A tight compact quadratically constrained convex relaxation of the Optimal Power Flow problem

Gespeichert in:

Autor*in:	Lambert, Amélie [verfasserIn]

Format:	E-Artikel
Sprache:	Englisch

Erschienen:	2024

Schlagwörter:	Semidefinite programming Global optimization Optimal Power Flow Quadratic convex relaxation Quadratically constrained quadratic programming

Übergeordnetes Werk:	Enthalten in: Computers & operations research - Amsterdam [u.a.] : Elsevier, 1974, 166(2024) vom: Juni, Artikel-ID 106626, Seite 1-12
Übergeordnetes Werk:	volume:166 ; year:2024 ; month:06 ; elocationid:106626 ; pages:1-12

Links:	Link aufrufen Link aufrufen

DOI / URN:	10.1016/j.cor.2024.106626

Katalog-ID:	1893546993

Internformat


LEADER	01000naa a2200265 4500
001	1893546993
003	DE-627
005	20240703071428.0
007	cr uuu---uuuuu
008	240703s2024 xx \|\|\|\|\|o 00\| \|\|eng c
024	7		\|a 10.1016/j.cor.2024.106626 \|2 doi
035			\|a (DE-627)1893546993
035			\|a (DE-599)KXP1893546993
040			\|a DE-627 \|b ger \|c DE-627 \|e rda
041			\|a eng
100	1		\|a Lambert, Amélie \|e verfasserin \|4 aut
245	1	2	\|a A tight compact quadratically constrained convex relaxation of the Optimal Power Flow problem \|c Amélie Lambert
264		1	\|c 2024
336			\|a Text \|b txt \|2 rdacontent
337			\|a Computermedien \|b c \|2 rdamedia
338			\|a Online-Ressource \|b cr \|2 rdacarrier
650		4	\|a Semidefinite programming \|7 (dpeaa)DE-206
650		4	\|a Global optimization \|7 (dpeaa)DE-206
650		4	\|a Optimal Power Flow \|7 (dpeaa)DE-206
650		4	\|a Quadratic convex relaxation \|7 (dpeaa)DE-206
650		4	\|a Quadratically constrained quadratic programming \|7 (dpeaa)DE-206
773	0	8	\|i Enthalten in \|t Computers & operations research \|d Amsterdam [u.a.] : Elsevier, 1974 \|g 166(2024) vom: Juni, Artikel-ID 106626, Seite 1-12 \|h Online-Ressource \|w (DE-627)306652668 \|w (DE-600)1499736-8 \|w (DE-576)081954336 \|x 0305-0548 \|7 nnns
773	1	8	\|g volume:166 \|g year:2024 \|g month:06 \|g elocationid:106626 \|g pages:1-12
856	4	0	\|u https://www.sciencedirect.com/science/article/pii/S0305054824000984/pdf \|x Verlag \|z kostenfrei
856	4	0	\|u https://doi.org/10.1016/j.cor.2024.106626 \|x Resolving-System \|z kostenfrei
912			\|a GBV_USEFLAG_U
912			\|a GBV_ILN_26
912			\|a ISIL_DE-206
912			\|a SYSFLAG_1
912			\|a GBV_KXP
912			\|a GBV_ILN_20
912			\|a GBV_ILN_22
912			\|a GBV_ILN_23
912			\|a GBV_ILN_24
912			\|a GBV_ILN_31
912			\|a GBV_ILN_32
912			\|a GBV_ILN_40
912			\|a GBV_ILN_60
912			\|a GBV_ILN_62
912			\|a GBV_ILN_65
912			\|a GBV_ILN_69
912			\|a GBV_ILN_70
912			\|a GBV_ILN_73
912			\|a GBV_ILN_74
912			\|a GBV_ILN_90
912			\|a GBV_ILN_95
912			\|a GBV_ILN_100
912			\|a GBV_ILN_105
912			\|a GBV_ILN_110
912			\|a GBV_ILN_150
912			\|a GBV_ILN_151
912			\|a GBV_ILN_187
912			\|a GBV_ILN_213
912			\|a GBV_ILN_224
912			\|a GBV_ILN_230
912			\|a GBV_ILN_370
912			\|a GBV_ILN_602
912			\|a GBV_ILN_702
912			\|a GBV_ILN_2001
912			\|a GBV_ILN_2003
912			\|a GBV_ILN_2004
912			\|a GBV_ILN_2005
912			\|a GBV_ILN_2007
912			\|a GBV_ILN_2009
912			\|a GBV_ILN_2010
912			\|a GBV_ILN_2011
912			\|a GBV_ILN_2014
912			\|a GBV_ILN_2015
912			\|a GBV_ILN_2020
912			\|a GBV_ILN_2021
912			\|a GBV_ILN_2025
912			\|a GBV_ILN_2026
912			\|a GBV_ILN_2027
912			\|a GBV_ILN_2034
912			\|a GBV_ILN_2044
912			\|a GBV_ILN_2048
912			\|a GBV_ILN_2049
912			\|a GBV_ILN_2050
912			\|a GBV_ILN_2055
912			\|a GBV_ILN_2056
912			\|a GBV_ILN_2059
912			\|a GBV_ILN_2061
912			\|a GBV_ILN_2064
912			\|a GBV_ILN_2106
912			\|a GBV_ILN_2110
912			\|a GBV_ILN_2111
912			\|a GBV_ILN_2112
912			\|a GBV_ILN_2122
912			\|a GBV_ILN_2129
912			\|a GBV_ILN_2143
912			\|a GBV_ILN_2152
912			\|a GBV_ILN_2153
912			\|a GBV_ILN_2190
912			\|a GBV_ILN_2232
912			\|a GBV_ILN_2336
912			\|a GBV_ILN_2470
912			\|a GBV_ILN_2507
912			\|a GBV_ILN_4035
912			\|a GBV_ILN_4037
912			\|a GBV_ILN_4112
912			\|a GBV_ILN_4125
912			\|a GBV_ILN_4242
912			\|a GBV_ILN_4249
912			\|a GBV_ILN_4251
912			\|a GBV_ILN_4305
912			\|a GBV_ILN_4306
912			\|a GBV_ILN_4307
912			\|a GBV_ILN_4313
912			\|a GBV_ILN_4322
912			\|a GBV_ILN_4323
912			\|a GBV_ILN_4324
912			\|a GBV_ILN_4326
912			\|a GBV_ILN_4333
912			\|a GBV_ILN_4334
912			\|a GBV_ILN_4338
912			\|a GBV_ILN_4393
912			\|a GBV_ILN_4700
912			\|a GBV_ILN_2403
912			\|a GBV_ILN_2403
912			\|a ISIL_DE-LFER
951			\|a AR
952			\|d 166 \|j 2024 \|c 6 \|i 106626 \|h 1-12
980			\|2 26 \|1 01 \|x 0206 \|b 454570283X \|y x1z \|z 03-07-24
980			\|2 2403 \|1 01 \|x DE-LFER \|b 4551110590 \|c 00 \|f --%%-- \|d --%%-- \|e n \|j --%%-- \|y l01 \|z 15-07-24
981			\|2 2403 \|1 01 \|x DE-LFER \|r https://doi.org/10.1016/j.cor.2024.106626
981			\|2 2403 \|1 01 \|x DE-LFER \|r https://www.sciencedirect.com/science/article/pii/S0305054824000984/pdf
982			\|2 26 \|1 00 \|x DE-206 \|b In this paper, we consider the Optimal Power Flow (OPF) problem which consists in determining the power production at each bus of an electric network by minimizing the production cost. Our contribution is an exact solution algorithm for the OPF problem. It consists in a spatial branch-and-bound algorithm based on a compact quadratically-constrained convex relaxation. It is computed by solving the semidefinite rank relaxation of OPF once at the root node of the algorithm. An important result is that the optimal value of our compact relaxation is equal to the rank relaxation value. Then, at every sub-nodes of our branch-and-bound, the lower bound is obtained by solving a quadratic convex problem instead of an SDP. Another contribution is that we add only O(n+m) variables that model the squares of the initial variables, where n is the number of buses in the power system and m the number of transmission lines, to construct our relaxation. Then, since the relations between the initial and auxiliary variables are non-convex, we relax them to get a quadratic convex relaxation. Finally, in our branch-and-bound algorithm, we only have to force a reduced number of equalities to prove global optimality. This quadratic convex relaxation approach is here tailored to the OPF problem, but it can address any application whose formulation is a quadratic optimization problem subject to quadratic equalities and ring constraints. Our first experiments on instances of the OPF problem show that our new algorithm Compact OPF (COPF) is more efficient than the standard solvers and other quadratic convex relaxation based methods we compare it with.

Indexfelder

author_variant	a l al
matchkey_str	article:03050548:2024----::tgtopcqartclyosriecnerlxtootep
hierarchy_sort_str	2024
publishDate	2024
allfields	10.1016/j.cor.2024.106626 doi (DE-627)1893546993 (DE-599)KXP1893546993 DE-627 ger DE-627 rda eng Lambert, Amélie verfasserin aut A tight compact quadratically constrained convex relaxation of the Optimal Power Flow problem Amélie Lambert 2024 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Semidefinite programming (dpeaa)DE-206 Global optimization (dpeaa)DE-206 Optimal Power Flow (dpeaa)DE-206 Quadratic convex relaxation (dpeaa)DE-206 Quadratically constrained quadratic programming (dpeaa)DE-206 Enthalten in Computers & operations research Amsterdam [u.a.] : Elsevier, 1974 166(2024) vom: Juni, Artikel-ID 106626, Seite 1-12 Online-Ressource (DE-627)306652668 (DE-600)1499736-8 (DE-576)081954336 0305-0548 nnns volume:166 year:2024 month:06 elocationid:106626 pages:1-12 https://www.sciencedirect.com/science/article/pii/S0305054824000984/pdf Verlag kostenfrei https://doi.org/10.1016/j.cor.2024.106626 Resolving-System kostenfrei GBV_USEFLAG_U GBV_ILN_26 ISIL_DE-206 SYSFLAG_1 GBV_KXP GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_150 GBV_ILN_151 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_370 GBV_ILN_602 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2007 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2034 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2106 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2470 GBV_ILN_2507 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4242 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4326 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 GBV_ILN_2403 GBV_ILN_2403 ISIL_DE-LFER AR 166 2024 6 106626 1-12 26 01 0206 454570283X x1z 03-07-24 2403 01 DE-LFER 4551110590 00 --%%-- --%%-- n --%%-- l01 15-07-24 2403 01 DE-LFER https://doi.org/10.1016/j.cor.2024.106626 2403 01 DE-LFER https://www.sciencedirect.com/science/article/pii/S0305054824000984/pdf 26 00 DE-206 In this paper, we consider the Optimal Power Flow (OPF) problem which consists in determining the power production at each bus of an electric network by minimizing the production cost. Our contribution is an exact solution algorithm for the OPF problem. It consists in a spatial branch-and-bound algorithm based on a compact quadratically-constrained convex relaxation. It is computed by solving the semidefinite rank relaxation of OPF once at the root node of the algorithm. An important result is that the optimal value of our compact relaxation is equal to the rank relaxation value. Then, at every sub-nodes of our branch-and-bound, the lower bound is obtained by solving a quadratic convex problem instead of an SDP. Another contribution is that we add only O(n+m) variables that model the squares of the initial variables, where n is the number of buses in the power system and m the number of transmission lines, to construct our relaxation. Then, since the relations between the initial and auxiliary variables are non-convex, we relax them to get a quadratic convex relaxation. Finally, in our branch-and-bound algorithm, we only have to force a reduced number of equalities to prove global optimality. This quadratic convex relaxation approach is here tailored to the OPF problem, but it can address any application whose formulation is a quadratic optimization problem subject to quadratic equalities and ring constraints. Our first experiments on instances of the OPF problem show that our new algorithm Compact OPF (COPF) is more efficient than the standard solvers and other quadratic convex relaxation based methods we compare it with.
spelling	10.1016/j.cor.2024.106626 doi (DE-627)1893546993 (DE-599)KXP1893546993 DE-627 ger DE-627 rda eng Lambert, Amélie verfasserin aut A tight compact quadratically constrained convex relaxation of the Optimal Power Flow problem Amélie Lambert 2024 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Semidefinite programming (dpeaa)DE-206 Global optimization (dpeaa)DE-206 Optimal Power Flow (dpeaa)DE-206 Quadratic convex relaxation (dpeaa)DE-206 Quadratically constrained quadratic programming (dpeaa)DE-206 Enthalten in Computers & operations research Amsterdam [u.a.] : Elsevier, 1974 166(2024) vom: Juni, Artikel-ID 106626, Seite 1-12 Online-Ressource (DE-627)306652668 (DE-600)1499736-8 (DE-576)081954336 0305-0548 nnns volume:166 year:2024 month:06 elocationid:106626 pages:1-12 https://www.sciencedirect.com/science/article/pii/S0305054824000984/pdf Verlag kostenfrei https://doi.org/10.1016/j.cor.2024.106626 Resolving-System kostenfrei GBV_USEFLAG_U GBV_ILN_26 ISIL_DE-206 SYSFLAG_1 GBV_KXP GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_150 GBV_ILN_151 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_370 GBV_ILN_602 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2007 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2034 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2106 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2470 GBV_ILN_2507 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4242 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4326 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 GBV_ILN_2403 GBV_ILN_2403 ISIL_DE-LFER AR 166 2024 6 106626 1-12 26 01 0206 454570283X x1z 03-07-24 2403 01 DE-LFER 4551110590 00 --%%-- --%%-- n --%%-- l01 15-07-24 2403 01 DE-LFER https://doi.org/10.1016/j.cor.2024.106626 2403 01 DE-LFER https://www.sciencedirect.com/science/article/pii/S0305054824000984/pdf 26 00 DE-206 In this paper, we consider the Optimal Power Flow (OPF) problem which consists in determining the power production at each bus of an electric network by minimizing the production cost. Our contribution is an exact solution algorithm for the OPF problem. It consists in a spatial branch-and-bound algorithm based on a compact quadratically-constrained convex relaxation. It is computed by solving the semidefinite rank relaxation of OPF once at the root node of the algorithm. An important result is that the optimal value of our compact relaxation is equal to the rank relaxation value. Then, at every sub-nodes of our branch-and-bound, the lower bound is obtained by solving a quadratic convex problem instead of an SDP. Another contribution is that we add only O(n+m) variables that model the squares of the initial variables, where n is the number of buses in the power system and m the number of transmission lines, to construct our relaxation. Then, since the relations between the initial and auxiliary variables are non-convex, we relax them to get a quadratic convex relaxation. Finally, in our branch-and-bound algorithm, we only have to force a reduced number of equalities to prove global optimality. This quadratic convex relaxation approach is here tailored to the OPF problem, but it can address any application whose formulation is a quadratic optimization problem subject to quadratic equalities and ring constraints. Our first experiments on instances of the OPF problem show that our new algorithm Compact OPF (COPF) is more efficient than the standard solvers and other quadratic convex relaxation based methods we compare it with.
allfields_unstemmed	10.1016/j.cor.2024.106626 doi (DE-627)1893546993 (DE-599)KXP1893546993 DE-627 ger DE-627 rda eng Lambert, Amélie verfasserin aut A tight compact quadratically constrained convex relaxation of the Optimal Power Flow problem Amélie Lambert 2024 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Semidefinite programming (dpeaa)DE-206 Global optimization (dpeaa)DE-206 Optimal Power Flow (dpeaa)DE-206 Quadratic convex relaxation (dpeaa)DE-206 Quadratically constrained quadratic programming (dpeaa)DE-206 Enthalten in Computers & operations research Amsterdam [u.a.] : Elsevier, 1974 166(2024) vom: Juni, Artikel-ID 106626, Seite 1-12 Online-Ressource (DE-627)306652668 (DE-600)1499736-8 (DE-576)081954336 0305-0548 nnns volume:166 year:2024 month:06 elocationid:106626 pages:1-12 https://www.sciencedirect.com/science/article/pii/S0305054824000984/pdf Verlag kostenfrei https://doi.org/10.1016/j.cor.2024.106626 Resolving-System kostenfrei GBV_USEFLAG_U GBV_ILN_26 ISIL_DE-206 SYSFLAG_1 GBV_KXP GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_150 GBV_ILN_151 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_370 GBV_ILN_602 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2007 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2034 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2106 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2470 GBV_ILN_2507 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4242 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4326 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 GBV_ILN_2403 GBV_ILN_2403 ISIL_DE-LFER AR 166 2024 6 106626 1-12 26 01 0206 454570283X x1z 03-07-24 2403 01 DE-LFER 4551110590 00 --%%-- --%%-- n --%%-- l01 15-07-24 2403 01 DE-LFER https://doi.org/10.1016/j.cor.2024.106626 2403 01 DE-LFER https://www.sciencedirect.com/science/article/pii/S0305054824000984/pdf 26 00 DE-206 In this paper, we consider the Optimal Power Flow (OPF) problem which consists in determining the power production at each bus of an electric network by minimizing the production cost. Our contribution is an exact solution algorithm for the OPF problem. It consists in a spatial branch-and-bound algorithm based on a compact quadratically-constrained convex relaxation. It is computed by solving the semidefinite rank relaxation of OPF once at the root node of the algorithm. An important result is that the optimal value of our compact relaxation is equal to the rank relaxation value. Then, at every sub-nodes of our branch-and-bound, the lower bound is obtained by solving a quadratic convex problem instead of an SDP. Another contribution is that we add only O(n+m) variables that model the squares of the initial variables, where n is the number of buses in the power system and m the number of transmission lines, to construct our relaxation. Then, since the relations between the initial and auxiliary variables are non-convex, we relax them to get a quadratic convex relaxation. Finally, in our branch-and-bound algorithm, we only have to force a reduced number of equalities to prove global optimality. This quadratic convex relaxation approach is here tailored to the OPF problem, but it can address any application whose formulation is a quadratic optimization problem subject to quadratic equalities and ring constraints. Our first experiments on instances of the OPF problem show that our new algorithm Compact OPF (COPF) is more efficient than the standard solvers and other quadratic convex relaxation based methods we compare it with.
allfieldsGer	10.1016/j.cor.2024.106626 doi (DE-627)1893546993 (DE-599)KXP1893546993 DE-627 ger DE-627 rda eng Lambert, Amélie verfasserin aut A tight compact quadratically constrained convex relaxation of the Optimal Power Flow problem Amélie Lambert 2024 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Semidefinite programming (dpeaa)DE-206 Global optimization (dpeaa)DE-206 Optimal Power Flow (dpeaa)DE-206 Quadratic convex relaxation (dpeaa)DE-206 Quadratically constrained quadratic programming (dpeaa)DE-206 Enthalten in Computers & operations research Amsterdam [u.a.] : Elsevier, 1974 166(2024) vom: Juni, Artikel-ID 106626, Seite 1-12 Online-Ressource (DE-627)306652668 (DE-600)1499736-8 (DE-576)081954336 0305-0548 nnns volume:166 year:2024 month:06 elocationid:106626 pages:1-12 https://www.sciencedirect.com/science/article/pii/S0305054824000984/pdf Verlag kostenfrei https://doi.org/10.1016/j.cor.2024.106626 Resolving-System kostenfrei GBV_USEFLAG_U GBV_ILN_26 ISIL_DE-206 SYSFLAG_1 GBV_KXP GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_150 GBV_ILN_151 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_370 GBV_ILN_602 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2007 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2034 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2106 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2470 GBV_ILN_2507 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4242 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4326 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 GBV_ILN_2403 GBV_ILN_2403 ISIL_DE-LFER AR 166 2024 6 106626 1-12 26 01 0206 454570283X x1z 03-07-24 2403 01 DE-LFER 4551110590 00 --%%-- --%%-- n --%%-- l01 15-07-24 2403 01 DE-LFER https://doi.org/10.1016/j.cor.2024.106626 2403 01 DE-LFER https://www.sciencedirect.com/science/article/pii/S0305054824000984/pdf 26 00 DE-206 In this paper, we consider the Optimal Power Flow (OPF) problem which consists in determining the power production at each bus of an electric network by minimizing the production cost. Our contribution is an exact solution algorithm for the OPF problem. It consists in a spatial branch-and-bound algorithm based on a compact quadratically-constrained convex relaxation. It is computed by solving the semidefinite rank relaxation of OPF once at the root node of the algorithm. An important result is that the optimal value of our compact relaxation is equal to the rank relaxation value. Then, at every sub-nodes of our branch-and-bound, the lower bound is obtained by solving a quadratic convex problem instead of an SDP. Another contribution is that we add only O(n+m) variables that model the squares of the initial variables, where n is the number of buses in the power system and m the number of transmission lines, to construct our relaxation. Then, since the relations between the initial and auxiliary variables are non-convex, we relax them to get a quadratic convex relaxation. Finally, in our branch-and-bound algorithm, we only have to force a reduced number of equalities to prove global optimality. This quadratic convex relaxation approach is here tailored to the OPF problem, but it can address any application whose formulation is a quadratic optimization problem subject to quadratic equalities and ring constraints. Our first experiments on instances of the OPF problem show that our new algorithm Compact OPF (COPF) is more efficient than the standard solvers and other quadratic convex relaxation based methods we compare it with.
allfieldsSound	10.1016/j.cor.2024.106626 doi (DE-627)1893546993 (DE-599)KXP1893546993 DE-627 ger DE-627 rda eng Lambert, Amélie verfasserin aut A tight compact quadratically constrained convex relaxation of the Optimal Power Flow problem Amélie Lambert 2024 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Semidefinite programming (dpeaa)DE-206 Global optimization (dpeaa)DE-206 Optimal Power Flow (dpeaa)DE-206 Quadratic convex relaxation (dpeaa)DE-206 Quadratically constrained quadratic programming (dpeaa)DE-206 Enthalten in Computers & operations research Amsterdam [u.a.] : Elsevier, 1974 166(2024) vom: Juni, Artikel-ID 106626, Seite 1-12 Online-Ressource (DE-627)306652668 (DE-600)1499736-8 (DE-576)081954336 0305-0548 nnns volume:166 year:2024 month:06 elocationid:106626 pages:1-12 https://www.sciencedirect.com/science/article/pii/S0305054824000984/pdf Verlag kostenfrei https://doi.org/10.1016/j.cor.2024.106626 Resolving-System kostenfrei GBV_USEFLAG_U GBV_ILN_26 ISIL_DE-206 SYSFLAG_1 GBV_KXP GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_150 GBV_ILN_151 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_370 GBV_ILN_602 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2007 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2034 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2106 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2470 GBV_ILN_2507 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4242 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4326 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 GBV_ILN_2403 GBV_ILN_2403 ISIL_DE-LFER AR 166 2024 6 106626 1-12 26 01 0206 454570283X x1z 03-07-24 2403 01 DE-LFER 4551110590 00 --%%-- --%%-- n --%%-- l01 15-07-24 2403 01 DE-LFER https://doi.org/10.1016/j.cor.2024.106626 2403 01 DE-LFER https://www.sciencedirect.com/science/article/pii/S0305054824000984/pdf 26 00 DE-206 In this paper, we consider the Optimal Power Flow (OPF) problem which consists in determining the power production at each bus of an electric network by minimizing the production cost. Our contribution is an exact solution algorithm for the OPF problem. It consists in a spatial branch-and-bound algorithm based on a compact quadratically-constrained convex relaxation. It is computed by solving the semidefinite rank relaxation of OPF once at the root node of the algorithm. An important result is that the optimal value of our compact relaxation is equal to the rank relaxation value. Then, at every sub-nodes of our branch-and-bound, the lower bound is obtained by solving a quadratic convex problem instead of an SDP. Another contribution is that we add only O(n+m) variables that model the squares of the initial variables, where n is the number of buses in the power system and m the number of transmission lines, to construct our relaxation. Then, since the relations between the initial and auxiliary variables are non-convex, we relax them to get a quadratic convex relaxation. Finally, in our branch-and-bound algorithm, we only have to force a reduced number of equalities to prove global optimality. This quadratic convex relaxation approach is here tailored to the OPF problem, but it can address any application whose formulation is a quadratic optimization problem subject to quadratic equalities and ring constraints. Our first experiments on instances of the OPF problem show that our new algorithm Compact OPF (COPF) is more efficient than the standard solvers and other quadratic convex relaxation based methods we compare it with.
language	English
source	Enthalten in Computers & operations research 166(2024) vom: Juni, Artikel-ID 106626, Seite 1-12 volume:166 year:2024 month:06 elocationid:106626 pages:1-12
sourceStr	Enthalten in Computers & operations research 166(2024) vom: Juni, Artikel-ID 106626, Seite 1-12 volume:166 year:2024 month:06 elocationid:106626 pages:1-12
format_phy_str_mv	Article
building	26:1 2403:0
institution	findex.gbv.de
selectbib_iln_str_mv	26@1z 2403@01
topic_facet	Semidefinite programming Global optimization Optimal Power Flow Quadratic convex relaxation Quadratically constrained quadratic programming
sw_local_iln_str_mv	26: DE-206:
isfreeaccess_bool	true
container_title	Computers & operations research
authorswithroles_txt_mv	Lambert, Amélie @@aut@@
publishDateDaySort_date	2024-06-01T00:00:00Z
hierarchy_top_id	306652668
id	1893546993
language_de	englisch
fullrecord	<?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>01000naa a2200265 4500</leader><controlfield tag="001">1893546993</controlfield><controlfield tag="003">DE-627</controlfield><controlfield tag="005">20240703071428.0</controlfield><controlfield tag="007">cr uuu---uuuuu</controlfield><controlfield tag="008">240703s2024 xx \|\|\|\|\|o 00\| \|\|eng c</controlfield><datafield tag="024" ind1="7" ind2=" "><subfield code="a">10.1016/j.cor.2024.106626</subfield><subfield code="2">doi</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-627)1893546993</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-599)KXP1893546993</subfield></datafield><datafield tag="040" ind1=" " ind2=" "><subfield code="a">DE-627</subfield><subfield code="b">ger</subfield><subfield code="c">DE-627</subfield><subfield code="e">rda</subfield></datafield><datafield tag="041" ind1=" " ind2=" "><subfield code="a">eng</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">Lambert, Amélie</subfield><subfield code="e">verfasserin</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="2"><subfield code="a">A tight compact quadratically constrained convex relaxation of the Optimal Power Flow problem</subfield><subfield code="c">Amélie Lambert</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="c">2024</subfield></datafield><datafield tag="336" ind1=" " ind2=" "><subfield code="a">Text</subfield><subfield code="b">txt</subfield><subfield code="2">rdacontent</subfield></datafield><datafield tag="337" ind1=" " ind2=" "><subfield code="a">Computermedien</subfield><subfield code="b">c</subfield><subfield code="2">rdamedia</subfield></datafield><datafield tag="338" ind1=" " ind2=" "><subfield code="a">Online-Ressource</subfield><subfield code="b">cr</subfield><subfield code="2">rdacarrier</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Semidefinite programming</subfield><subfield code="7">(dpeaa)DE-206</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Global optimization</subfield><subfield code="7">(dpeaa)DE-206</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Optimal Power Flow</subfield><subfield code="7">(dpeaa)DE-206</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Quadratic convex relaxation</subfield><subfield code="7">(dpeaa)DE-206</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Quadratically constrained quadratic programming</subfield><subfield code="7">(dpeaa)DE-206</subfield></datafield><datafield tag="773" ind1="0" ind2="8"><subfield code="i">Enthalten in</subfield><subfield code="t">Computers & operations research</subfield><subfield code="d">Amsterdam [u.a.] : Elsevier, 1974</subfield><subfield code="g">166(2024) vom: Juni, Artikel-ID 106626, Seite 1-12</subfield><subfield code="h">Online-Ressource</subfield><subfield code="w">(DE-627)306652668</subfield><subfield code="w">(DE-600)1499736-8</subfield><subfield code="w">(DE-576)081954336</subfield><subfield code="x">0305-0548</subfield><subfield code="7">nnns</subfield></datafield><datafield tag="773" ind1="1" ind2="8"><subfield code="g">volume:166</subfield><subfield code="g">year:2024</subfield><subfield code="g">month:06</subfield><subfield code="g">elocationid:106626</subfield><subfield code="g">pages:1-12</subfield></datafield><datafield tag="856" ind1="4" ind2="0"><subfield code="u">https://www.sciencedirect.com/science/article/pii/S0305054824000984/pdf</subfield><subfield code="x">Verlag</subfield><subfield code="z">kostenfrei</subfield></datafield><datafield tag="856" ind1="4" ind2="0"><subfield code="u">https://doi.org/10.1016/j.cor.2024.106626</subfield><subfield code="x">Resolving-System</subfield><subfield code="z">kostenfrei</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_USEFLAG_U</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_26</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">ISIL_DE-206</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">SYSFLAG_1</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_KXP</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_20</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_22</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_23</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_24</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_31</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_32</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_40</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_60</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_62</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_65</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_69</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_70</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_73</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_74</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_90</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_95</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_100</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_105</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_110</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_150</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_151</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_187</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_213</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_224</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_230</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_370</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_602</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_702</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2001</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2003</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2004</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2005</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2007</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2009</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2010</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2011</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2014</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2015</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2020</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2021</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2025</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2026</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2027</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2034</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2044</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2048</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2049</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2050</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2055</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2056</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2059</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2061</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2064</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2106</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2110</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2111</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2112</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2122</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2129</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2143</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2152</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2153</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2190</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2232</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2336</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2470</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2507</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_4035</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_4037</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_4112</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_4125</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_4242</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_4249</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_4251</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_4305</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_4306</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_4307</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_4313</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_4322</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_4323</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_4324</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_4326</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_4333</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_4334</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_4338</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_4393</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_4700</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2403</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2403</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">ISIL_DE-LFER</subfield></datafield><datafield tag="951" ind1=" " ind2=" "><subfield code="a">AR</subfield></datafield><datafield tag="952" ind1=" " ind2=" "><subfield code="d">166</subfield><subfield code="j">2024</subfield><subfield code="c">6</subfield><subfield code="i">106626</subfield><subfield code="h">1-12</subfield></datafield><datafield tag="980" ind1=" " ind2=" "><subfield code="2">26</subfield><subfield code="1">01</subfield><subfield code="x">0206</subfield><subfield code="b">454570283X</subfield><subfield code="y">x1z</subfield><subfield code="z">03-07-24</subfield></datafield><datafield tag="980" ind1=" " ind2=" "><subfield code="2">2403</subfield><subfield code="1">01</subfield><subfield code="x">DE-LFER</subfield><subfield code="b">4551110590</subfield><subfield code="c">00</subfield><subfield code="f">--%%--</subfield><subfield code="d">--%%--</subfield><subfield code="e">n</subfield><subfield code="j">--%%--</subfield><subfield code="y">l01</subfield><subfield code="z">15-07-24</subfield></datafield><datafield tag="981" ind1=" " ind2=" "><subfield code="2">2403</subfield><subfield code="1">01</subfield><subfield code="x">DE-LFER</subfield><subfield code="r">https://doi.org/10.1016/j.cor.2024.106626</subfield></datafield><datafield tag="981" ind1=" " ind2=" "><subfield code="2">2403</subfield><subfield code="1">01</subfield><subfield code="x">DE-LFER</subfield><subfield code="r">https://www.sciencedirect.com/science/article/pii/S0305054824000984/pdf</subfield></datafield><datafield tag="982" ind1=" " ind2=" "><subfield code="2">26</subfield><subfield code="1">00</subfield><subfield code="x">DE-206</subfield><subfield code="b">In this paper, we consider the Optimal Power Flow (OPF) problem which consists in determining the power production at each bus of an electric network by minimizing the production cost. Our contribution is an exact solution algorithm for the OPF problem. It consists in a spatial branch-and-bound algorithm based on a compact quadratically-constrained convex relaxation. It is computed by solving the semidefinite rank relaxation of OPF once at the root node of the algorithm. An important result is that the optimal value of our compact relaxation is equal to the rank relaxation value. Then, at every sub-nodes of our branch-and-bound, the lower bound is obtained by solving a quadratic convex problem instead of an SDP. Another contribution is that we add only O(n+m) variables that model the squares of the initial variables, where n is the number of buses in the power system and m the number of transmission lines, to construct our relaxation. Then, since the relations between the initial and auxiliary variables are non-convex, we relax them to get a quadratic convex relaxation. Finally, in our branch-and-bound algorithm, we only have to force a reduced number of equalities to prove global optimality. This quadratic convex relaxation approach is here tailored to the OPF problem, but it can address any application whose formulation is a quadratic optimization problem subject to quadratic equalities and ring constraints. Our first experiments on instances of the OPF problem show that our new algorithm Compact OPF (COPF) is more efficient than the standard solvers and other quadratic convex relaxation based methods we compare it with.</subfield></datafield></record></collection>
standort_str_mv	--%%--
standort_iln_str_mv	2403:--%%-- DE-LFER:--%%--
author	Lambert, Amélie
spellingShingle	Lambert, Amélie misc Semidefinite programming misc Global optimization misc Optimal Power Flow misc Quadratic convex relaxation misc Quadratically constrained quadratic programming A tight compact quadratically constrained convex relaxation of the Optimal Power Flow problem
authorStr	Lambert, Amélie
ppnlink_with_tag_str_mv	@@773@@(DE-627)306652668
format	electronic Article
delete_txt_mv	keep
author_role	aut
collection	KXP GVK SWB
remote_str	true
last_changed_iln_str_mv	26@03-07-24 2403@15-07-24
illustrated	Not Illustrated
issn	0305-0548
topic_title	26 00 DE-206 In this paper, we consider the Optimal Power Flow (OPF) problem which consists in determining the power production at each bus of an electric network by minimizing the production cost. Our contribution is an exact solution algorithm for the OPF problem. It consists in a spatial branch-and-bound algorithm based on a compact quadratically-constrained convex relaxation. It is computed by solving the semidefinite rank relaxation of OPF once at the root node of the algorithm. An important result is that the optimal value of our compact relaxation is equal to the rank relaxation value. Then, at every sub-nodes of our branch-and-bound, the lower bound is obtained by solving a quadratic convex problem instead of an SDP. Another contribution is that we add only O(n+m) variables that model the squares of the initial variables, where n is the number of buses in the power system and m the number of transmission lines, to construct our relaxation. Then, since the relations between the initial and auxiliary variables are non-convex, we relax them to get a quadratic convex relaxation. Finally, in our branch-and-bound algorithm, we only have to force a reduced number of equalities to prove global optimality. This quadratic convex relaxation approach is here tailored to the OPF problem, but it can address any application whose formulation is a quadratic optimization problem subject to quadratic equalities and ring constraints. Our first experiments on instances of the OPF problem show that our new algorithm Compact OPF (COPF) is more efficient than the standard solvers and other quadratic convex relaxation based methods we compare it with A tight compact quadratically constrained convex relaxation of the Optimal Power Flow problem Amélie Lambert Semidefinite programming (dpeaa)DE-206 Global optimization (dpeaa)DE-206 Optimal Power Flow (dpeaa)DE-206 Quadratic convex relaxation (dpeaa)DE-206 Quadratically constrained quadratic programming (dpeaa)DE-206
topic	misc Semidefinite programming misc Global optimization misc Optimal Power Flow misc Quadratic convex relaxation misc Quadratically constrained quadratic programming
topic_unstemmed	misc Semidefinite programming misc Global optimization misc Optimal Power Flow misc Quadratic convex relaxation misc Quadratically constrained quadratic programming
topic_browse	misc Semidefinite programming misc Global optimization misc Optimal Power Flow misc Quadratic convex relaxation misc Quadratically constrained quadratic programming
format_facet	Elektronische Aufsätze Aufsätze Elektronische Ressource
standort_txtP_mv	--%%--
format_main_str_mv	Text Zeitschrift/Artikel
carriertype_str_mv	cr
hierarchy_parent_title	Computers & operations research
hierarchy_parent_id	306652668
signature	--%%--
signature_str_mv	--%%--
hierarchy_top_title	Computers & operations research
isfreeaccess_txt	true
familylinks_str_mv	(DE-627)306652668 (DE-600)1499736-8 (DE-576)081954336
title	A tight compact quadratically constrained convex relaxation of the Optimal Power Flow problem
ctrlnum	(DE-627)1893546993 (DE-599)KXP1893546993
title_full	A tight compact quadratically constrained convex relaxation of the Optimal Power Flow problem Amélie Lambert
author_sort	Lambert, Amélie
journal	Computers & operations research
journalStr	Computers & operations research
callnumber-first-code	-
lang_code	eng
isOA_bool	true
recordtype	marc
publishDateSort	2024
contenttype_str_mv	txt
container_start_page	1
author_browse	Lambert, Amélie
selectkey	26:x 2403:l
container_volume	166
format_se	Elektronische Aufsätze
author-letter	Lambert, Amélie
doi_str_mv	10.1016/j.cor.2024.106626
title_sort	tight compact quadratically constrained convex relaxation of the optimal power flow problem
title_auth	A tight compact quadratically constrained convex relaxation of the Optimal Power Flow problem
collection_details	GBV_USEFLAG_U GBV_ILN_26 ISIL_DE-206 SYSFLAG_1 GBV_KXP GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_150 GBV_ILN_151 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_370 GBV_ILN_602 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2007 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2034 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2106 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2470 GBV_ILN_2507 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4242 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4326 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 GBV_ILN_2403 ISIL_DE-LFER
title_short	A tight compact quadratically constrained convex relaxation of the Optimal Power Flow problem
url	https://www.sciencedirect.com/science/article/pii/S0305054824000984/pdf https://doi.org/10.1016/j.cor.2024.106626
ausleihindikator_str_mv	26 2403:n
remote_bool	true
ppnlink	306652668
mediatype_str_mv	c
isOA_txt	true
hochschulschrift_bool	false
doi_str	10.1016/j.cor.2024.106626
callnumber-a	--%%--
up_date	2024-07-16T06:40:09.320Z
_version_	1804716746285776896
fullrecord_marcxml	<?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>01000naa a2200265 4500</leader><controlfield tag="001">1893546993</controlfield><controlfield tag="003">DE-627</controlfield><controlfield tag="005">20240703071428.0</controlfield><controlfield tag="007">cr uuu---uuuuu</controlfield><controlfield tag="008">240703s2024 xx \|\|\|\|\|o 00\| \|\|eng c</controlfield><datafield tag="024" ind1="7" ind2=" "><subfield code="a">10.1016/j.cor.2024.106626</subfield><subfield code="2">doi</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-627)1893546993</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-599)KXP1893546993</subfield></datafield><datafield tag="040" ind1=" " ind2=" "><subfield code="a">DE-627</subfield><subfield code="b">ger</subfield><subfield code="c">DE-627</subfield><subfield code="e">rda</subfield></datafield><datafield tag="041" ind1=" " ind2=" "><subfield code="a">eng</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">Lambert, Amélie</subfield><subfield code="e">verfasserin</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="2"><subfield code="a">A tight compact quadratically constrained convex relaxation of the Optimal Power Flow problem</subfield><subfield code="c">Amélie Lambert</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="c">2024</subfield></datafield><datafield tag="336" ind1=" " ind2=" "><subfield code="a">Text</subfield><subfield code="b">txt</subfield><subfield code="2">rdacontent</subfield></datafield><datafield tag="337" ind1=" " ind2=" "><subfield code="a">Computermedien</subfield><subfield code="b">c</subfield><subfield code="2">rdamedia</subfield></datafield><datafield tag="338" ind1=" " ind2=" "><subfield code="a">Online-Ressource</subfield><subfield code="b">cr</subfield><subfield code="2">rdacarrier</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Semidefinite programming</subfield><subfield code="7">(dpeaa)DE-206</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Global optimization</subfield><subfield code="7">(dpeaa)DE-206</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Optimal Power Flow</subfield><subfield code="7">(dpeaa)DE-206</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Quadratic convex relaxation</subfield><subfield code="7">(dpeaa)DE-206</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Quadratically constrained quadratic programming</subfield><subfield code="7">(dpeaa)DE-206</subfield></datafield><datafield tag="773" ind1="0" ind2="8"><subfield code="i">Enthalten in</subfield><subfield code="t">Computers & operations research</subfield><subfield code="d">Amsterdam [u.a.] : Elsevier, 1974</subfield><subfield code="g">166(2024) vom: Juni, Artikel-ID 106626, Seite 1-12</subfield><subfield code="h">Online-Ressource</subfield><subfield code="w">(DE-627)306652668</subfield><subfield code="w">(DE-600)1499736-8</subfield><subfield code="w">(DE-576)081954336</subfield><subfield code="x">0305-0548</subfield><subfield code="7">nnns</subfield></datafield><datafield tag="773" ind1="1" ind2="8"><subfield code="g">volume:166</subfield><subfield code="g">year:2024</subfield><subfield code="g">month:06</subfield><subfield code="g">elocationid:106626</subfield><subfield code="g">pages:1-12</subfield></datafield><datafield tag="856" ind1="4" ind2="0"><subfield code="u">https://www.sciencedirect.com/science/article/pii/S0305054824000984/pdf</subfield><subfield code="x">Verlag</subfield><subfield code="z">kostenfrei</subfield></datafield><datafield tag="856" ind1="4" ind2="0"><subfield code="u">https://doi.org/10.1016/j.cor.2024.106626</subfield><subfield code="x">Resolving-System</subfield><subfield code="z">kostenfrei</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_USEFLAG_U</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_26</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">ISIL_DE-206</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">SYSFLAG_1</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_KXP</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_20</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_22</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_23</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_24</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_31</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_32</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_40</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_60</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_62</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_65</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_69</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_70</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_73</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_74</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_90</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_95</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_100</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_105</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_110</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_150</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_151</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_187</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_213</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_224</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_230</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_370</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_602</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_702</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2001</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2003</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2004</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2005</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2007</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2009</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2010</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2011</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2014</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2015</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2020</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2021</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2025</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2026</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2027</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2034</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2044</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2048</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2049</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2050</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2055</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2056</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2059</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2061</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2064</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2106</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2110</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2111</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2112</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2122</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2129</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2143</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2152</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2153</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2190</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2232</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2336</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2470</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2507</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_4035</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_4037</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_4112</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_4125</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_4242</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_4249</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_4251</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_4305</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_4306</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_4307</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_4313</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_4322</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_4323</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_4324</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_4326</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_4333</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_4334</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_4338</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_4393</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_4700</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2403</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2403</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">ISIL_DE-LFER</subfield></datafield><datafield tag="951" ind1=" " ind2=" "><subfield code="a">AR</subfield></datafield><datafield tag="952" ind1=" " ind2=" "><subfield code="d">166</subfield><subfield code="j">2024</subfield><subfield code="c">6</subfield><subfield code="i">106626</subfield><subfield code="h">1-12</subfield></datafield><datafield tag="980" ind1=" " ind2=" "><subfield code="2">26</subfield><subfield code="1">01</subfield><subfield code="x">0206</subfield><subfield code="b">454570283X</subfield><subfield code="y">x1z</subfield><subfield code="z">03-07-24</subfield></datafield><datafield tag="980" ind1=" " ind2=" "><subfield code="2">2403</subfield><subfield code="1">01</subfield><subfield code="x">DE-LFER</subfield><subfield code="b">4551110590</subfield><subfield code="c">00</subfield><subfield code="f">--%%--</subfield><subfield code="d">--%%--</subfield><subfield code="e">n</subfield><subfield code="j">--%%--</subfield><subfield code="y">l01</subfield><subfield code="z">15-07-24</subfield></datafield><datafield tag="981" ind1=" " ind2=" "><subfield code="2">2403</subfield><subfield code="1">01</subfield><subfield code="x">DE-LFER</subfield><subfield code="r">https://doi.org/10.1016/j.cor.2024.106626</subfield></datafield><datafield tag="981" ind1=" " ind2=" "><subfield code="2">2403</subfield><subfield code="1">01</subfield><subfield code="x">DE-LFER</subfield><subfield code="r">https://www.sciencedirect.com/science/article/pii/S0305054824000984/pdf</subfield></datafield><datafield tag="982" ind1=" " ind2=" "><subfield code="2">26</subfield><subfield code="1">00</subfield><subfield code="x">DE-206</subfield><subfield code="b">In this paper, we consider the Optimal Power Flow (OPF) problem which consists in determining the power production at each bus of an electric network by minimizing the production cost. Our contribution is an exact solution algorithm for the OPF problem. It consists in a spatial branch-and-bound algorithm based on a compact quadratically-constrained convex relaxation. It is computed by solving the semidefinite rank relaxation of OPF once at the root node of the algorithm. An important result is that the optimal value of our compact relaxation is equal to the rank relaxation value. Then, at every sub-nodes of our branch-and-bound, the lower bound is obtained by solving a quadratic convex problem instead of an SDP. Another contribution is that we add only O(n+m) variables that model the squares of the initial variables, where n is the number of buses in the power system and m the number of transmission lines, to construct our relaxation. Then, since the relations between the initial and auxiliary variables are non-convex, we relax them to get a quadratic convex relaxation. Finally, in our branch-and-bound algorithm, we only have to force a reduced number of equalities to prove global optimality. This quadratic convex relaxation approach is here tailored to the OPF problem, but it can address any application whose formulation is a quadratic optimization problem subject to quadratic equalities and ring constraints. Our first experiments on instances of the OPF problem show that our new algorithm Compact OPF (COPF) is more efficient than the standard solvers and other quadratic convex relaxation based methods we compare it with.</subfield></datafield></record></collection>
score	7.1673384

Nicht das Richtige dabei?

Schreiben Sie uns!

A tight compact quadratically constrained convex relaxation of the Optimal Power Flow problem

Nicht das Richtige dabei?

Zugang & Verfügbarkeit

Vorhandene Bände

Nicht das Richtige dabei?