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Copula分位數回歸方法在風電超短期出力預測上的應用

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

  • 摘要: 風電出力具有較強的隨機性和波動性,相比于傳統預測,分位數預測方法能夠提供全面的風電功率概率分布信息,可實現更可靠的風電出力預報,對電網系統的安全和穩定運行具有重要意義. 以甘肅某風電站為案例,將數據按6∶2∶2劃分為訓練集、驗證集和測試集,采用基于Copula的分位數回歸方法(QCopula)進行功率區間預測,并與三個傳統的分位數回歸方法進行比較. 結果顯示,在不同置信區間下QCopula的修正預測區間精度范圍在0.701~0.773之間,預測精度平均值比傳統分位數回歸(QR)、隨機森林分位數回歸(QRF)和長短期記憶神經網絡分位數回歸(QLSTM)分別高出15%、9%和13%,優于其他三種分位數預測方法. 分位數交叉驗證中,QCopula未出現分位數交叉,每個樣本點的功率預測值均隨概率值單調遞增,而QR、QRF、QLSTM均出現不同程度的分位數交叉現象. 綜上所述,QCopula可以表征更小的區間寬度和更高的區間覆蓋率,且分位數曲線不存在交叉,可信度較高.

     

    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.

     

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