Voltage Stability Analysis in Medium-Voltage Distribution Networks Using a Second-Order Cone Approximation
This paper addresses the voltage stability margin calculation in medium-voltage distribution networks in the context of exact mathematical modeling. This margin calculation is performed with a second-order cone (SOCP) reformulation of the classical nonlinear non-convex optimal power flow problems. T...
- Autores:
-
Montoya, Oscar Danilo
Gil-González, Walter
Arias-Londoño, Andrés
Rajagopalan, Arul
Hernández, Jesus C.
- 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:20.500.12585/10046
- Acceso en línea:
- https://hdl.handle.net/20.500.12585/10046
- Palabra clave:
- Second order cone programming
Voltage stability analysis
Optimal power flow model
Convex optimization
LEMB
- Rights
- openAccess
- License
- http://creativecommons.org/licenses/by-nc-nd/4.0/
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Voltage Stability Analysis in Medium-Voltage Distribution Networks Using a Second-Order Cone Approximation |
| title |
Voltage Stability Analysis in Medium-Voltage Distribution Networks Using a Second-Order Cone Approximation |
| spellingShingle |
Voltage Stability Analysis in Medium-Voltage Distribution Networks Using a Second-Order Cone Approximation Second order cone programming Voltage stability analysis Optimal power flow model Convex optimization LEMB |
| title_short |
Voltage Stability Analysis in Medium-Voltage Distribution Networks Using a Second-Order Cone Approximation |
| title_full |
Voltage Stability Analysis in Medium-Voltage Distribution Networks Using a Second-Order Cone Approximation |
| title_fullStr |
Voltage Stability Analysis in Medium-Voltage Distribution Networks Using a Second-Order Cone Approximation |
| title_full_unstemmed |
Voltage Stability Analysis in Medium-Voltage Distribution Networks Using a Second-Order Cone Approximation |
| title_sort |
Voltage Stability Analysis in Medium-Voltage Distribution Networks Using a Second-Order Cone Approximation |
| dc.creator.fl_str_mv |
Montoya, Oscar Danilo Gil-González, Walter Arias-Londoño, Andrés Rajagopalan, Arul Hernández, Jesus C. |
| dc.contributor.author.none.fl_str_mv |
Montoya, Oscar Danilo Gil-González, Walter Arias-Londoño, Andrés Rajagopalan, Arul Hernández, Jesus C. |
| dc.subject.keywords.es_CO.fl_str_mv |
Second order cone programming Voltage stability analysis Optimal power flow model Convex optimization |
| topic |
Second order cone programming Voltage stability analysis Optimal power flow model Convex optimization LEMB |
| dc.subject.armarc.none.fl_str_mv |
LEMB |
| description |
This paper addresses the voltage stability margin calculation in medium-voltage distribution networks in the context of exact mathematical modeling. This margin calculation is performed with a second-order cone (SOCP) reformulation of the classical nonlinear non-convex optimal power flow problems. The main idea around the SOCP approximation is to guarantee the global optimal solution via convex optimization, considering as the objective function the λ-coefficient associated with the maximum possible increment of the load consumption at all the nodes. Different simulation cases are considered in one test feeder, described as follows: (i) the distribution network without penetration of distributed generation; (ii) the distribution network with penetration of distributed generation; and (iii) the distribution grid with capacitive compensation. Numerical results in the test system demonstrated the effectiveness of the proposed SOCP approximation to determine the λ-coefficient. In addition, the proposed approximation is compared with nonlinear tools available in the literature. All the simulations are carried out in the MATLAB software with the CVX package and the Gurobi solver. |
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2020 |
| dc.date.issued.none.fl_str_mv |
2020-11-02 |
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2021-02-18T20:19:33Z |
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2021-02-18T20:19:33Z |
| dc.date.submitted.none.fl_str_mv |
2021-02-15 |
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http://purl.org/coar/version/c_970fb48d4fbd8a85 |
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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_2df8fbb1 |
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publishedVersion |
| dc.identifier.citation.es_CO.fl_str_mv |
Montoya, Oscar D.; Gil-González, Walter; Arias-Londoño, Andrés; Rajagopalan, Arul; Hernández, Jesus C. 2020. "Voltage Stability Analysis in Medium-Voltage Distribution Networks Using a Second-Order Cone Approximation" Energies 13, no. 21: 5717. https://doi.org/10.3390/en13215717 |
| dc.identifier.uri.none.fl_str_mv |
https://hdl.handle.net/20.500.12585/10046 |
| dc.identifier.doi.none.fl_str_mv |
10.3390/en13215717 |
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Universidad Tecnológica de Bolívar |
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Repositorio Universidad Tecnológica de Bolívar |
| identifier_str_mv |
Montoya, Oscar D.; Gil-González, Walter; Arias-Londoño, Andrés; Rajagopalan, Arul; Hernández, Jesus C. 2020. "Voltage Stability Analysis in Medium-Voltage Distribution Networks Using a Second-Order Cone Approximation" Energies 13, no. 21: 5717. https://doi.org/10.3390/en13215717 10.3390/en13215717 Universidad Tecnológica de Bolívar Repositorio Universidad Tecnológica de Bolívar |
| url |
https://hdl.handle.net/20.500.12585/10046 |
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eng |
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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 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 |
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openAccess |
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15 páginas |
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application/pdf |
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Cartagena de Indias |
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Energies 2020, 13(21), 5717 |
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Universidad Tecnológica de Bolívar |
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Montoya, Oscar Danilo8a59ede1-6a4a-4d2e-abdc-d0afb14d4480Gil-González, Walter1747fed9-7818-4c10-a283-efb3c73ebb27Arias-Londoño, Andrés89909de0-da09-49a3-8e61-83197925ba34Rajagopalan, Arul6d04d6b3-17a1-49be-a90b-6ea66be6d1c6Hernández, Jesus C.349b3120-388b-42be-8bea-32156f0dc09d2021-02-18T20:19:33Z2021-02-18T20:19:33Z2020-11-022021-02-15Montoya, Oscar D.; Gil-González, Walter; Arias-Londoño, Andrés; Rajagopalan, Arul; Hernández, Jesus C. 2020. "Voltage Stability Analysis in Medium-Voltage Distribution Networks Using a Second-Order Cone Approximation" Energies 13, no. 21: 5717. https://doi.org/10.3390/en13215717https://hdl.handle.net/20.500.12585/1004610.3390/en13215717Universidad Tecnológica de BolívarRepositorio Universidad Tecnológica de BolívarThis paper addresses the voltage stability margin calculation in medium-voltage distribution networks in the context of exact mathematical modeling. This margin calculation is performed with a second-order cone (SOCP) reformulation of the classical nonlinear non-convex optimal power flow problems. The main idea around the SOCP approximation is to guarantee the global optimal solution via convex optimization, considering as the objective function the λ-coefficient associated with the maximum possible increment of the load consumption at all the nodes. Different simulation cases are considered in one test feeder, described as follows: (i) the distribution network without penetration of distributed generation; (ii) the distribution network with penetration of distributed generation; and (iii) the distribution grid with capacitive compensation. Numerical results in the test system demonstrated the effectiveness of the proposed SOCP approximation to determine the λ-coefficient. In addition, the proposed approximation is compared with nonlinear tools available in the literature. All the simulations are carried out in the MATLAB software with the CVX package and the Gurobi solver.15 páginasapplication/pdfenghttp://creativecommons.org/licenses/by-nc-nd/4.0/info:eu-repo/semantics/openAccessAttribution-NonCommercial-NoDerivatives 4.0 InternacionalAttribution-NonCommercial-NoDerivatives 4.0 Internacionalhttp://purl.org/coar/access_right/c_abf2Energies 2020, 13(21), 5717Voltage Stability Analysis in Medium-Voltage Distribution Networks Using a Second-Order Cone Approximationinfo:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_2df8fbb1http://purl.org/coar/version/c_970fb48d4fbd8a85Second order cone programmingVoltage stability analysisOptimal power flow modelConvex optimizationLEMBCartagena de IndiasInvestigadoresTemiz, A.; Almalki, A.M.; Kahraman, Ö.; Alshahrani, S.S.; Sönmez, E.B.; Almutairi, S.S.; Nadar, A.; Smiai, M.S.; Alabduljabbar, A.A. Investigation of MV Distribution Networks with High-Penetration Distributed PVs: Study for an Urban Area. Energy Procedia 2017, 141, 517–524.Hernández, J.; Medina, A.; Jurado, F. Impact comparison of PV system integration into rural and urban feeders. Energy Convers. Manag. 2008, 49, 1747–1765.Montoya, O.D.; Gil-González, W.; Giral, D.A. On the Matricial Formulation of Iterative Sweep Power Flow for Radial and Meshed Distribution Networks with Guarantee of Convergence. Appl. Sci. 2020, 10, 5802.Jiménez, R.; Serebrisky, T.; Mercado, J. Sizing Electricity Losses in Transmission and Distribution Systems in Latin America and the Caribbean; Techreport; Inter-American Development Bank: Washington, DC, USA, 2014.Prakash, K.; Lallu, A.; Islam, F.; Mamun, K. Review of Power System Distribution Network Architecture. In Proceedings of the 2016 3rd Asia-Pacific World Congress on Computer Science and Engineering (APWC on CSE), Nadi, Fiji, 5–6 December 2016; IEEE: Piscataway, NJ, USA, 2016.Zaheb, H.; Danish, M.S.S.; Senjyu, T.; Ahmadi, M.; Nazari, A.M.; Wali, M.; Khosravy, M.; Mandal, P. A Contemporary Novel Classification of Voltage Stability Indices. Appl. Sci. 2020, 10, 1639.Ghaffarianfar, M.; Hajizadeh, A. Voltage Stability of Low-Voltage Distribution Grid with High Penetration of Photovoltaic Power Units. Energies 2018, 11, 1960.Ranjan, R.; Das, D. Voltage Stability Analysis of Radial Distribution Networks. Electr. Power Compon. Syst. 2003, 31, 501–511.Aly, M.M.; Abdel-Akher, M. A continuation power-flow for distribution systems voltage stability analysis. 2012 IEEE International Conference on Power and Energy (PECon), Kota Kinabalu, Malaysia, 2–5 December 2012; IEEE: Piscataway, NJ, USA, 2012.Chen, C.; Wang, J.; Li, Z.; Sun, H.; Wang, Z. PMU uncertainty quantification in voltage stability analysis. IEEE Trans. Power Syst. 2014, 30, 2196–2197.Sumit, B.; Chattopadhyay, T.K.; Chanda, C.K. Voltage stability margin of distribution networks for composite loads. In Proceedings of the 2012 IEEE Annual IEEE India Conference (INDICON), Kochi, India, 7–9 December 2012; IEEE: Piscataway, NJ, USA, 2012; pp. 582–587.Song, Y.; Hill, D.J.; Liu, T. Static voltage stability analysis of distribution systems based on network-load admittance ratio. IEEE Trans. Power Syst. 2018, 34, 2270–2280.Triştiu, I.; Iantoc, A.; Poştovei, D.; Bulac, C.; Arhip, M. Theoretical analysis of voltage instability conditions in distribution networks. In Proceedings of the 2019 IEEE 54th International Universities Power Engineering Conference (UPEC), Bucharest, Romania, 3–6 September 2019; IEEE: Piscataway, NJ, USA, 2019; pp. 1–5.Sinder, R.L.; Assis, T.M.; Taranto, G.N. Impact of photovoltaic systems on voltage stability in islanded distribution networks. J. Eng. 2019, 18, 5023–5027.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.Amin, W.T.; Montoya, O.D.; Grisales-Noreña, L.F. Determination of the Voltage Stability Index in DC Networks with CPLs: A GAMS Implementation. In Communications in Computer and Information Science; Springer International Publishing: Berlin/Heidelberg, Germany, 2019; pp. 552–564.Montoya, O.D.; Gil-Gonzalez, W.; Garrido, V.M. Voltage Stability Margin in DC Grids With CPLs: A Recursive Newton Raphson Approximation. IEEE Trans. Circuits Syst. II 2020, 67, 300–304.Chen, Y.; Xiang, J.; Li, Y. SOCP Relaxations of Optimal Power Flow Problem Considering Current Margins in Radial Networks. Energies 2018, 11, 3164.Candelo, J.E.; Delgado, G.C. Voltage stability assessment using fast non-dominated sorting algorithm. DYNA 2019, 86, 60–68.Adebayo, I.; Sun, Y. New Performance Indices for Voltage Stability Analysis in a Power System. Energies 2017, 10, 2042.Lobo, M.S.; Vandenberghe, L.; Boyd, S.; Lebret, H. Applications of second-order cone programming. Linear Algebra Appl. 1998, 284, 193–228.Yamashita, M.; Mullin, T.J.; Safarina, S. An efficient second-order cone programming approach for optimal selection in tree breeding. Optim. Lett. 2018, 12, 1683–1697.Lavaei, J.; Low, S.H. Zero Duality Gap in Optimal Power Flow Problem. IEEE Trans. Power Syst. 2012, 27, 92–107.Montoya, O.D.; Gil-González, W.; Grisales-Noreña, L. An exact MINLP model for optimal location and sizing of DGs in distribution networks: A general algebraic modeling system approach. Ain Shams Eng. J. 2020, 11, 409–418.Tamilselvan, V.; Jayabarathi, T.; Raghunathan, T.; Yang, X.S. Optimal capacitor placement in radial distribution systems using flower pollination algorithm. Alex. Eng. J. 2018, 57, 2775–2786.Morais, H.; Sousa, T.; Perez, A.; Jóhannsson, H.; Vale, Z. Energy Optimization for Distributed Energy Resources Scheduling with Enhancements in Voltage Stability Margin. Math. Probl. Eng. 2016, 2016, 1–20.Onlam, A.; Yodphet, D.; Chatthaworn, R.; Surawanitkun, C.; Siritaratiwat, A.; Khunkitti, P. Power Loss Minimization and Voltage Stability Improvement in Electrical Distribution System via Network Reconfiguration and Distributed Generation Placement Using Novel Adaptive Shuffled Frogs Leaping Algorithm. Energies 2019, 12, 553.Montoya, O.D.; Serra, F.M.; Angelo, C.H.D. On the Efficiency in Electrical Networks with AC and DC Operation Technologies: A Comparative Study at the Distribution Stage. Electronics 2020, 9, 1352.Montoya, O.D.; Gil-González, W. Dynamic active and reactive power compensation in distribution networks with batteries: A day-ahead economic dispatch approach. Comput. Electr. Eng. 2020, 85, 106710.Montoya, O.D.; Gil-González, W.; Grisales-Noreña, L.; Orozco-Henao, C.; Serra, F. Economic Dispatch of BESS and Renewable Generators in DC Microgrids Using Voltage-Dependent Load Models. Energies 2019, 12, 4494.Diamond, S.; Boyd, S. CVXPY: A Python-embedded modeling language for convex optimization. J. Mach. Learn. Res. 2016, 17, 2909–2913.Quan, R.; Jian, J.B.; Mu, Y.D. Tighter relaxation method for unit commitment based on second-order cone programming and valid inequalities. Int. J. Electr. Power Energy Syst. 2014, 55, 82–90.Benson, H.Y.; Sağlam, Ü. Mixed-Integer Second-Order Cone Programming: A Survey. 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