Transient Stability Analysis of Electric Power Systems via Lur'e type Lyapunov Function : Part I

Abstract

In this paper, a Lur'e type Lyapunov function derived from the generalized Popov's theorem is applied to the transient stability problem of electric power systems. Also described is the method of evaluating the critical fault clearing time using the Lyapunov function V. On the occasion of the estimation of the critical fault clearing time or the assessment of the transient stability region via the Lyapunov direct method, the determination of the critical value of the Lyapunov function is as important as the construction of the function. In this paper, it is examined what the transient stability region of electric power systems is practically like. It is shown that the degree of the conservativeness of the estimation can be reduced, if Vᵘᶜ, the value of V at the unstable equilibrium point corresponding to the first swing, is used as the critical value instead of the minimum of the values of V at all of the unstable equilibrium points. Two methods of approximately calculating Vᵘᶜ are proposed, and applied to the model systems as numerical examples. Large estimation errors were seen in some cases due to the defect of the Lyapunov function used, which will be overcome in the companion paper.