{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,28]],"date-time":"2026-01-28T20:39:19Z","timestamp":1769632759208,"version":"3.49.0"},"reference-count":29,"publisher":"MDPI AG","issue":"6","license":[{"start":{"date-parts":[[2025,3,9]],"date-time":"2025-03-09T00:00:00Z","timestamp":1741478400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"European Union","award":["823802"],"award-info":[{"award-number":["823802"]}]},{"name":"European Union","award":["10.54499\/UIDB\/50022\/2020"],"award-info":[{"award-number":["10.54499\/UIDB\/50022\/2020"]}]},{"name":"Funda\u00e7\u00e3o para a Ci\u00eancia e a Tecnologia (FCT)","award":["823802"],"award-info":[{"award-number":["823802"]}]},{"name":"Funda\u00e7\u00e3o para a Ci\u00eancia e a Tecnologia (FCT)","award":["10.54499\/UIDB\/50022\/2020"],"award-info":[{"award-number":["10.54499\/UIDB\/50022\/2020"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Applied Sciences"],"abstract":"<jats:p>In this work, solar concentrating heliostat fields are modelled using computer ray-tracing techniques to investigate the parameters controlling the optical efficiency of those solar facilities. First, it is explained how the non-trivial problem of heliostat blocking and shading can be efficiently handled in ray-tracing simulations. These numerical techniques were implemented in our Light Analysis Modelling (LAM) software, which was then used to study realistic heliostat fields for a range of different geometries. Two locations were chosen, with the highest and the lowest latitudes, from the SFERA-III EU list of solar concentrating facilities with heliostat fields: J\u00fclich (Germany) and Protaras (Cyprus). The results indicate that shading and blocking can substantially reduce the radiation collected during the year (up to 20%). Accurate figures of merit are proposed to quantify the thermal efficiency of a heliostat field, independently of its size. Increasing the tower height mostly reduces blocking (especially when the sun is high and most energy is collected), while increasing the distance between heliostats or increasing the ground slope mostly reduces shading (especially when the sun is low and little energy is collected).<\/jats:p>","DOI":"10.3390\/app15062953","type":"journal-article","created":{"date-parts":[[2025,3,10]],"date-time":"2025-03-10T06:59:59Z","timestamp":1741589999000},"page":"2953","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["Computer Modelling of Heliostat Fields by Ray-Tracing Techniques: Simulating Shading and Blocking Effects"],"prefix":"10.3390","volume":"15","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-1608-4387","authenticated-orcid":false,"given":"Jos\u00e9 Carlos Garcia","family":"Pereira","sequence":"first","affiliation":[{"name":"Departamento de Engenharia Qu\u00edmica, Instituto Superior T\u00e9cnico, Universidade de Lisboa, Av. Rovisco Pais, 1049-001 Lisboa, Portugal"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-4730-3765","authenticated-orcid":false,"given":"Lu\u00eds Guerra","family":"Rosa","sequence":"additional","affiliation":[{"name":"IDMEC\u2014Instituto de Engenharia Mec\u00e2nica, Instituto Superior T\u00e9cnico, Universidade de Lisboa, Av. Rovisco Pais, 1049-001 Lisboa, Portugal"}]}],"member":"1968","published-online":{"date-parts":[[2025,3,9]]},"reference":[{"key":"ref_1","unstructured":"(2024, December 21). World\u2019s First Industrial Solar Furnace to Melt Steel Without Fuel or Electricity. Available online: https:\/\/energyindustryreview.com\/metals-mining\/worlds-first-industrial-solar-furnace-to-melt-steel-without-fuel-or-electricity\/."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"1511","DOI":"10.1016\/j.egypro.2014.03.160","article-title":"PSA vertical axis solar furnace SF5","volume":"49","author":"Zarza","year":"2014","journal-title":"Energy Procedia"},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"124664","DOI":"10.1016\/j.jclepro.2020.124664","article-title":"A comprehensive review on Dish\/Stirling concentrated solar power systems: Design, optical and geometrical analyses, thermal performance assessment, and applications","volume":"283","author":"Zayed","year":"2021","journal-title":"J. Clean. Prod."},{"key":"ref_4","doi-asserted-by":"crossref","unstructured":"Kumar, A., Pal, A., Kachhwaha, S.S., and Jain, P.K. (2021). A Current Review on Linear Fresnel Reflector Technology and Its Applications in Power Plants. Recent Advances in Mechanical Engineering (ICRAME 2020), Springer.","DOI":"10.1007\/978-981-15-9678-0"},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"07016","DOI":"10.1051\/e3sconf\/202132807016","article-title":"Design of solar water heater using collector cylindric parabolic and coil heater as absorber at focus point","volume":"328","author":"Dina","year":"2021","journal-title":"E3S Web Conf."},{"key":"ref_6","first-page":"10450","article-title":"Performance of inclined heliostat solar field with solar geometrical factors","volume":"46","author":"Bhattacharjee","year":"2020","journal-title":"Energy Sources Part A Recovery Util. Environ. Eff."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"456","DOI":"10.1016\/j.solener.2019.01.052","article-title":"Rapid design of a heliostat field by analytic geometry methods and evaluation of maximum optical efficiency map","volume":"180","author":"Wang","year":"2019","journal-title":"Sol. Energy"},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"292","DOI":"10.1016\/j.renene.2021.09.045","article-title":"A detailed account of calculation of shading and blocking factor of a heliostat field","volume":"181","author":"Rizvi","year":"2022","journal-title":"Renew. Energy"},{"key":"ref_9","doi-asserted-by":"crossref","unstructured":"Pidaparthi, A.S., Duvenhage, D.F., and Hoffmann, J.E. (November, January 31). A parametric study of heliostat size for reductions in levelized cost of electricity. Proceedings of the 4th Southern African Solar Energy Conference (SASEC 2016), Stellenbosch University, Stellenbosch, South Africa. Available online: https:\/\/www.researchgate.net\/publication\/314258829_A_Parametric_Study_of_Heliostat_Size_for_Reductions_in_Levelized_Cost_of_Electricity.","DOI":"10.1063\/1.4984381"},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/j.solener.2022.10.043","article-title":"Optical characterization of heliostat facets based on computational optimization","volume":"248","author":"Cruz","year":"2022","journal-title":"Sol. Energy"},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"031002","DOI":"10.1115\/1.3139139","article-title":"A new fast ray tracing tool for high-precision simulation of heliostat fields","volume":"131","author":"Belhomme","year":"2009","journal-title":"J. Sol. Energy Eng."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"792","DOI":"10.1016\/j.solener.2011.12.007","article-title":"Heliostat field optimization: A new computationally efficient model and biomimetic layout","volume":"86","author":"Noone","year":"2012","journal-title":"Sol. Energy"},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"063125","DOI":"10.1063\/1.4768546","article-title":"Error analysis for concentrated solar collectors","volume":"4","author":"Bonanos","year":"2012","journal-title":"J. Renew. Sustain. Energy"},{"key":"ref_14","unstructured":"Gonzalo, I.B., Mart\u00ednez-Hern\u00e1ndez, A., Romero, M., and Gonzalez-Aguilar, J. (2019, January 4\u20137). Efficient Ray-Tracing Program to Simulate the Optical Performance of Heliostats in Concentrated Solar Power Facilities. Proceedings of the ISES Solar World Congress 2019, Santiago, Chile."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"1170","DOI":"10.1016\/j.solener.2020.10.057","article-title":"Drift analysis in tilt-roll heliostats","volume":"211","author":"Gonzalo","year":"2020","journal-title":"Sol. Energy"},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"10","DOI":"10.54097\/91m0ng23","article-title":"Design of heliostat field based on ray tracing","volume":"87","author":"Deng","year":"2024","journal-title":"Highlights Sci. Eng. Technol."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"170","DOI":"10.54097\/bd517142","article-title":"Research on optimization design of heliostat field based on ray tracing","volume":"104","author":"Teng","year":"2024","journal-title":"Highlights Sci. Eng. Technol."},{"key":"ref_18","doi-asserted-by":"crossref","unstructured":"Pereira, J.C.G., Almeida, G., and Rosa, L.G. (2025). Computer modelling of heliostat fields by ray-tracing techniques: Simulating the Sun. Appl. Sci., 15.","DOI":"10.3390\/app15041739"},{"key":"ref_19","doi-asserted-by":"crossref","unstructured":"Pereira, J.C.G., Fernandes, J.C., and Guerra Rosa, L. (2019). Mathematical models for simulation and optimization of high-flux solar furnaces. Math. Comput. Appl., 24.","DOI":"10.3390\/mca24020065"},{"key":"ref_20","doi-asserted-by":"crossref","unstructured":"Pereira, J.C.G., Rodr\u00edguez, J., Fernandes, J.C., and Rosa, L.G. (2020). Homogeneous flux distribution in high-flux solar furnaces. Energies, 13.","DOI":"10.3390\/en13020433"},{"key":"ref_21","doi-asserted-by":"crossref","unstructured":"Pereira, J.C.G., Rahmani, K., and Rosa, L.G. (2021). Computer Modelling of the Optical Behavior of Homogenizers in High-Flux Solar Furnaces. Energies, 14.","DOI":"10.3390\/en14071828"},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"142","DOI":"10.1016\/j.rser.2012.11.076","article-title":"A review of optimized design layouts for solar power tower plants with campo code","volume":"20","author":"Collado","year":"2013","journal-title":"Renew. Sustain. Energy Rev."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"259","DOI":"10.1007\/s11227-016-1698-7","article-title":"High performance computing for the heliostat field layout evaluation","volume":"73","author":"Cruz","year":"2016","journal-title":"J. Supercomput."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"29","DOI":"10.54097\/ajst.v8i1.13563","article-title":"A method for calculating the optical efficiency of solar tower heliostats","volume":"8","author":"Zhang","year":"2013","journal-title":"Acad. J. Sci. Technol."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"957","DOI":"10.3103\/S0003701X23601230","article-title":"Research on modeling simulation and optimal layout of heliostat field optical efficiency for solar power tower plant","volume":"59","author":"Ali","year":"2023","journal-title":"Appl. Sol. Energy"},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"030044","DOI":"10.1063\/1.4984387","article-title":"Ultra-modular 500m2 heliostat field for high flux\/high temperature solar-driven processes","volume":"1850","author":"Romero","year":"2017","journal-title":"AIP Conf. Proc."},{"key":"ref_27","unstructured":"(2024, December 29). EU SFERA-III Project. Available online: https:\/\/sfera3.sollab.eu\/access\/#infrastructures."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"1140","DOI":"10.1016\/j.egypro.2014.10.100","article-title":"DNI estimation procedures for the assessment of solar radiation availability in concentrating systems","volume":"57","author":"Padovan","year":"2014","journal-title":"Energy Procedia"},{"key":"ref_29","unstructured":"Abreu, E.F.M. (2023). Direct Normal Irradiance and Circumsolar Radiation: Modelling, Measurement and Impact on Concentrating Solar Power. [Ph.D. Thesis, Universidade de \u00c9vora]. Available online: http:\/\/hdl.handle.net\/10174\/35737."}],"container-title":["Applied Sciences"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2076-3417\/15\/6\/2953\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,9]],"date-time":"2025-10-09T16:49:41Z","timestamp":1760028581000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2076-3417\/15\/6\/2953"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,3,9]]},"references-count":29,"journal-issue":{"issue":"6","published-online":{"date-parts":[[2025,3]]}},"alternative-id":["app15062953"],"URL":"https:\/\/doi.org\/10.3390\/app15062953","relation":{},"ISSN":["2076-3417"],"issn-type":[{"value":"2076-3417","type":"electronic"}],"subject":[],"published":{"date-parts":[[2025,3,9]]}}}