电力系统中的鞍结分叉和霍普夫分叉现象分析

简要介绍了鞍结分叉和霍普夫分叉的基本概念及发生机理。采用发电机经典二阶模型和第一类动态负荷模型,建立了描述系统动态行为的微分-代数方程组。利用延拓法追踪出了系统平衡解流形,搜索出了平衡解流形上存在的分叉点,分析了鞍结分叉和霍普夫分叉发生时的特征值演化情况。基于时域仿真方法,验证了数值计算结果的正确性。分析结果表明:电力系统中存在着鞍结分叉和霍普夫分叉现象。鞍结分叉和电压单调失稳有关,霍普夫分叉和电压振荡失稳有关。

Phenomenon of Saddle-node Bifurcation and Hopf Bifurcation in Power Systems

Briefly describes the basic concepts and mechanism of the saddle-node and Hopf bifurcation.Use the classical second-order model of generator and the first type of dynamic load model,establish differential-algebraic equations which can describe the dynamic behavior of the system.Trace out the equilibrium solution manifold by using the continuation power flow method,search out the saddle-node and Hopf bifurcation points,and analyze the evolution of the eigenvalues when saddle-node bifurcation and Hopf bifurcation occurs.Base on the time-domain simulation method to verify the correctness of the numerical calculation results.Analysis results show that：Saddle-node bifurcation and Hopf bifurcation phenomenon exist in power systems.There is a strong connection between saddle-node bifurcation and the voltage monotonic instability,and Hopf bifurcation has much more to do with the voltage oscillation instability.