电力系统暂态稳定域边界局部近似方法的研究

依据非线性动力系统理论，稳定域边界应由其所有不稳定平衡点的稳定流形的并集构成。该文采用一种新的方法寻找不稳定平衡点的稳定流形，该方法可确定平衡点的稳定流形所满足的偏微分方程。在此基础上，该文运用偏微分方程的二阶近似解，即二次超曲面，来近似不稳定平衡点局部的稳定域边界。与对角化或规范型(normal form)方法相比，该方法避免了求解Jacobian矩阵的全部特征根，从而使计算量显著下降。实际仿真结果表明，该方法取得了较好的局部近似效果，此局部近似结果有助于对稳定域边界形状的分析和研究，且对直接法的结果具有一定的参考和比较价值。

LOCAL APPROXIMATION OF TRANSIENT STABILITY BOUNDARY OF THE POWER SYSTEMS

According to the theory of nonlinear dynamic system, the stability boundary is the union of the stable manifolds of the equilibrium points on the stability boundary. In this paper a new method is adopted to search for the stable manifolds of unstable equilibrium points so that the stable manifolds of equilibrium points are found easily through partial differential equations. Furthermore, local stability boundary of the unstable equilibrium points is approximated by the second order hyper surfaces. Differing from the diagonalizable transformation or normal form, the method avoids solving all eigenvalues of the Jacobian matrixes except the eigenvalue with positive real part, and so the time-consuming computation is reduced greatly. The simulation results prove that the method has a high approximation precision to the local stability boundary. It not only helps to study the shape of stability boundary but also has some significance for the direct stability analysis method.