基于曲面二次标准型逼近的最近电压稳定临界点求取方法

针对切平面不能准确描述电压稳定极限曲面极限点邻域性质的缺陷,文中提出一种考虑负荷增长方向不确定性的基于曲面二次标准型逼近的两层规划模型,求解最近电压稳定临界点。该方法首先计算初始化负荷增长方向上的电压稳定临界点,并利用Weingarten映射获得该点处极限曲面的主曲率,进而获得极限曲面的二次标准型逼近,最后采用基于信赖域思想的二次规划法迭代搜索最近的电压稳定临界点。所提模型可同时考虑鞍节点分岔和极限诱导分岔两种临界点。对多个IEEE系统及中国东部某实际大区域电网等系统的分析证明了该方法的有效性。分析表明,所提方法具有收敛速度快、鲁棒性好,全局寻优能力强的优点,可快速确定电力系统的电压薄弱区域,并可直接用于大系统分析。

Solving of Closest Critical Point on Voltage Stability Limit Surface Based on Second-order Standard Approximation of Limit Surface

Facing the inability of cut-plane to accurately describe the neighborhood of the critical point on the voltage stability limit surface, a bi-level programming model based on second-order standard approximation of limit surface considering uncertainties of the load increase direction is proposed to solve the the critical point on the voltage stability limit surface. First, the critical point along the original load increase direction is obtained, and the Weingarten mapping is performed to attain the principal curvature of the limit surface at the point. Then the second-order standard approximation near the critical point is obtained. Finally, an iterative process is developed to search for the closest critical point of limit surface based on the trust region algorithm and quadratic programming. Saddle node bifurcation (SNB) and limit induced bifurcation (LIB) are all included in the proposed model. The simulations on IEEE systems and a real system in Eastern China show the validity of the proposed method. And the analysis not only proves the efficiency of the proposed method, but also suggests that the proposed method is fast and robust and have good global search ability, which is able to find the weak area of power system and be utilized in the real large system. This work is supported by the Key Program of National Natural Science Foundation of China (No. 51337005) and National Basic Research Program of China (973 Program) (No. 2014CB23903).