Geometrical Structure of Constraint Manifold in Power System Differential-Algebraic Model

Fundamental concepts in power system differential- algebraic equations (DAEs) model, like singular point and multiple energy function sheets defined on constraint manifolds, are studied. By the example of a two-generator single-load three-bus 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 DAEs model, is verified by small signal stability analysis, structure preserving energy function method and time domain simulation method. The reason why normal simulation method cannot find this equilibrium point is given. Several important findings, such as the essential differences in power system DAEs model and its singular perturbation model, inherent conservation of structure preserving energy function method in some scenarios, the relationship between singularity and system model and loading condition, are discovered.