Wind power has had a significant impact on power system stability due to its stochastic nature. In this paper, the impact of stochastic excitation on power-system small-signal stability is investigated based on stochastic differential equation (SDE) theory. The mechanical power input of an asynchronous wind turbine is considered as a stochastic excitation to the system and the system state equation is formulated based on SDE. The mean stability and mean square stability of such a system are demonstrated, and the steady-state expectation and covariance of the system state variables are obtained by mathematical deduction. The numerical simulations are presented on a two-machine infinite bus system and the IEEE 145-bus test system.
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Yuan et al. (2014) studied this question.
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