A power system dynamical model in the matrix polynomial description form

This paper proposes an alternative option to model a dynamical power system process. The model is based on a matrix polynomial form. The model can be obtained naturally writing the high order differential equations of some components (e.g. transmission line models modeled by sequences of RLC PI circuits in power systems) or some subsystems which compose the whole system. Another strategy would be by conversion of a known power system dynamical state-space representation. This latter was the option adopted in this paper. The conversion process from a model to another is done by carrying out successive Gaussian eliminations (GE) on an augmented frequency dependent matrix constructed from the state-space model. The equivalence of both approaches are evaluated and compared by accomplishing experiments in two dynamical systems. One of them is composed of RLC PI circuits calculated from the discretization process of transmission lines in the frequency domain. The results considering computation of transfer functions taking into account both methodologies demonstrate the equivalence of models.