Optimal design and modeling of hydrogen-based multi-energy system with solid oxide electrolyzer technology considering efficiency degradation

The integration of solid oxide electrolyzer cells (SOECs) in hydrogen-based multi-energy systems offers a promising pathway for efficient and low-emission hydrogen production. However, optimizing system-level economic performance requires a careful balance between electricity imports, waste heat recovery, and on-site generation. This study presents a mixed-integer linear programming (MILP) model for the optimal design and operation of key system components, including the SOEC stack, combined heat and power (CHP) unit, battery energy storage system (BESS), and hydrogen storage. A novel three-state SOEC operation model is introduced to represent thermal inertia and ramp-up limitations, enabling more realistic system-level scheduling and scenario evaluation. Based on this formulation, three scenarios are investigated: (S1) the SOEC’s heat requirement is met entirely by external waste heat, and recovered SOEC heat is reused to meet system thermal demand; (S2) the SOEC receives heat from a CHP unit, but recovered heat still contributes to overall demand; and (S3) all thermal needs are met solely by the CHP unit without heat recovery. Results show that thermal integration significantly enhances profitability, with S1 and S2 outperforming S3 by 19.5% and 15.7%, respectively. To assess environmental performance, the model is evaluated under different grid carbon intensities. Results show that electricity-related emissions play a decisive role, with France’s low-carbon grid enabling up to 87% lower CO₂ emissions compared to steam methane reforming (SMR). Furthermore, sensitivity analysis demonstrates that hydrogen and heat prices dominate revenue composition, with hydrogen contributing up to 92% of total revenue under favorable market conditions. Meanwhile, electricity and gas prices significantly influence system profitability, leading to as much as 60% variation in profit. These findings highlight the combined impact of thermal integration, market volatility, and carbon intensity in designing efficient, low-emission, and economically resilient hydrogen-based energy systems.