A Multi-Scale Framework for Deconstructing Residential Energy Consumption Heterogeneity Using Gaussian Mixture Models

Residential energy consumption exhibits substantial behavioral uncertainty and temporal heterogeneity, which pose challenges for demand-side management and residential load profiling. However, existing studies often focus on isolated temporal or spatial scales and predominantly employ hard clustering methods based on geometric distance metrics. To address these limitations, this study proposes a multi-scale residential load profiling framework utilizing the Gaussian Mixture Model (GMM) and nearly three years of hourly electricity consumption data from 13 residential buildings in Vancouver. First, schedule-driven and seasonal variations in residential energy consumption were examined through multi-temporal comparative analyses and paired-sample t-tests. The results indicate statistically significant differences between working-time and non-working-time energy consumption patterns in most buildings (p < 0.001). Second, individual-building clustering was performed to identify long-term intra-building daily load evolution characteristics, revealing 2–5 typical daily profiles across different households. Finally, inter-building clustering identified three representative residential groups characterized by low-energy stable patterns, high-energy intensive patterns, and intermediate commuting-oriented patterns. The average daily energy consumption levels of the three clusters were 13.11 kWh, 36.74 kWh, and 21.61 kWh, respectively. The proposed framework provides a data-driven approach for understanding residential energy-use heterogeneity across multiple scales and offers potential guidance for residential demand-side management and urban low-carbon energy planning.