Solar cell parameters extraction, with less than 10 % error, refining the Co-Content function through an integration of a polynomial fit of I-Isc, in the case of constant percentage noise, and a percentage noise of the maximum current, Imax.  Part 1: theoretical analysis and proposal

Solar cell parameters extraction, with less than 10 % error, refining the Co-Content function through an integration of a polynomial fit of I-Isc, in the case of constant percentage noise, and a percentage noise of the maximum current, Imax. Part 1: theoretical analysis and proposal | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Research Article Solar cell parameters extraction, with less than 10 % error, refining the Co-Content function through an integration of a polynomial fit of I-Isc, in the case of constant percentage noise, and a percentage noise of the maximum current, Imax. Part 1: theoretical analysis and proposal Victor-Tapio Rangel-Kuoppa This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-4631534/v1 This work is licensed under a CC BY 4.0 License Status: Under Review Version 1 posted 12 You are reading this latest preprint version Abstract In this Part 1 article of this series of articles, a new methodology to refine the Co-Content function \(\left(CC\left(V,I\right)\right)\) is proposed, consisting on fitting the current minus the short-circuit current \((I-{I}_{sc})\) , to an \(N-1\) order polynomial, where \({N}_{points}=N\) , is the number of measured current-voltage \(\left(IV\right)\) points, and integrating it to calculate \(CC\left(V,I\right)\) . The shunt resistance \(\left({R}_{sh}\right)\) , the series resistance \(\left({R}_{s}\right)\) , the ideality factor \(\left(n\right)\) , the light current \(\left({I}_{lig}\right)\) , and the saturation current \(\left({I}_{sat}\right)\) , are then deduced, in the case of a constant percentage noise or a percentage noise of the maximum current \(\left({I}_{max}\right)\) . In the former case, \({R}_{s}\) , \({R}_{sh}, n, \text{a}\text{n}\text{d} {I}_{lig},\) can be deduced with less than 10% error, using only \({P}_{V}=\) 51 \(\frac{number of points}{V}\) , even if the noise is as large as \({p}_{n}=0.1 \text{\%}\) , with a computation time around 80 ms. \({I}_{sat}\) needs \({p}_{n}=0.05 \text{\%}\) or less, and \({P}_{V}\) equal or larger than 501 \(\frac{number of points}{V}\) . For the latter case, \({R}_{s}\) , \(\text{a}\text{n}\text{d} {I}_{lig},\) can be obtained with less than 10% error, using only \({P}_{V}=\) 251 \(\frac{number of points}{V}\) , and \({p}_{n}=0.1 \text{\%}\) , or smaller, with total computation time around 49 s. \({R}_{sh}, {I}_{sat}, \text{a}\text{n}\text{d} n\) needs that \({p}_{n}\le 0.05 \text{\%}\) , and \({P}_{V}=\) 751 \(\frac{number of points}{V}\) or larger. A computation time expression of the form \(time=E{{N}_{points}}^{m}\) , is deduced. The methodology proposed in this article is appliable to unevenly/randomly distributed IV data points, and it is implemented in Part 2 in solar cells’ and photovoltaic modules’ experimental \(IV\) reported in the literature, to deduce their five solar cell parameters. Co-Content function saturation current light current ideality factor series resistance shunt resistance Full Text Additional Declarations No competing interests reported. Cite Share Download PDF Status: Under Review Version 1 posted Reviewers agreed at journal 31 Jul, 2024 Reviews received at journal 30 Jul, 2024 Reviewers agreed at journal 29 Jul, 2024 Reviews received at journal 18 Jul, 2024 Reviews received at journal 17 Jul, 2024 Reviewers agreed at journal 12 Jul, 2024 Reviewers agreed at journal 12 Jul, 2024 Reviewers agreed at journal 11 Jul, 2024 Reviewers invited by journal 11 Jul, 2024 Editor assigned by journal 08 Jul, 2024 Submission checks completed at journal 03 Jul, 2024 First submitted to journal 24 Jun, 2024 You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. As a division of Research Square Company, we’re committed to making research communication faster, fairer, and more useful. We do this by developing innovative software and high quality services for the global research community. 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Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {"props":{"pageProps":{"initialData":{"identity":"rs-4631534","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":328621676,"identity":"08aff8ac-6e85-4cb8-927c-263f9ceba8f6","order_by":0,"name":"Victor-Tapio Rangel-Kuoppa","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA80lEQVRIiWNgGAWjYJCCA1Ca8cAHIMnGTkA5D5IWhoMzQFqYidACB4fBPEJa7NnPHgS65568Of/iA4dtfm2T52NmYPzwMQePLTx5CUD3FBvunPEs4XBu323DNmYGZsmZ2/A5LMcA6J4Exg03zhgczu25zQjUwsbMi08L/xuwFvsNN85/OGzZc9uesBYJiC2JG873MBxm+HE7kbCWG++AfjFISN5wg83gYG/D7eQ2ZsZmvH5h7889/OFDRYLthvOHHz748ee27fz25oMfPuLRAokZAyCWSADGfxtIhLEBn3oGRGTyHwASfwgoHgWjYBSMghEJAHFiVgj4iv8RAAAAAElFTkSuQmCC","orcid":"","institution":"Lancaster University","correspondingAuthor":true,"prefix":"","firstName":"Victor-Tapio","middleName":"","lastName":"Rangel-Kuoppa","suffix":""}],"badges":[],"createdAt":"2024-06-24 16:38:45","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-4631534/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-4631534/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":61173780,"identity":"8dc2f55e-bfa3-471f-a400-5a41983441b3","added_by":"auto","created_at":"2024-07-26 15:01:53","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":1500704,"visible":true,"origin":"","legend":"","description":"","filename":"2ndfinalArticleBraJPhysP1.pdf","url":"https://assets-eu.researchsquare.com/files/rs-4631534/v1_covered_de64f475-276d-4ba0-9fb1-fd541a550a84.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"Solar cell parameters extraction, with less than 10 % error, refining the Co-Content function through an integration of a polynomial fit of I-Isc, in the case of constant percentage noise, and a percentage noise of the maximum current, Imax. Part 1: theoretical analysis and proposal","fulltext":[],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":false,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":false,"highlight":"","institution":"","isAcceptedByJournal":true,"isAuthorSuppliedPdf":true,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":true,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"discover-electronics","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"","sideBox":"Learn more about [Discover Electronics](https://www.springer.com/journal/44291)","snPcode":"44291","submissionUrl":"https://submission.nature.com/new-submission/44291","title":"Discover Electronics","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"stoa","reportingPortfolio":"Discover Series","inReviewEnabled":true,"inReviewRevisionsEnabled":true},"keywords":"Co-Content function, saturation current, light current, ideality factor, series resistance, shunt resistance","lastPublishedDoi":"10.21203/rs.3.rs-4631534/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-4631534/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eIn this Part 1 article of this series of articles, a new methodology to refine the Co-Content function \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\left(CC\\left(V,I\\right)\\right)\\)\u003c/span\u003e\u003c/span\u003e is proposed, consisting on fitting the current minus the short-circuit current \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\((I-{I}_{sc})\\)\u003c/span\u003e\u003c/span\u003e, to an \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(N-1\\)\u003c/span\u003e\u003c/span\u003e order polynomial, where \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({N}_{points}=N\\)\u003c/span\u003e\u003c/span\u003e, is the number of measured current-voltage \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\left(IV\\right)\\)\u003c/span\u003e\u003c/span\u003e points, and integrating it to calculate \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(CC\\left(V,I\\right)\\)\u003c/span\u003e\u003c/span\u003e. The shunt resistance \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\left({R}_{sh}\\right)\\)\u003c/span\u003e\u003c/span\u003e, the series resistance \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\left({R}_{s}\\right)\\)\u003c/span\u003e\u003c/span\u003e, the ideality factor \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\left(n\\right)\\)\u003c/span\u003e\u003c/span\u003e, the light current \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\left({I}_{lig}\\right)\\)\u003c/span\u003e\u003c/span\u003e, and the saturation current \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\left({I}_{sat}\\right)\\)\u003c/span\u003e\u003c/span\u003e, are then deduced, in the case of a constant percentage noise or a percentage noise of the maximum current \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\left({I}_{max}\\right)\\)\u003c/span\u003e\u003c/span\u003e. In the former case, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({R}_{s}\\)\u003c/span\u003e\u003c/span\u003e, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({R}_{sh}, n, \\text{a}\\text{n}\\text{d} {I}_{lig},\\)\u003c/span\u003e\u003c/span\u003e can be deduced with less than 10% error, using only \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({P}_{V}=\\)\u003c/span\u003e\u003c/span\u003e51 \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\frac{number of points}{V}\\)\u003c/span\u003e\u003c/span\u003e, even if the noise is as large as \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({p}_{n}=0.1 \\text{\\%}\\)\u003c/span\u003e\u003c/span\u003e, with a computation time around 80 ms. \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({I}_{sat}\\)\u003c/span\u003e\u003c/span\u003e needs \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({p}_{n}=0.05 \\text{\\%}\\)\u003c/span\u003e\u003c/span\u003e or less, and \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({P}_{V}\\)\u003c/span\u003e\u003c/span\u003e equal or larger than 501 \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\frac{number of points}{V}\\)\u003c/span\u003e\u003c/span\u003e. For the latter case, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({R}_{s}\\)\u003c/span\u003e\u003c/span\u003e, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\text{a}\\text{n}\\text{d} {I}_{lig},\\)\u003c/span\u003e\u003c/span\u003e can be obtained with less than 10% error, using only \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({P}_{V}=\\)\u003c/span\u003e\u003c/span\u003e251 \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\frac{number of points}{V}\\)\u003c/span\u003e\u003c/span\u003e, and \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({p}_{n}=0.1 \\text{\\%}\\)\u003c/span\u003e\u003c/span\u003e, or smaller, with total computation time around 49 s. \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({R}_{sh}, {I}_{sat}, \\text{a}\\text{n}\\text{d} n\\)\u003c/span\u003e\u003c/span\u003e needs that \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({p}_{n}\\le 0.05 \\text{\\%}\\)\u003c/span\u003e\u003c/span\u003e, and \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({P}_{V}=\\)\u003c/span\u003e\u003c/span\u003e 751 \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\frac{number of points}{V}\\)\u003c/span\u003e\u003c/span\u003e or larger. A computation time expression of the form \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(time=E{{N}_{points}}^{m}\\)\u003c/span\u003e\u003c/span\u003e, is deduced. The methodology proposed in this article is appliable to unevenly/randomly distributed \u003cem\u003eIV\u003c/em\u003e data points, and it is implemented in Part 2 in solar cells\u0026rsquo; and photovoltaic modules\u0026rsquo; experimental \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(IV\\)\u003c/span\u003e\u003c/span\u003e reported in the literature, to deduce their five solar cell parameters.\u003c/p\u003e","manuscriptTitle":"Solar cell parameters extraction, with less than 10 % error, refining the Co-Content function through an integration of a polynomial fit of I-Isc, in the case of constant percentage noise, and a percentage noise of the maximum current, Imax. Part 1: theoretical analysis and proposal","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2024-07-26 14:53:44","doi":"10.21203/rs.3.rs-4631534/v1","editorialEvents":[{"type":"communityComments","content":0},{"type":"reviewerAgreed","content":"76272566412153984596328444026330553023","date":"2024-08-01T00:52:00+00:00","index":"hide","fulltext":""},{"type":"editorInvitedReview","content":"","date":"2024-07-30T04:19:44+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"190663526271680186990563872018242165413","date":"2024-07-29T11:23:31+00:00","index":"hide","fulltext":""},{"type":"editorInvitedReview","content":"","date":"2024-07-18T09:42:36+00:00","index":"hide","fulltext":""},{"type":"editorInvitedReview","content":"","date":"2024-07-17T05:15:56+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"111291074227088316794061563824679633548","date":"2024-07-12T07:47:44+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"9297402584936241359066415395236370525","date":"2024-07-12T05:25:49+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"257990073028037872540022031951449007400","date":"2024-07-11T23:54:13+00:00","index":"hide","fulltext":""},{"type":"reviewersInvited","content":"","date":"2024-07-11T18:26:02+00:00","index":"","fulltext":""},{"type":"editorAssigned","content":"","date":"2024-07-08T09:03:45+00:00","index":"","fulltext":""},{"type":"checksComplete","content":"","date":"2024-07-03T19:13:56+00:00","index":"","fulltext":""},{"type":"submitted","content":"Discover Electronics","date":"2024-06-24T16:37:23+00:00","index":"","fulltext":""}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"discover-electronics","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"","sideBox":"Learn more about [Discover Electronics](https://www.springer.com/journal/44291)","snPcode":"44291","submissionUrl":"https://submission.nature.com/new-submission/44291","title":"Discover Electronics","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"stoa","reportingPortfolio":"Discover Series","inReviewEnabled":true,"inReviewRevisionsEnabled":true}}],"origin":"","ownerIdentity":"644eb897-52f9-4120-a1d9-c0f414a60334","owner":[],"postedDate":"July 26th, 2024","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"under-review","subjectAreas":[],"tags":[],"updatedAt":"2024-11-18T08:53:11+00:00","versionOfRecord":[],"versionCreatedAt":"2024-07-26 14:53:44","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-4631534","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-4631534","identity":"rs-4631534","version":["v1"]},"buildId":"qtupq5eGEP_6zYnWcrvyt","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}