Multi-period investment pathways - Modeling approaches to design distributed energy systems under uncertainty

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.