最近电压稳定临界点的两层规划模型和信赖域算法

考虑了负荷变化的不确定性，提出负荷分布范围的棱锥状模型。建立了求解最近电压稳定临界点的非线性二层规划模型，提出一种求解该问题的信赖域方法。该方法先计算已知负荷增长方向上的电压稳定临界点，然后建立只有上、下界约束的近似模型，基于信赖域方法的思想迭代搜索最近电压稳定临界点，求取临界点时考虑了发电机无功出力的限制。算例分析表明，该算法收敛速度快、鲁棒性好，全局寻优能力强，并可找出系统电压稳定的薄弱区域和母线。

A Bilevel Programming Formulation and Trust Region Approach for Closest Critical Point of Voltage Stability

A new load distribution domain (hyper-pyramid) model is presented for calculating closest critical point of voltage stability considering uncertainties of load change. The nonlinear bilevel programming formulation and the trust region based algorithm are used to search the closest critical point. Firstly, the critical point along a known load change direction is determined, then an approximate formulation with simple upper and lower bounds is built. An iterative process is established to search the closest critical point based on the idea of trust region method. The reactive power limits of generators are considered in calculating the critical points. Case studies show that the proposed method is fast and robust and have good global searching performance. The weak areas and nodes of the system for voltage stability can also be found.