Fuzzy copula model for wind speed correlation and its application in wind curtailment evaluation

Abstract

Wind parks always produce diverse percentages of their nominal power at the same time, leading to a concern about correlation between wind speeds. The assessments of wind speed correlation have been particularly focused on probabilistic modeling of aleatory uncertainty. However, poor historical data, imprecise parameter estimation and incomplete knowledge of wind speeds lead to another type of uncertainty, possibilistic uncertainty, which requires an explicit analysis. Therefore, a fuzzy copula model is firstly proposed to express the possibilistic uncertainty of wind speed correlation. The advantage of the proposed model is that the copula parameters can be interval numbers, triangular or trapezoidal fuzzy numbers based on the wind speed data and subjective judgment of decision makers. For estimating copula parameters, a complete decision rule and interval estimation method is developed based on cumulative probability and probability distributions of correlated wind speeds. The effectiveness of the proposed model is validated by the application in wind curtailment evaluation while a method is developed to evaluate and quantify wind curtailment in a hybrid power system involving different types of generation. The results demonstrate that the proposed model and method are capable of describing the possibilistic uncertainty and evaluating its effect on wind curtailment. Compared with previous research, the proposed model develops a new universal parameter estimation method and selection rule to provide more interval results, by calculating the membership function of copula parameters and wind curtailment. System planners and operators can apply the fuzzy results to various topics like reserve capacity evaluation or real-time dispatch depending on their level of risk tolerance.