基于扩展方程法的电力系统双参数分岔边界的计算

An extended equations method to compute two-dimensional parameter bifurcations boundary in power systems

通过对电力系统某些模型的研究,发现系统在鞍结分岔(SNB)前会经历Hopf分岔(HB)的失稳,采用Hopf分岔理论研究电力系统的稳定运行问题,能够比较全面地考虑非线性系统的非线性性态,深入揭示系统失稳的机理。然而以往的间接法在计算Hopf分岔点时,每次改变参数都要计算系统雅可比(Jacob ian)矩阵的特征值并判断是否出现一对实部为零的共轭虚根,导致计算量较大。而直接法对初值的要求比较严格。文中引入双参数构造系统的扩展方程求解SNB分岔曲线,并寻找系统的高阶分岔点TB点,由于TB点是SNB曲线与HB曲线的交点,以该点为初始值,采用扩展方程可以直接求解双参数下的Hopf分岔曲线,进而得到系统在双参数下的分岔边界。

By much research on power system models, the system will experience Hopf Bifurcation（HB） before the Saddle-Node Bi- furcation （SNB）. By using Hopf Bifurcation theory to analyze the stability operation of electric power system, the nonlinear characteristics of nonlinear systems can be totally involved and the instability reasons for systems is revealed deeply. While to calculate the Hopf Bifurcation point, the previous methods involve a great deal of computation of the eigenvalues of system＇s Jacobian matrix and decision whether the real parts of the eigenvalues were zero when there exist any changes of the parameters in the system. In this paper, by using two parameters, the extended equations is set up for getting SNB curve and the advanced bifurcation point, TB point. Since the TB point is the intersection point of the SNB curve and the Hopf Bifurcation curve, the Hopf Bifurcation curve of the system can be calculated by setting the TB point as the initial value of the extended equations. Furthermore, the two-dimensional parameter bifurcation boundary of the system can be obtained. This project is supported by National Natural Science Foundation of China（ No. 50337010） and Special Scientific and Research Funds for Doctoral Speciality of Institution of Higher Learning （ No. 200205061004）.