Stochastic Programming for Energy Models: A Blended Cross-Scenario Representative Periods Approach

Abstract

In this thesis, we investigate how representative periods can be used as a temporal reduction technique for stochastic programming formulations of large-scale energy models. We specifically apply this to generation expansion planning. The focus is on cost-efficient decisions as well as on robust decisions, especially since the latter is why uncertainty is incorporated in most energy models. For this, we build on recent work that uses instead of traditional clustering methods like $k$-means or $k$-medoids, a method to obtain a convex or bounded conical hull over the periods. We prove that when inter-period constraints are ignored and a perfect hull is found, we can ensure that a feasible solution for the original model exists, obtained from the optimal decision variables of the reduced model. The proof is suitable for both the traditional way of using representative periods in stochastic programming, as for an approach that shares representative periods across scenarios instead of making them scenario-dependent. We show that a greedy implementation of the hull approach can outperform standard clustering methods in terms of costs in small case studies when a valid hull is found. The near-optimal costs can be obtained with a low number of representatives, largely due to the absence of loss of load due to the hull methods. However, in more complex cases, such as a European-scale model with high renewable shares, finding such a hull with the greedy algorithm proves difficult. To address this, we propose adding extreme periods either beforehand or afterwards, and applying a blended weights approach to reduce conservativeness while maintaining feasibility. Our results on small case studies demonstrate that extreme representatives can significantly reduce loss of load, although not always at lower cost when applied to the large European case study. These findings suggest that targeted selection of extremes, a right weighting approach and improved hull approximations offer a promising direction for enabling scalable, robust planning under uncertainty.