电力系统微分代数模型的奇异性和多能量函数面

研究了电力系统微分代数模型的奇异性和定义在约束流形上的能量函数面等，将抽象的概念在简单的2机单负荷3节点系统中以图形形象地说明，考察了该系统在恒功率负荷模型和一种动态负荷模型下的代数约束曲面、奇异点、多能量函数面、平衡点等随系统负载的变化情况。采用小扰动稳定性分析法、结构保持能量函数法和时域仿真法证实了该小系统在恒功率负荷模型下存在非正常运行点的稳定平衡点，并解释了一般时域仿真法不能处理该平衡点的原因。所得研究成果揭示了微分代数模型与奇异扰动模型的本质区别、奇异性与系统模型和系统负载的联系、结构保持能量函数法可能具有的内在保守性等，这对深入理解电力系统微分代数方程模型的拓扑结构、结构保持能量函数法和暂态电压稳定及其与功角稳定的关系具有一定的价值。

Singular Point and Multiple Energy Function Sheets in Power System Differential-algebraic Model

Fundamental concepts in power system differential-algebraic equations (DAE) model, like singular point and multiple energy function sheets defined on constraint manifolds, are studied. By the example of two-generator single-load three-node system with constant power load model and a kind of dynamic load model, these abstract concepts are depicted visually. The influence of system load variation on algebraic constrained surface, system singular point, multiple energy function sheets and equilibriums are revealed. The stability of pseudo-stable equilibrium, which is another stable equilibrium besides normal stable equilibrium in DAE model, is verified by small signal stability analysis, structure preserved energy function method and time domain simulation method. The reason of why normal simulation method cannot find this equilibrium point is given. Several important findings, such as the essential difference between power system DAE model and its singular perturbation model, inherent conservation of structure preserved energy function method in some scenarios, the relationship between singularity and system model and loading condition, are discovered in the paper. These conclusions are helpful for understanding the essence of power system differential-algebraic model, structure preserved energy function method, transient voltage stability and its relationship to angle stability.