延拓法追踪电力系统机电稳定模型中的二维参数分岔边界

将延拓法应用于追踪电力系统微分-代数联立方程模型的平衡解曲线,并从计算所得的分岔点出发,将延拓法推广应用于求解描述微分-代数联立模型中的鞍结点分岔(SNB)和霍普夫分岔(HB)的非线性代数方程组.这些代数方程组不仅在原理上可适合应用延拓法来计算系统中任意二维参数的分岔边界,而且在形式上保存了电力系统稳定分析中的数据结构的稀疏性.同时,该方程包含系统的临界特征值和右特征向量等特征结构信息,因此,在追踪局部分岔边界的二维参数时,也能获得系统的临界特征信息.最后,以一多机电力系统为例,验证了该方法是可行的.

Continuation Method to Trace Two-parameter Local Bifurcation Segment in Power Systems Electro-mechanical Stability Model

The continuation method was applied to trace the equilibrium curve of power system differential-algebraic equations (DAEs) model, then from the calculated bifurcation value is was extended to solve the nonlinear algebraic equations that express the saddle-node and Hopf bifurcations occurred in DAEs. These algebraic equations that express the bifurcations not only are fit for calculating the bifurcations segment for any two-dimension parameter space in principle, but also keep the sparsity of the data structure in the analysis of power system dynamics in the form. Meantime, the information of the power system eigenproperty, such as the critical eigenvalue and its right eigenvector, is given during the calculating of the segment as by-product by this method. The method was applied in a multi-machine power system example to demonstrate its capability.