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The unpredictable nature of wind energy makes its integration to the electric grid highly challenging. However, these challenges can be addressed by incorporating storage devices (batteries) in the system. We perform an overall assessment of a single domestic power system with a wind turbine supported by an energy storage device. The aim is to investigate the best operation mode of the storage device such that the occurrence of large power spills can be minimized. For estimating the small probability of large power spills, we use the splitting technique for rare-event simulations. An appropriate Importance Function for splitting is formulated such that it reduces the work-load of the probability estimator as compared to the conventional Crude Monte Carlo probability estimator. Simulation results show that the ramp constraints imposed on the charging/discharging rate of the storage device plays a pivotal role in mitigating large power spills. It is observed that by employing a new charging strategy for the storage device large power spills can be minimized further. There exists a trade-off between reducing the large power spills versus reducing the average power spills.

The reliability of the transmission grid is challenged by the integration of intermittent renewable energy sources into the grid. For model-based reliability studies, it is important to have suitable models available of renewable energy sources like wind and solar power. In this study, we investigate to what extent the power output of wind farms can be modeled with discrete Hidden Markov Models (HMMs). The parameters of the HMMs are inferred from measurement data from multiple turbines in a wind farm. We use these models both for individual turbine output and for total aggregated power output of multiple turbines. When modeling individual turbine output, the hidden process in the HMM is instrumental in capturing the dependencies between the output of the different turbines. It is important to account for these dependencies in order to correctly capture the upper quantiles (90%, 95%, 99%) of the distribution of the wind farm aggregated power output. We show that despite their simple structure, HMMs are able to reproduce important features of the power output of wind farms. This opens up possibilities to model and analyze these features with methods and techniques stemming from the field of Markov models and stochastic processes.