Flow-Oriented Dynamic Time Warping for Characterizing Temporal Relationships in PV Building Energy Flows

Understanding how photovoltaic generation is distributed between local use, surplus export, and grid import requires analysis of the temporal structure of individual energy flows rather than only aggregate PV–load matching. This study proposes a flow-oriented Dynamic Time Warping (DTW) framework based on three physically interpretable relationships: self-consumption versus PV production (SC–PV), surplus export versus PV production (EXP–PV), and grid import versus total consumption (IMP–LOAD). The method was applied to 30 complete 24-h profiles recorded at 15-min resolution in a university building equipped with a 49.7 kWp rooftop PV system. SC–PV exhibited the lowest median normalized DTW distance (DTW* = 0.0186), EXP–PV the highest (0.4468), and IMP–LOAD an intermediate value (0.2323) with the greatest day-to-day variability. The differences among the three components were highly significant (Friedman X22=54.60, p<0.001, Kendall’s W = 0.91). Direct comparison with conventional PV–LOAD DTW* showed markedly different day-by-day associations for SC–PV (ρ = −0.523), EXP–PV (ρ = −0.006), and IMP–LOAD (ρ = −0.760), demonstrating that a single PV–LOAD distance does not retain the flow-specific information captured by the proposed representation. Cross-correlation provided complementary evidence, with a median optimal lag of zero for all three flow pairs. The proposed framework therefore provides a compact diagnostic representation of local PV utilization, surplus formation, and residual grid dependence without implying causal relationships.