A decomposition method for optimizing the operation of power-to-X energy systems with detailed process models

The growing reliance on renewable energy necessitates extending energy systems with complex processes such as power-to-X. Due to the diverse operational characteristics of these processes, the corresponding optimization problems are highly complex and result in models that are computationally difficult to solve. To address this computational challenge, this work proposes a decomposition method to solve operational optimization problems for complex energy systems with detailed process models. The method decomposes the original optimization problem into optimization problems with different levels of model granularity by incorporating a surrogate model for each process. Building on prior work focusing on a single continuous process system, this method is expanded to handle multiple and more complex process systems. To this end, we introduce a surrogate modeling approach for multistage process systems and develop three solution approaches for the operational optimization problems. The method is applied to minimize the daily operational cost of a power-to-X energy system with detailed process models of a PEM electrolyzer, a direct air capture plant and two methanation processes. All three solution approaches yield comparable operational costs, but differ in computational efficiency. The most efficient solution approach identifies an optimal operational strategy in under one hour. Additionally, a sensitivity study evaluates the impact of key parameters on the performance of the method, demonstrating its robustness and adaptability. The results highlight the potential of the proposed method to efficiently optimize the operations of complex energy systems with detailed process models.