRWKHG\QDPLFPHWKRGDOOWLPHFRQVWDQWVDUHVHWWR]HURLPPHGLDWHO\ZKLFKLPSOLHVWKDWWKHDFWLYHSRZHUUHDFKHVWKHVHWYDOXHDWRQFH

1HZWRQLWHUDWLRQVDUHSHUIRUPHGXQWLOFRQYHUJHQFHLVUHDFKHG 7KHWUDQVIRUPHUUDWLRVDUHVHWWRWKHSRVLWLRQVFORVHVWWRWKHFDOFXODWHG

VROXWLRQDQG1HZWRQLWHUDWLRQVDUHSHUIRUPHGDJDLQXQWLOFRQYHUJHQFHLVUHDFKHG

)RUWKLVSURMHFWWKHG\QDPLFPHWKRGLVXVHGH[FOXVLYHO\7KHUHZDVQRQHHGWRHPSOR\WKHSXUH1HZWRQPHWKRGVLQFHWKHFRPSXWDWLRQWLPHVZHUHVKRUWHQRXJK


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

DQGDQLQVWDQWDQHRXVYDOXHFRPSXWDWLRQPRGH7KHVLPXODWLRQVSHUIRUPHGLQWKLVSURMHFWDUHFDUULHGRXWLQWKHWUDQVLHQWVWDELOLW\PRGH,QWKHWUDQVLHQWVWDELOLW\PRGHWKHSRZHUIUHTXHQF\FRPSRQHQWVRIWKHDF

V\VWHPDQGWKHDYHUDJHYDOXHVRIWKHGFV\VWHPYROWDJHVDQGFXUUHQWVDUHFDOFXODWHGE\SKDVRUPRGHOV7KHSULPDU\FRPSRQHQWVDUHUHSUHVHQWHGDVSRVLWLYHQHJDWLYHDQG]HURVHTXHQFHVTXDQWLWLHVLQFDVHRIXQV\PPHWULFDOFRQGLWLRQVEXWIRUV\PPHWULFDOFRQGLWLRQVDVLQJOHSKDVHPRGHOZLWKRQO\SRVLWLYHVHTXHQFHSDUDPHWHUVDUHXVHG:LWKWKHH[FHSWLRQRIWKHWUDQVPLVVLRQV\VWHPHOHPHQWVDQGVWDWLFORDGVWKHV\VWHPFRPSRQHQWVDUHUHSUHVHQWHGE\G\QDPLFPRGHOVGHVFULEHGE\GLIIHUHQWLDOHTXDWLRQV7KHWLPHVWHSRIWKHFDOFXODWLRQVLVDGDSWHGDXWRPDWLFDOO\DVPDOOHUWLPHVWHSLVXVHGGXULQJSHULRGVZLWKUDSLGO\FKDQJLQJWUDQVLHQWVODUJHUWLPHVWHSVDUHXVHGZKHQWKHVWDWHFKDQJHVEHFRPHVORZHU $&V\VWHPPRGHO,QWKLVVHFWLRQWKHPRGHOVXVHGLQWKLVWKHVLVZLOOEHGHVFULEHG7KHUHDUHVHYHUDORWKHURSWLRQVLQ6LPSRZ)RUPRUHLQIRUPDWLRQRQ6LPSRZPRGHOVVHH>@ 7UDQVPLVVLRQV\VWHPHOHPHQWV7KHDFWUDQVPLVVLRQOLQHVDUHUHSUHVHQWHGDVπOLQNVZLWKUHVLVWDQFHLQGXFWDQFHDQGVXVFHSWDQFH%XVHVKDYH]HURLPSHGDQFH6KXQWLPSHGDQFHVDUHUHSUHVHQWHGE\DFWLYHDQGUHDFWLYHSRZHUDQGQRPLQDOYROWDJH /RDGV7KHORDGVDUHUHSUHVHQWHGE\WKHDFWLYHDQGUHDFWLYHSRZHUFRQVXPSWLRQDWQRPLQDOYROWDJH)RUWKHG\QDPLFVLPXODWLRQWKHYROWDJHGHSHQGHQF\H[SRQHQWVRIWKHORDGV$DQG%DUHJLYHQ

$8833 £

⋅= ¤ DQG

%8844 ¥

⋅= ¦


ZKHUH8 § LVWKHEDVHYROWDJHRIWKHORDGEXV8LVWKHDFWXDOYROWDJHDWWKHVDPHEXVDQG3 ¨ DQG4 ¨ LVWKHORDGSRZHUDWQRPLQDOYROWDJH)RUVRPHORDGVDIUHTXHQF\GHSHQGHQF\LVJLYHQDVZHOO 6\QFKURQRXVPDFKLQHV$OOJHQHUDWLRQH[FHSWDWWKHVODFNEXVDUHRIWKHW\SH83ZKLFKPHDQVWKDWLQWKHSRZHUIORZFDOFXODWLRQWKHYROWDJHDQGWKHDFWLYHSRZHUDUHNHSWFRQVWDQW)RUPRVWSURGXFWLRQVRXUFHVPD[LPXPDQGPLQLPXPUHDFWLYHSRZHUOLPLWVDUHJLYHQ$WWKHVODFNEXVWKHYROWDJHDQGWKHSKDVHDQJOHDUHNHSWFRQVWDQW)RUWKHG\QDPLFVLPXODWLRQWZRGLIIHUHQWPDFKLQHPRGHOVDUHXVHGLQWKH

V\VWHP%RWKPRGHOVKDYHRQHILHOGZLQGLQJDQGRQHGDPSHUZLQGLQJLQGD[LVEXWRQHRIWKHPRGHOVKDYHRQHGDPSHUZLQGLQJLQTD[LVDVZHOOZKLOHWKHRWKHUPRGHOKDVWZRGDPSHUZLQGLQJVLQTD[LV%RWKPRGHOVLQFOXGHVDWXUDWLRQ$OOV\QFKURQRXVPDFKLQHVDUHHTXLSSHGZLWKH[FLWHUVDQGPRVWRIWKHP

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

PRGHOVKDOODOORZWKHKYGFV\VWHPWRLQWHUDFWZLWKRWKHUSRZHUV\VWHPFRPSRQHQWVLQDUHDOLVWLFZD\,WGRHVQRWQHHGWRSURGXFHWKHGHWDLOVRIWKHLQWHUQDOVWDWHRIWKHFRQYHUWHUV+9'&V\VWHPVZLWKDQDUELWUDU\QXPEHURIFRQYHUWHUVPXOWLWHUPLQDO

FDQEHUHSUHVHQWHGLQ6LPSRZ


0DLQFRPSRQHQWV>@'&WUDQVPLVVLRQRYHUKHDGOLQHVDUHPRGHOOHGE\WKHLUUHVLVWDQFHDQGLQGXFWDQFHDQGGFFDEOHVDUHUHSUHVHQWHGE\UHVLVWDQFHDQGFDSDFLWDQFH7KHGFUHDFWRUVDUHPRGHOOHGDFFRUGLQJWRWKHLULQGXFWDQFH%RWKPRQRSRODUDQGELSRODUKYGFWUDQVPLVVLRQFDQEHUHSUHVHQWHG7KHFRQYHUWHUVDUHRIWKHFXUUHQWVRXUFHOLQHFRPPXWDWHGW\SHDQGDUH

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

&RQWURO6\VWHP7KHKYGFFRQWUROV\VWHPPRGHOOHGLQ6LPSRZLQFRUSRUDWHVDOOWKHQHFHVVDU\DQGUHOHYDQWFRQWUROIXQFWLRQV>@7KHVHDUHUHSUHVHQWHGE\WUDQVIHUIXQFWLRQVDQGLQFOXGHV &XUUHQWILULQJFRQWURO&)&SURYLGHVWKHGHOD\DQJOHWRWKHFRQYHUWHU &XUUHQWFRQWURODPSOLILHU&&$UHJXODWHVWKHFXUUHQWWKURXJKWKH

FRQYHUWHU &XUUHQWRUGHUOLPLWHU&2/UHGXFHVWKHGFFXUUHQWIRUORZGFYROWDJHV

DQGIDFLOLWDWHVWKHVWDUWXSRIWKHKYGFV\VWHPDIWHUDGLVWXUEDQFH 0DVWHUFRQWUROOHU0&DKLJKHUOHYHOFRQWUROOHUWKDWFRRUGLQDWHVWKH

FXUUHQWRUGHUVLQWKHGLIIHUHQWFRQYHUWHUV 3RZHUIUHTXHQF\FRQWUROOHU3)&DGMXVWVWKHDFWLYHSRZHURIDFRQYHUWHU

LQRUGHUWRFRQWUROWKHIUHTXHQF\RUGDPSHOHFWURPHFKDQLFDORVFLOODWLRQV $YROWDJHFRQWUROOHU9&YDULHVWKHPD[LPXPILULQJDQJOHRIDQLQYHUWHU

RUWKHPLQLPXPILULQJDQJOHRIDUHFWLILHUE\ZKLFKLWVUHDFWLYHSRZHUFDQEHXVHGWRFRQWURODQGVWDELOLVHLWVYROWDJH

0RUHGHWDLOVDERXWWKHFRQWUROV\VWHPLQ&KDSWHU&RQWURORIKYGFFRQYHUWHUVDQGLQ$SSHQGL[%&RQYHUWHUPRGHOOLQJLQ6LPSRZ7KHFRQWURORIWKHFRQYHUWHUWUDQVIRUPHUVLVRUJDQLVHGDVIROORZV7KH

UHFWLILHUWUDQVIRUPHUFRQWUROVWKHILULQJDQJOHRIWKHUHFWLILHUαDQGWKHSKDVHDQJOHRIWKHDFQRGHWRZKLFKWKHWUDQVIRUPHULVFRQQHFWHG7KHLQYHUWHUWUDQVIRUPHUFRQWUROVWKHPDJQLWXGHDQGSKDVHDQJOHRIWKHYROWDJHRIWKHDFQRGHWRZKLFKWKHWUDQVIRUPHULVFRQQHFWHG


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

PRGHOPD\QRWEHYDOLGGXULQJFRQGLWLRQVZLWKYHU\ORZDFYROWDJHVDQGKLJKGFFXUUHQWV

&KDSWHU7KHWHVWQHWZRUN

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

%86 7'& '& '& '&

7 %86


%XV 5HIHUHQFHEXV8 © N9%XV 8 © N9*HQHUDWRUEXV 6 © 09$*HQHUDWRUEXV 6 © 09$3 © 0:6KXQWFDSDFLWRUV 4 © 09$8 © N97UDQVIRUPHUV 6 © 09$&RQYHUWHUV 8 ª(© N9, ª(© N$, « N$, ª¬ N$6HULHVUHDFWRUV 5 Ω/ +'FOLQH / NP$FOLQH / NP$FWLYHORDGEXV 3 0:5HDFWLYHORDGEXV 4 09$U7DEOH 6PDOOV\VWHPGDWD 7HVWFDVHVDQGUHJXODWLRQ7RHYDOXDWHWKHGLIIHUHQWUHJXODWLRQSULQFLSOHVDQGWRILQGRXWKRZWRWXQHWKHUHJXODWRUVWZRGLIIHUHQWGLVWXUEDQFHVKDYHEHHQXVHG 7KHDFOLQHLVGLVFRQQHFWHG 6RPHRIWKHORDGDWEXVLVGLVFRQQHFWHG7KHIROORZLQJPDLQUHJXODWLRQRSWLRQVKDVEHHQVLPXODWHG :LWKRXWSRZHUIUHTXHQF\FRQWUROOHU3)&WKDWLVZLWKWKHEDVLFFRQWUROV

RQO\ :LWKD3)&VHHVHFWLRQDQG$SSHQGL[%UHVSRQGLQJWRYDULRXV

LQSXWVLJQDOV 7KHIUHTXHQF\LQEXV 7KHVSHHGRIWKHJHQHUDWRULQEXV 7KHWUDQVIHUUHGDFWLYHSRZHURQWKHDFOLQHRQO\IRUWHVWFDVH

:LWKDYROWDJHFRQWUROOHUERWKWRJHWKHUZLWKD3)&DQGRQLWVRZQ)RUHDFKUHJXODWLRQDOWHUQDWLYHWKHGLIIHUHQWUHJXODWRUSDUDPHWHUVKDVEHHQYDULHG7KHLQIOXHQFHRIWKHORDGYROWDJHGHSHQGHQF\KDVDOVREHHQLQYHVWLJDWHG7KHYROWDJHGHSHQGHQF\RIWKHORDGFDQEHH[SUHVVHGDV

$8833 ®

⋅= ¯ DQG

%8844 °

⋅= ±

8 ² LVWKHQRPLQDOYROWDJHDWWKHORDGEXVDQG8LVWKHDFWXDOYROWDJHDWWKHVDPHEXV3 ³ DQG4 ³ LVWKHQRPLQDOORDGSRZHUDWQRPLQDOYROWDJH7KHH[SRQHQWV$DQG%KDYHEHHQYDULHGEHWZHHQFRUUHVSRQGLQJWRDFRQVWDQWSRZHUORDGDQGFRUUHVSRQGLQJWRDFRQVWDQWLPSHGDQFHORDG


7KHODUJHV\VWHP7KHH[SHULHQFHIURPWKHVPDOOWHVWV\VWHPKDVEHHQLPSOHPHQWHGLQDODUJHUWUDQVPLVVLRQV\VWHP 2ULJLQ6LQFHWKHDLPRIWKHSURMHFWZDVWRLQYHVWLJDWHWKHFRQVHTXHQFHVRIWUDQVIHUULQJDQLQFUHDVLQJDPRXQWRIWKHSRZHULQDWUDQVPLVVLRQV\VWHPZLWKKYGFDWHVWWUDQVPLVVLRQV\VWHPZDVQHHGHG7KHFULWHULDIRUWKLVV\VWHPZDVWKDWLWVKRXOGEHODUJHHQRXJKWRSHUPLWDVWHSZLVHLQFUHDVHRIKYGFWUDQVPLVVLRQEXWVPDOOHQRXJKWREHHDVLO\DQDO\VHG,WVFKDUDFWHULVWLFVVKRXOGDOVREHZHOONQRZQ2QWKHEDVLVRIWKHVHFULWHULDWKH&LJUp1RUGLFQHWZRUNZDVFKRVHQDVWHVW

QHWZRUN7KLVV\VWHPLVEDVHGRQWKHWUDQVPLVVLRQV\VWHPLQ6FDQGLQDYLDDQGLVLQWHQGHGIRUVLPXODWLRQRIWUDQVLHQWVWDELOLW\DQGORQJWHUPG\QDPLFV6YHQVND.UDIWQlWXVHVWKLVQHWZRUNLQWKHLURSHUDWRUWUDLQLQJDQGD6LPSRZPRGHODOUHDG\H[LVWV7KLVVLPSOLILHVWKHLPSOHPHQWDWLRQRIWKHQHWZRUN *HQHUDORXWOLQHRIWKHQHWZRUN7KHRULJLQDO1RUGLFQHWZRUNFRQVLVWVRIIRXUPDMRUSDUWV1RUWK±/DUJHDPRXQWRIK\GURJHQHUDWLRQDQGVRPHORDG&HQWUDO±0XFKORDGDQGDJRRGGHDORIWKHUPDOSRZHUJHQHUDWLRQ6RXWKZHVW±6RPHWKHUPDOSRZHUJHQHUDWLRQDQGVRPHORDG([WHUQDO±&RQQHFWHGWRWKH1RUWKZLWKDPL[WXUHRIJHQHUDWLRQDQGORDG6LQFHWKHQHWZRUNLVEDVHGRQWKH6FDQGLQDYLDQWUDQVPLVVLRQV\VWHPLWLVTXLWHH[WHQVLYHLQWKHQRUWKVRXWKGLUHFWLRQ%HWZHHQQRUWKDQGFHQWUDOWKHUHDUHORQJWUDQVPLVVLRQOLQHVZKHUHWKHPDMRUSDUWRIWKHSRZHUWUDQVIHUWDNHVSODFH7KH6RXWKZHVWLVUDWKHUORRVHO\FRQQHFWHGWRWKHPDLQV\VWHP7KHQHWZRUNFRQVLVWVRIEXVHVZLWKDQRPLQDOYROWDJHRIN9

EXVHVDWN9DQGEXVHVDWN9$GGLWLRQDOO\VRPHORDGEXVHVDUHORFDWHGDWWKHORZYROWDJHVLGHRIWUDQVIRUPHUVZLWKWDSFKDQJHUV*HQHUDWLRQDQGORDGUDWLQJVIRUWKHRULJLQDOQHWZRUNFDQEHIRXQGLQ

DSSHQGL[$)RUPRUHGHWDLOVDERXWWKH1RUGLFQHWZRUNDQGQHWZRUNGDWDVHH>@


)LJXUH 6WUXFWXUHRIWKHPRGLILHGWHVWV\VWHP

´µ<¶:·

´µ<¶U¸

´µ&··

´µ¹·(¸

´µº¸¸ ´µº¸<·

´µº»<· ´µº»¸

´µ:´¸

´µ:´´ ´µ´»

´µ:´¼

´µ:´8¶´µ´&·

´µ:´½

´µ:½¾·

´µ¼&·

´µ:¼¸

´µ:¼»

¿À<ÁÂ Ã Ä<Å ·

¿À8ÁÂÃ Ä<Å ¸

¿À8ÁÂÃ Ä<Å »

Southwest

Central

NorthExternal

Æ(ÇÈ(ÈÉ:Ê*ËÌ ÈÈ(ÈÉ:ÍÌ ÈÈ(ÈÉºÍÇ(ÈÈÉ8Ê*ËÎ

ÇFÈÈÉ8Ê*ËÏ ÈÈÉ8ÍÏ ÈFÈÉ8ÍÐÑÈFÈÉ8ÊiËÎ

ÆFÈÈÉ8Ê*ËÎ

ÐÑÈFÈÉ8ÊiËÎ

ÏFÒ ÈÉºÊ*ËÏ ÈFÈÉºÍÌUÓIÒoÔ ÇÉ:Ê*Ë

Ð Ì ÈFÈÉºÊ*ËÕgÖ× ØÙUÚUÛUÖ

Ï ÈÈÉ8Ê*ËÌ ÇÈÉ8ÍÌÓ Æ(È(ÈÉ:Ê*ËÌÓIÏTÔ ÇÉ:Í

Ô ÈÈÉ8ÊiËÒ(Ï ÈÉ8Í

Ï ÈÈÉ8Ê*ËÈÉºÍ

Ç(ÆÈÉ8ÍÐ Ò ÈÉ8Ê*ËÎ

Ð(ÐIÇFÈÉºÍÐ Ï ÈÉ8Ê*ËÎÆ(ÈÈÉ8ÍÐÜÆÝÉ8Ê*ËÎ

Ý(ÈÈÉ8ÍÏ È Ï É8Ê*ËÎÝ(ÇÈÉ8ÍÐÜÆÈÉ8Ê*ËÎÞ Ì ÈFÈÉºÊ*ËÎ

Þ Ì È(ÈÉ:ÊËÎ

Þ ÐÜÈFÈÉºÊ*ËÎ

Ô ÈÈÉ8ÍÌ ÇÈÉ8Ê*ËÎ

ÐÜÈÈÉ8ÍÇ(ÈÉºÊiËÎ

ÌUÓIÒ ÈFÈÉºÊiËÌUÓ Ç(ÆFÈÉºÍ

ß ÈÈÉ8ÍÏ È Ì É8Ê*ËÎ

Þ ÐÑÈ(ÈÉ:Ê*ËÎ

Ô ÈÈÉ8Ê*ËÒ ÈÈÉ8Í ÇFÇÈÉ8Ê*ËÆFÈÈÉ8Í

ÇFÈÈÉ8ÍÐÑÆÝÉ8Ê*ËÎ

Ï ÈÈÉ8ÍÐÑÈÈÉ8Ê*ËÎ

Ò ÈÈÉ8Ê*ËÇ Ï ÈÉ8Í

ÌUÓIÒ È(ÈÉ:Ê*ËÌUÓ Ç Ï ÈÉ:ÍÇ(ÝÈÉ8ÍÏ ÈÈÉ8Ê*ËÎ

à¾á Ð

à&á Ç

â ãä â ãå

â ãæ

à&áTÌà&áTÏ

à¾áß

à&á Ð Ïâ ãç â ãèé â ãèè

â ãèê

â ãèæ â ãèë â ãèä â ãèå

ì áÌì á Ð Ò

ì áÏíãè

ì á Ç

ì á Æ

ì á Ý

íãå íãî

íãèæ íãèë

ì áÒ

ì á ÐFÐíãèé

íãèê

íãèï

ÌUÓIÒ ÈFÈÉºÍ


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

ðiñòóóó II33 ⋅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


%DVLFDOO\WZRW\SHVRIYROWDJHFROODSVHPD\RFFXU $QHYHQWWKDWZHDNHQVWKHWUDQVIHUV\VWHPIURPQRUWKWRFHQWUDOPD\FDXVH

DYROWDJHFROODSVHLQWKHUHJLRQEHWZHHQWKHVHWZRDUHDVHJEXV $Q HYHQW WKDW ZHDNHQV WKH YROWDJH VXSSRUW LQ WKH FHQWUDO ORDG DUHD PD\

FDXVHDYROWDJHFROODSVHLQWKDWUHJLRQHJEXV 7HVWFDVHV7RFRPSDUHGLIIHUHQWV\VWHPFRQILJXUDWLRQVDQGDQDO\VHGLIIHUHQFHVLQVWDELOLW\RUWUDQVIHUFDSDFLW\VRPHWHVWFDVHVKDGWREHGHILQHG,WZDVGHFLGHGWKDWWKHWHVWFDVHVVKRXOGOHDGWRV\VWHPFROODSVHLQWKHEDVHFDVHLHSXUHDFQHWZRUNLQRUGHUWREHDEOHWRHVWDEOLVKDQLPSURYHPHQWRIWKHV\VWHPEHKDYLRXUZLWKDGLIIHUHQWV\VWHPFRQILJXUDWLRQ7KHVHOHFWLRQRIWHVWFDVHVZDVEDVHGRQVFHQDULRVXVHGE\6YHQVND.UDIWQl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lFNQXFOHDUSRZHUSODQW


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


&KDSWHU6LPXODWLRQVDQGUHVXOWV

&KDSWHU 6LPXODWLRQVDQGUHVXOWV,QWKLVFKDSWHUWKHVLPXODWLRQVDQGWKHUHVXOWVDUHSUHVHQWHGLQWKHRUGHUWKH\ZHUHSHUIRUPHG7KHILUVWVLPXODWLRQVZHUHGRQHXVLQJWKHPRGLILHG1RUGLFV\VWHPDQGDQKYGFUHJXODWLRQWKDWSURYHGWREHXQVXLWDEOHIRUWKLVSXUSRVH7KHUHIRUHLWZDVGHFLGHGWKDWDVPDOOV\VWHPZRXOGEHLQWURGXFHGWRILQGDPRUHVXLWDEOHFRQWUROVWUDWHJ\$IWHUWKDWWKHODUJHV\VWHPZDVXVHGDJDLQXVLQJWKHH[SHULHQFHVREWDLQHGIURPWKHVPDOOV\VWHPVLPXODWLRQV 7KHILUVWKYGFPRGHO±VWDJH7KHLQLWLDODWWHPSWWRPRGHOWKHKYGFOLQNZLWKLWVUHJXODWLRQZDVGRQHRQWKHEDVLVRIWKH6LPSRZPRGHOXVHGIRUVLPXODWLRQVRIWKHKYGFOLQNEHWZHHQ6ZHGHQDQG3RODQGWKH6ZH3ROOLQN7KHUHJXODWLRQRIWKHKYGFFRQYHUWHUVLVEDVLFFRQVWDQWSRZHUFRQWUROZKLFKFKDQJHVWRFRQVWDQWFXUUHQWFRQWUROLIWKHGFYROWDJHGHFUHDVHVEHORZDVSHFLILHGYDOXHLQWKLVFDVHSXRIWKHUDWHGGFYROWDJH6LPXODWLRQVZHUHSHUIRUPHGIRUILYHGLIIHUHQWJHRJUDSKLFDOORFDWLRQVRIWKH

KYGFOLQNDQGIRUWKHILYHGLIIHUHQWWHVWFDVHVGHVFULEHGLQ&KDSWHU7KHGLIIHUHQWORFDWLRQVDUHQDPHG$(DQGDUHVKRZQLQILJXUH2QO\RQHKYGFOLQNDWDWLPHLVVLPXODWHG7KHORFDWLRQVZHUHFKRVHQRQEDVLVRIWKHORDGLQJRIWKHOLQHVDWQRUPDOKLJKORDGRSHUDWLRQ>@7KHUDWLQJDQGWKH6&5VKRUWFLUFXLWUDWLRRIWKHKYGFOLQNLQWKHGLIIHUHQWSRVLWLRQVDQGWKHLQLWLDOSRZHUWUDQVIHUVHWWLQJVDUHVKRZQLQWDEOH7KHLQLWLDOSRZHUWUDQVIHURQWKHKYGFOLQNLVDSSUR[LPDWHO\WKHVDPHDVWKHSRZHUWUDQVIHURQWKHFRUUHVSRQGLQJDFOLQHLQWKHFDVHRIDSXUHDFV\VWHP7KH6&5LVFDOFXODWHGDV>@

ôõ ô

3GF66&5 =

+HUH6 öU÷ LVWKHVKRUWFLUFXLWOHYHORIWKHDFQHWZRUNDWWKHFRQYHUWHUWHUPLQDO

DFEXVZLWKSXYROWDJHDQG3GF ÷ LVWKHUDWHGGFSRZHURIWKHFRQYHUWHU3RVLWLRQ 5DWLQJ ,QLWLDOSRZHUWUDQVIHU 6&5$ 0: 0: % 0: 0: & 0: 0: ' 0: 0: ( 0: 0:

7DEOH 5DWLQJ6&5VKRUWFLUFXLWUDWLRDQGLQLWLDOSRZHUWUDQVIHURIWKHKYGFOLQNLQGLIIHUHQWSRVLWLRQV7KH6&5IRUSRVLWLRQ'GHSHQGVRQWKHGLUHFWLRQRIWKHSRZHUIORZ7KHORZHUYDOXHLVZLWKWKHUHFWLILHUFRQQHFWHGWREXV


$VH[SODLQHGLQVHFWLRQDOOWHVWFDVHVZHUHVHOHFWHGVXFKWKDWWKH\ZRXOGOHDGWRDV\VWHPFROODSVHLQFDVHRIDSXUHDFQHWZRUN$OOVLPXODWLRQVVWDUWIURPKHDY\EXWVWDEOHORDGFRQGLWLRQV7KHORDGGLVWULEXWLRQRIWKHPRGLILHG1RUGLFQHWZRUNLVJLYHQLQDSSHQGL[&)LJXUHV±VKRZVVRPHFXUYHVIURPWKHVWDJHVLPXODWLRQV

&DVH7KHVFHQDULRLQFDVHLVGHVFULEHGEHORZ7KHVLPXODWLRQUHVXOWVDUHVKRZQLQWDEOHDQGILJXUHDDQGE7LPH (YHQWW V 'LVFRQQHFWLRQRIOLQH)/EHWZHHQEXVHVDQGW V 'LVFRQQHFWLRQRIRIWKHORDGDWEXV0:

09$UW V 'LVFRQQHFWLRQRIDQRWKHURIWKHORDGDWEXV0:

09$UW V 'LVFRQQHFWLRQRIWKHORDGDWEXV0:09$UW V 'LVFRQQHFWLRQRIRIWKHORDGDWEXV0:

09$U:LWKWKHGFOLQNLQSRVLWLRQ'WKHGLVFRQQHFWLRQRIOLQH)/UHPRYHVWKHRQO\V\QFKURQRXVFRQQHFWLRQEHWZHHQWKHVRXWKZHVWSDUWDQGWKHUHPDLQGHURIWKHV\VWHP7KHKYGFOLQNLVWKHQDFWLQJDVDFRQQHFWLRQEHWZHHQWZRQRWV\QFKURQLVHGV\VWHPV

:KHQDJHQHUDWRUIDOOVRXWRISKDVHWKHDQJOHEHWZHHQWKLVJHQHUDWRUDQGWKHUHIHUHQFHPDFKLQHKDVH[FHHGHG°

&DVH3XUHDF $WW VWKHJHQHUDWRUDWEXVIDOOVRXWRISKDVH3RV$ 1RVLJQLILFDQWFKDQJHFRPSDUHGWRWKHDFVLPXODWLRQ3RV% 1RVLJQLILFDQWFKDQJHFRPSDUHGWRWKHDFVLPXODWLRQ3RV& 1RVLJQLILFDQWFKDQJHFRPSDUHGWRWKHDFVLPXODWLRQ3RV' $WW VWKHXQGHUYROWDJHSURWHFWLRQIRUWKHJHQHUDWRUVLQ

EXVWULSVIROORZHGE\WKHJHQHUDWRULQEXV7KHYROWDJHDQGIUHTXHQF\LQWKH6:LVYHU\ORZ

3RV( 1RVLJQLILFDQWFKDQJHFRPSDUHGWRWKHDFVLPXODWLRQ

7DEOH6WDJH6LPXODWLRQUHVXOWVIRUWHVWFDVH


)LJXUH 3RVLWLRQLQJRIWKHKYGFOLQN

øù¾ú:û

øù¾úUü

øù&ûû

øù¹û(ü

øù:üü øù:ü<û

øù:ý<û øùºýü

øùø:ü

øùøø øù:øý

øù:øþ

øù:ø8úøù:ø¾û

øù:øÿ

øùÿ¾û

øù:þ¾û

øù:þü

øùþ:ý

Southwest

Central

NorthExternal

!

" "#

# # "

$ $ %

$ "

%

%

&

$ "

#

"

#

'()

'(+*

, -. , -/

, -0

1 '(2%3'(4

'(+5

'(6)4, -7 , -89 , -88

:, -8;<

, -80

:, -8=<

:, -8.<

, -8/

> (+2> (6)?

> (4@-8

> (+*

> (+A

> (B

@-/ @-C

@-80

@-8=

> (?

1 > ())D3@-89

@-8;

@-8E

3RVLWLRQ&

3RVLWLRQ$

3RVLWLRQ%

3RVLWLRQ(

3RVLWLRQ'

GF

GF

GF

GF


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


)LJXUHE 6WDJH&DVH)UHTXHQF\DWEXVHVDQGZLWKWKHGFOLQNLQSRVLWLRQ'

&DVH7KHVFHQDULRLQFDVHLVGHVFULEHGEHORZ7KHVLPXODWLRQUHVXOWVDUHVKRZQLQWDEOH6HHDOVRILJXUH6LPXODWLRQVDUHQRWSHUIRUPHGIRUFDVHZLWKWKHKYGFOLQNLQSRVLWLRQ(VLQFHWKLVWUDQVPLVVLRQOLQHLVGLVFRQQHFWHGLQWKHFDVHVFHQDULR7LPH (YHQWW V 'LVFRQQHFWLRQRIOLQH&/EHWZHHQEXVHVDQGW V 'LVFRQQHFWLRQRIRQHJHQHUDWRUDWEXV09$

&DVH3XUHDF $WW DQGVWKHXQGHUYROWDJHSURWHFWLRQIRU

JHQHUDWRUVDWEXVDQGWULSVGXHWRYROWDJHLQVWDELOLW\ZKLFKOHDGVWRDYROWDJHEUHDNGRZQ

3RV$ $WW VWKHJHQHUDWRUDWEXVIDOOVRXWRISKDVHGXHWRORZYROWDJH

3RV% 6WRSVDWW V6LPLODUVFHQDULRDVLQWKHDFVLPXODWLRQEXWFROODSVHLVUHDFKHGVRPHZKDWIDVWHU

3RV& $WW VWKHYROWDJHFROODSVHVLQDZD\VLPLODUWRDFDQG%VLPXODWLRQV

3RV' 1RVLJQLILFDQWFKDQJHFRPSDUHGWRWKHDFVLPXODWLRQ3RV( 1$

7DEOH 6WDJH6LPXODWLRQUHVXOWVIRUWHVWFDVH


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


&DVH3XUHDF $WW VWKHXQGHUYROWDJHSURWHFWLRQIRUJHQHUDWRUVDWEXV

DQGWULSV3RV$ $WW VWKHUHIHUHQFHPDFKLQHVSHHGEXVUHDFKHV

WKHPD[LPXPOLPLWSX3RV% $WW VWKHUHIHUHQFHPDFKLQHVSHHGEXVUHDFKHV

WKHPD[LPXPOLPLWSX3RV& $WW VWKHUHIHUHQFHPDFKLQHVSHHGEXVUHDFKHV

WKHPD[LPXPOLPLWSX3RV' $WW VWKHUHIHUHQFHPDFKLQHVSHHGEXVUHDFKHV

WKHPD[LPXPOLPLWSX3RV( $WW VWKHJHQHUDWRUDWEXVIDOOVRXWRISKDVH


)LJXUH 6WDJH&DVH9ROWDJHDWEXVDQGVSHHGRIWKH

UHIHUHQFHPDFKLQHDWEXV


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

&DVH3XUHDF $WW DQGVWKHXQGHUYROWDJHSURWHFWLRQIRUWKH

JHQHUDWRUVDWEXVDQGWULSV3RV$ $WW VWKHJHQHUDWRUDWEXVIDOOVRXWRISKDVHGXHWR

ORZYROWDJH3RV% 1RVLJQLILFDQWFKDQJHFRPSDUHGWRWKHDFVLPXODWLRQ3RV& 1RVLJQLILFDQWFKDQJHFRPSDUHGWRWKHDFVLPXODWLRQ3RV' 1RVLJQLILFDQWFKDQJHFRPSDUHGWRWKHDFVLPXODWLRQ3RV( 1$

7DEOH 6WDJH6LPXODWLRQUHVXOWVIRUWHVWFDVH&DVHLVDQRWKHUYDULDQWRIWKHFODVVLFDOYROWDJHFROODSVHVFHQDULRGHVFULEHGLQVHFWLRQEXWWKLVWLPHWKHFROODSVHLVDIDFWDVVRRQDVWKHOLQHLVGLVFRQQHFWHG7KHUHLVQRVLJQLILFDQWGLIIHUHQFHEHWZHHQWKHYDULRXVFRQILJXUDWLRQV


)LJXUH6WDJH&DVH$QJOHDQGYROWDJHDWEXV &DVH7KHVFHQDULRLQFDVHLVGHVFULEHGEHORZ7KHVLPXODWLRQUHVXOWVDUHVKRZQLQWDEOHDQGILJXUHVDDQGE7LPH (YHQWW V 'LVFRQQHFWLRQRIWKHJHQHUDWRUDWEXV09$W V 'LVFRQQHFWLRQRIOLQH)/EHWZHHQEXVHVDQGW V 'LVFRQQHFWLRQRIRIWKHORDGDWEXV0:

09$UW V 'LVFRQQHFWLRQRIRIWKHORDGDWEXV0:

09$UW V 'LVFRQQHFWLRQRIDQRWKHURIWKHORDGDWEXV0:

09$U$VLQFDVHZLWKWKHGFOLQNLQSRVLWLRQ'WKHKYGFOLQNLVDFWLQJDVDFRQQHFWLRQEHWZHHQWZRDV\QFKURQRXVV\VWHPVDIWHUWKHGLVFRQQHFWLRQRIOLQH)/


&DVH3XUHDF $WW VWKHUHIHUHQFHPDFKLQHVSHHGEXVUHDFKHVWKH

PD[LPXPOLPLWSX3RV$ 1RVLJQLILFDQWFKDQJHFRPSDUHGWRWKHDFVLPXODWLRQ3RV% 1RVLJQLILFDQWFKDQJHFRPSDUHGWRWKHDFVLPXODWLRQ3RV& 1RVLJQLILFDQWFKDQJHFRPSDUHGWRWKHDFVLPXODWLRQ3RV' $WW VWKHWKHXQGHUYROWDJHSURWHFWLRQIRUWKHJHQHUDWRU

DWEXVWULSV3RV( 1RVLJQLILFDQWFKDQJHFRPSDUHGWRWKHDFVLPXODWLRQ


)LJXUHD 6WDJH&DVH9ROWDJHDWEXVDQGVSHHGRIWKH

UHIHUHQFHJHQHUDWRUDWEXVZLWKVSHHGOLPLWDWLRQDWSX


)LJXUHE 6WDJH&DVH)UHTXHQF\DWEXVHVDQGZLWKWKHGFOLQNLQSRVLWLRQ'

,QFDVHVLPXODWLRQVWKHRQO\SRVLWLRQGLIIHULQJLQEHKDYLRXUIURPWKHRWKHUVLVSRVLWLRQ'$VLQFDVHLWLVFOHDUWKDWWKHVRXWKZHVWSDUWFDQQRWPDQDJHWRNHHSWKHIUHTXHQF\VWDEOHZKHQFRQQHFWHGWRWKHUHVWRIWKHV\VWHPZLWKRQO\DQKYGFOLQN7KHIUHTXHQF\GHFUHDVHVWDUWVDWWKHGLVFRQQHFWLRQRIOLQH)/DQGFDQQRWEHSUHYHQWHGE\ORDGGHFUHDVH,QWKHRWKHUSRVLWLRQVKRZHYHULIWKHVSHHGOLPLWRISXLVGHDFWLYDWHG

LWLVVHHQWKDWWKHIUHTXHQF\RQO\LQFUHDVHVDOLWWOHDERYHSXDQGWKHQGHFUHDVHVDQGVZLQJVWRZDUGVDVWDEOHYDOXHEHORZSXDJDLQVHHILJXUHF&RQVLGHULQJWKHWLPHLQWHUYDODURXQGVHFRQGVDQGWKDWWKHIUHTXHQF\RQO\LQFUHDVHVWRDPD[LPXPRISXWKLVEHKDYLRXULVDFFHSWDEOHDQGFDVHFDQQRWEHVDLGWRFDXVHDSRZHUV\VWHPFROODSVHH[FHSWZLWKWKHGFOLQNLQSRVLWLRQ'

)LJXUHF 6WDJH&DVH6SHHGRIWKHUHIHUHQFHPDFKLQHDWEXVZLWKRXWDQ\VSHHGOLPLWDWLRQ


&RPPHQWVWRVWDJHVLPXODWLRQV:KHQDQDO\VLQJWKHVLPXODWLRQUHVXOWVLWZDVIRXQGWKDWWKHKYGFOLQNGLGQRWLPSURYHWKHWROHUDQFHRIWKHQHWZRUNWRGLVWXUEDQFHV,QVRPHRIWKHVLWXDWLRQVIRUH[DPSOHFDVHZLWKWKHGFOLQNLQSRVLWLRQ&RU(QRVLJQLILFDQWFKDQJHIURPWKHSXUHDFV\VWHPVLPXODWLRQLVH[SHFWHG,QVRPHRWKHUFDVHVKRZHYHUIRUH[DPSOHFDVHZLWKWKHGFOLQNLQSRVLWLRQ'WKHKYGFOLQNVKRXOGEHDEOHWRLPSURYHWKHSRVWGLVWXUEDQFHEHKDYLRXURIWKHV\VWHPDVVXPLQJDSSURSULDWHUHJXODWLRQRIWKHKYGF$FORVHUORRNDWWKHWUDQVPLWWHGSRZHURQWKHGFOLQNFRPSDUHGWRWKH

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

)LJXUH 6WDJH&DVH7UDQVPLWWHGDFWLYHSRZHURQOLQHV)/EHWZHHQ

EXVHVDQGDQG)/DQGWKHGFOLQNUHVSHFWLYHO\EHWZHHQEXVHVDQG$WW VDJHQHUDWRUDWEXVLVGLVFRQQHFWHGDQGDWW VOLQH)/LVGLVFRQQHFWHG


$SSDUHQWO\WKHUHJXODWLRQXVHGLVQRWRSWLPDOIRUWKHVHVFHQDULRV7KH6ZH3ROOLQNLVPDLQO\XVHGWRWUDQVPLWEXONSRZHUDQGQRWWRVWDELOLVHWKHQHWZRUNWRZKLFKLWLVFRQQHFWHG+HQFHDGLIIHUHQWFRQWUROVWUDWHJ\PXVWEHGHYHORSHGRUSRVVLEO\RQHVWUDWHJ\IRUHDFKSRVLWLRQRIWKHGFOLQN 7KHVPDOOV\VWHP±VWDJH$IWHUVRPHDWWHPSWVWRILQGDEHWWHUFRQWUROVWUDWHJ\IRUWKHKYGFOLQNVLQFOXGHGLQWKHODUJHWUDQVPLVVLRQV\VWHPLWZDVGHFLGHGWRXVHDVPDOOV\VWHPPRGHOWRHYDOXDWHWKHGLIIHUHQWDYDLODEOHUHJXODWLRQSULQFLSOHV$VLQJOHOLQHGLDJUDPRIWKHVPDOOV\VWHPLVVKRZQLQILJXUHDQGDGHVFULSWLRQRIWKHV\VWHPLVIRXQGLQVHFWLRQ

)LJXUH 6LQJOHOLQHGLDJUDPRIWKHVPDOOWHVWV\VWHP,QWKHVPDOOWHVWV\VWHPWZRGLIIHUHQWVFHQDULRVDUHVLPXODWHG&DVH6 'LVFRQQHFWLRQRIWKHDFOLQH&DVH6 'LVFRQQHFWLRQRIRIWKHORDGDWEXV 0:DQG09$U

,QFDVH6WKHGLVFRQQHFWLRQRIWKHDFOLQHUHVXOWVLQORVVRIV\QFKURQLVPEHWZHHQEXVDQGEXV7KHIROORZLQJUHJXODWLRQRSWLRQVZHUHLQYHVWLJDWHG :LWKRXWSRZHUIUHTXHQF\FRQWUROOHU3)&WKDWLVZLWKWKHEDVLFFRQWUROV

RQO\5HVXOWVDUHSUHVHQWHGLQVHFWLRQ :LWKD3)&VHHVHFWLRQDQG$SSHQGL[%UHVSRQGLQJWRYDULRXV

LQSXWVLJQDOVH 7KHIUHTXHQF\LQEXVH 7KHVSHHGRIWKHJHQHUDWRULQEXVH 7KHWUDQVIHUUHGDFWLYHSRZHURQWKHDFOLQHRQO\IRUWHVWFDVH7KHUHVXOWVDUHSUHVHQWHGLQVHFWLRQ

:LWKDYROWDJHFRQWUROOHUERWKWRJHWKHUZLWKD3)&DQGRQLWVRZQ7KHUHVXOWVIURPWKHVHVLPXODWLRQVDUHQRWSUHVHQWHGLQWKLVWKHVLVVLQFHQRVLJQLILFDQWFKDQJHLQV\VWHPEHKDYLRXUZDVLQGLFDWHG

%86 7'& '& '& '&

7 %86


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

)LJXUHD 9ROWDJHDQGIUHTXHQF\DWEXVFDVH61RSRZHUIUHTXHQF\FRQWUROOHULVXVHG


)LJXUHE 7UDQVIHUUHGDFWLYHSRZHUDWWKHUHPDLQLQJOLQHFDVH61R

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


)LJXUHD 9ROWDJHDQGIUHTXHQF\DWEXVFDVH61RSRZHU IUHTXHQF\FRQWUROOHULVXVHG

)LJXUHE 7UDQVIHUUHGDFWLYHSRZHUFDVH61RSRZHUIUHTXHQF\FRQWUROOHULVXVHG7RSJUDSKWKHWUDQVIHUUHGSRZHURQRQHDFOLQHLQWKHSXUHDFV\VWHPDQGWKHWUDQVIHUUHGSRZHURQERWKWKHGFOLQHDQGWKHDFOLQHLQWKHPL[HGV\VWHP%RWWRPJUDSKWKHWRWDOWUDQVIHUUHGSRZHULQWKHSXUHDFV\VWHPDQGWKHWRWDOWUDQVIHUUHGSRZHULQWKHPL[HGV\VWHP


:LWKSRZHUIUHTXHQF\FRQWUROOHU,ID3)&LVLQFOXGHGLQWKHKYGFUHJXODWLRQDQXPEHURIRSWLRQVDUHDYDLODEOH7KHLQSXWVLJQDOWRWKH3)&PD\EHHLWKHUDIUHTXHQF\WKHVSHHGRIDURWDWLQJPDFKLQHRUWKHDFWLYHSRZHURQDOLQH,QDGGLWLRQWKHJDLQDQGWLPHFRQVWDQWVRIWKHUHJXODWRUPD\EHYDULHG

)RUFDVH6WKHEHVWUHVXOWZDVREWDLQHGZLWKWKHIUHTXHQF\DWEXVDVLQSXWVLJQDODQGZLWKWKHIROORZLQJSDUDPHWHUVIRUWKH3)&ZLWKUHIHUHQFHWRVHFWLRQ%DQGILJXUH%LQ$SSHQGL[%

5HJXODWRU'&5 0HDVXUHPHQWDQGFRPPXQLFDWLRQ)3'. IJK >0:RUN$SX@ ,QSXWGHYLDWLRQLQIUHTXHQF\DWEXV

LLMM V7.

V7.V*++

= . N OI >SXSX@. P >SXSX@ 7 Q >V@. R >SXSX@ 7 SUT >V@7 P >V@ 7 I >V@7 R >V@)LJXUHDVKRZVWKHYROWDJHDQGIUHTXHQF\DWEXVLQFDVH6ZLWKWKHSDUDPHWHUVOLVWHGDERYH)LJXUHEVKRZVWKHWUDQVIHUUHGSRZHULQWKHVDPHVLWXDWLRQ7KHPL[HGV\VWHPLVLQWKLVFDVHJLYLQJDVRPHZKDWEHWWHUUHVSRQVHWRWKHGLVWXUEDQFHWKDQWKHDFV\VWHPVLQFHWKHUHDUHOHVVLQLWLDORVFLOODWLRQVSUHVHQWLQWKHPL[HGV\VWHPFDVH,WLVFOHDUIURPILJXUHEWKDWWKHGFOLQNDGMXVWVWKHSRZHUWUDQVIHUDVVZLIWO\DVWKHDFV\VWHP

)LJXUHD 9ROWDJHDQGIUHTXHQF\DWEXVFDVH67KHSRZHUIUHTXHQF\

FRQWUROOHUUHVSRQGVWRWKHIUHTXHQF\FKDQJHDWEXV


)LJXUHE 7UDQVIHUUHGDFWLYHSRZHUFDVH67KHSRZHUIUHTXHQF\

FRQWUROOHUUHVSRQGVWRWKHIUHTXHQF\FKDQJHDWEXV,QFDVH6WKHEHVWVROXWLRQZDVWRXVHWKHGHYLDWLRQRIWKHSRZHUWUDQVIHUUHGE\WKHDFOLQHDVLQSXWVLJQDOWRWKH3)&7KHIROORZLQJSDUDPHWHUVZHUHXVHGIRUWKH3)&ZLWKUHIHUHQFHWRVHFWLRQ%DQGILJXUH%LQ$SSHQGL[%5HJXODWRU'&5 0HDVXUHPHQWDQGFRPPXQLFDWLRQ)3'. IJK >0:RUN$SX@ ,QSXWGHYLDWLRQLQDFWLYHSRZHURQ

SDUDOOHODFOLQHLLMM V7.

V7.V*++

= . N OI >SXSX@. P >SXSX@ 7 Q >V@. R >SXSX@ 7 SUT >V@7 P >V@ 7 I >V@7 R >V@ 7KHVLPXODWLRQUHVXOWVIRUFDVH6DUHVKRZQLQILJXUHVDDQGE$SSDUHQWO\WKHPL[HGV\VWHPDGDSWWRWKHORDGFKDQJHMXVWDVHDVLO\LQWKHGFFDVHDVLQWKHDFFDVH


)LJXUHD 9ROWDJHDQGIUHTXHQF\DWEXVFDVH67KHSRZHUIUHTXHQF\FRQWUROOHUUHVSRQGVWRWKHFKDQJHLQWUDQVIHUUHGSRZHUDWWKHSDUDOOHODFOLQH

)LJXUHE 7UDQVIHUUHGDFWLYHSRZHUFDVH67KHSRZHUIUHTXHQF\FRQWUROOHUUHVSRQGVWRWKHFKDQJHLQWUDQVIHUUHGSRZHUDWWKHSDUDOOHODFOLQH


,QIOXHQFHRIWKHYROWDJHGHSHQGHQF\RIWKHORDG:LWKUHIHUHQFHWRWKHZRUNGRQHE\,QpV5RPHUR1DYDUURSUHVHQWHGLQ>@LWZDVGHFLGHGWKDWWKHLQIOXHQFHRIWKHYROWDJHGHSHQGHQF\RIWKHORDGVKRXOGEHLQYHVWLJDWHG0V5RPHUR1DYDUURKDVIRXQGWKDWWKHGHSHQGHQF\H[SRQHQWLQKHUZRUNGHQRWHGα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

$8833 V

⋅= W DQG

%8844 X

⋅= Y

7KHH[SRQHQWV$DQG%KDVEHHQYDULHGDQGFRPELQHGDVVKRZQLQWDEOH7\SHRIORDG $ %2QO\3 3DQG4 3DQG4 7DEOH &RPELQDWLRQVRIORDGW\SHVDQGYROWDJHGHSHQGHQF\

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

LQWKHFDVHRIDSXUHO\UHVLVWLYHORDGWRSJUDSKWKHYROWDJHDWEXVUHWXUQVWRDYDOXHFORVHWRWKHLQLWLDOYDOXHDIWHUWKHGLVWXUEDQFH,QFDVHRIDPL[HGORDGRQWKHRWKHUKDQGERWWRPJUDSKWKHILQDOYROWDJHLVORZHUWKDQWKHLQLWLDOYROWDJH7KHUHDVRQIRUWKLVLVWKHGLIIHUHQFHLQUHDFWLYHSRZHUDYDLODEOHLQEXV:KHQWKHDFOLQHLVGLVFRQQHFWHGWKHUHDFWLYHSRZHUGHPDQGIURPWKHGFOLQHZLOOLQFUHDVHEHFDXVHRIWKHKLJKHUORDGLQJRIWKHOLQH:LWKDDFWLYHORDGRQO\WKHUHLVDVXUSOXVRIUHDFWLYHSRZHULQEXVWKDWFRYHUVWKHLQFUHDVHGUHDFWLYHSRZHUGHPDQGIURPWKHKYGFOLQN:KHQDQLQGXFWLYHORDGLVDGGHGLQEXVWKHUHZLOOVWLOOEHDVXUSOXVRIUHDFWLYHSRZHULQEXVEHIRUHWKHGLVFRQQHFWLRQRIWKHDFOLQHEXWQRWDVPXFKDVLQWKHFDVHRIDUHVLVWLYHORDG:KHQWKHORDGLQJRIWKHKYGFOLQHDQGWKXVWKHUHDFWLYHSRZHUGHPDQGLQFUHDVHVWKHUHZLOOLQVWHDGEHDGHILFLWLQUHDFWLYHSRZHULQEXV+HQFHWKHYROWDJHZLOOQRWUHDFKLWVLQLWLDOOHYHODJDLQ


)LJXUH 0D[LPXPDQGPLQLPXPYROWDJHDWEXVLQFDVH6ZLWKGLIIHUHQW

YROWDJHGHSHQGHQF\RIWKH0:UHVLVWLYHSDUWRIWKHORDG7KHLQGXFWLYHSDUWRIWKHORDGLV09$UDQGKDVDYROWDJHGHSHQGHQF\H[SRQHQW%

)LJXUH 7KHYROWDJHDWEXVLQFDVH67KHVROLGOLQHVKRZVWKHUHVXOWVIRUD0:UHVLVWLYHORDGRQO\DQGWKHGRWWHGOLQHVKRZVWKHUHVXOWVIRUDFRPELQHGUHVLVWLYHLQGXFWLYHORDGRI0:DQG09$U7KHYROWDJHGHSHQGHQF\H[SRQHQWVDUH$ DQG$ SOXV% UHVSHFWLYHO\


)LJXUH 0D[LPXPDQGPLQLPXPYROWDJHDWEXVLQFDVH6ZLWKGLIIHUHQWYROWDJHGHSHQGHQF\RIWKH0:UHVLVWLYHORDG

)LJXUH 9ROWDJHDWEXVLQFDVH6IRUGLIIHUHQWYROWDJHGHSHQGHQF\RI

WKH0:UHVLVWLYHORDG,QWKHERWWRPJUDSKD09$ULQGXFWLYHORDGLVDGGHGDVZHOOZLWK%


7KHPD[LPXPWUDQVIHUDEOHDFWLYHSRZHULQFDVH6DQGZLWKDYDU\LQJ$KDVEHHQSORWWHGLQILJXUH7KHWRSJUDSKVKRZVWKHPD[LPXPSRZHUWUDQVIHULQWKHFDVHRIDPL[HGORDGZKHUHWKHDPRXQWRIUHDFWLYHSRZHUORDGLV09$UDQGLWVH[SRQHQW% DQGWKHERWWRPJUDSKVKRZVWKHUHVXOWVZLWKDSXUHUHVLVWLYHORDG,WLVFOHDUWKDWWKHYROWDJHGHSHQGHQF\RIWKHORDGKDVDFRQVLGHUDEOHLQIOXHQFHRQWKHFDSDFLW\RIWKHV\VWHP,I$IRUH[DPSOHFKDQJHVIURPWRZLWKDUHVLVWLYHORDGWKHWUDQVIHUFDSDFLW\LQWKLVVPDOOV\VWHPLQFUHDVHVZLWK

)LJXUH 0D[LPXPDFWLYHSRZHUWUDQVIHUSRVVLEOHLQFDVH6IRUGLIIHUHQW

YROWDJHGHSHQGHQF\H[SRQHQWV7RSJUDSKERWKUHVLVWLYHDQGLQGXFWLYHORDGWKHLQGXFWLYHSDUWLV09$UDQG% %RWWRPJUDSKDUHVLVWLYHORDGRQO\


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

)LJXUH 0D[LPXPDQGPLQLPXPYROWDJHDWEXVLQFDVH6ZLWK

GLIIHUHQWYROWDJHGHSHQGHQF\RIWKH09$ULQGXFWLYHORDG7KHDFWLYHSDUWRIWKHORDGLV0:DQGLWVH[SRQHQW$


)LJXUH 0D[LPXPDFWLYHSRZHUWUDQVIHUSRVVLEOHLQFDVH6IRUGLIIHUHQWYROWDJHGHSHQGHQF\H[SRQHQWVRIWKH09$ULQGXFWLYHORDG7KHYROWDJHGHSHQGHQF\H[SRQHQWRIWKHDFWLYHSDUWRIWKHORDGLVNHSWDW$

&RPPHQWVWRVWDJHVLPXODWLRQV7KHVLPXODWLRQVSHUIRUPHGZLWKWKHVPDOOWHVWV\VWHPKDVVHUYHGPDLQO\WZRSXUSRVHV)LUVWO\LWKDVJLYHQWKHDXWKRUDGHHSHUNQRZOHGJHRIKRZWRKDQGOHWKHKYGFFRQWUROV\VWHPZKLFKSDUDPHWHUVWRZRUNZLWKHWF6HFRQGO\LWKDVJLYHQVRPHLGHDVRIKRZWRFRQWLQXHWKHZRUNRQWKHODUJHWHVWV\VWHP,WLVFOHDUWKDWWKHLQIOXHQFHRIWKHYROWDJHGHSHQGHQF\RIWKHORDGLVDQ

LQWHUHVWLQJDUHDWRORRNFORVHUDW,QKLJKORDGVLWXDWLRQVWKHNQRZOHGJHRIKRZWKHORDGDIIHFWVWKHVWDELOLW\RIWKHV\VWHPPD\EHFUXFLDO3HUKDSVLWLVSRVVLEOHWRWUDQVIHUPRUHSRZHUWKDQDVVXPHGLQDFHUWDLQWUDQVPLVVLRQFRUULGRUZLWKRXWMHRSDUGLVLQJWKHVXUYLYDORIWKHV\VWHP,IWKLVLVWKHFDVHVFKHGXOHGGLVFRQQHFWLRQRIORDGPD\EHDYRLGHG,QPDQ\VWDELOLW\VWXGLHVPDGHVRIDUWKHYROWDJHGHSHQGHQF\RIWKHORDGLV

SODLQO\DVVXPHGWREHDURXQG>@DQGWKLVLVDOVRZKDWLVSURSRVHGIRUWKH&LJUp1RUGLFQHWZRUN>@$FFRUGLQJWR>@>@DQG>@KRZHYHUWKLVPD\QRWEHDJRRGHQRXJKHVWLPDWLRQ,QERWK>@DQG>@WKHORDGYROWDJHGHSHQGHQFHIRUDFWLYHORDGLVH[SUHVVHGZLWKRQHWUDQVLHQWGHSHQGHQF\H[SRQHQWα Z DQGRQHVWHDG\VWDWHGHSHQGHQF\H[SRQHQWα [ α [ TXDQWLILHVWRZKDWGHJUHHDORDGKDVEHHQUHVWRUHGDIWHUUHFRYHU\α Z GHVFULEHVKRZWKHORDGEHKDYHVGXULQJDGLVWXUEDQFHα Z HTXDOWRPHDQVWKDWWKHORDGEHKDYHVDVDFRQVWDQWFXUUHQWDQGLIα Z LWEHKDYHVDVDFRQVWDQWLPSHGDQFH)URPILHOGPHDVXUHPHQWV5RPHUR1DYDUURILQGVWKDWWKHPRQWKO\PHDQYDOXHRIα Z YDULHVEHWZHHQDQG'XULQJWKHZLQWHUWKHXVHRIWKHUPRVWDWFRQWUROOHGKHDWLQJLQFUHDVHVZKLFKUHVXOWVLQDQLQFUHDVHGYDOXHRIα Z 7KHGDLO\YDULDWLRQRIα Z ORRNVGLIIHUHQWO\GHSHQGLQJRQWKHWLPHRI\HDU'XULQJVXPPHUα Z KDVLWVKLJKHVWYDOXHVGXULQJWKHGD\EXWLQWKHZLQWHUWKHKLJKHUYDOXHVFRUUHVSRQGWRWKHQLJKWKRXUV'HVSLWHDOOSDWWHUQVRQHFDQILQGLQWKHEHKDYLRXURIα Z LWLVDIDFWWKDWWKHYDOXHPD\YDU\EHWZHHQIRUH[DPSOHDQGGXULQJRQHVLQJOHGD\%RWK5RPHUR1DYDUUR>@DQG/H'RXV>@


ILQGWKDWIRUWUDQVLHQWYROWDJHFKDQJHVα Z LVLQWKHRUGHURIWR7KHVWHDG\VWDWHGHSHQGHQF\H[SRQHQWα [ LVIRXQGWREHFORVHWR]HURDWZLQWHUWLPHGXHWRWKHODUJHDPRXQWRIHOHFWULFDOKHDWLQJDQGLWKDVKLJKHUYDOXHVGXULQJWKHVXPPHUα [ DOVRVKRZVODUJHYDULDWLRQVRYHUWLPH7KHFRPELQDWLRQRIWKHVHUHVXOWVDQGWKHUHVXOWVREWDLQHGLQWKLVWKHVLVZKHUHLWLVVKRZQWKDWWKHSRZHUWUDQVIHUFDSDFLW\LVFOHDUO\LQIOXHQFHGE\WKHYROWDJHGHSHQGHQF\RIWKHORDGLQGLFDWHVWKDWLWPD\EHPHDQLQJIXOWRIXUWKHUVWXG\WKHLQWHUDFWLRQEHWZHHQORDGYROWDJHGHSHQGHQF\KYGFDQGVWDELOLW\LVVXHV

7KHODUJHSRZHUV\VWHP±VWDJH6WDJHRIWKHVLPXODWLRQVZDVWRXVHWKHODUJHWHVWV\VWHP&LJUp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

09$UW V 'LVFRQQHFWLRQRIDQRWKHURIWKHORDGDWEXV

0:09$UW V 'LVFRQQHFWLRQRIWKHORDGDWEXV0:09$UW V 'LVFRQQHFWLRQRIOLQH)/EHWZHHQEXVHVDQG


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


6LPXODWLRQV±&DVHB6LQFHFDVHBLQYROYHVGLVFRQQHFWLRQRIOLQH)/DQKYGFOLQNLQSRVLWLRQ

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

)LJXUH 6WDJH±&DVHSRVLWLRQ')UHTXHQF\DWEXVHVDQGDQGYROWDJHDWEXV6ROLGOLQHSXUHDFV\VWHPGDVKHGOLQHWKHILUVWKYGFPRGHOVWDJHGRWWHGOLQHLPSURYHGKYGFPRGHOZLWKWKHIUHTXHQF\DWEXVDVLQSXWVLJQDOWRWKH3)&


6LPXODWLRQV±&DVHB&DVHBLVDFODVVLFDOFDVHRIYROWDJHFROODSVHLQLWLDWHGE\WKHORVVRIWUDQVPLVVLRQFDSDFLW\IURPQRUWKHUQ6ZHGHQWRWKHFHQWUDOSDUWDQGIROORZHGE\WKHORVVRIDJHQHUDWRULQWKHVRXWKZHVWSDUW7KHPRVWEHQHILFLDOSRVLWLRQRIWKHKYGFOLQNLQWKLVFDVHZRXOGSUREDEO\EHHLWKHULQRQHRIWKHSRVLWLRQV$RU%ZKHUHLWPD\HQKDQFHWKHWUDQVPLVVLRQFRUULGRUEHWZHHQQRUWKHUQDQGFHQWUDO6ZHGHQRULQSRVLWLRQ'ZKHUHLWPD\KHOSLQEDODQFLQJWKHSRZHUIORZEHWZHHQWKHVRXWKZHVWDQGWKHFHQWUDOSDUWV7KHVLPXODWLRQVVKRZWKDWLIZHKDYHDGFOLQNLQSRVLWLRQ'LWLVHDV\WR

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

SRRUO\GDPSHGRVFLOODWLRQV)LJXUHVKRZVWKHYROWDJHDWEXVZLWKWKHSRZHUWUDQVIHUUHGDWOLQH&/EHWZHHQEXVHVDQGDVLQSXWWRWKH3)&


)LJXUHD 6WDJH±&DVHSRVLWLRQ'9ROWDJHDWEXV6ROLGOLQHSXUHDFV\VWHP'DVKHGOLQHWKHILUVWKYGFPRGHOVWDJH'RWWHGOLQHLPSURYHGKYGFPRGHOZLWKGHYLDWLRQLQIUHTXHQF\LQEXVLVXVHGDVLQSXWVLJQDOWRWKH3)&'DVKGRWWHGOLQHLPSURYHGKYGFPRGHOZLWKWKHGHYLDWLRQLQDFWLYHSRZHUWUDQVIHUUHGRQOLQH)/LVXVHGDVLQSXWVLJQDOWRWKH3)&

)LJXUHE 6WDJH±&DVHSRVLWLRQ'$FWLYHSRZHUDWOLQHV)/WRSJUDSKDQG)/GFOLQHERWWRPJUDSK6ROLGOLQHSXUHDFV\VWHP'DVKHGOLQHWKHILUVWKYGFPRGHOVWDJH'RWWHGOLQHLPSURYHGKYGFPRGHOZLWKGHYLDWLRQLQIUHTXHQF\LQEXVLVXVHGDVLQSXWVLJQDOWRWKH3)&'DVKGRWWHGOLQHLPSURYHGKYGFPRGHOZLWKWKHGHYLDWLRQLQDFWLYHSRZHUWUDQVIHUUHGRQOLQH)/LVXVHGDVLQSXWVLJQDOWRWKH3)&


)LJXUH 6WDJH±&DVHSRVLWLRQ%9ROWDJHDWEXV6ROLG

OLQHSXUHDFV\VWHP'DVKHGOLQHWKHILUVWKYGFPRGHOVWDJH'RWWHGOLQHLPSURYHGKYGFPRGHOZLWKWKHGHYLDWLRQLQDFWLYHSRZHUWUDQVIHUUHGRQOLQH&/LVXVHGDVLQSXWVLJQDOWRWKH3)&

6LPXODWLRQV±&DVHB&DVHBLQYROYHVWKHORVVRIDJHQHUDWRULQEXVFRPELQHGZLWKDQLQFUHDVHLQORDGLQWKHVDPHSDUWRIWKHV\VWHPDQGLQWKHVRXWKZHVW,WZLOOWKHQEHQHFHVVDU\WRLQFUHDVHWKHDPRXQWRISRZHUWUDQVIHUUHGIURPWKHQRUWKHUQSDUWWRWKHFHQWUDODQGVRXWKSDUWV7RLPSURYHWKHV\VWHPSHUIRUPDQFHLQWKLVFDVHLWLVSUREDEO\EHVWWRSODFHWKHKYGFOLQNLQSRVLWLRQ$RU%,QILJXUHWKHYROWDJHDWEXVLVVKRZQERWKLQWKHFDVHRIDSXUH

DFV\VWHPDQGZLWKDQKYGFOLQNLQSRVLWLRQ%7KHLQSXWWRWKHSRZHUIUHTXHQF\FRQWUROOHURIWKHKYGFLVWKHGHYLDWLRQLQDFWLYHSRZHURQOLQH&/EXWVHYHUDORWKHUFRQWURORSWLRQVLVIHDVLEOHWRSUHYHQWYROWDJHFROODSVH

)LJXUH 6WDJH±&DVHSRVLWLRQ%9ROWDJHDWEXV6ROLGOLQH

SXUHDFV\VWHP'DVKHGOLQHWKHILUVWKYGFPRGHOVWDJH'RWWHGOLQHLPSURYHGKYGFPRGHOZLWKWKHGHYLDWLRQLQDFWLYHSRZHUWUDQVIHUUHGRQOLQH&/LVXVHGDVLQSXWVLJQDOWRWKH3)&


&RPPHQWVWRVWDJHVLPXODWLRQV)URPWKHVLPXODWLRQVLQVWDJHLWFDQEHFRQFOXGHGWKDWWKHXVHRIDQKYGFOLQNPD\ZLWKWKHDSSURSULDWHFRQWUROPDNHWKHGLIIHUHQFHEHWZHHQDV\VWHPEUHDNGRZQDQGDWHPSRUDU\GLVWXUEDQFH7KHSRVLWLRQRIWKHKYGFOLQNDQGWKHFRQWURORSWLRQWRFKRRVHPXVWEHGHFLGHGIURPFDVHWRFDVH


&KDSWHU&RQFOXVLRQVDQGIXWXUHZRUN

&KDSWHU &RQFOXVLRQVDQGIXWXUHZRUN7KLVFKDSWHUZLOOVXPXSWKHFRQFOXVLRQVPDGHLQWKLVWKHVLVDQGSURSRVHVLGHDVIRUWKHFRQWLQXDWLRQRIWKHSURMHFW &RQFOXVLRQV$QLPSRUWDQWFRQFOXVLRQRIWKLVZRUNLVWKDWDQKYGFOLQNLQDSRZHUV\VWHPPD\KDYHDVLJQLILFDQWLQIOXHQFHRQWKHVWDELOLW\RIWKHV\VWHPGXULQJGLVWXUEHGFRQGLWLRQV7KLVLVWUXHHYHQLIWKHKYGFSDUWLVPXFKVPDOOHUWKDQWKHDFV\VWHP,WLVDOVRREYLRXVWKDWWKHFRQWURORIWKHKYGFOLQNPD\EHFUXFLDOWRWKHEHKDYLRXURIWKHHQWLUHQHWZRUN,QWKLVWKHVLVZHKDYHVKRZQWKDWDQKYGFOLQNLQWKHULJKWORFDWLRQLQD

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

DXWKRUZRXOGUHFRPPHQGWRSRVLWLRQDQKYGFOLQNLQSRVLWLRQ%WREHJLQZLWK,QWKLVSRVLWLRQWKHKYGFOLQNZLOOKHOSWRSUHYHQWVRPHVHULRXVFRQWLQJHQFLHVDQGDWWKHVDPHWLPHLWZLOOKHOSWRHQKDQFHWKHWUDQVIHUFDSDFLW\RIWKHFRUULGRUIURPWKHJHQHUDWLRQSODQWVLQWKHQRUWKHUQRI6ZHGHQWRWKHXVHUVLQWKHFHQWUDODQGVRXWKSDUWV)XUWKHUPRUHZHKDYHVHHQWKDWLQDPLQRUQHWZRUNWKHORDGYROWDJH

GHSHQGHQF\VHHPVWRKDYHDVLJQLILFDQWLQIOXHQFHRQV\VWHPSHUIRUPDQFH,WLVVKRZQWKDWWKHYROWDJHGHSHQGHQF\LQIOXHQFHVERWKWKHDPSOLWXGHRIWKHYROWDJHVZLQJVIROORZLQJDGLVWXUEDQFHDQGWKHPD[LPXPWUDQVIHUDEOHSRZHURYHUDQKYGFOLQHGXULQJDGLVWXUEDQFH7KLVLQGLFDWHVWKDWLQFDVHRIKLJKORDGVLWXDWLRQVZLWKDSRZHUGHILFLWLWLVEHQHILFLDOWRKDYHJRRGNQRZOHGJHDERXWWKHORDGYROWDJHGHSHQGHQF\LQRUGHUWRXWLOLVHWKHSRZHUV\VWHPHIILFLHQWO\

&KDSWHU&RQFOXVLRQVDQGIXWXUHZRUN

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

5HIHUHQFHV>@ :DOYH.´1RUGLF±$&LJUpWHVWV\VWHPIRUVLPXODWLRQVRIWUDQVLHQW

VWDELOLW\DQGORQJWHUPG\QDPLFV´6YHQVND.UDIWQlW6ZHGHQ>@ )UDQNKDXVHU+5HWDO´6,032:±DGLJLWDOSRZHUV\VWHPVLPXODWRU´

$%%5HYLHZQR>@ $%%LQWHUQHWVLWHRQ6LPSRZ,QWHUQHW85/

KWWSZZZDEEFRPVLPSRZ>@ 6LPSRZ8VHU0DQXDO5HOHDVHDQG([WHQGHGPDQXDO+9'&>@ .XQGXU3´3RZHU6\VWHP6WDELOLW\DQG&RQWURO´,6%1;

0F*UDZ+LOO>@ $UULODJD-´+LJKYROWDJHGLUHFWFXUUHQWWUDQVPLVVLRQ´,6%1

7KH,QVWLWXWLRQRI(OHFWULFDO(QJLQHHUV>@ 0RKDQ18QGHODQG70DQG5REELQV:3´3RZHU(OHFWURQLFV

&RQYHUWHUV$SSOLFDWLRQVDQG'HVLJQ´6HFRQG(G,6%1-RKQ:LOH\6RQV,QF

>@ $%%LQWHUQHWVLWHRQ+9'&DQG+9'&/LJKW,QWHUQHW85/

KWWSZZZDEEFRPJOREDODEE]KDEE]KQVI2SHQ'DWDEDVHGE JOREDO$%%=+$%%=+QVIY &H XVF $)$)&$)&

>@ 'U7$GKLNDUL*|UDQ,VDFVVRQ9'$PEHNDU´7KH&KDQGUDSXU±

3DGJKHKYGFELSROHWUDQVPLVVLRQ´SUHVHQWHGDW&LJUp6\PSRVLXP.XDOD/XPSXU0DOD\VLD6HSWHPEHU

>@ $+DPPDGHWDO´&RQWUROVPRGHOOLQJDQGYHULILFDWLRQIRUWKH3DFLILF

,QWHUWLHKYGFWHUPLQDOVFKHPH´,(((7UDQVDFWLRQVRQSRZHUGHOLYHU\9RO1R-DQXDU\

>@ +|JEHUJ.((ULFVVRQ0.XPDU$/LQGpQ.DQG:HLELQJ:

´6WDELOLW\,PSURYHPHQWIRU&HQWUDO&KLQD6\VWHP´SUHVHQWHGDW,&36&RQIHUHQFH:XKDQ&KLQD6HS

>@ 3HUVVRQ$&DUOVVRQ/cEHUJ0´1HZ WHFKQRORJLHV LQKYGFFRQYHUWHU

GHVLJQ´SUHVHQWHGDW6(323(FRQIHUHQFH5HFLIH%UDVLO0D\

>@ 5RPHUR1DYDUUR,³'\QDPLF/RDG0RGHOVIRU3RZHU6\VWHPV´ ,6%1/LFHQFLDWH7KHVLV/XQG8QLYHUVLW\>@ /H'RXV*³9ROWDJH6WDELOLW\LQ3RZHU6\VWHPV´,6%1

/LFHQFLDWH7KHVLV&KDOPHUV8QLYHUVLW\RI7HFKQRORJ\>@ %DUW]VFK&HWDO³7ULSOHWXQHGKDUPRQLFILOWHUVGHVLJQSULQFLSOHDQG

RSHUDWLQJH[SHULHQFH´,QWHUQDWLRQDO&RQIHUHQFHRQ3RZHU6\VWHP7HFKQRORJ\,163(&$FFHVVLRQ1XPEHU

>@ &DUOVVRQ/HQQDUW³´&ODVVLFDO´+9'&VWLOOFRQWLQXLQJWRHYROYH´0365HYLHZ7UDQVPLVVLRQ'LVWULEXWLRQ-XQH

>@ 5REHUWR5XGHUYDOO-3&KDUSHQWLHU5DJKXYHHU6KDUPD³+LJK9ROWDJH

'LUHFW&XUUHQW+9'&7UDQVPLVVLRQ6\VWHPV7HFKQRORJ\5HYLHZ3DSHU´SUHVHQWHGDW(QHUJ\:HHN:DVKLQJWRQ'&86$0DUFK

>@ (35,LQWHUQHWVLWH,QWHUQHW85/

KWWSZZZHSULFRPGHVWLQDWLRQVG\QDPLFGLOEHUWDVS"SURGXFWBLG >@ .DUOVVRQ'´9ROWDJH6WDELOLW\6LPXODWLRQV8VLQJ'HWDLOHG0RGHOV%DVHG

RQ)LHOG0HDVXUHPHQWV´,6%13K'7KHVLV&KDOPHUV8QLYHUVLW\RI7HFKQRORJ\

>@ $UULODJD-6PLWK%´$&'&3RZHU6\VWHP$QDO\VLV´ ,6%17KH,QVWLWXWLRQRI(OHFWULFDO(QJLQHHUV

$EEUHYLDWLRQV+9'& +LJKYROWDJHGLUHFWFXUUHQW6Y. 6YHQVND.UDIWQlW±DXWLOLW\ZKLFKRZQVDQGRSHUDWHVWKHVZHGLVK

QDWLRQDOHOHFWULFLW\JULG*72 *DWHWXUQRIIWK\ULVWRU,*%7 ,QVXODWHGJDWHELSRODUWUDQVLVWRU96& 9ROWDJHVRXUFHFRQYHUWHU3:0 3XOVHZLGWKPRGXODWLRQ&&& &DSDFLWRUFRPPXWDWHGFRQYHUWHU&& &XUUHQWFRQWURO&,$ &RQVWDQWLJQLWLRQDQJOHFRQWURO&($ &RQVWDQWH[WLQFWLRQDQJOHFRQWURO9'&2/ 9ROWDJHGHSHQGHQWFXUUHQWRUGHUOLPLW&)& &RQYHUWHUILULQJFRQWURO

'HQRWDWLRQV$Q\GHQRWDWLRQZLWKWKHVXIIL[UHJ8 \+]^ DUHDVVRFLDWHGZLWKWKHUHFWLILHU$Q\GHQRWDWLRQZLWKWKHVXIIL[LHJ8 \+]_ DUHDVVRFLDWHGZLWKWKHLQYHUWHU&DSLWDOOHWWHUVLQGLFDWHVUPVYDOXHVRIYROWDJHVDQGFXUUHQWVVPDOOOHWWHUVLQGLFDWHVLQVWDQWDQHRXVYDOXHV8 ` 8 a 8 b $&SKDVHYROWDJHV8c+c $Q\RIWKHWKUHHDFSKDVHYROWDJHV, ` , a , b $&SKDVHFXUUHQWV8 `a 8 `b 8 a%b $&SKDVHSKDVHYROWDJHV, \ 'LUHFWFXUUHQW, \+] 1RORDGGLUHFWFXUUHQW8 \ 'LUHFWYROWDJH8 \+] ,GHDOQRORDGYROWDJHZLWKQRORVVHVDQGZLWKRXWILULQJDQJOH

GHOD\α 9DOYHLJQLWLRQDQJOHRUILULQJDQJOHGHOD\UHFWLILHUα π±βγ 9DOYHH[WLQFWLRQDQJOHRUFRPPXWDWLRQPDUJLQLQYHUWHU γ = π − (α+X) X &RPPXWDWLRQLQWHUYDORURYHUODSDQJOHFRUUHVSRQGVWRWKHWLPH

LWZLOOWDNHIURPLQVWDQWRILJQLWLRQXQWLOWKHFRPPXWDWLRQLVFRPSOHWHG

β 7KHDGYDQFHDQJOHβ γ XDQGβ π α. L d!e 7KHFXUUHQWWKURXJKYDOYHVLPLODUIRUYDOYHV5 b (TXLYDOHQWFRPPXWDWLQJUHVLVWDQFH&RUUHVSRQGVWRYROWDJH

GURSLQWKHFRQYHUWHUGXHWRFRPPXWDWLRQRYHUODS/ b &RPPXWDWLQJLQGXFWDQFH; b &RPPXWDWLQJUHDFWDQFHWKHUHDFWDQFHEHWZHHQWKH

FRPPXWDWLQJYROWDJHDQGWKHFRQYHUWHUYDOYHV; b ω/ b Xfgb 9ROWDJHDFURVVWKHFRPPXWDWLQJUHDFWDQFH GW

GL/X hij i = 5c 'FOLQHUHVLVWDQFH, k &XUUHQWPDUJLQWKHGLIIHUHQFHEHWZHHQWKHUHFWLILHUDQGWKH

LQYHUWHUFXUUHQWRUGHUVFRVφ 3RZHUIDFWRURIDFRQYHUWHUφLVWKHSKDVHGLIIHUHQFHEHWZHHQ

WKHIXQGDPHQWDOIUHTXHQF\YROWDJHDQGFXUUHQWFRPSRQHQWV$ 9ROWDJHGHSHQGHQF\H[SRQHQWIRUUHVLVWLYHORDG% 9ROWDJHGHSHQGHQF\H[SRQHQWIRULQGXFWLYHFDSDFLWLYHORDG $

8833 l

⋅= m %

8844 n

⋅= o

$SSHQGL[$0RGLILFDWLRQVRIWKH1RUGLFQHWZRUN

$

$SSHQGL[$0RGLILFDWLRQVRIWKH1RUGLFQHWZRUN7KHVWUXFWXUHRI WKHRULJLQDO1RUGLFQHWZRUNFDQEH VHHQ LQ ILJXUHV$$7KHVWUXFWXUHRIWKHPRGLILHGEXVQHWZRUNLVVKRZQLQILJXUH$5HPRYHGFRPSRQHQWV%XVHV

/LQHV &RQQHFWHGEHWZHHQEXVHV

QRDQGQRDQGQRDQGQRDQGQRDQGQRDQGQRDQGQRQRDQGQRDQG

7UDQVIRUPHUVDQGDVVRFLDWHGUHJXODWLRQ

/RFDWHGEHWZHHQEXVHVQRQRQRQRDQGQRDQGQR

5DWLQJ09$

*HQHUDWLRQ &RQQHFWHGWREXV

5DWLQJ09$


$

5HPRYHGFRPSRQHQWVFRQW/RDG

&RQQHFWHGWREXV

30:

409$U

6KXQWLPSHGDQFHV

&RQQHFWHGWREXV

30:

409$U


$

1HZFRPSRQHQWV*HQHUDWLRQ &RQQHFWHGWREXV

5DWLQJ09$

/RDG &RQQHFWHGWREXV

30:

409$U

$OWHUHGFRPSRQHQWV*HQHUDWLRQ &RQQHFWHGWREXV

2OGUDWLQJ09$

1HZUDWLQJ09$


$

)LJXUH$ 1RUGLFQHWZRUNN9V\VWHP

6HFWLRQ

6HFWLRQ

6HFWLRQ

Southwest

Central

NorthExternal

pqrrtsvu%wx rrrtsvyx rr+rtsvyq+rrtszu!w

q+rrtsgu%w| rrtsgy| rrtszyrrtszu!w

p+rrtsgu%w

rrtszu!w~ rrtszu!w

rrrtsgu!wG GG

| rrtszu!wx qrtszy

| qrtszu!w| rtszy

!rrtszu!w | rtszy

| rrtszu!wrtszy

x rrtsvu%w

x rrsvu!w

r+rtsvu!w

x r+rtsvu!wx qp+rtsvy

r+rtsvu!w

!rrtszu!wrrtszy qqrtszu!wprrtszy

+rrtszu!wq | rtszy

x rrtsgu!wx q | rtsgy

q

x|

~

|

x

|

q

p

rrtszy


$

)LJXUH$ 1RUGLFQHWZRUNDQGN9V\VWHP

Central

North

¡¢t£z¤!¥¦

§+¢¢t£g¤!¥¦ §+¢¢t£v¤%¥¦

§+¢¢t£v¤%¥¦

D¨¡+¢t£v¤!¥¦

© ¢¢t£zª« ¢¢t£z¤!¥¦§ « ¢t£zª¨¢¢t£z¤!¥¦

« ¢¢t£zª© ¢t£v¤!¥¦

¬ ¢¢t£zª§¡¢t£z¤!¥¦

¢¢t£zª§¢¢t£z¤!¥¦

§ © ¢t£zª® ¡t£v¤!¥¦

« ¢¢t£zª¨¢¢t£z¤%¥¦

¨¢¢t£zª¯ ¢t£g¤!¥¦

§+¢¢t£zª© ¢t£v¤!¥¦ ¢¢t£z¤!¥« ¢¢t£zª

© ¢¢t£z¤%¥ ¢¢t£zª¬ ¢¢t£z¤!¥¡¡¢t£zª

§¡¢t£z¤!¥§¢¢t£zª ¢¢t£z¤%¥¯ ¢¢t£zª

¨¢¢t£zª« ¢t£v¤!¥¦

§+¢¢t£zª¡+¢t£v¤!¥¦© ¡¢t£z¤!¥¬ ¡¢t£zª

§¢¢t£z¤!¥¨ © ¢t£zª

¯ ¢¢t£z¤%¥« ¢t£zª


$

)LJXUH$ 1RUGLFQHWZRUNN9ORDGEXVHV

Southwest

Central

°±²t³z´µ °¶t³z·!¸¹

º ²²t³z´» ²t³v·!¸¹

°+²²t³z´¼+¼ µ ³z·!¸¹ » ²²t³z´µ ° º ³z·!¸¹

¼²²t³z´½°t³g·!¸¹

¾!²²t³z´¼±½t³z·!¸¹±+²²t³z´µ+º ±t³z·%¸¹

½+²²t³z´¼ µ ¶t³z·!¸¹

°½²t³z´¼ µ» ³z·!¸¹


$

)LJXUH$ 0RGLILHGEXVQHWZRUN

6HFWLRQ

6HFWLRQ

6HFWLRQ

Southwest

Central

NorthExternal

¿ÀÁÁtÂvÃ%ÄÅ ÁÁÁtÂvÆÅ ÁÁ+ÁtÂvÆÀÁÁtÂzÃ!ÄÇ

À+ÁÁtÂgÃ%ÄÈ ÁÁtÂgÆÈ ÁÁtÂzÆÉÁÁtÂzÃ!ÄÇ

¿+ÁÁtÂgÃ%ÄÇ

ÉÁÁtÂzÃ!ÄÇ

È+Ê ÁtÂzÃ!ÄÈ ÁÁtÂzÆ

Å+ËÊÍÌ ÀtÂvÃ!Ä

É Å ÁÁtÂgÃ!ÄÎÏGÐ ÑÒGÓGÔÏ

È ÁÁtÂzÃ!ÄÅ ÀÁtÂzÆÅ+Ë ¿+ÁÁtÂvÃ%ÄÅ+ËÈÍÌ ÀtÂvÆ

Ì ÁÁtÂzÃ!ÄÊÈ ÁtÂzÆ

È ÁÁtÂzÃ!ÄÁÕÂzÆ

À+¿ÁtÂgÆÉ Ê ÁtÂgÃ%ÄÇ

ÉÉÀÁtÂgÆÉ È ÁtÂzÃ!ÄÇ¿ÁÁtÂzÆÉ¿ÖtÂzÃ!ÄÇ

ÖÁÁtÂzÆÈ Á È ÂzÃ!ÄÇÖ+ÀÁtÂzÆÉ¿ÁtÂzÃ!ÄÇ

× Å ÁÁtÂvÃ!ÄÇ

× Å ÁÁÂvÃÄÇ

× ÉÁÁtÂgÃ!ÄÇ

Ì ÁÁtÂzÆÅ ÀÁtÂzÃ!ÄÇ

ÉÁÁtÂzÆÀÁtÂgÃ!ÄÇ

Å+ËÊ Á+ÁtÂvÃ!ÄÅ+Ë À¿+ÁtÂvÆ

Ø ÁÁtÂzÆÈ Á Å ÂzÃ!ÄÇ

× ÉÁÁtÂgÃ!ÄÇ

Ì ÁÁtÂzÃ!ÄÊ ÁÁtÂzÆ ÀÀÁtÂzÃ!Ä¿ÁÁtÂzÆ

ÀÁÁtÂzÆÉ¿ÖtÂzÃ!ÄÇ

È ÁÁtÂzÆÉÁÁtÂzÃ!ÄÇ

Ê ÁÁtÂzÃ!ÄÀ È ÁtÂzÆ

ÅËÊ ÁÁtÂgÃ!ÄÅË À È ÁtÂgÆÀ+ÖÁtÂzÆÈ ÁÁtÂzÃ!ÄÇ

ÙÚ É

ÙÚ À

Û ÜÝ Û ÜÞ

Û Üß

ÙÚÅÙÚÈ

ÙÚØ

ÙÚ É ÈÛ Üà Û Üáâ Û Üáá

Û Üáã

Û Üáß

Û Üáä Û Üá

ÝÛ ÜáÞ

å ÚÅå Ú É Ê

å ÚÈæÜá

å Ú À

å Ú ¿

å Ú Ö

æÜÞ æÜç

æÜáß

æÜáä

å ÚÊ

å Ú ÉÉ

æÜáâ

æÜáã

æÜáè

ÅËÊ ÁÁtÂgÆ


$

$SSHQGL[%&RQYHUWHUPRGHOOLQJLQ6LPSRZ

%

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éê LV WKHPHDQYDOXHRIWKHGFYROWDJH8 éê LVSURSRUWLRQDOWRWKHFRPPXWDWLRQYROWDJH8 ë RQWKH DF VLGH DQG WKH FRVLQH RI WKH GHOD\ DQJOH FRVα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αDQGWKHRYHUODSDQJOHX7KH GHOD\ DQJOH KDV D PLQLPXP DQG D PD[LPXP YDOXH 7KH PLQLPXP YDOXH LVGHFLGHGE\WKHIDFWWKDWDSRVLWLYHYROWDJHLVUHTXLUHGDFURVVWKHYDOYHEHIRUHILULQJ7KH PD[LPXP YDOXH RI WKH GHOD\ DQJOH LV OLPLWHG E\ WKH UHTXLUHG FRPPXWDWLRQPDUJLQDQG WKHRYHUODSDQJOH7KHPD[LPXPGHOD\DQJOHZLOOEH X−−= γπα ìíî ZKHUHγLVWKHFRPPXWDWLRQPDUJLQ%&RQYHUWHUSDUDPHWHUV7KHPDLQFLUFXLWRIWKHKYGFFRQYHUWHULVGHVFULEHGE\WKHIROORZLQJSDUDPHWHUV , ïð WKHUDWHGGLUHFWFXUUHQWRIWKHFRQYHUWHU 8 ï+ñ ò!ð WKHUDWHGLGHDOQRORDGGLUHFWYROWDJH G ó WKHUHODWLYHUHVLVWLYHGLUHFWYROWDJHGURSRIWKHFRQYHUWHU Gô WKHUHODWLYHLQGXFWLYHGLUHFWYROWDJHGURSRIWKHFRQYHUWHUG ó Gô


%

)LJXUH% (TXLYDOHQWFLUFXLWRIDFXUUHQWVRXUFHOLQHFRPPXWDWHGFRQYHUWHU

F

E

α'&

6\VWHP

, õ8õ

SKDVH$&

6\VWHP 8 ö

M; M /ö öω

8 ÷11$&

11'&

11'&

, ö11$&

8 ø

, øφ

ααùú û

γ

8 ü

, ü

11'&

11'&

11$&, ý8 ý

M; ý

8 þ , ÿ 8 ÿ

8 ÿ

O ýG G

8 ÿα ≤ α ≤ π γX

8 ý

8 þ, ý

, ý

, ý

M; ý , ý

5H

,P

88&

8&8

FRV

π

α

=

= α ILULQJDQJOHRUGHOD\DQJOHγ FRPPXWDWLRQPDUJLQDQJOHX RYHUODSDQJOH≤X≤ π8 FRPPXWDWLRQYROWDJH8 EDVHYROWDJHRQDFVLGH8 EDVHYROWDJHRQGFVLGHG UHODWLYHUHVLVWLYHGFYROWDJHGURSRIFRQYHUWHUG UHODWLYHLQGXFWLYHGFYROWDJHGURSRIFRQYHUWHU

D


%

7KHUDWLQJRIWKHFRQYHUWHULVJLYHQE\, DQG8 ZKLFKLVWKHGLUHFWYROWDJHDWRSHUDWLRQZLWKQRPLQDOILULQJDQJOHα RUγ ! 8 #" $% LVWKHQFDOFXODWHGIURP

FRV &'()* + (

) ( GG88

+−= α IRUDUHFWLILHU

FRV ,-./0 1 .

/ . GG88

−−= γ IRUDQLQYHUWHU%&RQYHUWHUWUDQVIRUPHU7KHUDWHGYROWDJHDQGSRZHURIWKHFRQYHUWHUWUDQVIRUPHUDUHUHODWHGWRWKHFRQYHUWHUSDUDPHWHUVDVIROORZV

7KHUDWHGYROWDJHRIWKHYDOYHZLQGLQJRIWKHWUDQVIRUPHU8 2 LVFDOFXODWHGIURPWKHUDWHGLGHDOQRORDGYROWDJHRIWKHFRQYHUWHU

35467 8 4 88 ⋅= π

7KHUDWHGFXUUHQWRIWKHYDOYHZLQGLQJRIWKHWUDQVIRUPHULVGHILQHGDVWKHUPVYDOXHIRUDUHFWDQJXODUZDYHVKDSHRIWKHDFFXUUHQWRIWKHFRQYHUWHUDWUDWHGGLUHFWFXUUHQW

9 :; : ,, =

7KHUDWHGSRZHURIWKHFRQYHUWHUWUDQVIRUPHUEHFRPHV< =<> ?@=A =A == ,8,86 ⋅=⋅⋅= π

7KHUHODWLYHVKRUWFLUFXLWUHDFWDQFHRIWKHWUDQVIRUPHUHB EHFRPHVUHODWHGWRWKHUHODWLYHLQGXFWLYHGLUHFWYROWDJHGURSRIWKHFRQYHUWHUGB CC GH = %&RQYHUWHUFRQWUROV\VWHP7KHFRQWUROV\VWHPLVGHVFULEHGLQJHQHUDOWHUPVLQFKDSWHU5HJXODWLRQDQGFRQWURORIKYGFFRQYHUWHUV,QWKLVVHFWLRQGHWDLOVOLNHWUDQVIHUIXQFWLRQVRIWKHGLIIHUHQWFRQWUROOHUVDQGLQSXWDQGRXWSXWSDUDPHWHUVZLOOEHPHQWLRQHG>@%&RQWURORIDSRZHUIORZFDOFXODWLRQ)RUWKHSRZHUIORZFDOFXODWLRQZKLFKDLPVDWFDOFXODWLQJWKHLQMHFWHGFXUUHQWVWRWKHGFDQGDFQRGHVRIWKHKYGFFRQYHUWHUWKHFRQYHUWHUPRGHOLVVXSSOHPHQWHGZLWKVWDWLFPRGHOVRIWKHFRQWUROOHUV$VH[SODLQHGLQFKDSWHUWKHILULQJDQJOHRIDFRQYHUWHULVXVHGWRYDU\WKHGFYROWDJH7KURXJKWKLVWKHGFFXUUHQWRUYROWDJHFDQEHUHJXODWHGWRDGHVLUHGYDOXHZLWKLQFHUWDLQOLPLWV7KHRWKHUEDVLFFRQWURORSWLRQLVWRXVHWKHWDSFKDQJHURIWKHFRQYHUWHUWUDQVIRUPHUWRFRQWUROWKHFRPPXWDWLRQYROWDJHRIWKHFRQYHUWHU7KLVPD\EHXVHGWRUHJXODWHWKHFRPPXWDWLRQYROWDJHLWVHOIDGFYROWDJHWKHILULQJDQJOHαRIDFXUUHQWFRQWUROOHGUHFWLILHURUWKHFRPPXWDWLRQPDUJLQγRIDFXUUHQWFRQWUROOHGLQYHUWHU

)RUV\PPHWULFDOVWHDG\VWDWHFRQGLWLRQVWKHFRQWUROOHGYDULDEOHZLOOEHFRPHHTXDOWR LWV RUGHUHG YDOXH XQOHVV WKH YDULDEOH LV RXWVLGH LWV OLPLWV ,Q WKDW FDVH LWZLOO EHHTXDOWRWKDWOLPLW


%

%&RQYHUWHUFRQWURO$VPHQWLRQHGWKHFRQWUROYDULDEOHRIWKHFRQYHUWHULVWKHILULQJDQJOHα,WFDQEHYDULHGEHWZHHQDPLQLPXPOLPLWα DFE GIH ZKLFKLVDFRQVWDQWOLPLWDQGDPD[LPXPOLPLWα DKJMLIH ZKLFKLVDIXQFWLRQRIWKHPLQLPXPFRPPXWDWLRQPDUJLQDQJOHγDFE GNH DQGWKHFRPPXWDWLRQRYHUODSDQJOHXDVα DKJLOH πXγ DFE GNH 7KHRYHUODSDQJOHGHSHQGVRQWKHGLUHFWFXUUHQWDQGWKHFRPPXWDWLRQYROWDJH$WQRUPDORSHUDWLRQLWLVFRPPRQWKDWWKHFRQYHUWHUVDUHFRQWUROOHGZLWKWKHREMHFWLYHWRNHHSWKHGFFXUUHQWFRQVWDQW7KHGFYROWDJHDFURVVWKHFRQYHUWHUYHUVXVWKHGLUHFWFXUUHQWLVVKRZQLQILJXUH%7KHGFYROWDJHFDQEHYDULHGZLWKLQWKHLQWHUYDO8 P α DFE GNH ≥8 P ≥8 P γDFE GNH DQGZLWKLQWKLVUDQJHWKHGFFXUUHQWFDQEHFRQWUROOHGRQDFRQVWDQWYDOXH

)LJXUH% 9ROWDJH±FXUUHQWFKDUDFWHULVWLFVIRUDQKYGFFRQYHUWHU7KHFXUUHQWRUGHUVIRUWKHGLIIHUHQWFRQYHUWHUVLQWKHV\VWHPDUHFKRVHQVXFKWKDWΣ, PQ#R STUV E W%E TS@X Y ±Σ, PQ#R E GZMTSV TS@X Y 7KHFXUUHQWPDUJLQLVDGGHGLQWKHFRQYHUWHUWKDWLVJLYHQWKHWDVNWRFRQWUROWKHYROWDJH7KHFXUUHQWPDUJLQZLOOIRUFHWKHILULQJDQJOHLQWKLVFRQYHUWHUWRDOLPLWZKLFKPHDQVWKDWWKHFRQYHUWHUFDQQRWFRQWUROLWVFXUUHQWVLQFHαLVORFNHGDQGZLOOFRQWUROWKHGFYROWDJHLQVWHDG,IWKLVYROWDJHFRQWUROOLQJVWDWLRQLVDUHFWLILHULWZLOORSHUDWHDWWKHPLQLPXPILULQJDQJOHOLPLW8 P α DFE GIH LQILJXUH%DQGLILWLVDQLQYHUWHULWZLOORSHUDWHZLWKDFRQVWDQWPLQLPXPPDUJLQRIFRPPXWDWLRQ8 P γDFE GNH LQILJXUH%

8 [

&&

&,$

&($

8 []\_^ `_aα

8 [b\c^ `_aγ


%

7KHIROORZLQJSDUDPHWHUVKDVWREHJLYHQLQRUGHUWRFRQWURODFRQYHUWHURQFRQVWDQWFXUUHQW 7KHFXUUHQWRUGHU, PQ 7KHFXUUHQWRUGHUFDQEHFKRVHQLQGHSHQGHQWO\LQDOO

FRQYHUWHUVH[FHSWRQH 7KHFXUUHQWPDUJLQ, D 7KHFXUUHQWPDUJLQLVDGGHGWRWKHFRQYHUWHUZKLFKLV

JLYHQWKHWDVNWRFRQWUROWKHGFYROWDJH, D LILWLVDQLQYHUWHUDQG, D !LILWLVDUHFWLILHU

α DFE GNH WKHPLQLPXPILULQJDQJOHIRUVWHDG\VWDWHFRQGLWLRQV7\SLFDOYDOXHVIRUDUHFWLILHULV°DQGIRUDQLQYHUWHU°

γDFE GNH WKHPLQLPXPPDUJLQRIFRPPXWDWLRQIRUVWHDG\VWDWHFRQGLWLRQV7\SLFDOYDOXHLV°IRUERWKLQYHUWHUDQGUHFWLILHU

7RFRQWURODFRQYHUWHURQFRQVWDQWGFYROWDJHWKHIROORZLQJSDUDPHWHUVPXVWEHJLYHQ 7KHYROWDJHRUGHU8 PQ α DFE GNH WKHPLQLPXPILULQJDQJOHIRUVWHDG\VWDWHFRQGLWLRQV γDFE GNH WKHPLQLPXPPDUJLQRIFRPPXWDWLRQIRUVWHDG\VWDWHFRQGLWLRQV%&RQWURORIWKHORDGWDSFKDQJHURIDFRQYHUWHUWUDQVIRUPHU7KHFRQWUROYDULDEOHRIWKHWDSFKDQJHULVWKHWXUQVUDWLRη7KHWXUQVUDWLRFDQEHYDULHGEHWZHHQDPLQLPXPDQGDPD[LPXPOLPLWDQGLVQRUPDOO\YDULHGLQVWHSVRIRIWKHUDWHGYROWDJH+RZHYHULQWKHSRZHUIORZFDOFXODWLRQLQ6LPSRZWKHGLVFUHWHQDWXUHRIηLVQHJOHFWHGDQGLWLVWUHDWHGDVFRQWLQXRXV7KHWDSFKDQJHUFRQWUROPD\EHXVHGWRUHJXODWHWKHGFYROWDJHWKHILULQJDQJOHRUWKHPDUJLQRIFRPPXWDWLRQDQJOHRIWKHFRQYHUWHURUWKHDFYROWDJHRQWKHFRQYHUWHUVLGHRIWKHWUDQVIRUPHU%&RQWURORIDG\QDPLFVLPXODWLRQ)RUVLPXODWLRQRIWUDQVLHQWFRQGLWLRQVWKHFRQWUROOHUVDUHUHSUHVHQWHGE\WKHLUWUDQVIHUIXQFWLRQVDQGOLPLWV,QWKLVVHFWLRQWKHPDLQFRQWUROPRGXOHVZLOOEHGHVFULEHG)LJXUH%JLYHVDQRYHUYLHZRIWKHFRQYHUWHUFRQWUROV\VWHP%&RQYHUWHUILULQJFRQWURO&)&(DFKFRQYHUWHUKDVLWVRZQILULQJFRQWURO,QILJXUH%WKHIXQFWLRQDOGLDJUDPRIWKH&)&LVVKRZQ2XWSXW7KH&)&SURYLGHVWKHILULQJDQJOHαWRWKHFRQYHUWHU,WLVXVHGDVWKHLQSXWVLJQDOWRWKHPRGHORIWKHFRQYHUWHU de f αααα φ ∆+∆+= ZKHUHα g@h LVWKHSULQFLSDORXWSXWIURPWKHPRGHORIWKHFRQYHUWHUILULQJV\VWHP∆αφLVDFRUUHFWLRQWKDWDGMXVWVWKHILULQJDQJOHWRWKHSKDVHRIWKHDFWXDOFRPPXWDWLRQYROWDJH∆α i LVDFRQWULEXWLRQIURPDVRFDOOHGG\QDPLFFXUUHQWFRPSRXQGLQJZKLFKPD\EHXVHGIRULQFUHDVLQJWKHYROWDJHVWDELOLW\ZKHQDQLQYHUWHULVRSHUDWLQJZLWKFRQVWDQWPDUJLQRIFRPPXWDWLRQFRQQHFWHGWRDZHDNDFV\VWHP

7KHILULQJDQJOHαLVDOVRXVHGDVDFRQWUROVLJQDOWRWKHFXUUHQWFRQWURODPSOLILHU&&$


%

)LJXUH% 2YHUYLHZRIWKHKYGFFRQWUROV\VWHP,QSXW7KHLQSXWWRWKH&)&LVWKHILULQJDQJOHRUGHUα j α g ∆α k ZKHUHα g LVWKHRXWSXWVLJQDOIURPWKH&&$DQG∆α k LVDQRSWLRQDOXVHUGHILQHGFRQWUROVLJQDO7UDQVIHUIXQFWLRQ7KHWUDQVIHUIXQFWLRQRIWKH&)&LVUHSUHVHQWHGE\DILOWHUZLWKWKHWLPHFRQVWDQW7l GULYHQE\α j DQGZLWKWKHRXWSXWVLJQDOα g@h /LPLWV'HULYDWLYHV 7KHWLPHGHULYDWLYHRIαLVOLPLWHGEHWZHHQPD[LPXPDQGPLQLPXP

YDOXHV mon pα DQG qsr5tα ZKLFKDUHFRQVWDQWOLPLWVα uKv w 7KHPLQLPXPILULQJDQJOHα uKv w RIDUHFWLILHUUHIHUUHGWRWKHSKDVH

RIWKHDFWXDOFRPPXWDWLQJYROWDJHLVDYDULDEOHOLPLW,WLVYROWDJHGHSHQGHQWDQGPD\EHLQIOXHQFHGE\DVXSSOHPHQWDU\DFRUGFYROWDJHFRQWUROOHU∆α uKv wKg RUE\DQRSWLRQDOXVHUGHILQHGFRQWUROYDULDEOH∆α uKv wKk 7KHYDOYHVDUHLJQLWHGIRUDFRQVWDQWLQVWDQWDQHRXVYDOXHRIWKHFRPPXWDWLRQYROWDJHKHQFHα uKv w LVLQFUHDVHGIRUGHFUHDVLQJFRPPXWDWLRQYROWDJH7KHPLQLPXPILULQJDQJOHRIDQLQYHUWHULVDFRQVWDQWYDOXH,WKDVWRSUHYHQWUHFWLILHURSHUDWLRQDQGWKXVKDVWREHFKRVHQ!°7KHSUH

Σ

3)&

0& 9'&2/

Σ

∆3

3 x, xzy |

, @x

&&$

&)&9&

∆8

α~

α

α'&

6\VWHP

, 8

, 8

SKDVH$&

6\VWHP∆ ∆ω ∆I 3

∆Ι

, x


%

VHWYDOXHLQ6LPSRZLVWKHYDOXHJLYHQIRUWKHLQLWLDOVWHDG\VWDWHFRQGLWLRQVα uKv w α uKv w

α uMh 7KHPD[LPXPILULQJDQJOHRIDFRQYHUWHUα uMh UHODWLYHWKHSKDVHRIWKHFRPPXWDWLRQYROWDJHLVDYDULDEOHOLPLWERWKIRUDUHFWLILHUDQGDQLQYHUWHUα uMh LVGHWHUPLQHGVXFKWKDWWKHPLQLPXPPDUJLQRIFRPPXWDWLRQγ uKv w LVDVVXUHG

φαγπα ∆−−−= o s5 X ZKHUHXLVWKHRYHUODSDQJOHRIWKHFRQYHUWHUα uMh ≥α uKv w IRUDQLQYHUWHUDQGα uMh ≥πIRUDUHFWLILHU

γ uKv w 7KHPLQLPXPPDUJLQRIFRPPXWDWLRQLVQRUPDOO\YDULDEOH,WLVGHFLGHGDVIRUERWKUHFWLILHUDQGLQYHUWHU

γγγγγ ∆+∆+∆+= o o o o ZKHUHγ uKv wK LVDYROWDJHGHSHQGHQWYDOXHRIWKHFRPPXWDWLRQPDUJLQγ uKv wk LVDQRSWLRQDOXVHUGHILQHGFRQWUROVLJQDOγ uv wKg LVDFRQWULEXWLRQIURPDVXSSOHPHQWDU\YROWDJHFRQWUROOHUVHHVHFWLRQ%DQGγ j l l LVDFRQVWDQWZKLFKDOORZVDQRIIVHWRIWKHPDUJLQRIFRPPXWDWLRQRIWKH&)&UHODWLYHWKDWRIWKH&&$

)LJXUH% )XQFWLRQDOGLDJUDPRIWKHFRQYHUWHUILULQJFRQWURO&)&

Σ Σ Σ

VπII

φ φ φ ∆αφ

Σ Σ

s % ¡z¢ £ ¤¡s¥

¦K§K¨ ©¤ª5

8'&∆γ«¬ ®z¯9&∆γ«¬ ®

8'&∆α

«° ±α

«¬ ®α α«¬ ®

α«° ±

8'&∆α«¬ ®#¯9&∆α«¬ ®

α ± αα

²7

V

. ³ Σ Σ´µ7V ¶

µ7V+

, ³

∆α³·

∆α³¸

∆α³

7R&&$

φV7I

I ⋅

&RQYHUWHUILULQJV\VWHP

8'& XVHUGHILQHGFRQWURO9& YROWDJHFRQWUROOHU

$GDSWLRQRI WRWKHSKDVHRIWKHFRPPXWDWLRQYROWDJHα

'\QDPLFFXUUHQWFRPSRXQGLQJ


%

%&XUUHQWFRQWURODPSOLILHU&&$$FXUUHQWFRQWURODPSOLILHUPD\EHFRPPRQWRVHYHUDOVHULHVFRQQHFWHGKYGFFRQYHUWHUVLQDSROH$EORFNGLDJUDPLVVKRZQLQILJXUH%2XWSXW7KHRXWSXWRIWKH&&$LVWKHILULQJDQJOHRUGHUGHQRWHGα ¹ ZKLFKVHUYHVDVWKHLQSXWVLJQDOWRWKH&)&WKHFRQYHUWHUILULQJFRQWUROV\VWHPVHHDOVRILJXUH%,QSXW7KHLQSXWVLJQDOWRWKH&&$LVDFRQWUROHUURUε ¹ ZKLFKLVGHWHUPLQHGLQWKHIROORZLQJZD\ º»¼»½¾ ,,, ∆+−=ε , ¿À LVWKHFXUUHQWRUGHUREWDLQHGIURPWKHFXUUHQWRUGHUOLPLWHU&2/, ¿¡Á LVWKHPHDVXUHGGLUHFWFXUUHQWRIWKHFRQYHUWHUDQG∆, Â LVDQRSWLRQDOXVHUGHILQHGVXSSOHPHQWDU\FXUUHQWRUGHU

)LJXUH% %ORFNGLDJUDPRIWKHFXUUHQWFRQWURODPSOLILHU&&$7UDQVIHUIXQFWLRQ7KHWUDQVIHUIXQFWLRQRIWKH&&$LVRIWKHSURSRUWLRQDOLQWHJUDOW\SH7KHJDLQRIWKHSURSRUWLRQDOSDUWPD\YDU\ZLWKWKHGFFXUUHQWGXHWRRYHUFXUUHQWFRQWURODQGZLWKWKHILULQJDQJOH

Σ&XUUHQWRUGHUOLPLWHU&2/

Σ

N Ã@Ä

αÅcÆ Ç

αÅoÈ É

N Ã Ê

. Ë

Ì7V+

Í7V+ Î

Ïαα

VLQVLQ

2YHUFXUUHQWFRQWURO

, Ð, Ð

, Ð Ñ

, Ð Ò

, Ò

8'& ,∆ Ó

εÔ

α

Õ7V− αÆ

αÃ

αÅ_Æ Ç

αÅoÈ ÉαÖ &RQYHUWHU

ILULQJFRQWUROOHU&)&

α∆α

∆α∆α∆α

Ò × Ø ÑÒ× Ø Ó

Ò× Ø ÔÙ Ð ÚÙ Û

8'&9&'&9&/,0756&2175'&/,1(3527*$00$2

)URP&)&


%

/LPLWVα ÜKÝ Þ α Üßà 7KHRXWSXWRIWKH&&$α á DQGLWVLQWHJUDOSDUWα Ý DUHERWKOLPLWHG

EHWZHHQDPD[LPXPDQGDPLQLPXPYDOXHα ÜßMà DQGα ÜKÝ Þ UHVSHFWLYHO\7KH\DUHERWKYDULDEOHOLPLWVGHWHUPLQHGDFFRUGLQJWR

α ÜKÝ Þ α ÜKÝ Þâ ∆α ÜKÝ ÞKã ∆α ÜKÝ Þá ∆α äMåæ ∆α äMß DQG α ÜßMà α ÜßMàçà ∆α ÜßMàèã ∆α ÜßMàá ∆α äMåæ ∆α äMß α ÜKÝ Þâ LVWKHPLQLPXPILULQJDQJOHIRUQRUPDOVWHDG\VWDWHRSHUDWLRQ ∆α ÜKÝ ÞKã DQG∆α ÜßMàã DUHRSWLRQDOXVHUGHILQHGFRQWUROVLJQDOV ∆α ÜKÝ Þá DQG∆α Üßàá DUHFRQWULEXWLRQVIURPDVXSSOHPHQWDU\YROWDJH

FRQWUROOHUVHHVHFWLRQ% ∆α äå%æ LVDFRQWULEXWLRQIURPDGFYROWDJHFRQWUROOHUIRUDUHFWLILHU

ZKLFKRSHUDWHVZLWKPLQLPXPILULQJDQJOHVHH'&9/,0FRQWUROOHUEHORZ

∆α äß ZLOOEH≥IRUWKHα ÜKÝ Þ OLPLWDQG≤IRUWKHα ÜßMà OLPLW,WLVDVSHFLDOWUDQVLHQWVXSSOHPHQWWRWKHPLQLPXPGHOD\DQJOHIRUDUHFWLILHURSHUDWLQJZLWKORZDFYROWDJHVHH756&2175DQG756&217,FRQWUROOHUEHORZ

'XULQJORZYROWDJHVWKHPLQLPXPILULQJDQJOHRIDQLQYHUWHULVFRQWUROOHGE\D*$00$2FRQWUROOHU'XULQJVKRUWFLUFXLWVLQWKHGFQHWZRUNWKHPD[LPXPDQGPLQLPXPILULQJDQJOHRIDUHFWLILHULVFRQWUROOHGE\D'&/,1(3527FRQWUROOHU%RWKFRQWUROOHUVDUHGHVFULEHGEHORZ

'&9/,0FRQWUROOHU7KHSXUSRVHRIWKH'&9/,0FRQWUROOHULVWROLPLWWKHGFYROWDJHRIDFRQYHUWHUXSZDUGIRURYHUYROWDJHVRQWKHDFVLGHRIWKHFRQYHUWHU$EORFNGLDJUDPLVVKRZQLQILJXUH%7KHWUDQVIHUIXQFWLRQLVRIWKHSURSRUWLRQDOLQWHJUDOW\SHDQGSURYLGHVDFRQWULEXWLRQ∆α äå%æ WRWKHFRQYHUWHUVHH/LPLWV)RUDQLQYHUWHUWKLVZLOOGHFUHDVHLWVPD[LPXPILULQJDQJOHα ÜßMà DQGIRUDUHFWLILHULWZLOOLQFUHDVHLWVPLQLPXPILULQJDQJOHα ÜKÝ Þ 7KH'&9/,0FRQWUROOHUPD\DOVREHXVHGIRUFRQWURORIWKHGFYROWDJHWRDFRQVWDQWYDOXH*$00$2FRQWUROOHU7KHUHVWDUWRIDQKYGFWUDQVPLVVLRQPD\EHLPSURYHGE\HVWDEOLVKLQJWKHGFYROWDJHEHIRUHWKHFXUUHQWLVSLFNHGXS7KLVFDQEHDFKLHYHGE\PHDQVRIWKH*$00$2FRQWUROOHUZKLFKIRUFHVWKHGHOD\DQJOHRIDQLQYHUWHUWRLWVPD[LPXPYDOXHGXULQJDVSHFLILHGWLPH7KHSULQFLSDOIXQFWLRQRIWKHFRQWUROOHULVVKRZQLQILJXUH%7KH*$00$2FRQWUROOHULVDFWLYDWHGZKHQWKHGFYROWDJHEHFRPHVOHVVWKDQDVSHFLILHGYDOXH8 ãéê DQGDIWHUDJLYHQGHOD\WLPH7 ëéê WKHPLQLPXPILULQJDQJOHLVVHWHTXDOWRWKHPD[LPXPILULQJDQJOHα ÜKÝ Þ α ÜßMà +RZHYHULIWKHDFYROWDJHDWWKHVDPHWLPHLVORZHUWKDQDVSHFLILHGYDOXHWKH*$00$2FRQWUROOHULVEORFNHG,IWKHGFYROWDJHLVUHHVWDEOLVKHGEHIRUH7 ëéê LVH[SLUHGWKHFRQWUROLVGHDFWLYDWHGRWKHUZLVHWKHFRQWUROLVQRWGHDFWLYDWHGXQWLOWKHGFYROWDJHULVHVDERYHDSUHVHWYDOXH8 ìéê DQGDIWHUDGHOD\WLPH7 íMéê α ÜÝ Þ LVFRQWUROOHGLQWKHQRUPDOZD\


%

)LJXUH% %ORFNGLDJUDPRIWKH'&9/,0FRQWUROOHU

)LJXUH% 3ULQFLSDOIXQFWLRQRIWKH*$00$2FRQWUROOHU756&2175FRQWUROOHU7KHWUDQVLHQWVDWDUHVWDUWRIDQKYGFWUDQVPLVVLRQDIWHUDVKRUWFLUFXLWFOHDULQJLQWKHDFQHWZRUNFRQQHFWHGWRDUHFWLILHUFDQEHGHFUHDVHGE\LQFUHDVLQJWKHPLQLPXPILULQJDQJOHRIDUHFWLILHUDWWKHIDXOWFOHDULQJ7KLVFDQEHGRQHE\XVLQJD756&2175FRQWUROOHU7KHSULQFLSDOIXQFWLRQRIWKLVFRQWUROOHULVVKRZQLQILJXUH%7KHFRQWUROLVDFWLYDWHGZKHQWKHDFYROWDJHGHFUHDVHVEHORZWKHFKRVHQYDOXH8 ëî ì 7KHPLQLPXPGHOD\DQJOHRIWKH&&$α ÜKÝ Þ LVWKHQGHFUHDVHGE\∆α äß VHHVHFWLRQ%/LPLWVDIWHUDJLYHQGHOD\WLPH7 ëî ì ,IWKHDFYROWDJHLVUHHVWDEOLVKHGEHIRUH7 ëî ì KDVH[SLUHGWKHFRQWUROLVGHDFWLYDWHG,IQRWWKH756&2175FRQWUROLVGHDFWLYDWHGZKHQWKHDFYROWDJHEHFRPHVODUJHUWKDQ8 ëî ì $IWHUWKDWWKHTXDQWLW\∆α äß LVJUDGXDOO\GHFUHDVHGWR]HURDVVKRZQLQILJXUH%756&217,FRQWUROOHU7KHSHUIRUPDQFHRIDQKYGFWUDQVPLVVLRQDIWHUDVKRUWFLUFXLWLQWKHDFQHWZRUNFRQQHFWHGWRDQLQYHUWHUPD\EHRSWLPLVHGE\GHFUHDVLQJWKHPD[LPXPILULQJDQJOH

ï ð7V

ï ð7V−

8 ñ

8 ò ó ô8 õ ó ô

7 ö óô 7 ÷ óôα αøcù ú øcû ü

W

W


%

RIWKHLQYHUWHU,WFDQEHGRQHE\PHDQVRID756&217,FRQWUROOHU7KHSULQFLSDOIXQFWLRQRIWKHFRQWUROOHULVVKRZQLQILJXUH%,WLVDFWLYDWHGZKHQWKHDFYROWDJHPHDVXUHGDWWKHGFVLGHRIWKHLQYHUWHUEHFRPHVORZHUWKDQWKHOHYHO8 ã î Ý $IWHUDGHOD\WLPH7 ëî Ý WKHPD[LPXPGHOD\DQJOHRIWKH&&$α ÜßMà LVGHFUHDVHGH[SRQHQWLDOO\DV∆α äß VHHVHFWLRQ%/LPLWVZLWKDWLPHFRQVWDQW7 íî Ý ,IWKHDFYROWDJHLVUHHVWDEOLVKHGEHIRUH7 ëî Ý KDVH[SLUHGWKHFRQWUROLVGHDFWLYDWHG,IQRWWKH756&217,FRQWUROLVGHDFWLYDWHGZKHQWKHDFYROWDJHEHFRPHVODUJHUWKDQ8 ì î Ý 7KHQWKHTXDQWLW\∆α äß LVH[SRQHQWLDOO\LQFUHDVHGWR]HURZLWKDWLPHFRQVWDQW7 ý%î Ý DVVKRZQLQILJXUH%

)LJXUH% 3ULQFLSDOIXQFWLRQRIWKH756&2175FRQWUROOHU

)LJXUH% 3ULQFLSDOIXQFWLRQRIWKH756&217,FRQWUROOHU


%

'&/,1(3527FRQWUROOHU$VKRUWFLUFXLWLQWKHGFQHWZRUNLVH[WLQJXLVKHGE\IRUFLQJWKHUHFWLILHUVLQWRLQYHUWHURSHUDWLRQ7KHFRQWUROLVSHUIRUPHGE\PHDQVRIDGFOLQHSURWHFWLRQWKH'&/,1(3527FRQWUROOHU:KHQWKHFRQWUROOHULVDFWLYDWHGWKHPLQLPXPILULQJDQJOHRIDUHFWLILHULVIRUFHGWRWKHPD[LPXPYDOXHα ÜKÝ Þ α ÜßMà $WWKHGHDFWLYDWLRQERWKOLPLWVDUHVHWWRDJLYHQYDOXHα ÜKÝ Þ α ÜßMà α å%áæ þ GXULQJDVSHFLILHGWLPH7 å%áæ þ 7KHLQVWDQWVIRUDFWLYDWLRQDQGGHDFWLYDWLRQDUHJLYHQE\WKHXVHU7KHSULQFLSDOIXQFWLRQLVVKRZQLQILJXUH%

)LJXUH% 3ULQFLSDOIXQFWLRQRIWKH'&/,1(3527FRQWUROOHU%&XUUHQWRUGHUOLPLWHU&2/7KHFXUUHQWRUGHUOLPLWHU&2/SURYLGHVWKHFXUUHQWFRQWURODPSOLILHU&&$ZLWKDQXSSHUDQGDORZHUOLPLWIRUWKHFXUUHQWRUGHUDVDIXQFWLRQRIWKHGFYROWDJH7KLVPD\EHXVHIXODWWKHVWDUWXSRIDQKYGFWUDQVPLVVLRQZLWKSDUDOOHOFRQYHUWHUVVLQFHWKHFXUUHQWRUGHUVIRUWKH&&$VRIWKHFRQYHUWHUVPD\EHWHPSRUDULO\UHGXFHGDVORQJDVWKHYROWDJHVDUHORZ$IXQFWLRQDOGLDJUDPRIWKH&2/LVJLYHQLQILJXUH%2XWSXW7KH&2/SURYLGHVWKHFXUUHQWRUGHU, åê WRWKH&&$VHHDOVRILJXUH%,QSXW7KHLQSXWVLJQDOWRWKH&2/LVWKHUHIHUHQFHYDOXHRIWKHFXUUHQWRUGHU, êMìÿ REWDLQHGIURPWKHPDVWHUFRQWURO0&VHHVHFWLRQ%7UDQVIHUIXQFWLRQ7KHLQSXWVLJQDOPD\EHVDPSOHGKROGDQGGHOD\HG7KHFXUUHQWRUGHULVREWDLQHGIURPWKHYROWDJHFXUUHQWFKDUDFWHULVWLFVLQILJXUH%7KHPHDVXULQJGHYLFHIRUWKHGLUHFWYROWDJH8 å¡Ü LVPRGHOOHGDVDILOWHUZLWKWZRWLPHFRQVWDQWV,IWKHGFYROWDJHLVORZWKHWLPHFRQVWDQW7 ë LVXVHG,WVKRXOGEHVPDOOWRWULJJHUDIDVWGHFUHDVHRIWKHFXUUHQWRUGHUZKHQWKHGLUHFWYROWDJHGURSVZKLFKPD\EHDQLQGLFDWLRQRIDGLVWXUEDQFH:KHQWKHGFYROWDJHULVHVDJDLQWKHWLPHFRQVWDQW7 í ZLOOEHXVHG,WVKRXOGEHVXIILFLHQWO\ODUJHWRDVVXUHDVPRRWKUHFRYHU\DIWHUDGLVWXUEDQFH


%

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

,,,, ∆+∆+= 2XWSXW7KHRXWSXWVLJQDOIURPWKHPDVWHUFRQWUROWRDFRQYHUWHURSHUDWHGLQWKHFXUUHQWFRQWUROPRGHLVWKHUHIHUHQFHYDOXHRILWVFXUUHQWRUGHU, êèìÿ 7KLVLVXVHGDVLQSXWWRWKHFRQYHUWHUFXUUHQWRUGHUOLPLWHUVHHILJXUH%

, 8

, ,

, ,

8 ! 8 ! 8 "7V+

8

,I8 8 WKHQ7 7 #ε,I8 !8 WKHQ7 7 $ε

0DVWHU&RQWUROOHU

0&6DPSOHDQGKROG7 %

&'(H−

, 8 )*

,

&XUUHQW&RQWURO$PSOLILHU&&$

, , ,


%

,QSXW)RUHDFKLQGHSHQGHQWFRQYHUWHUWKHIROORZLQJVLJQDOVDUHGHILQHGDVLQSXWWRWKH0&, åê 7KHFRQVWDQWFXUUHQWRUGHUIRUWKHVWHDG\VWDWHLQLWLDOSRZHUIORZ

FDOFXODWLRQ∆, åêèã $QRSWLRQDOXVHUGHILQHGFRQWURORIWKHGLUHFWFXUUHQWJLYHQE\D

WDEOH∆,þMá $QRSWLRQDOFRQWULEXWLRQIURPDFRQWUROOHUZKLFKYDULHVWKHGLUHFW

FXUUHQWLQUHVSRQVHWRFKDQJHVLQDIUHTXHQF\RUDSRZHUVHHVHFWLRQ%

3RZHUFRQWUROPRGH:LWKWKHFRQYHUWHULQWKHSRZHUFRQWUROPRGHWKHUHIHUHQFHYDOXHRIWKHFXUUHQWRUGHULVGHWHUPLQHGDV

+ ,,-./00

1 2 -0 8333, ∆+∆+

=

8 354 LVDGLUHFWYROWDJHGHWHUPLQHGDVIROORZV'XULQJQRUPDORSHUDWLRQZLWKWKHPHDVXUHGGLUHFWYROWDJHRIWKHFRQYHUWHU8 å¡Ü ODUJHUWKDQDORZHUOLPLW8 åæ WKHQ8 åþ LVHTXDOWRWKHPHDVXUHGYROWDJH8 åþ 8 å¡Ü 'XULQJGLVWXUEHGRSHUDWLRQZLWK8 å¡Ü ≤8 å%æ 8 åþ LVVHWWRDFRQVWDQWQRUPDOO\HTXDOWRWKHUDWHGYROWDJHRIWKHFRQYHUWHU7KLVLQIDFWPHDQVWKDWWKHFRQWUROHQWHUVLQWRFXUUHQWFRQWUROPRGHVLQFH8 åþ LVKHOGFRQVWDQW$IWHUWKHGLVWXUEDQFHSOXVDFHUWDLQWLPHGHOD\ZKHQ8 å¡Ü LQFUHDVHVDERYH8 åæ 8 åþ ZLOOEHVHWHTXDOWR8 å¡Ü DJDLQ2XWSXW$QDORJRXVWRWKHFXUUHQWFRQWUROPRGHWKHRXWSXWVLJQDOIURPWKHPDVWHUFRQWUROWRDFRQYHUWHURSHUDWHGLQWKHSRZHUFRQWUROPRGHLVWKHUHIHUHQFHYDOXHRILWVFXUUHQWRUGHU, êèìÿ 7KLVLVXVHGDVLQSXWWRWKHFRQYHUWHUFXUUHQWRUGHUOLPLWHU&2/,QSXW7KHIROORZLQJLQSXWVLJQDOVWRWKH0&DUHSRVVLEOHIRUHDFKFRQYHUWHULQSRZHUFRQWUROPRGH3 ê 7KHFRQVWDQWSRZHURUGHUIRUWKHVWHDG\VWDWHLQLWLDOSRZHUIORZ

FDOFXODWLRQ∆3 êèã $QRSWLRQDOXVHUGHILQHGVXSSOHPHQWDU\FRQWUROJLYHQE\DWDEOH∆3þMá $QRSWLRQDOFRQWULEXWLRQIURPDFRQWUROOHUZKLFKYDULHVWKHDFWLYH

SRZHURIWKHFRQYHUWHULQUHVSRQVHWRFKDQJHVLQDIUHTXHQF\RUDSRZHUVHHVHFWLRQ%


%

)LJXUH%)XQFWLRQDOGLDJUDPRIWKHPDVWHUFRQWURO0&&RRUGLQDWLRQRIWKHFXUUHQWRUGHUVIRUSDUDOOHOFRQYHUWHUV$VPHQWLRQHGLQFKDSWHUDV\VWHPRISDUDOOHOKYGFFRQYHUWHUVDUHXVXDOO\RSHUDWHGDFFRUGLQJWRWKHFXUUHQWPDUJLQSULQFLSOHZKHUHWKHFXUUHQWRUGHULVVHWLQGHSHQGHQWO\LQDOOFRQYHUWHUVEXWRQH7KHFXUUHQWRUGHULQWKHODVWFRQYHUWHUEHFRPHVGHSHQGHQWDQGLVGHWHUPLQHGIURP∑ ∑ =−

6 7"8"9 : ;: 7"6 < : =?>"7"6 9 7"6 <@A@A ,,

3)& &2/0&RILQGHSHQGHQWFRQYHUWHU

∆,BC D∆3 BC D

, EF G CH

3)& ∆, BC D

3)& ∆3 BC D

Σ

∆, IEJ , IE

&2/N

, EF G CK

Σ

∆3 ELJ 3 E

GLY

M7V+

3 E

&XUUHQWFRQWURO

3RZHUFRQWURO

8 N O

8 NP 8 N Q

8 8N ORN Q8 N O FRQVW

S7V+ 8 TVU

0&RILQGHSHQGHQWFRQYHUWHUN

0&RILQGHSHQGHQWFRQYHUWHUQ3)& ∆,BC D∆3 BC D

&2/Q

, EF G CWX H

∑=

YZ

[ [\ ] ^_,H

∑=

`Z

[ [\ ] ^_,H

Σ

5HFWLILHU

,QYHUWHU

&2/Q

, EF G CW

0&RILQGHSHQGHQWFRQYHUWHUQ

, EF G CW


%

7KLVHTXDWLRQLVYLVXDOLVHGLQILJXUH%ERWWRPVTXDUH,IWKHUHVXOWIURPWKLVHTXDWLRQVKRZVWKDWWKHUHIHUHQFHYDOXHIRUWKHFXUUHQWRUGHUIRUWKHODVWFRQYHUWHUEHFRPHVOHVVWKDQ]HURWKHFKRLFHRIFXUUHQWRUGHUVIRUWKHRWKHUFRQYHUWHUVLVQRWIHDVLEOHDQGPXVWEHFKDQJHG

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

7KHDFWLYHSRZHURIWKHKYGFOLQNLVYDULHGE\PHDQVRIDFRQWUROOHUFDOOHGSRZHUIUHTXHQF\FRQWUROOHU3)&WKDWUHVSRQGVWRYDULDWLRQVLQDIUHTXHQF\WKHVSHHGRIDURWDWLQJPDFKLQHRUWKHSRZHURQDOLQH$EORFNGLDJUDPRIWKH3)&LVVKRZQLQILJXUH%2XWSXW$VVKRZQLQILJXUH%WKHRXWSXWIURPWKH3)&LVDQLQSXWVLJQDOWRWKHPDVWHUFRQWUROOHU,IWKHPDVWHUFRQWUROOHULVLQFXUUHQWFRQWUROPRGHWKHVLJQDOLV∆,ab5c DQGLIWKH0&LVLQSRZHUFRQWUROPRGHWKHVLJQDOLV∆3ab5c ,QSXW7KHLQSXWWRWKH3)&PD\EHRQHRIWKHIROORZLQJTXDQWLWLHV3 d e f?g 3 d e f 7KHGHYLDWLRQRIWKHDFWLYHSRZHURQDVSHFLILHGOLQHIURPDGHVLUHG

YDOXHI g I 7KHGHYLDWLRQLQIUHTXHQF\LQDVSHFLILHGQRGHIURPDGHVLUHGYDOXHω g ±ω 7KHGHYLDWLRQRIWKHDQJXODUYHORFLW\RIDVSHFLILHGURWDWLQJPDFKLQH

IURPDGHVLUHGYDOXH7UDQVIHUIXQFWLRQ7KH3)&LVGLYLGHGLQWRWZRSDUWVDUHJXODWRU'&5DQGDPHDVXULQJDQGFRPPXQLFDWLRQOLQN)3'VHHILJXUH%7KHUHJXODWRULQFOXGHVDGHDGEDQGDQGDWUDQVIHUIXQFWLRQ*VZKLFKPD\EHFKRVHQDVDSURSRUWLRQDODSURSRUWLRQDOLQWHJUDORUDSURSRUWLRQDOLQWHJUDOGHULYDWLYHWUDQVIHUIXQFWLRQ,WPD\DOVREHPXOWLSOLHGZLWKDSLHFHZLVHOLQHDUIXQFWLRQRIWLPHGHILQHGE\WKHXVHU

7KHPHDVXULQJGHYLFHLVUHSUHVHQWHGE\DILUVWRUGHUILOWHUDQGWKHFRPPXQLFDWLRQOLQNE\DVDPSOHKROGDQGGHOD\FLUFXLW


%

)LJXUH%%ORFNGLDJUDPRIWKHSRZHUIUHTXHQF\FRQWUROOHU3)&ZKLFKLV

GLYLGHGLQWRWZRSDUWVDUHJXODWRUQDPHG'&5DQGDPHDVXULQJDQGWHOHFRPPXQLFDWLRQVOLQNQDPHG)3'

%$FRUGFYROWDJHFRQWURO9&7KHUHDUHIRXUSRVVLEOHZD\VWRXVHDYROWDJHFRQWUROOHU9&WRFRQWURODQDFRUDGFYROWDJHWZRIRUDQLQYHUWHUDQGWZRIRUDUHFWLILHU$EORFNGLDJUDPRIWKH9&LVVKRZQLQILJXUH%

$QLQYHUWHUZKLFKLVRSHUDWLQJDWPD[LPXPILULQJDQJOHPD\EHXVHGWRFRQWUROLWVDFRUGFYROWDJH7KLVFRQWUROLVDFKLHYHGHLWKHUE\YDU\LQJWKHPLQLPXPPDUJLQRIFRPPXWDWLRQRIWKHFRQYHUWHU&)&VHFWLRQ%∆γ hie jkc LRUE\YDU\LQJWKHPD[LPXPILULQJDQJOHRIWKHFRQYHUWHU&&$VHFWLRQ%∆α hml5noc L

6LPLODUO\DUHFWLILHURSHUDWLQJDWLWVPLQLPXPILULQJDQJOHPD\EHXVHGWRFRQWUROWKHDFRUGFYROWDJHRIWKHFRQYHUWHU7KLVLVGRQHHLWKHUE\YDU\LQJWKHPLQLPXP

Σ0HDVXUHP

DQGWHOHFRP

Σ. p

∆q. r s t [

) Wu

Σ

[ ) Wv

3Iw x y zzzω

3Iw x y

ω ∆ q ∆ q | ∆, q ∆3 q

'&5

0DVWHUFRQWUROOHU

0&+9'&FRQYHUWHU

$&6\VWHP

)3'

∆3

( )( )( )~~ 7V.7V.7V.7V.7V.6*

+++++=

*V

Σ

[ ) Wv

3I ω

3Iw x y

ω ∆ q ∆ q |

7V+ 6DPSOH

DQGKROG7

H 5 . q

)3'


%

ILULQJDQJOHRIWKHFRQYHUWHU&)&VHFWLRQ%∆α i k URUE\YDU\LQJWKHPLQLPXPILULQJDQJOHRIWKHFRQYHUWHU&&$VHFWLRQ%∆α i k U

$FKDQJHLQILULQJDQJOHFDXVHVDFKDQJHLQGFYROWDJHGLUHFWO\7RFKDQJHWKHDFYROWDJHKRZHYHUWKHSKDVHRIWKHDFFXUUHQWPXVWEHYDULHG7KHQWKHUHDFWLYHSRZHURIWKHFRQYHUWHUZLOOYDU\DVZHOODQGKHQFHWKHDFYROWDJHZLOOFKDQJH

)LJXUH%%ORFNGLDJUDPRIWKHYROWDJHFRQWUROOHU9&2XWSXW,IWKHYROWDJHFRQWUROOHURXWSXWLVXVHGDVDQLQSXWVLJQDOWRWKHFRQYHUWHUILULQJFRQWUROV\VWHP&)&WKHRXWSXWVLJQDOZLOOEH∆γ k i IRUDQLQYHUWHUDQG∆α i i IRUDUHFWLILHUVHHILJXUH%

,IWKHRXWSXWIURPWKH9&LVXVHGDVDQLQSXWWRWKHFXUUHQWFRQWURODPSOLILHU&&$WKHRXWSXWVLJQDOZLOOEH∆α m5o IRUDQLQYHUWHUDQG∆α i k IRUDUHFWLILHUVHHILJXUH%,QSXW7KHLQSXWWRWKHYROWDJHFRQWUROUHJXODWRULVWKHFRQWUROHUURUε 8 ±8ZKHUH8LVWKHPDJQLWXGHRIDQDFRUGFYROWDJHIRUDVSHFLILHGQRGHDQG8 LVWKHGHVLUHGYROWDJHLQWKDWQRGH

Σ

[ ) W

ε

8

8

* [) W

( )( )( )( ) 7V7V7V$7V$

7V$7V$++++

++

∆

∆

&)&

&&$2SWLRQV∆α¡¢ £¥¤ L∆α¡ ¦ §¨¤ U

∆α¡¨¦ §¨¤ U∆γ¡¨¦ §¨¤ L

$SSHQGL[&/RDGGLVWULEXWLRQ

&

$SSHQGL[&/RDGGLVWULEXWLRQRIWKHPRGLILHG1RUGLFQHWZRUN7KHVWUXFWXUHRIWKHPRGLILHG1RUGLFQHWZRUNLVVKRZQLQILJXUH&%XVHV7KHDQJOHφ LVWKHDQJOHEHWZHHQWKHEXVLQTXHVWLRQDQGWKHUHIHUHQFHEXVEXV7KHYROWDJHDWWKHEXVLVJLYHQLQERWWSXDQGN9/LQHV3RVLWLYHDFWLYHRUUHDFWLYHSRZHULQGLFDWHVWKDWWKHSRZHUIORZGLUHFWLRQLVLQWRWKHILUVWEXVPHQWLRQHGHJRQWKHOLQHEHWZHHQEXVDQGWKHDFWLYHSRZHUIORZVIURPEXVEXWWKHUHDFWLYHSRZHUIORZVLQWREXV3URGXFWLRQVORDGVDQGVKXQWLPSHGDQFHV3RVLWLYH DFWLYH RU UHDFWLYH SRZHU LQGLFDWHV WKDW SRZHU LV SURGXFHG&RQVHTXHQWO\QHJDWLYHSRZHULQGLFDWHVWKDWSRZHULVFRQVXPHG

%868 38.9φ = '(*5((6 0: 09$5/,1(%86%86&/ /,1(%86%86&/ /,1(%86%86&/ /,1(%86%86&/ 352'%86* %868 38 .9φ = '(*5((6 0: 09$56+81%86 /,1(%86%86&/ /,1(%86%86&/ /,1(%86%86&/ 352'%86* 352'%86*

$SSHQGL[&/RDG'LVWULEXWLRQ

&

%868 38

.9φ '(*5((6 0: 09$5/,1(%86%86&/ /,1(%86%86&/ /,1(%86%86&/ 352'%86* %868 38

.9φ '(*5((6

0: 09$5/,1(%86%86&/ /,1(%86%86&/ /,1(%86%86&/ /,1(%86%86&/ 352'%86* %868 38

.9φ '(*5((6

0: 09$5/,1(%86%86&/ /,1(%86%86&/ /,1(%86%86&/ /,1(%86%86&/ /,1(%86%86&/ 352'%86* 352'%86* %868 38

.9φ '(*5((6

0: 09$5/,1(%86%86&/ /,1(%86%86&/ /,1(%86%86&/ /,1(%86%86&/


&

%868 38

.9φ '(*5((6

0: 09$56+81%86 /,1(%86%86&/ /,1(%86%86&/ /,1(%86%86)/ /,1(%86%86)/ /2$'%86 /2$'%86 /2$'%86 127&211(&7('352'%86* (%868 38

.9φ '(*5((6

0: 09$5/,1(%86%86&/ /,1(%86%86&/ /,1(%86%86)/ /,1(%86%86)/ /2$'%86 /2$'%86 352'%86* %868 38

.9φ '(*5((6

0: 09$56+81%86 /,1(%86%86)/ /,1(%86%86)/ /,1(%86%86)/ /,1(%86%86)/ /2$'%86 /2$'%86 /2$'%86


&

%868 38

.9φ '(*5((6

0: 09$5/,1(%86%86&/ /,1(%86%86)/ /,1(%86%86)/ /,1(%86%86)/ /,1(%86%86)/ /,1(%86%86)/ /2$'%86 /2$'%86 /2$'%86 %868 38

.9φ '(*5((6

0: 09$56+81%86 /,1(%86%86)/ /,1(%86%86)/ /2$'%86 /2$'%86 /2$'%86 %868 38

.9φ '(*5((6

0: 09$5/,1(%86%86)/ /,1(%86%86)/ /2$'%86 352'%86* 352'%86*


&

%868 38

.9φ '(*5((6

0: 09$5/,1(%86%86)/ /,1(%86%86)/ /,1(%86%86)/ /,1(%86%86)/ /,1(%86%86)/ /2$'%86 /2$'%86 /2$'%86 127&211(&7('%868 38

.9φ '(*5((6

0: 09$56+81%86 /,1(%86%86)/ /,1(%86%86)/ /2$'%86 /2$'%86 127&211(&7('352'%86* 352'%86* 127&211(&7('%868 38

.9φ '(*5((6

0: 09$5/,1(%86%86)/ /,1(%86%86)/ /2$'%86 /2$'%86 /2$'%86


&

%868 38

.9φ '(*5((6

0: 09$5/,1(%86%86)/ /,1(%86%86)/ /,1(%86%86)/ /,1(%86%86)/ /2$'%86 /2$'%86 127&211(&7('352'%86* (%868 38

.9φ '(*5((6

0: 09$5/,1(%86%86)/ /,1(%86%86)/ /2$'%86 /2$'%86 352'%86* 352'%86* %868 38

.9φ '(*5((6

0: 09$56+81%86 /,1(%86%86&/ /,1(%86%86&/ /,1(%86%86&/ ( /,1(%86%86&/ ( /2$'%86 352'%86* %868 38

.9φ '(*5((6

0: 09$5/,1(%86%86&/ ( /,1(%86%86&/ ( /2$'%86 352'%86*


&

)LJXUH&0RGLILHGEXVQHWZRUN

6HFWLRQ

6HFWLRQ

6HFWLRQ

Southwest

Central

NorthExternal

©ª««¬m®¨¯° «««¬m±

° ««!«¬m±ª««¬o®¥¯³²

ª!««¬´®¨¯µ ««¬´±

µ « «¬o±¶V« «¬o®¥¯³²

©!««¬´®¨¯³²

¶V««¬o®¥¯³²

µ!· «¬o®¥¯µ « «¬o±

°!¸?·¹ ª¬m®¥¯

¶ ° ««¬´®¥¯ºV»L¼ ½ ¾L¿LÀ»

µ ««¬o®¥¯° ª«¬o±

°!¸ ©!««¬m®¨¯°!¸?µ¹ ª¬m±

¹ ««¬o®¥¯·µ «¬o±

µ ««¬o®¥¯«Á¬o±

ª!©«¬´±¶ · «¬´®¨¯³²

¶¶?ª«¬´±¶ µ «¬o®¥¯³²

©««¬o±¶5©Â¬o®¥¯³²

Â««¬o±µ « µ ¬o®¥¯³²

Â!ª «¬o±¶V© «¬o®¥¯³²

Ã ° ««¬m®¥¯³²

Ã ° ««¬m® ¯Ä²

Ã ¶V««¬´®¥¯³²

¹ ««¬o±° ª«¬o®¥¯³²

¶5««¬o±ª«¬´®¥¯³²

°!¸?· «!«¬m®¥¯°!¸ ª©!«¬m±

Å ««¬o±µ « ° ¬o®¥¯³²

Ã ¶5««¬´®¥¯³²

¹ ««¬o®¥¯· ««¬o±

ªª«¬o®¥¯©««¬o±

ª««¬o±¶5©Â¬o®¥¯³²

µ ««¬o±¶5««¬o®¥¯³²

· ««¬o®¥¯ª µ «¬o±

°Æ¸?· ««¬´®¥¯°Æ¸ ª µ «¬´±

ª!Â«¬o±µ ««¬o®¥¯³²

ÇkÈ ¶

ÇiÈ ª

É ÊË

É ÊÌ

É ÊÍ

ÇiÈÎ°

ÇiÈÎµ

ÇkÈÄÅ

ÇkÈ ¶ µÉ ÊÏ

É ÊÐÑ É ÊÐÐ

É ÊÐÒ

É ÊÐÍ

É ÊÐÓ É ÊÐ

ËÉ ÊÐÌ

Ô ÈÄ°Ô È ¶ ·

Ô ÈÎµÕÊÐ

Ô È ª

Ô È ©

Ô È Â

ÕÊÌ

ÕÊÖ

ÕÊÐÍ

ÕÊÐÓ

Ô ÈÄ·

Ô È ¶¶

ÕÊÐÑ

ÕÊÐÒ

ÕÊÐ×

°Æ¸?· ««¬´±


&

Documents

Operation and Control of HVDC links embedded in AC systems