  This paper studies the impacts of stochastic load fluctuations, namely the
fluctuation intensity and the load power variation speed, on power system
dynamic voltage stability. Additionally, the trade-off relationship between the
two parameters is revealed, which provides important insights regarding the
potential of using energy storage to maintain voltage stability under high
uncertainty. To this end, Stochastic Differential-Algebraic Equations (SDAEs)
are used to model the stochastic load variation; bifurcation analysis is
carried out to explain the influence of stochasticity. Numerical study and
Monte Carlo simulations on the IEEE 14-bus system demonstrate that a larger
fluctuation intensity or a slower load power variation speed may lead to a
smaller voltage stability margin. To the best of authors' knowledge, this work
uncovers the impacts of the time evolution property of the driving parameters,
i.e., the load power variation speed and its trade off effect with the
fluctuation intensity on the size of the dynamic voltage stability margin.
