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Electric load forecasting is increasingly important for the industry. This study addresses the load forecasting based on the discrete Fourier transform (DFT) interpolation. As the most common analysis method in the frequency domain, the conventional Fourier analysis cannot be directly applied to prediction. From the perspective of time-series analysis, electric load movement influenced by various factors is also a time-series, which is usually subject to cyclical variations. Then with periodic extension for the load movement, a forecasting approach based on the DFT interpolation is proposed for predicting its movement. The proposed DFT interpolation prediction model is applied to experiments of forecasting the daily EUNITE load movement and annual load movement of State Grid Corporation in China. The experimental results and analysis show potentiality of the proposed method. Performance comparisons indicate that the proposed DFT interpolation model performs better than the three commonly used interpolation algorithms as well as the classical autoregressive (AR) model, the ARMA model, and the BP-artificial neural network (ANN) model on the same forecasting tasks.

The current paper presents a data-driven detrending technique allowing to smooth complex sinusoidal trends from a real-world electric load time series before applying the Detrended Multifractal Fluctuation Analysis (MFDFA). The algorithm we call Smoothed Sort and Cut Fourier Detrending (SSC-FD) is based on a suitable smoothing of high power periodicities operating directly in the Fourier spectrum through a polynomial fitting technique of the DFT. The main aim consists of disambiguating the characteristic slow varying periodicities, that can impair the MFDFA analysis, from the residual signal in order to study its correlation properties. The algorithm performances are evaluated on a simple benchmark test consisting of a persistent series where the Hurst exponent is known, with superimposed ten sinusoidal harmonics. Moreover, the behavior of the algorithm parameters is assessed computing the MFDFA on the well-known sunspot data, whose correlation characteristics are reported in literature. In both cases, the SSC-FD method eliminates the apparent crossover induced by the synthetic and natural periodicities. Results are compared with some existing detrending methods within the MFDFA paradigm. Finally, a study of the multifractal characteristics of the electric load time series detrendended by the SSC-FD algorithm is provided, showing a strong persistent behavior and an appreciable amplitude of the multifractal spectrum that allows to conclude that the series at hand has multifractal characteristics.

Multifractal detrended fluctuation analysis (MF-DFA) method is applied to analyze the daily electric load time series. The results of the MF-DFA show that there are three crossover timescales at seven days, 15 days and 365 days approximately in the fluctuation function. Also we find that these fluctuations have multifractal nature with long range correlation behavior. The multifractal singularity spectrum of the daily electric load series has been fitted by the quadratic function model. Comparing the MF-DFA results of the original load series with those of shuffled and surrogate series, it concludes that the multifractal characteristics of the daily electric load time series is due to both broadness of the probability density function and long-range correlation, and the long-range correlation is dominant.