基于数据关联狄利克雷混合模型的电网净负荷不确定性表征研究

李远征; 孙天乐; 刘云; 赵勇; 曾志刚

doi:10.16383/j.aas.c210668

基于数据关联狄利克雷混合模型的电网净负荷不确定性表征研究

doi: 10.16383/j.aas.c210668

李远征^{1, 2,},
孙天乐^{1, 2,},
刘云^3,,
赵勇^{1, 2,},
曾志刚^{1, 2,}

1.
华中科技大学人工智能与自动化学院, 图像信息处理与智能控制教育部重点实验室武汉 430074
2.
中国−测控技术“一带一路” 联合实验室武汉 430074
3.
华南理工大学电力学院广州 510641

基金项目: 国家自然科学基金(62073148), 腾讯—犀牛鸟基金(RAGR20210102)资助

详细信息

作者简介:
李远征：华中科技大学人工智能与自动化学院副教授. 主要研究方向为人工智能及其在智能电网中的应用, 深度学习, 强化学习, 大数据分析. E-mail: yuanzheng_li@hust.edu.cn

孙天乐：华中科技大学人工智能与自动化学院硕士研究生. 主要研究方向为新能源不确定性表征, 在线预测. E-mail: stl_221@163.com

刘云：博士, 华南理工大学电力学院副教授. 主要研究方向为高比例新能源分布式协同控制, 主动配电网P2P能量交易, 电力信息安全与隐私防护, 人工智能在能源系统的应用. E-mail: liuyun19881026@gmail.com

赵勇：华中科技大学人工智能与自动化学院教授. 主要研究方向为决策理论、方法及应用, 大型工程项目管理, 社会经济系统的建模与仿真, 系统分析与集成. E-mail: zhiwei98530@hust.edu.cn

曾志刚：华中科技大学人工智能与自动化学院院长, 长江学者特聘教授, 国家杰出青年基金获得者. 主要研究方向为切换系统控制理论与应用, 计算智能, 系统稳定性, 联想记忆. 本文通信作者. E-mail: zgzeng@hust.edu.cn

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出版历程
- 收稿日期: 2021-07-16
- 录用日期: 2021-11-02
- 网络出版日期: 2022-02-16
- 刊出日期: 2022-03-25

Uncertainty Characterization of Power Grid Net Load of Dirichlet Process Mixture Model Based on Relevant Data

LI Yuan-Zheng^{1, 2
,},
SUN Tian-Le^{1, 2
,},
LIU Yun^3
,,
ZHAO Yong^{1, 2
,},
ZENG Zhi-Gang^{1, 2
,}

1.
School of Artificial Intelligence and Automation, Key Laboratory on Image Information Processing and Intelligent Control of Ministry of Education, Huazhong University of Science and Technology, Wuhan 430074
2.
China-Belt and Road Joint Laboratory on Measurement and Control Technology, Wuhan 430074
3.
School of Electrical Power Engineering, South China University of Technology, Guangzhou 510641

Funds: Supported by National Natural Science Foundation of China (62073148) and Tencent Rhinoceros Foundation of China (RAGR20210102)

More Information

Author Bio:
LI Yuan-Zheng　Associate professor at the School of Artificial Intelligence and Automation, Huazhong University of Science and Technology. His research interest covers artificial intelligence and its application in smart grid, deep learning, reinforcement learning, and big data analysis

SUN Tian-Le　Master student in system engineering at the School of Artificial Intelligence and Automation, Huazhong University of Science and Technology. His research interest covers random characterization of renewable energy and online prediction

LIU Yun　Ph.D., associate professor at South China University of Technology. His research interest covers distributed cooperative control of renewable generation, peer-to-peer energy trading, security of cyber physical system, and application of artificial intelligence in energy systems

ZHAO Yong　Professor at the School of Artificial Intelligence and Automation, Huazhong University of Science and Technology. His research interest covers decision-making theories, methods and applications, large-scale engineering project management, modeling and simulation of social economic systems, and system analysis and integration

ZENG Zhi-Gang　Dean and professor of the School of Artificial Intelligence and Automation, Huazhong University of Science and Technology. His research interest covers switching system control theory and application, computational intelligence, system stability, and associative memory. Corresponding author of this paper

摘要

摘要: 针对电网净负荷时序数据关联的特点, 提出基于数据关联的狄利克雷混合模型 (Data-relevance Dirichlet process mixture model, DDPMM)来表征净负荷的不确定性. 首先, 使用狄利克雷混合模型对净负荷的观测数据与预测数据进行拟合, 得到其混合概率模型; 然后, 提出考虑数据关联的变分贝叶斯推断方法, 改进后验分布对该混合概率模型进行求解, 从而得到混合模型的最优参数; 最后, 根据净负荷预测值的大小得到其对应的预测误差边缘概率分布, 实现不确定性表征. 本文基于比利时电网的净负荷数据进行检验, 算例结果表明: 与传统的狄利克雷混合模型和高斯混合模型 (Gaussian mixture model, GMM)等方法相比, 所提出的基于数据关联狄利克雷混合模型可以更为有效地表征净负荷的不确定性.
- 狄利克雷混合模型 /
- 净负荷 /
- 不确定性表征 /
- 时序序列 /
- 预测误差
Abstract: Considering the time sequence correlation of the net load in power grids, this paper proposes a non-parametric Bayesian framework based on the data-relevance Dirichlet process mixture model (DDPMM). First, the Dirichlet process mixture model is used to fit the observation data and the forecast data of net load, in order to obtain a joint mixed probability model. Then, we propose a modified variational Bayesian inference that considers the correlation of the time sequence to acquire optimal parameters of the mixture model. Afterwards, we obtain the corresponding net load forecast error probabilistic distribution according to different net load forecast values. Finally, this paper uses actual data from the Belgian power grid for verification. Compared with the traditional Dirichlet process mixture model and Gaussian mixture model (GMM), our proposed approach takes into account the correlation of time series. Therefore, it can better characterize the forecast error of the net load, and obtain the optimal number of component clusters that would capture the uncertainty of the net load with more efficiency.
- Dirichlet process mixture model (DPMM) /
- net load /
- uncertain characterization /
- time sequence /
- forecast error

HTML全文

图 1 净负荷数据关联图

Fig. 1 The data-relevance of net load

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图 2 数据关联狄利克雷混合模型变分贝叶斯框架

Fig. 2 The framework of DDPMM variational Bayes

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图 3 折棍构造过程

Fig. 3 The process of steak-breaking

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图 4 基分布示意图

Fig. 4 The base distribution

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图 5 狄利克雷混合模型

Fig. 5 Dirichlet process mixture model

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图 6 DPMM概率图模型

Fig. 6 DPMM probability graph model

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图 7 考虑数据关联性的DPMM概率模型图

Fig. 7 DPMM probability model graph considering data-relevance

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图 8 考虑数据关联的EM迭代图

Fig. 8 EM iterative graph considering data-relevance

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图 9 2019年7月1日净负荷与负荷曲线

Fig. 9 Net load and load curve on July 1, 2019

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图 10 基于2019年净负荷数据的DDPMM与DPMM迭代曲线

Fig. 10 DDPMM and DPMM iterative curves based on net load data in the year of 2019

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图 11 不同预测值下的净负荷预测误差条件概率分布

Fig. 11 The PDF of net load forecast error conditions under different forecast values

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图 12 0.95置信区间雷达图

Fig. 12 Interval radar chart with 0.95 confidence

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表 1 对数似然比较

Table 1 Comparison of log-likelihood

模型	Log-L/10³(test)
DDPMM (5)	1.639
DPMM (15)	1.625
GMM-AIC (20)	1.612
GMM-BIC (13)	1.611

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表 2 卡方拟合优度比较

Table 2 Comparison of goodness of fit of Chi-square

Test	(a)	(b)	(c)	(d)	(e)	(f)	(g)	(h)	(i)	(j)
DDPMM	4.36	3.03	3.58	1.63	1.54	1.96	1.59	1.96	5.32	5.11
DPMM	4.87	3.15	4.46	2.46	1.37	1.79	1.98	1.31	4.92	7.08
GMM-AIC	5.32	3.54	4.20	2.87	2.01	2.01	2.42	1.95	5.94	5.58
GMM-BIC	5.64	3.46	3.95	2.63	2.34	2.53	2.07	2.84	4.99	5.98

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表 3 0.95置信度下2020年3月区间指标

Table 3 Interval index for March 2020 with 0.95 confidence level

模型	Winkler/10²	PICP	CWC	AIS	MPICD/10²
DDPMM	33.57	0.80	4.14	−1.03	6.03
DPMM	37.18	0.70	22.58	−1.56	6.05
GMM-AIC	39.11	0.63	78.71	−1.84	6.07
GMM-BIC	36.86	0.69	26.93	−1.51	6.08

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表 4 0.95置信度下2020年6月区间指标

Table 4 Interval index for June 2020 with 0.95 confidence level

模型	Winkler/10²	PICP	CWC	AIS	MPICD/10²
DDPMM	29.84	0.93	0.50	−0.58	4.59
DPMM	30.91	0.86	1.18	−0.68	4.61
GMM-AIC	33.19	0.75	6.68	−1.02	4.65
GMM-BIC	31.46	0.84	1.56	−0.77	4.63

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表 5 0.95置信度下2020年9月区间指标

Table 5 Interval index for September 2020 with 0.95 confidence level

模型	Winkler/10²	PICP	CWC	AIS	MPICD/10²
DDPMM	30.60	0.89	0.93	−0.70	5.02
DPMM	32.59	0.80	3.71	−0.96	5.03
GMM-AIC	34.90	0.72	13.76	−1.32	5.03
GMM-BIC	32.85	0.79	3.68	−1.01	5.02

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表 6 0.95置信度下2020年12月区间指标

Table 6 Interval index for December 2020 with 0.95 confidence level

模型	Winkler/10²	PICP	CWC	AIS	MPICD/10²
DDPMM	39.18	0.72	20.4	−1.97	7.45
DPMM	44.51	0.61	138.23	−2.77	7.44
GMM-AIC	46.02	0.59	173.46	−3.00	7.42
GMM-BIC	43.31	0.64	82.32	−2.59	7.42

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表 7 0.8置信度下2020年6月区间指标

Table 7 Interval index for June 2020 with 0.8 confidence

模型	Winkler/10²	PICP	CWC	AIS
DDPMM	32.76	0.77	0.41	−0.91
DPMM	34.70	0.68	1.34	−1.20
GMM-AIC	37.53	0.56	9.86	−1.66
GMM-BIC	35.41	0.66	1.90	−0.32

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表 8 0.5置信度下2020年6月区间指标

Table 8 Interval index for June 2020 with 0.5 confidence

模型	Winkler/10²	PICP	CWC	AIS
DDPMM	39.84	0.49	0.16	−1.93
DPMM	41.73	0.38	0.73	−2.30
GMM-AIC	44.26	0.31	2.19	−2.73
GMM-BIC	42.33	0.38	0.66	−2.40

下载: 导出CSV

参考文献(25)

[1]	黄博南, 王勇, 李玉帅, 刘鑫蕊, 杨超. 基于分布式神经动态优化的综合能源系统多目标优化调度. 自动化学报, DOI: 10.16383/j.aas.c200168 Huang Bo-Nan, Wang Yong, Li Yu-Shuai, Liu Xin-Rui, Yang Chao. Multi-objective optimal scheduling of integrated energy systems based on distributed neurodynamic optimization. Acta Automatica Sinica, DOI: 10.16383/j.aas.c200168
[2]	唐昊, 刘畅, 杨明, 汤必强, 许丹, 吕凯. 考虑电网调峰需求的工业园区主动配电系统调度学习优化. 自动化学报, 2019, 47(10): 1-15 Tang Hao, Liu Chang, Yang Ming, Tang Bi-Qiang, Xu Dan, Lv Kai. Learning-based optimization of active distribution system dispatch in industrial park considering the peak operation demand of power grid. Acta Automatica Sinica, 2021, 47(10): 2449-2463
[3]	姜兆宇, 贾庆山, 管晓宏. 多时空尺度的风力发电预测方法综述. 自动化学报, 2019, 45(1): 51-71 Jiang Zhao-Yu, Jia Qing-Shan, Guan Xiao-Hong. A Review of Multi-temporal-and-spatial-scale Wind Power Forecasting Method. Acta Automatica Sinica, 2019, 45(1): 51-71
[4]	Sun M, Zhang T, Wang Y, Strbac G and Kang C. Using Bayesian deep learning to capture uncertainty for residential net load forecasting. IEEE Transactions on Power Systems, 2019, 35(1): 188-20
[5]	Wang Y, Zhang N, Chen Q, Kirschen D S, Li P, Xia Q. Data-driven probabilistic net load forecasting with high penetration of behind-the-meter PV. IEEE Transactions on Power Systems, 2017, 33(3): 3255-3264
[6]	Rajbhandari N, Li W F, Du P W, Sharma S, Blevins B. Analysis of net-load forecast error and new methodology to determine non-spin reserve service requirement. In: Proceedings of the 2016 IEEE Power and Energy Society General Meeting, Boston, MA, USA: IEEE, 2016: 1−5
[7]	Alvarado-Barrios L, Alvaro R, Valerino B, et al. Stochastic unit commitment in microgrids: Influence of the load forecasting error and the availability of energy storage. Renewable Energy, 2020, 146: 2060-2069 doi: 10.1016/j.renene.2019.08.032
[8]	Tang C, Jian X, Sun Y, et al. A versatile mixture distribution and its application in economic dispatch with multiple wind farms. IEEE Transactions on Sustainable Energy, 2017, 8(4): 1747-1762 doi: 10.1109/TSTE.2017.2709755
[9]	Dong B, Li Z, Rahman S M M, et al. A hybrid model approach for forecasting future residential electricity consumption. Energy and Buildings, 2016, 117: 341-351 doi: 10.1016/j.enbuild.2015.09.033
[10]	赵书强, 张婷婷, 李志伟, 等. 基于数值特性聚类的日前光伏出力预测误差分布模型. 电力系统自动化, 2019, 43(13): 36-45 doi: 10.7500/AEPS20180405002 Zhao Shu-qiang, Zhang Ting-ting, Li Zhi-wei, et al. Distribution Model of Day-ahead Photovoltaic Power Forecasting Error Based on Numerical Characteristic Clustering. Automation of Electric Power Systems, 2019, 43(13): 36-45 doi: 10.7500/AEPS20180405002
[11]	Yang Y, Wu W, Wang B, Li M. Analytical Reformulation for Stochastic Unit Commitment Considering Wind Power Uncertainty With Gaussian Mixture Model. IEEE Transactions on Power Systems, 2020, 35(4): 2769-2782 doi: 10.1109/TPWRS.2019.2960389
[12]	Sun W, Zamani M, Hesamzadeh M R, Zhang H. Data-Driven Probabilistic Optimal Power Flow with Nonparametric Bayesian Modeling and Inference. IEEE Transactions on Smart Grid, 2020, 11(2): 1077-1090 doi: 10.1109/TSG.2019.2931160
[13]	Brockwell P J, Davis R A, Berger J O, Fienberg S E, Singer B. Time Series: Theory and Methods. Berlin: Springer-Verlag, 2015. 48−59
[14]	Kun Il Park. Fundamentals of Probability and Stochastic Processes with Applications to Communications, Berlin: Springer, 2018. 171−183
[15]	Han L, Jing H, Zhang R, et al. Wind power forecast based on improved Long Short-Term Memory network. Energy, 2019: 116300
[16]	Blei D M, Jordan M I. Variational inference for Dirichlet process mixtures. Bayesian Analysis, 2006, 1(1): 121-143
[17]	Li Z, Li Y, Liu Y, Wang P, Lu R, Gooi H B. Deep Learning Based Densely Connected Network for Load Forecasting. IEEE Transactions on Power Systems, 2021, 36(4): 2829-2840 doi: 10.1109/TPWRS.2020.3048359
[18]	McLachlan G J, Peel D. Finite Mixture Models. Wiley Series in Probability and Statistics. John Wiley & Sons Inc. 2000, 521−541
[19]	Bishop C M. Pattern Recognition and Machine Learning. Journal of Electronic Imaging, 2006, 16(4): 140-155
[20]	Bouguila N, Ziou D. A Dirichlet Process Mixture of Generalized Dirichlet Distributions for Proportional Data Modeling. IEEE Transactions on Neural Networks, 2010, 21(1): 107-122 doi: 10.1109/TNN.2009.2034851
[21]	Sethuraman J. A Constructive Definition of the Dirichlet Prior. Statistica Sinica, 1994, 4(2): 639-650
[22]	Dong H, Dwk B, Csp C. Prior selection method using likelihood confidence region and Dirichlet process Gaussian mixture model for Bayesian inference of building energy models. Energy and Buildings, 2020, 224: 110293 doi: 10.1016/j.enbuild.2020.110293
[23]	Akaike H. A new look at the statistical model identification. IEEE Transactions on Automatic Control, 1976, 19(6): 716-723
[24]	Wang Y, Liu Q. Comparison of Akaike information criterion and Bayesian information criterion in selection of stock–recruitment relationships. Fisheries Research, 2006, 77(2): 220-225 doi: 10.1016/j.fishres.2005.08.011
[25]	Khosravi A, Nahavandi S, Creighton D, et al. Lower Upper Bound Estimation Method for Construction of Neural Network-Based Prediction Intervals. IEEE Transactions on Neural Networks, 2011, 22(3): 337-346 doi: 10.1109/TNN.2010.2096824