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.