A novel entropy-based method for quantifying urban energy demand aggregation: Implications for urban planning and policy

Urban energy demand aggregation (UEDA) is a key aspect of urban sustainability, as it can help to improve the energy efficiency of urban systems and reduce their environmental impacts. However, UEDA is a challenging task, as it involves aggregating heterogeneous and diverse energy demands of individual buildings into a collective demand at a given spatial scale. This paper proposes a novel entropy-based method for UEDA that quantifies the information loss or distortion resulting from this aggregation process. The method also identifies the optimal spatial scale for UEDA that minimizes information loss or distortion, and evaluates the quality and reliability of UEDA results using entropy-based metrics. We apply the method to a case study of Chicago, where we estimate and analyze the energy demand of buildings at 10 spatial scales, ranging from 1.5 km to 15 km, and for different types of energy sources. We calculate the entropy for each spatial scale and energy source, and compare it with building characteristics and ZIP codes. We also assess the quality and reliability of UEDA results using entropy-based metrics, such as information gain ratio and normalized mutual information. Our results show that different spatial scales reveal different patterns and relationships of energy demand, and that choosing an appropriate scale can enhance the accuracy and efficiency of UEDA. Our results also show that there is an optimal spatial scale for UEDA that balances information preservation and reduction, and that this scale may vary depending on the type of energy source and the urban context. Our findings contribute to the field of UEDA and urban sustainability by developing a novel perspective on urban energy dynamics, revealing the complexity and diversity of urban systems, such as population, land use, transportation, and energy demand.