Enhancing ultra-short-term wind power forecasting using the Copula quantile regression method

Abstract

In recent years, the shift toward renewable energy in China’s power industry has been remarkable, with the installed capacity of renewables surpassing that of coal-fired power. Among these, wind power output plays a pivotal role, although it is characterized by its strong randomness and volatility. Traditional prediction methods fall short as they cannot provide comprehensive probability distribution information on the wind power output. To bridge this gap, quantile prediction methods have emerged as superior options for achieving reliable wind power output predictions, which are crucial for the safe and stable operation of power grid systems. To address the inherent unpredictability of wind power, this study introduces a quantile regression method based on Copula (QCopula). The Copula function captures the correlation between the marginal distribution functions of the random variables and their joint distribution function. The process begins with selecting an optimal Copula function using the Akaike Information Criterion (AIC). This function elucidates the relationship between wind power and wind speed, enabling the expression of the conditional probability distribution function of power. By considering different conditional probability values, we obtained wind power prediction results at different quantiles, leading to interval prediction results across different confidence intervals. These results were compared with three traditional quantile regression methods (Quantile Regression (QR), Quantile regression Random Forests (QRF), and Quantile regression Long Short-Term Memory (QLSTM)) using three elevation metrics: Predictive Interval Coverage Probability (PICP), Predictive Interval Normalized Average Width (PINAW), and Corrected Predictive Interval Accuracy (CPIA). This comparison was aimed at evaluating the interval prediction accuracy of the four quantile regression methods. Finally, the crossover of the quantile curves for each method was analyzed. A case study was conducted at a wind power plant in Gansu Province, utilizing wind speed and power data (measured in MW at 15-minute intervals) from September 2022 to June 2023. With 29088 sample points in total, the data were divided into training, validating and testing sets in an 6∶2∶2 ratio. The training set facilitated model development through various quantile regression methods, the validating set was used for model parameterization, whereas the testing was used to evaluate the accuracy of each model. The results showed that the QCopula consistently outperformed the other methods across different confidence intervals, with its modified prediction interval accuracy ranging between 0.701 and 0.773. On average, it exceeded QR, QRF, and QLSTM by 15%, 9%, and 13%, respectively. Notably, the QCopula maintained a consistent increase in the predicted power values for each sample point with probability, without any instances of quantile crossing, a common issue observed in QR, QRF, and QLSTM. In summary, the QCopula offers narrower interval widths and higher interval coverage without the drawback of quantile curve crossing, thereby ensuring higher reliability.

Keywords

• copula function
• quantile regression
• wind power
• ultra-short-term
• output forecasts