中文摘要：

运用非线性分岔理论与特征分析法对一个经典3节点电力系统的电压稳定性进行了详细分析。通过逐步增大系统参数Q1，求取系统方程平衡点的雅可比矩阵的特征根，结合特征分析法判定系统的稳定性态，得到了系统运行的2个稳定区间。在此基础上考虑负荷的随机性建立了该系统的随机模型——一个4维随机微分方程组，并运用随机欧拉法对该随机微分方程组进行了数值仿真计算。数值结果表明，当系统运行在稳定边界的一个小邻域内时，负荷的随机扰动造成随机的小幅正向或负向累积，使得系统突然失去电压稳定，失稳模式既可能为霍普夫型，也可能为鞍结型。

英文摘要：

The nonlinear bifurcation theory and the eigenvalue analysis are applied in the voltage stability study of a classical three-bus power system. The Jacobian matrix eigenvalues of system equilibrium equations are obtained by gradual increasing the system parameter Q1 and two stability areas of system are set by eigenvalue analysis, based on which a stochastic model of system is built with the consideration of the randomicity of loads： a set of four-dimensional stochastic differential equations. The numerical simulations using the Euler-Maruyama method illustrate that, the positive or negative accumulation of random load may cause the power system to suddenly lose its voltage stability when it is near the stability boundary, and the voltage collapse may be of Hotel bifurcation or Saddle-node bifurcation type,