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An increased penetration of wind turbines have given rise to a need for wind speed/power models that generate realistic synthetic data. Such data, for example, might be used in simulations to size energy storage or spinning reserve. In much literature, Markov chains have been proposed as an acceptable method to generate synthetic wind data, but we have observed that the autocorrelation plots of wind speeds generated by Markov chains are often inaccurate. This paper describes when using Markov chains is appropriate and demonstrates the gross underestimation of storage requirements that occurs at short time steps. We found that Markov chains should not be used for time steps shorter than 15 to 40 minutes, depending on the order of the Markov chain and the number of wind power states. This result implies that Markov chains are of limited use as synthetic data generators for small microgrid models and other applications requiring short simulation time steps. New algorithms for generating synthetic wind data at shorter time steps must be developed.