Semidefinite relaxation and generalised benders decomposition to solve the transmission expansion network and reactive power planning
This study presents a methodology to solve simultaneously the alternating current (AC) transmission network expansion and reactive power planning problems, considering multiple stages and operating conditions. A mixed-integer non-linear programming model for the proposed planning problem is presente...
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| Vydáno v: | IET generation, transmission & distribution Ročník 14; číslo 11; s. 2160 - 2168 |
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| Médium: | Journal Article |
| Jazyk: | angličtina |
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The Institution of Engineering and Technology
05.06.2020
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| ISSN: | 1751-8687, 1751-8695 |
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| Abstract | This study presents a methodology to solve simultaneously the alternating current (AC) transmission network expansion and reactive power planning problems, considering multiple stages and operating conditions. A mixed-integer non-linear programming model for the proposed planning problem is presented and rewritten with semidefinite structures. Then, the generalised Benders decomposition is used to separate the overall problem into an upper-level (master) problem and several lower-level (slaves) problems. The master problem is a mixed-integer linear programming problem that optimises the investment cost and constraints of the multistage expansion. Each slave problem minimises the operating costs associated with each stage and operating condition (normal operation or contingency), considering the AC power flow via semidefinite relaxation. With the proposed methodology, the global optimality of generalised Benders decomposition can be preserved due to the use of semidefinite relaxation in each slave problem. Garver's 6-bus system and an IEEE 118-bus system are used to show the precision and convergence to near-global optimal solutions with small relaxation gaps through the proposed approach. |
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| AbstractList | This study presents a methodology to solve simultaneously the alternating current (AC) transmission network expansion and reactive power planning problems, considering multiple stages and operating conditions. A mixed‐integer non‐linear programming model for the proposed planning problem is presented and rewritten with semidefinite structures. Then, the generalised Benders decomposition is used to separate the overall problem into an upper‐level (master) problem and several lower‐level (slaves) problems. The master problem is a mixed‐integer linear programming problem that optimises the investment cost and constraints of the multistage expansion. Each slave problem minimises the operating costs associated with each stage and operating condition (normal operation or contingency), considering the AC power flow via semidefinite relaxation. With the proposed methodology, the global optimality of generalised Benders decomposition can be preserved due to the use of semidefinite relaxation in each slave problem. Garver's 6‐bus system and an IEEE 118‐bus system are used to show the precision and convergence to near‐global optimal solutions with small relaxation gaps through the proposed approach. |
| Author | Paredes, Miguel Alvarez, Erik F Rider, Marcos J |
| Author_xml | – sequence: 1 givenname: Erik F orcidid: 0000-0003-3862-9747 surname: Alvarez fullname: Alvarez, Erik F organization: 1Department of Systems and Energy, University of Campinas, Av. Albert Einstein 400, Campinas, SP 13083-852, Brazil – sequence: 2 givenname: Miguel surname: Paredes fullname: Paredes, Miguel organization: 2IBM Research, Sao Paulo, SP 04007-900, Brazil – sequence: 3 givenname: Marcos J orcidid: 0000-0001-5484-1161 surname: Rider fullname: Rider, Marcos J email: mjrider@dsee.fee.unicamp.br organization: 1Department of Systems and Energy, University of Campinas, Av. Albert Einstein 400, Campinas, SP 13083-852, Brazil |
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| CitedBy_id | crossref_primary_10_1016_j_segan_2024_101413 crossref_primary_10_1109_TPWRS_2021_3056637 crossref_primary_10_1109_TPWRS_2022_3200970 crossref_primary_10_61186_jgeri_2_2_48 crossref_primary_10_1049_gtd2_12586 crossref_primary_10_3389_fenrg_2023_1258689 crossref_primary_10_3390_su14116746 crossref_primary_10_1016_j_epsr_2021_107543 |
| Cites_doi | 10.1109/TPWRS.2013.2250318 10.1016/j.ejor.2018.10.035 10.1016/j.rser.2013.08.062 10.1109/TPWRS.2014.2385861 10.1109/TPWRS.2014.2359803 10.1109/TPAS.1970.292825 10.1109/TPWRS.2003.811168 10.1049/iet-gtd.2014.0001 10.1109/TPWRS.2017.2665695 10.1049/iet-gtd:20060465 10.1016/j.enconman.2011.10.020 10.1109/TPWRS.2013.2258044 10.1016/j.enconman.2011.02.023 10.1109/TPWRS.2017.2760699 10.1109/PESGM.2012.6345536 10.1109/TPWRS.2012.2228507 10.1109/TPWRS.2011.2169994 10.1109/NAPS.2011.6024862 10.1109/TSG.2018.2866068 10.1049/iet-gtd.2016.0081 10.1016/j.ijepes.2007.12.003 10.1109/TPWRS.2011.2160974 10.1109/TPWRS.2018.2848965 10.1016/j.epsr.2015.10.013 10.1109/TPWRS.2007.907452 10.1109/PESGM.2015.7286268 10.1109/TPWRS.2016.2562258 10.1049/iet-gtd.2014.1117 10.1007/978-3-319-29501-5 10.1109/TPWRS.2015.2425885 10.1007/BFb0121075 10.1017/CBO9780511804441 10.1007/978-1-4615-4381-7 10.1007/BF00934810 |
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| Copyright | The Institution of Engineering and Technology 2020 The Authors. IET Generation, Transmission & Distribution published by John Wiley & Sons, Ltd. on behalf of The Institution of Engineering and Technology |
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| Keywords | Garver 6-bus system multistage expansion AC power flow generalised Benders decomposition lower-level problems upper-level problem transmission expansion network mixed-integer linear programming problem investment cost semidefinite relaxation reactive power planning problems reactive power power transmission planning alternating current transmission network expansion minimisation semidefinite structures load flow IEEE 118-bus system |
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Power Syst. – start-page: 1 year: 2012 end-page: 8 article-title: Semidefinite programming for power system state estimation – volume: 18 start-page: 938 issue: 2 year: 2003 end-page: 946 article-title: Classification of publications and models on transmission expansion planning publication-title: IEEE Trans. Power Syst. – volume: 8 start-page: 1637 issue: 10 year: 2014 end-page: 1644 article-title: Transmission expansion planning using AC‐based differential evolution algorithm publication-title: IET Gen., Tran. and Dist. – volume: 10 start-page: 4637 issue: 4 year: 2019 end-page: 4647 article-title: SDP‐based optimal power flowwith steady‐state voltage stability constraints publication-title: IEEE Trans. Smart Grid – volume: 28 start-page: 3987 issue: 4 year: 2013 end-page: 3998 article-title: Implementation of a large‐scale optimal power flow solver based on semidefinite programming publication-title: IEEE Trans. Power Syst. – volume: 31 start-page: 1269 issue: 2 year: 2015 end-page: 1277 article-title: Lyapunov functions family approach to transient stability assessment publication-title: IEEE Trans. Power Syst. – volume: 10 start-page: 237 issue: 4 year: 1972 end-page: 260 article-title: Generalized benders decomposition publication-title: J. Optim. Theory Appl. – volume: 5 start-page: 62 year: 1985 end-page: 75 article-title: A generalized benders decomposition approach to reactive source planning in power systems publication-title: Math. Program. Essays Honor George B. Dantzig Part II – volume: 28 start-page: 2779 issue: 3 year: 2013 end-page: 2787 article-title: Optimization of AC transmission system planning publication-title: IEEE Trans. Power Syst. – volume: 52 start-page: 2844 issue: 8‐9 year: 2011 end-page: 2853 article-title: A multi‐stage stochastic transmission expansion planning method publication-title: Energy Convers. 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| Snippet | This study presents a methodology to solve simultaneously the alternating current (AC) transmission network expansion and reactive power planning problems,... |
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| SubjectTerms | AC power flow alternating current transmission network expansion Garver 6‐bus system generalised Benders decomposition IEEE 118‐bus system investment cost load flow lower‐level problems minimisation mixed‐integer linear programming problem multistage expansion power transmission planning reactive power reactive power planning problems Research Article semidefinite relaxation semidefinite structures transmission expansion network upper‐level problem |
| Title | Semidefinite relaxation and generalised benders decomposition to solve the transmission expansion network and reactive power planning |
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