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...
- 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
- 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/
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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 |
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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. 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