Lyapunov stability analysis of a synchronous machine with damping fluxes — Part II. Numerical estimation of the critical clearing time by the equivalent critical energy approach

Abstract After showing that the Lyapunov function presented in Part I is the system energy (in particular, the ‘limit value’ V L identifies the system ‘critical energy’), it is pointed out that, in spite of this, the numerical estimates of the critical clearing time are overly conservative. The reason for such a discrepancy is found in the fact that a generator fifth-order model with damping fluxes exhibits a three-timescale behaviour, as a result of which the dynamics of the state variables Ψ f (field flux) and Ψ A (direct damping flux) does not influence the first-swing electromechanical stability. Consequently the ‘interesting’ critical energy turns out to be equal to that of an equivalent synchronous generator represented by a third-order model whose equations are derived from the original ones by a direct reduction. This critical energy is termed the ‘equivalent critical energy’ and, as shown by the numerical application, it allows the determination of fairly accurate estimates of the critical clearing time under various operating conditions.