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Article(id=1210590155417710967, tenantId=1146029695717560320, journalId=1149653034449285133, issueId=1210590152548807015, articleNumber=null, orderNo=null, doi=10.16790/j.cnki.1009-9239.im.2024.09.011, pmid=null, cstr=null, oa=null, hot=null, price=null, onlineType=0, articleFormat=0, articleType=null, articleTypeStr=research-article, receivedDate=1698940800000, receivedDateStr=2023-11-03, revisedDate=1702396800000, revisedDateStr=2023-12-13, acceptedDate=null, acceptedDateStr=null, onlineDate=1766556784729, onlineDateStr=2025-12-24, pubDate=1726761600000, pubDateStr=2024-09-20, doiRegisterDate=null, doiRegisterDateStr=null, onlineIssueDate=1766556784729, onlineIssueDateStr=2025-12-24, onlineJustAcceptDate=null, onlineJustAcceptDateStr=null, onlineFirstDate=null, onlineFirstDateStr=null, sourceXml=null, magXml=null, createTime=1766556784729, creator=13701087609, updateTime=1766556784729, updator=13701087609, issue=Issue{id=1210590152548807015, tenantId=1146029695717560320, journalId=1149653034449285133, year='2024', volume='57', issue='9', pageStart='1', pageEnd='165', issueExtLink='null', onlineDate='null', pubDate='null', beforeIssueId=null, nextIssueId=null, price=null, status=1, issueComplete=1, articleOrder=1, issueType=-1, specialIssue=null, createTime=1766556784044, creator=13701087609, updateTime=1766563998200, updator=13701087609, preIssue=null, nextIssue=null, ext={EN=IssueExt(id=1210620410958312217, tenantId=1146029695717560320, journalId=1149653034449285133, issueId=1210590152548807015, language=EN, specialIssueTitle=, coverIllustrator=null, specialIssueEditor=, specialIssueAbout=), CN=IssueExt(id=1210620410958312218, tenantId=1146029695717560320, journalId=1149653034449285133, issueId=1210590152548807015, language=CN, specialIssueTitle=, coverIllustrator=null, specialIssueEditor=, specialIssueAbout=)}, issueFiles=null}, startPage=106, endPage=113, ext={EN=ArticleExt(id=1210590155702923648, articleId=1210590155417710967, tenantId=1146029695717560320, journalId=1149653034449285133, language=EN, title=Intelligent prediction of switching impulse discharge voltage in rod-plane long air gaps at different atmospheric environments, columnId=1190369198472794288, journalTitle=Insulating Materials, columnName=Insulation Technology, runingTitle=null, highlight=null, articleAbstract=

Air discharge results from the interaction between electric field and atmospheric environment, therefore the air gap switching impulse discharge voltage is affected by the interelectrode electric field distribution and the atmospheric parameters. In order to calculate the discharge voltage of rod-plane long air gaps at high altitude areas, we construct an insulation prediction model based on k-nearest neighbor (KNN) algorithm with air pressure, temperature, humidity, altitude, and electric field characteristic parameters as feature set. The KNN algorithm was trained by the test data in the altitude range of 55-4 300 m to establish the mapping relationship between air gap features and the insulation strength, and then discharge voltage prediction of rod-plane air gaps at the high altitude of 5 000 m with different gap distances was realized. The maximum relative error and the mean absolute percentage error are 8.58% and 3.78%, respectively, which verifies the effectiveness of the proposed method. When the model was extrapolated to the rod-plane air gaps in plain area under different atmospheric parameters, the predicted discharge voltages also had good agreement with the experimental values. This study results can provide references for the calculation of air gap insulation strength in different atmospheric environment.

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空气放电源于电场与大气环境的相互作用，空气间隙放电电压受到极间电场分布与大气参数的共同影响。为实现高海拔环境下棒-板长空气间隙的操作冲击放电电压计算，本文以气压、温度、绝对湿度、海拔以及电场特征量作为特征集，构建了一种基于k近邻（k-nearest neighbor，KNN）算法的绝缘预测模型。采用55～4 300 m海拔范围内的试验数据对KNN算法进行训练，建立气隙特征与其绝缘强度的映射关系，实现了5 000 m高海拔环境不同间隙距离的棒-板空气间隙放电电压预测，最大相对误差和平均绝对百分比误差分别为8.58%和3.78%，验证了所提方法的有效性。将模型外推至平原不同大气参数下的棒-板空气间隙时，放电电压预测值与试验值同样具有较好的一致性。研究结果可为不同大气环境下的空气间隙绝缘强度计算提供参考。

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邱志斌（1991-），男（汉族），江西南昌人，副教授，博士，研究方向为高电压与绝缘技术；

宋雨（1998-），女（汉族），宁夏固原人，硕士生，研究方向为高电压与绝缘技术。

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邱志斌（1991-），男（汉族），江西南昌人，副教授，博士，研究方向为高电压与绝缘技术；

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邱志斌（1991-），男（汉族），江西南昌人，副教授，博士，研究方向为高电压与绝缘技术；

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宋雨（1998-），女（汉族），宁夏固原人，硕士生，研究方向为高电压与绝缘技术。

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宋雨（1998-），女（汉族），宁夏固原人，硕士生，研究方向为高电压与绝缘技术。

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figureFileSmall=null, figureFileBig=null, tableContent=
H/md/mp/kPaT/℃h/(g/m3)U50/kVH/md/mp/kPaT/℃h/(g/m3)U50/kVH/md/mp/kPaT/℃h/(g/m3)U50/kV
55[15]2102.08.71.549779.01 016[17]588.8819.513.561 224.73 000[5]470.6518.007.38955
3102.07.51.583973.02 200[5]2.0077.2026.1512.26655571.0016.806.161 121
4102.06.71.6361 1492.9977.2026.2012.808925.0271.0017.056.661 166
5100.729.010.8791 2934.0077.1526.2513.511 079671.0017.306.751 279
6101.86.03.5171 3805.9977.5029.808.261 3827.571.0016.955.891 513
7101.525.018.5851 4326.9577.4529.407.311 5774 300[5]260.5014.104.05470
8101.99.11.4711 7057.0077.2025.0012.871 595360.5513.953.57631
9102.49.03.6531 8348.0077.3023.4012.561 751460.509.154.35841
10.5103.010.05.3472 0512 254[17]277.120.510.802661.9560.5513.353.65958
11.5103.010.05.3472 140377.120.410.749885.0660.706.955.141 134
12102.71.70.8962 137477.220.4510.6081 023.2760.4512.103.781 230
1 016[17]288.5519.513.55733.057720.610.3521 165.6860.2015.204.781 417
388.9519.513.56925.63 000[5]271.0015.905.80556960.3015.404.981 584
488.9019.513.561 073.4370.7518.005.65762
), ArticleFig(id=1218262753140200172, tenantId=1146029695717560320, journalId=1149653034449285133, articleId=1210590155417710967, language=CN, label=表1, caption=

不同海拔高度下的棒-板间隙训练样本集

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H/md/mp/kPaT/℃h/(g/m3)U50/kVH/md/mp/kPaT/℃h/(g/m3)U50/kVH/md/mp/kPaT/℃h/(g/m3)U50/kV
55[15]2102.08.71.549779.01 016[17]588.8819.513.561 224.73 000[5]470.6518.007.38955
3102.07.51.583973.02 200[5]2.0077.2026.1512.26655571.0016.806.161 121
4102.06.71.6361 1492.9977.2026.2012.808925.0271.0017.056.661 166
5100.729.010.8791 2934.0077.1526.2513.511 079671.0017.306.751 279
6101.86.03.5171 3805.9977.5029.808.261 3827.571.0016.955.891 513
7101.525.018.5851 4326.9577.4529.407.311 5774 300[5]260.5014.104.05470
8101.99.11.4711 7057.0077.2025.0012.871 595360.5513.953.57631
9102.49.03.6531 8348.0077.3023.4012.561 751460.509.154.35841
10.5103.010.05.3472 0512 254[17]277.120.510.802661.9560.5513.353.65958
11.5103.010.05.3472 140377.120.410.749885.0660.706.955.141 134
12102.71.70.8962 137477.220.4510.6081 023.2760.4512.103.781 230
1 016[17]288.5519.513.55733.057720.610.3521 165.6860.2015.204.781 417
388.9519.513.56925.63 000[5]271.0015.905.80556960.3015.404.981 584
488.9019.513.561 073.4370.7518.005.65762
), ArticleFig(id=1218262753232474866, tenantId=1146029695717560320, journalId=1149653034449285133, articleId=1210590155417710967, language=EN, label=Table 2, caption=Discharge voltage prediction results of rod-plane gaps at 5 000 m of altitude, figureFileSmall=null, figureFileBig=null, tableContent=
H/md/mp/kPaT/℃h/(g/m3)U50/kVUp1/kVUp2/kVUp3/kVe1/%e2/%e3/%
5 000[5]256.456.456.034314684754968.5810.2115.08
356.48.205.39637628655627-1.412.83-1.57
456.48.204.708028378278404.363.124.74
556.37.554.36973956985952-1.751.23-2.16
656.38.004.141 0981 1291 1441 1232.824.192.28
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5 000 m海拔环境下棒-板间隙的放电电压预测结果

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H/md/mp/kPaT/℃h/(g/m3)U50/kVUp1/kVUp2/kVUp3/kVe1/%e2/%e3/%
5 000[5]256.456.456.034314684754968.5810.2115.08
356.48.205.39637628655627-1.412.83-1.57
456.48.204.708028378278404.363.124.74
556.37.554.36973956985952-1.751.23-2.16
656.38.004.141 0981 1291 1441 1232.824.192.28
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温度d/mp/kPaT/℃h/(g/m3)U50/kVUp/kVe/%
低温3103.31.03.45943.79561.30
4102.32.03.641 1081 1433.16
5102.32.03.611 2551 3003.59
6102.42.42.991 4221 373-3.45
7102.13.63.551 5701 486-5.35
8104.13.51.231 6251 588-2.28
9104.02.03.331 8201 9376.43
10102.8-1.80.901 9261 9893.27
11102.8-0.90.882 0112 0622.54
高温3100.525.552.8972967-0.51
5101.127.012.11 2921 280-0.93
6101.525.018.61 3411 4175.67
6.2100.828.010.61 4301 4420.84
7101.426.019.41 4421 5386.66
7.38101.325.512.01 5861 581-0.32
8.58101.128.011.71 7461 8345.04
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不同大气参数下棒-板间隙放电电压预测结果

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温度d/mp/kPaT/℃h/(g/m3)U50/kVUp/kVe/%
低温3103.31.03.45943.79561.30
4102.32.03.641 1081 1433.16
5102.32.03.611 2551 3003.59
6102.42.42.991 4221 373-3.45
7102.13.63.551 5701 486-5.35
8104.13.51.231 6251 588-2.28
9104.02.03.331 8201 9376.43
10102.8-1.80.901 9261 9893.27
11102.8-0.90.882 0112 0622.54
高温3100.525.552.8972967-0.51
5101.127.012.11 2921 280-0.93
6101.525.018.61 3411 4175.67
6.2100.828.010.61 4301 4420.84
7101.426.019.41 4421 5386.66
7.38101.325.512.01 5861 581-0.32
8.58101.128.011.71 7461 8345.04
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不同大气环境下棒-板长空气间隙操作冲击放电电压智能预测
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邱志斌 , 宋雨 , 吴子建 , 陈文豪
绝缘材料 | 绝缘技术 2024,57(9): 106-113
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绝缘材料 | 绝缘技术 2024, 57(9): 106-113
不同大气环境下棒-板长空气间隙操作冲击放电电压智能预测
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邱志斌, 宋雨, 吴子建, 陈文豪
作者信息
  • 南昌大学 能源与电气工程系，江西 南昌 330031

    • 邱志斌（1991-），男（汉族），江西南昌人，副教授，博士，研究方向为高电压与绝缘技术；

    宋雨（1998-），女（汉族），宁夏固原人，硕士生，研究方向为高电压与绝缘技术。

Intelligent prediction of switching impulse discharge voltage in rod-plane long air gaps at different atmospheric environments
Zhibin QIU, Yu SONG, Zijian WU, Wenhao CHEN
Affiliations
  • Department of Energy and Electrical Engineering, Nanchang University, Nanchang 330031, China
出版时间: 2024-09-20 doi: 10.16790/j.cnki.1009-9239.im.2024.09.011
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摘要
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空气放电源于电场与大气环境的相互作用，空气间隙放电电压受到极间电场分布与大气参数的共同影响。为实现高海拔环境下棒-板长空气间隙的操作冲击放电电压计算，本文以气压、温度、绝对湿度、海拔以及电场特征量作为特征集，构建了一种基于k近邻（k-nearest neighbor，KNN）算法的绝缘预测模型。采用55～4 300 m海拔范围内的试验数据对KNN算法进行训练，建立气隙特征与其绝缘强度的映射关系，实现了5 000 m高海拔环境不同间隙距离的棒-板空气间隙放电电压预测，最大相对误差和平均绝对百分比误差分别为8.58%和3.78%，验证了所提方法的有效性。将模型外推至平原不同大气参数下的棒-板空气间隙时，放电电压预测值与试验值同样具有较好的一致性。研究结果可为不同大气环境下的空气间隙绝缘强度计算提供参考。

长空气间隙  /  大气参数  /  电场分布  /  放电电压预测

Air discharge results from the interaction between electric field and atmospheric environment, therefore the air gap switching impulse discharge voltage is affected by the interelectrode electric field distribution and the atmospheric parameters. In order to calculate the discharge voltage of rod-plane long air gaps at high altitude areas, we construct an insulation prediction model based on k-nearest neighbor (KNN) algorithm with air pressure, temperature, humidity, altitude, and electric field characteristic parameters as feature set. The KNN algorithm was trained by the test data in the altitude range of 55-4 300 m to establish the mapping relationship between air gap features and the insulation strength, and then discharge voltage prediction of rod-plane air gaps at the high altitude of 5 000 m with different gap distances was realized. The maximum relative error and the mean absolute percentage error are 8.58% and 3.78%, respectively, which verifies the effectiveness of the proposed method. When the model was extrapolated to the rod-plane air gaps in plain area under different atmospheric parameters, the predicted discharge voltages also had good agreement with the experimental values. This study results can provide references for the calculation of air gap insulation strength in different atmospheric environment.

long air gap  /  atmospheric parameters  /  electric field distribution  /  discharge voltage prediction
邱志斌, 宋雨, 吴子建, 陈文豪. 不同大气环境下棒-板长空气间隙操作冲击放电电压智能预测. 绝缘材料, 2024 , 57 (9) : 106 -113 . DOI: 10.16790/j.cnki.1009-9239.im.2024.09.011
Zhibin QIU, Yu SONG, Zijian WU, Wenhao CHEN. Intelligent prediction of switching impulse discharge voltage in rod-plane long air gaps at different atmospheric environments[J]. Insulating Materials, 2024 , 57 (9) : 106 -113 . DOI: 10.16790/j.cnki.1009-9239.im.2024.09.011
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0 引言
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我国能源资源与负荷分布特点决定了“西电东送”的发展格局，许多输电线路途经西部高海拔地区，海拔高度甚至超过5 000 m。高海拔地区的空气密度较低，对空气间隙的绝缘强度具有显著影响，在进行输电线路绝缘设计时，通常需要开展高海拔大气环境下的放电试验，以获取空气间隙的放电电压，或者以低海拔地区的试验数据为依据，选择合适的海拔校正方法将其校正至高海拔下。
长期以来，国内外针对不同海拔高度下的空气间隙开展了大量的操作冲击放电试验[1-5]。根据试验结果总结出各种海拔校正方法，主要包括IEC 60060-1:2010[6]和GB/T 19627.1—2011[7]推荐的g参数法，以及IEC 60071-2:2018[8]和GB 311.1—2012[9]推荐的m参数法。文献[1]对棒-板、导线-板、导线-塔窗等间隙结构在0～1 800 m海拔范围内的操作冲击放电特性开展了试验研究，为用于放电电压校正的g参数法提供了基础。文献[2]在3 000 m海拔环境下开展了外绝缘放电试验，指出文献[1]的校正方法仅适用于1 500 m以内的海拔范围，在更高海拔环境下的适用性较差。文献[3]根据放电试验结果提出了棒-板间隙在海拔2 100 m以下的直流、雷电和操作冲击放电电压的修正公式。文献[4-5]对0～5 000 m海拔范围内的棒-板等典型间隙开展了标准操作冲击放电试验，指出m参数法适用于海拔为2 200 m的环境，但当海拔高度进一步增加时，校正结果与试验结果的误差增大，而g参数法不适用于海拔3 000 m以上的棒-板间隙放电电压校正。文献[5]通过试验数据拟合提出了不同海拔地区棒-板间隙的放电电压校正方法。此外，GB/T 42001—2022[10]提供了输电线路与变电站空气间隙在0～5 000 m海拔范围内的操作冲击放电电压校正方法。
为确保高海拔地区输电线路绝缘设计的合理性，必须获取对应大气环境下的空气间隙绝缘强度，现有的海拔校正方法[6-10]是通过经验公式建立放电电压与空气相对密度、湿度、海拔高度、间隙距离、电压类型等因素的函数关系式，其适用范围往往存在局限性。空气间隙的放电电压与大气参数存在复杂的多维、非线性关系[11]，传统的数据拟合手段难以准确建立不同大气环境或海拔高度下的绝缘强度预测模型。近年来，部分学者尝试采用人工智能算法进行空气间隙放电电压预测，取得了一定的进展。文献[11-12]以气压、温度、相对湿度、风速等大气参数作为输入量，分别采用BP神经网络与Chebyshev神经网络建立了半球形电极间隙的放电电压预测模型。文献[13]以大气参数和电场特征作为支持向量机（support vector machine，SVM）模型的输入量，实现了雾中棒-板间隙的击穿电压预测。文献[14-15]以间隙距离和气压、温度、绝对湿度作为输入量，分别采用支持向量回归和极限随机树模型实现了棒-板间隙的放电电压预测。上述研究验证了人工智能算法用于空气间隙绝缘强度预测的可行性，然而，目前针对高海拔环境下的长空气间隙放电电压预测研究仍然较少。
在高海拔环境下，空气间隙在标准操作冲击下的50%放电电压（U50）主要取决于间隙结构与大气条件，合理表征不同间隙结构与不同海拔地区的大气环境，并选用有效的机器学习模型，是实现放电电压预测的关键。为此，本文以气压、温度、绝对湿度、海拔高度和间隙最短路径上的9维电场特征量作为输入量，提出了一种基于k近邻（k-nearest neighbor，KNN）算法的绝缘强度预测模型，通过模型训练建立输入量与放电电压的关联性，实现高海拔地区与不同大气环境下的棒-板长空气间隙正极性标准操作冲击放电电压预测。
1 大气参数与电场特征集
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选取棒-板长空气间隙作为研究对象，采用有限元法计算其静电场分布，提取极间最短路径上的电场特征量表征间隙结构，采用气压、温度、绝对湿度与海拔高度描述大气环境，共同构成高海拔环境下棒-板间隙的特征集，并对特征数据进行预处理，作为放电电压预测模型的输入量。
1.1 特征定义
对于半球头棒-板间隙，可建立其二维轴对称模型进行静电场仿真计算，采用三角形单元进行网格剖分，并在棒电极与气隙附近进行网格加密，以确保电场计算结果的准确性。对端部直径Φ为38 mm的棒电极施加单位电位1 kV，对板电极和空气边界施加零电位，间隙距离d=2 m的棒-板间隙电场分布云图与极间最短路径LAB上的电场分布曲线如图1所示。
从图1可以看出，电场强度最大值出现在棒电极端部表面A点，且电场强度沿LAB逐渐减小。对LAB路径上的电场强度值进行离散化，从电场强度、电场强度的标量梯度、电场强度的平方量、电场畸变率和间隙距离等多角度出发，定义9维电场特征量，具体如下：
（1）LAB上的电场强度最大值Em、平均值Ea、标准差Estd、平方和We、标量梯度的最大值Egm、以及电场畸变率Ed计算式如（1）所示。
Em=maxEi
Ea=1n∑i=1nEi
Estd=1n∑i=1n(Ei-Ea)2
We=∑i=1nEi2
Egm=max(-∇Ei)
Ed=(Em-En)/Ea
式（1）～（6）中：Ei为LAB上第i个取样点的电场强度；n为采样点总数；En为LAB上的电场强度最小值。
（2）LAB的长度定义为lAB，其值等于间隙距离d，LAB上Ei>Ea的局部路径La的长度定义为la。
（3）La上的电场强度积分Va计算式如式（7）所示。
Va=∫Ei≥EaEidl
除上述电场特征量以外，将气压p、温度T、绝对湿度h、海拔高度H作为大气参数特征，组合成描述高海拔环境棒-板间隙的特征集。
1.2 特征数据预处理
本文定义的电场特征量与大气参数具有不同的物理意义，不同特征量的量纲和数量级存在较大差异，为避免这种差异对空气间隙放电电压预测模型的影响，在开展模型训练之前，需要对特征数据进行归一化处理，将其变换到[0，1]区间内。如图2所示，当某特征量与放电电压为正相关或负相关时，将其定义为正向指标或逆向指标，并采用式（8）进行正向归一化或逆向归一化处理。
正相关: x¯i=xi-ximinximax-ximin负相关: x¯i=ximax-xiximax-ximin
式（8）中：xi为任一特征量；ximax、ximin分别为任一特征量的最大值和最小值；x¯i为归一化后的特征量。
2 空气间隙放电电压预测方法
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建立高海拔环境下棒-板间隙放电电压预测模型的基本思路是：构建大气参数与电场特征量组成的特征集，对不同海拔高度或大气环境、不同间隙尺度的棒-板间隙进行表征，采用KNN算法建立机器学习模型，并将上述特征集作为输入量，选取一定海拔范围内的试验数据对模型进行训练，使其具备预测更高海拔下棒-板间隙放电电压的能力。
2.1 KNN算法
KNN算法是一种基于样本相似性度量推断事物类别的分类方法[16]，具有很强的分类能力，可以有效解决二分类问题。本文针对训练集海拔范围外的样本进行预测，由于KNN算法对样本数据没有假设，准确性高，异常点敏感性较低，且通过调整单个超参数便可避免过拟合和欠拟合现象，本文采用KNN算法构建空气间隙绝缘强度计算模型。其核心思想是：对于任意w维输入特征，分别对应于特征空间中的一个点，输出为该特征量所对应的类别标签。KNN算法为惰性学习，仅记忆训练样本特征与标签的一一对应关系，并不会从训练集中学习得到一个判别函数，即推迟对训练数据的建模，直到需要对待测样本进行分类时再利用训练集进行决策，决策时通过度量训练样本与测试样本之间的距离来决定邻近测试样本的参考域，将参考域内出现频次最多的标签赋予测试样本，以此完成分类。具体步骤如下：
（1）给定一个训练样本集，记忆每个样本的特征值与标签值的对应关系。输入任一没有标签的测试样本Q，通过欧式距离公式计算测试样本与训练集各个样本之间的距离D，计算式如式（9）所示。
D(x, y)=∑j=1m(xj-yj)2
式（9）中：xj和yj分别表示测试样本与训练样本的第j个特征；m为单个样本的特征总数。
（2）任一测试样本Q与训练集各个样本之间的距离构成集合Dʹ={D1，D2，…，Di，…}，按照递增关系对Dʹ内的所有元素进行排序，选取距离最小的前k个D值对应的训练样本点。其中，k值是KNN算法的一个超参数，其含义为邻近测试样本参考域内标签值的个数。k值的大小决定模型的复杂程度和准确性，k值过小会导致模型较为复杂，使预测结果容易受异常点的影响，则模型容易过拟合；k值过大会导致模型较为简单，可能受样本均衡问题的影响而使模型容易欠拟合。一般k值的选取可以采用经验法、网格搜索法得到。
（3）对所得近邻中前k个训练样本点的分类结果进行投票，得到票数最高的标签类别，将该标签作为测试样本Q的预测结果。对于二分类问题，特征空间中任意w维训练样本将分别对应两种标签，如图3所示。假设k取3时，测试样本Q的前3个近邻点中有2个训练样本属于类别1，则判断待测样本Q也属于类别1；假设k取9时，测试样本Q的前k个近邻点中有5个训练样本属于类别2，则判断待测样本Q也属于类别2。依次输入待测样本，就能预测得到测试集中每个样本的分类类别。
2.2 放电电压预测流程
基于机器学习模型的空气间隙放电电压预测流程如图4所示，具体步骤如下：
（1）训练样本扩充和标签定义：以每个样本的放电电压U为中心，在中心左右10%的范围内按照步长0.01U对电压进行扩充。低于U的10个施加电压对应间隙耐受（标签为0），其余11个施加电压对应间隙击穿（标签为1），从而将单个样本扩充至21个样本，其施加电压序列为[0.9U，0.91U，…，1.09U，1.1U]，最终得到训练集T。对训练集T的所有特征进行归一化处理后输入模型进行训练。
（2）测试样本放电电压预测：对于任一待测样本，设置放电电压初始预估区间[Un1，Um1]和迭代精度ε，采用Fibonacci法生成该样本的施加电压值，将上述预估区间划分为[Un1，Ua1]、[Ua1，Ub1]、[Ub1，Um1] 3个部分，其中，Ua1=Um1-F1(Um1-Un1)，Ub1=Un1+F1(Um1-Un1)。以Ua1、Ub1作为加载电压对棒-板间隙进行电场仿真计算，提取对应的电场特征集并进行归一化处理，与大气参数共同作为KNN模型的输入，利用式（9）计算待测样本与所有训练样本之间的距离D并进行排序，票选获得其分类结果。
若KNN模型在Ua1、Ub1下均输出0，则将第二次预估电压区间[Un2，Um2]调整为[Ub1，Um1]；若模型均输出1，则将[Un2，Um2]调整为[Un1，Ua1]；若模型在Ua1下输出0，在Ub1下输出1，则调整为[Ua1，Ub1]。以此类推，不断调整Fibonacci分数Fs值并逐渐缩小预估电压区间[Uns，Ums]，生成新的加载电压Uas、Ubs进行迭代预测，直至Uml-Unl<ε时停止迭代，将Up=(Unl+Uml)/2作为待测样本的放电电压预测值，并与试验值对比进行误差分析。上述Fibonacci分数Fs=fs/fs+1（s=1，2，3，…，l），fs值源自Fibonacci数列，满足fs+1=fs-1+fs且f1=1，f2=2。
3 棒-板长空气间隙放电电压预测
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3.1 训练和测试样本
文献[5,15,17]在7种海拔高度下开展了直径Φ为38 mm半球头棒-板长空气间隙的正极性标准操作冲击放电试验，本文引用其试验数据作为样本集开展放电电压预测算例分析，验证KNN模型的有效性。按照海拔范围划分训练集和测试集：以55～4 300 m海拔范围内的41个棒-板间隙作为训练集，其间隙距离、气压、温度、湿度与U50试验值如表1所示；以5 000 m海拔下同样电极尺寸、d=2～6 m的5个棒-板间隙作为测试集，其间隙距离、气压、温度、绝对湿度与U50试验值如表2所示。
3.2 高海拔环境下的放电电压预测结果
在KNN算法中，超参数k值的选取对模型准确性具有重要影响，k值过大会导致模型欠拟合，而k值过小又会导致模型过拟合。为此，基于3折交叉验证的思想随机抽取表1所示试验数据样本的1/3作为选取最优k值的测试集。根据试验经验规则：k值大多取较小的奇数，且最大k值一般低于样本数的平方根[18]。本文用于k值寻优的测试集依据前文所述方法扩充，扩充后的样本数平方根大于10，故设置参数k范围为[1，10]，遍历所有候选参数，选取该测试集表现最优的参数作为最终k值。在不同参数取值下，上述测试集放电电压预测值与试验值的平均绝对百分比误差（mean absolute percentage error，MAPE）如图5所示。由图5可见，当k=5时，MAPE最小，因此，在KNN模型中取k值为5，即待测样本的分类结果为近邻中前5个训练样本点出现频率最高的标签。
利用KNN模型对5 000 m海拔下棒-板间隙的放电电压进行预测，同时建立BP（back-propagation）神经网络和CART（classification and regression tree）决策树模型进行性能对比。BP神经网络是一种单向传播的多层前向网络，由一个输入层、一个或多个隐藏层和一个输出层组成，其学习规则采用梯度下降法，通常使用Sigmoid激活函数实现非线性关系映射[19]。CART决策树[20]采用基尼系数（Gini index）作为特征分裂标准，通过多个条件判别过程将数据集分类，采用二分递归分割技术产生一棵二叉决策树获取数据分类结果。其中BP神经网络隐藏层数为2，训练次数为400，学习速率为0.01；CART决策树每个决策分割时随机选择的预测变量数为5。3种模型的训练集与测试集一致，将其放电电压预测结果分别记为Up1、Up2、Up3，与U50试验值之间的相对误差记为e1、e2和e3，如表2所示。
由表2可知，KNN、BP神经网络和CART决策树模型预测结果的相对误差最大值分别为8.58%、10.21%和15.08%，MAPE分别为3.78%、4.32%和5.17%。采用幂指数函数拟合放电电压预测值Up及试验值Ut与间隙距离d的关系曲线，结果如图6所示。由图6可见，KNN模型所得的Up-d曲线与Ut-d曲线具有十分接近的变化趋势，其偏差明显小于BP神经网络和CART决策树模型的预测结果，表明KNN算法可通过合理选择k值以避免过拟合现象，性能优于BP神经网络和CART决策树模型。此外，针对小样本测试集，由于KNN模型不存在训练过程，其计算速度也优于后两者。上述结果表明，以电场特征集和大气参数作为输入量，采用55～4 300 m海拔范围内的棒-板间隙试验数据作为训练集，在已知5 000 m海拔环境的气压、温度、绝对湿度条件下，通过KNN模型可以准确预测得到棒-板间隙的标准操作冲击放电电压。
3.3 平原地区不同大气参数下的放电电压预测结果
为进一步验证本文方法的适用性，将测试对象外推至平原地区不同大气参数下的棒-板间隙，以文献[14]在北京地区低温和高温天气下开展的标准操作冲击放电试验数据作为样本集，其间隙距离、大气参数和U50试验值如表3所示，海拔高度均取55 m。提取表3中棒-板间隙的大气参数和电场特征，经归一化处理后输入至KNN模型进行放电电压预测。其中，棒-板间隙的电极尺寸和采用的训练集与上述高海拔环境下的算例保持一致，放电电压预测结果如表3和图7所示。
从表3可以看出，在-1.8～3.6℃的低温环境下，d=3～11 m的棒-板间隙放电电压预测值的相对误差最大值为6.43%，9个样本的MAPE为3.49%；在25～28℃的高温环境下，d=3～8.58 m的棒-板间隙放电电压预测值的相对误差最大值为6.66%，MAPE为2.85%。从图7可以看出，KNN模型预测结果的Up-d曲线与试验结果的Ut-d曲线基本吻合，进一步验证了本文方法用于预测不同大气参数下棒-板间隙放电电压的有效性与准确性。
4 结论
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本文针对高海拔与不同大气环境下的棒-板长空气间隙开展了正极性标准操作冲击放电电压智能预测研究，得出以下结论：
（1）采用气压、温度、绝对湿度、海拔高度与极间最短路径上的9维电场特征量作为输入量，以55～4 300 m海拔范围内的放电试验数据对KNN算法进行训练，可以实现5 000 m高海拔环境下的棒-板长空气间隙操作冲击放电电压预测，预测值与试验值具有较好的一致性，MAPE仅为3.78%。
（2）KNN算法对5 000 m高海拔环境下的棒-板长空气间隙放电电压的预测精度高于BP神经网络与CART决策树模型，后两者预测结果的MAPE分别为4.32%和5.17%。
（3）将KNN模型外推至平原地区不同大气参数下的棒-板间隙放电电压预测，同样取得了较好的预测效果，研究结果可为不同大气环境下的空气间隙绝缘强度计算提供参考。
基金
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  • 国家自然科学基金资助项目(52167001)
  • 江西省研究生创新专项资金项目(YC2021-S055)
文献
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2024年第57卷第9期
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doi: 10.16790/j.cnki.1009-9239.im.2024.09.011
  • 接收时间：2023-11-03
  • 首发时间：2025-12-24
  • 出版时间：2024-09-20
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  • 收稿日期：2023-11-03
  • 修回日期：2023-12-13
基金
国家自然科学基金资助项目(52167001)
江西省研究生创新专项资金项目(YC2021-S055)
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    南昌大学 能源与电气工程系，江西 南昌 330031
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