Distributionally robust optimization of power-to-hydrogen-to-ammonia systems considering wind-solar uncertainty and electrolyzer cold-start characteristics

The growing integration of volatile renewable energy exacerbates the demand for grid flexibility. To address this challenge, Power-to-hydrogen-to-ammonia (PtHtA) systems offer a viable solution, converting renewable electricity into storable ammonia and thereby bridging the power and chemical sectors. However, PtHtA operation involves a pronounced time-scale mismatch. Upstream renewable generations fluctuate at short time-scales, alkaline electrolyzers are constrained by hour-scale cold-start transitions, and downstream ammonia synthesis requires a relatively stable hydrogen feedstock. Existing scheduling frameworks often overlook the energy loss and time delays caused by electrolyzer cold starts, as well as the inter-source and temporal correlations of renewable uncertainties, thereby undermining both flexibility and economic viability. This study first develops a refined four-state electrolyzer model that explicitly quantifies the non-productive power consumption and time delays during cold starts. Then, a data-driven ambiguity set with 1-norm and ∞-norm constraints is established to capture the inter-source and temporal uncertainties of wind and solar power. Building on this, a two-stage distributionally robust optimization (TS-DRO) framework is proposed to co-optimize the discrete startup/shutdown and continuous regulation processes under the worst-case probability distribution. Case studies demonstrate that the refined electrolyzer model captures operational flexibility more accurately, enabling a better cost-benefit trade-off and achieving a 66.5% increase in worst-case profit. Moreover, the TS-DRO framework improves net profit by 20.5% over the conventional two-stage robust optimization and outperforms stochastic optimization by up to 30.36% under high uncertainty. This work offers an economically viable scheduling strategy reconciling intermittent renewables with continuous chemical production for PtHtA Systems.