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

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.