{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,12]],"date-time":"2026-04-12T02:00:46Z","timestamp":1775959246776,"version":"3.50.1"},"reference-count":24,"publisher":"MDPI AG","issue":"1","license":[{"start":{"date-parts":[[2020,1,2]],"date-time":"2020-01-02T00:00:00Z","timestamp":1577923200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Energies"],"abstract":"<jats:p>A novel ensemble algorithm based on kernel density estimation (KDE) is proposed to forecast distributed generation (DG) from renewable energy sources (RES). The proposed method relies solely on publicly available historical input variables (e.g., meteorological forecasts) and the corresponding local output (e.g., recorded power generation). Given a new case (with forecasted meteorological variables), the resulting power generation is forecasted. This is performed by calculating a KDE-based similarity index to determine a set of most similar cases from the historical dataset. Then, the outputs of the most similar cases are used to calculate an ensemble prediction. The method is tested using historical weather forecasts and recorded generation of a PV installation in Portugal. Despite only being given averaged data as input, the algorithm is shown to be capable of predicting uncertainties associated with high frequency weather variations, outperforming deterministic predictions based on solar irradiance forecasts. Moreover, the algorithm is shown to outperform a neural network (NN) in most test cases while being exceptionally faster (32 times). Given that the proposed model only relies on public locally-metered data, it is a convenient tool for DG owners\/operators to effectively forecast their expected generation without depending on private\/proprietary data or divulging their own.<\/jats:p>","DOI":"10.3390\/en13010216","type":"journal-article","created":{"date-parts":[[2020,1,3]],"date-time":"2020-01-03T04:43:03Z","timestamp":1578026583000},"page":"216","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":40,"title":["A Novel Ensemble Algorithm for Solar Power Forecasting Based on Kernel Density Estimation"],"prefix":"10.3390","volume":"13","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-3838-1166","authenticated-orcid":false,"given":"Mohamed","family":"Lotfi","sequence":"first","affiliation":[{"name":"Faculty of Engineering, University of Porto, 4200-465 Porto, Portugal"},{"name":"INESC TEC, 4200-465 Porto, Portugal"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-1484-2594","authenticated-orcid":false,"given":"Mohammad","family":"Javadi","sequence":"additional","affiliation":[{"name":"INESC TEC, 4200-465 Porto, Portugal"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-8328-9708","authenticated-orcid":false,"given":"Gerardo J.","family":"Os\u00f3rio","sequence":"additional","affiliation":[{"name":"C-MAST, University of Beira Interior, 6201-001 Covilha, Portugal"}]},{"given":"Cl\u00e1udio","family":"Monteiro","sequence":"additional","affiliation":[{"name":"Faculty of Engineering, University of Porto, 4200-465 Porto, Portugal"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-2105-3051","authenticated-orcid":false,"given":"Jo\u00e3o P. S.","family":"Catal\u00e3o","sequence":"additional","affiliation":[{"name":"Faculty of Engineering, University of Porto, 4200-465 Porto, Portugal"},{"name":"INESC TEC, 4200-465 Porto, Portugal"}]}],"member":"1968","published-online":{"date-parts":[[2020,1,2]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Kotsalos, K., Miranda, I., Silva, N., and Leite, H. (2019). A Horizon Optimization Control Framework for the Coordinated Operation of Multiple Distributed Energy Resources in Low Voltage Distribution Networks. Energies, 12.","DOI":"10.3390\/en12061182"},{"key":"ref_2","doi-asserted-by":"crossref","unstructured":"Dev, S., Alskaif, T., Hossari, M., Godina, R., Louwen, A., and Van Sark, W. (2018). Solar Irradiance Forecasting Using Triple Exponential Smoothing. 2018 International Conference on Smart Energy Systems and Technologies, SEST 2018-Proceedings, Institute of Electrical and Electronics Engineers Inc.","DOI":"10.1109\/SEST.2018.8495816"},{"key":"ref_3","doi-asserted-by":"crossref","unstructured":"Gough, M., Lotfi, M., Castro, R., Madhlopa, A., Khan, A., and Catal\u00e3o, J.P.S. (2019). Urban Wind Resource Assessment: A Case Study on Cape Town. Energies, 12.","DOI":"10.3390\/en12081479"},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"21336","DOI":"10.1109\/ACCESS.2017.2753246","article-title":"The Effect of Inverter Failures on the Return on Investment of Solar Photovoltaic Systems","volume":"5","author":"Formica","year":"2017","journal-title":"IEEE Access"},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"483","DOI":"10.1016\/j.ijepes.2018.06.005","article-title":"New Probabilistic Price Forecasting Models: Application to the Iberian Electricity Market","volume":"103","author":"Monteiro","year":"2018","journal-title":"Int. J. Electr. Power Energy Syst."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"1548","DOI":"10.1016\/j.rser.2017.05.234","article-title":"Recent Advances in Electricity Price Forecasting: A Review of Probabilistic Forecasting","volume":"81","author":"Nowotarski","year":"2018","journal-title":"Renew. Sustain. Energy Rev."},{"key":"ref_7","doi-asserted-by":"crossref","unstructured":"Palmer, T. The ECMWF Ensemble Prediction System: Looking Back (More than) 25 Years and Projecting Forward 25 Years. Q. J. R. Meteorol. Soc., 2018.","DOI":"10.1002\/qj.3383"},{"key":"ref_8","doi-asserted-by":"crossref","unstructured":"Su, D., Batzelis, E., and Pal, B. (2019, January 9\u201311). Machine Learning Algorithms in Forecasting of Photovoltaic Power Generation. Proceedings of the 2019 International Conference on Smart Energy Systems and Technologies (SEST), Porto, Portugal.","DOI":"10.1109\/SEST.2019.8849106"},{"key":"ref_9","doi-asserted-by":"crossref","unstructured":"Bracale, A., Carpinelli, G., and De Falco, P. (2019). Developing and Comparing Different Strategies for Combining Probabilistic Photovoltaic Power Forecasts in an Ensemble Method. Energies, 12.","DOI":"10.3390\/en12061011"},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"939","DOI":"10.1016\/j.apenergy.2018.10.080","article-title":"A Review and Discussion of Decomposition-Based Hybrid Models for Wind Energy Forecasting Applications","volume":"235","author":"Qian","year":"2019","journal-title":"Appl. Energy."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"551","DOI":"10.1109\/TSTE.2016.2610523","article-title":"A Probabilistic Competitive Ensemble Method for Short-Term Photovoltaic Power Forecasting","volume":"8","author":"Bracale","year":"2017","journal-title":"IEEE Trans. Sustain. Energy"},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"465","DOI":"10.1016\/j.energy.2018.08.207","article-title":"Tree-Based Ensemble Methods for Predicting PV Power Generation and Their Comparison with Support Vector Regression","volume":"164","author":"Ahmad","year":"2018","journal-title":"Energy"},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"762","DOI":"10.1016\/j.ijforecast.2018.05.007","article-title":"Ensemble Forecast of Photovoltaic Power with Online CRPS Learning","volume":"34","author":"Thorey","year":"2018","journal-title":"Int. J. Forecast."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"268","DOI":"10.1109\/TSTE.2018.2832634","article-title":"A Solar Time Based Analog Ensemble Method for Regional Solar Power Forecasting","volume":"10","author":"Zhang","year":"2019","journal-title":"IEEE Trans. Sustain. Energy"},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"291","DOI":"10.1016\/j.solener.2019.07.061","article-title":"A Recursive Ensemble Model for Forecasting the Power Output of Photovoltaic Systems","volume":"189","author":"Liu","year":"2019","journal-title":"Sol. Energy"},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"4624","DOI":"10.1109\/TII.2018.2882598","article-title":"An Ensemble Framework For Day-Ahead Forecast of PV Output in Smart Grids","volume":"15","author":"Raza","year":"2018","journal-title":"IEEE Trans. Ind. Inform."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"112921","DOI":"10.1109\/ACCESS.2019.2935273","article-title":"Day-Ahead Hourly Forecasting of Solar Generation Based on Cluster Analysis and Ensemble Model","volume":"7","author":"Pan","year":"2019","journal-title":"IEEE Access"},{"key":"ref_18","unstructured":"AlKandari, M., and Ahmad, I. Solar Power Generation Forecasting Using Ensemble Approach Based on Deep Learning and Statistical Methods. Appl. Comput. Inform., 2019."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"363","DOI":"10.1016\/j.enconman.2014.01.063","article-title":"Electricity Prices Forecasting by a Hybrid Evolutionary-Adaptive Methodology","volume":"80","author":"Matias","year":"2014","journal-title":"Energy Convers. Manag."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"137","DOI":"10.1109\/TPWRS.2010.2049385","article-title":"Hybrid Wavelet-PSO-ANFIS Approach for Short-Term Electricity Prices Forecasting","volume":"26","author":"Catalao","year":"2011","journal-title":"IEEE Trans. Power Syst."},{"key":"ref_21","doi-asserted-by":"crossref","unstructured":"Os\u00f3rio, G., Lotfi, M., Shafie-khah, M., Campos, V., Catal\u00e3o, J., Os\u00f3rio, G.J., Lotfi, M., Shafie-khah, M., Campos, V.M.A., and Catal\u00e3o, J.P.S. (2018). Hybrid Forecasting Model for Short-Term Electricity Market Prices with Renewable Integration. Sustainability, 11.","DOI":"10.3390\/su11010057"},{"key":"ref_22","unstructured":"Nowotarski, J., and Weron, R. (2016). To Combine or Not to Combine? Recent Trends in Electricity Price Forecasting. HSC Research Report, Hugo Steinhaus Center, Wroclaw University of Technology."},{"key":"ref_23","unstructured":"(2019, December 14). Global Forecast System (GFS) | National Centers for Environmental Information (NCEI) formerly known as National Climatic Data Center (NCDC), Available online: https:\/\/www.ncdc.noaa.gov\/data-access\/model-data\/model-datasets\/global-forcast-system-gfs."},{"key":"ref_24","unstructured":"The Mathworks Inc. (2019). Statistics and Machine Learning Toolbox User\u2019s Guide R2019, The Mathworks Inc."}],"container-title":["Energies"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1996-1073\/13\/1\/216\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,13]],"date-time":"2025-10-13T13:42:08Z","timestamp":1760362928000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1996-1073\/13\/1\/216"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2020,1,2]]},"references-count":24,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2020,1]]}},"alternative-id":["en13010216"],"URL":"https:\/\/doi.org\/10.3390\/en13010216","relation":{},"ISSN":["1996-1073"],"issn-type":[{"value":"1996-1073","type":"electronic"}],"subject":[],"published":{"date-parts":[[2020,1,2]]}}}