Application of a Cyclic Stochastic Process Model for Analyzing Electricity Consumption

Abstract

The accuracy of electricity consumption forecasting is a critical factor for the efficiency of modern power systems; however, traditional approaches rely on the assumption of deterministic seasonality, neglecting the stochastic variability of cyclic parameters. The objective of this study is to validate a mathematical model of electricity consumption as a cyclical random process to adequately describe the stochastic nature of cyclic fluctuations. The paper employs the mathematical framework of cyclical random processes and conducts a statistical analysis of real-world hourly electricity consumption data acquired from residential smart meters. A model is proposed that enables the structural modeling of the randomness inherent in the cycle parameters themselves (amplitude and phase), in contrast to existing approaches that only model fluctuations around a fixed cycle. Empirical analysis confirmed periodic variations in mathematical expectation, variance, and higher-order moments, thereby demonstrating the cyclical nature of the process and the inadequacy of traditional stationary models. The correlation analysis revealed distinctive peaks in the autocovariance function, indicating the system's "memory" of its diurnal cycle. The results hold practical significance for enhancing forecasting accuracy in power systems and can be adapted for the analysis of other cyclic processes across various domains