Power System Steady-state Stability Criteria and the Jacobian of Dynamical Systems

The paper is devoted to the theoretical problems of Power System stability (PSS) and plausible definitions, acceptable to distinguish the steady state stability (SSS) margin in the context of generalized theory of dynamic systems. The true criteria of aperiodic SSS are considered and comprehensively studied. The distinctive term in the form of static resistance factor has been determined, which is the reciprocal value of the static gain of the dynamic system with reference to the observed (controlled) variable deviation, induced by the contingent disturbance.It has been evidently shown, that for an arbitrary dynamic system, represented with differential and algebraic equations (DAE) of any specific structure, the computed value of the Jacobian always coincides with the free term of characteristic equation with an accuracy of a constant multiplying factor.