Describing the dynamics, distributions, and multiscale relationships in the time evolution of residential building energy consumption

Residential buildings may be described as complex social-technological systems expressing component interdependence and chaotic temporal variability. As such, we characterized the dynamics and multiscale relationships of hourly electricity consumption data for 13 occupied Florida houses from calendar year 2013. Statistical approaches included: (1) exploratory data analyses with distribution-based descriptive statistics; (2) normality testing; (3) spectral and monofractal analyses; (4) multifractal detrended fluctuation analyses (MFDFA) with surrogate testing; and (5) Ward's minimum variance method for hierarchical agglomerative clustering. Results suggested the energy-use patterns were non-normal, nonlinear, and exhibited predominantly anti-persistent fractal complexities. Thus, classical descriptive statistics presuming Gaussian probability density function (PDF) distributions neither well fit, nor well described, the data and their interdependent characteristics. Notably, clusters of comparable houses were categorically and statistically different when using descriptors based on normality (e.g., mean, variance, skewness, kurtosis) versus those based on fractality (e.g., Hurst exponent, multifractal spectrum width). We believe MFDFA statistical outputs may serve as novel indicators of residential building dynamics as they better characterize the complex, nonlinear asset and occupancy interactions and they require no assumptions regarding the PDF distribution shape. We offer guidance on the data management, transformation, parameterization, and interpretation processes necessary to apply MFDFA to whole-house, short-interval, electricity consumption time series data. Multifractal quantification of building performance time series data may be useful on multiple fronts: (1) detecting under-performing households; (2) improving segmentation, targeting, and pre/post analyses of energy efficiency interventions; (3) diagnosing building system failure risks; and (4) improving smart grid supply and load balancing.