标题： 通过稀疏回归的电网系统PDF估计 显示英文标题

标题： PDF estimation for power grid systems via sparse regression

摘要： 我们提出了一种数值方法，用于估计受不确定发电和负荷波动影响的电力系统中感兴趣量（QoI）的概率密度函数（PDF）。 在我们的方法中，发电和负荷波动通过时间相关的自相关随机过程建模，并通过Karhunen-Loève近似用有限集的随机参数来表示。 从随机参数到QoI的映射通过Hermite多项式展开来逼近。 我们提出了一种基于压缩感知的新方法，利用少量实现（采样点）来估计Hermite展开中的系数。 通过迭代旋转识别出的线性变换被引入以提高Hermite表示的稀疏性，从而利用映射的内在低维结构。 因此，与标准最小二乘法相比，所提出的方案显著减少了所需的采样点数量以达到给定的精度。 所提出的方法被应用于估计由自相关随机发电驱动的经典机器系统的相对角速度和母线电压的PDF。 通过Kullback-Leibler散度衡量，使用比基本蒙特卡洛采样所需更少的实现即可获得更准确的PDF估计值。 显示英文摘要

摘要： We present a numerical approach for estimating the probability density function (PDF) of quantities of interest (QoIs) of power grid systems subject to uncertain power generation and load fluctuations. In our approach, generation and load fluctuations are modeled by means of autocorrelated-in-time random processes, which are approximated in terms of a finite set of random parameters by means of Karhunen-Lo\`{e}ve approximations. The map from random parameters to QoIs is approximated by means of Hermite polynomial expansions. We propose a new approach based on compressive sensing to estimate the coefficients in the Hermite expansions from a small number of realizations (sampling points). Linear transforms identified by iterative rotations are introduced to improve the sparsity of the Hermite representations, exploiting the intrinsic low-dimensional structure of the map. As such, the proposed approach significantly reduces the required number of sampling points to achieve a given accuracy compared to the standard least squares method. The proposed approach is employed to estimate the PDF of relative angular velocities and bus voltages of systems of classical machines driven by autocorrelated random generation. More accurate PDF estimates, as measured by the Kullback-Leibler divergence, are achieved using fewer realizations than required by basic Monte Carlo sampling.