Delay margin comparisons for power systems with constant and time-varying delays

Abstract

The paper shows that, for certain classes of power system models, if time-varying delays are replaced with their average value, the small-signal stability analysis returns conservative results, while showing a lower computational burden. The paper first compares, through an exact analytical approach, the delay margin of a second-order electromechanical model with inclusion of constant, square-wave, and Gamma distributed delays. Since the analytical approach is not viable for realistic power system models, the paper also develops a novel general method to calculate the eigenvalues for systems with time-varying stochastic delays that cannot be described by an analytical probability distribution function. These kind of delays are relevant for the study of wide-area measurement systems (WAMSs). The IEEE 14-bus system serves to compare the stability margin and the critical damping ratio of a constant and two WAMS delay models solved with the proposed numerical method.