Clustering algorithms for the selection of typical demand days for the optimal design of building energy systems

The optimal design of building energy systems (BES) is a complex problem due to the variety of available generation and storage devices as well as the high-resolution input data required for consider seasonal and intraday fluctuations in the thermal and electrical loads. A common measure to reduce the problem’s size and complexity is to cluster the demands into representative periods. There exist many different algorithms for the clustering, but to the best of our knowledge, no comparison has been made that illustrates which algorithms are the most appropriate for BES optimization problems. Therefore, this paper compares five aggregation methods for reducing full year input data to typical demand days for optimally designing and sizing BES. We consider monthly averaging classification and sophisticated clustering methods such as k-centers, k-means, k-medians and k-medoids for aggregating the heat and electricity demand as well as solar irradiation onto the roof of a single family house and an apartment building. The results show that clustering can significantly reduce the computing times of the optimization problem. Regarding approximation of the input data, the results indicate that k-means and k-medians provide the best approximation by computing a representative rather than choosing an existing day to represent each cluster. Yet, the resulting loss of temporal relationship between each input, leads to large deviations in the BES total costs for k-means and the monthly method compared with k-centers, k-medoids and k-medians. All clustering methods have been able to compute a close to optimal BES configuration, but the BES operation is approximated best with k-centers and k-medoids.