基于VMD分解下的皮尔逊相关性分析及T-tFD的混合储能容量配置

doi:10.11930/j.issn.1004-9649.202403025

摘要/Abstract

摘要：

在清洁能源发展迅速的大环境下，风电出力的随机性和波动性会对电力系统的稳定造成影响，因此对风电波动平抑是当前清洁能源发展的一个基础性问题。提出一种基于改进后的北方苍鹰算法（sine-cosine northern goshawk optimization，SCNGO）优化变分模态分解（VMD）参数平抑风电波动的混合储能容量配置策略，对风电功率进行参数优化的VMD过后利用皮尔逊相关性分析判断强弱相关分界点，经过2次分配后得到并网功率与混合储能功率；对混合储能功率进行基于t检验分频算法的功率分配，得到蓄电池/超级电容的容量配置。基于此策略，以储能元件年综合成本作为模型，结合算例进行经济性评估并对并网功率进行波动量分析及改进北方苍鹰算法的优越性分析。结果表明：基于SCNGO-VMD的储能容量配置策略能有效平抑风电波动，平抑后的并网功率1 min、10 min的最大波动量仅为国家要求的18.2%、45.52%，相应的储能配置成本为传统配置策略中的最低值。其配置的混合储能容量更具经济性，验证了改进的北方苍鹰算法在迭代速度与精度上均优于传统的智能优化算法。

关键词: 混合储能, 容量配置, 变分模态分解, 北方苍鹰算法, 皮尔逊相关性分析, t检验

Abstract:

In the context of rapid development of clean energy, the stochasticity and volatility of wind power output have significant impacts on the stability of power system, so wind power fluctuation smoothing is a basic problem for the current clean energy development. A hybrid energy storage capacity allocation strategy based on SCNGO-VMD is proposed to smooth wind power fluctuations. After variational mode decomposition (VMD) of the wind power parameter optimization, the Pearson correlation analysis is used to judge the boundary points of strong and weak correlation, and the grid-connected power and hybrid energy storage power are obtained after two allocations; The hybrid energy storage power is allocated based on T-test frequency division (T-tFD) algorithm, and the capacity configuration of battery/ultra-capacitor is obtained. Based on this strategy, the annual comprehensive cost of energy storage components is used as the model to evaluate the economics through case study. And the fluctuation of grid-connected power and the superiority of the SCNGO are analyzed. The results show that the energy storage capacity allocation strategy based on SCNGO-VMD can effectively smooth wind power fluctuations. The maximum fluctuation of the smoothed grid-connected power for 1 minute and 10 minutes is only 18.2% and 45.52% of the national requirements, and the corresponding energy storage configuration cost is the lowest among traditional configuration strategies. The configured hybrid energy storage capacity is more economical. Meanwhile, it is verified that the SCNGO is superior to the traditional intelligent optimization algorithm in iteration speed and accuracy.

Key words: hybrid energy storage, capacity allocation, variational mode decomposition, northern goshawk optimization, Pearson correlation analysis, t-test

刘抒睿, 李培强, 陈家煜, 郭雅诗. 基于VMD分解下的皮尔逊相关性分析及T-tFD的混合储能容量配置[J]. 中国电力, 2024, 57(7): 82-97.

Shurui LIU, Peiqiang LI, Jiayu CHEN, Yashi GUO. Allocation of Hybrid Energy Storage Capacity Based on Pearson Correlation Analysis and T-tFD Algorithm under VMD Decomposition[J]. Electric Power, 2024, 57(7): 82-97.

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链接本文: https://www.electricpower.com.cn/CN/10.11930/j.issn.1004-9649.202403025

https://www.electricpower.com.cn/CN/Y2024/V57/I7/82

图/表 25

图 1 风储联合系统拓扑

Fig.1 Topology of wind power-storage joint system

表 1 国家标准风电波动要求

Table 1 Wind power fluctuation requirements by national standard

装机容量/MW	1 min最大波动量/MW	10 min最大波动量/MW
＜30	3	10
30~50	装机容量/10	装机容量/3
＞50	15	50

图 2 本文功率分配方法

Fig.2 Power allocation method used in this article

图 3 步长搜索因子与权重值曲线

Fig.3 Step search factor and weight value curve

图 4 SCNGO-VMD算法流程

Fig.4 SCNGO-VMD algorithm flowchart

图 5 功率分配算法流程

Fig.5 Power allocation algorithm flowchart

图 6 风电出力

Fig.6 Wind power output

表 2 1 min与10 min波动量分析

Table 2 Analysis of 1 min and 10 min fluctuations

数据	10 min最大波动/MW	1 min最大波动/MW
国家标准并网要求	17.1	5.00
本文P_wind	18.1	9.46

图 7 最优值在散点图以及空间拟合的分布

Fig.7 The distribution of optimal values in spatial fitting and scatter plots

图 8 第1次相关性分析结果

Fig.8 Results of the first correlation analysis

图 9 风电出力与部分IMF分量对比

Fig.9 Comparison between wind power output and some IMF components

图 10 第2次相关性分析结果

Fig.10 Results of the second correlation analysis

图 11 强相关分量曲线特征

Fig.11 Characteristics of strongly correlated component curves

表 3 t检验结果

Table 3 T-test results

IMF分量		1		2		3		4		5		6		7		8		9
t检验结果		1		1		0		0		0		0		0		0		0

图 12 IMF(1)与IMF(9)的包络线

Fig.12 IMF(1) and IMF(9) envelope lines

图 13 蓄电池/超级电容器功率分配

Fig.13 Battery/supercapacitor power distribution

图 14 1 min波动量对比

Fig.14 Comparison of 1-minute volatility

图 15 10 min波动量对比

Fig.15 Comparison of 10-minute volatility

表 4 储能相关参数

Table 4 Energy storage related parameters

储能类型	参数	数值
蓄电池（BAT）	单位功率成本/(元·kW^–1)	3400
	单位容量成本/(元·(kW·h)^–1)	2200
	年运行成本/(元·(kW·h)^–1)	370
	年维护成本/(元·(kW·h)^–1)	90
	年报废置换成本/(元·(kW·h)^–1)	120
	充放电效率/%	85
	SOC上下限	(0.8, 0.2)
	蓄电池寿命/年	10
超级电容器（SC）	单位功率成本/(元·kW^–1)	1100
	单位容量成本/(元·(kW·h)^–1)	12000
	年运行成本/(元·(kW·h)^–1)	200
	年维护成本/(元·(kW·h)^–1)	0
	年报废置换成本/(元·(kW·h)^–1)	30
	充放电效率/%	95
	SOC上下限	(0.9, 0.1)
	超级电容寿命/年	20
其他	风电工程寿命/年	20
其他	贴现率/%	0.06

图 16 不同分界点功率/容量曲线

Fig.16 Power/capacity curves at different boundary points

图 17 EMD、VMD不同分界点成本曲线

Fig.17 Cost curves at different boundary points of EMD and VMD

图 18 VMD分解各IMF频谱

Fig.18 Spectra of each IMF after VMD decomposition

图 19 EMD分解各IMF频谱

Fig.19 Spectra of each IMF after EMD decomposition

表 5 各分配策略结果分析

Table 5 Results of different allocation strategies

策略	P_bN/MW	E_bN/(MW·h)	P_sN/MW	E_sN/(MW·h)	C_HESS/万元
蓄电池	7.595	0.207	—	—	4398.212
超级电容	—	—	7.195	0.153	4458.735
EMD+ T-tFD	5.878	0.205	6.198	0.097	4178.735
VMD+ T-tFD	5.807	0.201	5.797	0.059	2198.760

图 20 迭代次数对比

Fig.20 Comparison of iteration times

参考文献 28

1	王浩浩, 陈嘉俊, 朱涛, 等. 计及储能寿命与调频性能的风储联合投标模型及算法[J]. 电网技术, 2021, 45 (1): 208- 217.
	WANG Haohao, CHEN Jiajun, ZHU Tao, et al. Joint bidding model and algorithm of wind-storage system considering energy storage life and frequency regulation performance[J]. Power System Technology, 2021, 45 (1): 208- 217.
2	张丽英, 叶廷路, 辛耀中, 等. 大规模风电接入电网的相关问题及措施[J]. 中国电机工程学报, 2010, 30 (25): 1- 9.
	ZHANG Liying, YE Tinglu, XIN Yaozhong, et al. Problems and measures of power grid accommodating large scale wind power[J]. Proceedings of the CSEE, 2010, 30 (25): 1- 9.
3	杜刚, 赵冬梅, 刘鑫. 计及风电不确定性优化调度研究综述[J]. 中国电机工程学报, 2023, 43 (7): 2608- 2627.
	DU Gang, ZHAO Dongmei, LIU Xin. Research review on optimal scheduling considering wind power uncertainty[J]. Proceedings of the CSEE, 2023, 43 (7): 2608- 2627.
4	朱向芬. 基于粒子群算法的混合储能系统容量优化配置[D]. 银川: 宁夏大学, 2014.
	ZHU Xiangfen. Capacity optimization of hybrid energy storage on PSO algorithm[D]. Yinchuan: Ningxia University, 2014.
5	吴振威, 蒋小平, 马会萌, 等. 用于混合储能平抑光伏波动的小波包–模糊控制[J]. 中国电机工程学报, 2014, 34 (3): 317- 324.
	WU Zhenwei, JIANG Xiaoping, MA Huimeng, et al. Wavelet packet-fuzzy control of hybrid energy storage systems for PV power smoothing[J]. Proceedings of the CSEE, 2014, 34 (3): 317- 324.
6	王成山, 于波, 肖峻, 等. 平滑可再生能源发电系统输出波动的储能系统容量优化方法[J]. 中国电机工程学报, 2012, 32 (16): 1- 8.
	WANG Chengshan, YU Bo, XIAO Jun, et al. Sizing of energy storage systems for output smoothing of renewable energy systems[J]. Proceedings of the CSEE, 2012, 32 (16): 1- 8.
7	韩晓娟, 田春光, 程成, 等. 基于经验模态分解的混合储能系统功率分配方法[J]. 太阳能学报, 2014, 35 (10): 1889- 1896. DOI
	HAN Xiaojuan, TIAN Chunguang, CHENG Cheng, et al. Power allocation method of hybrid energy storage system based on empirical mode decomposition[J]. Acta Energiae Solaris Sinica, 2014, 35 (10): 1889- 1896. DOI
8	韩晓娟, 陈跃燕, 张浩, 等. 基于小波包分解的混合储能技术在平抑风电场功率波动中的应用[J]. 中国电机工程学报, 2013, 33 (19): 8- 13, 24.
	HAN Xiaojuan, CHEN Yueyan, ZHANG Hao, et al. Application of hybrid energy storage technology based on wavelet packet decomposition in smoothing the fluctuations of wind power[J]. Proceedings of the CSEE, 2013, 33 (19): 8- 13, 24.
9	李鑫, 王娟, 邱亚, 等. 基于VMD的混合储能容量优化配置[J]. 太阳能学报, 2022, 43 (2): 88- 96.
	LI Xin, WANG Juan, QIU Ya, et al. Optimal allocation of hybrid energy storage capacity based on variational mode decomposition[J]. Acta Energiae Solaris Sinica, 2022, 43 (2): 88- 96.
10	黄利祥, 张新燕, 梁帅, 等. 一种用于平抑风光功率波动的混合储能容量配置方法[J]. 现代电子技术, 2023, 46 (9): 173- 177.
	HUANG Lixiang, ZHANG Xinyan, LIANG Shuai, et al. Method of hybrid energy storage capacity allocation for stabilizing fluctuation of wind-PV power[J]. Modern Electronics Technique, 2023, 46 (9): 173- 177.
11	高晓芝, 王磊, 田晋, 等. 基于参数优化变分模态分解的混合储能功率分配策略[J]. 储能科学与技术, 2022, 11 (1): 147- 155.
	GAO Xiaozhi, WANG Lei, TIAN Jin, et al. Research on hybrid energy storage power distribution strategy based on parameter optimization variational mode decomposition[J]. Energy Storage Science and Technology, 2022, 11 (1): 147- 155.
12	程昱明, 孟高军, 贾鹏, 等. 用于平抑风电功率波动的混合储能容量优化配置方法[J/OL]. 电源学报, 1–13[2024-03-06]. http://kns.cnki.net/kcms/detail/12.1420.TM.20230106.1644.003.html.
	CHENG Yuming, MENG Gaojun, JIA Peng, et al. Optimization configuration method of hybrid energy storage capacity for suppressing wind power fluctuations [J/OL]. Journal of Power Supply, 1–13 [2024-03-06]. http://kns.cnki.net/kcms/detail/12.1420.TM.20230106.1644.003.html.
13	冯磊, 杨淑连, 徐达, 等. 考虑风电输出功率波动性的混合储能容量多级优化配置[J]. 热力发电, 2019, 48 (10): 44- 50.
	FENG Lei, YANG Shulian, XU Da, et al. Multistage optimal capacity configuration of hybrid energy storage considering wind power fluctuation[J]. Thermal Power Generation, 2019, 48 (10): 44- 50.
14	李学斌, 赵号. 基于维纳随机过程的风电场储能配置方法[J]. 电网技术, 2022, 46 (9): 3437- 3446.
	LI Xuebin, ZHAO Hao. Wind farm energy storage configuration based on Wiener stochastic process[J]. Power System Technology, 2022, 46 (9): 3437- 3446.
15	国家质量监督检验检疫总局, 中国家标准化管理委员会. 风电场接入电力系统技术规定: GB/Z 19963—2005[S]. 北京: 中国标准出版社, 2006.
	General Administration of Quality Supervision, Inspection and Quarantine of the People’s Republic of China, Standardization Administration of the People’s Republic of China. Technical rule for connecting wind farm to power network: GB/Z 19963—2005[S]. Beijing: Standards Press of China, 2006.
16	李霄, 胡长生, 刘昌金, 等. 基于超级电容储能的风电场功率调节系统建模与控制[J]. 电力系统自动化, 2009, 33 (9): 86- 90. DOI
	LI Xiao, HU Changsheng, LIU Changjin, et al. Modelling and controlling of SCES based wind farm power regulation system[J]. Automation of Electric Power Systems, 2009, 33 (9): 86- 90. DOI
17	LI W, JOÓS G, ABBEY C. Wind power impact on system frequency deviation and an ESS based power filtering algorithm solution[C]//2006 IEEE PES Power Systems Conference and Exposition. Atlanta, GA, USA. IEEE, 2006: 2077–2084.
18	毛志宇, 李培强, 马德鑫, 等. 基于风功率波动平抑的复合储能两次功率分配容量配置方法研究[J]. 电网技术, 2023, 47 (10): 4111- 4123.
	MAO Zhiyu, LI Peiqiang, MA Dexin, et al. Double power allocation of capacity configuration of compound energy storage based on wind power smoothing[J]. Power System Technology, 2023, 47 (10): 4111- 4123.
19	戴申华, 王琨玥, 曹蓓, 等. 基于CEEMDAN功率分解的火电厂混合储能容量优化配置[J]. 电气工程学报, 2024, 19 (1): 57- 66.
	DAI Shenhua, WANG Kunyue, CAO Bei, et al. Optimal configuration of hybrid energy storage capacity in thermal power plants based on CEEMDAN power decomposition[J]. Journal of Electrical Engineering, 2024, 19 (1): 57- 66.
20	DRAGOMIRETSKIY K, ZOSSO D. Variational mode decomposition[J]. IEEE Transactions on Signal Processing, 2014, 62 (3): 531- 544. DOI
21	王玉梅, 郑义. 基于参数优化的VMD与TEO融合的微电网电能质量检测方法[J]. 电气工程学报, 2023, 18 (2): 164- 173. DOI
	WANG Yumei, ZHENG Yi. Microgrid power quality detection method based on parameter optimization fusion of VMD and TEO[J]. Journal of Electrical Engineering, 2023, 18 (2): 164- 173. DOI
22	DEHGHANI M, HUBÁLOVSKÝ Š, TROJOVSKÝ P. Northern goshawk optimization: a new swarm-based algorithm for solving optimization problems[J]. IEEE Access, 2021, 9, 162059- 162080. DOI
23	邵鹏, 吴志健, 周炫余, 等. 基于折射原理反向学习模型的改进粒子群算法[J]. 电子学报, 2015, 43 (11): 2137- 2144. DOI
	SHAO Peng, WU Zhijian, ZHOU Xuanyu, et al. Improved particle swarm optimization algorithm based on opposite learning of refraction[J]. Acta Electronica Sinica, 2015, 43 (11): 2137- 2144. DOI
24	刘波, 张焰, 杨娜. 改进的粒子群优化算法在分布式电源选址和定容中的应用[J]. 电工技术学报, 2008, 23 (2): 103- 108. DOI
	LIU Bo, ZHANG Yan, YANG Na. Improved particle swarm optimization method and its application in the siting and sizing of distributed generation planning[J]. Transactions of China Electrotechnical Society, 2008, 23 (2): 103- 108. DOI
25	MIRJALILI S. SCA: a Sine Cosine Algorithm for solving optimization problems[J]. Knowledge-Based Systems, 2016, 96, 120- 133. DOI
26	牛东晓, 李媛媛, 乞建勋, 等. 基于经验模式分解与因素影响的负荷分析方法[J]. 中国电机工程学报, 2008, 28 (16): 96- 102. DOI
	NIU Dongxiao, LI Yuanyuan, QI Jianxun, et al. A novel approach for load analysis based on empirical mode decomposition and influencing factors[J]. Proceedings of the CSEE, 2008, 28 (16): 96- 102. DOI
27	姜飞, 林政阳, 王文烨, 等. 考虑最小平均包络熵负荷分解的最优Bagging集成超短期多元负荷预测[J]. 中国电机工程学报, 2024, 44 (5): 1777- 1789.
	JIANG Fei, LIN Zhengyang, WANG Wenye, et al. Optimal bagging ensemble ultra short term multi-energy load forecasting considering least average envelope entropy load decomposition[J]. Proceedings of the CSEE, 2024, 44 (5): 1777- 1789.
28	S A R M, R N C, B C B, et al. Online feature Selection using Pearson Correlation Technique[C]//2022 IEEE 7th International Conference on Recent Advances and Innovations in Engineering (ICRAIE). MANGALORE, India. IEEE, 2022: 172–177.

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