基于延拓法的电力系统稳定模型中二维参数局部分岔边界的计算

CONTINUATION METHOD TO COMPUTE TWO-DIMENSIONAL PARAMETER LOCAL BIFURCATIONS BOUNDARY IN POWER SYSTEM STABILITY DIFFERENTIAL-ALGEBRAIC EQUATION MODEL

该文提出表示微分-代数模型中的奇异性、鞍结点和霍普夫分岔的代数方程以便应用延拓法来求解获得二维参数的分岔边界。该方程保留了电力系统稳定微分-代数模型的形式不变,也未涉及到矩阵求逆或行列式值的计算,同时该方程也具有直接法计算分岔时速度快的优点。其缺点是方程的维数增加了。应用所提方法计算了一简单电压稳定和一多机电力系统稳定模型中的二维参数局部分岔边界,并和实域仿真进行比较,结果表明该方法是准确可行的。

Based on two numerical methods used in bifurcation analysis, this paper proposed a set of algebraic equations that could be solved by continuation method to calculate two-dimensional singularity induced, saddle-node and Hopf bifurcations boundary in differential- algebraic equations (DAE). These algebraic equations keep the form of power system stability DAE model unchanged, also they need neither to inverse matrix nor compute the determinant, in the meantime they have the same advantage of rapid convergent speed as the direct method. The drawback is that their dimension is increased.. The method was applied in a simple voltage stability power system and a multi-machine power system to calculate their two-dimensional parameter local bifurcation boundary The results are checked with those obtained by time domain simulation method to illustrate its capability and accuracy.