Johnson system based reliability evaluation of composite power system with wind farms

With the increasing integration of wind farms, not only the fluctuation of wind power, but also the correlations among wind farms should be considered in power system reliability evaluation. A Johnson system based non-sequential Monte Carlo simulation method for reliability evaluation of composite power system with wind farms is proposed. If distribution function of wind speed is not known, but historical data of wind velocity are given, the relationship between standard normal distribution and wind speed distribution can be constructed by Johnson system. Then, arbitrary amount of wind speed samples with specific correlations can be obtained by normal distribution and Johnson system. Correlation matrix is proven to be nonnegative, and singular value decomposition (SVD) is used to decompose the correlation matrix, which overcomes the drawback that Cholesky decomposition (CD) can´t be applied to non-positive matrix. The accuracy of the Johnson system is shown in the following diagram and validity of the proposed algorithm is verified by the case study in the modified IEEE RTS-24 system.