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Article(id=1203281643470565636, tenantId=1146029695717560320, journalId=1149653034449285133, issueId=1203281635908231645, articleNumber=null, orderNo=null, doi=10.16790/j.cnki.1009-9239.im.2025.06.014, pmid=null, cstr=null, oa=null, hot=null, price=null, onlineType=0, articleFormat=0, articleType=null, articleTypeStr=research-article, receivedDate=1721318400000, receivedDateStr=2024-07-19, revisedDate=1726675200000, revisedDateStr=2024-09-19, acceptedDate=null, acceptedDateStr=null, onlineDate=1764814299694, onlineDateStr=2025-12-04, pubDate=1750348800000, pubDateStr=2025-06-20, doiRegisterDate=null, doiRegisterDateStr=null, onlineIssueDate=1764814299694, onlineIssueDateStr=2025-12-04, onlineJustAcceptDate=null, onlineJustAcceptDateStr=null, onlineFirstDate=null, onlineFirstDateStr=null, sourceXml=null, magXml=null, createTime=1764814299694, creator=13701087609, updateTime=1764814299694, updator=13701087609, issue=Issue{id=1203281635908231645, tenantId=1146029695717560320, journalId=1149653034449285133, year='2025', volume='58', issue='6', pageStart='1', pageEnd='148', issueExtLink='null', onlineDate='null', pubDate='null', beforeIssueId=null, nextIssueId=null, price=null, status=1, issueComplete=0, articleOrder=1, issueType=-1, specialIssue=null, createTime=1764814297892, creator=13701087609, updateTime=1764815002353, updator=13701087609, preIssue=null, nextIssue=null, ext={EN=IssueExt(id=1203284590690545746, tenantId=1146029695717560320, journalId=1149653034449285133, issueId=1203281635908231645, language=EN, specialIssueTitle=, coverIllustrator=null, specialIssueEditor=, specialIssueAbout=), CN=IssueExt(id=1203284590694740051, tenantId=1146029695717560320, journalId=1149653034449285133, issueId=1203281635908231645, language=CN, specialIssueTitle=, coverIllustrator=null, specialIssueEditor=, specialIssueAbout=)}, issueFiles=null}, startPage=115, endPage=121, ext={EN=ArticleExt(id=1203281644795965737, articleId=1203281643470565636, tenantId=1146029695717560320, journalId=1149653034449285133, language=EN, title=Analysis on polar coordinate pattern characteristics of stator winding insulation for 10 kV three-phase asynchronous motor, columnId=1190369198472794288, journalTitle=Insulating Materials, columnName=Insulation Technology, runingTitle=null, highlight=

The stator winding insulation of 10 kV three-phase asynchronous motor will subject to thermal, electrical, environmental, and mechanical stresses during operation, which will generate insulation defects and lead to partial discharge (PD). It is very difficult to obtain the reference voltage waveform in on-line monitoring condition, and the loss of reference phase makes it impossible to use PRPD pattern in PD recognition. To solve these problems, three kinds of PD models, e.g. internal discharge, slot discharge, and corona discharge, were made in the laboratory conditions, and the PD signals were collected. The polar coordinate method was used to convert PRPD pattern into circular polar coordinate pattern to solve the problem of reference phase loss. The results indicate that different types of PDs have different polar coordinate pattern characteristic distributions, the internal discharge has symmetrical distribution in the first and third quadrants. Slot discharge and corona discharge have unsymmetrical distribution, and the amplitude of the third quadrant is much larger than that of the first quadrant. The slot discharge has larger point cluster discharge concentration range and wider discharge shape than corona discharge. The characteristic parameters such as skewness, kurtosis, and discharge proportion are obviously different in different discharge types. With the increase of voltage level, the distribution and characteristic parameters of polar coordinate pattern will change obviously.

, articleAbstract=

The stator winding insulation of 10 kV three-phase asynchronous motor will subject to thermal, electrical, environmental, and mechanical stresses during operation, which will generate insulation defects and lead to partial discharge (PD). It is very difficult to obtain the reference voltage waveform in on-line monitoring condition, and the loss of reference phase makes it impossible to use PRPD pattern in PD recognition. To solve these problems, three kinds of PD models, e.g. internal discharge, slot discharge, and corona discharge, were made in the laboratory conditions, and the PD signals were collected. The polar coordinate method was used to convert PRPD pattern into circular polar coordinate pattern to solve the problem of reference phase loss. The results indicate that different types of PDs have different polar coordinate pattern characteristic distributions, the internal discharge has symmetrical distribution in the first and third quadrants. Slot discharge and corona discharge have unsymmetrical distribution, and the amplitude of the third quadrant is much larger than that of the first quadrant. The slot discharge has larger point cluster discharge concentration range and wider discharge shape than corona discharge. The characteristic parameters such as skewness, kurtosis, and discharge proportion are obviously different in different discharge types. With the increase of voltage level, the distribution and characteristic parameters of polar coordinate pattern will change obviously.

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10 kV三相异步电动机定子绝缘在运行中会受到热、电、环境和机械等多应力作用，形成各种绝缘缺陷并导致局部放电，而在线监测过程中存在参考电压波形难获取、利用局部放电谱相位图（PRPD）进行放电识别时存在参考电压相位易丢失等问题。针对这一问题，本文在实验室中制作了内部放电、槽放电及电晕放电3种局部放电模型，并采集局部放电信号。利用极坐标法将PRPD谱图转化为圆形的极坐标谱图，解决电压相位信息丢失的问题。结果表明：不同放电类型具有不同的极坐标谱图特征分布，内部放电在第一、三象限呈现对称分布特征；槽放电与电晕放电分布不对称，第三象限的幅值远大于第一象限。槽放电比电晕放电的点簇放电脉冲范围更大，放电形状更宽。不同放电类型的偏斜度、陡峭度、放电占比等特征参数具有明显的不同。随着电压等级的升高，极坐标谱图分布及特征参数发生明显变化。

, articleAbstract=

10 kV三相异步电动机定子绝缘在运行中会受到热、电、环境和机械等多应力作用，形成各种绝缘缺陷并导致局部放电，而在线监测过程中存在参考电压波形难获取、利用局部放电谱相位图（PRPD）进行放电识别时存在参考电压相位易丢失等问题。针对这一问题，本文在实验室中制作了内部放电、槽放电及电晕放电3种局部放电模型，并采集局部放电信号。利用极坐标法将PRPD谱图转化为圆形的极坐标谱图，解决电压相位信息丢失的问题。结果表明：不同放电类型具有不同的极坐标谱图特征分布，内部放电在第一、三象限呈现对称分布特征；槽放电与电晕放电分布不对称，第三象限的幅值远大于第一象限。槽放电比电晕放电的点簇放电脉冲范围更大，放电形状更宽。不同放电类型的偏斜度、陡峭度、放电占比等特征参数具有明显的不同。随着电压等级的升高，极坐标谱图分布及特征参数发生明显变化。

, correspAuthors=null, authorNote=null, correspAuthorsNote=
康爱亮（1988-），男（汉族），河北廊坊人，讲师，博士，主要从事发电机及高压电动机主绝缘局部放电检测与诊断；
赵世杰（2000-），男（汉族），山西晋城人，硕士生，主要从事高电压与绝缘的研究；
吝伶艳（1969-），女（汉族），山西临汾人，副教授，博士，主要从事电气故障诊断及绝缘性能的研究；
陈占清（1991-），男（汉族），河南许昌人，讲师，博士，主要从事高压真空开关、脉冲功率开关技术、真空电弧等离子体的研究。
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张利柄（2000-），男（汉族），山西晋中人，硕士生，主要从事高电压与绝缘的研究；

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张利柄（2000-），男（汉族），山西晋中人，硕士生，主要从事高电压与绝缘的研究；

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张利柄（2000-），男（汉族），山西晋中人，硕士生，主要从事高电压与绝缘的研究；

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Shanxi Province Key Laboratory of Coal Mine Electrical Equipment and Intelligent Control, Taiyuan University of Technology, Taiyuan 030024, China), AuthorCompanyExt(id=1203362942143148708, tenantId=1146029695717560320, journalId=1149653034449285133, articleId=1203281643470565636, companyId=1203362942126371491, language=CN, country=null, province=null, city=null, postcode=null, companyName=null, departmentName=null, remark=太原理工大学，a.矿用智能电器技术国家地方联合工程实验室；b.煤矿电气设备与智能控制山西省重点实验室，山西 太原 030024)])])], keywords=[Keyword(id=1203362944202552109, tenantId=1146029695717560320, journalId=1149653034449285133, articleId=1203281643470565636, language=EN, orderNo=1, keyword=stator winding), Keyword(id=1203362944307409715, tenantId=1146029695717560320, journalId=1149653034449285133, articleId=1203281643470565636, language=EN, orderNo=2, keyword=insulation defect), Keyword(id=1203362944399684413, tenantId=1146029695717560320, journalId=1149653034449285133, articleId=1203281643470565636, language=EN, orderNo=3, keyword=PRPD pattern), Keyword(id=1203362944491959106, tenantId=1146029695717560320, journalId=1149653034449285133, articleId=1203281643470565636, language=EN, orderNo=4, keyword=polar coordinate pattern), Keyword(id=1203362944584233799, tenantId=1146029695717560320, journalId=1149653034449285133, articleId=1203281643470565636, language=CN, orderNo=1, keyword=定子绕组), Keyword(id=1203362945804776269, tenantId=1146029695717560320, journalId=1149653034449285133, articleId=1203281643470565636, language=CN, orderNo=2, keyword=绝缘缺陷), Keyword(id=1203362945964159830, tenantId=1146029695717560320, journalId=1149653034449285133, articleId=1203281643470565636, language=CN, orderNo=3, keyword=PRPD谱图), Keyword(id=1203362946178069347, tenantId=1146029695717560320, journalId=1149653034449285133, articleId=1203281643470565636, language=CN, orderNo=4, keyword=极坐标谱图)], refs=[Reference(id=1203362950556921914, tenantId=1146029695717560320, journalId=1149653034449285133, articleId=1203281643470565636, doi=null, pmid=null, pmcid=null, year=2019, volume=39, issue=2, pageStart=395, pageEnd=406,637, url=null, language=null, rfNumber=[1], rfOrder=0, authorNames=郑大勇, 张品佳, journalName=中国电机工程学报, refType=null, unstructuredReference=郑大勇,张品佳.交流电机定子绝缘故障诊断与在线监测技术综述[J].中国电机工程学报,2019,39(2):395-406,637., articleTitle=交流电机定子绝缘故障诊断与在线监测技术综述, refAbstract=null), Reference(id=1203362950645002300, tenantId=1146029695717560320, journalId=1149653034449285133, articleId=1203281643470565636, doi=null, pmid=null, pmcid=null, year=2019, volume=39, issue=2, pageStart=395, pageEnd=406,637, url=null, language=null, rfNumber=[1], rfOrder=1, authorNames=ZHENGDayong, ZHANGPinjia, journalName=Proceedings of the CSEE, refType=null, unstructuredReference=ZHENGDayong, ZHANGPinjia. 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Journal of Electrical Engineering,2022,17(2):235-242., articleTitle=Study on partial discharge pattern recognition for distribution cable based on T-F clustering and PRPD spectrum analysis, refAbstract=null)], funds=[Fund(id=1203362948879200284, tenantId=1146029695717560320, journalId=1149653034449285133, articleId=1203281643470565636, awardId=2022L062, language=CN, fundingSource=山西省高等学校科技创新计划(2022L062), fundOrder=null, country=null), Fund(id=1203362949009223716, tenantId=1146029695717560320, journalId=1149653034449285133, articleId=1203281643470565636, awardId=2022L063, language=CN, fundingSource=山西省高等学校科技创新计划(2022L063), fundOrder=null, country=null), Fund(id=1203362949105692712, tenantId=1146029695717560320, journalId=1149653034449285133, articleId=1203281643470565636, awardId=202203021212274, language=CN, fundingSource=山西省基础研究计划青年科学研究项目(202203021212274), fundOrder=null, country=null), Fund(id=1203362950343012397, tenantId=1146029695717560320, journalId=1149653034449285133, articleId=1203281643470565636, awardId=202203021212225, language=CN, fundingSource=山西省基础研究计划青年科学研究项目(202203021212225), fundOrder=null, country=null)], companyList=[AuthorCompany(id=1203362942126371491, tenantId=1146029695717560320, journalId=1149653034449285133, articleId=1203281643470565636, xref=null, ext=[AuthorCompanyExt(id=1203362942134760099, tenantId=1146029695717560320, journalId=1149653034449285133, articleId=1203281643470565636, companyId=1203362942126371491, language=EN, country=null, province=null, city=null, postcode=null, companyName=null, departmentName=null, remark=a. 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Shanxi Province Key Laboratory of Coal Mine Electrical Equipment and Intelligent Control, Taiyuan University of Technology, Taiyuan 030024, China), AuthorCompanyExt(id=1203362942143148708, tenantId=1146029695717560320, journalId=1149653034449285133, articleId=1203281643470565636, companyId=1203362942126371491, language=CN, country=null, province=null, city=null, postcode=null, companyName=null, departmentName=null, remark=太原理工大学，a.矿用智能电器技术国家地方联合工程实验室；b.煤矿电气设备与智能控制山西省重点实验室，山西 太原 030024)])], figs=[ArticleFig(id=1203362946433921908, tenantId=1146029695717560320, journalId=1149653034449285133, articleId=1203281643470565636, language=EN, label=Fig.1, caption=The experimental stator coil, figureFileSmall=WXClB6Q/KIKZGbRvnfeI6Q==, figureFileBig=HkMXdAx5aZ38/y+fDf+0Gg==, tableContent=null), ArticleFig(id=1203362946538779514, tenantId=1146029695717560320, journalId=1149653034449285133, articleId=1203281643470565636, language=CN, label=图1, caption=试验定子线圈, figureFileSmall=WXClB6Q/KIKZGbRvnfeI6Q==, figureFileBig=HkMXdAx5aZ38/y+fDf+0Gg==, tableContent=null), ArticleFig(id=1203362946761077641, tenantId=1146029695717560320, journalId=1149653034449285133, articleId=1203281643470565636, language=EN, label=Fig.2, caption=Typical insulation defect models, figureFileSmall=vuEP7xtnNYi2FSbQF3MguA==, figureFileBig=v7yfHvKmIXpwjN1OSeBu6Q==, tableContent=null), ArticleFig(id=1203362946933044113, tenantId=1146029695717560320, journalId=1149653034449285133, articleId=1203281643470565636, language=CN, label=图2, caption=典型绝缘缺陷模型

(a) 槽线圈磨损 (b) 电晕放电缺陷

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电压等级/kVD1SKx1KUx1SKy1KUy1点簇1质心点簇1范围
60.5001.3714.4331.8326.149(90.05°,0.108)28.7°～133.2°
80.4511.1373.6711.1474.527（90.08°,0.139）24.5°～137.4°
100.4571.7216.592.2410.97(90.087°,0.141)25.2°～140.6°
电压等级/kVD3SKx2KUx2SKy2KUy2点簇2质心点簇2范围
60.483-2.70410.75-2.84311.89(270.15°,0.104)205.2°～308.6°
80.451-2.3148.494-1.926.13(270.17°,0.151)204.1°～318.5°
100.479-2.79514.99-2.69912.06

(270.19°,

0.153)

202°～319.6°
), ArticleFig(id=1203362948216501238, tenantId=1146029695717560320, journalId=1149653034449285133, articleId=1203281643470565636, language=CN, label=表1, caption=

内部放电极坐标图的特征参数

, figureFileSmall=null, figureFileBig=null, tableContent=
电压等级/kVD1SKx1KUx1SKy1KUy1点簇1质心点簇1范围
60.5001.3714.4331.8326.149(90.05°,0.108)28.7°～133.2°
80.4511.1373.6711.1474.527（90.08°,0.139）24.5°～137.4°
100.4571.7216.592.2410.97(90.087°,0.141)25.2°～140.6°
电压等级/kVD3SKx2KUx2SKy2KUy2点簇2质心点簇2范围
60.483-2.70410.75-2.84311.89(270.15°,0.104)205.2°～308.6°
80.451-2.3148.494-1.926.13(270.17°,0.151)204.1°～318.5°
100.479-2.79514.99-2.69912.06

(270.19°,

0.153)

202°～319.6°
), ArticleFig(id=1203362948308775930, tenantId=1146029695717560320, journalId=1149653034449285133, articleId=1203281643470565636, language=EN, label=Table 2, caption=Characteristic parameters of slot discharge polar coordinate pattern, figureFileSmall=null, figureFileBig=null, tableContent=
电压等级/kVD1SKx1KUx1SKy1KUy1点簇1质心点簇1范围
60.5241.4834.231.0312.99(90.187°,0.059)18.9°～75.6°
80.5071.0543.2340.9072.90(90.22°,0.079)10.08°～79.2°
100.444-1.698.470.8263.4890.41°,0.103)6.44°～86°
电压等级/kVD3SKx2KUx2SKy2KUy2点簇2质心点簇2范围
60.475-2.77810.455-2.2987.45(270.28°,0.134)199.8°～264.6°
80.492-2.2347.141-2.0316.213(270.11°,0.186)183.4°～266.2°
100.451-1.9066.24-1.9455.98(270.50°,0.205)184°～288.4°
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槽放电极坐标图的特征参数

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电压等级/kVD1SKx1KUx1SKy1KUy1点簇1质心点簇1范围
60.5241.4834.231.0312.99(90.187°,0.059)18.9°～75.6°
80.5071.0543.2340.9072.90(90.22°,0.079)10.08°～79.2°
100.444-1.698.470.8263.4890.41°,0.103)6.44°～86°
电压等级/kVD3SKx2KUx2SKy2KUy2点簇2质心点簇2范围
60.475-2.77810.455-2.2987.45(270.28°,0.134)199.8°～264.6°
80.492-2.2347.141-2.0316.213(270.11°,0.186)183.4°～266.2°
100.451-1.9066.24-1.9455.98(270.50°,0.205)184°～288.4°
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电压等级/kVD1SKx1KUx1SKy1KUy1点簇1质心点簇1范围
80.5410.5822.4621.7386.064(90.037°,0.082)26.1°～105.5°
100.4790.5232.4151.0213.295(90.177°,0.082)22.8°～106.5°
120.4270.6562.912.2815.09(90.077°,0.059)25.2°～108.5°
电压等级/kVD3SKx2KUx2SKy2KUy2点簇2质心点簇2范围
80.428-2.0416.781-2.5289.475(270.1°,0.132)203.1°～268.4°
100.485-2.0526.299-2.287.651(270.3°,0.165)198.5°～274.4°
120.559-1.956.014-2.146.84(270.2°,0.112)195.1°～281.6°
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电晕放电极坐标图的特征参数

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电压等级/kVD1SKx1KUx1SKy1KUy1点簇1质心点簇1范围
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100.4790.5232.4151.0213.295(90.177°,0.082)22.8°～106.5°
120.4270.6562.912.2815.09(90.077°,0.059)25.2°～108.5°
电压等级/kVD3SKx2KUx2SKy2KUy2点簇2质心点簇2范围
80.428-2.0416.781-2.5289.475(270.1°,0.132)203.1°～268.4°
100.485-2.0526.299-2.287.651(270.3°,0.165)198.5°～274.4°
120.559-1.956.014-2.146.84(270.2°,0.112)195.1°～281.6°
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10 kV三相异步电动机定子绝缘局部放电极坐标谱图分布特性分析
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张利柄 , 康爱亮 , 赵世杰 , 吝伶艳 , 陈占清
绝缘材料 | 绝缘技术 2025,58(6): 115-121
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绝缘材料 | 绝缘技术 2025, 58(6): 115-121
10 kV三相异步电动机定子绝缘局部放电极坐标谱图分布特性分析
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张利柄, 康爱亮, 赵世杰, 吝伶艳, 陈占清
作者信息
  • 太原理工大学，a.矿用智能电器技术国家地方联合工程实验室；b.煤矿电气设备与智能控制山西省重点实验室，山西 太原 030024

    • 张利柄（2000-），男（汉族），山西晋中人，硕士生，主要从事高电压与绝缘的研究；

通讯作者:

康爱亮（1988-），男（汉族），河北廊坊人，讲师，博士，主要从事发电机及高压电动机主绝缘局部放电检测与诊断；
赵世杰（2000-），男（汉族），山西晋城人，硕士生，主要从事高电压与绝缘的研究；
吝伶艳（1969-），女（汉族），山西临汾人，副教授，博士，主要从事电气故障诊断及绝缘性能的研究；
陈占清（1991-），男（汉族），河南许昌人，讲师，博士，主要从事高压真空开关、脉冲功率开关技术、真空电弧等离子体的研究。
Analysis on polar coordinate pattern characteristics of stator winding insulation for 10 kV three-phase asynchronous motor
Libing ZHANG, Ailiang KANG, Shijie ZHAO, Lingyan LIN, Zhanqing CHEN
Affiliations
  • a. National and Provincial Joint Engineering Laboratory of Mining Intelligent Electrical Apparatus Technology; b. Shanxi Province Key Laboratory of Coal Mine Electrical Equipment and Intelligent Control, Taiyuan University of Technology, Taiyuan 030024, China
出版时间: 2025-06-20 doi: 10.16790/j.cnki.1009-9239.im.2025.06.014
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摘要
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10 kV三相异步电动机定子绝缘在运行中会受到热、电、环境和机械等多应力作用，形成各种绝缘缺陷并导致局部放电，而在线监测过程中存在参考电压波形难获取、利用局部放电谱相位图（PRPD）进行放电识别时存在参考电压相位易丢失等问题。针对这一问题，本文在实验室中制作了内部放电、槽放电及电晕放电3种局部放电模型，并采集局部放电信号。利用极坐标法将PRPD谱图转化为圆形的极坐标谱图，解决电压相位信息丢失的问题。结果表明：不同放电类型具有不同的极坐标谱图特征分布，内部放电在第一、三象限呈现对称分布特征；槽放电与电晕放电分布不对称，第三象限的幅值远大于第一象限。槽放电比电晕放电的点簇放电脉冲范围更大，放电形状更宽。不同放电类型的偏斜度、陡峭度、放电占比等特征参数具有明显的不同。随着电压等级的升高，极坐标谱图分布及特征参数发生明显变化。

定子绕组  /  绝缘缺陷  /  PRPD谱图  /  极坐标谱图

The stator winding insulation of 10 kV three-phase asynchronous motor will subject to thermal, electrical, environmental, and mechanical stresses during operation, which will generate insulation defects and lead to partial discharge (PD). It is very difficult to obtain the reference voltage waveform in on-line monitoring condition, and the loss of reference phase makes it impossible to use PRPD pattern in PD recognition. To solve these problems, three kinds of PD models, e.g. internal discharge, slot discharge, and corona discharge, were made in the laboratory conditions, and the PD signals were collected. The polar coordinate method was used to convert PRPD pattern into circular polar coordinate pattern to solve the problem of reference phase loss. The results indicate that different types of PDs have different polar coordinate pattern characteristic distributions, the internal discharge has symmetrical distribution in the first and third quadrants. Slot discharge and corona discharge have unsymmetrical distribution, and the amplitude of the third quadrant is much larger than that of the first quadrant. The slot discharge has larger point cluster discharge concentration range and wider discharge shape than corona discharge. The characteristic parameters such as skewness, kurtosis, and discharge proportion are obviously different in different discharge types. With the increase of voltage level, the distribution and characteristic parameters of polar coordinate pattern will change obviously.

stator winding  /  insulation defect  /  PRPD pattern  /  polar coordinate pattern
张利柄, 康爱亮, 赵世杰, 吝伶艳, 陈占清. 10 kV三相异步电动机定子绝缘局部放电极坐标谱图分布特性分析. 绝缘材料, 2025 , 58 (6) : 115 -121 . DOI: 10.16790/j.cnki.1009-9239.im.2025.06.014
Libing ZHANG, Ailiang KANG, Shijie ZHAO, Lingyan LIN, Zhanqing CHEN. Analysis on polar coordinate pattern characteristics of stator winding insulation for 10 kV three-phase asynchronous motor[J]. Insulating Materials, 2025 , 58 (6) : 115 -121 . DOI: 10.16790/j.cnki.1009-9239.im.2025.06.014
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0 引言
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高压电机广泛应用于工业生产中，对经济的稳定发展至关重要。在高压电机运行过程中，其定子绝缘经常遭受热、电、环境和机械等多种应力作用，形成各种绝缘缺陷，进而引起局部放电的发生[1-3]。在长期局部放电的作用下，缺陷处的绝缘性能会进一步降低，最终导致绝缘故障。因此，对定子绝缘进行局部放电检测能够及时发现绝缘中的潜在缺陷[4-7]。
当前，对局部放电进行模式识别或特征分析时，通常利用局部放电谱相位图（phase resolved partial discharge，PRPD）进行分析。PRPD谱图包含3个特征参数，即放电次数n、放电相位φ和放电幅值q，它是将一段时间的放电活动对应到交流周期360°的局部放电活动[8-10]。但在局部放电在线监测时，很难获得参考电压的波形，且参考放电相位φ的缺失导致PRPD谱图在电机局部放电识别时易出现错误。此外，对于某些放电特性较为相似的放电类型，其PRPD谱图特征也较为相似，因而在放电识别及特征分析时也易出现错误[11-13]。极坐标谱图是一种与PRPD谱图不同的、用以表征局部放电分布的模式方法，以放电幅度q为极半径、以放电相位φ为极角度作图，相位首尾相连，可以更直观地观察局部放电的相位特性。该方法最早由R W HODGE在20世纪70年代提出用于分析局部放电数据[14]，在电力设备的绝缘检测和故障诊断中得到广泛应用。黄建华等[14]对电缆的局部放电试验结果进行分析，利用放电信号的脉冲幅值q与电压放电相位φ的余弦和正弦函数乘积绘制极坐标谱图，指出了极坐标谱图的特点。姚锐等[15-16]利用极坐标谱图研究了GIS浮置电极缺陷局部放电特性，分析了极坐标谱图的质心、幅值、放电参数随电压等级升高的变化规律，并通过声学结果检验了极坐标谱图的可行性。
本文在实验室环境下采集10 kV三相异步电动机定子线圈的局部放电信息，利用极坐标法将不同局部放电类型的PRPD谱图转化为圆形的极坐标谱图，并分析其谱图分布特征及特征参数变化规律。
1 试验方案
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1.1 试验线圈
采用若干根全新10 kV三相异步电动机定子线圈作为试验对象，绝缘等级为F级，其主绝缘厚度为2.04 mm，如图1所示。对线圈施加10 kV电压持续30 min，利用MPD600局部放电分析仪对全新线圈进行局放测试，观察PRPD放电图谱，若谱图呈现正负半周对称的内部放电特性，则证明线圈绝缘良好，可以进行后续试验。
1.2 典型绝缘缺陷机理及缺陷模型的制作
本文制作了定子绝缘中常见的3种局部放电模型，即内部放电、槽放电以及防晕层破坏引起的电晕放电。
定子线圈在制造过程中会不可避免地存在微小气隙，在电压作用下，气隙中的电场强度远高于周围介质的电场强度，因而会在气隙内发生放电，称为内部放电[17]。本文通过对全新线圈施加电压来模拟内部放电。
定子线圈在运行过程中会遭受频率为100 Hz的电磁应力作用，如果线圈不牢固，线圈表面会因机械振动而被定子铁心磨损。在电应力作用下，磨损处会产生局部放电，称为槽放电[18-19]。本文通过对定子线圈槽部进行磨损来模拟槽放电，如图2(a)所示。
高压电机定子绕组出槽口部位属于典型的套管型电场，此处电场十分集中，容易发生电晕放电[20-22]。涂覆防电晕涂层能显著改善绕组端部的电场分布。本文通过破坏线圈防晕层的方式来模拟电晕放电，如图2(b)所示。
1.3 局部放电试验方法
本文采用脉冲电流法提取局部放电信号，局部放电信号提取系统如图3所示。其中，通过50 kV/ 5 kVA的无局放变压器T来提供试验所需工频高压；采用滤波器LPF滤除来自低压侧的谐波信号；R为水电阻，阻值为150 kΩ，其作用为当试样击穿时限制回路电流，进而保护试验变压器；容量为1 000 pF的耦合电容器Ck为局部放电信号提供高频通道，局部放电采集频率为100～400 kHz。
2 局部放电极坐标谱图
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2.1 极坐标图谱构建
在极坐标谱图中，以放电幅度q为极半径，以放电相位φ为极角度作极坐标图。使用公式（1）归一化局部放电脉冲qs的放电幅度，其中，qmin为放电的最小幅度，而qmax为放电的最大幅度，qnorm为归一化后的放电幅度。
qnorm=(qs-qmin)/(qmax-qmin)
本文使用改进的K-Means++聚类算法，将PD脉冲分为两个点簇[23]，用蓝色表示点簇1，橘色表示点簇2，由此可以有效选择初始聚类中心，提高聚类的精确度。K-means++算法具体聚类步骤如下：
（1）在局部放电数据中随机选择一个点作为第1个聚类中心，计算每个数据点与当前聚类中心的最短距离d(x)。该值越大，表示被选为聚类中心的概率越大；用轮盘法选择下一个聚类中心[24]，直到选出2个聚类中心。
（2）分别计算每个数据点到2个聚类中心的距离，一般取欧氏距离或余弦距离[25]，找到离数据点最近的簇核心，将它归属到对应的点簇；最终N个局放数据点分为2个点簇。
（3）重新计算每个点簇的重心，将其定为新的“簇核心”，反复迭代得到聚类点簇。
2.2 极坐标谱图特征参数
为了进一步反映极坐标谱图的特征，本文提取了极坐标谱图中的统计特征参数。xi、yi是极坐标图中每个点的横、纵坐标，它们可根据式（2）计算，其中φnormi表示每个点的放电角度，qnormi表示每个点的放电幅值。统计极坐标谱图特征参数包括各象限放电占比、偏斜度和陡峭度，其中各象限放电占比用Di（i=1，2，3，4）表示，它表示每个象限的放电数量占总放电数量的百分比。SKx和SKy分别表示横纵坐标的偏斜度，可以反映正态分布的不对称度，其公式如式（3）所示，其中σx、σy表示每个点横纵坐标的标准差，N1表示每个点簇的局放脉冲总数，SK=0表示正态分布是对称的，SK>0表示正态分布向左不对称，SK<0表示正态分布向右不对称。KUx和KUy分别表示横纵坐标的陡峭度，可以反映图形的尖锐程度，其公式如式（4）所示。如果图形的尖锐度与正态分布相同，则KU=0；如果尖锐度比正态分布更尖锐，则KU>0；反之则KU<0。利用式（3）和式（4）分别对点簇1和点簇2计算统计特征参数。
xi=qnormi×cosφnormiyi=qnormi×sinφnormi
SKx=1σx3∑i=1N1(xi-x¯)3SKy=1σy3∑i=1N1(yi-y¯)3
KUx=1σx4∑i=1N1(xi-x¯)4-3KUy=1σy4∑i=1N1(yi-y¯)4-3
3 结果与分析
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3.1 内部放电极坐标谱图
图4为不同电压等级内部放电的PRPD谱图和极坐标谱图。由图4的PRPD谱图可知，不同电压等级下内部放电的正负半周在放电幅值及放电重复率上具有较好的对称性。此外，内部放电的放电幅值较低，当电压为6 kV时，最大放电量仅为0.08 nC，随着电压等级的升高，放电幅值有所增加，当电压为10 kV时，最大放电量为0.6 nC。
从图4的极坐标谱图可以看出，内部放电脉冲在第一和第三象限聚类成两个对称的放电点簇。当电压为6 kV时，点簇1的质心坐标为（90.05°，0.108），点簇2的质心坐标为（270.15°，0.104）；点簇1的放电脉冲集中在28.7°～133.2°，点簇2的放电脉冲集中在205.2°～308.6°。随着电压等级的提高，质心的极角基本不变，极半径缓慢变大，放电脉冲范围逐渐变宽。
表1为内部放电极坐标谱图的特征参数。由表1可知，随着电压等级的提高，第一与第三象限的放电占比均先减小后增大。点簇2的偏斜度是负数，其余的偏斜度和陡峭度均为正数，它们的绝对值都随电压等级的提高先减小后增大。
3.2 槽放电极坐标谱图
图5为不同电压等级槽放电的PRPD谱图和极坐标谱图。由图5的PRPD谱图可知，不同电压等级下槽放电的正负半周在放电幅值及放电重复率上具有明显不对称性，负半周的放电幅值要远高于正半周，正半周的放电重复率远高于负半周。此外，槽放电一旦发生即具有很高的放电幅值，然而随着电压等级的升高，正负半周放电幅值无明显变化，但放电重复率随着电压的升高显著增加。
从图5的极坐标谱图可以看出，槽放电在第一和第三象限聚类成两个幅值明显不对称的放电点簇。第三象限的放电幅值要远高于第一象限。当电压为6 kV时，点簇1的质心坐标为（90.187°，0.059），点簇2的质心坐标为（270.28°，0.134）；点簇1的放电脉冲集中在18.9°～75.6°，点簇2的放电脉冲集中在199.8°～264.6°。随着电压等级的提高，质心的极角基本不变，极半径缓慢增大，第三象限的放电脉冲范围明显变宽。
表2为槽放电极坐标谱图的特征参数。由表2可知，随着电压等级的升高，第一象限放电占比逐渐减小，第三象限放电占比先增大后减小；点簇1的偏斜度逐渐减小，陡峭度先减小后增大。点簇2的偏斜度是负数，陡峭度为正数，它们的绝对值均随电压等级的提高而逐渐减小。
3.3 电晕放电极坐标谱图
图6为不同电压等级电晕放电的PRPD谱图和极坐标谱图。由图6的PRPD谱图可知，不同电压等级下电晕放电的电压正负半周在放电幅值及放电重复率上具有明显不对称性。正半周的放电重复率高于负半周，负半周的放电幅值明显高于正半周。此外，电晕放电的放电幅值较高，当电压为8 kV时，最大放电量约为15 nC，随着电压等级的升高，放电幅值显著增加，当电压为12 kV时，在电压负半周210°附近出现少量高幅值放电脉冲，其最大放电量达到了25 nC。
从图6的极坐标谱图可以看出，电晕放电脉冲在第一和第三象限聚类成两个幅值不对称的放电点簇，第三象限的幅值要远高于第一象限。当电压为8 kV时，点簇1的质心为（90.037°，0.081），点簇2的质心为（270.1°，0.132）；点簇1的放电脉冲集中在26.1°～105.5°，点簇2的放电脉冲集中在203.1°～268.4°。随着电压等级的提高，质心的极角基本不变，极半径缓慢变大，放电形状与槽放电有明显区分。
表3为电晕放电极坐标谱图的特征参数。由表3可知，随着电压等级的升高，第一象限放电占比逐渐减小，第三象限放电占比逐渐增大。点簇1的偏斜度和陡峭度都是正数，并且都随电压等级的提高先减小后增大。点簇2的偏斜度是负数，陡峭度为正数，它们的绝对值均随电压等级的提高而减小。
4 结论
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本文在实验室环境下获取了10 kV三相异步电动机定子绝缘的3种局部放电信息，并分别绘制了PRPD谱图及极坐标谱图，计算了极坐标谱图的特征参数。从极坐标谱图质心位置、点簇分布特征、特征参数等方面综合分析，发现不同放电类型具有不同的谱图特征及特征参数。内部放电点簇在第一、三象限分布对称。槽放电与电晕放电点簇分布不对称，第三象限的幅值远大于第一象限，且槽放电比电晕放电的点簇放电脉冲范围更大，放电形状更宽。随着电压等级的升高，3种放电类型的放电幅值和放电范围均增大。不同放电类型的偏斜度、陡峭度以及象限放电占比等特征参数随电压等级的升高其变化规律均不同。
基金
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  • 山西省高等学校科技创新计划(2022L062)
  • 山西省高等学校科技创新计划(2022L063)
  • 山西省基础研究计划青年科学研究项目(202203021212274)
  • 山西省基础研究计划青年科学研究项目(202203021212225)
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2025年第58卷第6期
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doi: 10.16790/j.cnki.1009-9239.im.2025.06.014
  • 接收时间：2024-07-19
  • 首发时间：2025-12-04
  • 出版时间：2025-06-20
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  • 收稿日期：2024-07-19
  • 修回日期：2024-09-19
基金
山西省高等学校科技创新计划(2022L062)
山西省高等学校科技创新计划(2022L063)
山西省基础研究计划青年科学研究项目(202203021212274)
山西省基础研究计划青年科学研究项目(202203021212225)
作者信息
    太原理工大学，a.矿用智能电器技术国家地方联合工程实验室；b.煤矿电气设备与智能控制山西省重点实验室，山西 太原 030024

通讯作者:

康爱亮（1988-），男（汉族），河北廊坊人，讲师，博士，主要从事发电机及高压电动机主绝缘局部放电检测与诊断；
赵世杰（2000-），男（汉族），山西晋城人，硕士生，主要从事高电压与绝缘的研究；
吝伶艳（1969-），女（汉族），山西临汾人，副教授，博士，主要从事电气故障诊断及绝缘性能的研究；
陈占清（1991-），男（汉族），河南许昌人，讲师，博士，主要从事高压真空开关、脉冲功率开关技术、真空电弧等离子体的研究。
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https://castjournals.cast.org.cn/joweb/jycl/CN/10.16790/j.cnki.1009-9239.im.2025.06.014
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2种不同金属材料的力学参数
科
Family		 属数
Number of
genus		 种数
Number of
species		 占总种数比例
Percentage of
total species (%)		 属
Genus		 种数
Number of
species		 占总种数比例
Percentage of total
species (%)
鹅膏菌科Amanitaceae 2 11 5.26 鹅膏菌属 Amanita 10 4.78
小菇科 Mycenaceae 2 12 5.74 丝盖伞属 Inocybe 5 2.39
多孔菌科 Polyporaceae 8 14 6.70 蜡蘑属 Laccaria 5 2.39
红菇科 Russulaceae 3 23 11.00 小皮伞属 Marasmius 6 2.87
小菇属 Mycena 11 5.26
光柄菇属 Pluteus 5 2.39
红菇属 Russula 17 8.13
栓菌属 Trametes 5 2.39
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