A mixed-integer convex model for the optimal placement and sizing of distributed generators in power distribution networks
The optimal placement and sizing of distributed generators is a classical problem in power distribution networks that is usually solved using heuristic algorithms due to its high complexity. This paper proposes a different approach based on a mixed-integer second-order cone programming (MI-SOCP) mod...
- Autores:
-
Gil-González, Walter
Garcés, Alejandro
Montoya, Oscar Danilo
Hernández, Jesus C.
- Tipo de recurso:
- Fecha de publicación:
- 2021
- Institución:
- Universidad Tecnológica de Bolívar
- Repositorio:
- Repositorio Institucional UTB
- Idioma:
- eng
- OAI Identifier:
- oai:repositorio.utb.edu.co:20.500.12585/10038
- Palabra clave:
- Distributed generators
Convex optimization
Second-order cone programming
Branch & bound
Method
Integer optimization
Power losses minimization
LEMB
- Rights
- openAccess
- License
- http://creativecommons.org/licenses/by-nc-nd/4.0/
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A mixed-integer convex model for the optimal placement and sizing of distributed generators in power distribution networks |
| title |
A mixed-integer convex model for the optimal placement and sizing of distributed generators in power distribution networks |
| spellingShingle |
A mixed-integer convex model for the optimal placement and sizing of distributed generators in power distribution networks Distributed generators Convex optimization Second-order cone programming Branch & bound Method Integer optimization Power losses minimization LEMB |
| title_short |
A mixed-integer convex model for the optimal placement and sizing of distributed generators in power distribution networks |
| title_full |
A mixed-integer convex model for the optimal placement and sizing of distributed generators in power distribution networks |
| title_fullStr |
A mixed-integer convex model for the optimal placement and sizing of distributed generators in power distribution networks |
| title_full_unstemmed |
A mixed-integer convex model for the optimal placement and sizing of distributed generators in power distribution networks |
| title_sort |
A mixed-integer convex model for the optimal placement and sizing of distributed generators in power distribution networks |
| dc.creator.fl_str_mv |
Gil-González, Walter Garcés, Alejandro Montoya, Oscar Danilo Hernández, Jesus C. |
| dc.contributor.author.none.fl_str_mv |
Gil-González, Walter Garcés, Alejandro Montoya, Oscar Danilo Hernández, Jesus C. |
| dc.subject.keywords.es_CO.fl_str_mv |
Distributed generators Convex optimization Second-order cone programming Branch & bound Method Integer optimization Power losses minimization |
| topic |
Distributed generators Convex optimization Second-order cone programming Branch & bound Method Integer optimization Power losses minimization LEMB |
| dc.subject.armarc.none.fl_str_mv |
LEMB |
| description |
The optimal placement and sizing of distributed generators is a classical problem in power distribution networks that is usually solved using heuristic algorithms due to its high complexity. This paper proposes a different approach based on a mixed-integer second-order cone programming (MI-SOCP) model that ensures the global optimum of the relaxed optimization model. Second-order cone programming (SOCP) has demonstrated to be an efficient alternative to cope with the non-convexity of the power flow equations in power distribution networks. Of relatively new interest to the power systems community is the extension to MI-SOCP models. The proposed model is an approximation. However, numerical validations in the IEEE 33-bus and IEEE 69-bus test systems for unity and variable power factor confirm that the proposed MI-SOCP finds the best solutions reported in the literature. Being an exact technique, the proposed model allows minimum processing times and zero standard deviation, i.e., the same optimum is guaranteed at each time that the MI-SOCP model is solved (a significant advantage in comparison to metaheuristics). Additionally, load and photovoltaic generation curves for the IEEE 69-node test system are included to demonstrate the applicability of the proposed MI-SOCP to solve the problem of the optimal location and sizing of renewable generators using the multi-period optimal power flow formulation. Therefore, the proposed MI-SOCP also guarantees the global optimum finding, in contrast to local solutions achieved with mixed-integer nonlinear programming solvers available in the GAMS optimization software. All the simulations were carried out via MATLAB software with the CVX package and Gurobi solver. |
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2021 |
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2021-02-17T20:44:53Z |
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2021-02-17T20:44:53Z |
| dc.date.issued.none.fl_str_mv |
2021-01-11 |
| dc.date.submitted.none.fl_str_mv |
2021-02-17 |
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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 |
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Gil-González, Walter; Garces, Alejandro; Montoya, Oscar D.; Hernández, Jesus C. 2021. "A Mixed-Integer Convex Model for the Optimal Placement and Sizing of Distributed Generators in Power Distribution Networks" Appl. Sci. 11, no. 2: 627. https://doi.org/10.3390/app11020627 |
| dc.identifier.uri.none.fl_str_mv |
https://hdl.handle.net/20.500.12585/10038 |
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https://www.mdpi.com/2076-3417/11/2/627 |
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10.3390/app11020627 |
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2076-3417 |
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Universidad Tecnológica de Bolívar |
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Repositorio Universidad Tecnológica de Bolívar |
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Gil-González, Walter; Garces, Alejandro; Montoya, Oscar D.; Hernández, Jesus C. 2021. "A Mixed-Integer Convex Model for the Optimal Placement and Sizing of Distributed Generators in Power Distribution Networks" Appl. Sci. 11, no. 2: 627. https://doi.org/10.3390/app11020627 10.3390/app11020627 2076-3417 Universidad Tecnológica de Bolívar Repositorio Universidad Tecnológica de Bolívar |
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https://hdl.handle.net/20.500.12585/10038 https://www.mdpi.com/2076-3417/11/2/627 |
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eng |
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eng |
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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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Applied Sciences 2021, 11(2), 627 |
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Gil-González, Walter72191491-1c75-451d-a5c5-f7f45373ecd0Garcés, Alejandro1f6fb709-fba4-4fc8-9381-be1f0ca81b82Montoya, Oscar Danilo8a59ede1-6a4a-4d2e-abdc-d0afb14d4480Hernández, Jesus C.349b3120-388b-42be-8bea-32156f0dc09d2021-02-17T20:44:53Z2021-02-17T20:44:53Z2021-01-112021-02-17Gil-González, Walter; Garces, Alejandro; Montoya, Oscar D.; Hernández, Jesus C. 2021. "A Mixed-Integer Convex Model for the Optimal Placement and Sizing of Distributed Generators in Power Distribution Networks" Appl. Sci. 11, no. 2: 627. https://doi.org/10.3390/app11020627https://hdl.handle.net/20.500.12585/10038https://www.mdpi.com/2076-3417/11/2/62710.3390/app110206272076-3417Universidad Tecnológica de BolívarRepositorio Universidad Tecnológica de BolívarThe optimal placement and sizing of distributed generators is a classical problem in power distribution networks that is usually solved using heuristic algorithms due to its high complexity. This paper proposes a different approach based on a mixed-integer second-order cone programming (MI-SOCP) model that ensures the global optimum of the relaxed optimization model. Second-order cone programming (SOCP) has demonstrated to be an efficient alternative to cope with the non-convexity of the power flow equations in power distribution networks. Of relatively new interest to the power systems community is the extension to MI-SOCP models. The proposed model is an approximation. However, numerical validations in the IEEE 33-bus and IEEE 69-bus test systems for unity and variable power factor confirm that the proposed MI-SOCP finds the best solutions reported in the literature. Being an exact technique, the proposed model allows minimum processing times and zero standard deviation, i.e., the same optimum is guaranteed at each time that the MI-SOCP model is solved (a significant advantage in comparison to metaheuristics). Additionally, load and photovoltaic generation curves for the IEEE 69-node test system are included to demonstrate the applicability of the proposed MI-SOCP to solve the problem of the optimal location and sizing of renewable generators using the multi-period optimal power flow formulation. Therefore, the proposed MI-SOCP also guarantees the global optimum finding, in contrast to local solutions achieved with mixed-integer nonlinear programming solvers available in the GAMS optimization software. All the simulations were carried out via MATLAB software with the CVX package and 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_abf2Applied Sciences 2021, 11(2), 627A mixed-integer convex model for the optimal placement and sizing of distributed generators in power distribution networksinfo:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_2df8fbb1http://purl.org/coar/version/c_970fb48d4fbd8a85Distributed generatorsConvex optimizationSecond-order cone programmingBranch & boundMethodInteger optimizationPower losses minimizationLEMBCartagena de IndiasInvestigadoresKefayat, M.; Ara, A.L.; Niaki, S.N. A hybrid of ant colony optimization and artificial bee colony algorithm for probabilistic optimal placement and sizing of distributed energy resources. Energy Convers. Manag. 2015, 92, 149–161. [CrossRef]Montoya, O.D.; Gil-González, W.; Grisales-Noreña, L. Relaxed convex model for optimal location and sizing of DGs in DC grids using sequential quadratic programming and random hyperplane approaches. Int. J. Electr. Power Energy Syst. 2020, 115, 105442. [CrossRef]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. [CrossRef]Katyara, S.; Staszewski, L.; Leonowicz, Z. Protection coordination of properly sized and placed distributed generations–methods, applications and future scope. Energies 2018, 11, 2672. [CrossRef]Floudas, C.A.; Pardalos, P.M. (Eds.) 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A combination of genetic algorithm and particle swarm optimization for optimal DG location and sizing in distribution systems. Int. J. Electr. Power Energy Syst. 2012, 34, 66–74. [CrossRef]Bocanegra, S.Y.; Montoya, O.D. Heuristic Approach for Optimal Location and Sizing of Distributed Generators in AC Distribution Networks. Wseas Trans. Power Syst. 2019, 14, 113–121.Sultana, S.; Roy, P.K. Multi-objective quasi-oppositional teaching learning based optimization for optimal location of distributed generator in radial distribution systems. Int. J. Electr. Power Energy Syst. 2014, 63, 534–545. [CrossRef]Bayat, A.; Bagheri, A. Optimal active and reactive power allocation in distribution networks using a novel heuristic approach. Appl. Energy 2019, 233-234, 71–85. [CrossRef]Muthukumar, K.; Jayalalitha, S. Optimal placement and sizing of distributed generators and shunt capacitors for power loss minimization in radial distribution networks using hybrid heuristic search optimization technique. Int. J. Electr. Power Energy Syst. 2016, 78, 299–319. [CrossRef]Kaur, S.; Kumbhar, G.; Sharma, J. A MINLP technique for optimal placement of multiple DG units in distribution systems. Int. J. Electr. Power Energy Syst. 2014, 63, 609–617. [CrossRef]Gholami, K.; Parvaneh, M.H. A mutated salp swarm algorithm for optimum allocation of active and reactive power sources in radial distribution systems. Appl. Soft Comput. 2019, 85, 105833. [CrossRef]Nowdeh, S.A.; Davoudkhani, I.F.; Moghaddam, M.H.; Najmi, E.S.; Abdelaziz, A.; Ahmadi, A.; Razavi, S.; Gandoman, F. Fuzzy multi-objective placement of renewable energy sources in distribution system with objective of loss reduction and reliability improvement using a novel hybrid method. Appl. Soft Comput. 2019, 77, 761–779. [CrossRef]Hung, D.Q.; Mithulananthan, N. Multiple distributed generator placement in primary distribution networks for loss reduction. IEEE Trans. Ind. Electron. 2011, 60, 1700–1708. 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