正规形理论在电力系统稳定性研究中的应用(二)——电力系统主导不稳定平衡点上局部流形的计算

Application of normal form in study of power system stability Part 2:Cal culation of local manifolds on controlling unstable equilibrium point of el ectric power system

应用正规形理论,采用文献[1]给出的两个不同方向的非线性变换,计算了用二元二次的非线性微分方程描述的一个故障后的单机无穷大系统在主导不稳定平衡点上的局部流形,从而得到了该电力系统的稳定边界;介绍了在不稳定平衡点上的局部稳定和不稳定流形对应于电力系统稳定性问题中的物理含义。算例的结果表明,两个不同方向的非线性变换都可以较好地近似原始系统的实际局部流形。

By applying normal form theory and adopting the two nonlinear transformations gi ven in paper [1] ,the local manifolds on the controlling unstable equilibrium points of a po st-fault single-generator power system is calculated and its stability boundar y is obtained.The system is normally described by binary quadratic differential equations.The physical meanings of stable and unstable manifolds on a controll ing unstable equilibrium point in electric power system are introduced.The cal culation results show that the local manifolds are right approximated by the tw o nonlinear transformations with different direction.