On the prediction of power outage length based on linear multifractional Lévy stable motion

In the power system, failure interruption hugely compromises the power system reliability. Therefore, an efficient method to correctly predict how long the power outage last would significantly improve the efficiency. To address this problem, we propose a method based on a suitable stochastic motion. First, we introduce linear multifractional Lévy stable motion (LMLSM). Then, by computing the global and local fractal characteristics we show that the LMLSM is multifractal and possesses the long-range dependence (LRD) property. Besides, the non-Gaussian characteristics of the LMLSM are analyzed, which means it can better describe the constant peak values in the stochastic time series. Furthermore, a discrete iterative prediction model is derived with fractional Black-Scholes differential equation. At last, a case study is provided based on the real failure interruption duration (FID) dataset in the power grid, by illustrating the validity of the proposed prediction method for power grid reliability.