{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,8]],"date-time":"2026-03-08T19:08:16Z","timestamp":1772996896455,"version":"3.50.1"},"reference-count":11,"publisher":"Springer Science and Business Media LLC","issue":"1","license":[{"start":{"date-parts":[[2023,8,1]],"date-time":"2023-08-01T00:00:00Z","timestamp":1690848000000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"},{"start":{"date-parts":[[2023,8,1]],"date-time":"2023-08-01T00:00:00Z","timestamp":1690848000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Sci Rep"],"abstract":"<jats:title>Abstract<\/jats:title><jats:p>Renewable energies are increasingly playing an important role in the world\u2019s energy supply. Society demands new solutions to solve environmental issues caused by fossil fuels. The importance of photovoltaic technology has been increasing and consequently, the necessity to have more accurate models to characterise the performance of solar cells during their entire lifetime has rose as well. Performance problems may appear during devices\u2019 lifetimes associated with factors, such as weather conditions or faulty installation. Cracking might occur, leading to abrupt reductions on the produced power, quite difficult and expensive to fix. The I\u2013V curves of a defected or cracked solar cell might not have the shape imposed by the usual models as 1M5P. In this article, cracked c-Si solar cells are modelled using a novel model: d1MxP. This model is based on the discretisation of the diode\u2019s response on models as 1M5P. Instead of imposing a shape and compute some parameters to fit it on experimental data, the proposed model connects every two points. The results suggest a better fit using the proposed model in comparison with the 1M5P, not only in the original curves, but also modelling cracked cells. As consequence of a better fitting, the computation of important figures of merit as maximum power point or fill factor, reveals to be more precise. It is concluded that the proposed model might characterise the performance of a solar cell, even cracked, which is a huge advance aiming the possibility of simulating complex problems during the cells\u2019 operation lifetime.<\/jats:p>","DOI":"10.1038\/s41598-023-39769-0","type":"journal-article","created":{"date-parts":[[2023,8,1]],"date-time":"2023-08-01T17:02:28Z","timestamp":1690909348000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":9,"title":["Modelling the effect of defects and cracks in solar cells\u2019 performance using the d1MxP discrete model"],"prefix":"10.1038","volume":"13","author":[{"given":"Ricardo A.","family":"Marques Lameirinhas","sequence":"first","affiliation":[]},{"given":"Catarina","family":"P. Correia V. Bernardo","sequence":"additional","affiliation":[]},{"given":"Jo\u00e3o Paulo","family":"N. Torres","sequence":"additional","affiliation":[]},{"given":"Helena Isabel","family":"Veiga","sequence":"additional","affiliation":[]},{"given":"Pedro","family":"Mendon\u00e7a dos Santos","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2023,8,1]]},"reference":[{"key":"39769_CR1","doi-asserted-by":"publisher","first-page":"15","DOI":"10.3390\/en15051823","volume":"1823","author":"RA Marques Lameirinhas","year":"2022","unstructured":"Marques Lameirinhas, R. A., Torres, J. P. N. & de Melo Cunha, J. P. A photovoltaic technology review: History, fundamentals and applications. Energies 1823, 15. https:\/\/doi.org\/10.3390\/en15051823 (2022).","journal-title":"Energies"},{"key":"39769_CR2","doi-asserted-by":"publisher","first-page":"3289","DOI":"10.3390\/en16073289","volume":"16","author":"JPN Torres","year":"2023","unstructured":"Torres, J. P. N. et al. Analysis of different third-generation solar cells using the discrete electrical model d1MxP. Energies 16, 3289. https:\/\/doi.org\/10.3390\/en16073289 (2023).","journal-title":"Energies"},{"key":"39769_CR3","doi-asserted-by":"publisher","first-page":"2018","DOI":"10.3390\/en16042018","volume":"16","author":"JPN Torres","year":"2023","unstructured":"Torres, J. P. N., Marques-Lameirinhas, R. A., Correia, V. B., Veiga, H. I. & dos-Santos, P. M. A discrete electrical model for photovoltaic solar cells-d1MxP. Energies 16, 2018. https:\/\/doi.org\/10.3390\/en16042018 (2023).","journal-title":"Energies"},{"key":"39769_CR4","doi-asserted-by":"publisher","first-page":"100082","DOI":"10.1016\/j.ecmx.2021.100082","volume":"10","author":"SAA dos-Santos","year":"2021","unstructured":"dos-Santos, S. A. A., Torres, J. P. N., Fernandes, C. A. F. & Lameirinhas, R. A. M. The impact of aging of solar cells on the performance of photovoltaic panels. Energy Convers. Manage. X 10, 100082. https:\/\/doi.org\/10.1016\/j.ecmx.2021.100082 (2021).","journal-title":"Energy Convers. Manage. 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Nanomaterials 2021, 2615. https:\/\/doi.org\/10.3390\/nano11102615 (2021).","journal-title":"Nanomaterials"},{"issue":"4","key":"39769_CR9","doi-asserted-by":"publisher","first-page":"1156","DOI":"10.1109\/JPHOTOV.2014.2316371","volume":"4","author":"BC Babu","year":"2014","unstructured":"Babu, B. C. & Gurjar, S. A novel simplified two-diode model of photovoltaic (PV) module. IEEE J. Photovolt. 4(4), 1156\u20131161. https:\/\/doi.org\/10.1109\/JPHOTOV.2014.2316371 (2014).","journal-title":"IEEE J. Photovolt."},{"key":"39769_CR10","doi-asserted-by":"publisher","first-page":"2140","DOI":"10.3390\/en14082140","volume":"14","author":"R Castro","year":"2021","unstructured":"Castro, R. & Silva, M. Experimental and theoretical validation of one diode and three parameters-based PV models. Energies 14, 2140. https:\/\/doi.org\/10.3390\/en14082140 (2021).","journal-title":"Energies"},{"key":"39769_CR11","volume":"147","author":"L Yuqiang","year":"2020","unstructured":"Yuqiang, L. et al. High-efficiency silicon heterojunction solar cells: Materials, devices and applications. Mater. Sci. Eng. Rep. 147, 100579 (2020).","journal-title":"Mater. Sci. Eng. 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