Modeling and Forecasting Nonstationary Voltage Fluctuation Based on Grey System Theory

Conventional voltage fluctuation, which causes light to flicker, is modeled by some sinusoidal signals which are modulated in voltage amplitude. In this approximate model, amplitude fluctuation is assumed to be stationary and deterministic. Field measurements and practical records show nonstationary treatments of the voltage fluctuation. Accurate modeling and forecasting of the envelope signal is necessary for power-quality enhancement and compensative devices control. In this paper, after extracting a voltage envelope by enhanced phase-locked loop, the envelope signal is filtered and uniformly sampled. Hence, the discrete-time envelope signal can be considered as a time series. Grey system theory-based models, such as GM(1,1) and the rolling Grey model are utilized to model and predict the time series. To increase the accuracy of resulting models, residuals are employed for the correction process. For this purpose, the Fourier correction Grey Model (FGM) is used to improve precision of GM(1,1). Since the number of used data in a Grey model is rather small, an iterative strategy is proposed to model and predict the entire envelope signal. In other words, the Grey models, which are local predictors, are modified to apply them as global ones by the proposed iterative method. The simulation results show that modified Grey models have high performances both on model fitting and forecasting. Among these Grey models, the precision of FGM is the highest. Also, the effect of datum numbers on the accuracy of models is investigated. The results confirm that the smaller number of data, the higher precision is yielded.