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.  ... Read more

In this thesis, we evaluate the statistical procedure based on the similarity index proposed by Ypma and Ross in 'Determing the similarity between expected and observed ageing behavior'. The function for the similarity index is defined based on the inner product of two probability density functions, assumed to be related to the Weibull distribution. The evaluated statistical test aims to verify whether an observation of censored lifetime data is compliant with a given reference distribution. The test is compared to both the likelihood ratio test and a test using a variation of the similarity index. The comparison between these tests is based on their power function. First, a clear explanation of the complete statistical procedure using the similarity index is provided. Then the observations for which the test can be used are explained further. Its application and small limitations are shown using an example. Then, the two alternative tests are introduced. This will be followed by a theoretical overview of the power comparison method. Finally, the simulation for the power comparison is conducted. The power function is estimated for multiple relevant base cases along a few alternative parameter lines. It can then be concluded that the likelihood ratio test has consistently higher power than the similarity index test. However, the variation of the similarity index demonstrates a varying power, with instances of both higher and lower values than the original similarity index test.
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