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<InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(_{\textrm{th}}\)</EquationSource> </InlineEquation> 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 <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(\alpha =0.95\)</EquationSource> </InlineEquation>, while the full site-plus-hydrogen formulation applies <InlineEquation ID="IEq3"> <EquationSource Format="TEX">\(\alpha =0.80\)</EquationSource> </InlineEquation>. Across the deterministic campaign, critical site electricity is fully protected in all cases. Under commercial-style financing, <Emphasis FontCategory="NonProportional">KAPSARC2030</Emphasis> remains in a low-investment partial-substitution regime, whereas <Emphasis FontCategory="NonProportional">Case2050</Emphasis> 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 <Emphasis FontCategory="NonProportional">KAPSARC2030</Emphasis> 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.

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

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2026年7月3日

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Flaviano Augusto Moreira de Andrade

摘要

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 \(_{\textrm{th}}\) 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 \(\alpha =0.95\) , while the full site-plus-hydrogen formulation applies \(\alpha =0.80\) . Across the deterministic campaign, critical site electricity is fully protected in all cases. Under commercial-style financing, KAPSARC2030 remains in a low-investment partial-substitution regime, whereas Case2050 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 KAPSARC2030 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.