Towards optimal estimation of blackout probability based on sequential importance sampling simulations

A cascading outage can lead to catastrophic consequences albeit the probability is very small, hence is recognized as extremely rare event. It is still a great challenge to estimate the probabilities of blackouts with different load shedding levels due to the intractable computational complexity. To improve the estimation efficiency and reduce the estimation variance of the traditional Monte Carlo simulation based methods, the (sequential) importance sampling approach (IS/SIS) has been proposed and proved effective if appropriate proposal probability distribution (PPD) is set. However, the selection of the PPD is far from trivial as a certain PPD is only suitable for the blackout analysis under specific levels of load shedding and the performance will deteriorate when it is utilized for blackout probability analysis with other PPDs. In this regard, we propose a probability estimation approach with mixed PPDs. We first conduct a set of pilot simulations with a group of supportive PPDs. Then we devise an optimal model to optimize the weights of the supportive PPD. Finally we establish an additional optimization model to achieve the smallest sample set using the optimally weighted supportive PPDs subject to the desired variance constraints. Case studies confirm the effectiveness of our method.