Abstract
The impact of the wind power forecast error (WPFE) on the reliability of the wind power system may be quantified by using the sensitivity, which is difficult to calculate because the distribution of the WPFE is unknown. The assumption that the WPFE follows the normal distribution is often impractical. The non-standard third-order polynomial normal transformation (NSTPNT) method is newly proposed. And the analytical expressions of the probability weighted moments (PWMs) of the normal random variable are newly derived to directly calculate the polynomial coefficients. The non-normal WPFE is resembled by a non-standard normal random variable using the NSTPNT method, which ensures the accuracy of the reliability assessment and the convenience for calculating sensitivities. Combining the NSTPNT method and the discrete WPFE, the reliability sensitivities of the wind power system respect to the distribution parameters, expectation, and standard deviation, of the WPFE following the non-normal distributions are established respectively. In numerical results, the accuracy of the NSTPNT method and the sensitivities are verified. Different reserve capacities with high level of the wind power penetration are examined. The effects of the reserve capacity and the standard deviation of the forecast error on the reliability sensitivities are analyzed.
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