基于DBSCAN聚类和区间回归的多谐波责任划分

doi:10.11930/j.issn.1004-9649.202303072

中国电力 ›› 2024, Vol. 57 ›› Issue (2): 138-148.DOI: 10.11930/j.issn.1004-9649.202303072

基于DBSCAN聚类和区间回归的多谐波责任划分

陈仕龙(), 吴涛, 郭成(), 张梓睿, 孙竟豪

1. 昆明理工大学电力工程学院，云南昆明　650500

收稿日期:2023-03-15 接受日期:2023-12-19 出版日期:2024-02-28 发布日期:2024-02-28
作者简介:陈仕龙（1973—），男，博士，教授，从事电力系统新型继电保护、电能质量分析等研究，E-mail：chenshilong3@126.com
郭成（1978—），男，通信作者，博士，教授，从事为电能质量分析与控制、电力系统性稳定分析等研究，E-mail：gc325@126.com
基金资助:
国家自然科学基金资助项目（特高压多端混合直流输电线路行波边界保护研究，52067009）；云南省联合基金重点项目（高比例新能源与异步系统的机网协调特性及控制策略研究，202201BE070001-15）。

Division of Multi-harmonic Responsibilities Based on DBSCAN Clustering and Interval Regression

Shilong CHEN(), Tao WU, Cheng GUO(), Zirui ZHANG, Jinghao SUN

1. Faculty of Electric Power Engineering, Kunming University of Science and Technology, Kunming 650500, China

Received:2023-03-15 Accepted:2023-12-19 Online:2024-02-28 Published:2024-02-28
Supported by:
This work is supported by National Natural Science Foundation of China (Research on Travelling Wave Boundary Protection for Multi-terminal Hybrid UHVDC Transmission Line, No.52067009) and Key Project of Yunnan Provincial Joint Foundation (Research on Machine Network Coordination Characteristics and Control Strategies of High Ratio New Energy and Asynchronous Systems, No. 202201BE070001-15).

摘要/Abstract

摘要：

在背景谐波阻抗变化和背景谐波电压波动的情况下，传统谐波责任划分方法难以适用于现有的统计型谐波监测数据，提出一种背景谐波变化下基于监测数据的多谐波责任划分方法。首先，构建谐波监测数据区间样本集，并建立背景谐波变化下的多谐波源区间谐波责任划分数学模型；其次，利用基于密度的聚类算法（DBSCAN）将采集到的统计型谐波数据集以簇为评价周期进行场景划分，并采用滑窗动态相关性分析方法筛选出满足线性关系阈值要求的数据；最后，利用基于参数化回归算法（PM）的区间线性进行方程参数计算并获取最佳样本划分方案，在构造的区间谐波责任划分基础上计算中长期时间范畴的谐波责任。利用实际电网中的谐波监测数据对所提方法进行验证，验证了该方法能利用现有的统计型谐波监测数据在背景谐波变化的情况下对每个谐波源进行合理时间尺度的谐波责任划分，可为实际电力系统运行过程中的多谐波责任划分提供一种新的思路。

关键词: 电能质量, 监测数据, DBSCAN聚类, 区间回归, 谐波责任划分

Abstract:

The traditional harmonic responsibility division methods are not applicable to the existing statistical harmonic monitoring data in the context of background harmonic impedance changes and background harmonic voltage fluctuations. Therefore, this paper proposes a multi-harmonic responsibility division method based on monitoring data under background harmonic changes. Firstly, a harmonic monitoring data interval sample set is constructed, and a mathematical model of multi-harmonic source interval harmonic responsibility division under background harmonic changes is established. Secondly, the collected statistical harmonic data set is clustered as the evaluation period by DBSCAN, and the data satisfying the linear relationship threshold requirement is screened by sliding window dynamic correlation analysis. Finally, the equation parameter and the optimal sample division scheme are obtained with the PM algorithm-based interval linear regression method, and the harmonic responsibility in the medium and long term time scope is calculated on the basis of the constructed interval harmonic responsibility division. The harmonic monitoring data of an actual power grid is used to verify the proposed method, and it is proved that the proposed method can use the existing statistical harmonic monitoring data to allocate the harmonic responsibility of each harmonic source in a reasonable time scale under background harmonic changes, which can provide new ideas for the division of responsibility for multiple harmonics during the operation of the actual power system.

Key words: power quality, monitoring data, DBSCAN clustering, interval regression, harmonic responsibility division

陈仕龙, 吴涛, 郭成, 张梓睿, 孙竟豪. 基于DBSCAN聚类和区间回归的多谐波责任划分[J]. 中国电力, 2024, 57(2): 138-148.

Shilong CHEN, Tao WU, Cheng GUO, Zirui ZHANG, Jinghao SUN. Division of Multi-harmonic Responsibilities Based on DBSCAN Clustering and Interval Regression[J]. Electric Power, 2024, 57(2): 138-148.

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链接本文: https://www.electricpower.com.cn/CN/10.11930/j.issn.1004-9649.202303072

https://www.electricpower.com.cn/CN/Y2024/V57/I2/138

图/表 12

图 1 电能质量监测系统与数据采集示意

Fig.1 Schematic diagram of power quality monitoring system and data acquisition

图 2 谐波电压向量关系

Fig.2 Harmonic voltage vector relationship

图 3 谐波阻抗变化与谐波电压波动示意

Fig.3 Schematic diagram of harmonic impedance variation and harmonic voltage fluctuation

图 4 谐波责任划分方法流程

Fig.4 Harmonic responsibility division method flow chart

图 5 dSSE与L关系

Fig.5 Relationship between dSSE and L

表 1 9次谐波各场景区间参数[α1]计算结果

Table 1 Calculation results of the parameter [α1] for the interval of each scenario of the 9th harmonic

场景	馈线1	馈线2	馈线3
1	[11.40, 12.64]	[–3.58, –2.65]	[0.27, 0.31]
2	[12.36, 13.81]	[–3.72, –2.78]	[0.33, 0.36]
3	[10.56, 12.19]	[–2.19, –0.82]	[0.23, 0.29]
4	[11.95, 13.25]	[–2.74, –1.84]	[0.31, 0.35]
5	[12.28, 13.58]	[–2.85, –1.50]	[0.21, 0.24]
6	[11.48, 12.62]	[–3.33, –2.37]	[0.29, 0.33]
7	[12.21, 13.97]	[–2.23, –1.61]	[0.25, 0.28]

图 6 动态9次谐波责任箱线图

Fig.6 Dynamic 9th harmonic responsibility box line diagram

表 2 各场景下9次谐波责任标幺值的划分

Table 2 Division of responsibility p.u. for the 9th harmonic in each scenario

场景	馈线1	馈线2	馈线3
1	0.1754	–0.2362	1.0608
2	0.1634	–0.2587	1.0953
3	0.1373	–0.0762	0.9389
4	0.1767	–0.2131	1.0364
5	0.1543	–0.1922	1.0379
6	0.1497	–0.2635	1.1138
7	0.1238	–0.2473	1.1235

表 3 9次谐波责任标幺值的划分统计分析

Table 3 Statistical analysis of the division of responsibility p.u. for the 9th harmonic

谐波源馈线	动态谐波责任指标		全时段总谐波责任值指标
谐波源馈线	最大责任值	最小责任值	全时段总谐波责任值指标
1	0.176 7	0.123 8	0.154 4
2	–0.263 5	–0.076 2	–0.212 5
3	1.123 5	0.938 9	1.058 1

图 7 馈线9次谐波电流和母线9次谐波电压概率密度曲线

Fig.7 Feeder 9th harmonic current and busbar 9th harmonic voltage probability density curve

表 4 各场景下的7次谐波责任标幺值的划分

Table 4 Division of the responsibility p.u. for the 7th harmonic in each scenario

场景	馈线1	馈线2	馈线3
1	0.9059	–0.2583	0.3524
2	0.8868	–0.2994	0.4126
3	0.8291	–0.0881	0.2590
4	0.9659	–0.2532	0.2873
5	0.9481	–0.2631	0.3150
6	0.9300	–0.3386	0.4086
7	0.7395	–0.3826	0.6431

表 5 7次谐波责任标幺值的划分统计分析

Table 5 Statistical analysis of the division of responsibility p.u. for the 7th harmonic

谐波源馈线	动态谐波责任指标		全时段总谐波责任值指标
谐波源馈线	最大责任值	最小责任值	全时段总谐波责任值指标
1	0.965 9	0.739 5	0.886 5
2	–0.382 6	–0.088 1	–0.269 0
3	0.643 1	0.259 0	0.382 6

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基于DBSCAN聚类和区间回归的多谐波责任划分

Division of Multi-harmonic Responsibilities Based on DBSCAN Clustering and Interval Regression

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基于DBSCAN聚类和区间回归的多谐波责任划分

Division of Multi-harmonic Responsibilities Based on DBSCAN Clustering and Interval Regression

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