Advanced Application Guidelines for Ground Fault Protection George E. Alexander, Joe Mooney, and William Tyska Schweitzer Engineering Laboratories, Inc. Presented at the 28th Annual Western Protective Relay Conference Spokane, Washington October 23–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³VHULHVFDSDFLWRU´UHIHUVWRD³EDQN´RIPXOWLSOHLQGLYLGXDOFDSDFLWRUFDQVFRQQHFWHGLQD VHULHVSDUDOOHODUUDQJHPHQW)RUVLPSOLFLW\LQWKLVSDSHUZHXVH³VHULHVFDSDFLWRU´LQSODFHRIWKH PRUHFXPEHUVRPH³VHULHVFDSDFLWRUEDQN´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³LPSHGDQFHVSLUDO´SURGXFHGE\WKHVXEKDUPRQLFWUDQVLHQWV PHQWLRQHGDERYH)RUWXQDWHO\WKLVLPSHGDQFHVSLUDOFDQEHUHDGLO\DQDO\]HGIRUJURXQGGLVWDQFH IXQFWLRQVLPSOHPHQWHGLQGLJLWDORUQXPHULFUHOD\VWKDWHPSOR\DFRVLQHGLVFUHWH)RXULHU WUDQVIRUPRURWKHUGLJLWDOILOWHU 7KHIROORZLQJDQDO\VLVGHVFULEHVWKHLPSHGDQFHVSLUDOSKHQRPHQRQ1RWHWKDWWKHHIIHFWVRI E\SDVVSURWHFWLRQDUHQRWFRQVLGHUHG²WKHFDSDFLWDQFHYDOXHQHYHUFKDQJHV)LJXUHGHSLFWVRQH SKDVHRIDVHULHVFRPSHQVDWHGWUDQVPLVVLRQOLQH7KHVZLWFKFORVHVDWW WRDSSO\DQ$*IDXOW DWWKHUHPRWHEXVRIWKHWUDQVPLVVLRQOLQH =V =F =O YEXV YW =V =F =O 6RXUFH,PSHGDQFH 6HULHV&DSDFLWRU,PSHGDQFH 5HSOLFD/LQH,PSHGDQFH )LJXUH 6HULHVFRPSHQVDWHGWUDQVPLVVLRQOLQHV 7KHVROXWLRQLVREWDLQHGE\VROYLQJHTXDWLRQIRUWKHIDXOWFXUUHQWLWDQGVXEVHTXHQWO\VROYLQJ IRUWKHEXVYROWDJHYEXVW YW = 9 VLQ W + = LW 5 + GLW / + LW GW & GW × 7KHIROORZLQJYDOXHVZHUHXVHG 6RXUFH =V = =V = µ=V = µ /LQH =O = =O = µ=O = µ &DSDFLWRU =F = µ ± 9ROWDJH 9 = » YROWV 7KH$SKDVHIDXOWFXUUHQWLWLVVKRZQLQ)LJXUH )DXOW&XUUHQW IW IW ± ± ± 7LPHVHFRQGV )LJXUH )DXOW&XUUHQW:DYHIRUPV ,Q)LJXUHIWLVWKH+]FRPSRQHQWRIWKH$SKDVHIDXOWFXUUHQWDQGIWWKHEROGHGOLQH LVWKH+]QDWXUDOIUHTXHQF\WUDQVLHQW 7KH$SKDVHYROWDJHYEXVWLVVKRZQLQ)LJXUH %XV9ROWDJH IW IW ± ± 7LPHVHFRQGV )LJXUH %XV9ROWDJH:DYHIRUPV ,Q)LJXUHIWLVWKH+]FRPSRQHQWDQGIWWKHEROGHGOLQHLVWKH+]QDWXUDO IUHTXHQF\WUDQVLHQW 7KHQH[WVWHSLVWRVROYHIRUWKHDSSDUHQWLPSHGDQFHVHHQE\WKH$SKDVHJURXQGGLVWDQFHUHOD\ )LUVWWKHWLPHGRPDLQVROXWLRQIRULWDQGYEXVWDUHVDPSOHGWLPHVSHUF\FOH$IXOOF\FOH QRQUHFXUVLYHGLJLWDOILOWHUWKHQFRQYHUWVWKHVDPSOHGYDOXHVWRSKDVRUV7KHFXUUHQWSKDVRUVDUH WKHQFRPSHQVDWHGE\DGGLQJ>=±==@Â,WRWKHSKDVHFXUUHQWDQGWKHDSSDUHQWLPSHGDQFH LVFDOFXODWHGZKHUH, Â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²DGLUHFWLRQDOJURXQG GLVWDQFHIXQFWLRQDQHJDWLYHVHTXHQFHGLUHFWLRQDOIXQFWLRQRUD]HURVHTXHQFHGLUHFWLRQDO IXQFWLRQ²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³SRODUL]LQJ´TXDQWLW\DQGWRXVHWKHSUHIDXOW YDOXHRI97KHSUHIDXOWRU³PHPRU\´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³EXVVLGH´RU³OLQHVLGH´RIWKHVHULHVFDSDFLWRULVRQHIDFWRUWKDWGHWHUPLQHVZKDWKDSSHQV7KH GHVLJQRIWKHGLUHFWLRQDOIXQFWLRQFDQPLWLJDWHRUHOLPLQDWHWKHVHSUREOHPV³&RPSHQVDWHG´ GLUHFWLRQDOIXQFWLRQVSURYLGHWKHXVHUZLWKVHWWLQJVWKDWYLUWXDOO\³PRYH´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³]HURVHTXHQFHFXUUHQWFRPSHQVDWLRQ´RIWKHSKDVHFXUUHQWWRFRUUHFWO\GHWHUPLQHWKHWUXH SRVLWLYHVHTXHQFHLPSHGDQFHIURPWKHUHOD\WRDJURXQGIDXOW$FRQFLVHGHULYDWLRQRIWKH]HUR VHTXHQFHFXUUHQWFRPSHQVDWLRQIDFWRULVSUHVHQWHGLQ$SSHQGL[$ 7KH]HURVHTXHQFHFXUUHQWFRPSHQVDWLRQLVGHILQHGDVIROORZV ,D + N , N= = - = = ,DLVWKHSKDVHFXUUHQWDWWKHUHOD\DQG,LVWKH]HURVHTXHQFHFXUUHQWDWWKHUHOD\=LVWKH]HUR VHTXHQFHLPSHGDQFHDQG=LVWKHSRVLWLYHVHTXHQFHLPSHGDQFHRIWKHSURWHFWHGOLQH)RUD VHULHVFDSDFLWRUFRPSHQVDWHGWUDQVPLVVLRQOLQHVKRXOGWKHHYDOXDWLRQRINXVHXQFRPSHQVDWHG LPSHGDQFHV=DQG=RUFRPSHQVDWHGLPSHGDQFHV=±M;FDQG=±M;F";FLVWKHUHDFWDQFH RIWKHVHULHVFDSDFLWRUVORFDWHGEHWZHHQWKHUHOD\DQGWKHHQGRIWKHOLQH9ROWDJHWUDQVIRUPHU ORFDWLRQGHWHUPLQHVUHOD\ORFDWLRQ:HQH[WHYDOXDWHDQ$*IDXOWDWWKHUHPRWHEXVIRUWKHVHULHV FRPSHQVDWHGWUDQVPLVVLRQOLQHV\VWHPLQ)LJXUHWRKHOSDQVZHUWKLVTXHVWLRQ $VVXPHWKDWWKHVHULHVFDSDFLWRULVQRWE\SDVVHGGXULQJWKHIDXOWDQGWKDWXQFRPSHQVDWHGYDOXHV RI=DQG=DUHXVHGWRFDOFXODWHN N= µ - µ = µ - µ ,D = µ - , = µ - 9D = µ - 9D = µ ,D + N , $VVXPLQJWKHYROWDJHWUDQVIRUPHULVORFDWHGRQWKHEXVVLGHRIWKHVHULHVFDSDFLWRUZHNQRZWKDW WKHSRVLWLYHVHTXHQFHLPSHGDQFHIURPWKHUHOD\WRWKHIDXOWLVµµ± µ 7KHJURXQGGLVWDQFHUHOD\GRHVQRWFDOFXODWHWKHH[SHFWHGYDOXHRISRVLWLYHVHTXHQFHLPSHGDQFH 1H[WDVVXPHWKDWNLVFDOFXODWHGXVLQJFRPSHQVDWHGYDOXHVRI=DQG= N= (µ + µ - ) - (µ + µ - ) = µ - (µ + µ - ) 9D = µ ,D + N , 7KHGHVLUHGUHVXOWLVREWDLQHG,QIDFWWKHVSLUDOLQJLPSHGDQFHSORWWHGLQ)LJXUHZDVFDOFXODWHG XVLQJN µ± 7KHUHIRUHWKHDSSDUHQWDQVZHUWRWKHTXHVWLRQLVWRFDOFXODWHNXVLQJ=±M;FDQG=±M;FIRU JURXQGGLVWDQFHIXQFWLRQVWKDWDUHH[SHFWHGWRRSHUDWHEHIRUHWKHVHULHVFDSDFLWRULVE\SDVVHGDQG WRFDOFXODWHNXVLQJ=DQG=IRUJURXQGGLVWDQFHIXQFWLRQVWKDWDUHH[SHFWHGWRRSHUDWHDIWHUWKH VHULHVFDSDFLWRULVE\SDVVHG7KLVLVRQHRIWKRVHORJLFDODQVZHUVWKDWKDVQRYDOXHLQSUDFWLFHWKH SULPDU\YDULDEOHWKDWGHWHUPLQHVZKHQRULIDVHULHVFDSDFLWRULVE\SDVVHGRUWKHGHJUHHRI UHVLVWRUVKXQWLQJLI029¶VDUHXVHGLVWKHPDJQLWXGHRIIDXOWFXUUHQW%HFDXVHDJURXQGIDXOWDW DSDUWLFXODUORFDWLRQPD\EHDGLUHFWJURXQGRUDKLJKLPSHGDQFHJURXQGGHSHQGLQJXSRQZKDW FDXVHVWKHIDXOWJURXQGIDXOWFXUUHQWPDJQLWXGHVPD\YDU\IRUDJLYHQIDXOWORFDWLRQ )RUWKH)LJXUHH[DPSOHXVLQJN µ±FRXOGFDXVHD=RQHJURXQGGLVWDQFHIXQFWLRQ WRRYHUUHDFKIRUDUHPRWHEXVIDXOWLIWKHWUDQVPLVVLRQOLQHZDVRSHUDWHGZLWKWKHVHULHVFDSDFLWRU UHPRYHGIURPVHUYLFHVKRUWHG&RQVHTXHQWO\WKHEHVWSUDFWLFHLVWRFDOFXODWHNXVLQJWKH XQFRPSHQVDWHGYDOXHVRI=DQG= 6HWWLQJDQG6HOHFWLRQ*XLGHOLQHV :KDWLVWKHEHVWUHOD\VFKHPHWRXVHIRUVHULHVFRPSHQVDWHGWUDQVPLVVLRQOLQHSURWHFWLRQ²FXUUHQW GLIIHUHQWLDORUGLUHFWLRQDOFRPSDULVRQ"%HIRUHWKHDGYHQWRIVRSKLVWLFDWHGVWDWLFDQDORJDQG GLJLWDOQXPHULFUHOD\GHVLJQVWKHPRVWSRSXODUDQVZHUZDVSKDVHFRPSDULVRQDVXEVHWRI FXUUHQWGLIIHUHQWLDO7RGD\ERWKFXUUHQWGLIIHUHQWLDODQGGLUHFWLRQDOFRPSDULVRQVFKHPHVDUH DYDLODEOHIRUVHULHVFRPSHQVDWHGWUDQVPLVVLRQOLQHSURWHFWLRQ²RIWHQIURPWKHVDPH PDQXIDFWXUHU1RWDOOFXUUHQWGLIIHUHQWLDOUHOD\VDUHVXLWDEOH1RWDOOGLVWDQFHGLUHFWLRQDOIXQFWLRQ EDVHGGLUHFWLRQDOFRPSDULVRQVFKHPHVDUHVXLWDEOH7KHNH\LVWRNQRZDQGHYDOXDWHWKH FDSDELOLWLHVDQGOLPLWDWLRQVRIDJLYHQUHOD\V\VWHP6RPHUHOD\VFRPELQHFXUUHQWGLIIHUHQWLDODQG GLUHFWLRQDOFRPSDULVRQVFKHPHVLQRQHSDFNDJH 7KHUHTXLUHGFRPPXQLFDWLRQVFKDQQHOFDSDELOLWLHVVKRXOGEHFORVHO\VFUXWLQL]HG,QJHQHUDO GLUHFWLRQDOFRPSDULVRQVFKHPHVUHTXLUHOHVVFKDQQHOFDSDELOLW\WKDQGRFXUUHQWGLIIHUHQWLDO VFKHPHV:LWKWKHLQFUHDVLQJDYDLODELOLW\RIILEHURSWLFVZLGHUEDQGZLGWKFKDQQHOVDUHRIWHQ DYDLODEOHWRDOORZWKHXVHRIFXUUHQWGLIIHUHQWLDOVFKHPHV :KHQDXVHULVFRQVLGHULQJDSSOLFDWLRQRIDSDUWLFXODUUHOD\RUUHOD\VFKHPHRQDVHULHV FRPSHQVDWHGOLQHIRUWKHILUVWWLPHSUHDQGSRVWSXUFKDVHWHVWLQJRQDPRGHOSRZHUV\VWHP VLPXODWRUVKRXOGEHFRQVLGHUHG,QWKHSUHSXUFKDVHRUHYDOXDWLRQVWDJHVXFKWHVWLQJSHUPLWV VFUHHQLQJEHWZHHQFRPSHWLQJSURGXFWVDQGE\LQFUHDVLQJWKHXVHU¶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³&RPELQHG´RU³,QWHJUDWHG´VFKHPH,QWKLVW\SHRIVFKHPHWKHVDPHPHDVXULQJ HOHPHQWVDUHXVHGIRUERWKIDXOWGHWHFWLRQDQGSKDVHVHOHFWLRQ$QH[DPSOHRIWKLVW\SHRIVFKHPH PLJKWEHDQLQGLYLGXDOSKDVHOLQHFXUUHQWGLIIHUHQWLDOUHOD\7KHLQGLYLGXDOSKDVHGLIIHUHQWLDO HOHPHQWVZLOOGHWHFWWKHIDXOWDQGGHWHUPLQHZKLFKSKDVHVDUHLQYROYHGLQWKHIDXOW 7KHVHFRQGDSSURDFKLVD³6HSDUDWHG´VFKHPH,QWKLVVFKHPHGLIIHUHQWHOHPHQWVDUHXVHGWR GHWHFWWKHIDXOWDQGWRGHWHUPLQHWKHIDXOWHGSKDVH$QH[DPSOHRIWKLVLVDWKUHHSKDVHWULSSLQJ VFKHPHWKDWLVFRQYHUWHGWRVLQJOHSKDVHWULSSLQJE\WKHDGGLWLRQRISKDVHVHOHFWRUHOHPHQWVDQG DVVRFLDWHGORJLF :LWKWRGD\¶VPXOWLIXQFWLRQUHOD\VDVLQJOHSKDVHWULSSLQJVFKHPHLVPRVWOLNHO\WREHD FRPELQDWLRQRIWKHWUDGLWLRQDOVFKHPHV6RPHRIWKHPHDVXULQJHOHPHQWVSRVVLEO\JURXQG GLVWDQFHIXQFWLRQVDUHGHVLJQHGWRUHVSRQGRQO\WRVLQJOHOLQHWRJURXQGIDXOWV+RZHYHURWKHU HOHPHQWVLQWKHUHOD\VXFKDV]HURDQGQHJDWLYHVHTXHQFHRYHUFXUUHQWHOHPHQWVDUHLQKHUHQWO\ QRQSKDVHVHOHFWLYHDQGPXVWLQFOXGHVHSDUDWHSKDVHVHOHFWLRQHOHPHQWVZKHQDSSOLHGLQVLQJOH SKDVHWULSSLQJDSSOLFDWLRQV (IIHFWVRIDQ2SHQ3KDVH $QRSHQSKDVHRQDWUDQVPLVVLRQOLQHFUHDWHVXQEDODQFHVWKDWFDQDIIHFWQRWRQO\WKHUHOD\VRQWKH OLQHZLWKWKHRSHQSKDVHEXWDOVRRWKHUUHOD\VWKURXJKRXWWKHV\VWHP(LWKHUWKHSURWHFWLRQ HOHPHQWVPXVWEHGHVLJQHGWREHLPPXQHWRWKHHIIHFWVRIXQEDODQFHVRUWKH\PXVWEHGHVHQVLWL]HG RUUHPRYHGIURPVHUYLFHGXULQJWKHRSHQSROHSHULRGIROORZLQJDVLQJOHSKDVHWULS&RQVLGHU WKHVLPSOHV\VWHPRI)LJXUH7KLVVLPSOHV\VWHPLVXVHGWRVKRZWKHXQEDODQFHVUHVXOWLQJIURP DQRSHQSKDVHZLWKORDG0RGHOLQJRIDQRSHQSKDVHLVGLVFXVVHGLQ$SSHQGL[% / 5 /LQH /LQH /LQH /LQH )LJXUH 3DUDOOHO/LQH6\VWHP 7DEOH $OO3KDVHV&ORVHG &XUUHQW6HFRQGDU\$PSHUHV /LQH /LQH /LQH ,$ µ µ µ ,% µ± µ± µ± ,& µ µ µ , µ µ µ , , 9ROWDJHV6HFRQGDU\ %XV/ %XV5 9$ µ µ 9% µ± µ± 9& µ µ 9 µ µ 9 9 7DEOH $3KDVH2SHQLQ/LQH &XUUHQW6HFRQGDU\$PSHUHV /LQH /LQH /LQH ,$ µ µ ,% µ± µ± µ± ,& µ µ µ , µ µ µ , µ± µ µ± , µ± µ µ± 9ROWDJHV6HFRQGDU\ %XV/ %XV5 9$ µ µ 9% µ± µ± 9& µ µ 9 µ µ 9 µ µ± 9 µ µ± ,IWKHUHOD\SRWHQWLDOLVREWDLQHGIURPWKHOLQHUDWKHUWKDQWKHEXVDQG]HURYROWDJHLVDVVXPHGIRU $SKDVHWKHQWKHUHOD\RQ/LQHLVSUHVHQWHGZLWKWKHIROORZLQJDQDORJVLJQDOV 9ROWDJHV6HFRQGDU\ %XV/ %XV5 9$ 9% µ± µ± 9& µ µ 9 µ µ 9 µ± µ± 9 µ± µ±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µ 9% µ µ 9%& ± µ 9%& ± 9% 9& µ µ µ µ 9& 9$ 9$ µ ± 9%& ± µ ± )LJXUH (IIHFWRI2SHQ3ROHRQ4XDGUDWXUH3RODUL]LQJ9ROWDJH 7KHUHVXOWLQJSKDVHVKLIWDQGPDJQLWXGHFKDQJHVIRUWKHSRVLWLYHVHTXHQFHYROWDJHDUHVKRZQLQ )LJXUH7KHSRODUL]LQJYROWDJHIRUWKH$*JURXQGPKRGLVWDQFHHOHPHQWVLVUHGXFHGLQ PDJQLWXGHEXWWKHSKDVHDQJOHGRHVQRWFKDQJH 3RVLWLYHVHTXHQFHSRODUL]LQJYROWDJHLVUHFRPPHQGHGIRUPKRGLVWDQFHHOHPHQWVXVHGLQVLQJOH SKDVHWULSSLQJDSSOLFDWLRQV 1RUPDO&RQGLWLRQV 3KDVH%2SHQ 9$ 9$ µ 9% 9 9$ µ 9& µ 3KDVH&2SHQ µ ± µ µ 9& 9% µ µ 9 µ 9 ± µ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µ = WNPµ 6KHDWK5HWXUQ2QO\ = WNPµ 6KHDWKDQG(DUWK5HWXUQ = WNPµ (DUWK5HWXUQ2QO\ 8VLQJ(TXDWLRQWKH]HURVHTXHQFHFRPSHQVDWLRQIDFWRUVIRUHDFK]HURVHTXHQFHLPSHGDQFH DUHOLVWHGEHORZ N µ± 6KHDWK5HWXUQ2QO\ N µ± N µ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µ± $SSDUHQW= 0KR 4XDG±,5 =,PSHGDQFH 4XDG±, 6KHDWK5HWXUQ2QO\ Wµ 6KHDWKDQG(DUWK5HWXUQ Wµ (DUWK5HWXUQ Wµ 7DEOH =HUR6HTXHQFH&RPSHQVDWLRQ)DFWRU8VLQJ6KHDWKDQG(DUWK5HWXUQ =,PSHGDQFH 6KHDWKDQG(DUWK5HWXUQN µ± $SSDUHQW= 0KR 4XDG±,5 4XDG±, 6KHDWK5HWXUQ2QO\ Wµ 6KHDWKDQG(DUWK5HWXUQ Wµ (DUWK5HWXUQ Wµ 7DEOH =HUR6HTXHQFH&RPSHQVDWLRQ)DFWRU8VLQJ(DUWK5HWXUQ2QO\ =,PSHGDQFH (DUWK5HWXUQ2QO\N µ $SSDUHQW= 0KR 4XDG±,5 4XDG±, 6KHDWK5HWXUQ2QO\ Wµ± 6KHDWKDQG(DUWK5HWXUQ Wµ (DUWK5HWXUQ Wµ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±,&5±,&6 ZKHUH , 1HJDWLYHVHTXHQFHIDXOWFXUUHQWVXSSOLHGIURP6RXUFH5 5 , 1HJDWLYHVHTXHQFHIDXOWFXUUHQWIORZLQJWKURXJKWKHOLQHWHUPLQDODW 6WDWLRQ6 , 1HJDWLYHVHTXHQFHVKXQWFXUUHQWDW6WDWLRQ5 6 &5 , ,6 &6 1HJDWLYHVHTXHQFHVKXQWFXUUHQWDW6WDWLRQ6 6 5 5HOD\ ,&6 ,&5 ,5 5HOD\ )LJXUH 1HJDWLYH6HTXHQFH&XUUHQW'LVWULEXWLRQ²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±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³UHGXFH´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iQ³'LUHFWLRQDO(OHPHQW'HVLJQDQG(YDOXDWLRQ´ VW$QQXDO:HVWHUQ3URWHFWLYH5HOD\&RQIHUHQFH6SRNDQH:DVKLQJWRQ2FWREHU >@ -HVXV9DUJDV$UPDQGR*X]PiQ-RUJH5REOHV³8QGHUJURXQG6XEPDULQH&DEOH3URWHFWLRQ 8VLQJ$1HJDWLYH6HTXHQFH'LUHFWLRQDO&RPSDULVRQ6FKHPH´WK$QQXDO:HVWHUQ 3URWHFWLYH5HOD\&RQIHUHQFH6SRNDQH:$2FWREHU >@ (26FKZHLW]HU,,,DQG-5REHUWV³'LVWDQFH5HOD\(OHPHQW'HVLJQ´WK$QQXDO:HVWHUQ 3URWHFWLYH5HOD\&RQIHUHQFH6SRNDQH:$2FWREHU >@ -RH0RRQH\DQG-DFNLH3HHU³$SSOLFDWLRQ*XLGHOLQHVIRU*URXQG)DXOW3URWHFWLRQ´ WK$QQXDO:HVWHUQ3URWHFWLYH5HOD\&RQIHUHQFH6SRNDQH:$2FWREHU >@ -HII5REHUWV(GPXQG26FKZHLW]HU5HQX$URUDDQG(UQLH3RJJL³/LPLWVWRWKH6HQVLWLYLW\ RI*URXQG'LUHFWLRQDODQG'LVWDQFH3URWHFWLRQ´QG$QQXDO:HVWHUQ3URWHFWLYH5HOD\ &RQIHUHQFH6SRNDQH:$2FWREHU >@ .HQQHWK&%HKUHQGW³5HOD\WR5HOD\'LJLWDO/RJLF&RPPXQLFDWLRQIRU/LQH3URWHFWLRQ 0RQLWRULQJDQG&RQWURO´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Ë = - = Û = ,D + Ì Ü , = Í = Ý = = 6HW N = 9D = - = ,D + , = = - = = 7KHUHIRUH = = 9D ,D+ N , 1RWHWKDWµN¶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±,,7KHUHODWLRQVKLSRI, ±,,LVLGHQWLFDOWRWKDW REWDLQHGIRUDSKDVHWRSKDVHWRJURXQGIDXOWRQDUDGLDOV\VWHPZLWKWKHUHPRWHEUHDNHURSHQ 7KHUHOD\VDWERWKHQGVRIWKHOLQHDUHDOVRVXEMHFWHGWRWKHVDPHVHTXHQFHFXUUHQWVVLQFH,, DQG,DUHWKHHTXLYDOHQWIRUERWKHQGVRIWKHOLQH )LJXUH 6\PPHWULFDO&RPSRQHQWV&RQQHFWLRQIRU6LQJOH3KDVH2SHQ&RQGLWLRQ )LJXUH 6\PPHWULFDO&RPSRQHQWV&RQQHFWLRQIRU3KDVHWR3KDVHWR*URXQG)DXOW 7KHV\PPHWULFDOFRPSRQHQWFRQQHFWLRQLQ)LJXUHFDQEHUHGXFHGWRDSDUDOOHOFRQQHFWLRQRI WKHQHJDWLYHDQG]HURVHTXHQFHQHWZRUNVLQVHULHVZLWKWKHSRVLWLYHVHTXHQFHOLQHDQGVRXUFH LPSHGDQFHVVKRZQLQ)LJXUH5HGXFLQJWKHQHWZRUNVKRZVWKDWWKHQHJDWLYHDQG]HUR VHTXHQFHFXUUHQWVDUHIORZLQJLQRSSRVLWHGLUHFWLRQVRQWKHVXSSO\EXVWKHEXVVXSSO\LQJSUHIDXOW ORDGFXUUHQWDQGWKHORDGEXVIRUWKLVV\VWHP )LJXUH 6LPSOLILHG3DUDOOHO&RQQHFWLRQ1HJDWLYHDQG=HUR6HTXHQFH1HWZRUNV $VLQJOHSKDVHRSHQFRQGLWLRQGXULQJORDGSUHVHQWVWKHUHOD\VDWERWKHQGVRIWKHOLQHZLWK QHJDWLYHDQG]HURVHTXHQFHFXUUHQWVDQGYROWDJHV7KHPDJQLWXGHVRIQHJDWLYHDQG]HUR VHTXHQFHFXUUHQWVDQGYROWDJHVSURGXFHGDUHGHWHUPLQHGE\WKHORDGIORZDQGWKHVWUHQJWK PDJQLWXGHDQGDQJOHRIWKHVRXUFHV,IWKHORDGIORZLV]HURQRVHTXHQFHFXUUHQWRSHUDWLQJ TXDQWLWLHVDUHVXSSOLHGWRWKHUHOD\V$VORDGIORZLQFUHDVHVWKHVHTXHQFHFXUUHQWRSHUDWLQJ TXDQWLWLHVDYDLODEOHWRWKHUHOD\VEHFRPHODUJHU %,2*5$3+,(6 *HRUJH($OH[DQGHUKROGVD%6((GHJUHHIURP9LOODQRYD8QLYHUVLW\DQGDQ06((GHJUHH IURP'UH[HO8QLYHUVLW\+HLVDUHJLVWHUHGSURIHVVLRQDOHQJLQHHULQWKHVWDWHRI3HQQV\OYDQLD+H KDVRYHU\HDUVH[SHULHQFHLQWKHGHVLJQDQGDSSOLFDWLRQRIWUDQVPLVVLRQOLQHUHOD\LQJDQG KROGVVHYHUDO86SDWHQWVLQWKLVDUHD0U$OH[DQGHUKDVEHHQLQYROYHGLQWKHGHYHORSPHQWDQG 0RGHO3RZHU6\VWHPWHVWLQJRIVROLGVWDWHK\EULGDQDORJGLJLWDODQGIXOO\GLJLWDOSURWHFWLYH UHOD\LQJV\VWHPV+HMRLQHG6(/LQDQGLVFXUUHQWO\UHJLRQDOVHUYLFHPDQDJHUIRUWKH1RUWK 86DQG(DVWHUQ&DQDGD -RVHSK%0RRQH\3(UHFHLYHGKLV%6FLQ(OHFWULFDO(QJLQHHULQJIURP:DVKLQJWRQ6WDWH 8QLYHUVLW\LQ+HMRLQHG3DFLILF*DVDQG(OHFWULF&RPSDQ\XSRQJUDGXDWLRQDVD6\VWHP 3URWHFWLRQ(QJLQHHU,QKHOHIW3DFLILF*DVDQG(OHFWULFDQGZDVHPSOR\HGE\%RQQHYLOOH 3RZHU$GPLQLVWUDWLRQDVD6\VWHP3URWHFWLRQ0DLQWHQDQFH'LVWULFW6XSHUYLVRU,QKHOHIW %RQQHYLOOH3RZHU$GPLQLVWUDWLRQDQGMRLQHG6FKZHLW]HU(QJLQHHULQJ/DERUDWRULHVDVDQ $SSOLFDWLRQ(QJLQHHU6KRUWO\DIWHUVWDUWLQJZLWK6(/KHZDVSURPRWHGWR$SSOLFDWLRQ (QJLQHHULQJ0DQDJHU,QKHEHFDPH0DQDJHURIWKH3RZHU(QJLQHHULQJ*URXSRIWKH 5HVHDUFKDQG'HYHORSPHQWGHSDUWPHQWDW6FKZHLW]HU(QJLQHHULQJ/DERUDWRULHV+HLVD UHJLVWHUHG3URIHVVLRQDO(QJLQHHULQWKHVWDWHVRI&DOLIRUQLDDQG:DVKLQJWRQ :LOOLDP7\VNDUHFHLYHGD%6((IURP&ODUNVRQ8QLYHUVLW\DQGVXEVHTXHQWO\FRPSOHWHG*(¶V 3RZHU6\VWHP(QJLQHHULQJ&RXUVH+LVZRUNH[SHULHQFHLQFOXGHVGHVLJQDQGDSSOLFDWLRQRI SURWHFWLYHUHOD\HTXLSPHQWIRU\HDUVZLWK*(+HLVWKHDXWKRURUFRDXWKRURIUHOD\ FRQIHUHQFHSDSHUVUHODWHGWRSRZHUV\VWHPSURWHFWLRQ3UHVHQWO\KHLVHPSOR\HGDVDSRZHU HQJLQHHULQWKH.LQJRI3UXVVLD3$RIILFHRI6FKZHLW]HU(QJLQHHULQJ/DERUDWRULHV,QF &RS\ULJKW6(/ $OOULJKWVUHVHUYHG 3ULQWHGLQ86$
© Copyright 2024 Paperzz