Attractive ellipsoidal design for robust stabilization of time-delay stochastic power systems under a series of lightning surges

Numerous stochastic external disturbances (such as wind power generation, random loads, line parameter modification owing to wind speed variation, etc.) may have an impact on power systems. Topological changes may also occur for a variety of reasons, one of which is a succession of lightning strikes linked to lines on/off caused by the action of circuit breakers. In this study, new, robust power system stabilizers (PSS) are presented, considering only this type of perturbation and the time delay in states used for feedback. Both instantaneous and delayed state effects are considered in the proposed PSS. A multi-machine linear model is developed, representing stochastic parameter fluctuations and topology changes (Markov jumps). A novel invariant-ellipsoid design is developed in terms of a stochastic version of the Lyapunov- Krasovskii approach using linear matrix inequalities (LMI). The suggested PSS's effectiveness is evaluated on the IEEE two-area multi-machine system.