N-1故障后系统小干扰电压稳定极限点计算

Computation of small disturbance voltage stability limit point of power systems under N-1 contingencies

构建了负荷采用三阶感应电动机并联恒阻抗表示的电力系统短期电压稳定分析数学模型,并推导出负荷增减的表示方法。根据系统小干扰方程状态矩阵特征值为零的特点,提出了计算小干扰电压稳定极限点的数学模型,以求得N-1故障后系统从当前运行状态到电压稳定极限点需增减的负荷。通过对发电机稳态方程中功角的三角函数项引入辅助变量,将极限点计算模型转化为关于未知量的线性或二次函数,进而可采用最优乘子牛顿法计算极限点,以解决极限点处系统稳态方程雅可比矩阵奇异带来的收敛困难。IEEE9节点系统和IEEE39节点系统的计算结果表明该方法能够可靠地收敛到N-1故障后系统的小干扰电压稳定极限点。

The three-order induction motor paralleled with constant impedance model is used to represent the load,and the mathematical model of analyzing the short-term voltage stability of power system is established.The representation of load increasing and shedding is also deduced.Based on the characteristic that the state matrix of small disturbance equations has zero eigenvalue,the mathematical model of computing the small disturbance voltage stability limit point is proposed,and the load need to be increased or be sheded from current state to voltage stability limit point of the system under N-1 contingencies can be computed.By introducing auxiliary variables to represent the trigonometric functions of rotor angle in the steady equations of generators,the mathematical model of computing the limit point is transferred into the linear and quadratic functions of unknown variables,and the optimal multiplier Newton method can be used to compute the limit point,and the problem that the Jacobian matrix of the steady equations of the system is singular at the limit point and results in the convergence difficulty is solved.Computations in the IEEE 9-bus system and IEEE 39-bus system show that the proposed algorithm can converge to voltage stability limit point of the system under N-1 contingencies reliably.