Quadratically Constrained Quadratic Programming Formulation of Contingency Constrained Optimal Power Flow with Photovoltaic Generation
Contingency Constrained Optimal Power Flow (CCOPF) differs from traditional Optimal Power Flow (OPF) because its generation dispatch is planned to work with state variables between constraint limits, considering a specific contingency. When it is not desired to have changes in the power dispatch aft...
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| Vydáno v: | Energies (Basel) Ročník 13; číslo 13; s. 3310 |
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| Médium: | Journal Article |
| Jazyk: | angličtina |
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Basel
MDPI AG
01.07.2020
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| ISSN: | 1996-1073, 1996-1073 |
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| Abstract | Contingency Constrained Optimal Power Flow (CCOPF) differs from traditional Optimal Power Flow (OPF) because its generation dispatch is planned to work with state variables between constraint limits, considering a specific contingency. When it is not desired to have changes in the power dispatch after the contingency occurs, the CCOPF is studied with a preventive perspective, whereas when the contingency occurs and the power dispatch needs to change to operate the system between limits in the post-contingency state, the problem is studied with a corrective perspective. As current power system software tools mainly focus on the traditional OPF problem, having the means to solve CCOPF will benefit power systems planning and operation. This paper presents a Quadratically Constrained Quadratic Programming (QCQP) formulation built within the matpower environment as a solution strategy to the preventive CCOPF. Moreover, an extended OPF model that forces the network to meet all constraints under contingency is proposed as a strategy to find the power dispatch solution for the corrective CCOPF. Validation is made on the IEEE 14-bus test system including photovoltaic generation in one simulation case. It was found that in the QCQP formulation, the power dispatch calculated barely differs in both pre- and post-contingency scenarios while in the OPF extended power network, node voltage values in both pre- and post-contingency scenarios are equal in spite of having different power dispatch for each scenario. This suggests that both the QCQP and the extended OPF formulations proposed, could be implemented in power system software tools in order to solve CCOPF problems from a preventive or corrective perspective. |
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| AbstractList | Contingency Constrained Optimal Power Flow (CCOPF) differs from traditional Optimal Power Flow (OPF) because its generation dispatch is planned to work with state variables between constraint limits, considering a specific contingency. When it is not desired to have changes in the power dispatch after the contingency occurs, the CCOPF is studied with a preventive perspective, whereas when the contingency occurs and the power dispatch needs to change to operate the system between limits in the post-contingency state, the problem is studied with a corrective perspective. As current power system software tools mainly focus on the traditional OPF problem, having the means to solve CCOPF will benefit power systems planning and operation. This paper presents a Quadratically Constrained Quadratic Programming (QCQP) formulation built within the matpower environment as a solution strategy to the preventive CCOPF. Moreover, an extended OPF model that forces the network to meet all constraints under contingency is proposed as a strategy to find the power dispatch solution for the corrective CCOPF. Validation is made on the IEEE 14-bus test system including photovoltaic generation in one simulation case. It was found that in the QCQP formulation, the power dispatch calculated barely differs in both pre- and post-contingency scenarios while in the OPF extended power network, node voltage values in both pre- and post-contingency scenarios are equal in spite of having different power dispatch for each scenario. This suggests that both the QCQP and the extended OPF formulations proposed, could be implemented in power system software tools in order to solve CCOPF problems from a preventive or corrective perspective. |
| Author | Bretas, Arturo S. Leon, Luis M. Rivera, Sergio |
| Author_xml | – sequence: 1 givenname: Luis M. orcidid: 0000-0001-9873-2979 surname: Leon fullname: Leon, Luis M. – sequence: 2 givenname: Arturo S. orcidid: 0000-0003-4006-0764 surname: Bretas fullname: Bretas, Arturo S. – sequence: 3 givenname: Sergio orcidid: 0000-0002-2995-1147 surname: Rivera fullname: Rivera, Sergio |
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| Cites_doi | 10.1016/j.ijepes.2017.09.023 10.1109/AEIT.2015.7415271 10.1109/TPWRS.2010.2051168 10.1109/PTC.2017.7981225 10.1109/ISGT.2019.8791673 10.3390/en10081199 10.1109/TPWRS.2016.2551278 10.1109/TPWRS.2008.2002175 10.1109/MPE.2016.2573862 10.1109/TCNS.2014.2309732 10.1109/ICPEICES.2016.7853437 10.1109/TPWRS.2012.2219080 10.1016/j.epsr.2011.04.003 10.3906/elk-1704-209 10.1109/PTC.2019.8810833 10.1109/TPWRS.2015.2396523 10.1016/j.ijepes.2019.105646 10.3390/en13030516 10.1109/ISCAS.2012.6271569 10.1145/2851613.2851899 10.1155/2011/942672 |
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| References | Capitanescu (ref_9) 2008; 23 ref_14 ref_13 ref_12 ref_11 ref_10 Tang (ref_2) 2016; 32 Vargas (ref_27) 2011; 14 Ngoc (ref_3) 2017; 25 ref_18 Capitanescu (ref_1) 2019; 81 ref_16 Nasr (ref_17) 2020; 117 ref_15 Cao (ref_8) 2015; 31 Wang (ref_19) 2012; 28 Zimmerman (ref_21) 2011; 26 ref_24 ref_22 ref_20 Karbalaei (ref_7) 2018; 96 Low (ref_25) 2014; 1 ref_26 Bernal (ref_23) 2019; 18 ref_5 ref_4 ref_6 |
| References_xml | – volume: 96 start-page: 23 year: 2018 ident: ref_7 article-title: A new method for solving preventive security-constrained optimal power flow based on linear network compression publication-title: Int. J. Electr. Power Energy Syst. doi: 10.1016/j.ijepes.2017.09.023 – ident: ref_5 – ident: ref_10 doi: 10.1109/AEIT.2015.7415271 – ident: ref_26 – volume: 26 start-page: 12 year: 2011 ident: ref_21 article-title: MATPOWER: Steady-State Operations, Planning and Analysis Tools for Power Systems Research and Education publication-title: IEEE Trans. Power Syst. doi: 10.1109/TPWRS.2010.2051168 – ident: ref_11 doi: 10.1109/PTC.2017.7981225 – ident: ref_15 doi: 10.1109/ISGT.2019.8791673 – ident: ref_13 doi: 10.3390/en10081199 – ident: ref_16 – volume: 32 start-page: 590 year: 2016 ident: ref_2 article-title: An automated transient stability constrained optimal power flow based on trajectory sensitivity analysis publication-title: IEEE Trans. Power Syst. doi: 10.1109/TPWRS.2016.2551278 – volume: 23 start-page: 1533 year: 2008 ident: ref_9 article-title: A new iterative approach to the corrective security-constrained optimal power flow problem publication-title: IEEE Trans. Power Syst. doi: 10.1109/TPWRS.2008.2002175 – volume: 18 start-page: 137 year: 2019 ident: ref_23 article-title: Mathematical Uncertainty Cost Functions for Controllable Photo-Voltaic Generators considering Uniform Distributions publication-title: WSEAS Trans. Math. – volume: 14 start-page: 38 year: 2011 ident: ref_27 article-title: Latin American Energy Markets: Investment Opportunities in Nonconventional Renewables publication-title: IEEE Power Energy Mag. doi: 10.1109/MPE.2016.2573862 – volume: 1 start-page: 15 year: 2014 ident: ref_25 article-title: Convex relaxation of optimal power flow—Part I: Formulations and equivalence publication-title: IEEE Trans. Control Netw. Syst. doi: 10.1109/TCNS.2014.2309732 – ident: ref_12 doi: 10.1109/ICPEICES.2016.7853437 – volume: 28 start-page: 1666 year: 2012 ident: ref_19 article-title: A computational strategy to solve preventive risk-based security-constrained OPF publication-title: IEEE Trans. Power Syst. doi: 10.1109/TPWRS.2012.2219080 – volume: 81 start-page: 1731 year: 2019 ident: ref_1 article-title: State of the art, challenges, and future trends in security constrained optimal power flow publication-title: Electr. Power Syst. Res. doi: 10.1016/j.epsr.2011.04.003 – volume: 25 start-page: 4696 year: 2017 ident: ref_3 article-title: A novel approach to solve transient stability constrained optimal power flow problems publication-title: Turkish J. Electr. Eng. Comput. Sci. doi: 10.3906/elk-1704-209 – ident: ref_14 doi: 10.1109/PTC.2019.8810833 – volume: 31 start-page: 485 year: 2015 ident: ref_8 article-title: An improved corrective security constrained OPF for meshed AC/DC grids with multi-terminal VSC-HVDC publication-title: IEEE Trans. Power Syst. doi: 10.1109/TPWRS.2015.2396523 – volume: 117 start-page: 105646 year: 2020 ident: ref_17 article-title: A multi-objective voltage stability constrained energy management system for isolated microgrids publication-title: Int. J. Electr. Power Energy Syst. doi: 10.1016/j.ijepes.2019.105646 – ident: ref_4 doi: 10.3390/en13030516 – ident: ref_22 – ident: ref_20 – ident: ref_18 doi: 10.1109/ISCAS.2012.6271569 – ident: ref_6 doi: 10.1145/2851613.2851899 – ident: ref_24 doi: 10.1155/2011/942672 |
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| Title | Quadratically Constrained Quadratic Programming Formulation of Contingency Constrained Optimal Power Flow with Photovoltaic Generation |
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