{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,27]],"date-time":"2026-03-27T07:20:48Z","timestamp":1774596048758,"version":"3.50.1"},"reference-count":55,"publisher":"MDPI AG","issue":"1","license":[{"start":{"date-parts":[[2021,1,25]],"date-time":"2021-01-25T00:00:00Z","timestamp":1611532800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Programa Operacional Portugal 2020 and Programa Operacional CRESC Algarve 2020","award":["01\/SAICT\/2018"],"award-info":[{"award-number":["01\/SAICT\/2018"]}]},{"DOI":"10.13039\/501100001871","name":"Funda\u00e7\u00e3o para a Ci\u00eancia e a Tecnologia","doi-asserted-by":"publisher","award":["UIDB\/50022\/2020"],"award-info":[{"award-number":["UIDB\/50022\/2020"]}],"id":[{"id":"10.13039\/501100001871","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Inventions"],"abstract":"<jats:p>Accurate photovoltaic (PV) power forecasting is crucial to achieving massive PV integration in several areas, which is needed to successfully reduce or eliminate carbon dioxide from energy sources. This paper deals with short-term multi-step PV power forecasts used in model-based predictive control for home energy management systems. By employing radial basis function (RBFs) artificial neural networks (ANN), designed using a multi-objective genetic algorithm (MOGA) with data selected by an approximate convex-hull algorithm, it is shown that excellent forecasting results can be obtained. Two case studies are used: a special house located in the USA, and the other a typical residential house situated in the south of Portugal. In the latter case, one-step-ahead values for unscaled root mean square error (RMSE), mean relative error (MRE), normalized mean average error (NMAE), mean absolute percentage error (MAPE) and R2 of 0.16, 1.27%, 1.22%, 8% and 0.94 were obtained, respectively. These results compare very favorably with existing alternatives found in the literature.<\/jats:p>","DOI":"10.3390\/inventions6010012","type":"journal-article","created":{"date-parts":[[2021,1,25]],"date-time":"2021-01-25T12:28:31Z","timestamp":1611577711000},"page":"12","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":15,"title":["Short-Term Forecasting Photovoltaic Solar Power for Home Energy Management Systems"],"prefix":"10.3390","volume":"6","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-5904-2166","authenticated-orcid":false,"given":"Karol","family":"Bot","sequence":"first","affiliation":[{"name":"Faculdade de Ci\u00eancia e Tecnologia, Universidade do Algarve, 8005-294 Faro, Portugal"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-6308-8666","authenticated-orcid":false,"given":"Antonio","family":"Ruano","sequence":"additional","affiliation":[{"name":"Faculdade de Ci\u00eancia e Tecnologia, Universidade do Algarve, 8005-294 Faro, Portugal"},{"name":"IDMEC, Instituto Superior T\u00e9cnico, Universidade de Lisboa, 1049-001 Lisboa, Portugal"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0014-9257","authenticated-orcid":false,"given":"Maria da Gra\u00e7a","family":"Ruano","sequence":"additional","affiliation":[{"name":"Faculdade de Ci\u00eancia e Tecnologia, Universidade do Algarve, 8005-294 Faro, Portugal"},{"name":"CISUC, University of Coimbra, 3030-290 Coimbra, Portugal"}]}],"member":"1968","published-online":{"date-parts":[[2021,1,25]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"78","DOI":"10.1016\/j.solener.2016.06.069","article-title":"Review of photovoltaic power forecasting","volume":"136","author":"Antonanzas","year":"2016","journal-title":"Sol. Energy"},{"key":"ref_2","unstructured":"Stine, W.B., and Harrigan, R.W. (1985). Solar Energy Fundamentals and Design, John Wiley and Sons, Inc."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"32094","DOI":"10.1088\/1755-1315\/252\/3\/032094","article-title":"Research Status and Difficulties of Ultra-short-term Prediction of Photovoltaic Power","volume":"252","author":"Kong","year":"2019","journal-title":"IOP Conf. Ser. Earth Environ. Sci."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"108688","DOI":"10.1016\/j.automatica.2019.108688","article-title":"Estimation of Photovoltaic Generation Forecasting Models using Limited Information","volume":"113","author":"Bianchini","year":"2020","journal-title":"Automatica"},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"723","DOI":"10.1016\/j.jpowsour.2016.06.076","article-title":"Nonlinear Predictive Energy Management of Residential Buildings with Photovoltaics & Batteries","volume":"325","author":"Sun","year":"2016","journal-title":"J. Power Sources"},{"key":"ref_6","doi-asserted-by":"crossref","unstructured":"Coimbra, C.F.M., Kleissl, J., and Marquez, R. (2013). Chapter 8: Overview of solar-forecasting methods and a metric for accuracy evaluation. Solar Energy Forecasting and Resource Assessment, Elsevier Academic Press.","DOI":"10.1016\/B978-0-12-397177-7.00008-5"},{"key":"ref_7","unstructured":"Fahrenbruch, A., and Bube, R. (2012). Fundamentals of Solar Cells: Photovoltaic Solar Energy Conversion, Elsevier."},{"key":"ref_8","unstructured":"Tiwari, G.N. (2002). Solar Energy: Fundamentals, Design, Modelling and Applications, Alpha Science Int\u2019l Ltd."},{"key":"ref_9","unstructured":"McEvoy, A., Markvart, T., Casta\u00f1er, L., Markvart, T., and Castaner, L. (2003). Practical Handbook of Photovoltaics: Fundamentals and Applications, Elsevier."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"65","DOI":"10.1016\/j.rser.2013.06.042","article-title":"Review of Solar Irradiance Forecasting Methods and a Proposition for Small-Scale Insular Grids","volume":"27","author":"Diagne","year":"2013","journal-title":"Renew. Sustain. Energy Rev."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"15750","DOI":"10.3390\/s121115750","article-title":"A Neural Network based Intelligent Predictive Sensor for Cloudiness, Solar Radiation, and Air Temperature","volume":"12","author":"Ferreira","year":"2012","journal-title":"Sensors"},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"88","DOI":"10.1016\/j.matcom.2015.05.010","article-title":"Analysis and Validation of 24 Hours Ahead Neural Network Forecasting of Photovoltaic Output Power","volume":"131","author":"Leva","year":"2017","journal-title":"Math. Comput. Simul."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"267","DOI":"10.1016\/j.solener.2015.12.031","article-title":"Calculating the Financial Value of a Concentrated Solar Thermal Plant Operated using Direct Normal Irradiance Forecasts","volume":"125","author":"Law","year":"2016","journal-title":"Sol. Energy"},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"569","DOI":"10.1016\/j.renene.2016.12.095","article-title":"Machine Learning Methods for Solar Radiation Forecasting: A Review","volume":"105","author":"Voyant","year":"2017","journal-title":"Renew. Energy"},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"778","DOI":"10.1016\/j.rser.2015.11.078","article-title":"Prediction and Application of Solar Radiation with Soft Computing Over Traditional and Conventional Approach\u2013A Comprehensive Review","volume":"56","author":"Mohanty","year":"2016","journal-title":"Renew. Sustain. Energy Rev."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/j.jclepro.2015.04.041","article-title":"The Artificial Neural Network for Solar Radiation Prediction and Designing Solar Systems: A Systematic Literature Review","volume":"104","author":"Qazi","year":"2015","journal-title":"J. Clean. Prod."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"772","DOI":"10.1016\/j.rser.2013.08.055","article-title":"Solar Radiation Prediction Using Artificial Neural Network Techniques: A Review","volume":"33","author":"Yadav","year":"2014","journal-title":"Renew. Sustain. Energy Rev."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"287","DOI":"10.1016\/j.solener.2014.07.008","article-title":"Direct Normal Irradiance Forecasting and its Application to Concentrated Solar Thermal Output Forecasting\u2014A Review","volume":"108","author":"Law","year":"2014","journal-title":"Sol. Energy"},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"912","DOI":"10.1016\/j.rser.2017.08.017","article-title":"Forecasting of Photovoltaic Power Generation and Model Optimization: A Review","volume":"81","author":"Das","year":"2018","journal-title":"Renew. Sustain. Energy Rev."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"272","DOI":"10.1016\/j.rser.2013.03.004","article-title":"State of the art in Building Modelling and Energy Performances Prediction: A review","volume":"23","author":"Foucquier","year":"2013","journal-title":"Renew. Sustain. Energy Rev."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"403","DOI":"10.1016\/j.buildenv.2016.05.034","article-title":"Ten Questions Concerning Model Predictive Control for Energy Efficient Buildings","volume":"105","author":"Killian","year":"2016","journal-title":"Build. Environ."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"459","DOI":"10.1016\/j.enconman.2017.11.019","article-title":"Solar Photovoltaic Generation Forecasting Methods: A Review","volume":"156","author":"Sobri","year":"2018","journal-title":"Energy Convers. Manag."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"125","DOI":"10.1016\/j.solener.2016.06.073","article-title":"On Recent Advances in PV Output Power Forecast","volume":"136","author":"Raza","year":"2016","journal-title":"Sol. Energy"},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"37","DOI":"10.1049\/PBCE070E_ch2","article-title":"An Overview of Nonlinear Identification and Control with Neural Networks","volume":"Volume 70","author":"Ruano","year":"2005","journal-title":"Intelligent Control Systems using Computational Intelligence Techniques"},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"917","DOI":"10.1109\/TSTE.2014.2313600","article-title":"A Weather-Based Hybrid Method for 1-Day Ahead Hourly Forecasting of PV Power Output","volume":"5","author":"Yang","year":"2014","journal-title":"IEEE Trans. Sustain. Energy"},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"274","DOI":"10.1016\/j.renene.2017.02.052","article-title":"Short-term photovoltaic power forecasting using Artificial Neural Networks and an Analog Ensemble","volume":"108","author":"Cervone","year":"2017","journal-title":"Renew. Energy"},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"380","DOI":"10.1016\/j.enconman.2016.05.025","article-title":"Univariate and multivariate methods for very short-term solar photovoltaic power forecasting","volume":"121","author":"Rana","year":"2016","journal-title":"Energy Convers. Manag."},{"key":"ref_28","first-page":"497","article-title":"Solar photovoltaic power forecasting in jordan using artificial neural networks","volume":"8","author":"Alomari","year":"2018","journal-title":"Int. J. Electr. Comput. Eng."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"443","DOI":"10.1016\/j.enconman.2018.11.074","article-title":"Generative adversarial networks and convolutional neural networks based weather classification model for day ahead short-term photovoltaic power forecasting","volume":"181","author":"Wang","year":"2019","journal-title":"Energy Convers. Manag."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"78063","DOI":"10.1109\/ACCESS.2019.2923006","article-title":"Short-Term Photovoltaic Power Forecasting Based on Long Short Term Memory Neural Network and Attention Mechanism","volume":"7","author":"Zhou","year":"2019","journal-title":"IEEE Access"},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"113315","DOI":"10.1016\/j.apenergy.2019.113315","article-title":"A comparison of day-ahead photovoltaic power forecasting models based on deep learning neural network","volume":"251","author":"Wang","year":"2019","journal-title":"Appl. Energy"},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"175871","DOI":"10.1109\/ACCESS.2020.3025860","article-title":"Photovoltaic Power Forecasting With a Hybrid Deep Learning Approach","volume":"8","author":"Li","year":"2020","journal-title":"IEEE Access"},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"172524","DOI":"10.1109\/ACCESS.2020.3024901","article-title":"Short-Term Photovoltaic Power Forecasting Using an LSTM Neural Network and Synthetic Weather Forecast","volume":"8","author":"Hossain","year":"2020","journal-title":"IEEE Access"},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"157","DOI":"10.1016\/j.solener.2014.10.016","article-title":"A suite of metrics for assessing the performance of solar power forecasting","volume":"111","author":"Zhang","year":"2015","journal-title":"Sol. Energy"},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"515","DOI":"10.1016\/j.asoc.2016.06.014","article-title":"A convex hull-based data selection method for data driven models","volume":"47","author":"Khosravani","year":"2016","journal-title":"Appl. Soft Comput."},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"164","DOI":"10.1090\/qam\/10666","article-title":"A method for the solution of certain non-linear problems in least squares","volume":"2","author":"Levenberg","year":"1944","journal-title":"Q. Appl. Math."},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"431","DOI":"10.1137\/0111030","article-title":"An algorithm for least-squares estimation of nonlinear parameters","volume":"11","author":"Marquardt","year":"1963","journal-title":"J. Soc. Ind. Appl. Math."},{"key":"ref_38","unstructured":"Ruano, A.E.B., Jones, D.I., and Fleming, P.J. (1991, January 11\u201313). A New Formulation of the Learning Problem for a Neural Network Controller. Proceedings of the 30th IEEE Conference on Decision and Control, Brighton, UK."},{"key":"ref_39","doi-asserted-by":"crossref","unstructured":"Ferreira, P.M., and Ruano, A.E. (2008, January 1\u20138). Application of Computational Intelligence Methods to Greenhouse Environmental Modelling. Proceedings of the IEEE International Joint Conference on Neural Networks (IJCNN\u201908), Hong Kong, China.","DOI":"10.1109\/IJCNN.2008.4634310"},{"key":"ref_40","doi-asserted-by":"crossref","first-page":"414","DOI":"10.3182\/20090921-3-TR-3005.00073","article-title":"Evolving RBF predictive models to forecast the Portuguese electricity consumption","volume":"42","author":"Ferreira","year":"2009","journal-title":"IFAC Proc. Vol."},{"key":"ref_41","doi-asserted-by":"crossref","first-page":"109","DOI":"10.1016\/j.cmpb.2017.05.005","article-title":"An intelligent support system for automatic detection of cerebral vascular accidents from brain CT images","volume":"146","author":"Hajimani","year":"2017","journal-title":"Comput. Methods Programs Biomed."},{"key":"ref_42","doi-asserted-by":"crossref","unstructured":"Khosravani, H., Castilla, M., Berenguel, M., Ruano, A., and Ferreira, P. (2016). A Comparison of Energy Consumption Prediction Models Based on Neural Networks of a Bioclimatic Building. Energies, 9.","DOI":"10.3390\/en9010057"},{"key":"ref_43","doi-asserted-by":"crossref","first-page":"145","DOI":"10.1016\/j.enbuild.2016.03.043","article-title":"The IMBPC HVAC system: A complete MBPC solution for existing HVAC systems","volume":"120","author":"Ruano","year":"2016","journal-title":"Energy Build."},{"key":"ref_44","doi-asserted-by":"crossref","first-page":"81741","DOI":"10.1109\/ACCESS.2019.2923905","article-title":"Ensemble Approach of Optimized Artificial Neural Networks for Solar Photovoltaic Power Prediction","volume":"7","author":"Ayadi","year":"2019","journal-title":"IEEE Access"},{"key":"ref_45","unstructured":"Honda (2020, December 21). Honda Smart Home US. Available online: https:\/\/www.hondasmarthome.com\/."},{"key":"ref_46","unstructured":"Ferreira, P.M., and Ruano, A.E. (2000, January 1\u20134). Exploiting the separability of linear and nonlinear parameters in radial basis function networks. Proceedings of the Adaptive Systems for Signal Processing, Communications, and Control Symposium (AS-SPCC), Lake Louise, AB, Canada."},{"key":"ref_47","doi-asserted-by":"crossref","first-page":"157","DOI":"10.1109\/72.363440","article-title":"Optimal adaptive k-means algorithm with dynamic adjustment of learning rate","volume":"6","author":"Chinrungrueng","year":"1995","journal-title":"IEEE Trans. Neural Netw."},{"key":"ref_48","doi-asserted-by":"crossref","first-page":"1633","DOI":"10.5194\/hess-11-1633-2007","article-title":"Updated world map of the K\u00f6ppen-Geiger climate classification","volume":"11","author":"Peel","year":"2007","journal-title":"Hydrol. Earth Syst. Sci."},{"key":"ref_49","doi-asserted-by":"crossref","first-page":"135","DOI":"10.1127\/0941-2948\/2010\/0430","article-title":"Observed and projected climate shifts 1901-2100 depicted by world maps of the K\u00f6ppen-Geiger climate classification","volume":"19","author":"Rubel","year":"2010","journal-title":"Meteorol. Z."},{"key":"ref_50","unstructured":"(2020, December 21). Europe-Solar-Store. Sharp NU-AK300. Available online: https:\/\/www.europe-solarstore.com\/sharp-nu-ak300.html."},{"key":"ref_51","unstructured":"Kostal (2020, December 21). Plenticore Plus. Available online: https:\/\/www.kostal-solar-electric.com\/en-gb\/products\/hybrid-inverters\/plenticore-plus."},{"key":"ref_52","unstructured":"Eft, S. (2020, December 21). Battery Box HV. Available online: https:\/\/www.eft-systems.de\/en\/TheB-BOX\/product\/BatteryBoxHV\/3."},{"key":"ref_53","doi-asserted-by":"crossref","first-page":"31005","DOI":"10.3390\/s151229841","article-title":"An Intelligent Weather Station","volume":"15","author":"Mestre","year":"2015","journal-title":"Sensors"},{"key":"ref_54","doi-asserted-by":"crossref","first-page":"44821","DOI":"10.1109\/ACCESS.2020.2978635","article-title":"Ultra-Short-Term Photovoltaic Power Prediction Based on Self-Attention Mechanism and Multi-Task Learning","volume":"8","author":"Ju","year":"2020","journal-title":"IEEE Access"},{"key":"ref_55","doi-asserted-by":"crossref","first-page":"9","DOI":"10.1186\/s40807-017-0043-y","article-title":"An experimental study on effect of dust on power loss in solar photovoltaic module","volume":"4","author":"Hussain","year":"2017","journal-title":"Renew. Wind Water Solar"}],"container-title":["Inventions"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2411-5134\/6\/1\/12\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T05:14:53Z","timestamp":1760159693000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2411-5134\/6\/1\/12"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,1,25]]},"references-count":55,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2021,3]]}},"alternative-id":["inventions6010012"],"URL":"https:\/\/doi.org\/10.3390\/inventions6010012","relation":{},"ISSN":["2411-5134"],"issn-type":[{"value":"2411-5134","type":"electronic"}],"subject":[],"published":{"date-parts":[[2021,1,25]]}}}