The path to fully decarbonising an off-grid phosphate complex: MILP formulation and techno-economics

This study develops a sequential two-pass lexicographic mixed-integer linear programme (MILP) for the decarbonisation of an off-grid phosphate complex in Saudi Arabia. The baseline comprises approximately 21 MWe of continuous electricity demand and 115 MW ₜₕ of dryer heat, supplied by diesel generation and heavy fuel oil (HFO), respectively. The model co-optimises photovoltaic generation (PV), concentrating solar power with thermal energy storage (CSP-TES), battery energy storage (BESS), and PEM electrolysis to replace diesel-based electricity and substitute HFO with green hydrogen. Pass 1 minimises annual unserved critical site electricity ; Pass 2 minimises annual net cost over the reliability-feasible set, preserving a security-first design hierarchy without weighted objective trade-offs. Inter-annual solar uncertainty is represented through a Conditional Value-at-Risk (CVaR) extension using hourly NASA POWER irradiance data for 2013–2022. The site-only formulation applies α =0.95 , while the full site-plus-hydrogen formulation applies α =0.80 . Across the deterministic campaign, critical site electricity is fully protected in all cases. Under commercial-style financing, remains in a low-investment partial-substitution regime, whereas shifts to a high-investment design with approximately 1.24 BUSD of CAPEX, 19.74 kt yr −1 of hydrogen production, and 68.13 GWh yr −1 of residual unmet hydrogen service. Activating the hydrogen-service penalty raises production to 21.15 kt yr −1 and reduces unmet service to 1.07 GWh yr −1 . Representative gross hydrogen cost is 3.85−4.39 USD kg −1 under a 2% financing assumption. The CVaR results quantify the resilience premium associated with multi-year solar resource risk. Relative to the deterministic design, the full-penalty CVaR solution increases CAPEX from 1.305 to 2.202 BUSD, eliminates 53.9 GWh yr −1 of unserved energy, and raises hydrogen production from 20.0 to 21.2 kt yr −1 . Across deterministic and risk-aware runs, the preferred architecture remains TES-dominant rather than BESS-dominant, indicating that temporal firmness and sustained electrolyser utilisation matter more than short-duration battery shifting alone. Overall, environmental pricing improves the case for deep decarbonisation, but the cost of capital is the stronger determinant of whether ambitious hydrogen-substitution targets are realised.