A discrete time-varying grey Fourier model with fractional order terms for electricity consumption forecast

Accurate electricity consumption forecast plays an important role in managing and operating a country’s power system and is a challenging task due to the data exhibiting the mixture characteristics of trend, periodicity and randomness. To accurately describe the dynamic changes of seasonal fluctuations of electricity consumption, a novel discrete time-varying grey Fourier model with fractional order terms is proposed by coupling Fourier functions with fractional order time-varying terms, as the grey action, to fit the amplitude variations hidden in seasonal pattern and improve the fitting and forecasting accuracy. Moreover, the mechanism and properties of the proposed model are discussed. Then the optimal fractional order is determined by the Dingo Optimization Algorithm (DOA) and the optimal Fourier order is selected by the hold-out method to enhance the robustness of the model. Subsequently, the results of designed experiments based on Monte-Carlo method testify the validity of the Fourier order selection method and the proposed model. Finally, this model is applied to predict the monthly residential electricity consumption of China from 2015 to 2022. The results indicate that the proposed model captures the dynamic amplitude variations of the time series and has better prediction performances than other benchmark grey prediction models and non-grey prediction models.