概率潮流问题的耦合Karhunen-Loève和各向异性稀疏网格插值法
A Coupled Karhunen--Loève and Anisotropic Sparse Grid Interpolation Method for the Probabilistic Load Flow Problem
摘要：
在传统的潮流分析中，一个关键的假设是输入变量，即，发电机输出和客户需求在时间上是固定的，并且相关联的响应没有可变性。然而，这种假设不再有效，因为采用可再生能源给现代电力系统增加了更多的可变性和不确定性。解决这些问题是概率潮流（PLF）问题的定义。PLF问题的挑战在于处理高维输入不确定性和潮流方程的非线性。解决这些问题的最直接的方法，但以计算时间为代价，是执行蒙特卡罗方法。然而，这项工作解决了这些问题-准确性，高维性和计算时间-与耦合Karhunen-Loève（KL）扩展和各向异性稀疏网格算法。所提出的方法实现和测试的IEEE 118总线测试系统和现代化版本的IEEE可靠性测试系统-1996，可靠性测试系统-电网现代化实验室联盟（RTS-GMLC）。194维的情况下，结果显示减少计算时间相比，10,000样本的蒙特卡罗方法给出了一个约束的平均值和标准偏差误差。
英文摘要：
In the traditional load flow analysis, a key assumption is that the input variables, i.e., generator output and customer demand, are fixed in time and the associated response has no variability. This assumption, however, is no longer valid as the adoption of renewable energy resources add more variability and uncertainty to the modern electrical system. Addressing these concerns is the definition of the Probabilistic Load Flow (PLF) problem. The challenge of the PLF problem lies in handling high-dimensional input uncertainties and the non-linearity of the load flow equations. The most straightforward way to address these problems, but at the cost of computational time, is to perform a Monte Carlo method. This work, however, solves these problems -- accuracy, high-dimensionality, and computational time -- with a coupled Karhunen-Loève (KL) expansion and Anisotropic Sparse Grid algorithm. The proposed method is implemented and tested on the IEEE 118-bus test system and a modernized version of the IEEE Reliability Test System - 1996, the Reliability Test System - Grid Modernization Lab Consortium (RTS-GMLC). Results for the 194-dimensional case show a decrease in computational time when compared to the 10,000 sample Monte Carlo method given a bound on mean and standard deviation error.
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