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.

中文翻译：

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基于线性多重分数Lévy稳定运动的停电长度预测

在电力系统中，故障中断极大地损害了电力系统的可靠性。因此，一种正确预测停电持续时间的有效方法将显着提高效率。为了解决这个问题，我们提出了一种基于适当随机运动的方法。首先，我们介绍线性多重分数 Lévy 稳定运动（LMLSM）。然后，通过计算全局和局部分形特征，我们表明LMLSM是多重分形的并且具有长程依赖性（LRD）特性。此外，还分析了LMLSM的非高斯特性，这意味着它可以更好地描述随机时间序列中的恒定峰值。进一步利用分数阶Black-Scholes微分方程推导了离散迭代预测模型。最后，基于电网实际故障中断持续时间（FID）数据集进行案例研究，说明所提出的电网可靠性预测方法的有效性。