Modeling and Analysis of Residential Electricity Consumption Statistics: A Tracy-Widom Mixture Density Approximation

Residential electricity loads highly fluctuate which makes it challenging to predict and estimate changes and anomalies. This article studies the statistical distribution of the maximum load of residential settlements and proposes a new model that is more reliable than conventional methods to predict extreme events in residential electricity consumption. Specially, a multimodal Tracy-Widom distribution is proposed to characterize the maximum residential electricity consumption data. We also propose a numerical method to approximate the density function of the multimodal Tracy-Widom distribution as opposed to the conventional approach in the literature, where a multimodal normal distribution is utilized. A simulated electricity consumption data set is used to test and validate the proposed methods. The results demonstrate that the multimodal Tracy-Widom distribution is more accurate than conventional methods in modeling residential electricity consumption data. In addition, the numerical results show that residential electricity consumption behavior is determined by certain socioeconomic factors for which correlations with household electricity consumption exist.

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