电力系统电压稳定与功角稳定的统一分析原理

Theoretical Foundation of Power System Voltage and Angle Stability Unified Analysis

电压稳定与功角稳定只是电力系统稳定分析的两种极端情形。电力系统潮流雅可比矩阵奇异,既是电压稳定临界点,也是静态功角稳定临界点。根据一般非线性方程组的极值分析原理,证明电力系统静态功角稳定与电压稳定的等价关系;基于潮流方程,引入电流辅助变量,提出电力系统分散综合动态等值方法;利用潮流雅可比矩阵所包含的系统动态参数信息,根据非线性电路的动态分析原理,建立电压稳定与功角稳定统一分析的动态分析方法;应用复变电流(电压)的方向微分,研究系统综合动态等值阻抗与负荷静态等值阻抗的关系,提出综合评价电压稳定与静态功角稳定的电阻裕度指标。电阻裕度是将负荷的极限功率单位化,同时将功率–角度特性曲线变换为功率–电阻裕度特性曲线。电阻裕度不仅是一个灵敏度指标,还具有确定的非线性性质。进一步考虑注入系统功率的时间动态特性,有限地推广了电阻裕度在电力系统静态稳定、暂态稳定与动态稳定分析中的在线应用价值。

Voltage stability and angle stability are only two extreme conditions of power system stability analysis. When Jacobian matrix is singular, it＇s not only critical point of voltage stability, but static critical point of angle stability. According to the general principle of extreme value analysis of nonlinear equations, the equivalence relation of static angle stability and voltage stability, was proved. The decentralized dynamic equivalent method was proposed, by introducing current auxiliary variable and flow equations. The unified analysis method of dynamic voltage stability and angle stability was established by using the dynamic parameters in Jacobian matrix and the nonlinear dynamic analysis principle. Through the application of direction differential of complex current （voltage）, the relationship between integrated dynamic equivalent impedance and load static equivalent impedance were studied and the comprehensive evaluation of voltage stability and static angle stability margin index were proposed. Impedance margin means the unitization of limit load power and the transformation of angle curve into power-impedance curve. The impedance margin is not only a sensitivity index, but has good nonlinear properties. Take the dynamic characteristics of injection power into account further; we will promote the online application value of resistance margin in the static stability, transient stability and dynamic stability analysis.