Fuzzy Metric Hierarchical Clustering Method for Wind Farm Wideband Oscillation Research

doi:10.11985/2024.01.028

Abstract

Abstract:

On account of the pressing goal of “carbon peaking and carbon neutrality”, it is extremely urgent to develop wind power and study the broadband oscillation problem of wind farm connected to the grid. With the purpose of establishing a simulation model suitable for wind farm oscillation research, which is able to accurately and efficiently reflect the actual wind farm output characteristics, a fuzzy hierarchical clustering method is proposed that improves the clustering result offset caused by distance measurement in traditional balanced iterative reducing and clustering using hierarchies. Besides, F test is used to evaluate the clustering effect quantitatively, and F score can be used to horizontally compare to determine the optimal cluster number and longitudinal comparison to determine the optimal clustering scheme. Compared with traditional clustering method, fuzzy metric hierarchical clustering method has the highest F score. Finally, a wind farm simulation example consisting of 25 wind turbines with actual parameters in PSCAD is set up, and the conclusion is obtained that the most suitable clustering method for wind farms is fuzzy metric hierarchical clustering method.

Key words: Wind farm, broadband oscillation, fuzzy metric hierarchical clustering, F test, clustering evaluation

CLC Number:

TM614

SONG Rui, GAN Jiatian, WANG Zejia, XU Decao, BAI Zuoxia, HAN Minxiao. Fuzzy Metric Hierarchical Clustering Method for Wind Farm Wideband Oscillation Research[J]. Journal of Electrical Engineering, 2024, 19(1): 261-271.

Figures/Tables 18

References 21

[1]	何君毅, 周瑀涵, 王康, 等. 主导模态保持的风电场站自适应等值方法[J]. 电力系统自动化, 2021, 45(11):28-36.
	HE Junyi, ZHOU Yuhan, WANG Kang, et al. Adaptive equivalent method of wind farm station based on dominant mode maintenance[J]. Automation of Electric Power Systems, 2021, 45(11):28-36.
[2]	杨茂, 彭天, 苏欣. 基于预测信息二维坐标动态划分的风电集群功率超短期预测[J]. 中国电机工程学报, 2022, 42(24):1-11.
	YANG Mao, PENG Tian, SU Xin. Ultra-short term wind power prediction based on two-dimensional coordinate dynamic division of prediction information[J]. Proceedings of the CSEE, 2022, 42(24):1-11.
[3]	李光辉, 王伟胜, 张兴, 等. 双馈风电场并网次/超同步振荡建模与机理分析:阻抗特性与振荡机理分析[J]. 中国电机工程学报, 2022, 42(10):3614-3626.
	LI Guanghui, WANG Weisheng, ZHANG Xing, et al. Modeling and mechanism analysis of sub- and super-synchronous oscillation of grid-connected dfig wind farms:Analysis of impedance characteristic and oscillation mechanism[J]. Proceedings of the CSEE, 2022, 42(10):3614-3626.
[4]	董文凯, 杜文娟, 王海风. 用于振荡稳定性分析的并网风电场动态等效模型[J]. 中国电机工程学报, 2021, 41(1):75-87.
	DONG Wenkai, DU Wenjuan, WANG Haifeng. Dynamic equivalent model of a grid-connected wind farm for oscillation stability analysis[J]. Proceedings of the CSEE, 2021, 41(1):75-87.
[5]	姜齐荣, 王玉芝. 电力电子设备高占比电力系统电磁振荡分析与抑制综述[J]. 中国电机工程学报, 2020, 40(22):7185-7201.
	JIANG Qirong, WANG Yuzhi. Overview of the analysis and mitigation methods of electromagnetic oscillations in power systems with high proportion of power electronic equipment[J]. Proceedings of the CSEE, 2020, 40(22):7185-7201.
[6]	孙瑶, 韩民晓, 黄永宁, 等. 考虑换流器外环特性的双馈风电场并网稳定性分析[J]. 电工电能新技术, 2021, 40(2):15-24. doi: 10.12067/ATEEE2006003
	SUN Yao, HAN Minxiao, HUANG Yongning, et al. General impedance model with out-loop for DFIG wind farm stability analysis[J]. Advanced Technology of Electrical Engineering, 2021, 40(2):15-24.
[7]	于一鸣. 风电场中高频谐振分析模型与抑制策略[D]. 北京: 华北电力大学, 2020.
	YU Yiming. Middle and high frequency resonance analysis model and suppression strategy of wind farm[D]. Beijing: North China Electric Power University, 2020.
[8]	王东风, 李嘉宇, 黄宇, 等. 风电场风速预测的密度峰值聚类方法研究[J]. 太阳能学报, 2021, 42(12):110-118.
	WANG Dongfeng, LI Jiayu, HUANG Yu, et al. Research on density peak clustering method for wind speed prediction of wind farm[J]. Acta Energiae Solaris Sinica, 2021, 42(12):110-118.
[9]	吴红斌, 何叶, 赵波, 等. 基于改进K-means聚类算法的风电场动态等值[J]. 太阳能学报, 2018, 39(11):3232-3238.
	WU Hongbin, HE Ye, ZHAO Bo, et al. Dynamic equivalence of wind farm based on improved K-means clustering algorithm[J]. Acta Energiae Solaris Sinica, 2018, 39(11):3232-3238.
[10]	孙启硕. 基于希尔伯特空间的含风电场电力系统随机稳定性分析[D]. 上海: 上海电机学院, 2020.
	SUN Qishuo. Stability analysis of power system with wind farm based on Hilbert space[D]. Shanghai: Shanghai DianJi University, 2020.
[11]	高金. 基于Dpeak等值建模的风电并网暂态电压稳定性分析[D]. 兰州: 兰州理工大学, 2021.
	GAO Jin. Transient voltage stability analysis of wind power grid connected based on Dpeak equivalent modeling[D]. Lanzhou: Lanzhou University of Technology, 2021.
[12]	徐玉琴, 王娜. 基于聚类分析的双馈机组风电场动态等值模型的研究[J]. 华北电力大学学报, 2013, 40(3):1-5.
	XU Yuqin, WANG Na. Study on dynamic equivalence of wind farms with DFIG based on clustering analysis[J]. Journal of North China Electric Power University, 2013, 40(3):1-5.
[13]	师洪涛, 闫佳, 丁茂生, 等. 基于新型多维功率趋势聚类的风电功率预测方法[J]. 高电压技术, 2022, 48(2):430-438.
	SHI Hongtao, YAN Jia, DING Maosheng, et al. Wind power prediction method based on novel multi-dimensional power trend clustering[J]. High Voltage Engineering, 2022, 48(2):430-438.
[14]	王一珺, 杜文娟, 王海风. 大规模风电汇集系统小干扰稳定性研究综述[J]. 电网技术, 2022, 46(5):1934-1946.
	WANG Yijun, DU Wenjuan, WANG Haifeng. Research on small signal stability analysis of large-scale wind power collection system:An overview[J]. Power System Technology, 2022, 46(5):1934-1946.
[15]	马静, 沈雅琦, 杜延菱, 等. 适应宽频振荡的风电并网系统主动阻尼技术综述[J]. 电网技术, 2021, 45(5):1673-1686.
	MA Jing, SHEN Yaqi, DU Yanling, et al. Overview on active damping technology of wind power integrated system adapting to broadband oscillation[J]. Power System Technology, 2021, 45(5):1673-1686.
[16]	李明节, 于钊, 许涛, 等. 新能源并网系统引发的复杂振荡问题及其对策研究[J]. 电网技术, 2017, 41(4):1035-1042.
	LI Mingjie, YU Zhao, XU Tao, et al. Study of complex oscillation caused by renewable energy integration and its solution[J]. Power System Technology, 2017, 41(4):1035-1042.
[17]	SU Zhongyue, WANG Jianzhou, LU Haiyan, et al. A new hybrid model optimized by an intelligent optimization algorithm for wind speed forecasting[J]. Energy Conversion & Management, 2014,85:443-452.
[18]	LIU Da, WANG Jilong, WANG Hui. Short-term wind speed forecasting based on spectral clustering and optimised echo state networks[J]. Renewable Energy, 2015,78:599-608.
[19]	WANG Xiaohui, YU Hao, LIN Yong, et al. Dynamic equivalent modeling for wind farms with DFIGs using the artificial bee colony with K-Means algorithm[J]. IEEE Access, 2020,8:173723-173731.
[20]	RODRIGUEZ A, LAIO A. Clustering by fast search and find of density peaks[J]. Science, 2014, 344(6191):1492-1496. doi: 10.1126/science.1242072
[21]	谢季坚, 刘承平. 模糊数学方法及其应用[M]. 4 版. 武汉: 华中科技大学出版社, 2013.
	XIE Jijian, LIU Chengping. Fuzzy mathematics methods and applications[M]. 4th ed. Wuhan: Huazhong University of Science and Technology Press, 2013.

电机参数	取值	控制参数	取值
额定容量S/(MV·A)	2	RSC内环PI	1.2+0.025/s
额定线电压U/V	690	RSC外环PI	2+0.02/0.05(P/Q)/s
额定频率f/Hz	50	RSC PLL PI	2.2+0.238/s
定/转子变比	0.85	GSC内环PI	1+0.01/s
定子电阻R_s/p.u.	0.005 4	GSC外环PI	0.4+0.01(U_dc)/s
转子电阻R_r/p.u.	0.006 07	GSC PLL PI	1.2+0.05/s
励磁互感L_m/p.u.	4.5	直流电容C/p.u.	4.396
定子漏感L_1s/p.u.	0.099 8	滤波器电感L_f/p.u.	1.524×10^-6
转子漏感L_1r/p.u.	0.109 8	滤波器电容C_f/p.u.	0.061 544
电机漏磁系数σ	0.045	变压器变比N1/2/3	35/0.69/0.69

机组编号	风速/(m/s)	有功功率/MW	无功功率/MVar	出口电流/kA
1	8.33	1.198	0.005 80	0.018 5
2	8.53	1.25	0.005 65	0.019 6
3	12.7	2.001	0.002 73	0.032 2
4	10.87	2.012	0.000 70	0.032 0
5	8.71	1.278	0.001 30	0.021 0
6	11.3	2.008	0.000 36	0.032 3
7	9.21	1.476	0.001 39	0.023 7
8	12.88	2.003	0.004 26	0.032 2
9	9.47	1.565	0.001 34	0.024 7
10	9.64	1.624	0.005 13	0.026 0
11	9.84	1.702	0.001 53	0.027 2
12	9.9	1.722	0.009 29	0.028 4
13	13.11	2.005	0.000 72	0.032 0
14	13.45	2.005	0.005 26	0.032 1
15	13.56	2.001	0.007 97	0.032 0
16	11.28	2.001	0.006 06	0.032 3
17	10.2	1.86	0.006 83	0.030 6
18	10.51	2.006	0.006 11	0.032 8
19	10.63	2.017	0.009 80	0.032 8
20	10.8	2.003	0.006 09	0.032 7
21	11.2	2.004	0.006 79	0.032 0
22	11.45	2.004	0.000 65	0.032 1
23	11.52	2.005	0.001 34	0.032 1
24	12.1	1.991	0.006 23	0.032 8
25	14.23	1.999	0.004 88	0.032 8

簇编号	风机聚类结果	中心机组特性[V, P, Q, I]
①	{3, 4, 6, 8, 13, 14, 15, 16, 18, 19, 20, 21, 22, 23, 24, 25}	[11.974, 2.004, 0.043 7, 0.032 3]
②	{10, 11, 12, 17}		[9.895, 1.727, 0.056 9, 0.028 0]
③	{1, 2, 5, 7, 9}		[8.85, 1.353, 0.030 9, 0.021 5]

特性	自由度	均方差	F平分	P(P<0.001时显著)
风速	2	1.117	108.43	<0.001
有功	2	1.240	140.972	<0.001
无功	2	0.085	0.897	0.422
电流	2	1.115	121.948	<0.001
多变量检验结果：三簇聚类F评分为62.284

簇编号	风机聚类结果	中心机组特性[V, P, Q, I]
①	{8, 12, 14, 15, 16, 17, 18, 19, 20, 21, 24, 25}	[11.9, 2.004, 0.005 37, 0.032 4]
②	{3, 4, 6, 13, 22, 23}	[12.195, 2.004, 0.013 6, 0.032 1]
③	{10, 11, 12, 17}	[9.895, 1.727, 0.056 9, 0.028 0]
④	{1, 2, 5, 7, 9}	[8.85, 1.353, 0.030 9, 0.021 5]