基于在线LASSO VAR和EGARCH模型的风场功率集成概率预测

doi:10.16183/j.cnki.jsjtu.2021.377

摘要/Abstract

摘要：

由于风速波动性大,风力发电往往呈现一定的不确定性.传统风能预测模型以均值为0、方差固定的正态分布度量不确定性,但方差可能随时间变化,即具有异方差性.为提升预测精度,基于在线最小绝对收缩和选择算子的向量自回归(LASSO VAR)和指数自回归条件异方差(EGARCH)模型,提出一种考虑异方差性的风场级功率集成概率预测模型.首先使用在线LASSO VAR模型预测风力机的有功功率,再利用自回归条件异方差检验验证残差的异方差性,并利用信息冲击曲线和动态显著线评估正负残差对未来条件方差的不对称影响.然后针对异方差性和不对称性,使用EGARCH模型对单风力机有功功率的残差进行预测,得到有功功率的条件方差.最后,考虑各风力机有功功率的相关性,将风场中各风力机的有功功率求和,得到整个风场总有功功率的概率预测结果.将该方法应用于中国华东某地风场,验证了该模型能有效提高预测精度.

关键词: 在线LASSO VAR, 异方差, 指数条件异方差模型, 概率预测

Abstract:

Wind power generation has uncertainty due to the high fluctuation of wind speed. In traditional wind power prediction models, the uncertainty is measured by normal distribution with zero mean and constant variance. However, the variance may vary with time, which means the variance has heteroscedasticity. To improve the prediction accuracy, this paper proposes a new integrated probabilistic wind power prediction model for wind farm considering heteroscedasticity based on online least absolute shrinkage and selection operator and vector autoregression (LASSO VAR) and the exponential generalized autoregressive conditional heteroskedasticity (EGARCH) model. First, online LASSO VAR is used to forecast power output. Then, heteroscedasticity of residuals is validated by autoregressive conditional heteroskedasticity test. Considering heteroscedasticity, the news impact curve and dynamic significance line verify that positive and negative residuals affect future volatility asymmetrically. Thus, the EGARCH model is used to forecast the residuals to obtain the conditional variance of point prediction results. Finally, the probabilistic result of total power output is obtained by summing the power output of turbines in the wind farm considering the correlation of the active wind power of wind turbines. This method is applied to forecast the power output of a wind farm in East China and is proved effective in improving the prediction accuracy.

Key words: online least absolute shrinkage and selection operator and vector autoregression (LASSO VAR), heteroscedasticity, exponential generalized autoregressive conditional heteroskedasticity (EGARCH) model, probabilistic forecasting

中图分类号:

TM614

王鹏, 李艳婷, 张宇. 基于在线LASSO VAR和EGARCH模型的风场功率集成概率预测[J]. 上海交通大学学报, 2023, 57(7): 845-858.

WANG Peng, LI Yanting, ZHANG Yu. Probabilistic Forecasting of Wind Power Generation Using Online LASSO VAR and EGARCH Model[J]. Journal of Shanghai Jiao Tong University, 2023, 57(7): 845-858.

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参考文献 40

[1]	Global Wind Energy Council. Global wind report 2022[R/OL]. (2022-12-31)[2023-02-16]. https://gwec.net/global-wind-report-2022/.
[2]	LANDBERG L, WATSON S J. Short-term prediction of local wind conditions[J]. Boundary-Layer Meteorology, 1994, 70(1): 171-195. doi: 10.1007/BF00712528 URL
[3]	FOCKEN U, LANGE M, WALDL H. Previento-A wind power prediction system with an innovative upscaling algorithm[C/OL]. (2001-01-01)[2021-07-30]. https://www.researchgate.net/publication/250448566_Previento_-_A_Wind_Power_Prediction_System_with_an_Innovative_Upscaling_Algorithm.
[4]	方江晓, 周晖, 黄梅, 等. 基于统计聚类分析的短期风电功率预测[J]. 电力系统保护与控制, 2011, 39(11): 67-73.
	FANG Jiangxiao, ZHOU Hui, HUANG Mei, et al. Short-term wind power prediction based on statistical clustering analysis[J]. Power System Protection & Control, 2011, 39(11): 67-73.
[5]	AASIM, SINGH S N, MOHAPATRA A, Repeated wavelet transform based ARIMA model for very short-term wind speed forecasting[J]. Renewable Energy, 2019, 136: 758-768. doi: 10.1016/j.renene.2019.01.031 URL
[6]	YANG D Z. On post-processing day-ahead NWP forecasts using Kalman filtering[J]. Solar Energy, 2019, 182: 179-181. doi: 10.1016/j.solener.2019.02.044
[7]	戚创创, 王向文. 考虑风向和大气稳定度的海上风电功率短期预测[J]. 电网技术, 2021, 45(7): 2773-2780.
	QI Chuangchuang, WANG Xiangwen. Short-term prediction of offshore wind power considering wind direction and atmospheric stability[J]. Power System Technology, 2021, 45(7): 2773-2780.
[8]	李永刚, 王月, 刘丰瑞, 等. 基于Stacking融合的短期风速预测组合模型[J]. 电网技术, 2020, 44(8): 2875-2882.
	LI Yonggang, WANG Yue, LIU Fengrui, et al. Combination model of short-term wind speed prediction based on stacking fusion[J]. Power System Technology, 2020, 44(8): 2875-2882.
[9]	WANG Y, HU Q H, MENG D Y, et al. Deterministic and probabilistic wind power forecasting using a variational Bayesian-based adaptive robust multi-Kernel regression model[J]. Applied Energy, 2017, 208: 1097-1112. doi: 10.1016/j.apenergy.2017.09.043 URL
[10]	李洪涛, 马志勇, 芮晓明. 基于数值天气预报的风能预测系统[J]. 中国电力, 2012, 45(2): 64-68.
	LI Hongtao, MA Zhiyong, RUI Xiaoming. Forecasting system based on numerical weather prediction[J]. Electric Power, 2012, 45(2): 64-68.
[11]	OKUMUS I, DINLER A. Current status of wind energy forecasting and a hybrid method for hourly predictions[J]. Energy Conversion and Management, 2016, 123: 362-371. doi: 10.1016/j.enconman.2016.06.053 URL
[12]	钱政, 裴岩, 曹利宵, 等. 风电功率预测方法综述[J]. 高电压技术, 2016, 42(4): 1047-1060.
	QIAN Zheng, PEI Yan, Cao Lixiao, et al. Review of wind power forecasting method[J]. High Voltage Engineering, 2016, 42(4): 1047-1060.
[13]	DOWELL J, PINSON P. Very-short-term probabilistic wind power forecasts by sparse vector autoregression[J]. IEEE Transactions on Smart Grid, 2016, 7(2): 763-770.
[14]	MESSNER J, PINSON P. Online adaptive lasso estimation in vector autoregressive models for high dimensional wind power forecasting[J]. International Journal of Forecasting, 2019, 35(4): 1485-1498. doi: 10.1016/j.ijforecast.2018.02.001 URL
[15]	LANGE M. On the uncertainty of wind power predictions-Analysis of the forecast accuracy and statistical distribution of errors[J]. Journal of Solar Energy Engineering, 2005, 127(2): 177-184. doi: 10.1115/1.1862266 URL
[16]	刘兴杰, 谢春雨. 基于贝塔分布的风电功率波动区间估计[J]. 电力自动化设备, 2014, 34(12): 26-30.
	LIU Xingjie, XIE Chunyu. Wind power fluctuation interval estimation based on beta distribution[J]. Electric Power Automation Equipment, 2014, 34(12): 26-30.
[17]	李海燕. 基于数据挖掘与非线性分位数回归的风电功率概率密度预测方法[D]. 合肥: 合肥工业大学, 2018.
	LI Haiyan. Wind power probability density forecasting method based on data mining and non-linear quantile regression[D]. Hefei: Hefei University of Technology, 2018.
[18]	ZHANG Y, LIU K, QIN L, et al. Deterministic and probabilistic interval prediction for short-term wind power generation based on variational mode decomposition and machine learning methods[J]. Energy Conversion & Management, 2016, 112: 208-219.
[19]	QIN X, CAO L, RUNDENSTEINER E A, et al. Scalable kernel density estimation-based local outlier detection over large data streams[J]. Advances in Database Technology-EDBT, 2019, 3: 421-432.
[20]	SLOUGHTER J M, GNEITING T, RAFTERY A E. Probabilistic wind speed forecasting using ensembles and Bayesian model averaging[J]. Journal of the American Statistical Association, 2010, 105(489): 25-35. doi: 10.1198/jasa.2009.ap08615 URL
[21]	WANG G, JIA R, LIU J, et al. A hybrid wind power forecasting approach based on Bayesian model averaging and ensemble learning[J]. Renewable Energy, 2020, 145: 2426-2434. doi: 10.1016/j.renene.2019.07.166 URL
[22]	刘帅, 朱永利, 张科, 等. 基于误差修正ARMA-GARCH模型的短期风电功率预测[J]. 太阳能学报, 2020, 41(10): 268-275.
	LIU Shuai, ZHU Yongli, ZHANG Ke, et al. Short-term wind power forecasting based on error correction arma-garch model[J]. Acta Energiae Solaris Sinica, 2020, 41(10): 268-275.
[23]	李力行, 苗世洪, 涂青宇, 等. 考虑异方差效应的风电不确定性建模及其在调度中的应用[J]. 电力系统自动化, 2020, 44(8): 36-47.
	LI Lixing, MIAO Shihong, TU Qingyu, et al. Modelling of wind power uncertainty considering heteroskedasticity effect and its application in power system dispatching[J]. Automation of Electric Power Systems, 2020, 44(8): 36-47.
[24]	POGGI P, MUSELLI M, NOTTON G, et al. Forecasting and simulating wind speed in Corsica by using an autoregressive model[J]. Energy Conversion & Management, 2003, 44(20): 3177-3196.
[25]	孙春顺, 王耀南, 李欣然. 小时风速的向量自回归模型及应用[J]. 中国电机工程学报, 2008, 28(14): 112-117.
	SUN Chunshun, WANG Yaonan, LI Xinran. A vector autoregression model of hourly wind speed and its applications in hourly wind speed forecasting[J]. Proceedings of the CSEE, 2008, 28(14): 112-117.
[26]	CAVALCANTE L, BESSA R J, REIS M, et al. LASSO vector autoregression structures for very short-term wind power forecasting[J]. Wind Energy, 2017, 20(4): 657-675. doi: 10.1002/we.v20.4 URL
[27]	FRIEDMAN J, HASTIE T, HÖFLING H, et al. Pathwise coordinate optimization[J]. The Annals of Applied Statistics, 2007, 1(2): 302-332.
[28]	MESSNER J W, PINSON P. Online adaptive lasso estimation in vector autoregressive models for high dimensional wind power forecasting[J]. International Journal of Forecasting, 2019, 35(4): 1485-1498. doi: 10.1016/j.ijforecast.2018.02.001 URL
[29]	朱金蝶. 回归模型中异方差检验方法研究[D]. 太原: 山西大学, 2019.
	ZHU Jindie. Study on the methods of testing heteroscedasticity in regression model[D]. Taiyuan: Shanxi University, 2019.
[30]	ENGLE R F. Autoregressive conditional heteroscedasticity with estimates of the variance of United Kingdom inflation[J]. Econometrica, 1982, 50(4): 987. doi: 10.2307/1912773 URL
[31]	BOLLERSLEV T. Generalized autoregressive conditional heteroskedasticity[J]. Journal of Econometrics, 1986, 31(3): 307-327. doi: 10.1016/0304-4076(86)90063-1 URL
[32]	BLACK F. Studies of stock market volatility changes[J]. Proceedings of the American Statistical Association Business & Economic Statistics Section, 1976, 177-181.
[33]	NELSON D B. Conditional heteroskedasticity in asset returns: A new approach[J]. Econometrica, 1991, 59(2): 347-370. doi: 10.2307/2938260 URL
[34]	HAFNER C M, LINTON O. An almost closed form estimator for the egarch model[J]. Econometric Theory, 2017, 33(4): 1013-1038. doi: 10.1017/S0266466616000256 URL
[35]	BERNDT E K, HALL B H, et al. Annals of economic and social measurement[M]. USA: NBER, 1974: 653-665.
[36]	WANG Z, WANG W S, LIU C, et al. Probabilistic forecast for multiple wind farms based on regular vine copulas[J]. IEEE Transactions on Power Systems, 2018, 33(1): 578-589. doi: 10.1109/TPWRS.2017.2690297 URL
[37]	GRIMIT E P, GNEITING T, BERROCAL V J, et al. The continuous ranked probability score for circular variables and its application to mesoscale forecast ensemble verification[J]. Quarterly Journal of the Royal Meteorological Society, 2006, 132(621C): 2925-2942. doi: 10.1256/qj.05.235 URL
[38]	CHEN H, GAO S. A study on the structure of asymmetric volatility in load series[C]// 2008 Third International Conference on Electric Utility Deregulation and Restructuring and Power Technologies. Nanjing, China: IEEE, 2008: 737-744.
[39]	张晓英, 张晓敏, 廖顺, 等. 基于聚类与非参数核密度估计的风电功率预测误差分析[J]. 太阳能学报, 2019, 40(12): 3594-3604.
	ZHANG Xiaoying, ZHANG Xiaomin, LIAO Shun, et al. Prediction error analysis of wind power based on clustering and non-parametric kernel density estimation[J]. Acta Energiae Solaris Sinica, 2019, 40(12): 3594-3604.
[40]	MEINSHAUSEN N, RIDGEWAY G. Quantile regression forests[J]. Journal of Machine Learning Research, 2006, 7(6): 983-999.

模型	RMSE	MAE	SMAPE
在线LASSO VAR(4)	397.08	272.03	55.65
在线LASSO VAR(3)	397.24	272.27	53.00
在线LASSO VAR(2)	406.98	280.50	54.16
在线LASSO VAR(1)	406.80	280.10	54.04
Batch LASSO VAR(4)	399.05	273.76	53.07
Batch LASSO VAR(3)	399.31	274.03	53.11
Batch LASSO VAR(2)	399.64	274.17	53.16
Batch LASSO VAR(1)	408.54	279.34	53.99
在线AR(4)	420.52	287.19	55.05

模型	RMSE	MAE	SMAPE
LASSO VAR(3)	399.31	274.03	53.11
ENET VAR(3)	399.03	278.56	53.90
Hierarchical Sparse VAR(3)	418.82	295.31	56.55
气象预测+功率曲线	449.6	308.56	54.22
添加气象数据的LASSO VAR(3)	407.1	280.4	54.12

模型	中位数预测 RMSE	K_t	CRPS
EGARCH (1, 1)	8019.4	-40401.8	4057.5
GARCH (1, 1)	8019.4	-40532.8	4070.8
BMA_48	8421.7	-43291.0	4389.9
BMA_24	8936.9	-45535.7	4640.5
KDE	32461.5	-158444	11345.67
QR	14918.7	-70989.3	7201.1
QRF	9182.3	-45429.4	4594.0