Multi-modal distributed energy system planning is applied in the context of smart grids, industrial energy supply, and in the building energy sector. In real-world applications, these systems are commonly characterized by existing system structures of different age where monitoring and investment are conducted in a closed-loop, with the iterative possibility to invest. The literature contains two main approaches to approximate this computationally intensive multi-period investment problem. The first approach simplifies the temporal decision-making process collapsing the multi-stage decision to a two-stage decision, considering uncertainty in the second stage decision variables. The second approach considers multi-period investments under the assumption of perfect foresight. In this work, we propose a multi-stage stochastic optimization model that captures multi-period investment decisions under uncertainty and solves the problem to global optimality, serving as a first-best benchmark to the problem. To evaluate the performance of conventional approaches applied in a multi-year setup, we propose a rolling horizon heuristic that on the one hand reveals the performance of conventional approaches applied in a multi-period set-up and on the other hand enables planners to identify approximate solutions to the original multi-stage stochastic problem. We conduct a real-world case study and investigate solution quality as well as the computational performance of the proposed approaches. Our findings indicate that the approximation of multi-period investments by two-stage stochastic approaches yield the best results regarding constraint satisfaction, while deterministic multi-period approximations yield better economic and computational performance.

多模式分布式能源系统规划适用于智能电网，工业能源供应以及建筑能源领域。在实际应用中，这些系统通常以不同年龄的现有系统结构为特征，在这些系统中，闭环进行监视和投资，具有反复投资的可能性。文献包含两种主要方法来近似此计算密集型的多期投资问题。考虑到第二阶段决策变量的不确定性，第一种方法简化了将多阶段决策折叠为两阶段决策的时间决策过程。第二种方法在完美的远见的假设下考虑了多期投资。在这项工作中 我们提出了一个多阶段随机优化模型，该模型可以捕获不确定性下的多周期投资决策，并将问题解决为全局最优性，以此作为问题的最佳基准。为了评估在多年设置中使用的常规方法的性能，我们提出了一种滚动式启发式方法，该方法一方面揭示了在多个时期设置中应用的常规方法的性能，另一方面使计划人员能够确定原始多阶段随机问题的近似解。我们进行了一个实际案例研究，并研究了解决方案质量以及所提出方法的计算性能。