Combining State-Based Clustering and Dynamic Time Warping for the Analysis of Photovoltaic–Building Energy Interactions

This paper investigates the dynamic interaction between photovoltaic (PV) generation and building electricity demand with a focus on temporal alignment. A combined framework integrating state-based clustering and Dynamic Time Warping (DTW) is proposed to jointly analyze instantaneous operating states and time-dependent profile similarity. High-resolution (15 min) data from a 50 kWp building-integrated PV system supplying an administrative university building were analyzed for March 2025. Unsupervised k-means clustering was applied in the production–consumption state space to identify typical operating regimes, while DTW was used to compare daily PV generation and load profiles accounting for temporal shifts. The results show that days classified as similar based on instantaneous energy states may exhibit substantially different temporal structures that remain invisible in state-based analyses. To assess the practical relevance of temporal similarity, DTW distances were related to daily energy performance indicators. No significant relationship was observed between DTW distance and the self-consumption ratio under high-load conditions; however, a strong and statistically significant correlation (Pearson r = −0.60, p < 0.001; Spearman ρ = −0.53, p < 0.01) was found between DTW distance and a temporal overlap index quantifying the fraction of building load occurring during the PV-active period. The authors demonstrate that the applied DTW algorithm identifies temporal mismatches that have a measurable impact on energy metrics directly linked to load–generation coincidence. These findings confirm that temporal alignment constitutes an independent and operationally meaningful dimension of PV–building energy interaction that cannot be fully captured by state-based or energy-aggregated indicators alone.