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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. [Display omitted] • A power system linearized model is developed with stochastic external disturbances. • A new sufficient condition is developed for a time-delay stochastic power system. • Utilized the Attractive Ellipsoid Method for selecting controller pole locations. • The proposed power system stabilizers used rotor speed variation for feedback. [ABSTRACT FROM AUTHOR]

We study the behaviour of stochastic discrete-time models controlled by an output linear feedback during a tracking process. The controlled system is assumed to be nonlinear satisfying the global ‘quasi-Lipschitz’ condition and subjected to stochastic input and output disturbances. Two gain matrices (in a feedback and in an observer) define an ‘averaged’ ellipsoid in the tracking-error space where all system's trajectories arrive ‘with probability one’. The selection of the ‘best’ gain matrices is realised numerically by application of the robust attractive ellipsoid method with the linear matrix inequality technique application. The suggested approach is illustrated by designing of a robust tracking controller for a benchmark example in the presence of stochastic noises both in the state dynamics and in the output observations. [ABSTRACT FROM AUTHOR]

• A Markov jump modeling for power system under a series of lightning stokes+stochastic external independent disturbances which are admitted to have any distribution with bounded second moment. • Designing a state estimator to generate the missing states when both the dynamic of states model and measurable outputs are disturbed by stochastic noise. • Developing a new output feedback controller based on the AEM to obtain the controller-observer gain matrices: before the AEM has never been applied to stochastic models with jumping parameters. Power systems are subject to stochastic fluctuations which can be classified as topological or parametric. This paper models the random topological changes due to a series of lightning strokes hitting a transmission line (associated with open/reclose of circuit breakers) in a power system as a Markov jump system. Whereas the line reactance (depending on the phase conductors spacing) changes due to the random wind speed fluctuations, are represented as a stochastic external disturbances. A novel excitation control for a stochastic power system is developed. The optimal two-controller and observer gains are designed based on the attracting ellipsoid method and the linear matrix inequalities (LMI) optimization. The effectiveness of the proposed control is tested on a multimachine system. [ABSTRACT FROM AUTHOR]