电力系统暂态稳定域边界特征不变流形计算

Calculation of Characteristic Invariant Manifolds on the Boundary of Transient Stability Region in Power Systems

电力系统暂态稳定边界可信域的研究对确定近似边界的适用范围有十分重要的意义。特征不变流形的计算是可信域求解的关键步骤之一。实际上,特征不变流形是位于稳定边界上一些特殊的低维不变流形,与高维不变流形相比,其高阶Taylor级数解求解容易。该文提出一种系统的求解特征不变流形的方法。该方法利用与不变流形相关的奇异偏微分方程组的特点,借助符号运算软件包,将不变流形Taylor级数展开各项系数的求解简化成对一组线性方程组的求解。理论上该方法不受系统维数和电力系统复杂模型的限制。文中通过WSCC4机11节点电力系统经典模型算例,进行相关计算仿真,结果验证了该方法的正确性和有效性。

The study of credible region plays an important role to assess the valid range of the transient stability approximate boundary. Calculation of characteristic invariant manifolds （CIMs） is one of the major steps in obtaining the credible region of the approximate boundary. The characteristic invariant manifolds are some special low-dimensional invariants on the stability boundary. Their Taylor coefficients can be calculated more rapidly than those of the high-dimensional ones. In the paper, a systematic method is given for computing the coefficients of the Taylor series expansions of the invariant manifolds which are associated with some singular partial different equations （PDEs） by resolving a group of linear equations easily with the aid of a symbolic software package. Theoretically the proposed method is not constrained by the dimension number or the complex modeling of power systems. Calculation and simulation results of the WSCC 4-generator 11-bus test system with classical modeling verify the correctness and efficiency of the theoretical prediction.