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Aiming at the problem of the lack of historical data on arc faults in most photovoltaic power stations, this paper proposes a photovoltaic system series arc fault diagnosis method based on ultrasonic sensors and isolation forest after collecting arc ultrasonic signals and analyzing their characteristics. Firstly, arc ultrasonic signals are collected and their characteristics and advantages are analyzed. Secondly, the S-transform is used to convert the transient voltage signal of the ultrasonic wave during the occurrence of series arc faults to the time-frequency domain. Then, the Teager energy operator is used to amplify the spectral differences. Subsequently, the time-frequency entropy is used to extract the time-frequency domain features of arc faults. Finally, arc faults are diagnosed based on dynamic thresholds and isolation forest without the need for historical data. Experimental results show that the proposed method can accurately identify series arc faults, with a diagnosis accuracy rate of 97.25%, and has strong anti-interference ability.

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针对大部分光伏电站电弧故障历史数据缺乏的问题,本文在采集电弧超声信号并分析其特点后,提出一种基于超声波传感器与孤立森林的光伏系统串联电弧故障诊断方法。首先,利用S变换将发生串联电弧故障时的超声波暂态电压信号转化至时频域;接着,利用Teager能量算子放大频谱差异性,并通过时频熵提取电弧故障时频域特征;最后,基于动态阈值与孤立森林实现电弧故障诊断且无需历史数据。实验结果表明,所提方法能准确识别串联电弧故障,诊断准确率达到97.25%,且具备较强的抗干扰能力。

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黄晨昊(2000—),男,福建省宁德市人,硕士研究生,主要从事光伏系统电弧故障检测与定位方面的研究工作。

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黄晨昊(2000—),男,福建省宁德市人,硕士研究生,主要从事光伏系统电弧故障检测与定位方面的研究工作。

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黄晨昊(2000—),男,福建省宁德市人,硕士研究生,主要从事光伏系统电弧故障检测与定位方面的研究工作。

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参数 数值
Pmpp/W 270
Vmpp/V 31.3
Impp/A 8.63
Voc/V 38.5
Isc/A 9.09
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光伏组件参数

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参数 数值
Pmpp/W 270
Vmpp/V 31.3
Impp/A 8.63
Voc/V 38.5
Isc/A 9.09
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参数 数值
型号 SG6KTL—MT
启动电压/V 250
最大功率点电压调整范围/V [200, 1 000]
输入电压/V [200, 1 100]
输出电压/V 220
开关频率/kHz 16
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逆变器参数

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参数 数值
型号 SG6KTL—MT
启动电压/V 250
最大功率点电压调整范围/V [200, 1 000]
输入电压/V [200, 1 100]
输出电压/V 220
开关频率/kHz 16
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数据类型 样本数量
正常 200
电弧故障 200
机械噪声 100
强风噪声 100
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数据样本类型及数量

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数据类型 样本数量
正常 200
电弧故障 200
机械噪声 100
强风噪声 100
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孤立树数量/棵 异常分数标准差 计算时间/ms
40 0.138 7 18.91
60 0.115 8 28.35
80 0.109 4 37.53
100 0.108 1 46.87
120 0.107 5 56.28
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不同规模孤立森林异常分数标准差与计算时间

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孤立树数量/棵 异常分数标准差 计算时间/ms
40 0.138 7 18.91
60 0.115 8 28.35
80 0.109 4 37.53
100 0.108 1 46.87
120 0.107 5 56.28
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频率/kHz 运行状态 不使用TEO 使用TEO
[20, 30] 正常 0.991 1.007
故障 2.153 4.532
[30, 40] 正常 1.036 1.004
故障 2.009 4.075
[40, 50] 正常 0.952 1.013
故障 2.194 4.101
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TEO处理前后Di

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频率/kHz 运行状态 不使用TEO 使用TEO
[20, 30] 正常 0.991 1.007
故障 2.153 4.532
[30, 40] 正常 1.036 1.004
故障 2.009 4.075
[40, 50] 正常 0.952 1.013
故障 2.194 4.101
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干扰 准确率/%
机械噪声 96
强风噪声 97
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干扰样本诊断准确率

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干扰 准确率/%
机械噪声 96
强风噪声 97
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算法 准确率/% 计算时间/ms
KNN 73.25 63.93
One-Class SVM 94.50 125.37
IF 97.25 71.32
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不同异常评价算法的检测结果

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算法 准确率/% 计算时间/ms
KNN 73.25 63.93
One-Class SVM 94.50 125.37
IF 97.25 71.32
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方法 准确率/% 计算时间/ms
文献[10]方法 65.32 13.79
文献[23]方法 98.75 154.58
本文方法 97.25 71.32
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不同方法的诊断结果

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方法 准确率/% 计算时间/ms
文献[10]方法 65.32 13.79
文献[23]方法 98.75 154.58
本文方法 97.25 71.32
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基于超声波传感器与孤立森林的光伏系统串联电弧故障诊断方法
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黄晨昊 , 高伟
电气技术 | 研究与开发 2025,26(5): 10-16
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电气技术 | 研究与开发 2025, 26(5): 10-16
基于超声波传感器与孤立森林的光伏系统串联电弧故障诊断方法
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黄晨昊, 高伟
作者信息
  • 福州大学电气工程与自动化学院, 福州 350108
  • 黄晨昊(2000—),男,福建省宁德市人,硕士研究生,主要从事光伏系统电弧故障检测与定位方面的研究工作。

Series arc fault diagnosis method for photovoltaic system based on ultrasonic sensor and isolation forest
Chenhao HUANG, Wei GAO
Affiliations
  • College of Electrical Engineering and Automation, Fuzhou University, Fuzhou 350108
出版时间: 2025-05-15
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针对大部分光伏电站电弧故障历史数据缺乏的问题,本文在采集电弧超声信号并分析其特点后,提出一种基于超声波传感器与孤立森林的光伏系统串联电弧故障诊断方法。首先,利用S变换将发生串联电弧故障时的超声波暂态电压信号转化至时频域;接着,利用Teager能量算子放大频谱差异性,并通过时频熵提取电弧故障时频域特征;最后,基于动态阈值与孤立森林实现电弧故障诊断且无需历史数据。实验结果表明,所提方法能准确识别串联电弧故障,诊断准确率达到97.25%,且具备较强的抗干扰能力。

光伏系统  /  电弧故障诊断  /  超声波信号  /  S变换  /  孤立森林

Aiming at the problem of the lack of historical data on arc faults in most photovoltaic power stations, this paper proposes a photovoltaic system series arc fault diagnosis method based on ultrasonic sensors and isolation forest after collecting arc ultrasonic signals and analyzing their characteristics. Firstly, arc ultrasonic signals are collected and their characteristics and advantages are analyzed. Secondly, the S-transform is used to convert the transient voltage signal of the ultrasonic wave during the occurrence of series arc faults to the time-frequency domain. Then, the Teager energy operator is used to amplify the spectral differences. Subsequently, the time-frequency entropy is used to extract the time-frequency domain features of arc faults. Finally, arc faults are diagnosed based on dynamic thresholds and isolation forest without the need for historical data. Experimental results show that the proposed method can accurately identify series arc faults, with a diagnosis accuracy rate of 97.25%, and has strong anti-interference ability.

photovoltaic system  /  arc fault diagnosis  /  ultrasonic signal  /  S-transform  /  isolation forest
黄晨昊, 高伟. 基于超声波传感器与孤立森林的光伏系统串联电弧故障诊断方法. 电气技术, 2025 , 26 (5) : 10 -16 .
Chenhao HUANG, Wei GAO. Series arc fault diagnosis method for photovoltaic system based on ultrasonic sensor and isolation forest[J]. Electrical Engineering, 2025 , 26 (5) : 10 -16 .
近年来,不可再生能源消耗巨大,太阳能作为一种可再生的清洁能源备受关注[1-3]。截至2024年底,全国光伏发电装机容量达8.87亿kW[4]。长时间运行的光伏发电系统可能存在导线绝缘受损、电缆接头松动等问题,易出现电弧故障,严重时甚至引发火灾[5-6]。串联电弧故障特征微弱,不易被常规保护识别[7]。因此,进行光伏发电系统串联电弧故障研究,提出一种快速、准确的诊断方法很有必要。
目前,国内外学者已提出多种光伏发电系统串联电弧故障诊断方法,根据特征量的不同可分为电信号诊断法与伴生物理量诊断法。电信号诊断法主要通过对电压、电流信号进行特征提取实现故障诊断。文献[8]采集线路电流与电源电压并计算其变化率与标准差,结合多个阈值实现电弧故障检测。文献[9]提出一种基于电容电流极性和振幅的新型电弧故障诊断方法,分析并确定了电容电流频谱的积分是区分直流串联电弧故障与其他系统变化的关键。文献[10]分析了电弧故障的时域与频域特性,选取电流最值差与连续谐波幅值作为特征量,利用固定阈值判断电弧故障;该方法简单、高效,但在面对环境变化与逆变器干扰时效果不佳。文献[11]提出一种轻量级卷积神经网络用于电弧故障检测,并验证了干扰条件下该方法的鲁棒性。电信号诊断法检测范围广,信号易于采集,但易受辐照度变化与逆变器启动的影响。
伴生物理量诊断法以电弧故障伴生的光、声与电磁辐射等作为特征量。文献[12]研究光伏直流电弧电磁辐射信号特征及测量方法,为基于电磁辐射的诊断方法奠定了基础。文献[13]利用四阶Hilbert天线检测直流电弧故障的电磁辐射信号,并分析了多种因素对电磁辐射特性的影响。文献[14-15]将超声信号作为检测电弧故障的特征量。超声信号具有抗干扰性强、对采样设备要求低的特点,因此本文选取超声信号作为电弧故障的特征量,以此进行诊断方法的研究。超声信号在空气中传播存在衰减现象,当故障距离传感器较远时信号较弱,诊断方法可能表现不佳。另外,电弧故障是光伏发电系统发生的小概率事件,难以获取足够的历史数据,限制了目前很多诊断算法的应用。
针对上述问题,本文提出一种基于超声特征与孤立森林(isolation forest, IF)的串联电弧故障诊断算法,摆脱历史数据对算法应用的限制。首先,介绍实验平台,分析超声信号的特点。其次,利用S变换与Teager能量算子(Teager energy operator, TEO)揭示与放大电弧超声信号的时频特性,解决信号特征弱的问题,并通过时频熵提取电弧故障特征。随后,结合IF与动态阈值实现无需历史数据的电弧故障诊断。最后,利用实验数据分析所提方法的有效性和抗干扰能力。
在光伏发电并网系统中进行电弧实验,其主要由光伏阵列、直流汇流箱、逆变器与保护装置构成,结构如图1所示。图1中的光伏阵列由12个光伏组件串联,2个光伏串并联组成,并通过汇流箱与逆变器并网。光伏组件与逆变器参数分别见表1表2。其中,Pmpp为光伏组件最大工作功率,Vmpp为光伏组件最大工作电压,Impp为光伏组件最大工作电流,VocIsc分别为光伏组件的开路电压与短路电流。
分别在串首、串中与串尾3种位置进行串联电弧故障实验,即图1中的①~③处,并采集超声波电压信号。串联电弧故障由电弧故障发生器来模拟,其主要由移动铜电极、固定铜电极、步进电机与底座组成。文献[16]指出,电弧超声波信号频带能量集中在20~70kHz,高频超声波在空气中衰减严重,因此选用中心频率为40kHz的超声波传感器采集环境中的超声波信号,并利用示波器采集转化后的电压数据。
为保证样本的多样性,充分验证所提方法的性能,电弧故障实验在辐照度范围为300~800W/m2条件下进行。将电弧故障发生器分别安装于距超声波传感器0~4m处进行电弧故障实验。数据样本类型及数量见表3,其中200组正常样本,200组电弧故障样本,100组机械噪声样本,100组强风噪声样本。
光伏系统发生直流电弧故障时,电弧电流信号与超声波电压信号波形如图2所示。当电弧故障刚发生时,电流波动明显;当电弧稳定燃烧时,电流较为平稳;当电弧熄灭时,电流迅速下降。超声波电压信号波形的变化相对较少:当电弧故障发生时,电弧向环境辐射超声波信号,超声波电压信号幅值迅速增大;当电弧消失时,超声波电压信号幅值迅速降低到正常水平。电弧燃弧阶段的超声波电压信号幅值略大于稳定燃烧阶段。综合检测速度与信号强弱情况,选取超声波暂态信号用于电弧故障的诊断。
光伏系统的两种常见干扰,即逆变器启动与辐照度变化下的电流信号与超声波电压信号波形分别如图3图4所示。从图3图4可以看出,在这两种干扰下,电流信号均发生一定的变化,从而影响诊断算法的性能;而超声波信号均保持稳定,不受其影响。因此,相较于电流信号,将超声波信号作为诊断算法特征量存在明显优势。文献[17]论证了电弧参数仅影响超声波的幅值而不影响超声波的频率特性,因此本文利用超声波信号的时频域特征进行故障诊断。
利用S变换将时序信号转化至时频域,构造时频域矩阵并挖掘电弧故障超声信号的时频域特征;然后通过TEO对时频域矩阵进行差分处理,从而放大电弧故障特征;最后利用时频熵进行时频特征提取。该方法能有效提取超声波信号的多维时频特征,相较单一时域特征,具有更强的鲁棒性。
1)S变换
针对短时傅里叶变换中窗函数固定的缺陷,S变换使用随频率变化的窗函数,能够有效平衡时域分辨率与频域分辨率;与连续小波变换相比,S变换省去了小波函数选取这一复杂步骤。对于超声波电压信号x(t),其S变换定义[18]
$S(\tau,f)=\left|{\displaystyle {\int }_{\text{ }-\infty }^{\text{ }\infty }x(t)}\text{ }w(\tau -t,f){\text{e}}^{-\text{i}2\text{π}ft}\text{d}t\right|$
$w(\tau -t,f)=\frac{f}{\sqrt{2\text{π}}}{\text{e}}^{\frac{-{(\tau -t)}^{2}{f}^{2}}{2}}$
式中:f为频率;$\varphi $为调节高斯窗时域位置的参数;$w(\tau -t,f)$为高斯窗函数。根据卷积定理,可将S变换表示为超声波电压信号x(t)的傅里叶变换$F\text{( }f\text{)}$的函数,即
$S(\tau,f)=\left|{\displaystyle {\int }_{\text{ }-\infty }^{\text{ }\infty }F(\alpha +f)\text{ }}{\text{e}}^{-\frac{2{\text{π}}^{2}{\alpha }^{2}}{{f}^{2}}}{\text{e}}^{\text{i}2\text{π}\alpha \tau }\text{d}\alpha \right|$
式中,$\alpha $为积分变量。
这样可以通过傅里叶变换实现S变换的快速计算。
2)Teager能量算子
TEO具有计算简单、运算量小的特点[19],能够有效放大信号的幅值波动。对于时频模矩阵,其处理过程为
$\psi \left[S(\tau,f)\right]={S}^{2}(\tau,f)-S(\tau -1,f)S(\tau +1,f)$
式中,$\psi \left[S(\tau,f)\right]$为TEO处理后的信号。采用TEO对时频模矩阵进行差分处理,以增强电弧故障发生前后的差异性。处理后的时频模矩阵如图5所示。观察处理后的矩阵,电弧故障特征主要集中在20~50kHz。
3)时频熵
信息熵是一种用于衡量信号包含信息量的指标[20]。当电弧故障发生时,时频模矩阵包含的信息会明显增加,因此可以通过计算时频矩阵的信息熵进行特征提取。这里将提取到的信息熵称为时频熵,具体计算步骤为,将时频模矩阵进行时频分割,得到m×n个大小相等的子矩阵,随后按照式(5)、式(6)计算各子矩阵的时频熵。
$H(j,k)=-{\displaystyle \sum _{i=1}^{N}p\left({x}_{i}\right)}\mathrm{lg}p\left({x}_{i}\right)$
$p\left({x}_{i}\right)=\frac{{x}_{i}}{{\displaystyle \sum _{i=1}^{N}{x}_{i}}}$
式中:$H(j,k)$为时频熵;${x}_{i}$为子矩阵元素;$p\left({x}_{i}\right)$为子矩阵每个元素的概率;N为子矩阵元素个数。
基于机器学习的诊断算法可以捕捉复杂的模式和非线性关系,从而提供更高的诊断精度,但其对历史数据的高依赖性限制了此类方法的应用。因此,本文利用时域切割生成小样本,结合IF算法与自适应阈值,实现无历史数据下的高准确率电弧故障诊断。
1)孤立森林
IF算法通过随机切分数据找到多个样本中的异常样本,即孤立点,实现异常检测。IF算法无需计算距离或密度等指标,具有计算量小、检测速度快的特点[21]。检测步骤为:首先,从样本集中抽取样本与特征,依照随机分割算法构建多个孤立树,形成孤立森林;其次,利用孤立树进行样本分割并通过式(7)~式(9)计算样本在每棵孤立树上的路径长度;最后,利用数据在孤立森林中的平均路径长度,按照式(10)计算其异常评分,从而区分样本。
$H(a)=\mathrm{ln}a+\gamma $
$c(a)=\left\{\begin{array}{ll}2H(a-1)-2\frac{a-1}{a}\hfill & a\text{ }\text{ }>\text{ }\text{ }2\hfill \\ 1\hfill & a=2\hfill \\ 0\hfill & a\text{ }\text{ }<\text{ }\text{ }2\hfill \end{array}\right.$
$h(x)=\text{e}+c(a)$
式中:a为孤立树数量;H(a)为谐波调和级数;$\gamma $为欧拉常数,$\gamma $=0.577 215 664 9;c(a)为标准化因子;h(x)为数据x在孤立树中的路径长度。
$s(x,a)={2}^{-\text{ }\frac{E(h(x))}{c(a)}}$
式中:s(x,a)为数据x的异常评分;E(h(x))为数据x在孤立森林中的平均路径长度。
2)动态阈值
基于采样信号特点,本文提出一种动态阈值计算方法。分析采集的暂态信号特点,将暂态信号分为前半部分(正常信号)与后半部分(异常信号)。电弧故障会导致异常点显著增加,因此可以通过记录异常信号的异常点数判定是否发生电弧故障。基于正常信号的异常点数生成动态阈值$\varphi $作为故障与否的分界线,阈值计算公式为
$\varphi =dy+b$
式中:d为检测系数;y为前半部分样本异常点个数,b为基本偏差。
采用累计投票机制,即按照时间次序依次对样本进行异常评估,并记录异常点的数量,以此替代对所有样本统一评级后再计数的传统方法。通过这种累计投票机制,可以有效减少需要评估的样本数量,降低计算量,从而加快故障检测的速度。
本文所提电弧故障诊断方法包括特征提取和故障诊断两部分,故障诊断流程如图6所示。
1)采集电弧故障暂态超声波电压数据,将信号经S变换转化为二维时频模矩阵,利用TEO进行差分处理以凸显故障特征。
2)通过计算时频熵进行特征提取。
3)将时频熵矩阵划分成由多个时间向量组成的集合A={X1, X2,…, Xn},时间向量Xk=(H(1,k), H(2,k),…, H(m,k)),k =1, 2,…, n
4)利用集合A实时训练IF模型,并构建动态阈值$\varphi $
5)对集合A的每个时间向量进行异常评价并累计异常点数。当异常点数超出阈值时,判定为电弧故障,反之则判定为正常。
本文选用的超声波传感器中心频率为40kHz,依据香农-奈奎斯特定理,采用100kHz的采样率对电压信号进行分析。文献[22]指出,时间窗包含故障前后各500个点较为合适,因此本文以10ms作为诊断算法的时间窗。文献[21]指出,生成更多的孤立树能够减小异常分数的偏差,但也增加了算法的计算量,因此通过增加孤立树的方式确定孤立森林的规模。不同规模孤立森林的异常分数标准差与计算时间见表4。从表4可以看出,计算时间与孤立树数量近似成正比,当孤立树数量为80棵时,异常分数标准差已趋于稳定。因此,选择生成80棵孤立树组成孤立森林。
图7展示了超声波电压信号经特征提取算法转换为时频熵矩阵的过程。当电弧故障发生时,故障电弧向环境辐射超声波,引起超声波发生暂态变化,如图7(a)所示;但时域信号的抗干扰性较弱,因此利用S变换将其转化至时频域内,得到图7(b)所示波形;随后利用TEO揭示并增强时频域特征,如图7(c)所示;最终对时频模矩阵提取时频熵特征,得到图7(d)
对比图7(b)图7(c)可以看出,故障发生后多个频段的幅值有所增加,故障前后存在一定的差异性。经TEO处理后,故障前频域幅值变化幅度降低,而故障后频域幅值变化幅度增大,故障前后差异性明显增强。
为验证TEO的有效性,通过式(12)计算故障发生前后离散性变化,来评价TEO性能。
${D}_{i}=\frac{{\sigma }_{1}}{{\sigma }_{2}}$
式中:${\sigma }_{1}$${\sigma }_{2}$为故障后和故障前第i频段幅值的标准差;Di为故障前后第i频段离散性的变化程度。Di越大表明故障前后的离散性差异越明显,更易识别故障。TEO处理前后的Di值见表5
对比表5中正常运行与故障状态的Di值可以看出,在正常运行时,各频段离散性未发生明显改变,电弧故障发生后,各频段幅值分布出现了明显离散。对比TEO处理前后的Di值可以看出,TEO处理不会明显改变正常状态下的离散性,且能显著放大电弧故障引起的频段离散性差异。在各特征频段,TEO处理后的Di值提升为处理之前Di值的约2倍,使故障特征更加明显。这种放大效应有助于后续诊断中异常值的识别,从而进一步提高诊断性能。
利用数据集对所提算法的有效性、准确性进行检验,得到如图8所示的混淆矩阵。可以发现,诊断模型具有97.25%的整体准确率,存在5个漏检与6个误判。对漏检样本进行分析,由于超声波信号在空气中传播会出现衰减,当电弧发生点超出传感器的有效探测范围时,采集到的信号较弱。尽管TEO将特征进行了放大,但仍有少部分故障特征较正常情况差距不大,从而导致漏检。误判主要由正常样本的特征变化较小、异常分数差异不大引起。此外,由于实时训练模型的样本量有限,特征学习不充分也是误判原因之一。
在实际运行的光伏发电系统中,电弧故障诊断方法的准确率会受到各种环境因素的干扰。光伏发电系统在辐照度突变与最大功率点跟踪(maximum power point tracking, MPPT)启动情况下,并不会向周围辐射超声波,不会引起算法误判。因此,本文主要分析光伏发电系统中较为常见的环境噪声:电动机带来的机械噪声与工业风机模拟强风噪声。干扰样本诊断准确率见表6。根据表6,所提方法面对机械噪声与强风噪声时的准确率与正常情况一致,说明算法能够有效抵御环境噪声的干扰,验证了其良好的抗干扰能力。
为了验证IF在异常检测方面的优异特性,选取无监督学习中常用的K最近邻(K-nearest neighbor, KNN)算法与单类支持向量机(one-class support vector machine, One-Class SVM)算法替代IF进行异常评价,不同异常评价算法的检测结果见表7
表7可以看出,KNN算法通过计算距离来评判异常点,计算速度最快,但其忽略了各个特征的差异性,导致诊断准确率较低;One-Class SVM较好地学习到了样本多特征的差异,检测准确率较高,但其计算量相对较大,检测速度慢;本文使用的IF具有最高的准确率,与KNN相比,检测速度稍慢但检测准确率明显提高。
为验证所提方法的有效性与优越性,将所提方法与文献[10]、文献[23]中的方法进行对比。文献[10]通过提取电弧故障时电流信号的时域与频域特征结合固定阈值完成故障诊断,文献[23]采用互补集合经验模态分解算法对信号进行分解,挑选有效模态进行信号重构并提取特征量,结合K均值聚类实现故障诊断。在相同的实验条件下进行对比,不同方法的诊断结果见表8
表8可以看出,文献[10]方法通过简单的特征提取结合固定阈值的方式能够实现快速电弧故障诊断,但诊断准确率相对较低;文献[23]方法具有最高的准确率,但其使用的互补集合经验模态分解算法的计算量相对较大,使计算时间相对较长,同时K均值聚类需要一定量的历史数据进行训练来保证模型的准确率,这在一定程度上限制了该方法的应用;本文所提方法的准确率与文献[23]方法相差不大,但所需计算时间更短且无需历史数据。综合来看,本文所提方法具有较大优势。
针对传统光伏阵列串联电弧故障诊断方法存在的缺陷,本文提出了一种基于超声特征与IF的串联电弧故障诊断方法。分析了超声波信号的特点与优势,利用S变换和TEO揭示并放大了电弧时频域特征,并通过时频熵提取特征。利用时域分割结合IF与动态阈值,实现了历史数据缺乏情况下的高准确率电弧故障诊断。经实验验证,所提方法不仅能在无历史数据的条件下以97.25%的准确率诊断出电弧故障,而且诊断准确率不受光伏发电系统中常见的机械噪声与强风噪声影响,与其他方法相比具有较大优势。
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  • 接收时间:2025-01-09
  • 首发时间:2025-11-05
  • 出版时间:2025-05-15
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  • 收稿日期:2025-01-09
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    福州大学电气工程与自动化学院, 福州 350108
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