基于Pade近似的时滞电力系统特征值计算方法

A Method for Computing Eigenvalue of Time-delayed Power Systems Based on Pade Approximation

考虑广域反馈时滞后,电力系统的特征方程含有超越项,试图通过直接求解该方程得到系统的关键特征值变得非常困难。文中利用Pade近似有理多项式来逼近时滞环节,提出了一种计算时滞电力系统部分特征值的方法。将Pade近似有理多项式转化为状态空间表达式并进行平衡化处理,通过与无时滞电力系统和广域阻尼控制器相连接,建立时滞电力系统的线性化模型。根据系数矩阵的稀疏特性,可以利用稀疏特征值算法求解系统的部分特征值。该方法使得沿用常规电力系统小干扰稳定性的特征值分析方法理论和框架来分析时滞电力系统的小干扰稳定性和设计广域阻尼控制器成为可能。2区4机和新英格兰10机39节点算例系统的特征值及其对时滞的灵敏度计算结果表明,该方法能够较准确地求解与时滞系统中动态元件相关的部分特征值,正确求解与时滞环节相关的特征值个数和计算精度与有理多项式的阶数有关。

Transcendental terms appear in the characteristic equaiton of a power system when time delays of wide area feedback signals are considered.This makes it very difficult to obtain critical system eiganvalues via direct solution of the equation.A method for computation of partial eigenvalues of time-delayed power system is proposed by using Pade rational polynomials to approximate the delay terms.The polynomials are firstly transformed into equivalent state-space representations then balanced.Based on interconnections with the original power system without time delay and the wide area damping controllers,the linear model for the time-delayed power system is established.Finally,sparse eigenvalue algorithms can be used to compute partial eigenvalues of the system according to the sparse characteristics of system coefficient matrices.The method makes it possible to analyze power system small disturbance stability and design wide area damping controller by inheriting the conventional method and theoretical framework of eigenvalue.The eigenvalues and their sensitivities with respect to time delay on both the two-area four-machine and the New England10-machine39-bus test systems demonstrate that the method proposed can accurately compute some eigenvalues relating to system dynamic components.The number of correctly solved eigenvalues corresponding to the time delay and their accuracy strongly relates to the order of the Pade rational polynomial.