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Article(id=1199644780151009795, tenantId=1146029695717560320, journalId=1149653034449285133, issueId=1199644777219191267, articleNumber=null, orderNo=null, doi=10.16790/j.cnki.1009-9239.im.2023.12.007, pmid=null, cstr=null, oa=null, hot=null, price=null, onlineType=0, articleFormat=0, articleType=null, articleTypeStr=research-article, receivedDate=1676908800000, receivedDateStr=2023-02-21, revisedDate=1680105600000, revisedDateStr=2023-03-30, acceptedDate=null, acceptedDateStr=null, onlineDate=1763947203910, onlineDateStr=2025-11-24, pubDate=1703001600000, pubDateStr=2023-12-20, doiRegisterDate=null, doiRegisterDateStr=null, onlineIssueDate=1763947203910, onlineIssueDateStr=2025-11-24, onlineJustAcceptDate=null, onlineJustAcceptDateStr=null, onlineFirstDate=null, onlineFirstDateStr=null, sourceXml=null, magXml=null, createTime=1763947203910, creator=13701087609, updateTime=1763947203910, updator=13701087609, issue=Issue{id=1199644777219191267, tenantId=1146029695717560320, journalId=1149653034449285133, year='2023', volume='56', issue='12', pageStart='1', pageEnd='135', issueExtLink='null', onlineDate='null', pubDate='null', beforeIssueId=null, nextIssueId=null, price=null, status=1, issueComplete=1, articleOrder=1, issueType=-1, specialIssue=null, createTime=1763947203211, creator=13701087609, updateTime=1766563728010, updator=13701087609, preIssue=null, nextIssue=null, ext={EN=IssueExt(id=1210619277716099586, tenantId=1146029695717560320, journalId=1149653034449285133, issueId=1199644777219191267, language=EN, specialIssueTitle=, coverIllustrator=null, specialIssueEditor=, specialIssueAbout=), CN=IssueExt(id=1210619277716099587, tenantId=1146029695717560320, journalId=1149653034449285133, issueId=1199644777219191267, language=CN, specialIssueTitle=, coverIllustrator=null, specialIssueEditor=, specialIssueAbout=)}, issueFiles=null}, startPage=54, endPage=62, ext={EN=ArticleExt(id=1199644780457193999, articleId=1199644780151009795, tenantId=1146029695717560320, journalId=1149653034449285133, language=EN, title=Research on characteristics and mechanism of streamer branching in alternative gas-to-liquid transformer oil, columnId=1199644778280350182, journalTitle=Insulating Materials, columnName=Advanced Electrical Materials for Large Capacity Offshore Wind Power Transmission, runingTitle=null, highlight=null, articleAbstract=

In this paper, the heterogeneous non-naphthenic transformer oil based on natural gas-to-liquid technology and traditional naphthenic transformer oil were used as research object. The streamer branching patterns in oil samples in the 25 mm point-to-plate electrode system was observed under positive lightning impulse voltage. The streamer discharge images were conducted multifractal analysis to obtain the multifractal parameters as the classification and evaluation index of streamer branching morphology. The results show that when the applied voltage is lower than the accelerated voltage, the streamer branching process in the two oil samples can be classified as a two-stage model dominated by the steady growth of side branch and main branch. When the applied voltage is higher than the accelerated voltage, the streamer branching process in naphthenic oil is a three-stage model, each stage dominated by steady growth of side branch, steady growth of main branch, and rapid growth of main branch, respectively, and the streamer branching process in gas-to-liquid transformer oil only includes two stages, which are steady growth stage of main branch and rapid growth stage of main branch. Further theoretical analysis shows that the competition between space charge and primary electric field is distorted due to the higher ionization energy of gas-to-liquid transformer oil components, which is the main reason for the abrupt change of streamer branching model in gas-to-liquid transformer oil under accelerating voltage.

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以基于天然气制油技术的异构非环烷基变压器油和传统的环烷基变压器油作为研究对象，在正极性雷电冲击电压下对25 mm针-板电极结构中的油中流注分叉形态进行了观测。对获取的流注放电图像进行多重分形分析，求取多重分形参量作为流注分叉模式的分类评价指标。结果表明：当外加电压低于加速电压时，两种油样中流注分叉过程均可归为侧枝和主枝平稳增长分别占主导的两阶段模型；当外加电压高于加速电压时，环烷基油中流注分叉过程为侧枝平稳增长、主枝平稳增长和跃迁式增长分别占主导的三阶段模型，而气制油中流注分叉过程只包含主枝平稳增长和跃迁式增长两个阶段。进一步的理论分析表明，气制油成分较高的电离能导致空间电荷与原生电场的博弈效应减弱是造成其在加速电压下流注分叉模型发生突变的主要原因。

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卢武（1991-），男（汉族），安徽亳州人，副教授，主要研究方向为液相放电机理与高压绝缘数值计算。
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张浩（1998-），男（汉族），山东日照人，硕士生，主要研究方向为液体绝缘材料放电机理与高电压试验技术。

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张浩（1998-），男（汉族），山东日照人，硕士生，主要研究方向为液体绝缘材料放电机理与高电压试验技术。

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张浩（1998-），男（汉族），山东日照人，硕士生，主要研究方向为液体绝缘材料放电机理与高电压试验技术。

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油样电压等级/kV时间/μs传播速度/(km/s)多重分形参数流注分叉模型
f(α)maxΔfΔα
矿物油14021.681.360.360.25球I型
103.621.590.320.25球Ⅱ型
18022.491.390.390.25球I型
83.641.670.330.26球Ⅱ型
2200.62.501.200.370.26球I型
1.015.101.330.510.25圆柱I型
1.617.451.490.540.26圆柱Ⅱ型
2600.36.501.210.380.25球I型
0.620.501.360.530.26圆柱I型
0.886.901.520.550.26圆柱Ⅱ型
气制油12021.991.340.370.25球I型
92.211.580.270.26球Ⅱ型
15021.641.360.400.25球I型
72.491.620.250.26球Ⅱ型
2100.4819.001.190.370.26球I型
0.64189.881.470.520.25圆柱Ⅱ型
2500.3537.401.210.380.25球I型
0.45247.201.490.540.26圆柱Ⅱ型
), ArticleFig(id=1211311079020426170, tenantId=1146029695717560320, journalId=1149653034449285133, articleId=1199644780151009795, language=CN, label=表1, caption=

两种油样中流注多重分形参数的分类汇总

, figureFileSmall=null, figureFileBig=null, tableContent=
油样电压等级/kV时间/μs传播速度/(km/s)多重分形参数流注分叉模型
f(α)maxΔfΔα
矿物油14021.681.360.360.25球I型
103.621.590.320.25球Ⅱ型
18022.491.390.390.25球I型
83.641.670.330.26球Ⅱ型
2200.62.501.200.370.26球I型
1.015.101.330.510.25圆柱I型
1.617.451.490.540.26圆柱Ⅱ型
2600.36.501.210.380.25球I型
0.620.501.360.530.26圆柱I型
0.886.901.520.550.26圆柱Ⅱ型
气制油12021.991.340.370.25球I型
92.211.580.270.26球Ⅱ型
15021.641.360.400.25球I型
72.491.620.250.26球Ⅱ型
2100.4819.001.190.370.26球I型
0.64189.881.470.520.25圆柱Ⅱ型
2500.3537.401.210.380.25球I型
0.45247.201.490.540.26圆柱Ⅱ型
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可替代型气制变压器油中流注分叉特性及其机理研究
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张浩 1, 2 , 李珂 3 , 许红运 1 , 王哲铭 1 , 周文强 1 , 卢武 1
绝缘材料 | 面向大容量海上风电送出的先进电工材料 2023,56(12): 54-62
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绝缘材料 | 面向大容量海上风电送出的先进电工材料 2023, 56(12): 54-62
可替代型气制变压器油中流注分叉特性及其机理研究
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张浩1, 2, 李珂3, 许红运1, 王哲铭1, 周文强1, 卢武1
作者信息
  • 1上海电力大学 电气工程学院,上海 200090
  • 2国网日照供电公司,山东 日照 276800
  • 3国家电网有限公司华东分部,上海 200120

    • 张浩（1998-），男（汉族），山东日照人，硕士生，主要研究方向为液体绝缘材料放电机理与高电压试验技术。

通讯作者:

卢武（1991-），男（汉族），安徽亳州人，副教授，主要研究方向为液相放电机理与高压绝缘数值计算。
Research on characteristics and mechanism of streamer branching in alternative gas-to-liquid transformer oil
Hao ZHANG1, 2, Ke LI3, Hongyun XU1, Zheming WHANG1, Wenqiang ZHOU1, Wu LU1
Affiliations
  • 1School of Electric Engineering, Shanghai University of Electric Power, Shanghai 200090, China
  • 2State Grid Rizhao Power Supply Company, Rizhao 276800, China
  • 3East China Branch of State Grid Co., Ltd., Shanghai 200120, China
出版时间: 2023-12-20 doi: 10.16790/j.cnki.1009-9239.im.2023.12.007
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摘要
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以基于天然气制油技术的异构非环烷基变压器油和传统的环烷基变压器油作为研究对象，在正极性雷电冲击电压下对25 mm针-板电极结构中的油中流注分叉形态进行了观测。对获取的流注放电图像进行多重分形分析，求取多重分形参量作为流注分叉模式的分类评价指标。结果表明：当外加电压低于加速电压时，两种油样中流注分叉过程均可归为侧枝和主枝平稳增长分别占主导的两阶段模型；当外加电压高于加速电压时，环烷基油中流注分叉过程为侧枝平稳增长、主枝平稳增长和跃迁式增长分别占主导的三阶段模型，而气制油中流注分叉过程只包含主枝平稳增长和跃迁式增长两个阶段。进一步的理论分析表明，气制油成分较高的电离能导致空间电荷与原生电场的博弈效应减弱是造成其在加速电压下流注分叉模型发生突变的主要原因。

天然气制油  /  流注放电  /  多重分形  /  分叉特性  /  空间电荷

In this paper, the heterogeneous non-naphthenic transformer oil based on natural gas-to-liquid technology and traditional naphthenic transformer oil were used as research object. The streamer branching patterns in oil samples in the 25 mm point-to-plate electrode system was observed under positive lightning impulse voltage. The streamer discharge images were conducted multifractal analysis to obtain the multifractal parameters as the classification and evaluation index of streamer branching morphology. The results show that when the applied voltage is lower than the accelerated voltage, the streamer branching process in the two oil samples can be classified as a two-stage model dominated by the steady growth of side branch and main branch. When the applied voltage is higher than the accelerated voltage, the streamer branching process in naphthenic oil is a three-stage model, each stage dominated by steady growth of side branch, steady growth of main branch, and rapid growth of main branch, respectively, and the streamer branching process in gas-to-liquid transformer oil only includes two stages, which are steady growth stage of main branch and rapid growth stage of main branch. Further theoretical analysis shows that the competition between space charge and primary electric field is distorted due to the higher ionization energy of gas-to-liquid transformer oil components, which is the main reason for the abrupt change of streamer branching model in gas-to-liquid transformer oil under accelerating voltage.

gas-to-liquid  /  streamer discharge  /  multifractal  /  branching morphology  /  space charge
张浩, 李珂, 许红运, 王哲铭, 周文强, 卢武. 可替代型气制变压器油中流注分叉特性及其机理研究. 绝缘材料, 2023 , 56 (12) : 54 -62 . DOI: 10.16790/j.cnki.1009-9239.im.2023.12.007
Hao ZHANG, Ke LI, Hongyun XU, Zheming WHANG, Wenqiang ZHOU, Wu LU. Research on characteristics and mechanism of streamer branching in alternative gas-to-liquid transformer oil[J]. Insulating Materials, 2023 , 56 (12) : 54 -62 . DOI: 10.16790/j.cnki.1009-9239.im.2023.12.007
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0 引言
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为实现“双碳”目标，加强生态文明建设、促进绿色能源发展，我国海上风电产业蓬勃发展，海上风电场离岸距离越来越远、输送容量越来越大。在高温、高湿、高盐雾的海洋环境工况下，海上风电变压器的运行和维护成本远高于陆上变压器，一旦发生故障将造成巨大的经济损失与社会影响[1-2]。海上风电变压器主要采用油-纸绝缘系统，目前多采用环烷基变压器油作为其液体绝缘材料。环烷基变压器油虽然具有良好的电气性能与低使用成本，但其生物降解性差，燃点与闪点较低，且在不断开采下，环烷基油储量逐年降低[3-4]。因此，寻找能够代替环烷基油的环保型液体绝缘介质已成为海上风电变压器设计领域的研究热点。近年来，一种被称为纯天然气制油（gas-to-liquid）的新技术兴起[5-6]。这种技术可以把天然气转换成高品质的异构非环烷基变压器油。气制油具有优良的电气和理化性能，不含腐蚀性硫且对环境友好，有望替代传统环烷基油应用于海上风电场升压站变压器油纸绝缘等场景[7-8]。
海上风电变压器在运行过程中易遭受雷电冲击电压、脉冲电压叠加工频电压等复杂电应力的影响[9]。在这些外施强电场作用下，变压器内部绝缘薄弱处可能会产生流注放电现象，严重时诱发大间距油隙的绝缘失效[10]。流注放电通道在传播过程中往往会分裂成数条而形成分叉现象，如侧枝较多的灌木丛状分叉或主枝为主的树枝状分叉等[11]。流注通道的分叉特性影响流注的发展速率，直接决定变压器油的击穿特性。虽然现阶段国内外在探索变压器油中流注分叉特性与外施电压大小、电压极性、液体类型等因素的相关性方面已开展了大量研究[12-14]，但由于流注分叉特性的主导机制具有高度不确定性，受各类直接及间接因素影响，现阶段的理论与实验分析手段尚不能为流注分叉形成机制提供有力证据。因此，亟需详细分析每种影响因素对于流注分叉现象的作用机制，建立自起始至击穿阶段的流注分叉现象的演化模型，为使用气制油的海上风电变压器绝缘设计优化提供理论参考。
为详细研究气制油中流注分叉过程和理解分叉形成机制，本文搭建了使用25 mm针-板电极系统的绝缘油中流注放电观测试验平台，在1.2/50 μs正极性标准雷电冲击电压下，利用高速相机对典型的气制变压器油和环烷基变压器油中流注发展现象进行观测。利用图像处理程序对流注放电影像进行多重分形分析，提取广义分形维数、多重分形谱宽度、最大和最小概率子集分形维数差作为不同流注分叉模式的多重分形特征，通过比较两种油样中流注分叉现象的演化差异，讨论流注尖端空间电荷积聚与原生电场畸变在流注主枝和侧枝形成过程中的作用机制，研究绝缘油中流注在不同传播模式与阶段下的分叉特性与机理。
1 流注分叉特性观测及分析方法
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1.1 实验方法
1.1.1 实验对象
本文选取壳牌公司生产的Diala S3 ZX-I型环烷基矿物油和Diala S4 ZX-I型气制石蜡基油（下文分别简称为矿物油和气制油）作为研究对象，两种油样的主要电气、理化性能参考文献[15-16]，其中矿物油中95%以上成分为环烷基与少量芳香族化合物，气制油中95%以上为石蜡基化合物，几乎不含芳香族化合物。油样在实验前需进行过滤、脱气和除水预处理[17]，处理后的油样相对含水量小于10%，100 mL油样中直径大于5 μm的杂质颗粒数量少于500，满足测试油样对于干燥程度和纯净程度的要求。
1.1.2 测试平台
本文搭建的绝缘油中流注放电观测平台如图1所示。放电腔体由透明的有机玻璃制成，以便对流注放电现象进行观测。高压电极与有机玻璃之间通过陶瓷套管进行绝缘隔离，以防止沿面闪络现象。腔体内部设置间距为25 mm的针-板电极系统，浸没在绝缘油中，用以模拟极不均匀电场。采用针尖曲率半径不超过50 μm的钨针作为高压电极，边缘弯曲半径为5 mm的黄铜圆板作为接地平板电极。测试中采用电容式分压器采集冲击电压信号并由通道示波器进行记录。采用Memrecam ACS-1 M60型高速相机对流注放电图像进行拍摄与记录，冲击电压发生器、高速相机与平行光源由同一个触发系统进行同步触发。
1.1.3 观测过程
参照IEC 60897:1987，对两种油样进行正极性雷电冲击测试。对浸入油样的腔体施加波形为1.2/50 μs的正极性标准雷电冲击电压，从流注起始电压开始，按照5 kV的步长，逐级升高电压直至电极间隙击穿。在击穿电压以上，将升压步长增加到10 kV。在每个电压水平下进行3次测试，两次测试的时间间隔为3 min，取3次测试的平均值作为该时刻的流注传播速度。
1.2 流注的轮廓与多重分形特征分析方法
在外加高场强作用下，变压器油中的流注放电通道会分裂成数条，形成主枝和侧枝共同发展的分叉现象，具有明显的多重分形特征[18]。因此，本研究采用MATLAB软件自行开发了对于流注图像处理的多重分形谱计算程序，提取流注放电的多重分形特征，用于分析在放电发展过程中的流注分叉特性演化规律。如图2所示，首先对流注本体图像进行降噪、对比度增强和二值化处理，统一压缩为512×512大小的二值化图像，随后对二值化图像中的流注本体进行轮廓提取和骨架化处理，最后通过多重分形谱计算得到广义分形维数、多重分形谱宽度和最大最小概率子集分形维数差等特征参数。
通过多重分形谱计算得到各类分形特征的方法如下：首先利用像素尺寸为r×r（r=512, 256, 128,…, 1）大小的盒子对二值化后的流注图像进行分割，令ε=r/512，流注本体出现在盒子（i j）中的概率 Pi j(ɛ)可以表示为式（1）。
Pijε=nijε∑nijε=nijεN
式（1）中：(i j)表示盒子中心点的像素坐标；ni j(ɛ)为流注本体在尺寸为ε的盒子(i j)内占据的像素值；N为流注本体在最大尺寸的盒子内占据的像素值。根据公式（1），可得到配分函数λq(ɛ)如式（2）所示。
λq(ε)≡∑Pi jq(ε)=εq
式（2）中，q为阶矩，一般取值为正无穷大到负无穷大。根据公式（2），质量指数τ(q)可定义为式（3）。
τ(q)=limε→0lnλq(ε)lnε
根据公式（3），流注本体的广义分形维数Dq可以定义为式（4）。
Dq=τ(q)q-1=1q-1limε→0lnλq(ε)lnε, q≠1limε→0∑Pi jq(ε)lnPi jq(ε)lnε, q=1
q=0时，D0等于常用的豪斯多夫分形维数Df （Hausdorff fractcal dimension，下文统称分形维数）。进一步地，流注的多重分形谱f(α)与奇异强度α(q)之间的关系可以通过勒让德变换（Legendre Transformation）得到，如式（5）～（6）所示。
f(α)=α(q)-(q-1)Dq
α=dτ(q)dq=ddq[(q-1)]Dq
典型的流注多重分形谱如图3所示。其中多重分形谱峰值f(a)max为表征流注分叉总体复杂程度的分形维数，f(a)max越大，则流注分叉几何复杂程度越高。此外，多重分形谱宽度Δα可以定义为式（7）。
Δα=αmax-αmin
Δα反映了流注中不同分支出现的概率范围，Δα越大，表明流注中出现的分支种类和形态越多样化。最大最小概率子集分形维数差Δf(α)可以定义为式（8）。
Δf(α)=f(αmin)-f(αmax)
Δf反映了流注分叉过程中出现概率最大的主枝与出现概率最小的侧枝在数目上的比例关系。Δf越大，则流注主枝在所有分支中占比越高。
2 结果与讨论
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2.1 流注平均传播速度
现有的实验研究主要依据传播速度对流注传播模式进行划分，正极性雷电冲击电压下矿物油与气制油中流注的平均传播速度如图4所示。本文中击穿电压Vb为流注通道贯穿两电极时的电压，常用来衡量在实验条件下小油隙中的绝缘特性；加速电压Va为流注传播速度发生突变的电压，常用来衡量在实际高电压等级下大油隙中的绝缘特性。当外加电压低于加速电压时，矿物油与气制油中流注的传播速度均为1～5 km/s，此时可以认为流注以慢流注模式传播；当外加电压高于加速电压时，矿物油中流注速度突变至15 km/s以上，气制油中流注速度突变至30 km/s以上，此时可以认为流注以快流注模式传播。
从图4可以看出，矿物油的击穿电压为55 kV，加速电压为200 kV；气制油的击穿电压为70 kV，加速电压为170 kV。说明在小绝缘油隙中气制油的绝缘性能优于矿物油，在高电压等级大绝缘油隙中，矿物油的绝缘性能优于气制油。在进一步应用中，可以考虑通过添加低电离电位添加剂来提高气制油的加速电压[19]。
本文以两种油样的加速电压为分界点，选取矿物油中180 kV、气制油中150 kV下的典型慢流注放电图像与矿物油中260 kV、气制油250 kV下的典型快流注放电图像进行分析，探讨矿物油和气制油中慢流注和快流注的多重分形特征及分叉特征演化规律。
2.2 慢流注放电特征及多重分形参数变化规律
图5为外加电压在加速电压以下时，矿物油与气制油中拍摄到的典型慢流注放电过程。从图5可以看出，在慢流注传播模式下，两种油中流注放电有着相似的分叉特性。在慢流注起始阶段均表现为有着少量分支、发出微弱可见光的细丝状暗通道。随着流注放电时间增加，流注放电通道向地电极逐渐发展，并出现越来越多的侧枝，最终呈现为茂密的灌木状暗通道。在整个发展过程中，流注传播速度基本不变。流注的传播速度与几何形态之间具有普遍对应规律，慢流注模式下传播速度较慢，两种油中流注均表现为主枝与侧枝同步发展的球状形态。
基于多重分形特征的变化，可以进一步对慢流注传播模式下两种油中的流注发展过程进行量化分析。两种油中的多重分形谱变化趋势如图6所示，可以发现两种慢流注的多重分形谱模式均为典型的左钩型。在流注传播过程中，f(α)max存在明显的上升趋势直至饱和，表明慢流注分叉复杂程度随传播时间增加而逐渐增加，并在最终阶段趋于稳定。慢流注传播过程中Δα的数值基本不变，表明流注分叉种类的概率分布情况稳定。慢流注的传播是一个自相似的过程，其整体结构波动较小。在矿物油与气制油中，Δf在流注发展过程中基本不变，表明流注传播过程中主枝与侧枝的占比基本不变。此外，矿物油中流注的f(α)max数值明显高于气制油，表明相同条件下矿物油中流注分叉更为明显。更多的流注分支会造成相互之间的屏蔽效应，减缓慢流注向快流注的转变过程，导致矿物油中的加速电压更高[19]。
2.3 快流注放电特征及多重分形参数变化规律
图7为外加电压在加速电压以上时，矿物油与气制油中拍摄到的典型快流注放电过程。
从图7可以看出，在快流注传播模式下，矿物油中流注的分叉过程可分为起始、中间与最终三个阶段。在起始阶段，流注为微小的灌木丛状暗通道，传播速度为4～10 km/s，初始阶段的持续时间一般在0.2 μs以内，并随外施电压等级的提高而缩短。随后，流注传播进入中间阶段，此时在流注暗通道中形成细树枝状的亮通道分支，并以比暗通道更快的传播速度与暗通道一起向前发展，此阶段的亮通道传播速度一般为10～30 km/s。亮通道向前发展的过程中，暗通道分支继续向四周产生侧枝分叉，暗通道长度略微增加。暗通道发展至一定长度后发生停滞，此时进入流注传播的最终阶段，亮通道作为流注主枝迅速向地电极传播，传播过程中亮流注通道直径明显增加，由细树枝状转变为粗树枝状，并在主枝基础上继续产生新的亮通道侧枝，最终亮通道主枝发展至地电极引起击穿。流注主枝的传播速度随电压等级升高而增加，可达100 km/s以上。
在气制油中快流注则具有两个阶段的发展过程，与矿物油相比，气制油中快流注传播不包括亮、暗通道一起发展的中间阶段。在起始阶段，气制油中快流注通道表现为微小的气泡状暗通道，暗通道的传播速度一般在10 km/s以下，随后流注迅速进入最终阶段，此时流注表现为具有较少侧枝的树枝状亮通道，瞬时传播速度最高可超过200 km/s。在加速电压以上，快流注模式下的传播速度较高，并随外加电压的升高而迅速上升，形态上表现为分支较少、较稀疏的树枝状亮通道，流注主枝占比较高，形态上总体呈圆柱状。
基于多重分形特征的变化，可以进一步对快流注传播模式下两种油中的流注发展过程进行量化分析。两种油中的多重分形谱变化趋势如图8所示，与慢流注相似，快流注模式下矿物油与气制油中f(α)max随时间增加呈上升趋势且Δα数值基本不变，表明快流注发展过程中流注分叉复杂程度随传播时间增加而逐渐增加，且整体结构波动较小。在两种油中，Δf在流注发展过程中均逐渐增大，表明快流注模式下主枝在流注发展过程中占据主导地位，且主枝的主导地位在流注传播过程中不断增强，即侧枝占比不断减少。
2.4 流注分叉阶段的演化模型
由2.2～2.3节中不同传播模式下流注放电特征及多重分形参数的变化规律可知，慢流注与快流注虽然在整体外观有着显著差异，如慢流注主枝和侧枝均由暗通道组成，而快流注主枝主要由亮通道构成，侧枝主要为暗通道，但在两种流注的完整发展过程中，存在着放电特征与多重分形参数相似的发展阶段，如慢流注和快流注在起始阶段均表现为成簇的慢流注通道。因此，本节对计算得到的流注多重分形参数进行分类汇总（如表1所示），总结出流注分叉阶段的一般化演化模型。
图9为流注分叉阶段的一般化演化模型。如图9(a)所示，在初始阶段，矿物油与气制油中慢流注发展均以细丝状的暗通道主枝为主，此时流注分支较少，整体形状呈球体。由表1可知，此时流注的f(α)max取值范围为1.29～1.39，Δf取值范围为0.36～0.40，Δα取值范围为0.25～0.26，下文统称此时的流注分叉模型为“球I型”；之后慢流注侧枝数量与长度迅速增加，流注开始表现为主枝和侧枝同步发展，整体形状呈球体。由表1可知，此时流注的f(α)max取值范围为1.58～1.67，Δf取值范围为0.25～0.33，Δα取值范围为0.25～0.26，下文统称此时的流注分叉模型为“球II型”。通过流注多重分形参数的对比可知，“球II型”的分叉几何复杂程度较高，且主枝占比小于“球I型”。
如图9(b)所示，与慢流注类似，在初始阶段，矿物油与气制油中快流注同样以细丝状的暗通道分叉为主，由表1可知，此时流注的多重分形参数与慢流注初始阶段基本相同，因此认为此时流注分叉模型同样为“球I型”。在中间阶段，矿物油中的快流注发展以稀疏的树枝状亮通道主枝为主，整体形态呈圆柱体，由表1可知，此时流注的f(α)max取值范围为1.33～1.36，Δf取值范围为0.51～0.53，Δα取值范围为0.25～0.26，下文统称此时的流注分叉模型为“圆柱I型”。在最终阶段，此时两种油中的快流注发展均以多条同步分叉的树枝状亮通道主枝为主，整体形状呈圆柱体，由表1可知，此时流注的f(α)max取值范围为1.47～1.52，Δf取值范围为0.52～0.55，Δα取值范围为0.25～0.26，下文统称此时的流注分叉模型为“圆柱II型”。通过流注多重分形参数的对比可知，“圆柱II型”的主枝分叉数量更多，分叉趋势更强，几何复杂程度远高于“圆柱I型”。
2.5 基于流注尖端原生电场与空间电荷博弈效应的流注分叉机理分析
由2.4节流注分叉阶段的划分可知，具有不同化学成分的变压器油中流注分叉阶段的演化模型具有一般性，如矿物油和气制油中慢流注分叉均为“球I型+球II型”模型。虽然气制油中快流注不存在“圆柱I型”模型代表的分叉中间阶段，但是在初始和最终阶段两种油中快流注均为“球I型+圆柱II型”模型。本节从流注尖端原生电场与空间电荷博弈的角度出发，提出统一的油中流注分叉机理模型，如图10所示，以阐明流注分叉形态上的共通性。
如图10所示，变压器油中流注放电通道的发展可近似认为由流注尖端的电场分量Ez和Er共同决定。其中z轴正方向为由针电极指向地电极中心的轴向方向，r轴正方向为由针电极中心向四周扩展的径向方向。Ez分量主要影响主枝的发展，Er分量主要影响侧枝的发展。流注传播过程中其尖端可认为是针电极的延伸[20]，因此Ez分量主要由外加电压在尖端产生的瞬时场强决定（下文统称原生电场）。同时在流注传播过程中，由于碰撞电离、光电离和场致电离[12]等导致尖端附近产生空间电荷积聚，造成电场畸变情况，主要影响Er分量的大小。
如图10(a)所示，在慢流注传播初始阶段，外加电压处于上升沿初期，电压瞬时值较小，此时流注尖端场强Ez较小。绝缘油中仅有电离能较低的分子能发生电离，空间电荷效应导致的Er分量同样不明显，此时Ez和Er分量在流注分叉过程中的作用差异性不大，流注分叉以向空间中随机发展的主枝为主，即为“球I型”模型；当流注进一步发展时，流注通道的气-液分界面增多且表面积增大，空间电荷积聚效应持续增强，导致Er分量显著提升。虽然流注尖端原生场强也随外加电压波形的演化而持续增强，但由于慢流注的外加电压峰值一般较低，因此可认为在此阶段Er分量在流注分叉过程中占主导地位，流注分叉以发展逐渐停止的主枝和主枝四周新产生的侧枝为主，即为“球II型”模型。
如图10(b)所示，以矿物油为例，在快流注传播初始阶段，此时与慢流注中的情况类似，Ez和Er分量在流注分叉过程中的作用差异性不大，流注分叉为“球I型”模型；当快流注进一步发展时，一方面油中具有较高电离能的环烷与链烷烃类分子在高场强下开始发生电离，流注通道的导电性大幅提升，流注主枝由暗通道转变为亮通道。另一方面，由于外加电压的幅值较高，快流注尖端电场强度较慢流注传播模式下大幅提升，可认为在此阶段Ez分量在流注分叉过程中占主导地位，流注分叉以向地电极快速发展的主枝为主，即为“圆柱I型”模型；当快流注传播进入最终阶段时，由于流注尖端与地电极的距离大幅缩短，外加电压施加在流注尖端产生的原生电场相较于初始阶段会获得几何倍数的提升，在此阶段Ez分量在流注分叉过程中占据绝对优势地位，流注以向地电极方向分叉发展的主枝为主，即为“圆柱II型”模型。
相比于矿物油，气制油中快流注分叉不存在“圆柱I型”模型，这主要是因为其化学组成中几乎不含有低电离能的芳香烃类分子。由于气制油分子普遍具有较高的电离能，导致气制油中快流注在经历“球I型”模型代表的初始发展阶段后，后续产生的亮通道导电性较矿物油会进一步提升。气制油中亮通道中的电压更小，流注尖端原生电场产生的Ez分量更强。这意味着一旦气制油中亮通道产生后，Ez分量便在流注分叉过程中占据绝对优势地位，气制油中快流注随即在经历“球I型”模型阶段后直接进入“圆柱II型”模型阶段。
3 结论
收起
（1）异构非环烷基气制变压器油和传统环烷基变压器油中慢流注与快流注存在不同的放电形态，两种油中慢流注起始形态均为有少量分支、发出微弱可见光的细丝状暗通道，并最终呈现为茂密的灌木状暗通道。矿物油中快流注起始阶段为微小的灌木状暗通道，之后形成细树枝状的亮通道分支并与暗通道一起向前发展，最终转变为粗树枝状亮通道直至引起击穿；而气制油中快流注的传播过程不包括亮、暗通道一起发展的中间阶段。
（2）按照流注主枝与侧枝的不同传播方式将流注发展进程分为四类演化模型。其中矿物油与气制油中慢流注皆为“球I型+球II型”模型，矿物油中快流注为“球I型+圆柱I型+圆柱II型”模型，气制油中快流注为“球I型+圆柱II型”模型。
（3）影响流注传播的电场分为主要影响主枝发展的轴向分量Ez与主要影响侧枝发展的径向分量Er。由于气制油中几乎不含有低电离能的芳香烃类分子，Ez分量在流注分叉过程中占据绝对优势地位，从而使气制油中快流注在经历“球I型”模型阶段后直接进入“圆柱II型”模型。
基金
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  • 国家自然科学基金资助项目(51707113)
  • 上海市“晨光计划”项目(21CGA63)
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doi: 10.16790/j.cnki.1009-9239.im.2023.12.007
  • 接收时间：2023-02-21
  • 首发时间：2025-11-24
  • 出版时间：2023-12-20
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  • 收稿日期：2023-02-21
  • 修回日期：2023-03-30
基金
国家自然科学基金资助项目(51707113)
上海市“晨光计划”项目(21CGA63)
作者信息
    1上海电力大学 电气工程学院,上海 200090
    2国网日照供电公司,山东 日照 276800
    3国家电网有限公司华东分部,上海 200120

通讯作者:

卢武（1991-），男（汉族），安徽亳州人，副教授，主要研究方向为液相放电机理与高压绝缘数值计算。
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