在风电功率预测中,预测误差分布具有多模态和非对称特性,易导致局部概率密度失真与区间估计偏差问题。针对上述问题,提出一种基于双阶段参数优化多核核密度估计的风电功率区间预测方法。首先,根据不同核函数的概率密度估计特性,通过加权融合多个不同核密度估计函数,解决单核核密度估计在多模态场景下的局部概率密度失真问题;其次,针对多核核密度估计中权重和带宽参数的高维非线性耦合优化难题,提出双阶段参数优化方法：第一阶段采用基于白鲸优化算法（BWO）的参数对分域搜索策略,对权重和带宽进行初步优化;第二阶段引入基于留一法交叉验证（LOOCV）的带宽细化调优方法,提升带宽的精度。最后,通过在公开数据集和现场实测数据集上进行实验,验证所提方法的误差概率密度拟合效果优于单核核密度估计方法,与现有区间预测方法相比,具有更优的预测性能。
Abstract
In wind power prediction, the multimodal and asymmetric characteristics of prediction error distributions often lead to local probability density distortion and interval estimation deviations. To address these challenges, this paper proposes a wind power interval prediction method based on dual-stage parameter optimized multiple kernel-based kernel density estimation. Firstly, by investigating the probability density estimation characteristics of different kernel functions, multiple kernel density estimation functions are weighted and fused to resolve the local probability density distortion issue of single-kernel kernel density estimation in multi-modal scenarios. Secondly, to tackle the high-dimensional nonlinear coupling optimization problem of weight and bandwidth parameters in multiple kernel-based kernel density estimation, a dual-stage parameter optimization framework is developed： In the first stage, a parameter-pair partitioned domain search strategy based on the beluga whale optimization （BWO） algorithm is proposed for preliminary optimization of weights and bandwidths. The second stage employs a bandwidth refinement tuning method utilizing leave-one-out cross validation （LOOCV） to improve bandwidth precision. Finally, experiments conducted on both public and field-measured datasets demonstrate that the proposed method outperforms single-kernel kernel density estimation in error probability density fitting. Furthermore, comparative analyses with existing interval prediction methods reveal its superior predictive performance.
关键词
风电功率 /
区间预测 /
核密度估计 /
白鲸优化算法 /
留一法交叉验证
Key words
wind power /
interval prediction /
kernel density estimation /
beluga whale optimization algorithm /
leave-one-out cross validation
{{custom_sec.title}}
{{custom_sec.title}}
{{custom_sec.content}}
参考文献
[1] 杨茂, 于欣楠. 考虑风电场功率爬坡的超短期组合预测[J]. 东北电力大学学报, 2022, 42(1): 63-70.
Yang M, Yu X N.An ultra-short term combined prediction considering wind farm power climbing[J]. Journal of Northeast Electric Power University, 2022, 42(1): 63-70.
[2] 李娟, 王玲, 孙康杰, 等. 考虑风电不确定性和有功无功联合调整的两阶段优化调度[J]. 东北电力大学学报, 2023, 43(3): 72-81.
Li J, Wang L, Sun K J, et al.Two-stage optimal dispatch considering uncertainty of wind power and joint regulaiton of active and reactive power[J]. Journal of Northeast Electric Power University, 2023, 43(3): 72-81.
[3] 朱立轩, 万灿, 鞠平. 计及不确定性的电力系统区间分析研究综述[J]. 电力自动化设备, 2023, 43(7): 1-11.
Zhu L X, Wan C, Ju P.Review on power system interval analysis considering uncertainty[J]. Electric Power Automation Equipment, 2023, 43(7): 1-11.
[4] 黎静华, 骆怡辰, 杨舒惠, 等. 可再生能源电力不确定性预测方法综述[J]. 高电压技术, 2021, 47(4): 1144-1157.
Li J H, Luo Y C, Yang S H, et al.Review of uncertainty forecasting methods for renewable energy power[J]. High Voltage Engineering, 2021, 47(4): 1144-1157.
[5] 柳天虹, 齐胜利, 裔扬, 等. 基于分位数回归的改进权重GRU风电功率区间预测[J]. 太阳能学报, 2024, 45(12): 291-298.
Liu T H, Qi S L, Yi Y, et al.Improved weighted GRU wind power interval prediction based on quantile regression[J]. Acta Energiae Solaris Sinica, 2024, 45(12): 291-298.
[6] Xie Y Y, Li C S, Li M Y, et al.An overview of deterministic and probabilistic forecasting methods of wind energy[J]. IScience, 2023, 26(1): 105804.
[7] 王森, 孙永辉, 侯栋宸, 等. 基于多窗宽核密度估计的风电功率超短期自适应概率预测[J]. 高电压技术, 2024, 50(7): 3070-3079.
Wang S, Sun Y H, Hou D C, et al.Ultrashort-term adaptive probabilistic forecasting of wind power based on multi-band width kernel density estimation[J]. High Voltage Engineering, 2024, 50(7): 3070-3079.
[8] Hu J M, Luo Q X, Tang J W, et al.Conformalized temporal convolutional quantile regression networks for wind power interval forecasting[J]. Energy, 2022, 248: 123497.
[9] Wang K, Zhang Y, Lin F, et al.Nonparametric probabilistic forecasting for wind power generation using quadratic spline quantile function and autoregressive recurrent neural network[J]. IEEE Transactions on Sustainable Energy, 2022, 13(4): 1930-1943.
[10] Von Krannichfeldt L, Wang Y, Zufferey T, et al.Online ensemble approach for probabilistic wind power forecasting[J]. IEEE Transactions on Sustainable Energy, 2022, 13(2): 1221-1233.
[11] 杨锡运, 张璜, 关文渊, 等. 基于滑动分块百分位数Bootstrap法的风电功率概率区间预测[J]. 太阳能学报, 2019, 40(2): 430-437.
Yang X Y, Zhang H, Guan W Y, et al.Probabilistic intervals forecasting of wind power based on moving block percentile bootstrap method[J]. Acta Energiae Solaris Sinica, 2019, 40(2): 430-437.
[12] 胡文慧, 苏欣, 姜林, 等. 考虑预测误差时空相依性的短期风电功率概率预测[J]. 南方电网技术, 2023, 17(2): 137-144.
Hu W H, Su X, Jiang L, et al.Probabilistic prediction of short-term wind power considering the temporal and spatial dependence of prediction errors[J]. Southern Power System Technology, 2023, 17(2): 137-144.
[13] Quan H, Zhang W, Zhang W J, et al.An interval prediction approach of wind power based on skip-GRU and block-bootstrap techniques[J]. IEEE Transactions on Industry Applications, 2023, 59(4): 4710-4719.
[14] Niu D X, Sun L J, Yu M, et al.Point and interval forecasting of ultra-short-term wind power based on a data-driven method and hybrid deep learning model[J]. Energy, 2022, 254: 124384.
[15] Zhou B W, Ma X J, Luo Y H, et al.Wind power prediction based on LSTM networks and nonparametric kernel density estimation[J]. IEEE Access, 2019, 7: 165279-165292.
[16] Dong W C, Sun H X, Tan J X, et al.Regional wind power probabilistic forecasting based on an improved kernel density estimation, regular vine copulas, and ensemble learning[J]. Energy, 2022, 238: 122045.
[17] 李天白. 基于循环神经网络与核密度估计的超短期风电功率预测[D]. 天津: 河北工业大学, 2025: 41-46.
Li T B.Ultra-short-term wind power prediction based on recurrent neural networks and kernel density estimation[D]. Tianjin: Hebei University of Technology, 2025: 41-46.
[18] Chen J Q, He Y L, Cheng Y C, et al.A multiple kernel-based kernel density estimator for multimodal probability density functions[J]. Engineering Applications of Artificial Intelligence, 2024, 132: 107979.
[19] Zhong C T, Li G, Meng Z.Beluga whale optimization: a novel nature-inspired metaheuristic algorithm[J]. Knowledge-based Systems, 2022, 251: 109215.
[20] 杨茂, 张书天, 王勃, 等. 基于门控循环加权共形分位数回归的风电功率短期区间预测[J]. 中国电机工程学报, 2025, 45(19): 7565-7575.
Yang M, Zhang S T, Wang B, et al.Short-term wind power interval prediction based on weighted gated recurrent conformalized quantile regression[J]. Proceedings of the CSEE, 2025, 45(19): 7565-7575.
[21] Du B G, Huang S, Guo J, et al.Interval forecasting for urban water demand using PSO optimized KDE distribution and LSTM neural networks[J]. Applied Soft Computing, 2022, 122: 108875.
基金
国家自然科学基金（62302147）; 天津市自然科学基金（22JCQNJC01450）
PDF(1529 KB)
