电力系统小干扰稳定性评估的多重谱变换方法

A Multi-Spectral Transform Approach for Assessing Small Signal Stability in Power Systems

针对电力系统小干扰稳定性分析过程中遗漏不稳定特征值的问题,提出了一种求解大规模系统不稳定特征值的多重谱变换方法。该方法首先利用所提出的多重谱变换将全部不稳定特征值映射为主导特征值;在利用Krylov-Schur方法收敛得到全部主导特征值之后,通过逆变换得到相应的不稳定特征值;该方法还揭示了指数变换与位移逆变换以及凯莱变换之间的内在联系。相较于位移逆变换和凯莱变换,多重谱变换方法由于具有类似于指数变换的良好谱特性,从而有利于特征值收敛;同时其又避免了指数变换引起的指数矩阵与向量的乘积,从而具有更高的计算效率和计算精度。在Xingo6u和Xingo3012这两个源于巴西互联电网上的算例分析结果表明,所提出的多重谱变换方法不仅保证了不遗漏不稳定特征值,而且相较于指数变换方法,计算精度提升了约3个数量级,计算耗时减少了90%以上。

To address missing unstable eigenvalues in small signal stability analysis of power systems,a multi-spectral transform method for calculating the unstable eigenvalues of large-scale systems is proposed.Firstly,this method utilizes the proposed multi-spectral transform technique to map all unstable eigenvalues into dominant eigenvalues.Subsequently,the Krylov-Schur method is employed to ensure convergence and obtain all dominant eigenvalues.Finally,the inverse transformation allows for the retrieval of the corresponding unstable eigenvalues.Furthermore,this method establishes the intrinsic relationship between various transforms,including the exponential transform,shift-and-invert transform,and Cayley transform.Compared with the shift-and-invert transform and Cayley transform,the multi-spectral transform exhibits superior spectral performance akin to the exponential transform,facilitating eigenvalue convergence.At the same time,it avoids calculating the multiplication of exponential matrix and vector caused by the exponential transform,thereby having higher computational efficiency and accuracy.Experimental results obtained from the Xingo6u and Xingo3012 system of the Brazilian interconnected power grid demonstrate the effectiveness of this method.Notably,it ensures that unstable eigenvalues are not overlooked,enhances calculation accuracy by about 3 orders of magnitude,and reduces the calculation time by more than 90%compared to the exponential transform method.