{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,6]],"date-time":"2026-01-06T13:07:22Z","timestamp":1767704842946,"version":"build-2065373602"},"reference-count":29,"publisher":"MDPI AG","issue":"2","license":[{"start":{"date-parts":[[2020,2,13]],"date-time":"2020-02-13T00:00:00Z","timestamp":1581552000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>Renewable energy today is no longer just an affordable alternative, but a requirement for mitigating global environmental problems such as climate change. Among renewable energies, the use of solar energy is one of the most widespread. Concentrating Solar Power (CSP) systems, however, is not yet fully widespread despite having demonstrated great efficiency, mainly thanks to parabolic-trough collector (PTC) technology, both on a large scale and on a small scale for heating water in industry. One of the main drawbacks to this energy solution is the large size of the facilities. For this purpose, several models have been developed to avoid shadowing between the PTC lines as much as possible. In this study, the classic shadowing models between the PTC rows are reviewed. One of the major challenges is that they are studied geometrically as a fixed installation, while they are moving facilities, as they have a tracking movement of the sun. In this work, a new model is proposed to avoid shadowing by taking into account the movement of the facilities depending on their latitude. Secondly, the model is tested to an existing facility as a real case study located in southern Spain. The model is applied to the main existing installations in the northern hemisphere, thus showing the usefulness of the model for any PTC installation in the world. The shadow projected by a standard, the PTC (S) has been obtained by means of a polynomial approximation as a function of the latitude (Lat) given by S = 0.001 \u2212 Lat2 + 0.0121 \u2212 Lat + 10.9 with R2 of 99.8%. Finally, the model has been simplified to obtain in the standard case the shadows in the running time of a PTC facility.<\/jats:p>","DOI":"10.3390\/sym12020278","type":"journal-article","created":{"date-parts":[[2020,2,26]],"date-time":"2020-02-26T04:18:29Z","timestamp":1582690709000},"page":"278","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":7,"title":["A Simplified Method to Avoid Shadows at Parabolic-Trough Solar Collectors Facilities"],"prefix":"10.3390","volume":"12","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-8980-6163","authenticated-orcid":false,"given":"Nuria","family":"Novas","sequence":"first","affiliation":[{"name":"Department of Engineering, University of Almeria, ceiA3, 04120 Almeria, Spain"}]},{"given":"Ar\u00e1nzazu","family":"Fern\u00e1ndez-Garc\u00eda","sequence":"additional","affiliation":[{"name":"CIEMAT-Plataforma Solar de Almer\u00eda, Ctra. Sen\u00e9s, 04200 Tabernas, Spain"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0085-030X","authenticated-orcid":false,"given":"Francisco","family":"Manzano-Agugliaro","sequence":"additional","affiliation":[{"name":"Department of Engineering, University of Almeria, ceiA3, 04120 Almeria, Spain"}]}],"member":"1968","published-online":{"date-parts":[[2020,2,13]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"1753","DOI":"10.1016\/j.rser.2010.12.008","article-title":"Optimization methods applied to renewable and sustainable energy: A review","volume":"15","author":"Montoya","year":"2011","journal-title":"Renew. Sustain. Energy Rev."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"867","DOI":"10.1038\/nclimate1584","article-title":"Long-term sea-level rise implied by 1.5 \u00b0C and 2 \u00b0C warming levels","volume":"2","author":"Schaeffer","year":"2012","journal-title":"Nat. Clim. Chang."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"893","DOI":"10.1016\/j.solener.2018.08.011","article-title":"The future of low carbon industrial process heat: A comparison between solar thermal and heat pumps","volume":"173","author":"Meyers","year":"2018","journal-title":"Sol. Energy"},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"1177","DOI":"10.1016\/j.jclepro.2017.09.225","article-title":"Driving effect of technology innovation on energy utilization efficiency in strategic emerging industries","volume":"170","author":"Miao","year":"2018","journal-title":"J. Clean. Prod."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"262","DOI":"10.1016\/j.enbuild.2017.07.089","article-title":"Intelligent homes\u2019 technologies to optimize the energy performance for the net zero energy home","volume":"153","author":"Alfaris","year":"2017","journal-title":"Energy Build."},{"key":"ref_6","doi-asserted-by":"crossref","unstructured":"Massidda, L., and Marrocu, M. (2017). Decoupling Weather Influence from User Habits for an Optimal Electric Load Forecast System. Energies, 10.","DOI":"10.3390\/en10122171"},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"141","DOI":"10.1016\/j.solener.2017.02.007","article-title":"Use of Multilinear Adaptive Regression Splines and numerical weather prediction to forecast the power output of a PV plant in Borkum, Germany","volume":"146","author":"Massidda","year":"2017","journal-title":"Sol. Energy"},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"987","DOI":"10.1016\/j.rser.2018.04.097","article-title":"A comprehensive review of state-of-the-art concentrating solar power (CSP) technologies: Current status and research trends","volume":"91","author":"Islam","year":"2018","journal-title":"Renew. Sustain. Energy Rev."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"216","DOI":"10.1016\/j.rser.2014.10.025","article-title":"Solar energy resource assessment in Mexican states along the Gulf of Mexico","volume":"43","year":"2015","journal-title":"Renew. Sustain. Energy Rev."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"1576","DOI":"10.1016\/j.rser.2017.07.003","article-title":"Energy and exergy analyses of various typical solar energy applications: A comprehensive review","volume":"82","author":"Sansaniwal","year":"2018","journal-title":"Renew. Sustain. Energy Rev."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"51","DOI":"10.1016\/j.rser.2018.03.003","article-title":"The National Solar Radiation Data Base (NSRDB)","volume":"89","author":"Sengupta","year":"2018","journal-title":"Renew. Sustain. Energy Rev."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"134","DOI":"10.1016\/j.rser.2012.10.020","article-title":"Scientific production of renewable energies worldwide: An overview","volume":"18","author":"Alcayde","year":"2013","journal-title":"Renew. Sustain. Energy Rev."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"1709","DOI":"10.1016\/j.rser.2011.11.025","article-title":"Characterization of solar flat plate collectors","volume":"16","author":"Palomar","year":"2012","journal-title":"Renew. Sustain. Energy Rev."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"12","DOI":"10.1016\/j.rser.2013.02.017","article-title":"A review of studies on central receiver solar thermal power plants","volume":"23","author":"Behar","year":"2013","journal-title":"Renew. Sustain. Energy Rev."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"272","DOI":"10.1016\/j.jclepro.2014.11.018","article-title":"A parabolic-trough collector for cleaner industrial process heat","volume":"89","author":"Rojas","year":"2015","journal-title":"J. Clean. Prod."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"361","DOI":"10.1016\/j.solmat.2019.01.008","article-title":"Acceptance criteria for accelerated aging testing of silvered-glass mirrors for concentrated solar power technologies","volume":"193","author":"Sutter","year":"2019","journal-title":"Sol. Energy Mater. Sol. Cells"},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"688","DOI":"10.1016\/j.enconman.2017.11.064","article-title":"Solar collectors and photovoltaics as combined heat and power systems: A critical review","volume":"156","author":"Kasaeian","year":"2018","journal-title":"Energy Convers. Manag."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"109955","DOI":"10.1016\/j.solmat.2019.109955","article-title":"Influence of gaseous pollutants and their synergistic effects on the aging of reflector materials for concentrating solar thermal technologies","volume":"200","author":"Ariza","year":"2019","journal-title":"Sol. Energy Mater. Sol. Cells"},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"958","DOI":"10.1016\/j.apenergy.2017.04.065","article-title":"Similarity analysis of parabolic-trough solar collectors","volume":"204","author":"Jin","year":"2017","journal-title":"Appl. Energy"},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"114496","DOI":"10.1016\/j.applthermaleng.2019.114496","article-title":"Enhancing the performance of a parabolic trough collector with combined thermal and optical techniques","volume":"164","author":"Bellos","year":"2020","journal-title":"Appl. Therm. Eng."},{"key":"ref_21","unstructured":"Asociaci\u00f3n Espa\u00f1ola para la Promoci\u00f3n de la Industria Termosolar (2019, December 10). Informe de Transici\u00f3n del sector El\u00e9ctrico Horizonte 2030. Available online: http:\/\/www.protermosolar.com."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"81","DOI":"10.1016\/j.pecs.2018.11.001","article-title":"Alternative designs of parabolic trough solar collectors","volume":"71","author":"Bellos","year":"2019","journal-title":"Prog. Energy Combust. Sci."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"171","DOI":"10.1016\/j.enconman.2018.11.008","article-title":"Investigation of a nanofluid-based concentrating thermal photovoltaic with a parabolic reflector","volume":"180","author":"Bellos","year":"2019","journal-title":"Energy Convers. Manag."},{"key":"ref_24","doi-asserted-by":"crossref","unstructured":"Fern\u00e1ndez-Garc\u00eda, A., Juaidi, A., Sutter, F., Mart\u00ednez-Arcos, L., and Manzano-Agugliaro, F. (2018). Solar Reflector Materials Degradation Due to the Sand Deposited on the Backside Protective Paints. Energies, 11.","DOI":"10.3390\/en11040808"},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"343","DOI":"10.1016\/j.cie.2015.05.028","article-title":"Evaluation of suitable locations for the installation of solar thermoelectric power plants","volume":"87","author":"Lamata","year":"2015","journal-title":"Comput. Ind. Eng."},{"key":"ref_26","unstructured":"Kalogirou, S. (2014). Solar Energy Engineering, Processes and Systems, Academic Press."},{"key":"ref_27","unstructured":"IDEA (Instituto para la Diversificaci\u00f3n y Ahorro de la Energ\u00eda) (2011). Anexo III. C\u00e1lculo de p\u00e9rdidas de radiaci\u00f3n solar por sombras. Instalaciones de Energ\u00eda Solar T\u00e9rmica, Pliego de Condiciones T\u00e9cnicas de Instalaciones de Baja Temperatura, IDEA."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/j.apenergy.2015.01.060","article-title":"Optimal displacement of photovoltaic array\u2019s rows using a novel shading model","volume":"144","author":"Castellano","year":"2015","journal-title":"Appl. Energy"},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"1695","DOI":"10.1016\/j.rser.2010.03.012","article-title":"Parabolic-trough solar collectors and their applications","volume":"14","author":"Zarza","year":"2010","journal-title":"Renew. Sustain. Energy Rev."}],"container-title":["Symmetry"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2073-8994\/12\/2\/278\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T08:57:21Z","timestamp":1760173041000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2073-8994\/12\/2\/278"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2020,2,13]]},"references-count":29,"journal-issue":{"issue":"2","published-online":{"date-parts":[[2020,2]]}},"alternative-id":["sym12020278"],"URL":"https:\/\/doi.org\/10.3390\/sym12020278","relation":{},"ISSN":["2073-8994"],"issn-type":[{"type":"electronic","value":"2073-8994"}],"subject":[],"published":{"date-parts":[[2020,2,13]]}}}