电力系统非线性模式分析方法的比较

该文对2种电力系统非线性模式分析方法--模态级数法和正规形法进行比较。定性比较模态级数法和正规形法的2阶参与因子。在正规形法原有指标的基础上定义一个非线性指标，并以4机2区系统的算例验证该非线性指标的有效性。为比较模态级数法、正规形法和线性模式分析法所得解对时域仿真解的逼近程度，定义一误差指标，并在4机2区系统中做相关分析。发现模态级数法和线性模式分析法的有效性均不受系统共振的影响，而正规形法的有效性受系统共振情况的影响较大，在系统的2阶共振点附近，其有效域面积较小。通过延长故障的持续时间来改变系统的非线性程度，发现随着系统非线性的增强，模态级数法的误差及其增加速度都是最小的，正规形法次之。

Comparison Between Methods for Power System Nonlinear Modal Analysis

Two methods for power system nonlinear modal analysis, i.e., modal series method and normal form method, are compared. Two types of second-order participation factors of modal series method are proposed and qualitatively compared with that of normal form method. A nonlinearity index for normal form method is defined based on the original index, and its validity is verified by the case studies in two-area four-generator power system. To evaluate the precision of solutions obtained by modal series method, normal form method and linear modal method, an error index describing the approximation to the nonlinear simulation is defined and then applied to the same system. It is found that the validity of modal series method and linear modal method is not influenced by the second-order resonance condition, which has a great influence on normal form method. When the operating condition is near the second-order resonance condition, the valid area of normal form method is quite small. The degree of system stress can be increased by changing the fault duration. It is found that as the system stress increases, the error index and its growing speed of modal series method are the smallest, and that of normal form method take second place.