{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,2]],"date-time":"2026-06-02T16:13:10Z","timestamp":1780416790942,"version":"3.54.1"},"reference-count":68,"publisher":"MDPI AG","issue":"11","license":[{"start":{"date-parts":[[2022,5,31]],"date-time":"2022-05-31T00:00:00Z","timestamp":1653955200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100004054","name":"Deputyship for Research and Innovation, Ministry of Education in Saudi Arabia","doi-asserted-by":"publisher","award":["IFPRC-048-135-2020"],"award-info":[{"award-number":["IFPRC-048-135-2020"]}],"id":[{"id":"10.13039\/501100004054","id-type":"DOI","asserted-by":"publisher"}]},{"name":"King Abdulaziz University","award":["IFPRC-048-135-2020"],"award-info":[{"award-number":["IFPRC-048-135-2020"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>There are three standard equivalent circuit models of solar cells in the literature\u2014single-diode, double-diode, and triple-diode models. In this paper, first, a modified version of the single diode model, called the Improved Single Diode Model (ISDM), is presented. This modification is realized by adding resistance in series with the diode to enable better power loss dissipation representation. Second, the mathematical expression for the current\u2013voltage relation of this circuit is derived in terms of Lambert\u2019s W function and solved by using the special trans function theory. Third, a novel hybrid algorithm for solar cell parameters estimation is proposed. The proposed algorithm, called SA-MRFO, is used for the parameter estimation of the standard single diode and improved single diode models. The proposed model\u2019s accuracy and the proposed algorithm\u2019s efficiency are tested on a standard RTC France solar cell and SOLAREX module MSX 60. Furthermore, the experimental verification of the proposed circuit and the proposed solar cell parameter estimation algorithm on a solar laboratory module is also realized. Based on all the results obtained, it is shown that the proposed circuit significantly improves current\u2013voltage solar cell representation in comparison with the standard single diode model and many results in the literature on the double diode and triple diode models. Additionally, it is shown that the proposed algorithm is effective and outperforms many literature algorithms in terms of accuracy and convergence speed.<\/jats:p>","DOI":"10.3390\/s22114173","type":"journal-article","created":{"date-parts":[[2022,5,31]],"date-time":"2022-05-31T05:25:42Z","timestamp":1653974742000},"page":"4173","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":40,"title":["Single Diode Solar Cells\u2014Improved Model and Exact Current\u2013Voltage Analytical Solution Based on Lambert\u2019s W Function"],"prefix":"10.3390","volume":"22","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-6035-5733","authenticated-orcid":false,"given":"Muhyaddin","family":"Rawa","sequence":"first","affiliation":[{"name":"Smart Grids Research Group, Center of Research Excellence in Renewable Energy and Power Systems, King Abdulaziz University, Jeddah 21589, Saudi Arabia"},{"name":"Department of Electrical and Computer Engineering, Faculty of Engineering, K. A. CARE Energy Research and Innovation Center, Jeddah 21589, Saudi Arabia"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7693-3494","authenticated-orcid":false,"given":"Martin","family":"Calasan","sequence":"additional","affiliation":[{"name":"Faculty of Electrical Engineering, University of Montenegro, 81000 Podgorica, Montenegro"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-8025-0453","authenticated-orcid":false,"given":"Abdullah","family":"Abusorrah","sequence":"additional","affiliation":[{"name":"Smart Grids Research Group, Center of Research Excellence in Renewable Energy and Power Systems, King Abdulaziz University, Jeddah 21589, Saudi Arabia"},{"name":"Department of Electrical and Computer Engineering, Faculty of Engineering, K. A. CARE Energy Research and Innovation Center, Jeddah 21589, Saudi Arabia"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-8685-4207","authenticated-orcid":false,"given":"Abdullah Ali","family":"Alhussainy","sequence":"additional","affiliation":[{"name":"Smart Grids Research Group, Center of Research Excellence in Renewable Energy and Power Systems, King Abdulaziz University, Jeddah 21589, Saudi Arabia"},{"name":"Department of Electrical and Computer Engineering, Faculty of Engineering, K. A. CARE Energy Research and Innovation Center, Jeddah 21589, Saudi Arabia"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Yusuf","family":"Al-Turki","sequence":"additional","affiliation":[{"name":"Smart Grids Research Group, Center of Research Excellence in Renewable Energy and Power Systems, King Abdulaziz University, Jeddah 21589, Saudi Arabia"},{"name":"Department of Electrical and Computer Engineering, Faculty of Engineering, K. A. 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