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Power system stability is greatly affected by two types of stochastic or random disturbances: (1) topological and (2) parametric. The topological stochastic disturbances due to line faults caused by a series of lightning strikes (associated with circuit breaker, C.B., opening, and auto-reclosing) are modeled in this paper as continuous-time Markov jumps. Additionally, the stochastic parameter changes e.g., the line reactance, are influenced by the phase separation, which in turn depends on the stochastic wind speed. This is modeled as a stochastic disturbance. In this manuscript, the impact of the above stochastic disturbance on power system small-disturbance stability is studied based on stochastic differential equations (SDEs). The mean-square stabilization of such a system is conducted through a novel excitation control. The invariant ellipsoid and linear matrix inequality (LMI) optimization are used to construct the control system. The numerical simulations are presented on a multi-machine test system. [ABSTRACT FROM AUTHOR]

This work concerns the robust stabilization of a class of "Quasi- Lipschitz" nonlinear uncertain systems governed by stochastic Differential Equa- tions (SDE) subject to both multiplicative and additive stochastic noises mod- eled by a vector Brownian motion. The state-vector is admitted to be non- completely available, and be estimated by a Luenberger-type filter. The stabi- lization around the origin is realized by a linear feedback proportional to the current state-estimates. First, the class of feedback matrices and filter matrix- gains, providing the boundedness of the stochastic trajectories with probability one in a vicinity of the origin, is specified. Then a corresponding ellipsoid, con- taining these trajectories, is found. Its"size" (the trace of the ellipsoid matrix) is derived as a function of the applied gain matrices. To make this ellipsoid"as small as possible" the corresponding constrained optimization problem is suggested to be solved. These constraints are given by a system of Matrix In- equalities (MI's) which under a specific change of variables may be converted into a conventional system of Bilinear Matrix Inequalities (BMI's). The last may be resolved by the standard MATLAB toolboxes such as "penbmiTL, Tomlab toolbox". Finally, a numerical example, containing the arctangent- type nonlinearities, is presented to illustrate the effectiveness of the suggested methodology [ABSTRACT FROM AUTHOR]