两种负荷裕度对控制参数灵敏度求解方法研究

A Study on Two Method for Computing the Sensitivity of Loading Margin to Voltage Stability with Respect to Parameters

鞍结型分岔和极限诱导分岔是与电压崩溃密切相关的两种常见分岔类型。在两种分岔点处,负荷裕度对控制参数的灵敏度计算,可以从左特征向量和等价线性方程组两个角度进行推导。左特征向量乘子法首先需要求解出雅克比矩阵在分岔点处零特征根对应的左特征向量,再进行一定的数学运算获得灵敏度。等效线性方程组法可以直接通过等效的扩展线性方程组求解,无需求解左特征向量。详细分析和推导了两种静态电压稳定裕度对控制参数的灵敏度求解方法,并且理论上分析证明了两种灵敏度求解方法的等价性。IEEE9仿真结果验证了两种求解法的有效性以及两者的等价性。

Saddle-node bifurcation and limit-induced bifurcation are closely related with voltage collapse. The sensitivity of loading margin to voltage stability with respect to parameters can be derived by left eigenvectors multiplier method or equivalent linear equations method. The former method needs to compute the left eigenvector associated with the zeros eigenvalue of power flow Jacobian matrix, evaluated at critical point. And the sensitivity can be derived with left eigenvector by additional computation. The latter method can directly compute the sensitivity. This paper analyzes and deduces the two methods in detail, and demonstrates the equivalence of the two methods. Numerical results with IEEE9 bus test system verify the validity of the two methods and equivalence of the two methods.