On the Conic Convex Approximation to Locate and Size Fixed-Step Capacitor Banks in Distribution Networks
The problem of the optimal siting and sizing of fixed-step capacitor banks is studied in this research from the standpoint of convex optimization. This problem is formulated through a mixed-integer nonlinear programming (MINLP) model, in which its binary/integer variables are related to the nodes wh...
- Autores:
-
Montoya, Oscar Danilo
Gil-González, Walter
Garcés, Alejandro
- Tipo de recurso:
- Fecha de publicación:
- 2022
- Institución:
- Universidad Tecnológica de Bolívar
- Repositorio:
- Repositorio Institucional UTB
- Idioma:
- eng
- OAI Identifier:
- oai:repositorio.utb.edu.co:20.500.12585/10696
- Acceso en línea:
- https://hdl.handle.net/20.500.12585/10696
https:// doi.org/10.3390/computation10020032
- Palabra clave:
- Capacitor banks
Distribution networks
Second-order cone programming model
Power losses minimization
LEMB
- Rights
- openAccess
- License
- http://creativecommons.org/licenses/by-nc-nd/4.0/
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On the Conic Convex Approximation to Locate and Size Fixed-Step Capacitor Banks in Distribution Networks |
| title |
On the Conic Convex Approximation to Locate and Size Fixed-Step Capacitor Banks in Distribution Networks |
| spellingShingle |
On the Conic Convex Approximation to Locate and Size Fixed-Step Capacitor Banks in Distribution Networks Capacitor banks Distribution networks Second-order cone programming model Power losses minimization LEMB |
| title_short |
On the Conic Convex Approximation to Locate and Size Fixed-Step Capacitor Banks in Distribution Networks |
| title_full |
On the Conic Convex Approximation to Locate and Size Fixed-Step Capacitor Banks in Distribution Networks |
| title_fullStr |
On the Conic Convex Approximation to Locate and Size Fixed-Step Capacitor Banks in Distribution Networks |
| title_full_unstemmed |
On the Conic Convex Approximation to Locate and Size Fixed-Step Capacitor Banks in Distribution Networks |
| title_sort |
On the Conic Convex Approximation to Locate and Size Fixed-Step Capacitor Banks in Distribution Networks |
| dc.creator.fl_str_mv |
Montoya, Oscar Danilo Gil-González, Walter Garcés, Alejandro |
| dc.contributor.author.none.fl_str_mv |
Montoya, Oscar Danilo Gil-González, Walter Garcés, Alejandro |
| dc.subject.keywords.es_CO.fl_str_mv |
Capacitor banks Distribution networks Second-order cone programming model Power losses minimization |
| topic |
Capacitor banks Distribution networks Second-order cone programming model Power losses minimization LEMB |
| dc.subject.armarc.none.fl_str_mv |
LEMB |
| description |
The problem of the optimal siting and sizing of fixed-step capacitor banks is studied in this research from the standpoint of convex optimization. This problem is formulated through a mixed-integer nonlinear programming (MINLP) model, in which its binary/integer variables are related to the nodes where the capacitors will be installed. Simultaneously, the continuous variables are mainly associated with the power flow solution. The main contribution of this research is the reformulation of the exact MINLP model through a mixed-integer second-order cone programming model (MI-SOCP). This mixed-integer conic model maintains the nonlinearities of the original MINLP model; however, it can be solved efficiently with the branch & bound method combined with the interior point method adapted for conic programming models. The main advantage of the proposed MI-SOCP model is the possibility of finding the global optimum based on the convex nature of the power flow problem for each binary/integer variable combination in the branch & bound search tree. The numerical results in the IEEE 33- and IEEE 69-bus systems demonstrate the effectiveness and robustness of the proposed MI-SOCP model compared to different metaheuristic approaches. The MISOCP model finds the final power losses of the IEEE 33- and IEEE 69-bus systems of 138.416 kW and 145.397 kW, which improves the best literature results reached with the flower pollination algorithm, i.e., 139.075 kW, and 145.860 kW, respectively. The simulations are carried out in MATLAB software using its convex optimizer tool known as CVX with the Gurobi solver. |
| publishDate |
2022 |
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2022-05-19T21:17:09Z |
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2022-05-19T21:17:09Z |
| dc.date.issued.none.fl_str_mv |
2022-02-20 |
| dc.date.submitted.none.fl_str_mv |
2022-05-19 |
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info:eu-repo/semantics/article |
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info:eu-repo/semantics/restrictedAccess |
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http://purl.org/coar/resource_type/c_2df8fbb1 |
| dc.identifier.citation.es_CO.fl_str_mv |
Montoya, O.D.; Gil-González, W.; Garcés, A. On the Conic Convex Approximation to Locate and Size Fixed-Step Capacitor Banks in Distribution Networks. Computation 2022, 10, 32. https://doi.org/10.3390/computation10020032 |
| dc.identifier.uri.none.fl_str_mv |
https://hdl.handle.net/20.500.12585/10696 |
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https:// doi.org/10.3390/computation10020032 |
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Universidad Tecnológica de Bolívar |
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Repositorio Universidad Tecnológica de Bolívar |
| identifier_str_mv |
Montoya, O.D.; Gil-González, W.; Garcés, A. On the Conic Convex Approximation to Locate and Size Fixed-Step Capacitor Banks in Distribution Networks. Computation 2022, 10, 32. https://doi.org/10.3390/computation10020032 Universidad Tecnológica de Bolívar Repositorio Universidad Tecnológica de Bolívar |
| url |
https://hdl.handle.net/20.500.12585/10696 https:// doi.org/10.3390/computation10020032 |
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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 |
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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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14 Páginas |
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application/pdf |
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Cartagena de Indias |
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Computation - Vol. 10 N° 8 (2022). |
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Universidad Tecnológica de Bolívar |
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Montoya, Oscar Danilo8a59ede1-6a4a-4d2e-abdc-d0afb14d4480Gil-González, Walterce1f5078-74c6-4b5c-b56a-784f85e52a08Garcés, Alejandro1f6fb709-fba4-4fc8-9381-be1f0ca81b822022-05-19T21:17:09Z2022-05-19T21:17:09Z2022-02-202022-05-19Montoya, O.D.; Gil-González, W.; Garcés, A. On the Conic Convex Approximation to Locate and Size Fixed-Step Capacitor Banks in Distribution Networks. Computation 2022, 10, 32. https://doi.org/10.3390/computation10020032https://hdl.handle.net/20.500.12585/10696https:// doi.org/10.3390/computation10020032Universidad Tecnológica de BolívarRepositorio Universidad Tecnológica de BolívarThe problem of the optimal siting and sizing of fixed-step capacitor banks is studied in this research from the standpoint of convex optimization. This problem is formulated through a mixed-integer nonlinear programming (MINLP) model, in which its binary/integer variables are related to the nodes where the capacitors will be installed. Simultaneously, the continuous variables are mainly associated with the power flow solution. The main contribution of this research is the reformulation of the exact MINLP model through a mixed-integer second-order cone programming model (MI-SOCP). This mixed-integer conic model maintains the nonlinearities of the original MINLP model; however, it can be solved efficiently with the branch & bound method combined with the interior point method adapted for conic programming models. The main advantage of the proposed MI-SOCP model is the possibility of finding the global optimum based on the convex nature of the power flow problem for each binary/integer variable combination in the branch & bound search tree. The numerical results in the IEEE 33- and IEEE 69-bus systems demonstrate the effectiveness and robustness of the proposed MI-SOCP model compared to different metaheuristic approaches. The MISOCP model finds the final power losses of the IEEE 33- and IEEE 69-bus systems of 138.416 kW and 145.397 kW, which improves the best literature results reached with the flower pollination algorithm, i.e., 139.075 kW, and 145.860 kW, respectively. The simulations are carried out in MATLAB software using its convex optimizer tool known as CVX with the Gurobi solver.14 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_abf2Computation - Vol. 10 N° 8 (2022).On the Conic Convex Approximation to Locate and Size Fixed-Step Capacitor Banks in Distribution Networksinfo:eu-repo/semantics/articleinfo:eu-repo/semantics/restrictedAccesshttp://purl.org/coar/resource_type/c_2df8fbb1Capacitor banksDistribution networksSecond-order cone programming modelPower losses minimizationLEMBCartagena de IndiasRidzuan, M.I.M.; Fauzi, N.F.M.; Roslan, N.N.R.; Saad, N.M. Urban and rural medium voltage networks reliability assessment. SN Appl. Sci. 2020, 2, 241Kien, L.C.; Nguyen, T.T.; Pham, T.D.; Nguyen, T.T. Cost reduction for energy loss and capacitor investment in radial distribution networks applying novel algorithms. Neural Comput. Appl. 2021, 33, 15495–15522.Riaño, F.E.; Cruz, J.F.; Montoya, O.D.; Chamorro, H.R.; Alvarado-Barrios, L. Reduction of Losses and Operating Costs in Distribution Networks Using a Genetic Algorithm and Mathematical Optimization. Electronics 2021, 10, 419Lavorato, M.; Franco, J.F.; Rider, M.J.; Romero, R. Imposing Radiality Constraints in Distribution System Optimization Problems. IEEE Trans. Power Syst. 2012, 27, 172–180.Paz-Rodríguez, A.; Castro-Ordoñez, J.F.; Montoya, O.D.; Giral-Ramírez, D.A. Optimal Integration of Photovoltaic Sources in Distribution Networks for Daily Energy Losses Minimization Using the Vortex Search Algorithm. Appl. Sci. 2021, 11, 4418Águila, A.; Ortiz, L.; Orizondo, R.; López, G. Optimal location and dimensioning of capacitors in microgrids using a multicriteria decision algorithm. Heliyon 2021, 7, e08061Madruga, E.P.; Canha, L.N. 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