Second-order cone approximation for voltage stability analysis in direct-current networks
In this study, the voltage stability margin for direct current (DC) networks in the presence of constant power loads is analyzed using a proposed convex mathematical reformulation. This convex model is developed by employing a second-order cone programming (SOCP) optimization that transforms the non...
- Autores:
-
Montoya, Oscar Danilo
Gil-González, Walter
Molina-Cabrera, Alexander
- Tipo de recurso:
- Fecha de publicación:
- 2020
- Institución:
- Universidad Tecnológica de Bolívar
- Repositorio:
- Repositorio Institucional UTB
- Idioma:
- eng
- OAI Identifier:
- oai:repositorio.utb.edu.co:20.500.12585/9553
- Palabra clave:
- Convex reformulation
Direct current networks
Non-linear optimization
Numerical example
Second-order cone programming
Voltage stability margin
- Rights
- openAccess
- License
- http://creativecommons.org/licenses/by-nc-nd/4.0/
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| dc.title.spa.fl_str_mv |
Second-order cone approximation for voltage stability analysis in direct-current networks |
| title |
Second-order cone approximation for voltage stability analysis in direct-current networks |
| spellingShingle |
Second-order cone approximation for voltage stability analysis in direct-current networks Convex reformulation Direct current networks Non-linear optimization Numerical example Second-order cone programming Voltage stability margin |
| title_short |
Second-order cone approximation for voltage stability analysis in direct-current networks |
| title_full |
Second-order cone approximation for voltage stability analysis in direct-current networks |
| title_fullStr |
Second-order cone approximation for voltage stability analysis in direct-current networks |
| title_full_unstemmed |
Second-order cone approximation for voltage stability analysis in direct-current networks |
| title_sort |
Second-order cone approximation for voltage stability analysis in direct-current networks |
| dc.creator.fl_str_mv |
Montoya, Oscar Danilo Gil-González, Walter Molina-Cabrera, Alexander |
| dc.contributor.author.none.fl_str_mv |
Montoya, Oscar Danilo Gil-González, Walter Molina-Cabrera, Alexander |
| dc.subject.keywords.spa.fl_str_mv |
Convex reformulation Direct current networks Non-linear optimization Numerical example Second-order cone programming Voltage stability margin |
| topic |
Convex reformulation Direct current networks Non-linear optimization Numerical example Second-order cone programming Voltage stability margin |
| description |
In this study, the voltage stability margin for direct current (DC) networks in the presence of constant power loads is analyzed using a proposed convex mathematical reformulation. This convex model is developed by employing a second-order cone programming (SOCP) optimization that transforms the non-linear non-convex original formulation by reformulating the power balance constraint. The main advantage of the SOCP model is that the optimal global solution of a problem can be obtained by transforming hyperbolic constraints into norm constraints. Two test systems are considered to validate the proposed SOCP model. Both systems have been reported in specialized literature with 6 and 69 nodes. Three comparative methods are considered: (a) the Newton-Raphson approximation based on the determinants of the Jacobian matrices, (b) semidefinite programming models, and (c) the exact non-linear formulation. All the numerical simulations are conducted using the MATLAB and GAMS software. The effectiveness of the proposed SOCP model in addressing the voltage stability problem in DC grids is verified by comparing the objective function values and processing time. |
| publishDate |
2020 |
| dc.date.accessioned.none.fl_str_mv |
2020-11-04T21:50:23Z |
| dc.date.available.none.fl_str_mv |
2020-11-04T21:50:23Z |
| dc.date.issued.none.fl_str_mv |
2020-09-24 |
| dc.date.submitted.none.fl_str_mv |
2020-11-04 |
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http://purl.org/coar/version/c_970fb48d4fbd8a85 |
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http://purl.org/coar/resource_type/c_2df8fbb1 |
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info:eu-repo/semantics/article |
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info:eu-repo/semantics/publishedVersion |
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http://purl.org/coar/resource_type/c_6501 |
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publishedVersion |
| dc.identifier.citation.spa.fl_str_mv |
Montoya, O.D.; Gil-González, W.; Molina-Cabrera, A. Second-Order Cone Approximation for Voltage Stability Analysis in Direct-Current Networks. Symmetry 2020, 12, 1587. |
| dc.identifier.uri.none.fl_str_mv |
https://hdl.handle.net/20.500.12585/9553 |
| dc.identifier.url.none.fl_str_mv |
https://www.mdpi.com/2073-8994/12/10/1587 |
| dc.identifier.doi.none.fl_str_mv |
10.3390/sym12101587 |
| dc.identifier.instname.spa.fl_str_mv |
Universidad Tecnológica de Bolívar |
| dc.identifier.reponame.spa.fl_str_mv |
Repositorio Universidad Tecnológica de Bolívar |
| identifier_str_mv |
Montoya, O.D.; Gil-González, W.; Molina-Cabrera, A. Second-Order Cone Approximation for Voltage Stability Analysis in Direct-Current Networks. Symmetry 2020, 12, 1587. 10.3390/sym12101587 Universidad Tecnológica de Bolívar Repositorio Universidad Tecnológica de Bolívar |
| url |
https://hdl.handle.net/20.500.12585/9553 https://www.mdpi.com/2073-8994/12/10/1587 |
| dc.language.iso.spa.fl_str_mv |
eng |
| language |
eng |
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http://purl.org/coar/access_right/c_abf2 |
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http://creativecommons.org/licenses/by-nc-nd/4.0/ |
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info:eu-repo/semantics/openAccess |
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Attribution-NonCommercial-NoDerivatives 4.0 Internacional |
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http://creativecommons.org/licenses/by-nc-nd/4.0/ Attribution-NonCommercial-NoDerivatives 4.0 Internacional http://purl.org/coar/access_right/c_abf2 |
| eu_rights_str_mv |
openAccess |
| dc.format.extent.none.fl_str_mv |
11 páginas |
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application/pdf |
| dc.publisher.place.spa.fl_str_mv |
Cartagena de Indias |
| dc.source.spa.fl_str_mv |
Symmetry 2020, 12(10), 1587 |
| institution |
Universidad Tecnológica de Bolívar |
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Montoya, Oscar Danilo8a59ede1-6a4a-4d2e-abdc-d0afb14d4480Gil-González, Walterce1f5078-74c6-4b5c-b56a-784f85e52a08Molina-Cabrera, Alexander01b29f76-a1f3-4151-a070-ce883ba398492020-11-04T21:50:23Z2020-11-04T21:50:23Z2020-09-242020-11-04Montoya, O.D.; Gil-González, W.; Molina-Cabrera, A. Second-Order Cone Approximation for Voltage Stability Analysis in Direct-Current Networks. Symmetry 2020, 12, 1587.https://hdl.handle.net/20.500.12585/9553https://www.mdpi.com/2073-8994/12/10/158710.3390/sym12101587Universidad Tecnológica de BolívarRepositorio Universidad Tecnológica de BolívarIn this study, the voltage stability margin for direct current (DC) networks in the presence of constant power loads is analyzed using a proposed convex mathematical reformulation. This convex model is developed by employing a second-order cone programming (SOCP) optimization that transforms the non-linear non-convex original formulation by reformulating the power balance constraint. The main advantage of the SOCP model is that the optimal global solution of a problem can be obtained by transforming hyperbolic constraints into norm constraints. Two test systems are considered to validate the proposed SOCP model. Both systems have been reported in specialized literature with 6 and 69 nodes. Three comparative methods are considered: (a) the Newton-Raphson approximation based on the determinants of the Jacobian matrices, (b) semidefinite programming models, and (c) the exact non-linear formulation. All the numerical simulations are conducted using the MATLAB and GAMS software. The effectiveness of the proposed SOCP model in addressing the voltage stability problem in DC grids is verified by comparing the objective function values and processing time.11 páginasapplication/pdfenghttp://creativecommons.org/licenses/by-nc-nd/4.0/info:eu-repo/semantics/openAccessAttribution-NonCommercial-NoDerivatives 4.0 Internacionalhttp://purl.org/coar/access_right/c_abf2Symmetry 2020, 12(10), 1587Second-order cone approximation for voltage stability analysis in direct-current networksinfo:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501http://purl.org/coar/version/c_970fb48d4fbd8a85http://purl.org/coar/resource_type/c_2df8fbb1Convex reformulationDirect current networksNon-linear optimizationNumerical exampleSecond-order cone programmingVoltage stability marginCartagena de IndiasPúblico generalDragiˇcevi´c, T.; Lu, X.; Vasquez, J.C.; Guerrero, J.M. DC microgrids–Part I: A review of control strategies and stabilization techniques. IEEE Trans. Power Electron. 2016, 31, 4876–4891.Garces, A. Uniqueness of the power flow solutions in low voltage direct current grids. Electr. Power Syst. Res. 2017, 151, 149–153.Garcés, A. On the Convergence of Newton’s Method in Power Flow Studies for DC Microgrids. IEEE Trans. Power Syst. 2018, 33, 5770–5777.Gan, L.; Low, S.H. Optimal power flow in direct current networks. IEEE Trans. Power Syst. 2014, 29, 2892–2904.Rouzbehi, K.; Miranian, A.; Candela, J.I.; Luna, A.; Rodriguez, P. A Generalized Voltage Droop Strategy for Control of Multiterminal DC Grids. IEEE Trans. Ind. Appl. 2015, 51, 607–618.Rouzbehi, K.; Miranian, A.; Luna, A.; Rodriguez, P. DC Voltage Control and Power Sharing in Multiterminal DC Grids Based on Optimal DC Power Flow and Voltage-Droop Strategy. IEEE J. Emerg. Sel. Top. Power Electron. 2014, 2, 1171–1180,Hamad, A.A.; El-Saadany, E.F. Multi-agent supervisory control for optimal economic dispatch in DC microgrids. Sustain. Cities Soc. 2016, 27, 129–136Barabanov, N.; Ortega, R.; Griñó, R.; Polyak, B. On Existence and Stability of Equilibria of Linear Time-Invariant Systems With Constant Power Loads. IEEE Trans. Circuits Syst. I 2016, 63, 114–121,Montoya, O.D. Numerical Approximation of the Maximum Power Consumption in DC-MGs With CPLs via an SDP Model. IEEE Trans. Circuits Syst. II 2019, 66, 642–646,Grisales-Noreña, L.F.; Gonzalez Montoya, D.; Ramos-Paja, C.A. Optimal sizing and location of distributed generators based on PBIL and PSO techniques. Energies 2018, 11, 1018.Montoya, O.D.; Gil-González, W.; Garrido, V.M. Voltage Stability Margin in DC Grids with CPLs: A Recursive Newton–Raphson Approximation. IEEE Trans. Circuits Syst. II 2019, 67, 300–304.Grisales-Noreña, L.F.; Garzon-Rivera, O.D.; Montoya, O.D.; Ramos-Paja, C.A. Hybrid Metaheuristic Optimization Methods for Optimal Location and Sizing DGs in DC Networks. In Workshop on Engineering Applications; Chapter Applied Computer Sciences in Engineering; Figueroa-García, J., Duarte-González, M., Jaramillo-Isaza, S., Orjuela-Cañon, A., Díaz-Gutierrez, Y., Eds.; Springer: Berlin, Germany, 2019; Volume 1052, pp. 552–564.Li, J.; Liu, F.; Wang, Z.; Low, S.H.; Mei, S. Optimal Power Flow in Stand-Alone DC Microgrids. IEEE Trans. Power Syst. 2018, 33, 5496–5506.Xie, Y.; Chen, X.; Wu, Q.; Zhou, Q. Second-order conic programming model for load restoration considering uncertainty of load increment based on information gap decision theory. Int. J. Electr. Power Energy Syst. 2019, 105, 151–158.Montoya, O.D.; Garrido, V.M.; Gil-González, W.; Grisales-Noreña, L.F. Power Flow Analysis in DC Grids: Two Alternative Numerical Methods. IEEE Trans. Circuits Syst. II 2019, 66, 1865–1869.Lavaei, J.; Low, S.H. Zero Duality Gap in Optimal Power Flow Problem. IEEE Trans. Power Syst. 2012, 27, 92–107Hindi, H. A tutorial on convex optimization. In Proceedings of the 2004 American Control Conference, Boston, MA, USA, 30 June–2 July 2004; Volume 4, pp. 3252–3265.Alizadeh, F.; Goldfarb, D. Second-order cone programming. Math Program 2003, 95, 3–51.Yuan, Z.; Hesamzadeh, M.R. Second-order cone AC optimal power flow: Convex relaxations and feasible solutions. J. Mod. Power Syst. Clean Energy 2018, 7, 268–280.Luo, Z.Q.; Yu, W. An introduction to convex optimization for communications and signal processing. IEEE J. Sel. Areas Commun. 2006, 24, 1426–1438.http://purl.org/coar/resource_type/c_2df8fbb1ORIGINAL99.pdf99.pdfArtículo principalapplication/pdf302797https://repositorio.utb.edu.co/bitstream/20.500.12585/9553/1/99.pdf8724ab0e37c9679392e6e454cd9ea15dMD51CC-LICENSElicense_rdflicense_rdfapplication/rdf+xml; charset=utf-8805https://repositorio.utb.edu.co/bitstream/20.500.12585/9553/2/license_rdf4460e5956bc1d1639be9ae6146a50347MD52LICENSElicense.txtlicense.txttext/plain; charset=utf-83182https://repositorio.utb.edu.co/bitstream/20.500.12585/9553/3/license.txte20ad307a1c5f3f25af9304a7a7c86b6MD53TEXT99.pdf.txt99.pdf.txtExtracted texttext/plain33019https://repositorio.utb.edu.co/bitstream/20.500.12585/9553/4/99.pdf.txt414160062d4a69fe8547a9321f06c5e1MD54THUMBNAIL99.pdf.jpg99.pdf.jpgGenerated Thumbnailimage/jpeg91918https://repositorio.utb.edu.co/bitstream/20.500.12585/9553/5/99.pdf.jpg775ecd5bb8b3ed4137df1d0ca17aed2dMD5520.500.12585/9553oai:repositorio.utb.edu.co:20.500.12585/95532020-11-25 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