A hybrid approach based on socp and the discrete version of the sca for optimal placement and sizing dgs in ac distribution networks

This paper deals with the problem of the optimal placement and sizing of distributed generators (DGs) in alternating current (AC) distribution networks by proposing a hybrid master–slave optimization procedure. In the master stage, the discrete version of the sine–cosine algorithm (SCA) determines t...

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Autores:: Montoya, Oscar Danilo
Molina-Cabrera, Alexander
Chamorro, Harold R.
Alvarado-Barrios, Lázaro
Rivas-Trujillo, Edwin

Tipo de recurso:

Fecha de publicación:: 2020

Institución:: Universidad Tecnológica de Bolívar

Repositorio:: Repositorio Institucional UTB

Idioma:: eng

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dc.title.spa.fl_str_mv	A hybrid approach based on socp and the discrete version of the sca for optimal placement and sizing dgs in ac distribution networks
title	A hybrid approach based on socp and the discrete version of the sca for optimal placement and sizing dgs in ac distribution networks
spellingShingle	A hybrid approach based on socp and the discrete version of the sca for optimal placement and sizing dgs in ac distribution networks Distributed generation Mixed-integer nonlinear programming Optimal power flow Second-cone programming Discrete-sine cosine algorithm Metaheuristic optimization LEMB
title_short	A hybrid approach based on socp and the discrete version of the sca for optimal placement and sizing dgs in ac distribution networks
title_full	A hybrid approach based on socp and the discrete version of the sca for optimal placement and sizing dgs in ac distribution networks
title_fullStr	A hybrid approach based on socp and the discrete version of the sca for optimal placement and sizing dgs in ac distribution networks
title_full_unstemmed	A hybrid approach based on socp and the discrete version of the sca for optimal placement and sizing dgs in ac distribution networks
title_sort	A hybrid approach based on socp and the discrete version of the sca for optimal placement and sizing dgs in ac distribution networks
dc.creator.fl_str_mv	Montoya, Oscar Danilo Molina-Cabrera, Alexander Chamorro, Harold R. Alvarado-Barrios, Lázaro Rivas-Trujillo, Edwin
dc.contributor.author.none.fl_str_mv	Montoya, Oscar Danilo Molina-Cabrera, Alexander Chamorro, Harold R. Alvarado-Barrios, Lázaro Rivas-Trujillo, Edwin
dc.subject.keywords.spa.fl_str_mv	Distributed generation Mixed-integer nonlinear programming Optimal power flow Second-cone programming Discrete-sine cosine algorithm Metaheuristic optimization
topic	Distributed generation Mixed-integer nonlinear programming Optimal power flow Second-cone programming Discrete-sine cosine algorithm Metaheuristic optimization LEMB
dc.subject.armarc.none.fl_str_mv	LEMB
description	This paper deals with the problem of the optimal placement and sizing of distributed generators (DGs) in alternating current (AC) distribution networks by proposing a hybrid master–slave optimization procedure. In the master stage, the discrete version of the sine–cosine algorithm (SCA) determines the optimal location of the DGs, i.e., the nodes where these must be located, by using an integer codification. In the slave stage, the problem of the optimal sizing of the DGs is solved through the implementation of the second-order cone programming (SOCP) equivalent model to obtain solutions for the resulting optimal power flow problem. As the main advantage, the proposed approach allows converting the original mixed-integer nonlinear programming formulation into a mixed-integer SOCP equivalent. That is, each combination of nodes provided by the master level SCA algorithm to locate distributed generators brings an optimal solution in terms of its sizing; since SOCP is a convex optimization model that ensures the global optimum finding. Numerical validations of the proposed hybrid SCA-SOCP to optimal placement and sizing of DGs in AC distribution networks show its capacity to find global optimal solutions. Some classical distribution networks (33 and 69 nodes) were tested, and some comparisons were made using reported results from literature. In addition, simulation cases with unity and variable power factor are made, including the possibility of locating photovoltaic sources considering daily load and generation curves. All the simulations were carried out in the MATLAB software using the CVX optimization tool.
publishDate	2020
dc.date.issued.none.fl_str_mv	2020-12-27
dc.date.accessioned.none.fl_str_mv	2021-02-17T21:09:05Z
dc.date.available.none.fl_str_mv	2021-02-17T21:09:05Z
dc.date.submitted.none.fl_str_mv	2021-02-17
dc.type.coarversion.fl_str_mv	http://purl.org/coar/version/c_970fb48d4fbd8a85
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dc.identifier.citation.spa.fl_str_mv	Montoya, Oscar D.; Molina-Cabrera, Alexander; Chamorro, Harold R.; Alvarado-Barrios, Lazaro; Rivas-Trujillo, Edwin. 2021. "A Hybrid Approach Based on SOCP and the Discrete Version of the SCA for Optimal Placement and Sizing DGs in AC Distribution Networks" Electronics 10, no. 1: 26. https://doi.org/10.3390/electronics10010026
dc.identifier.uri.none.fl_str_mv	https://hdl.handle.net/20.500.12585/10043
dc.identifier.url.none.fl_str_mv	https://www.mdpi.com/2079-9292/10/1/26
dc.identifier.doi.none.fl_str_mv	10.3390/electronics10010026
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, Oscar D.; Molina-Cabrera, Alexander; Chamorro, Harold R.; Alvarado-Barrios, Lazaro; Rivas-Trujillo, Edwin. 2021. "A Hybrid Approach Based on SOCP and the Discrete Version of the SCA for Optimal Placement and Sizing DGs in AC Distribution Networks" Electronics 10, no. 1: 26. https://doi.org/10.3390/electronics10010026 10.3390/electronics10010026 Universidad Tecnológica de Bolívar Repositorio Universidad Tecnológica de Bolívar
url	https://hdl.handle.net/20.500.12585/10043 https://www.mdpi.com/2079-9292/10/1/26
dc.language.iso.spa.fl_str_mv	eng
language	eng
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dc.rights.cc.*.fl_str_mv	Attribution-NonCommercial-NoDerivatives 4.0 Internacional
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eu_rights_str_mv	openAccess
dc.format.extent.none.fl_str_mv	18 páginas
dc.format.mimetype.spa.fl_str_mv	application/pdf
dc.publisher.place.spa.fl_str_mv	Cartagena de Indias
dc.source.spa.fl_str_mv	Electronics 2021, 10(1), 26
institution	Universidad Tecnológica de Bolívar
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spelling	Montoya, Oscar Danilo8a59ede1-6a4a-4d2e-abdc-d0afb14d4480Molina-Cabrera, Alexander01b29f76-a1f3-4151-a070-ce883ba39849Chamorro, Harold R.59e2dcd8-f603-4e1f-8459-da694d5a324dAlvarado-Barrios, Lázaro57fdbc12-9b16-4b46-abf4-0ba206be4700Rivas-Trujillo, Edwin0720b1ee-acdc-4aea-b24b-fc319c4dd61c2021-02-17T21:09:05Z2021-02-17T21:09:05Z2020-12-272021-02-17Montoya, Oscar D.; Molina-Cabrera, Alexander; Chamorro, Harold R.; Alvarado-Barrios, Lazaro; Rivas-Trujillo, Edwin. 2021. "A Hybrid Approach Based on SOCP and the Discrete Version of the SCA for Optimal Placement and Sizing DGs in AC Distribution Networks" Electronics 10, no. 1: 26. https://doi.org/10.3390/electronics10010026https://hdl.handle.net/20.500.12585/10043https://www.mdpi.com/2079-9292/10/1/2610.3390/electronics10010026Universidad Tecnológica de BolívarRepositorio Universidad Tecnológica de BolívarThis paper deals with the problem of the optimal placement and sizing of distributed generators (DGs) in alternating current (AC) distribution networks by proposing a hybrid master–slave optimization procedure. In the master stage, the discrete version of the sine–cosine algorithm (SCA) determines the optimal location of the DGs, i.e., the nodes where these must be located, by using an integer codification. In the slave stage, the problem of the optimal sizing of the DGs is solved through the implementation of the second-order cone programming (SOCP) equivalent model to obtain solutions for the resulting optimal power flow problem. As the main advantage, the proposed approach allows converting the original mixed-integer nonlinear programming formulation into a mixed-integer SOCP equivalent. That is, each combination of nodes provided by the master level SCA algorithm to locate distributed generators brings an optimal solution in terms of its sizing; since SOCP is a convex optimization model that ensures the global optimum finding. Numerical validations of the proposed hybrid SCA-SOCP to optimal placement and sizing of DGs in AC distribution networks show its capacity to find global optimal solutions. Some classical distribution networks (33 and 69 nodes) were tested, and some comparisons were made using reported results from literature. In addition, simulation cases with unity and variable power factor are made, including the possibility of locating photovoltaic sources considering daily load and generation curves. All the simulations were carried out in the MATLAB software using the CVX optimization tool.18 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_abf2Electronics 2021, 10(1), 26A hybrid approach based on socp and the discrete version of the sca for optimal placement and sizing dgs in ac distribution networksinfo:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_2df8fbb1http://purl.org/coar/version/c_970fb48d4fbd8a85Distributed generationMixed-integer nonlinear programmingOptimal power flowSecond-cone programmingDiscrete-sine cosine algorithmMetaheuristic optimizationLEMBCartagena de IndiasInvestigadoresShaw, R.; Attree, M.; Jackson, T. Developing electricity distribution networks and their regulation to support sustainable energy. Energy Policy 2010, 38, 5927–5937Lavorato, 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.Pegado, R.; Ñaupari, Z.; Molina, Y.; Castillo, C. Radial distribution network reconfiguration for power losses reduction based on improved selective BPSO. Electr. Power Syst. Res. 2019, 169, 206–213Muthukumar, 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.Verma, H.K.; Singh, P. Optimal Reconfiguration of Distribution Network Using Modified Culture Algorithm. J. Inst. Eng. Ser. B 2018, 99, 613–622.Rao, R.S.; Satish, K.; Narasimham, S.V.L. Optimal Conductor Size Selection in Distribution Systems Using the Harmony Search Algorithm with a Differential Operator. Electr. Power Compon. Syst. 2011, 40, 41–56.Zhao, Z.; Mutale, J. Optimal Conductor Size Selection in Distribution Networks with High Penetration of Distributed Generation Using Adaptive Genetic Algorithm. Energies 2019, 12, 2065Grisales-Noreña, L.; Montoya, D.G.; Ramos-Paja, C. Optimal Sizing and Location of Distributed Generators Based on PBIL and PSO Techniques. Energies 2018, 11, 1018.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.Kacejko, P.; Adamek, S.; Wydra, M. Optimal voltage control in distribution networks with dispersed generation. In Proceedings of the 2010 IEEE PES Innovative Smart Grid Technologies Conference Europe (ISGT Europe), Gothenberg, Sweden, 11–13 October 2010.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.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, 409–418Hassan, A.S.; Sun, Y.; Wang, Z. Optimization techniques applied for optimal planning and integration of renewable energy sources based on distributed generation: Recent trends. Cogent Eng. 2020, 7.Bukhsh, W.A.; Grothey, A.; McKinnon, K.I.M.; Trodden, P.A. Local Solutions of the Optimal Power Flow Problem. IEEE Trans. Power Syst. 2013, 28, 4780–4788.Molzahn, D.K. Identifying and Characterizing Non-Convexities in Feasible Spaces of Optimal Power Flow Problems. IEEE Trans. Circuits Syst. II Express Briefs 2018, 65, 672–676.Melo, W.; Fampa, M.; Raupp, F. An overview of MINLP algorithms and their implementation in Muriqui Optimizer. Ann. Oper. Res. 2018, 286, 217–241.Lavaei, J.; Low, S.H. Zero Duality Gap in Optimal Power Flow Problem. IEEE Trans. Power Syst. 2012, 27, 92–107.Farivar, M.; Low, S.H. Branch Flow Model: Relaxations and Convexification—Part I. IEEE Trans. Power Syst. 2013, 28, 2554–2564Gil-González, W.; Molina-Cabrera, A.; Montoya, O.D.; Grisales-Noreña, L.F. An MI-SDP Model for Optimal Location and Sizing of Distributed Generators in DC Grids That Guarantees the Global Optimum. Appl. Sci. 2020, 10, 7681.Sultana, U.; Khairuddin, A.B.; Aman, M.; Mokhtar, A.; Zareen, N. A review of optimum DG placement based on minimization of power losses and voltage stability enhancement of distribution system. Renew. Sustain. Energy Rev. 2016, 63, 363–378.Montoya, O.D.; Gil-González, W.; Orozco-Henao, C. Vortex search and Chu-Beasley genetic algorithms for optimal location and sizing of distributed generators in distribution networks: A novel hybrid approach. Eng. Sci. Technol. Int. J. 2020.Moradi, M.; Abedini, M. 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.Injeti, S.K.; Kumar, N.P. A novel approach to identify optimal access point and capacity of multiple DGs in a small, medium and large scale radial distribution systems. Int. J. Electr. Power Energy Syst. 2013, 45, 142–151.large scale radial distribution systems. Int. J. Electr. Power Energy Syst. 2013, 45, 142–151. [CrossRef] 24. Gupta, S.; Saxena, A.; Soni, B.P. Optimal Placement Strategy of Distributed Generators based on Radial Basis Function Neural Network in Distribution Networks. Procedia Comput. Sci. 2015, 57, 249–257.Moradi, M.; Abedini, M. A novel method for optimal DG units capacity and location in Microgrids. Int. J. Electr. Power Energy Syst. 2016, 75, 236–244Bayat, A.; Bagheri, A. Optimal active and reactive power allocation in distribution networks using a novel heuristic approach. Appl. Energy 2019, 233–234, 71–85.Sultana, S.; Roy, P.K. Krill herd algorithm for optimal location of distributed generator in radial distribution system. Appl. Soft Comput. 2016, 40, 391–404.Deshmukh, R.; Kalage, A. Optimal Placement and Sizing of Distributed Generator in Distribution System Using Artificial Bee Colony Algorithm. In Proceedings of the 2018 IEEE Global Conference on Wireless Computing and Networking (GCWCN), Lonavala, India, 23–24 November 2018.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.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, 105833Bocanegra, 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.ChithraDevi, S.; Lakshminarasimman, L.; Balamurugan, R. Stud Krill herd Algorithm for multiple DG placement and sizing in a radial distribution system. Eng. Sci. Technol. Int. J. 2017, 20, 748–759.Yang, Q.; Chu, S.C.; Pan, J.S.; Chen, C.M. Sine Cosine Algorithm with Multigroup and Multistrategy for Solving CVRP. Math. Probl. Eng. 2020, 2020, 1–10.Attia, A.F.; Sehiemy, R.A.E.; Hasanien, H.M. Optimal power flow solution in power systems using a novel Sine–Cosine algorithm. Int. J. Electr. Power Energy Syst. 2018, 99, 331–343.Manrique, M.L.; Montoya, O.D.; Garrido, V.M.; Grisales-Noreña, L.F.; Gil-González, W. Sine–Cosine Algorithm for OPF Analysis in Distribution Systems to Size Distributed Generators. In Communications in Computer and Information Science; Springer International Publishing: Berlin/Heidelberg, Germany, 2019; pp. 28–39.Montoya, O.D.; Gil-González, W.; Grisales-Noreña, L.F. Sine–cosine algorithm for parameters’ estimation in solar cells using datasheet information. J. Phys. Conf. Ser. 2020, 1671, 012008.Mirjalili, S.M.; Mirjalili, S.Z.; Saremi, S.; Mirjalili, S. Sine Cosine Algorithm: Theory, Literature Review, and Application in Designing Bend Photonic Crystal Waveguides. In Nature-Inspired Optimizers; Springer International Publishing: Berlin/Heidelberg, Germany, 2019; pp. 201–217.Qu, C.; Zeng, Z.; Dai, J.; Yi, Z.; He, W. A Modified Sine–Cosine Algorithm Based on Neighborhood Search and Greedy Levy Mutation. Comput. Intell. Neurosci. 2018, 2018, 1–19.Sahin, O.; Akay, B. Comparisons of metaheuristic algorithms and fitness functions on software test data generation. Appl. Soft Comput. 2016, 49, 1202–1214.Dahal, K.; Remde, S.; Cowling, P.; Colledge, N. Improving Metaheuristic Performance by Evolving a Variable Fitness Function. 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A hybrid approach based on socp and the discrete version of the sca for optimal placement and sizing dgs in ac distribution networks

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