Optimal sizing of Power-to-Ammonia plants: A stochastic two-stage mixed-integer programming approach

Power-to-ammonia, a process that converts renewable electricity into green ammonia, has emerged as a promising solution for cross-sector decarbonization and large-scale energy storage. Power-to-ammonia plants are a combination of electrolysis, ammonia synthesis, air-separation processes, and multiple storage facilities, each characterized by distinct operational envelopes and cost structures. Sizing optimization of these production and storage modules is one of the most important tasks for the engineering of power-to-ammonia plants. In this paper, this optimal sizing problem is formulated as a two-stage stochastic mixed-integer program, in which the first stage determines the capacity configuration of these modules, while the second stage focuses on scheduling the hourly operations of various modules. The resulting program is challenging to solve due to its size, as a large number of scenarios are required to represent the stochastic renewable generation, and its mathematical structure, owing to the presence of both discrete and continuous variables in two stages. The Benders dual decomposition method is employed as the solution framework. To accelerate the convergence of the Benders dual decomposition method and mitigate its inherent duality gap, a random dissimilarity scenario bundling scheme along with a novel type of optimality cut is proposed. Built on these two elements, an improved Benders dual decomposition method is developed, yielding better lower bounds and higher-quality primal feasible solutions. Computational results show that the proposed method outperforms the Benders dual decomposition method and other classical decomposition methods in both relative gap closing and solution time. Particularly for cases with highly intermittent inputs, the proposed method is the only one that achieves a relative gap lower than 1.0% among all examined decomposition methods. It is also found that the hydrogen storage requirement for inflexible Haber–Bosch reactors can be nearly four times higher than that for flexible reactors, while the total installation cost of power-to-ammonia plants can differ by up to 25%.