A tight compact quadratically constrained convex relaxation of the Optimal Power Flow problem
Autor*in: |
Lambert, Amélie [verfasserIn] |
---|
Format: |
E-Artikel |
---|---|
Sprache: |
Englisch |
Erschienen: |
2024 |
---|
Schlagwörter: |
---|
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: |
---|
DOI / URN: |
10.1016/j.cor.2024.106626 |
---|
Katalog-ID: |
1893546993 |
---|
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. |
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 |