基于VMD和Duffing振子算法的配电网差动保护

doi:10.11930/j.issn.1004-9649.202307005

摘要/Abstract

摘要：

配电网经消弧线圈接地，发生单相接地故障时，存在着故障特征弱、不明显的特点，很难准确找到故障线路，近年来随着通信等相关技术的发展，差动保护成本不断降低，使得配网差动保护的实现成为可能。提出变分模态分解（variational mode decomposition，VMD）和Duffing振子系统相结合的选线方法，VMD获取暂态零序电流的高频分量，将线路两侧高频零序电流相位差加入Duffing系统中，通过分析线路两侧高频分量相位差和Duffing系统状态的联系，构造了基于动态时间弯曲（dynamic time warping，DTW）描述系统状态变化的区内区外故障判据，实现故障准确定位，最后通过数值仿真证明该选线方法在不同过渡电阻、有分布式电源等情况下能够快速、准确定位线路上发生单相接地故障的区段，验证了该方法的有效性。所提故障区段定位算法可以有效提取故障特征，提高了保护的可靠性和选线的准确率。

关键词: 差动保护, 小电流系统, 变分模态分解, Duffing振子, 动态时间弯曲

Abstract:

The distribution network is grounded through arc suppression coil. When a single-phase grounding fault occurs, the faulting characteristics are often weak and unobvious, which makes it difficult to accurately locate the fault line. In recent years, with the development of communication and other related technologies, the cost of differential protection has decreased continuously, which makes it possible to realize the differential protection of distribution network. Therefore, a line selection method based on variational mode decomposition (VMD) and Duffing oscillator system is proposed. Firstly, the high-frequency component of transient zero-sequence current is obtained with VMD, and the phase difference of high-frequency zero-sequence current on both sides of the line is added to the Duffing system. And then, by analyzing the relationship between the phase difference of high-frequency components on both sides of the line and the state of the Duffing system, a fault criterion based on dynamic time warping (DTW) is constructed to realize the accurate location of the fault. Finally, numerical simulation proves that the proposed line selection method can quickly and accurately locate the single-phase ground fault sections for the lines that have different transition resistances and distributed power sources. The proposed fault section localization algorithm can effectively extract fault characteristics, thereby improving the reliability of protection and the accuracy of line selection.

Key words: differential protection, small current system, variational mode decomposition, Duffing oscillator, dynamic time warping

张健宝, 王磊, 江伟建. 基于VMD和Duffing振子算法的配电网差动保护[J]. 中国电力, 2024, 57(11): 26-35.

Jianbao ZHANG, Lei WANG, Weijian JIANG. Differential Protection of Distribution Network Based on VMD and Duffing Oscillator[J]. Electric Power, 2024, 57(11): 26-35.

导出引用管理器 EndNote|Ris|BibTeX

链接本文: https://www.electricpower.com.cn/CN/10.11930/j.issn.1004-9649.202307005

https://www.electricpower.com.cn/CN/Y2024/V57/I11/26

图/表 15

图 1 系统相轨迹

Fig.1 System phase trajectory

图 2 分解层数示意

Fig.2 Schematic diagram of decomposition level

图 3 幅值F随相位φ变化

Fig.3 Change of amplitude F with phase angle φ

图 4 不同φ1相轨迹对应的dx/x时间序列

Fig.4 The dx/x time series corresponding to different φ1 phase trajectories

图 5 不同φ1时DTW距离

Fig.5 Variation of DTW distance with φ1

图 6 故障选线流程

Fig.6 Fault line selection process

图 7 小电流接地系统双端电源主接线

Fig.7 The main wiring diagram of double-ended power supply in small current grounding system

图 8 线路L1区内、外单相接地短路两侧零序电流VMD分解

Fig.8 VMD decomposition of zero-sequence current on both sides of single-phase grounding short circuit inside and outside line L1

图 9 线路L1区内、外发生单相接地短路两侧暂态零序电流高频分量

Fig.9 High-frequency components of transient zero-sequence current on both sides of single-phase grounding short circuit inside and outside of line L1

表 1 发生A相经不同过渡电阻接地时的DTW距离

Table 1 The DTW distance of A phase grounding through different transition resistances

故障类型	故障位置	过渡电阻/Ω	D_k	故障区段
区内故障	K2	70	26.66	L1
		200	37.59	L1
		1000	29.48	L1
区外故障	K5	50	0.15	L2
		400	0.13	L2
		2000	0.13	L2

表 2 不同故障位置下的DTW距离

Table 2 The DTW distance at different fault locations

故障类型	故障位置	D_k	故障区段
区内故障	K1	28.84	L1
	K2	25.20	L1
	K3	26.53	L1
区外故障	K4	0.15	L2
	K5	0.13	L2
	K6	0.52	L2

图 10 不同合闸初相角和故障类型下的DTW距离

Fig.10 The DTW distance under different closing initial phase angles and fault types

图 11 考虑在DG接入的情况下的主接线

Fig.11 The main wiring with DG access

表 3 考虑DG接入的DTW距离

Table 3 The DTW distance with DG access

故障类型	故障位置	过渡电阻/Ω	D_k	故障区段
区内故障	K1	10	22.54	L1
		300	17.89	L1
		1300	24.01	L1
区外故障	K4	90	0.69	L2
		150	0.13	L2
		2100	0.13	L2

图 12 不同算法的故障识别准确率

Fig.12 The fault recognition accuracy of different algorithms

参考文献 25

1	刘斯琪, 喻锟, 曾祥君, 等. 基于零序电流幅值连调的小电流接地系统故障区段定位方法[J]. 电力系统保护与控制, 2021, 49 (9): 48- 56.
	LIU Siqi, YU Kun, ZENG Xiangjun, et al. Fault location method of a non-effective earthed system based on zero sequence current amplitude continuous regulation[J]. Power System Protection and Control, 2021, 49 (9): 48- 56.
2	刘志文, 董旭柱, 邹林, 等. 基于零序电流衰减周期分量的高阻接地故障区段定位[J]. 电力系统自动化, 2020, 44 (7): 161- 168. DOI
	LIU Zhiwen, DONG Xuzhu, ZOU Lin, et al. Section location method for high impedance grounding fault based on declining periodic component of zero sequence current[J]. Automation of Electric Power Systems, 2020, 44 (7): 161- 168. DOI
3	袁佳歆, 李响, 张哲维. 基于注入信号的有源配电网单相接地故障选线方法[J]. 电测与仪表, 2020, 57 (5): 44- 49.
	YUAN Jiaxin, LI Xiang, ZHANG Zhewei. Research on single-phase grounding fault selection technology for active distribution network based on injected signal[J]. Electrical Measurement & Instrumentation, 2020, 57 (5): 44- 49.
4	CHEN B C, YU N, CHEN B, et al. Fault location for underground cables in ungrounded MV distribution networks based on ZSC signal injection[J]. IEEE Transactions on Power Delivery, 2021, 36 (5): 2965- 2977. DOI
5	SONG G B, HOU J J, GUO B, et al. Single-ended active injection for fault location in hybrid MMC-HVDC systems[J]. International Journal of Electrical Power & Energy Systems, 2021, 124, 106344.
6	胡福年, 孙守娟. 基于图论的矩阵算法在配电网故障定位中的应用[J]. 中国电力, 2016, 49 (3): 94- 98. DOI
	HU Funian, SUN Shoujuan. Fault location of distribution network by applying matrix algorithm based on graph theory[J]. Electric Power, 2016, 49 (3): 94- 98. DOI
7	赵乔, 王增平, 董文娜, 等. 基于免疫二进制粒子群优化算法的配电网故障定位方法研究[J]. 电力系统保护与控制, 2020, 48 (20): 83- 89.
	ZHAO Qiao, WANG Zengping, DONG Wenna, et al. Research on fault location in a distribution network based on an immune binary particle swarm algorithm[J]. Power System Protection and Control, 2020, 48 (20): 83- 89.
8	高锋阳, 李昭君, 袁成, 等. 量子计算和免疫优化算法相结合的有源配电网故障定位[J]. 高电压技术, 2021, 47 (2): 396- 406.
	GAO Fengyang, LI Zhaojun, YUAN Cheng, et al. Fault location for active distribution network based on quantum computing and immune optimization algorithm[J]. High Voltage Engineering, 2021, 47 (2): 396- 406.
9	杨涛, 金华锋, 曾兵元, 等. 能量法小电流接地方向判据的应用研究[J]. 电力系统保护与控制, 2022, 50 (18): 116- 122.
	YANG Tao, JIN Huafeng, ZENG Bingyuan, et al. Application of the criterion of small current grounding direction of the energy method[J]. Power System Protection and Control, 2022, 50 (18): 116- 122.
10	周宇, 汤涛, 曾祥君, 等. 基于零序电流幅值比倍增系数的灵活接地系统故障选线方法[J]. 电力系统保护与控制, 2022, 50 (23): 112- 120.
	ZHOU Yu, TANG Tao, ZENG Xiangjun, et al. Fault line detection method for a flexible grounding system based on a zero-sequence current amplitude ratio multiplication coefficient[J]. Power System Protection and Control, 2022, 50 (23): 112- 120.
11	白杰, 邵文权, 程远, 等. 基于调节脱谐度的谐振接地系统故障选线方法的研究[J]. 电力电容器与无功补偿, 2019, 40 (3): 143- 147.
	BAI Jie, SHAO Wenquan, CHENG Yuan, et al. Study on fault line selection method of resonant grounding system based on adjusting detuning degree[J]. Power Capacitor & Reactive Power Compensation, 2019, 40 (3): 143- 147.
12	薛永端, 李天友, 李伟新, 等. 小电流接地故障暂态分析及区段定位新方法[J]. 电力系统自动化, 2014, 38 (23): 101- 107. DOI
	XUE Yongduan, LI Tianyou, LI Weixin, et al. A novel method of transient analysis and faulty section location for single-phase earth fault in non-effectively earthed network[J]. Automation of Electric Power Systems, 2014, 38 (23): 101- 107. DOI
13	徐艳春, 赵彩彩, 孙思涵, 等. 基于改进LMD和能量相对熵的主动配电网故障定位方法[J]. 中国电力, 2021, 54 (11): 133- 143.
	XU Yanchun, ZHAO Caicai, SUN Sihan, et al. Fault location for active distribution network based on improved LMD and energy relative entropy[J]. Electric Power, 2021, 54 (11): 133- 143.
14	孙永超, 邰能灵, 郑晓冬. 含分布式电源的配电网单相接地故障区段定位新方法[J]. 电力科学与技术学报, 2016, 31 (3): 73- 80. DOI
	SUN Yongchao, TAI Nengling, ZHENG Xiaodong. Research on single-phase grounding fault location of distribution network with DG[J]. Journal of Electric Power Science and Technology, 2016, 31 (3): 73- 80. DOI
15	王聪博, 贾科, 毕天姝, 等. 基于暂态电流波形相似度识别的柔性直流配电线路保护[J]. 电网技术, 2019, 43 (10): 3823- 3832.
	WANG Congbo, JIA Ke, BI Tianshu, et al. Protection for flexible DC distribution system based on transient current waveform similarity identification[J]. Power System Technology, 2019, 43 (10): 3823- 3832.
16	汤涛, 黄纯, 江亚群, 等. 基于高低频段暂态信号相关分析的谐振接地故障选线方法[J]. 电力系统自动化, 2016, 40 (16): 105- 111.
	TANG Tao, HUANG Chun, JIANG Yaqun, et al. Fault line selection method in resonant earthed system based on transient signal correlation analysis under high and low frequencies[J]. Automation of Electric Power Systems, 2016, 40 (16): 105- 111.
17	李卫国, 许文文, 王旭光, 等. 基于广义S变换的有源配电网故障定位方法[J]. 电测与仪表, 2021, 58 (6): 105- 112.
	LI Weiguo, XU Wenwen, WANG Xuguang, et al. Fault location method for active distribution network based on generalized S transform[J]. Electrical Measurement & Instrumentation, 2021, 58 (6): 105- 112.
18	王帅, 李立生, 宋晓东, 等. 基于小波包频段分解及综合能量系数的小电流接地系统故障定段方案[J]. 现代电子技术, 2019, 42 (1): 113- 118.
	WANG Shuai, LI Lisheng, SONG Xiaodong, et al. Fault section location strategy of small current grounding system based on wavelet packet frequency band decomposition and comprehensive energy coefficient[J]. Modern Electronics Technique, 2019, 42 (1): 113- 118.
19	张翠玲, 李云路. EMD及其能量变化曲线在小电流接地系统故障选线中的应用[J]. 电测与仪表, 2016, 53 (15): 101- 105. DOI
	ZHANG Cuiling, LI Yunlu. Application of EMD and energy curve to fault line detection in un-effectively grounded system[J]. Electrical Measurement & Instrumentation, 2016, 53 (15): 101- 105. DOI
20	DRAGOMIRETSKIY K, ZOSSO D. Variational mode decomposition[J]. IEEE Transactions on Signal Processing, 2014, 62 (3): 531- 544. DOI
21	赖志慧. 基于Duffing振子混沌和随机共振特性的微弱信号检测方法研究[D]. 天津: 天津大学, 2014.
	LAI Zhihui. Weak-signal detection based on the chaotic and stochastic-resonance characteristics of duffing oscillator[D]. Tianjin: Tianjin University, 2014.
22	许伯强, 郑泽慧. 基于Duffing系统与APES算法的DFIG定子匝间故障检测新方法[J]. 电力自动化设备, 2019, 39 (5): 103- 108.
	XU Boqiang, ZHENG Zehui. Novel method based on Duffing system and APES algorithm for stator winding inter-turn fault detection of DFIG[J]. Electric Power Automation Equipment, 2019, 39 (5): 103- 108.
23	CHEN T, CAO X Y, NIU D Z. Model modification and feature study of Duffing oscillator[J]. Journal of Low Frequency Noise Vibration and Active Control, 2022, 41 (1): 230- 243. DOI
24	牛耕, 周龙, 裴玮, 等. 低压有源配电网在线故障区间定位与识别方法[J]. 中国电机工程学报, 2017, 37 (9): 2525- 2539.
	NIU Geng, ZHOU Long, PEI Wei, et al. On-line fault section location and classification technique for low voltage active distribution network[J]. Proceedings of the CSEE, 2017, 37 (9): 2525- 2539.
25	童晓阳, 杨明杰, 张广骁. 基于改进DTW的行波波形相似性的高压直流输电线路保护方案[J]. 中国电机工程学报, 2020, 40 (12): 3878- 3888.
	TONG Xiaoyang, YANG Mingjie, ZHANG Guangxiao. A protection scheme for HVDC transmission line based on traveling waveform similarity using improved DTW algorithm[J]. Proceedings of the CSEE, 2020, 40 (12): 3878- 3888.

[1]	郑涛, 于佳旭, 眭程曦, 申由, 薛玉石, 武剑. 基于磁路耦合的Sen变压器差动保护方案[J]. 中国电力, 2025, 58(3): 108-118.
[2]	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.
[3]	王宇飞, 杜桐, 边伟国, 张钊, 刘慧婷, 杨丽君. 基于DTW K-medoids与VMD-多分支神经网络的多用户短期负荷预测[J]. 中国电力, 2024, 57(6): 121-130.
[4]	张博智, 张茹, 焦东翔, 王龙宇, 周一凡, 周丽霞. 基于VMD-SAST的电能质量扰动分类识别方法[J]. 中国电力, 2024, 57(2): 34-40.
[5]	陈庆斌, 杨耿煌, 耿丽清, 苏娟, 孙京生. 基于相似日选取和数据重构的短期光伏功率组合预测方法[J]. 中国电力, 2024, 57(12): 71-81.
[6]	王海燕, 钱林宇. 基于NGO-VMD的混合储能功率分配策略[J]. 中国电力, 2024, 57(11): 119-128.
[7]	朱佳, 王峰, 李一泉, 焦邵麟, 徐晓春, 赵青春. 基于Tanimoto相似度的变压器零序差动保护约束方案[J]. 中国电力, 2023, 56(8): 193-199.
[8]	徐艳春, 范钟耀, 孙思涵, MI Lu. 基于去趋势分析的大规模双馈风电场送出变压器差动保护[J]. 中国电力, 2023, 56(7): 186-197.
[9]	赵隆, 温冠儒, 刘志成, 袁鹏, 董新胜. 基于参数优化的VMD-SVD和LSTM的输电杆塔倾斜状态识别[J]. 中国电力, 2023, 56(12): 217-226, 237.
[10]	李文武, 石强, 李丹, 胡群勇, 唐芸, 梅锦超. 基于VMD和PSO-SVR的短期电力负荷多阶段优化预测[J]. 中国电力, 2022, 55(8): 171-177.
[11]	马宗彪, 许素安, 朱少斌, 王晶. 基于特征加权模糊聚类的电力负荷分类[J]. 中国电力, 2022, 55(6): 25-32.
[12]	张娜, 任强, 刘广忱, 郭力萍, 李静宇. 基于VMD-GWO-ELMAN的光伏功率短期预测方法[J]. 中国电力, 2022, 55(5): 57-65.
[13]	沙骏, 徐雨森, 刘冲冲, 冯定东, 胥峥, 臧海祥. 基于变分模态分解和分位数卷积-循环神经网络的短期风功率预测[J]. 中国电力, 2022, 55(12): 61-68.
[14]	杨胡萍, 余阳, 汪超, 李向军, 胡奕涛, 饶楚楚. 基于VMD-CNN-BIGRU的电力系统短期负荷预测[J]. 中国电力, 2022, 55(10): 71-76.
[15]	李满礼, 陈学通, 刘东洋, 丁卫东. 信息物理融合视角下的电流纵差保护可靠性分析[J]. 中国电力, 2019, 52(1): 25-31.