A Framework for Dynamic Stability Analysis of Power Systems with Volatile Wind Power

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.