Title: A Framework for Dynamic Stability Analysis of Power Systems with Volatile Wind Power,
Abstract: We propose a framework employing stochastic differential equations to
facilitate the long-term stability analysis of power grids with intermittent
wind power generations. This framework takes into account the discrete dynamics
which play a critical role in the long-term stability analysis, incorporates
the model of wind speed with different probability distributions, and also
develops an approximation methodology (by a deterministic hybrid model) for the
stochastic hybrid model to reduce the computational burden brought about by the
uncertainty of wind power. The theoretical and numerical studies show that a
deterministic hybrid model can provide an accurate trajectory approximation and
stability assessments for the stochastic hybrid model under mild conditions. In
addition, we discuss the critical cases that the deterministic hybrid model
fails and discover that these cases are caused by a violation of the proposed
sufficient conditions. Such discussion complements the proposed framework and
methodology and also reaffirms the importance of the stochastic hybrid model
when the system operates close to its stability limit.