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Article(id=1149789678045459085, tenantId=1146029695717560320, journalId=1146123166801305609, issueId=1149768563956826506, articleNumber=null, orderNo=null, doi=10.12404/j.issn.1671-1815.2406617, pmid=null, cstr=null, oa=null, hot=null, price=null, onlineType=0, articleFormat=0, articleType=null, articleTypeStr=null, receivedDate=1725292800000, receivedDateStr=2024-09-03, revisedDate=1742400000000, revisedDateStr=2025-03-20, acceptedDate=null, acceptedDateStr=null, onlineDate=1752060821305, onlineDateStr=2025-07-09, pubDate=1749312000000, pubDateStr=2025-06-08, doiRegisterDate=null, doiRegisterDateStr=null, onlineIssueDate=1752060821305, onlineIssueDateStr=2025-07-09, onlineJustAcceptDate=null, onlineJustAcceptDateStr=null, onlineFirstDate=null, onlineFirstDateStr=null, sourceXml=null, magXml=null, createTime=1752060821305, creator=13701087609, updateTime=1752060821305, updator=13701087609, issue=Issue{id=1149768563956826506, tenantId=1146029695717560320, journalId=1146123166801305609, year='2025', volume='25', issue='16', pageStart='6587', pageEnd='7021', issueExtLink='null', onlineDate='null', pubDate='null', beforeIssueId=null, nextIssueId=null, price=null, status=1, issueComplete=1, articleOrder=1, issueType=-1, specialIssue=0, createTime=1752055787314, creator=13701087609, updateTime=1768456850262, updator=13701087609, preIssue=null, nextIssue=null, ext={EN=IssueExt(id=1218559607937618069, tenantId=1146029695717560320, journalId=1146123166801305609, issueId=1149768563956826506, language=EN, specialIssueTitle=, coverIllustrator=, specialIssueEditor=, specialIssueAbout=), CN=IssueExt(id=1218559607937618070, tenantId=1146029695717560320, journalId=1146123166801305609, issueId=1149768563956826506, language=CN, specialIssueTitle=, coverIllustrator=, specialIssueEditor=, specialIssueAbout=)}, issueFiles=null}, startPage=6789, endPage=6796, ext={EN=ArticleExt(id=1149789678280340110, articleId=1149789678045459085, tenantId=1146029695717560320, journalId=1146123166801305609, language=EN, title=Lightning Strike Warning in Wind Farm Delivery System Based on Stepped Calculation Method, columnId=1156262729162810294, journalTitle=Science Technology and Engineering, columnName=Papers·Automation and Computational Technology, runingTitle=null, highlight=null, articleAbstract=

The advantages of renewable wind energy lead to a rapid growth in the scale of wind power, while lightning strike accidents on wind farm delivery systems have a significant impact on the new power system. The traditional lightning strike warning method requires high data types and sample sizes, and lacks consideration of relative location as well as the distribution of lightning density. A lightning strike warning method for wind farm delivery systems based on the stepped lightning strike probability calculation method was proposed. Firstly, the data of lightning points around a wind farm in Hainan, China in 2020 were analyzed, and the Monte Carlo method was used to find the center of mass of the clusters as well as the density of lightning points to fit the trajectory of the thunderclouds. Then, based on the relative position of the movement trajectory and transmission line, the stepped lightning strike probability calculation method was combined to calculate the value of the lightning strike probability in a short period of time. Finally, the simulation was combined with the operation monitoring data of a wind farm in Hainan from 2020 to 2022. The results show that the relative error of the proposed method is within 15%, and the impact of the difference in the density of lightning points on the warning accuracy is effectively reduced, which ensures the safety of the wind farm delivery system.

, correspAuthors=Miao YU, authorNote=null, correspAuthorsNote=null, copyrightStatement=null, copyrightOwner=null, extLink=null, articleAbsUrl=null, sourceXml=null, magXml=null, pdfUrl=null, pdf=null, pdfFileSize=null, pdfExtLink=null, richHtmlUrl=null, mobilePdfUrl=null, reviewReport=null, pdfFirstPage=null, abstractGraph=null, abstractGraphContent=null, abstractVideo=null, citation=null, cebUrl=null, magXmlContent=null, mapNumber=null, authorCompany=null, fund=null, authors=null, authorsList=Miao YU, Yi-xiao WU, Shuo-shuo TIAN, Jia-xin YAN, Jian-qun SUN, Bin SONG), CN=ArticleExt(id=1149789698320724074, articleId=1149789678045459085, tenantId=1146029695717560320, journalId=1146123166801305609, language=CN, title=基于阶梯化概率计算法的风电场送出系统雷击预警, columnId=1156262729783567290, journalTitle=科学技术与工程, columnName=论文·自动化技术、计算机技术, runingTitle=null, highlight=null, articleAbstract=

风能的可再生优点使得风电规模迅速发展,而风电场送出系统雷击事故会对新型电力系统造成重大影响。传统雷击预警对数据种类及样本数量要求较高,且未充分考虑相对位置以及落雷密度分布。对此提出一种基于阶梯化雷击概率计算法的风电场送出系统雷击预警方法。首先分析2020年中国海南某风电场周边落雷点数据,运用蒙特卡罗法求取聚类云团质心以及落雷点密度,拟合雷暴云运动轨迹。再根据运动轨迹与线路走向的相对位置,结合阶梯化雷击概率计算法得出短时间内的雷击概率值。最后结合2020—2022年海南某风电场运行监测数据进行仿真模拟。结果表明:所提出方法的相对误差在15%以内,并同时有效减少落雷密度差异对于预警精度影响,最大限度地保证风电场送出系统安全。

, correspAuthors=于森, authorNote=null, correspAuthorsNote=null, copyrightStatement=null, copyrightOwner=null, extLink=null, articleAbsUrl=null, sourceXml=5t75ledWftVcc7JKEWkQGg==, magXml=jvA7rQeq892RYIIlrZCzYw==, pdfUrl=null, pdf=eVJzmcT67CUO3ZUT+clR4g==, pdfFileSize=null, pdfExtLink=null, richHtmlUrl=null, mobilePdfUrl=null, reviewReport=null, pdfFirstPage=null, abstractGraph=null, abstractGraphContent=null, abstractVideo=null, citation=null, cebUrl=null, magXmlContent=zs8ZMudx/d7eV4bT4t5IzA==, mapNumber=null, authorCompany=null, fund=null, authors=

于淼(1982—),男,汉族,北京人,博士(后),副教授。研究方向:电力系统辨识与控制。E-mail:。

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于淼(1982—),男,汉族,北京人,博士(后),副教授。研究方向:电力系统辨识与控制。E-mail:。

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于淼(1982—),男,汉族,北京人,博士(后),副教授。研究方向:电力系统辨识与控制。E-mail:。

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Automation of Electric Power Systems, 2021, 45(15): 158-165., articleTitle=Wide-area backup protection algorithm based on regional phasor measurement unit and nadal fault-injection current, refAbstract=null), Reference(id=1178036462709781319, tenantId=1146029695717560320, journalId=1146123166801305609, articleId=1149789678045459085, doi=null, pmid=null, pmcid=null, year=1987, volume=2, issue=3, pageStart=859, pageEnd=870, url=null, language=null, rfNumber=[18], rfOrder=26, authorNames=Eriksson A J, journalName=IEEE Transactions on Power Delivery, refType=null, unstructuredReference=Eriksson A J. The incidence of lightning strikes to power lines[J]. 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journalId=1146123166801305609, articleId=1149789678045459085, language=CN, label=图8, caption=聚类云团预测轨迹图

总误差∑S=ΔS1+ΔS2

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Comparison of algorithm

, figureFileSmall=null, figureFileBig=null, tableContent=
聚类方法 拟合线路 SSE RMSE ∑ i = 1 nΔSi
DBSCAN Y=-1.468X+177.9 0.607×10-3 0.017 5.977
K-means Y=-3.652X+414.5 2.339×10-3 0.034 2.385
FCM Y=-4.127X+465.8 3.146×10-3 0.396 2.267
IFCM Y=-4.126X+465.8 0.936×10-3 0.021 1.565
), ArticleFig(id=1178036459840877342, tenantId=1146029695717560320, journalId=1146123166801305609, articleId=1149789678045459085, language=CN, label=表1, caption=

算法性能指标对比

, figureFileSmall=null, figureFileBig=null, tableContent=
聚类方法 拟合线路 SSE RMSE ∑ i = 1 nΔSi
DBSCAN Y=-1.468X+177.9 0.607×10-3 0.017 5.977
K-means Y=-3.652X+414.5 2.339×10-3 0.034 2.385
FCM Y=-4.127X+465.8 3.146×10-3 0.396 2.267
IFCM Y=-4.126X+465.8 0.936×10-3 0.021 1.565
), ArticleFig(id=1178036459975095071, tenantId=1146029695717560320, journalId=1146123166801305609, articleId=1149789678045459085, language=EN, label=Table 2, caption=

Center of mass coordinates and motion data of clustered cloud

, figureFileSmall=null, figureFileBig=null, tableContent=
聚类云团 速度/
(km·h-1)		 时间段/
24 h		 质心经度/
(°)		 质心纬度/
(°)
C1 19.152 08:00—08:05 108.307 18.920
08:05—08:10 108.337 18.826
08:10—08:15 108.364 18.716
08:15—08:20 108.393 18.565
C2 16.169 08:00—08:05 109.511 19.528
08:05—08:10 109.543 19.746
08:10—08:15 109.571 19.445
08:15—08:20 109.614 19.380
C3 37.154 08:00—08:05 109.773 20.231
08:05—08:10 109.809 20.173
08:10—08:15 109.909 20.140
08:15—08:20 110.012 20.045
), ArticleFig(id=1178036460046398240, tenantId=1146029695717560320, journalId=1146123166801305609, articleId=1149789678045459085, language=CN, label=表2, caption=

聚类云团质心坐标及运动数据

, figureFileSmall=null, figureFileBig=null, tableContent=
聚类云团 速度/
(km·h-1)		 时间段/
24 h		 质心经度/
(°)		 质心纬度/
(°)
C1 19.152 08:00—08:05 108.307 18.920
08:05—08:10 108.337 18.826
08:10—08:15 108.364 18.716
08:15—08:20 108.393 18.565
C2 16.169 08:00—08:05 109.511 19.528
08:05—08:10 109.543 19.746
08:10—08:15 109.571 19.445
08:15—08:20 109.614 19.380
C3 37.154 08:00—08:05 109.773 20.231
08:05—08:10 109.809 20.173
08:10—08:15 109.909 20.140
08:15—08:20 110.012 20.045
), ArticleFig(id=1178036460113507105, tenantId=1146029695717560320, journalId=1146123166801305609, articleId=1149789678045459085, language=EN, label=Table 3, caption=

Predicted trajectory error

, figureFileSmall=null, figureFileBig=null, tableContent=
聚类云团 总误差/
km		 时间段/
24 h		 绝对误差/
km		 相对误差/
%
C1 1.865 08:20—08:25 0.251 3.37
08:25—08:30 1.314 10.69
C2 2.048 08:20—08:25 0.902 9.62
08:25—08:30 1.145 14.53
C3 3.452 08:20—08:25 1.867 12.11
08:25—08:30 1.585 13.69
), ArticleFig(id=1178036460176421666, tenantId=1146029695717560320, journalId=1146123166801305609, articleId=1149789678045459085, language=CN, label=表3, caption=

预测运动轨迹误差

, figureFileSmall=null, figureFileBig=null, tableContent=
聚类云团 总误差/
km		 时间段/
24 h		 绝对误差/
km		 相对误差/
%
C1 1.865 08:20—08:25 0.251 3.37
08:25—08:30 1.314 10.69
C2 2.048 08:20—08:25 0.902 9.62
08:25—08:30 1.145 14.53
C3 3.452 08:20—08:25 1.867 12.11
08:25—08:30 1.585 13.69
), ArticleFig(id=1178036460243530531, tenantId=1146029695717560320, journalId=1146123166801305609, articleId=1149789678045459085, language=EN, label=Table 4, caption=

Cloud layers data

, figureFileSmall=null, figureFileBig=null, tableContent=
云层 落雷次数/
次		 云层面积/
km2		 落雷密度/
(次·km-2)		 落雷占比
L1 134 380.39 0.353 0.665
L2 55 882.83 0.061 0.271
L3 13 1 925.44 0.005 0.064
C 202 3 188.66 0.063 1.000
), ArticleFig(id=1178036460306445092, tenantId=1146029695717560320, journalId=1146123166801305609, articleId=1149789678045459085, language=CN, label=表4, caption=

云层数据

, figureFileSmall=null, figureFileBig=null, tableContent=
云层 落雷次数/
次		 云层面积/
km2		 落雷密度/
(次·km-2)		 落雷占比
L1 134 380.39 0.353 0.665
L2 55 882.83 0.061 0.271
L3 13 1 925.44 0.005 0.064
C 202 3 188.66 0.063 1.000
), ArticleFig(id=1178036460360971045, tenantId=1146029695717560320, journalId=1146123166801305609, articleId=1149789678045459085, language=EN, label=Table 5, caption=

Predicted results for the number of trips on 20 transmission lines

, figureFileSmall=null, figureFileBig=null, tableContent=
线路名称 跳闸次数 运动情况分类
传统 本文 实际
TL-01 0 0 0 ⑦
TL-02 6 6 1 ⑦
TL-03 0 0 0 ⑤
TL-04 0 1 1 ⑦
TL-05 1 0 0 ①
TL-06 1 1 0 ②
TL-07 0 0 0 ⑥
TL-08 1 8 2 ③
TL-09 0 0 0 ④
TL-10 2 2 1 ⑥
TL-11 9 2 1 ①
TL-12 0 0 1 ②
TL-13 5 0 0 ①
TL-14 1 1 0 ⑥
TL-15 0 6 2 ③
TL-16 8 9 1 ⑥
TL-17 0 1 0 ⑤
TL-18 4 4 1 ⑦
TL-19 1 2 1 ⑥
TL-20 0 0 0 ②
), ArticleFig(id=1178036460423885606, tenantId=1146029695717560320, journalId=1146123166801305609, articleId=1149789678045459085, language=CN, label=表5, caption=

20条输电线路跳闸次数预测结果

, figureFileSmall=null, figureFileBig=null, tableContent=
线路名称 跳闸次数 运动情况分类
传统 本文 实际
TL-01 0 0 0 ⑦
TL-02 6 6 1 ⑦
TL-03 0 0 0 ⑤
TL-04 0 1 1 ⑦
TL-05 1 0 0 ①
TL-06 1 1 0 ②
TL-07 0 0 0 ⑥
TL-08 1 8 2 ③
TL-09 0 0 0 ④
TL-10 2 2 1 ⑥
TL-11 9 2 1 ①
TL-12 0 0 1 ②
TL-13 5 0 0 ①
TL-14 1 1 0 ⑥
TL-15 0 6 2 ③
TL-16 8 9 1 ⑥
TL-17 0 1 0 ⑤
TL-18 4 4 1 ⑦
TL-19 1 2 1 ⑥
TL-20 0 0 0 ②
), ArticleFig(id=1178036460490994471, tenantId=1146029695717560320, journalId=1146123166801305609, articleId=1149789678045459085, language=EN, label=Table 6, caption=

Indicators for assessing the warning performance of the two methods

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计算方法 AWCR/% AWR/% FWR/% MWR/%
传统 65 70 40 30
阶梯化 75 90 20 10
), ArticleFig(id=1178036460587463464, tenantId=1146029695717560320, journalId=1146123166801305609, articleId=1149789678045459085, language=CN, label=表6, caption=

评估两种方法预警性能的指标

, figureFileSmall=null, figureFileBig=null, tableContent=
计算方法 AWCR/% AWR/% FWR/% MWR/%
传统 65 70 40 30
阶梯化 75 90 20 10
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基于阶梯化概率计算法的风电场送出系统雷击预警
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于淼 1, 2 , 吴屹潇 1, 2 , 田硕硕 3 , 严佳欣 1, 2 , 孙建群 1, 2 , 宋斌 4
科学技术与工程 | 论文·自动化技术、计算机技术 2025,25(16): 6789-6796
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科学技术与工程 | 论文·自动化技术、计算机技术 2025, 25(16): 6789-6796
基于阶梯化概率计算法的风电场送出系统雷击预警
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于淼1, 2 , 吴屹潇1, 2, 田硕硕3, 严佳欣1, 2, 孙建群1, 2, 宋斌4
作者信息
  • 1 北京建筑大学机电与车辆工程学院, 北京 100044
  • 2 北京市建筑安全检测工程技术研究中心, 北京 100044
  • 3 山东大学电气工程学院, 济南 250061
  • 4 中国科学院电工研究所可再生能源发电系统研究部, 北京 100190

    • 于淼(1982—),男,汉族,北京人,博士(后),副教授。研究方向:电力系统辨识与控制。E-mail:。

Lightning Strike Warning in Wind Farm Delivery System Based on Stepped Calculation Method
Miao YU1, 2 , Yi-xiao WU1, 2, Shuo-shuo TIAN3, Jia-xin YAN1, 2, Jian-qun SUN1, 2, Bin SONG4
Affiliations
  • 1 School of Mechanical-electronic and Vehicle Engineering, Beijing University of Civil Engineering and Architecture, Beijing 100044, China
  • 2 Beijing Engineering Research Center for Building Safety Inspection, Beijing 100044, China
  • 3 School of Electrical Engineering, Shandong University, Jinan 250061, China
  • 4 Renewable Energy Generation System Research Department, Institute of Electrical Engineering, Chinese Academy of Sciences, Beijing 100190, China
出版时间: 2025-06-08 doi: 10.12404/j.issn.1671-1815.2406617
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摘要
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风能的可再生优点使得风电规模迅速发展,而风电场送出系统雷击事故会对新型电力系统造成重大影响。传统雷击预警对数据种类及样本数量要求较高,且未充分考虑相对位置以及落雷密度分布。对此提出一种基于阶梯化雷击概率计算法的风电场送出系统雷击预警方法。首先分析2020年中国海南某风电场周边落雷点数据,运用蒙特卡罗法求取聚类云团质心以及落雷点密度,拟合雷暴云运动轨迹。再根据运动轨迹与线路走向的相对位置,结合阶梯化雷击概率计算法得出短时间内的雷击概率值。最后结合2020—2022年海南某风电场运行监测数据进行仿真模拟。结果表明:所提出方法的相对误差在15%以内,并同时有效减少落雷密度差异对于预警精度影响,最大限度地保证风电场送出系统安全。

雷击预警  /  风电场送出系统  /  阶梯化雷击概率计算法  /  蒙特卡罗法  /  集输电线路

The advantages of renewable wind energy lead to a rapid growth in the scale of wind power, while lightning strike accidents on wind farm delivery systems have a significant impact on the new power system. The traditional lightning strike warning method requires high data types and sample sizes, and lacks consideration of relative location as well as the distribution of lightning density. A lightning strike warning method for wind farm delivery systems based on the stepped lightning strike probability calculation method was proposed. Firstly, the data of lightning points around a wind farm in Hainan, China in 2020 were analyzed, and the Monte Carlo method was used to find the center of mass of the clusters as well as the density of lightning points to fit the trajectory of the thunderclouds. Then, based on the relative position of the movement trajectory and transmission line, the stepped lightning strike probability calculation method was combined to calculate the value of the lightning strike probability in a short period of time. Finally, the simulation was combined with the operation monitoring data of a wind farm in Hainan from 2020 to 2022. The results show that the relative error of the proposed method is within 15%, and the impact of the difference in the density of lightning points on the warning accuracy is effectively reduced, which ensures the safety of the wind farm delivery system.

lightning strike warning  /  wind farm delivery system  /  stepped lightning strike probability calculation method  /  Monte Carlo method  /  transmission line
于淼, 吴屹潇, 田硕硕, 严佳欣, 孙建群, 宋斌. 基于阶梯化概率计算法的风电场送出系统雷击预警. 科学技术与工程, 2025 , 25 (16) : 6789 -6796 . DOI: 10.12404/j.issn.1671-1815.2406617
Miao YU, Yi-xiao WU, Shuo-shuo TIAN, Jia-xin YAN, Jian-qun SUN, Bin SONG. Lightning Strike Warning in Wind Farm Delivery System Based on Stepped Calculation Method[J]. Science Technology and Engineering, 2025 , 25 (16) : 6789 -6796 . DOI: 10.12404/j.issn.1671-1815.2406617
正文
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在“碳达峰”和“碳中和”目标的驱动下,可再生能源技术的开发和应用受到人们广泛关注。中国将继续加强风能等开发设备的建设,2022 年中国新增的光伏和风电新增装机容量突破1.2×108 kW,突破历史新高。具体计划于 2050 年风电装机容量达到15×108~20×108 kW[1-3]。同时,雷击事故率也会随着风电机组容量的不断增大而成倍增长[4]。据统计数据,丹麦、瑞典和德国每年有4%~8%的风力涡轮机被雷电损坏[5]。雷击故障将导致电力系统不稳定,甚至造成大规模停电严重电力事故[6],因此研究雷击风电场送出系统预警工作意义重大。
为更好应对雷击事故,做好被动式防雷的同时开展主动式防雷预警工作同样重要。Saito等[7]通过使用2001—2005 年12月和1月的闪电定位系统数据,调查了因风机建设而导致的雷电击中风力发电机组的频率。Chen等[8]根据闪电定位系统获得的雷电数据,对中国东南部风电场安装前后的雷电活动密度、多样性、峰值电流等特征进行了量化比较,发现风机500 m范围内的回击密度增加了27.9%。寇晓适等[9]以长短期记忆网络为核心,提出了基于雷达回波外推技术和深度学习技术的强对流气象要素预报方法,该模型对极值点的预测效果有待提升,同时针对微地形区域的效果有待提高。张毅龙等[10]提出了风光储混合系统具有多端源载混合的特征,初步建立了混合系统的雷电暂态电路分析模型。郭志民等[11]根据临近时段雷电定位系统数据,基于雷电流幅值分布计算了线路雷击风险。鲍捷等[12]基于雷电定位数据的数据驱动方法,对紧凑型电力走廊的连续雷击跳闸进行早期预警,通过分析大量历史雷电数据提高预警精准度。Zhang等[13]提出了基于多维数据的输电线路雷电风险预警综合方法。该方法数据源包括雷电位置数据、微地形数据和分布式监测数据等,对数据量要求较高。Ukkonen等[14]使用神经网络再分析雷暴数据,根据闪电位置数据得出芬兰上空随后6 h的雷暴发生情况,可应用至风电场集输电线路雷击预警中。Datsios等[15]研究了国际大电网委员会(International Council on Large Electric Systems, CIGRE)雷电流波形参数对150 kV和400 kV架空线路绝缘闪络过电压和临界雷电流计算的影响,为雷击预警提供了计算基础。
在上述雷击预警研究中,需对目标集输电线路进行详细的高精度建模,可靠性较高同时针对性较高,对于其余线路则不具备适用性。此外数据需求量较大且数据种类固定,不利于大范围推广,数据样本量成为不可或缺的待解决问题。
基于此,首先结合风电场送出系统附近落雷点数据,对目标雷暴云进行特征数据提取,根据所得质心数据拟合运动轨迹,再结合阶梯化雷击概率计算法得出预警结果。在保证预警准确率的同时降低了对数据量的要求,且计算法对所有送出系统具有普适性。最后对计算结果进行验算,验证该方法在实际情况下的可靠性。结果表明,本文方法为风电场送出系统防雷工作提供了参考依据。
1 基于Monte Carlo法的落雷点数据特征提取
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1.1 落雷点聚类分析
为合理划分雷暴云单体范围,捕捉雷暴云运动轨迹,现对已有落雷点数据进行聚类分析。根据雷暴云大小分布函数将聚类水平范围下限阈值设定为5 km,可包含90%的雷暴云[14]。将各聚类簇统一称为聚类云团,同时根据文献[16],将雷暴云5 min内包含最少落雷点数量设定为10,未达到设定密度阈值区域视为噪声,剔除出聚类云团覆盖区域。
1.2 雷暴云轨迹预测
选定距离风电场送出集输电线路10 km内区域为监测区域[17],结合预测轨迹进行判断是否需要进行下一步雷击概率计算。详细步骤如下。
步骤1 降噪处理原始数据,得到落雷点数据。
步骤2 对落雷点数据聚类分析,得到聚类云团分类及轮廓,并求取质心坐标,后续在此基础上使用Monte Carlo方法进行参数计算。
步骤3 使用质心坐标拟合得出聚类云团运动轨迹,同时结合轮廓,预测聚类云团覆盖区域。
步骤4 判断覆盖区域与风电场集输电线路区域是否相交,若有则进行雷击概率计算,若无则返回步骤1。
轨迹预测具体流程如图1所示。
1.3 基于Monte Carlo法的云团面积计算
在计算聚类云团面积时,由于形状复杂,若直接使用规则图形面积计算公式,会使造成较大误差。为更好地融合落雷点数据进行参数计算,引入Monte Carlo方法计算不规则云团面积,具体步骤如下。
步骤1 作矩形α完全覆盖住云团区域,矩形面积记为Sα。
步骤2 在α内随机产生一A点,从云团质心C作一条经过A点的射线,与云团轮廓相交于B点。若lAC<lBC,则记A点位于云团覆盖区内(lAC为步骤2中所述A点到C点距离,lBC为B点到C点距离)。
步骤3 在α内作N个随机点,数目记为n1,统计位于云团覆盖区内点数目n2。
步骤4 云团面积可由式(1)求得。
Scloud= n 2 n 1Sα
具体流程如图2所示。
1.4 落雷点密度特征数据提取
雷击概率值与雷电密度分布有着高度正比例关联性,在落雷点数据基础之上计算得出云团落雷密度,计算公式为
ρ= n S c l o u d
式(2)中:Scloud为聚类云团面积;n为云团覆盖区域内落雷点个数。
2 基于落雷点密度的阶梯化雷击概率计算法
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2.1 雷击跳闸的判断
海南某地新能源风电场内8台风电机组的拓扑结构图如图3所示。风电机组升压后由35 kV电缆并联接入集电线路(collector line, CL),二次升压后接入110 kV输电线路(transmission line, TL)。
从地域跨度分析,风电场送出系统中集电线路与输电线路受雷击可能性最大。因此将集输电线路视为送出系统雷击事故的考虑对象。在后续雷击分析时,需将距离因素纳入考虑范围之内。线路走廊两端一定宽度范围内,集输电线路对落雷具有“吸引”能力,若在此范围内有落雷活动,即可默认为线路遭受雷击[18]。该宽度被称为等值受雷宽度,该范围被称为引雷区,如图4所示。
《架空输电线路雷电防护导则》(DL/T 2209—2021)中,等值受雷宽度的计算公式为
WLS=bg+4hg
式(3)中:bg为雷线间距,根据《架空输电线路雷电防护导则》(DL/T 2209—2021)取bg=14 m;hg为杆塔高度,取hg=36 m。
2.2 传统雷击概率计算法
传统计算方法未考虑雷暴云内雷电密度变化情况,统一视为均匀分布,如图5[18]所示。
图5中,针对雷暴云L,运动穿过后集输电线路后记为L',区域A为雷暴云覆盖区域与除引雷区之外的红色预警区交集,ρ为落雷点密度区域A'为雷暴云覆盖区域与引雷区交集。
n=ρSA
n'=ρSA'
式中:n、n'分别为A与A'内落雷点总数;SA、SA'分别为A与A'区域面积,默认为矩形区域,单位时间取5 min。
最终概率的计算公式为
P=1- S A S ' A + S A n + n '
2.3 阶梯化雷击概率计算法
为解决传统计算方法中雷电分布密度造成的误差,提出一种基于蒙特卡罗法的阶梯化雷击预警计算法。当雷暴云边缘与引雷区有交集时,若按传统理论计算雷击概率,便会使得预警概率值出现误差,这种情况在雷暴云运动轨迹与风电场集输电线路平行时尤其明显。阶梯化雷击概率计算法涉及雷云密度分布及相对运动情况,可计算得出客观的概率结果。图6中根据落雷密度,将聚类云团按密度由高到低划分为L1、L2和L3三层,其中L2和L3为分别不包括内层的环形区域,各分层轮廓假定为云团外轮廓线等比例缩小。此外将聚类云团L1、L2和L3与引雷区的相交区域标注为A1、A2和A3,各区域内雷击概率同式(6),目标线路雷击概率见式(7)与式(8)。
Pi= S A i S A ' i + S A i n i + n ' i
P=1- ∏ i = 1 n(1-Pi)
式中: S A i、 S A ' i分别为第i阶云层内A与A'区域面积;ni、n'i为第i阶云层内落雷次数;Pi为第i阶云层与红色预警区交集内落雷击中风电场集输电线路的概率;n为划分云层阶数,取n=3。
为更详细地实现雷击预警,现将式(8)中所得概率结果进行二次处理,对P-n图像期望值取整,所得结果即预测雷击次数,期望值的计算公式为
Pmean= ∑ i = 1 nnPn
3 仿真及结果分析
收起
3.1 落雷点聚类
海南省某风电场区域年均雷暴日较高,需要对集输电线路进行雷击预警。数据来源为雷电定位系统于2020年7月13日08:00—08:30的风电场周边雷暴监测数据,每5 min进行一次数据收集,共30 min落雷点数据。在代入数据之前对数据集进行降噪处理,所提雷电数据默认为降噪后的落雷点数据,为同时兼顾模型样本真实性与结果校验准确性,将使用前20 min进行模型建立,后10 min数据进行结果校验,在样本量足够情况下可实现更长时间的预测。
使用08:00—08:30部分落雷点数据进行聚类效果评估,从聚类效果与预测效果两方面进行对比,备选聚类算法为:DBSCAN、高斯混合模型(Gaussian mixture model, GMM)、模糊C均值(fuzzy C-means, FCM)和K-means,计算结果如表1所示。
从表1中可以看出,DBSCAN算法可以处理任意形状的簇,因此聚类效果最佳,但对于参数选择(如雷云半径和最少落雷点数)敏感,导致预测效果最差。FCM算法效果居中,GMM算法效果较佳,但需预先指定簇的数量,计算复杂度较高。K-means算法效果居中,每个簇由其聚类云团质心来表示,实现简单效率高,适用于落雷点数据。综合以上对比,下文将默认采用K-means算法进行聚类分析。
现进行基于落雷点聚类分析,剔除落雷点密度过低处的个别落雷点数据,结果如图7所示。
图7中落雷点数据总共分为3簇,即雷暴云数量为3,形状轮廓及落雷密度变化不大,有东南方向的移动趋势,与实际情况相符。现分别计算云团质心坐标与运动速度,具体数据情况如表2所示。为方便表述,在表2中将聚类云团编号,从左至右分别为C1、C2和C3,下文中的1号云、2号云和3号云同理。
表2中数据表明,相比之下聚类云团C3平均速度较高,经度跨度更大,C1纬度跨度更大。整体而言C1、C2和C3平均速度均偏低,有利于减小轨迹偏差。
3.2 聚类云团轨迹预测
根据表2中数据,在图8中分别做出聚类云团C1、C2和C3的质心坐标。数据种类及样本限制曲线运动轨迹拟合阶数为一次曲线。计算确定系数R2、误差平方和(sum of squares error,SSE)以及标准差(root mean squared error,RMSE)3项指标,记录于图8左下角表格中。对08:00—08:20质心坐标进行曲线拟合处理,适当延长聚类云团拟合轨迹,作为预测轨迹。同时将08:25、08:30时刻的雷暴云质心与预测轨迹之间的误差距离分别记为ΔS1与ΔS2,记于图8所示的表格中。
由图8可知,聚类云团C1、C2和C3移动方向基本一致,均为东偏南,与实际情况相符。表中数据表明,预测轨迹线路与质心点拟合效果较好,保证了后续风电场集输电线路雷击预警的准确性。
现计算预测轨迹与08:20—08:30质心的绝对误差与相对误差,结果如表3所示。其中,绝对误差为质心与预测轨迹的间距,相对误差为质心运动距离与绝对误差之比。
相比之下,由于C3云团运动速度较快,在相同时间段下运动距离较远,故垂直方向上的偏差度易受影响而出现波动。因此在表3中,C3云团绝对误差值较大,但相对误差值不受影响,均在10%以内。可见,本文方法在未来10 min内可以有效地预测雷暴云运动轨迹,可以在其基础之上进行风电场集输电线路雷电预警研究。
3.3 阶梯化雷击概率计算法
为兼顾计算结果与计算效率,取云层阶数为3层,对应高、中、低3种密度分布区域。现于相同背景条件下进行模拟,对比传统方法与阶梯化计算法的雷击概率计算结果。将08:00—08:20时间段数据代入模拟模型中,计算得出单位时间内不同云层的落雷次数(取整)、云层面积平均值与落雷密度,结果如表4所示。
现假设以下7种情况进行算法准确度对比:①云团运动方向与输电线路大致平行,同时仅L1覆盖于线路上方;②同①,仅L2覆盖于线路上方;③同①,仅L3覆盖于线路上方;④同①,L1、L2同时覆盖于线路上方;⑤同①,L2、L3同时覆盖于线路上方;⑥云团运动方向与输电线路大致呈45°夹角,L1、L2与L3同时覆盖于线路上方;⑦云团运动方向与输电线路大致垂直,L1、L2与L3同时覆盖于线路上方。
概率计算结果如图9所示。图9中所列数据结果表明,传统计算方法在计算云团运动方向与线路相交并具有较大夹角时,最终结果差距较小。而情况①~情况⑤表明,当云团运动方向与线路大致平行时,传统方法结果与实际情况不符,尤其情况③差别巨大。可见阶梯化雷击概率计算法在多场景下的普适性,能保证模型能够最大限度地趋于现实。
为进一步验证所提方法的预测效果,现选取2020—2022年海南省某风电场集输电线路周边20例雷电坐标数据进行分析,其中线路雷击同时期数据占比为50%。根据阶梯式雷击概率计算法,计算出当前情况下的雷击概率值,并根据式(9)计算出具体的预测雷击次数,预测结果如表5所示。
表5中已标注漏报(missed warning, MW)与误报(fault warning, FW)。表5中的结果与图8中的模拟结果对比表明,由于闪电坐标密度因素,传统方法在情况①~情况③中的误报率较高。但在其余情况下,传统方法与本文方法效果接近。
为对传统方法与本文方法性能进行比较,现引入预警性能评估指标:预警分类正确率(correct warning classification rate, AWCR)、预警准确率(accelerate warning rate, AWR)、虚警率(fault warning rate, FWR)和漏警率(missed warning rate, MWR),其计算公式分别为
AWCR= N A W + N N W N A W + N N W + N F W + N M W×100%
AWR= N A W N A W + N M W×100%
FWR= N F W N A W + N F W×100%
MWR= N M W N A W + N M W×100%
式中:NAW为线路有预警且实际也发生雷击跳闸的个数;NMW为线路无预警而实际发生雷击跳闸的个数;NFW为线路有预警而实际未发生雷击跳闸的个数;NNW为线路无预警且实际也没有发生雷击跳闸的个数。
本文方法与传统方法的各项评估指标如表6所示。
相较之下本文方法能大致反映出实际的雷击跳闸现象,性能指标皆较为理想,在提升分类正确率与准确率的同时,有效降低了虚警率与漏警率。面对复杂天气情况具有更好的普适性与准确性,表明本文方法对风电场集输电线路的跳闸现象有良好的预判效果。
4 结论
收起
在风电场送出系统雷击预警方面,对比各种聚类算法且运用于落雷点数据分析,通过质心拟合来预测雷暴云的运动轨迹。并在已有方法基础上融合Monte Carlo方法,提出阶梯化雷击率计算法,对目标雷暴云进行密度层级划分,实现次数预测雷击预警。结果表明该方法增强了预测模型的准确性,同时保证了雷暴云与风电场集输电线路在不同相对位置情况下的预警概率准确性。后续研究将结合风向数据,提升预测运动线路的维数,以获得更好的预测效果。
基金
收起
  • 北京市自然科学基金面上项目(4242035)
  • 北京建筑大学金字塔人才培养工程项目(JDYC20200324)
  • 北京建筑大学培育项目专项(X23050)
  • 国家自然科学基金青年科学基金(51407201)
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2025年第25卷第16期
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doi: 10.12404/j.issn.1671-1815.2406617
  • 接收时间：2024-09-03
  • 首发时间：2025-07-09
  • 出版时间：2025-06-08
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  • 收稿日期：2024-09-03
  • 修回日期：2025-03-20
基金
北京市自然科学基金面上项目(4242035)
北京建筑大学金字塔人才培养工程项目(JDYC20200324)
北京建筑大学培育项目专项(X23050)
国家自然科学基金青年科学基金(51407201)
作者信息
    1 北京建筑大学机电与车辆工程学院, 北京 100044
    2 北京市建筑安全检测工程技术研究中心, 北京 100044
    3 山东大学电气工程学院, 济南 250061
    4 中国科学院电工研究所可再生能源发电系统研究部, 北京 100190
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