基于随机矩阵理论的电网状态分析与扰动定位方法

随着电力技术的不断发展,电网的规模和复杂程度在不断增加,导致相应的电力数据也在以指数级的速度增加。传统的模型法无法充分利用历史和实时数据,同时具有不可避免的假设与简化,而以数据为驱动的随机矩阵理论方法不依赖于具体的机理建模。文中首先介绍了大维统计分析,结合经典多元统计分析的局限,分析了随机矩阵原理的重要作用,重点介绍了单环定理和线性谱统计量的概念。然后,引出了高维统计指标,即文中使用的平均谱半径。结合已有的知识体系分析了随机矩阵理论的应用基础和数据来源,给出了电网状态分析的具体思路,提出了基于电压数据的电网扰动定位方法。最后,通过算例的验证,证明了所提方法的有效性。

State Analysis and Disturbance Positioning Method of Power Grid Based on Random Matrix Theory

With the continuous development of power technology, the scale and complexity of power grid are constantly increasing. It results in corresponding power data increasing exponentially. The conventional model method can not make full use of historical and real-time data, and has inevitable assumptions and simplifications. However, the random matrix theory method driven by data does not rely on specific mechanism modeling. This paper firstly describes large dimensional statistical analysis and analyzes the important role of random matrix principle with consideration of the limitations of classical multivariate statistical analysis. Then the concepts of single ring theorem and linear spectral statistics are emphatically introduced. The high-dimensional statistical index is derived, i.e., the mean spectral radius. Combined with the existing knowledge system, the application basis and data sources of the random matrix theory are analyzed, and the concrete idea of power grid state analysis is given. Thereby the disturbance positioning method of power grid based on voltage data is proposed. Finally, the effectiveness of the method is verified through several examples.