Fully Decarbonising an Off-Grid Phosphate Complex: MILP Formulation and Techno-Economics

Fully Decarbonising an Off-Grid Phosphate Complex: MILP Formulation and Techno-Economics | 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 Fully Decarbonising an Off-Grid Phosphate Complex: MILP Formulation and Techno-Economics Flaviano Augusto Moreira de Andrade This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-7676038/v1 This work is licensed under a CC BY 4.0 License Status: Posted Version 1 posted You are reading this latest preprint version Abstract This study develops a two-pass, lexicographic mixed-integer linear programme (MILP) to size and hourly dispatch a hybrid system—photovoltaics (PV), concentrating solar power (CSP) with thermal energy storage (TES), battery storage (BESS), and PEM electrolysers—for an off-grid phosphate complex currently powered by diesel (electricity) and heavy fuel oil (HFO, process heat). The aim is full decarbonisation by substituting diesel with PV–CSP–BESS and replacing HFO with green hydrogen, thereby establishing a techno-economic baseline for net-zero investment decisions. Pass~1 minimises unserved \emph{critical} electricity over 8{,}760~h, treating reliability as a hard constraint. Pass~2 fixes this reliability and minimises annualised net cost (CAPEX, OPEX, water, savings from HFO displacement and avoided road freight, carbon revenues, export credits, and unmet-demand penalties). The linear network-flow structure retains integer capacity choices (PV, BESS, electrolyser, CSP turbines, TES, heliostat field) and cyclic TES/BESS; deterministic runs close within 0.5\% optimality and yield an irradiance-shaped LCOH $<\,$USD\,2\,kg$^{-1}$ (see Appendix~\ref{app:lcoh}). Inter-annual solar variability is captured using a NASA POWER hourly ensemble (2013–2022) for plane-of-array (PV) and direct-normal irradiance (CSP). A CVaR extension \emph{preserves linearity via scenario-weighted loss variables} and quantifies resilience premia under two scopes: (i) \emph{site-only} electricity and (ii) \emph{site+hydrogen} (electricity + process heat). A carbon-price sweep (\$0–\$150\,tCO\(_2^{-1}\)) endogenously shifts capacities and dispatch. The results report impacts on net cost, reliability, hydrogen output, and emissions, alongside hourly–annual ledgers for transparency and replication, and derive risk-adjusted pathways to 2050. Off-grid industrial decarbonisation PV–CSP–BESS hybrid systems PEM electrolysis (green hydrogen) Lexicographic MILP and CVaR Full Text Additional Declarations No competing interests reported. Cite Share Download PDF Status: Posted Version 1 posted 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. 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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-7676038","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":534069714,"identity":"e17185ef-9344-4d3d-9ea1-94389651d003","order_by":0,"name":"Flaviano Augusto Moreira de Andrade","email":"data:image/png;base64,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","orcid":"","institution":"Imperial College London","correspondingAuthor":true,"prefix":"","firstName":"Flaviano","middleName":"Augusto Moreira","lastName":"de Andrade","suffix":""}],"badges":[],"createdAt":"2025-09-22 13:08:24","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-7676038/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-7676038/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":94493167,"identity":"e6e159f6-8d7a-4767-aceb-d6537a85bacd","added_by":"auto","created_at":"2025-10-27 17:31:01","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":1983378,"visible":true,"origin":"","legend":"","description":"","filename":"Article.pdf","url":"https://assets-eu.researchsquare.com/files/rs-7676038/v1/2f89a5ed05016801e32a22e8.pdf"},{"id":94493127,"identity":"b3ce50a6-898a-4a80-8cdd-569f6f981c6f","added_by":"auto","created_at":"2025-10-27 17:30:39","extension":"json","order_by":1,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":4912,"visible":true,"origin":"","legend":"","description":"","filename":"a1cfd71142574aa7a0c820e197d60494.json","url":"https://assets-eu.researchsquare.com/files/rs-7676038/v1/3cd0c8e70e821148ee1ce5bb.json"},{"id":94493221,"identity":"7d9771da-382e-43da-ab1d-42eb58fdcf89","added_by":"auto","created_at":"2025-10-27 17:31:20","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":1581976,"visible":true,"origin":"","legend":"","description":"","filename":"Article.pdf","url":"https://assets-eu.researchsquare.com/files/rs-7676038/v1_covered_ee3ccdb4-1fef-4280-8811-5dcced0da4d2.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"Fully Decarbonising an Off-Grid Phosphate Complex: MILP Formulation and Techno-Economics","fulltext":[],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":false,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":true,"highlight":"","institution":"","isAcceptedByJournal":false,"isAuthorSuppliedPdf":true,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":true,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true},"keywords":"Off-grid industrial decarbonisation, PV–CSP–BESS hybrid systems, PEM electrolysis (green hydrogen), Lexicographic MILP and CVaR","lastPublishedDoi":"10.21203/rs.3.rs-7676038/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-7676038/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eThis study develops a two-pass, lexicographic mixed-integer linear programme (MILP) to size and hourly dispatch a hybrid system—photovoltaics (PV), concentrating solar power (CSP) with thermal energy storage (TES), battery storage (BESS), and PEM electrolysers—for an off-grid phosphate complex currently powered by diesel (electricity) and heavy fuel oil (HFO, process heat). The aim is full decarbonisation by substituting diesel with PV–CSP–BESS and replacing HFO with green hydrogen, thereby establishing a techno-economic baseline for net-zero investment decisions.\u0026nbsp;\u003c/p\u003e\n\u003cp\u003ePass~1 minimises unserved \\emph{critical} electricity over 8{,}760~h, treating reliability as a hard constraint. Pass~2 fixes this reliability and minimises annualised net cost (CAPEX, OPEX, water, savings from HFO displacement and avoided road freight, carbon revenues, export credits, and unmet-demand penalties). The linear network-flow structure retains integer capacity choices (PV, BESS, electrolyser, CSP turbines, TES, heliostat field) and cyclic TES/BESS; deterministic runs close within 0.5\\% optimality and yield an irradiance-shaped LCOH $\u0026lt;\\,$USD\\,2\\,kg$^{-1}$ (see Appendix~\\ref{app:lcoh}).\u0026nbsp;\u003c/p\u003e\n\u003cp\u003eInter-annual solar variability is captured using a NASA POWER hourly ensemble (2013–2022) for plane-of-array (PV) and direct-normal irradiance (CSP). A CVaR extension \\emph{preserves linearity via scenario-weighted loss variables} and quantifies resilience premia under two scopes: (i) \\emph{site-only} electricity and (ii) \\emph{site+hydrogen} (electricity + process heat). A carbon-price sweep (\\$0–\\$150\\,tCO\\(_2^{-1}\\)) endogenously shifts capacities and dispatch. The results report impacts on net cost, reliability, hydrogen output, and emissions, alongside hourly–annual ledgers for transparency and replication, and derive risk-adjusted pathways to 2050.\u003c/p\u003e","manuscriptTitle":"Fully Decarbonising an Off-Grid Phosphate Complex: MILP Formulation and Techno-Economics","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2025-10-27 17:29:25","doi":"10.21203/rs.3.rs-7676038/v1","editorialEvents":[{"type":"communityComments","content":0}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true}}],"origin":"","ownerIdentity":"655c7d45-43c7-4aaa-80b2-c4154fad1130","owner":[],"postedDate":"October 27th, 2025","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"posted","subjectAreas":[],"tags":[],"updatedAt":"2026-05-18T09:23:17+00:00","versionOfRecord":[],"versionCreatedAt":"2025-10-27 17:29:25","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-7676038","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-7676038","identity":"rs-7676038","version":["v1"]},"buildId":"8U1c8b4HqxoKbykW_rLl7","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}