Derivation of completely controllable and completely observable state models for multimachine power system stability studies†

The object of the present paper is to develop state models for multimachine power system stability studies which are completely controllable and completely observable. They are necessary for any stability studies based on the second method of Lyapunov. Starting from the definition of the degree of a rational function matrix, the minimal realizations for a two- and three-machine power system with uniform and nonuniform damping are obtained and are shown to be completely controllable and completely observable. A generalization for an H-machine power system follows as a natural consequence. Further, the present work provides the theoretical basis for the proper choice of state variables, i.e. relative rotor angles instead of absolute rotor angles as state variables.