Optimizing capacity expansion modeling with a novel hierarchical clustering and systematic elbow method: A case study on power and storage units in Spain

To reduce the computational complexity of Capacity Expansion Models, the planning horizon must be simplified into representative time-periods. Also, to accurately model the expansion of power and storage units, these representative time periods must reveal the mid-term dynamics of the planning horizon. In this paper, a novel hierarchical clustering algorithm is presented that retains the chronology of the original data in creating representative time periods. The proposed algorithm, first, determines the optimal number of clusters with a modified elbow method, enhanced with a stopping criterion to prevent it from running uselessly. The designed stopping criterion works based on percentage variance and runtime to determine the number of clusters systematically. Then, the proposed clustering algorithm employs a novel selection strategy based on the Euclidean distance, k-Medoid, and k-Means to determine the most proper representative vector in each cluster. In this way, it reduces the computational time of capacity expansion models while maintaining the accuracy of final answers. To evaluate its performance, the proposed algorithm is tested on energy data, including demand, photovoltaic, wind, and hydrogen generation, across hourly, daily, and weekly time periods. Also, the performance of the proposed clustering algorithm in selecting the number of clusters and clustering is compared with the results of some well-known methods on accuracy and runtime metrics. Numerical results show that the proposed clustering method selects a more appropriate number of clusters in less computational time than other systematic approaches. Moreover, findings on clustering show that the proposed algorithm achieves the highest accuracy on weekly and daily time periods compared to well-known clustering methods, with the error rate of 118 % and 52 %, respectively. Furthermore, implementation results show that the proposed clustering reduces the computational time of capacity expansion models by 84.81 % and 55.91 % on weekly and daily time periods. Additionally, this study assesses the robustness of the clustering methods through a sensitivity analysis, which shows that the proposed algorithm outperforms the others in this metric, as well.