Available online at www.sciencedirect.com ScienceDirect Energy Procedia 100 (2016) 137 –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mail address:OLXVKLGU#\DKRRFRP 1876-6102 © 2016 The Authors Published by Elsevier Ltd This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/) Peer-review under responsibility of the organizing committee of CPESE 2016 doi:10.1016/j.egypro.2016.10.155 138 Ying Sun et al / Energy Procedia 100 (2016) 137 – 140 3URSHURUWKRJRQDOGHFRPSRVLWLRQ7KHRU\ 6LQJXODU9DOXH'HFRPSRVLWLRQ69'LVDPHWKRGWRH[WUDFWGRPLQDQW³IHDWXUHV´DQGFRKHUHQWVWUXFWXUHVIURP GDWDDQGWRFRPSUHVVWKDWLQIRUPDWLRQLQWRDIHZORZRUGHU³ZHLJKWV´VLQJXODUYDOXHVDQGDVVRFLDWHGRUWKRQRUPDO HLJHQIXQFWLRQV7KH69'RIWKHPDWUL[5LVFDOFXODWHGE\WKHHTXDWLRQ 869T 7KHILUVWPFROXPQVRI8JLYHDQRUWKRQRUPDOEDVLVIRUWKHDSSUR[LPDWLRQRIWKHGDWD ĭi 8i d i d m 7KHHLJHQYDOXH Oi RI5FDQGHWHUPLQHWKHLPSRUWDQFHRIWKHFRUUHVSRQGLQJ32'PRGH>@7KHUHODWLYH³HQHUJ\´ FDSWXUHGE\WKHILUVWS32'PRGHVLVJLYHQE\ p N ¦O ¦O E i i i i 7KHLPSURYHPHQWRIWKH32'PHWKRGLQWURGXFHGE\(YHUVRQDQG6LURYLFK>@FDQUHFRQVWUXFWPLVVLQJGDWDXVLQJ D 32' EDVLV $ PDVN YHFWRU LV GHILQHG WR GHVFULEH ZKHUH GDWD DUH DYDLODEOH RU PLVVLQJ IRU D IORZ YHFWRU E\ SRLQWZLVHPXOWLSOLFDWLRQ n i L m n mi im )RUWKHIORZYHORFLW\ILHOG i WKHFRUUHVSRQGLQJPDVNYHFWRULVGHILQHG LI im LV PLVVLQJ RU LQFRUUHFW n i LI im LV DYDLODEOH ZKHUH im GHQRWHG WKH m WK HOHPHQW RI DV n i YHFWRU i /HWJEHD&)'VROXWLRQWKHUHFRQVWUXFWHGYHFWRU J FDQEHUHSUHVHQWHGLQWHUPVRID32'EDVLVRISYHFWRUV m m p J | ¦ bi ĭ i i 7KHEHVWDJUHHPHQWEHWZHHQWKHVROXWLRQJDQGWKHUHFRQVWUXFWHGYHFWRU J LVREWDLQHGE\PLQLPL]LQJWKHHUURU H J J H n 7KHFRHIILFLHQWV bi WKDWPLQLPL]HWKHHUURUFDQEHIRXQGE\GLIIHUHQWLDWLQJZLWKUHVSHFWWRHDFK bi LQWXUQ7KLV OHDGVWRWKHOLQHDUV\VWHPRIHTXDWLRQV 0E I ĭ i ĭ j n fi ZKHUH ij J ĭ i n DQGELVWKHPDWUL[RIWKH bi V %\VROYLQJ(TIRUEDQGXVLQJWKHUHFRQVWUXFWHGYHFWRU J FDQEHREWDLQHGZLWKDUHODWLYHHUURU J J J u H 6LPXODWLRQDQG5HVXOWV 3.1 Simulation model and typical solution \ \ [ [ )LJD9HORFLW\ILHOGXVLQJWKHILUVW32'PRGHVFRPSDUHGZLWKWKH&)'VROXWLRQVEHQODUJHPHQWRI)LJD 139 Ying Sun et al / Energy Procedia 100 (2016) 137 – 140 $VXIILFLHQWQXPEHURIIORZILHOGVDPSOHVQDPHO\³VQDSVKRWV´DUHQHHGHGWRH[WUDFWWKH32'EDVLV,QWKLVVWXG\ WKHIORZILHOGVDURXQGDPRXQWDLQDUHDPRGHODUHVLPXODWHGYLD&)'IRUDUDQJHRIWKHZLQGVSHHGIURPWRPV ZLWK DQ LQFUHPHQW RI PV DQG FRUUHVSRQGLQJO\ IORZ ILHOGV DUH FDOFXODWHG WR IRUP WKH VQDSVKRW PDWUL[ 7KH VLPXODWLRQGRPDLQLVIRUPHGHQFRPSDVVLQJWZRSDUWLDOO\RYHUODSSHGKLOOVDQGVXUURXQGLQJDUHDDQGWKHVKDSHRIWKH ILUVWKLOODQGWKHVHFRQGKLOOLVVLPXODWHGUHVSHFWLYHO\E\DFRVLQHPRGHO>@ H > F RVS U L @ U x y ZKHUH H m H m L H L H )RUHDFKRIWKH&)'UHVXOWVZLWKDGLIIHUHQWLQOHWZLQGVSHHGGDWDDUHH[WUDFWHGRQDJULGRISRLQWVLQ[ FRRUGLQDWHDQGLQ\FRRUGLQDWH$Qỵ³VQDSVKRW´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ensitivity via numbers of POD mode ,Q WKH SUHFHGLQJ H[DPSOH 32' PRGHV ZHUH XVHG IRU WKH GDWD UHFRQVWUXFWLRQ +RZHYHU WKH QXPEHU RI 32' PRGHVFDQLQIOXHQFHVWKHDFFXUDF\RIWKHUHVXOWV2XULQYHVWLJDWLRQLQWRWKHLQIOXHQFHRIWKHQXPEHURI32'PRGHV VKRZVWKHFKDQJHVRIRYHUDOOUHFRQVWUXFWLRQHUURUYHUVXVWKHQXPEHUVRI32'PRGHVDQGWKHIDFWWKHUHFRQVWUXFWLRQ DFFXUDF\LQFUHDVHVVLJQLILFDQWO\ZLWKWKHQXPEHURIWKH32'PRGHVRQO\XSWRDPRGHQXPEHURI7KHRYHUDOO HUURUHYHQULVHZKHQ32'PRGHVH[FHHGUHYHDOLQJDSURVSHFWIRUIXUWKHUDOJRULWKPLPSURYHPHQW 3.3 Sensitivity via numbers of sensors )RUFRQYHQWLRQDOZLQGIRUHFDVWLQJKLJKHUDFFXUDF\UHTXLUHVPRUHVHQVRUV+RZHYHUIRUUHGXFHGFRVWUHDVRQDEO\ DFFXUDWHIRUHFDVWLQJZLWKDOLPLWHGQXPEHURIVHQVRUVLVGHVLUHG)LJVKRZVWKHUHODWLRQVKLSEHWZHHQWKHQXPEHURI VHQVRUV DQG WKH RYHUDOO UHFRQVWUXFWLRQ HUURU ZLWK 32' PRGHV ,W FDQ EH VHHQ FOHDUO\ WKDW ZLWK WKH VDPH QXPEHURIVHQVRUVPRUH32'PRGHVFDQUHGXFHWKHRYHUDOOFRQVWUXFWLRQHUURU+RZHYHUWKHLPSURYHPHQWGXHWR LQFUHDVLQJ32'PRGHJUDGXDOO\GLPLQLVKHVDVKLJKHU32'PRGHVFDUU\OHVVLQIRUPDWLRQHQHUJ\ 3.4 Sensitivity via measurement errors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ing Sun et al / Energy Procedia 100 (2016) 137 –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