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This paper presents a Monte Carlo based generation system reliability evaluation method that can accurately model correlations between multiple wind speeds following different probability distributions. The assumption of normal distribution in the traditional correlation matrix method is eliminated. Applications to the Weibull, Burr, lognormal and gamma distributions which are popular for wind speed representation are analyzed in detail. The reliability evaluation procedure considering correlations of wind speeds following different distributions is developed. The IEEE-RTS with four additional wind farms whose wind speeds follow different types of distributions is used to demonstrate the application of the presented method in generation system reliability evaluation.