Optimal Power Dispatch of PV Generators in AC Distribution Networks by Considering Solar, Environmental, and Power Demand Conditions from Colombia

This paper deals with the problem regarding the optimal operation of photovoltaic (PV) generation sources in AC distribution networks with a single-phase structure, taking into consid eration different objective functions. The problem is formulated as a multi-period optimal power flow applied to AC...

Full description

Autores:
Grisales-Noreña, Luis Fernando
Montoya, Oscar Danilo
Cortés-Caicedo, Brandon
Zishan, Farhad
Rosero-García, Javier
Tipo de recurso:
Fecha de publicación:
2023
Institución:
Universidad Tecnológica de Bolívar
Repositorio:
Repositorio Institucional UTB
Idioma:
eng
OAI Identifier:
oai:repositorio.utb.edu.co:20.500.12585/11840
Acceso en línea:
https://hdl.handle.net/20.500.12585/11840
https://doi.org/10.3390/math11020484
Palabra clave:
Day-ahead operation of PV sources
Energy purchasing costs
Operation and maintenance costs of PV sources
Energy losses costs
Nonlinear programming formulation
GAMS software
LEMB
Rights
openAccess
License
http://creativecommons.org/licenses/by-nc-nd/4.0/
id UTB2_8d75dc94f6d7977e5e1bc705ca62c2f6
oai_identifier_str oai:repositorio.utb.edu.co:20.500.12585/11840
network_acronym_str UTB2
network_name_str Repositorio Institucional UTB
repository_id_str
dc.title.spa.fl_str_mv Optimal Power Dispatch of PV Generators in AC Distribution Networks by Considering Solar, Environmental, and Power Demand Conditions from Colombia
title Optimal Power Dispatch of PV Generators in AC Distribution Networks by Considering Solar, Environmental, and Power Demand Conditions from Colombia
spellingShingle Optimal Power Dispatch of PV Generators in AC Distribution Networks by Considering Solar, Environmental, and Power Demand Conditions from Colombia
Day-ahead operation of PV sources
Energy purchasing costs
Operation and maintenance costs of PV sources
Energy losses costs
Nonlinear programming formulation
GAMS software
LEMB
title_short Optimal Power Dispatch of PV Generators in AC Distribution Networks by Considering Solar, Environmental, and Power Demand Conditions from Colombia
title_full Optimal Power Dispatch of PV Generators in AC Distribution Networks by Considering Solar, Environmental, and Power Demand Conditions from Colombia
title_fullStr Optimal Power Dispatch of PV Generators in AC Distribution Networks by Considering Solar, Environmental, and Power Demand Conditions from Colombia
title_full_unstemmed Optimal Power Dispatch of PV Generators in AC Distribution Networks by Considering Solar, Environmental, and Power Demand Conditions from Colombia
title_sort Optimal Power Dispatch of PV Generators in AC Distribution Networks by Considering Solar, Environmental, and Power Demand Conditions from Colombia
dc.creator.fl_str_mv Grisales-Noreña, Luis Fernando
Montoya, Oscar Danilo
Cortés-Caicedo, Brandon
Zishan, Farhad
Rosero-García, Javier
dc.contributor.author.none.fl_str_mv Grisales-Noreña, Luis Fernando
Montoya, Oscar Danilo
Cortés-Caicedo, Brandon
Zishan, Farhad
Rosero-García, Javier
dc.subject.keywords.spa.fl_str_mv Day-ahead operation of PV sources
Energy purchasing costs
Operation and maintenance costs of PV sources
Energy losses costs
Nonlinear programming formulation
GAMS software
topic Day-ahead operation of PV sources
Energy purchasing costs
Operation and maintenance costs of PV sources
Energy losses costs
Nonlinear programming formulation
GAMS software
LEMB
dc.subject.armarc.none.fl_str_mv LEMB
description This paper deals with the problem regarding the optimal operation of photovoltaic (PV) generation sources in AC distribution networks with a single-phase structure, taking into consid eration different objective functions. The problem is formulated as a multi-period optimal power flow applied to AC distribution grids, which generates a nonlinear programming (NLP) model with a non-convex structure. Three different objective functions are considered in the optimization model, each optimized using a single-objective function approach. These objective functions are (i) an operating costs function composed of the energy purchasing costs at the substation bus, added with the PV maintenance costs; (ii) the costs of energy losses; and (iii) the total CO2 emissions at the substation bus. All these functions are minimized while considering a frame of operation of 24 h, i.e., in a day-ahead operation environment. To solve the NLP model representing the studied problem, the General Algebraic Modeling System (GAMS) and its SNOPT solver are used. Two different test feeders are used for all the numerical validations, one of them adapted to the urban operation characteristics in the Metropolitan Area of Medellín, which is composed of 33 nodes, and the other one adapted to isolated rural operating conditions, which has 27 nodes and is located in the department of Chocó, Colombia (municipality of Capurganá). Numerical comparisons with multiple combinatorial optimization methods (particle swarm optimization, the continuous genetic algorithm, the Vortex Search algorithm, and the Ant Lion Optimizer) demonstrate the effectiveness of the GAMS software to reach the optimal day-ahead dispatch of all the PV sources in both distribution grids.
publishDate 2023
dc.date.accessioned.none.fl_str_mv 2023-05-05T19:25:09Z
dc.date.available.none.fl_str_mv 2023-05-05T19:25:09Z
dc.date.issued.none.fl_str_mv 2023-01-16
dc.date.submitted.none.fl_str_mv 2023-05-05
dc.type.coarversion.fl_str_mv http://purl.org/coar/version/c_b1a7d7d4d402bcce
dc.type.driver.spa.fl_str_mv info:eu-repo/semantics/article
dc.type.hasversion.spa.fl_str_mv info:eu-repo/semantics/draft
dc.type.spa.spa.fl_str_mv http://purl.org/coar/resource_type/c_2df8fbb1
status_str draft
dc.identifier.citation.spa.fl_str_mv Grisales-Noreña, L.F.; Montoya, O.D.; Cortés-Caicedo, B.; Zishan, F.; Rosero-García, J. Optimal Power Dispatch of PV Generators in AC Distribution Networks by Considering Solar, Environmental, and Power Demand Conditions from Colombia. Mathematics 2023, 11, 484. https://doi.org/10.3390/math11020484
dc.identifier.uri.none.fl_str_mv https://hdl.handle.net/20.500.12585/11840
dc.identifier.doi.none.fl_str_mv https://doi.org/10.3390/math11020484
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 Grisales-Noreña, L.F.; Montoya, O.D.; Cortés-Caicedo, B.; Zishan, F.; Rosero-García, J. Optimal Power Dispatch of PV Generators in AC Distribution Networks by Considering Solar, Environmental, and Power Demand Conditions from Colombia. Mathematics 2023, 11, 484. https://doi.org/10.3390/math11020484
Universidad Tecnológica de Bolívar
Repositorio Universidad Tecnológica de Bolívar
url https://hdl.handle.net/20.500.12585/11840
https://doi.org/10.3390/math11020484
dc.language.iso.spa.fl_str_mv eng
language eng
dc.rights.coar.fl_str_mv http://purl.org/coar/access_right/c_abf2
dc.rights.uri.*.fl_str_mv http://creativecommons.org/licenses/by-nc-nd/4.0/
dc.rights.accessrights.spa.fl_str_mv info:eu-repo/semantics/openAccess
dc.rights.cc.*.fl_str_mv Attribution-NonCommercial-NoDerivatives 4.0 Internacional
rights_invalid_str_mv 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 20 Páginas
dc.format.mimetype.spa.fl_str_mv application/pdf
dc.coverage.spatial.none.fl_str_mv Colombia
dc.publisher.place.spa.fl_str_mv Cartagena de Indias
dc.publisher.sede.spa.fl_str_mv Campus Tecnológico
dc.source.spa.fl_str_mv Mathematics Vol. 11 No. 2 (2023)
institution Universidad Tecnológica de Bolívar
bitstream.url.fl_str_mv https://repositorio.utb.edu.co/bitstream/20.500.12585/11840/1/mathematics-11-00484.pdf
https://repositorio.utb.edu.co/bitstream/20.500.12585/11840/2/license_rdf
https://repositorio.utb.edu.co/bitstream/20.500.12585/11840/3/license.txt
https://repositorio.utb.edu.co/bitstream/20.500.12585/11840/4/mathematics-11-00484.pdf.txt
https://repositorio.utb.edu.co/bitstream/20.500.12585/11840/5/mathematics-11-00484.pdf.jpg
bitstream.checksum.fl_str_mv 14e10f9beff38f1ba1a4f022d171e394
4460e5956bc1d1639be9ae6146a50347
e20ad307a1c5f3f25af9304a7a7c86b6
7023010f7eb7653d314cd80c84855b58
a8111d19119d29d8f6643421a8b6dbaf
bitstream.checksumAlgorithm.fl_str_mv MD5
MD5
MD5
MD5
MD5
repository.name.fl_str_mv Repositorio Institucional UTB
repository.mail.fl_str_mv repositorioutb@utb.edu.co
_version_ 1814021736245493760
spelling Grisales-Noreña, Luis Fernando7c27cda4-5fe4-4686-8f72-b0442c58a5d1Montoya, Oscar Danilo8a59ede1-6a4a-4d2e-abdc-d0afb14d4480Cortés-Caicedo, Brandon0b676225-338d-48dc-8f2a-694085d9bb42Zishan, Farhad041e882b-354f-48b5-87bc-d4748b261f08Rosero-García, Javierad2b3c9d-a0c5-4637-ae34-313e64637ee6Colombia2023-05-05T19:25:09Z2023-05-05T19:25:09Z2023-01-162023-05-05Grisales-Noreña, L.F.; Montoya, O.D.; Cortés-Caicedo, B.; Zishan, F.; Rosero-García, J. Optimal Power Dispatch of PV Generators in AC Distribution Networks by Considering Solar, Environmental, and Power Demand Conditions from Colombia. Mathematics 2023, 11, 484. https://doi.org/10.3390/math11020484https://hdl.handle.net/20.500.12585/11840https://doi.org/10.3390/math11020484Universidad Tecnológica de BolívarRepositorio Universidad Tecnológica de BolívarThis paper deals with the problem regarding the optimal operation of photovoltaic (PV) generation sources in AC distribution networks with a single-phase structure, taking into consid eration different objective functions. The problem is formulated as a multi-period optimal power flow applied to AC distribution grids, which generates a nonlinear programming (NLP) model with a non-convex structure. Three different objective functions are considered in the optimization model, each optimized using a single-objective function approach. These objective functions are (i) an operating costs function composed of the energy purchasing costs at the substation bus, added with the PV maintenance costs; (ii) the costs of energy losses; and (iii) the total CO2 emissions at the substation bus. All these functions are minimized while considering a frame of operation of 24 h, i.e., in a day-ahead operation environment. To solve the NLP model representing the studied problem, the General Algebraic Modeling System (GAMS) and its SNOPT solver are used. Two different test feeders are used for all the numerical validations, one of them adapted to the urban operation characteristics in the Metropolitan Area of Medellín, which is composed of 33 nodes, and the other one adapted to isolated rural operating conditions, which has 27 nodes and is located in the department of Chocó, Colombia (municipality of Capurganá). Numerical comparisons with multiple combinatorial optimization methods (particle swarm optimization, the continuous genetic algorithm, the Vortex Search algorithm, and the Ant Lion Optimizer) demonstrate the effectiveness of the GAMS software to reach the optimal day-ahead dispatch of all the PV sources in both distribution grids.20 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_abf2Mathematics Vol. 11 No. 2 (2023)Optimal Power Dispatch of PV Generators in AC Distribution Networks by Considering Solar, Environmental, and Power Demand Conditions from Colombiainfo:eu-repo/semantics/articleinfo:eu-repo/semantics/drafthttp://purl.org/coar/resource_type/c_2df8fbb1http://purl.org/coar/version/c_b1a7d7d4d402bcceDay-ahead operation of PV sourcesEnergy purchasing costsOperation and maintenance costs of PV sourcesEnergy losses costsNonlinear programming formulationGAMS softwareLEMBCartagena de IndiasCampus TecnológicoPúblico generalAhmed, I.; Rehan, M.; Basit, A.; Hong, K.S. Greenhouse gases emission reduction for electric power generation sector by efficient dispatching of thermal plants integrated with renewable systems. Sci. Rep. 2022, 12, 12380.akhrani, A.Q.; Othman, A.K.; Rigit, A.R.H.; Samo, S.R. Estimation of carbon footprints from diesel generator emissions. In Proceedings of the 2012 International Conference on Green and Ubiquitous Technology, Besancon, France, 20–23 November 2012.Issa, M.; Ibrahim, H.; Hosni, H.; Ilinca, A.; Rezkallah, M. Effects of Low Charge and Environmental Conditions on Diesel Generators Operation. Eng 2020, 1, 137–152.Yang, L.; Sun, Q.; Zhang, N.; Li, Y. Indirect Multi-Energy Transactions of Energy Internet With Deep Reinforcement Learning Approach. IEEE Trans. Power Syst. 2022, 37, 4067–4077.Ahmad, L.; Khordehgah, N.; Malinauskaite, J.; Jouhara, H. Recent advances and applications of solar photovoltaics and thermal technologies. Energy 2020, 207, 118254.Tan, J.D.; Chang, C.C.W.; Bhuiyan, M.A.S.; Minhad, K.N.; Ali, K. Advancements of wind energy conversion systems for low-wind urban environments: A review. Energy Rep. 2022, 8, 3406–3414.Zhang, N.; Sun, Q.; Yang, L.; Li, Y. Event-Triggered Distributed Hybrid Control Scheme for the Integrated Energy System. IEEE Trans. Ind. Inform. 2022, 18, 835–846Aybar-Mejía, M.; Villanueva, J.; Mariano-Hernández, D.; Santos, F.; Molina-García, A. A Review of Low-Voltage Renewable Microgrids: Generation Forecasting and Demand-Side Management Strategies. Electronics 2021, 10, 2093Shafiullah, G. Impacts of renewable energy integration into the high voltage (HV) networks. In Proceedings of the 2016 4th International Conference on the Development in the in Renewable Energy Technology (ICDRET), Shenzhen, China, 30–31 December 2016Zheng, H.; Yuan, X.; Cai, J.; Sun, P.; Zhou, L. Large-Signal Stability Analysis of DC Side of VSC-HVDC System Based on Estimation of Domain of Attraction. IEEE Trans. Power Syst. 2022, 37, 3630–3641.Surinkaew, T.; Ngamroo, I. Coordinated Robust Control of DFIG Wind Turbine and PSS for Stabilization of Power Oscillations Considering System Uncertainties. IEEE Trans. Sustain. Energy 2014, 5, 823–833.López, A.R.; Krumm, A.; Schattenhofer, L.; Burandt, T.; Montoya, F.C.; Oberländer, N.; Oei, P.Y. Solar PV generation in Colombia - A qualitative and quantitative approach to analyze the potential of solar energy market. Renew. Energy 2020, 148, 1266–1279.Montoya, O.D.; Grisales-Noreña, L.F.; Perea-Moreno, A.J. Optimal Investments in PV Sources for Grid-Connected Distribution Networks: An Application of the Discrete–Continuous Genetic Algorithm. Sustainability 2021, 13, 13633Saidi, A.S. Impact of grid-tied photovoltaic systems on voltage stability of tunisian distribution networks using dynamic reactive power control. Ain Shams Eng. J. 2022, 13, 101537Schultz, H.S.; Carvalho, M. Design, Greenhouse Emissions, and Environmental Payback of a Photovoltaic Solar Energy System. Energies 2022, 15, 6098Valencia, A.; Hincapie, R.A.; Gallego, R.A. Optimal location, selection, and operation of battery energy storage systems and renewable distributed generation in medium–low voltage distribution networks. J. Energy Storage 2021, 34, 102158Montoya, O.D.; Ramos-Paja, C.A.; Grisales-Noreña, L.F. An Efficient Methodology for Locating and Sizing PV Generators in Radial Distribution Networks Using a Mixed-Integer Conic Relaxation. Mathematics 2022, 10, 2626.Cortés-Caicedo, B.; Molina-Martin, F.; Grisales-Noreña, L.F.; Montoya, O.D.; Hernández, J.C. Optimal Design of PV Systems in Electrical Distribution Networks by Minimizing the Annual Equivalent Operative Costs through the Discrete-Continuous Vortex Search Algorithm. Sensors 2022, 22, 851Pal, P.; Krishnamoorthy, P.A.; Rukmani, D.K.; Antony, S.J.; Ocheme, S.; Subramanian, U.; Elavarasan, R.M.; Das, N.; Hasanien, H.M. Optimal Dispatch Strategy of Virtual Power Plant for Day-Ahead Market Framework. Appl. Sci. 2021, 11, 3814NASA. NASA Prediction of Worldwide Energy Resources. Available online: https://power.larc.nasa.gov/ (accessed on 21 September 2022).Instituto de Planificación y Promoción de Soluciones Energéticas para Zonas No Interconectadas. Informes Mensuales de Telimetría, Colombia. Available online: https://ipse.gov.co/cnm/informe-mensuales-telemetria/ (accessed on 21 September 2022).XM SA ESP. Sinergox Database, Colombia. Available online: https://sinergox.xm.com.co/Paginas/Home.aspx (accessed on 21 September 2022)Zagirnyak, M.; Rodkin, D.; Romashykhin, I. The possibilities of Tellegen’s theorem in the identification electrotechnical problems. In Proceedings of the 2017 International Conference on Modern Electrical and Energy Systems (MEES), Kremenchuk, Ukraine, 15–17 November 2017El-Sobky, B.; Abo-Elnaga, Y.; Mousa, A.A.A.; El-Shorbagy, M.A. Trust-Region Based Penalty Barrier Algorithm for Constrained Nonlinear Programming Problems: An Application of Design of Minimum Cost Canal Sections. Mathematics 2021, 9, 1551.Grisales-Noreña, L.F.; Rosales-Mu noz, A.A.; Cortés-Caicedo, B.; Montoya, O.D.; Andrade, F. Optimal Operation of PV Sources in DC Grids for Improving Technical, Economical, and Environmental Conditions by Using Vortex Search Algorithm and a Matrix Hourly Power Flow. Mathematics 2022, 11, 93Montoya, 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.Naghiloo, A.; Abbaspour, M.; Mohammadi-Ivatloo, B.; Bakhtari, K. GAMS based approach for optimal design and sizing of a pressure retarded osmosis power plant in Bahmanshir river of Iran. Renew. Sustain. Energy Rev. 2015, 52, 1559–1565Soroudi, A. Power System Optimization Modeling in GAMS; Springer International Publishing: Berlin/Heidelberg, Germany, 2017.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, 409–418Kaur, 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.Tartibu, L.; Sun, B.; Kaunda, M. Multi-objective optimization of the stack of a thermoacoustic engine using GAMS. Appl. Soft Comput. 2015, 28, 30–43Skworcow, P.; Paluszczyszyn, D.; Ulanicki, B.; Rudek, R.; Belrain, T. Optimisation of Pump and Valve Schedules in Complex Large-scale Water Distribution Systems Using GAMS Modelling Language. Procedia Eng. 2014, 70, 1566–1574.Bocanegra, S.Y.; Montoya, O.D.; Molina-Cabrera, A. Parameter estimation in singe-phase transformers employing voltage and current measures (In Spanish). Rev. Uis Ing. 2020, 19, 63–75Dubey, S.; Sarvaiya, J.N.; Seshadri, B. Temperature Dependent Photovoltaic (PV) Efficiency and Its Effect on PV Production in the World—A Review. Energy Procedia 2013, 33, 311–321.Jaya, S.; Vijay, A.S.; Khan, I.; Shukla, A.; Doolla, S. Mode Transition in DC Microgrids with Non-Dispatchable Sources. In Proceedings of the 2021 IEEE Energy Conversion Congress and Exposition (ECCE). IEEE, Vancouver, BC, Canada, 10–14 October 2021.Ramirez-Vergara, J.; Bosman, L.B.; Leon-Salas, W.D.; Wollega, E. Ambient temperature and solar irradiance forecasting prediction horizon sensitivity analysis. Mach. Learn. Appl. 2021, 6, 100128.Hassan, Q.; Jaszczur, M.; Przenzak, E.; Abdulateef, J. The PV cell temperature effect on the energy production and module efficiency. Contemp. Probl. Power Eng. Environ. Prot. 2016, 33, 33–40.Schwingshackl, C.; Petitta, M.; Wagner, J.; Belluardo, G.; Moser, D.; Castelli, M.; Zebisch, M.; Tetzlaff, A. Wind Effect on PV Module Temperature: Analysis of Different Techniques for an Accurate Estimation. Energy Procedia 2013, 40, 77–86.Sistema Único de Información de Servicios Públicos Domicialiarios. Consolidado de Energía por Empresa y Departamento, Colombia. Available online: https://sui.superservicios.gov.co/Reportes-del-sector/Energia/Reportes-comerciales/Consolidado de-energia-por-empresa-y-departamento (accessed on 21 September 2022).Wang, P.; Wang, W.; Xu, D. Optimal Sizing of Distributed Generations in DC Microgrids With Comprehensive Consideration of System Operation Modes and Operation Targets. IEEE Access 2018, 6, 31129–31140XM SA EPS. En Colombia Factor de Emisión de CO2 por Generación eléCtrica del Sistema Interconectado: 164.38 Gramos de CO2 por Kilovatio Hora, Colombia. Available online: https://www.xm.com.co/noticias/en-colombia-factor-de-emision-de-co2 -por-generacion-electrica-del-sistema-interconectado (accessed on 21 September 2022)Academia Colombiana de Ciencias Exactas, Físicas y Naturales. Factores de Emisión de los Combustibles Colombianos, Colombia, 2016. Available online: https://www.scribd.com/document/157258400/18-FECOC-factores-emision-colombia-docx# (accessed on 21 September 2022).Normas Técnicas y Certificación (ICONTEC). Tensiones y Frecuencia Nominales en Sistemas de Energía Elécrica en Redes de Servicio Público NTC1340; ICONTEC: Bogotá, Colombia, 2004.Baran, M.; Wu, F. Network reconfiguration in distribution systems for loss reduction and load balancing. IEEE Trans. Power Deliv. 1989, 4, 1401–1407.Falaghi, H.; Ramezani, M.; Haghifam, M.R.; Milani, K. Optimal selection of conductors in radial distribution systems with time varying load. In Proceedings of the 18th International Conference and Exhibition on Electricity Distribution (CIRED 2005), Turin, Italy, 6–9 June 2005.Eberhart, R.; Kennedy, J. Particle swarm optimization. In Proceedings of the IEEE International Conference on Neural Networks, Perth, WA, Australia, 27 November–1 December 1995; Citeseer: Piscataway, NJ, USA, 1995; Volume 4, pp. 1942–1948Chu, P.C.; Beasley, J.E. A genetic algorithm for the multidimensional knapsack problem. J. Heuristics 1998, 4, 63–86.Do ˘gan, B.; Ölmez, T. A new metaheuristic for numerical function optimization: Vortex Search algorithm. Inf. Sci. 2015, 293, 125–145Mirjalili, S. The ant lion optimizer. Adv. Eng. Softw. 2015, 83, 80–98.Wicaksana, M.G.S.; Putranto, L.M.; Waskito, F.; Yasirroni, M. Optimal placement and sizing of PV as DG for losses minimization using PSO algorithm: A case in Purworejo area. In Proceedings of the 2020 International Conference on Sustainable Energy Engineering and Application (ICSEEA), Online, 18–20 November 2020; pp. 1–6.KS, G.D. Hybrid genetic algorithm and particle swarm optimization algorithm for optimal power flow in power system. J. Comput. Mech. Power Syst. Control 2019, 2, 31–37Ramavath, D.; Sharma, M. Optimal Power Flow Using Modified ALO. In Proceedings of the 2020 International Conference on Renewable Energy Integration into Smart Grids: A Multidisciplinary Approach to Technology Modelling and Simulation (ICREISG), Bhubaneshwar, India, 14–15 February 2020; pp. 84–89.http://purl.org/coar/resource_type/c_2df8fbb1ORIGINALmathematics-11-00484.pdfmathematics-11-00484.pdfapplication/pdf526986https://repositorio.utb.edu.co/bitstream/20.500.12585/11840/1/mathematics-11-00484.pdf14e10f9beff38f1ba1a4f022d171e394MD51CC-LICENSElicense_rdflicense_rdfapplication/rdf+xml; charset=utf-8805https://repositorio.utb.edu.co/bitstream/20.500.12585/11840/2/license_rdf4460e5956bc1d1639be9ae6146a50347MD52LICENSElicense.txtlicense.txttext/plain; charset=utf-83182https://repositorio.utb.edu.co/bitstream/20.500.12585/11840/3/license.txte20ad307a1c5f3f25af9304a7a7c86b6MD53TEXTmathematics-11-00484.pdf.txtmathematics-11-00484.pdf.txtExtracted texttext/plain66812https://repositorio.utb.edu.co/bitstream/20.500.12585/11840/4/mathematics-11-00484.pdf.txt7023010f7eb7653d314cd80c84855b58MD54THUMBNAILmathematics-11-00484.pdf.jpgmathematics-11-00484.pdf.jpgGenerated Thumbnailimage/jpeg8090https://repositorio.utb.edu.co/bitstream/20.500.12585/11840/5/mathematics-11-00484.pdf.jpga8111d19119d29d8f6643421a8b6dbafMD5520.500.12585/11840oai:repositorio.utb.edu.co:20.500.12585/118402023-05-26 11:15:19.004Repositorio Institucional UTBrepositorioutb@utb.edu.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