We propose a data-driven approach for propagating uncertainty in stochastic power grid simulations and apply it to the estimation of transmission line failure probabilities. A reduced-order equation governing the evolution of the observed line energy probability density function is derived from the Fokker--Planck equation of the full-order continuous Markov process. Our method consists of estimates produced by numerically integrating this reduced equation. Numerical experiments for scalar- and vector-valued energy functions are conducted using the classical multimachine model under spatiotemporally correlated noise perturbation. The method demonstrates a more sample-efficient approach for computing probabilities of tail events when compared with kernel density estimation. Moreover, it produces vastly more accurate estimates of joint event occurrence when compared with independent models.

翻译：我们提出了一种在随机电网仿真中传播不确定性的数据驱动方法，并将其应用于输电线路故障概率估计。从全阶连续马尔可夫过程的福克-普朗克方程出发，推导出描述观测线路能量概率密度函数演化的降阶方程。该方法通过数值积分该降阶方程生成估计值。针对标量和向量值能量函数，在时空相关噪声扰动下采用经典多机模型进行了数值实验。与核密度估计相比，该方法在计算尾事件概率时展现出更高的样本效率。此外，与独立模型相比，该方法在估计联合事件发生概率时产生了显著更精确的结果。