{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T02:21:59Z","timestamp":1760235719421,"version":"build-2065373602"},"reference-count":32,"publisher":"MDPI AG","issue":"10","license":[{"start":{"date-parts":[[2021,9,25]],"date-time":"2021-09-25T00:00:00Z","timestamp":1632528000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Algorithms"],"abstract":"<jats:p>In an effort to quantify and manage uncertainties inside power systems with penetration of renewable energy, uncertainty costs have been defined and different uncertainty cost functions have been calculated for different types of generators and electric vehicles. This article seeks to use the uncertainty cost formulation to propose algorithms and solve the problem of optimal power flow extended to controllable renewable systems and controllable loads. In a previous study, the first and second derivatives of the uncertainty cost functions were calculated and now an analytical and heuristic algorithm of optimal power flow are used. To corroborate the analytical solution, the optimal power flow was solved by means of metaheuristic algorithms. Finally, it was found that analytical algorithms have a much higher performance than metaheuristic methods, especially as the number of decision variables in an optimization problem grows.<\/jats:p>","DOI":"10.3390\/a14100276","type":"journal-article","created":{"date-parts":[[2021,9,27]],"date-time":"2021-09-27T01:59:47Z","timestamp":1632707987000},"page":"276","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["Algorithms for Optimal Power Flow Extended to Controllable Renewable Systems and Loads"],"prefix":"10.3390","volume":"14","author":[{"given":"Elkin D.","family":"Reyes","sequence":"first","affiliation":[{"name":"Electrical and Electronic Engineering, Universidad Nacional de Colombia, Sede Bogot\u00e1, Bogot\u00e1 111321, Colombia"},{"name":"GERS Colombia, Bogot\u00e1 111321, Colombia"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-2995-1147","authenticated-orcid":false,"given":"Sergio","family":"Rivera","sequence":"additional","affiliation":[{"name":"Electrical and Electronic Engineering, Universidad Nacional de Colombia, Sede Bogot\u00e1, Bogot\u00e1 111321, Colombia"}]}],"member":"1968","published-online":{"date-parts":[[2021,9,25]]},"reference":[{"key":"ref_1","unstructured":"UPME (2021, August 24). Solicitudes de Conexi\u00f3n de Proyectos de Generaci\u00f3n. Available online: https:\/\/www.grupoenergiabogota.com\/transmision\/nosotros\/solicitudes-de-conexion-de-generacion."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"145","DOI":"10.1016\/j.rser.2018.07.056","article-title":"How to deal with uncertainties in electric power systems? A review","volume":"96","author":"Jordehi","year":"2018","journal-title":"Renew. Sustain. Energy Rev."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"603","DOI":"10.1109\/TEC.2007.914171","article-title":"An economic dispatch model incorporating wind power","volume":"23","author":"Hetzer","year":"2008","journal-title":"IEEE Trans. Energy Convers."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"171","DOI":"10.1504\/IJPEC.2019.098620","article-title":"Uncertainty cost functions for solar photovoltaic generation, wind energy generation, and plug-in electric vehicles: Mathematical expected value and verification by Monte Carlo simulation","volume":"10","author":"Arevalo","year":"2019","journal-title":"Int. J. Power Energy Convers."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"29","DOI":"10.21500\/20275846.2683","article-title":"Formulaci\u00f3n de funciones de costo de incertidumbre en peque\u00f1as centrales hidroel\u00e9ctricas dentro de una microgrid","volume":"8","author":"Molina","year":"2017","journal-title":"Ing. USBMed"},{"key":"ref_6","first-page":"137","article-title":"Mathematical uncertainty cost functions for controllable photo-voltaic generators considering uniform distributions","volume":"18","author":"Bernal","year":"2019","journal-title":"WSEAS Trans. Math."},{"key":"ref_7","doi-asserted-by":"crossref","unstructured":"Vargas, S., Rodriguez, D., and Rivera, S. (2019). Mathematical formulation and numerical validation of uncertainty costs for controllable loads. Rev. Int. M\u00e9todos Num\u00e9ricos Calculo Dise\u00f1o Ing., 35.","DOI":"10.23967\/j.rimni.2019.01.002"},{"key":"ref_8","first-page":"2389","article-title":"Modelaci\u00f3n cuadr\u00e1tica de costos de incertidumbre para generaci\u00f3n renovable y su aplicaci\u00f3n en el despacho econ\u00f3mico","volume":"5","author":"Martinez","year":"2018","journal-title":"Rev. MATUA"},{"key":"ref_9","first-page":"324","article-title":"Application of analytical uncertainty costs of solar, wind and electric vehicles in optimal power dispatch","volume":"22","author":"Santos","year":"2017","journal-title":"Ingenieria"},{"key":"ref_10","doi-asserted-by":"crossref","unstructured":"Li, P., Zhou, Z., and Shi, R. (2014, January 27\u201331). Probabilistic optimal operation management of microgrid using point estimate method and improved bat algorithm. Proceedings of the 2014 IEEE PES General Meeting | Conference Exposition, National Harbor, MD, USA.","DOI":"10.1109\/PESGM.2014.6938932"},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"889","DOI":"10.1109\/TII.2012.2205398","article-title":"Optimal dispatch of electric vehicles and wind power using enhanced particle swarm optimization","volume":"8","author":"Zhao","year":"2012","journal-title":"IEEE Trans. Ind. Inform."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"75","DOI":"10.15665\/rp.v16i2.1642","article-title":"Optimal energy dispatch in multiple periods of time considering the variability and uncertainty of generation from renewable sources\/Despacho de energ\u00eda \u00f3ptimo en m\u00faltiples periodos de tiempo considerando la variabilidad y la incertidumbre de la generaci\u00f3n a partir de fuentes renovables","volume":"16","author":"Rivera","year":"2018","journal-title":"Prospectiva"},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"49","DOI":"10.25054\/22161325.1535","article-title":"Modelado de cargas controlables en el despacho de sistemas con fuentes renovables y veh\u00edculos el\u00e9ctricos","volume":"17","author":"Guzman","year":"2017","journal-title":"Ing. Reg."},{"key":"ref_14","first-page":"8","article-title":"Generation and demand scheduling in a micro-grid with battery-based storage systems, hybrid renewable systems and electric vehicle aggregators","volume":"10","author":"Romero","year":"2019","journal-title":"WSEAS Trans. Power Syst."},{"key":"ref_15","first-page":"48","article-title":"Despacho de energ\u00eda \u00f3ptimo en m\u00faltiples periodos considerando la incertidumbre de la generaci\u00f3n a partir de fuentes renovables en un modelo reducido del sistema de potencia colombiano","volume":"15","author":"Rivera","year":"2018","journal-title":"Av. Investig. Ing."},{"key":"ref_16","unstructured":"UPME (2021, August 24). Plan de Expansi\u00f3n de Generaci\u00f3n-Transmisi\u00f3n 2017\u20132031. Available online: https:\/\/www.acolgen.org.co\/estudio-servicios-complementarios-2\/."},{"key":"ref_17","doi-asserted-by":"crossref","unstructured":"Gomez-Exposito, A., Conejo, A., and Canizares, C. (2017). Electric Energy Systems: Analysis and Operation, CRC Press.","DOI":"10.1201\/9781420007275"},{"key":"ref_18","unstructured":"Zimmerman, R.D., and Murillo-S\u00e1nchez, C.E. (2021, August 24). MATPOWER User\u2019s Manual. Available online: https:\/\/matpower.org\/docs\/MATPOWER-manual.pdf."},{"key":"ref_19","unstructured":"Stevenson, J.J.G.W.D. (2021, August 24). An\u00e1lisis de Sistemas de Potencia. Available online: https:\/\/ingenieria.udistrital.edu.co\/course\/view.php?id=1408."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"652","DOI":"10.1109\/TPWRS.2015.2407054","article-title":"Enhanced security-constrained unit commitment with emerging utility-scale energy storage","volume":"31","author":"Wen","year":"2016","journal-title":"IEEE Trans. Power Syst."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"2974","DOI":"10.1109\/TPWRS.2014.2313513","article-title":"Unit commitment with ideal and generic energy storage units","volume":"29","author":"Pozo","year":"2014","journal-title":"IEEE Trans. Power Syst."},{"key":"ref_22","doi-asserted-by":"crossref","unstructured":"Miranda, V., and Alves, R. (2013, January 8\u201311). Differential Evolutionary Particle Swarm Optimization (DEEPSO): A Successful Hybrid. Proceedings of the 2013 BRICS Congress on Computational Intelligence and 11th Brazilian Congress on Computational Intelligence, Ipojuca, Brazil.","DOI":"10.1109\/BRICS-CCI-CBIC.2013.68"},{"key":"ref_23","unstructured":"Kennedy, J., and Eberhart, R. (December, January 27). Particle swarm optimization. Proceedings of the ICNN\u201995-International Conference on Neural Networks, Perth, WA, Australia."},{"key":"ref_24","first-page":"1","article-title":"Particle swarm optimization: Algorithm and its codes in matlab","volume":"8","author":"Alam","year":"2016","journal-title":"ResearchGate"},{"key":"ref_25","first-page":"98","article-title":"2018 competition on operational planning of sustainable power systems: Testsbeds and results","volume":"14","author":"Arevalo","year":"2019","journal-title":"WSEAS Trans. Power Syst."},{"key":"ref_26","unstructured":"Mostapha Kalami, H. (2021, August 24). Practical Genetic Algorithms in Python and MATLAB\u2014Video Tutorial. Available online: https:\/\/www.udemy.com\/course\/genetic-algorithms-in-python-and-matlab\/."},{"key":"ref_27","first-page":"69","article-title":"A comparative analysis of selection schemes used in genetic algorithms","volume":"1","author":"Goldberg","year":"1990","journal-title":"FOGA"},{"key":"ref_28","first-page":"193","article-title":"Genetic algorithms, tournament selection, and the effects of noise","volume":"9","author":"Miller","year":"1995","journal-title":"Complex Syst."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"1185","DOI":"10.1109\/TPWRS.2007.901301","article-title":"On computational issues of market-based optimal power flow","volume":"22","author":"Wang","year":"2007","journal-title":"IEEE Trans. Power Syst."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"25","DOI":"10.1007\/s10107-004-0559-y","article-title":"On the implementation of an interior-point filter line-search algorithm for large-scale nonlinear programming","volume":"106","author":"Biegler","year":"2006","journal-title":"Math. Program."},{"key":"ref_31","unstructured":"Parkinson, A.R., Balling, R., and Hedengren, J. (2018). Optimization Methods for Engineering Design, Brigham Young University. [2nd ed.]."},{"key":"ref_32","doi-asserted-by":"crossref","unstructured":"Reyes, E.D., Bretas, A.S., and Rivera, S. (2020). Marginal uncertainty cost functions for solar photovoltaic, wind energy, hydro generators, and plug-in electric vehicles. Energies, 13.","DOI":"10.3390\/en13236375"}],"container-title":["Algorithms"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1999-4893\/14\/10\/276\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T07:04:50Z","timestamp":1760166290000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1999-4893\/14\/10\/276"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,9,25]]},"references-count":32,"journal-issue":{"issue":"10","published-online":{"date-parts":[[2021,10]]}},"alternative-id":["a14100276"],"URL":"https:\/\/doi.org\/10.3390\/a14100276","relation":{},"ISSN":["1999-4893"],"issn-type":[{"type":"electronic","value":"1999-4893"}],"subject":[],"published":{"date-parts":[[2021,9,25]]}}}