Application of Signal Denoising Technology Based on Improved Spectral Subtraction in Arc Fault Detection

: In the research of fault arc detection technology, proper signal denoising can greatly improve the recognition ability of the arc fault detection algorithm. Therefore, this study proposes a current signal enhancement algorithm based on improved spectral subtraction from the statistical law of electrical noise in a low-voltage distribution system and the principle of the arc fault detection algorithm. According to the results of the arc fault detection algorithm, the algorithm selects an appropriate reference current as the basis for noise estimation and further assumes that the types and quantities of power loads are relatively ﬁxed and the current noise is relatively stable in a certain power consumption period in the same power consumption place, so as to obtain the current noise in the current power consumption environment, and then uses improved spectral subtraction to realize the real-time noise reduction of current signals required by the arc fault detection algorithm. The experimental results show that this method and the arc fault detection algorithm complement each other, and the processing of current signal is more targeted, which can make the selected arc fault characteristics more different between the normal state and fault state, eliminate the interference of high-frequency clutter in current signal on arc fault characteristics and greatly improve the sensitivity of the original detection algorithm on the premise of unchanged detection reliability.


Introduction
When the power supply and distribution system has hidden dangers such as poor contact at the joint, damage or aging of the insulation layer caused by external factors, an arc fault will be caused under the action of voltage and current [1].Generally, a current of only 0.5 A can cause the arc temperature to reach 2000 degrees or even higher [2], while maintaining stable arc combustion only requires a voltage of 20 V [3].As shown in Figure 1, once the arc fault is ignited, it becomes the ignition source of electrical fire because it is difficult to extinguish.
For many years, because of the fire hazard of arc faults and their characteristics that are difficult to identify, arc fault detection has become an important topic of industrial and scientific research [4][5][6][7].However, as of now, there is still no truly mature arc detection product that can quickly and accurately identify series fault arcs in the line before a fire occurs.There are two main reasons for this situation: on the one hand, the working current of some electrical appliances is very similar to the arc current [8], and the arc fault feature is easily concealed or weakened by the current of electrical appliances, while the arc fault feature used by the existing detection algorithm is very small in the normal state and fault state; on the other hand, due to the existence of various electromagnetic interference in the electrical environment and the imperfect electromagnetic compatibility treatment of some electrical appliances, there is a lot of noise in the fault current monitoring [9][10][11], which is easy to cause serious interference to the characteristics of arc faults in the actual test process.
Electronics 2023, 12, x FOR PEER REVIEW 2 of 12 monitoring [9][10][11], which is easy to cause serious interference to the characteristics of arc faults in the actual test process.In order to reduce the interference of noise in the power network on the dynamic characteristic analysis of arc faults, an effective means is to denoise the current signal [12][13][14].For this, Luan et al. used the wavelet packet threshold denoising method to preprocess the current measurement [1]; Zhang et al. subtracted the adjacent periodic waveforms of line current, used wavelet threshold to denoise and normalize the current signal, and then took the amplitude difference of the periodic waveform as the arc fault feature [15]; Ahmadi et al. believed that the circuit noise was mainly concentrated within 1 kHz, so in the process of sampling the line current, the high pass filter was directly used to filter out the current noise unrelated to arc faults [16]; Gao et al. used wavelet threshold denoising, piecewise linear fitting and first-order difference processing to eliminate interference noise and highlight arc fault characteristics [17]; for the serious interference of power supply harmonics and load noise, Han et al. proposed a recognition method based on Kernel Principal Component Analysis (KPCA) and Firefly Algorithm Optimized Support Vector Machine (FA-SVM) [18]; Zhang et al. proposed an adaptive arc fault diagnosis model with data enhancement function [19].In addition, the signal processing method based on artificial intelligence has become a trend [14,20].However, the above methods have played a very positive role in the application of the arc fault detection algorithm, but they are basically used as the preprocessing of signals to be detected and have little relevance with the subsequent development of the arc fault detection algorithm.In other words, these noise reduction algorithms have their own independence and are not completely proposed for the subsequent arc fault detection algorithm.As a result, the signal denoising method used in the current arc fault diagnosis field does not match the subsequent arc fault detection algorithm very well, so the ultimate improvement of arc fault detection performance does not play a maximum role.
Therefore, in order to better improve the performance of the arc fault detection algorithm, according to the statistical law of electrical noise in low-voltage distribution system and the principle of the arc fault detection algorithm, a current signal denoising algorithm specifically for arc fault diagnosis technology is designed.Referring to the results of the arc fault detection algorithm, the algorithm selectively screens out the normal current signal without arc fault information, and then filters out the low-frequency part so as to obtain the high-frequency noise of the current and complete the spectrum estimation of the current noise.Furthermore, the improved spectral subtraction method is used to denoise the newly acquired current signal so that the current signal denoising algorithm and the arc fault detection algorithm complement each other to maximize the application effect.
The remainder of this work is organized as follows.The second section discusses the general laws of current noise in low-voltage power consumption networks.In the third section, by analyzing the general laws of current noise in a low-voltage power grid and the principle of the arc fault detection algorithm, the idea and algorithm of current signal In order to reduce the interference of noise in the power network on the dynamic characteristic analysis of arc faults, an effective means is to denoise the current signal [12][13][14].For this, Luan et al. used the wavelet packet threshold denoising method to preprocess the current measurement [1]; Zhang et al. subtracted the adjacent periodic waveforms of line current, used wavelet threshold to denoise and normalize the current signal, and then took the amplitude difference of the periodic waveform as the arc fault feature [15]; Ahmadi et al. believed that the circuit noise was mainly concentrated within 1 kHz, so in the process of sampling the line current, the high pass filter was directly used to filter out the current noise unrelated to arc faults [16]; Gao et al. used wavelet threshold denoising, piecewise linear fitting and first-order difference processing to eliminate interference noise and highlight arc fault characteristics [17]; for the serious interference of power supply harmonics and load noise, Han et al. proposed a recognition method based on Kernel Principal Component Analysis (KPCA) and Firefly Algorithm Optimized Support Vector Machine (FA-SVM) [18]; Zhang et al. proposed an adaptive arc fault diagnosis model with data enhancement function [19].In addition, the signal processing method based on artificial intelligence has become a trend [14,20].However, the above methods have played a very positive role in the application of the arc fault detection algorithm, but they are basically used as the preprocessing of signals to be detected and have little relevance with the subsequent development of the arc fault detection algorithm.In other words, these noise reduction algorithms have their own independence and are not completely proposed for the subsequent arc fault detection algorithm.As a result, the signal denoising method used in the current arc fault diagnosis field does not match the subsequent arc fault detection algorithm very well, so the ultimate improvement of arc fault detection performance does not play a maximum role.
Therefore, in order to better improve the performance of the arc fault detection algorithm, according to the statistical law of electrical noise in low-voltage distribution system and the principle of the arc fault detection algorithm, a current signal denoising algorithm specifically for arc fault diagnosis technology is designed.Referring to the results of the arc fault detection algorithm, the algorithm selectively screens out the normal current signal without arc fault information, and then filters out the low-frequency part so as to obtain the high-frequency noise of the current and complete the spectrum estimation of the current noise.Furthermore, the improved spectral subtraction method is used to denoise the newly acquired current signal so that the current signal denoising algorithm and the arc fault detection algorithm complement each other to maximize the application effect.
The remainder of this work is organized as follows.The second section discusses the general laws of current noise in low-voltage power consumption networks.In the third section, by analyzing the general laws of current noise in a low-voltage power grid and the principle of the arc fault detection algorithm, the idea and algorithm of current signal denoising based on the improved spectral subtraction method are given.Section 4 gives the experimental verification and discussion of the proposed current signal denoising method.Conclusions of this work are given in Section 5.

Noise Analysis of Power Lines
In general, the current noise on power lines can be divided into man-made noise and non-man-made noise according to the differences of its causes [21].Among them, non-human noise refers to electromagnetic interference caused by unavoidable natural phenomena such as lightning strike; man-made noise is caused by various electrical equipment in the power system itself and the power network, mainly including a small amount of harmonics caused by the non-strict symmetry of the three-phase winding generator, the non-strict uniformity of the steel core and other uncertain factors, the harmonics generated by the transformer in the magnetic saturation state of the steel core, the frequency doubling and monopulse harmonics generated by nonlinear electrical equipment such as televisions, air conditioners, etc.The above noises can usually be divided into five categories, namely: colored background noise, narrow-band noise, periodic impulse noise asynchronous to power frequency, periodic impulse noise synchronous to power frequency and random impulse noise.
Generally speaking, colored background noise is mainly generated by household appliances and can cause interference within the maximum frequency range of 30 MHz, but its power spectral density will decrease with the increase of frequency.This kind of noise changes slowly at any time, which can basically be regarded as a stationary random process.Its power spectral density usually takes several minutes or even hours to change, so it can be modeled by autoregressive model.Narrow-band noise is mostly sinusoidal signal with frequency concentrated in a narrow range, which is mainly caused by crosstalk in the propagation of short-wave radio broadcasting.Its amplitude changes slowly, usually in days.Periodic pulse noise that is not synchronized with the power frequency generally refers to a type of noise in which the power spectrum of some high-power electrical appliances is offline during switching.These three types of noise change relatively slowly and can be classified as background noise.Periodic pulse noise synchronized with power frequency refers to the pulses generated by certain electrical equipment when operating at a frequency of 50 Hz.The frequency of this type of noise is generally an integer multiple of 50 Hz or 100 Hz.It is characterized by high noise power, wide frequency coverage and short duration, and its power spectral density will decrease with the increase of frequency.Random impulse noise refers to the pulse signal generated by the instantaneous switching action of some electrical equipment in the power network.This type of noise generally lasts for a very short time, basically on the order of milliseconds or even shorter.Compared with background noise, periodic pulses and random pulses synchronized with power frequency have great time variability and can be classified as impulse noise.Impulse noise is usually sudden, with higher power spectral density than background noise, and its duration is uncertain.
For a low-voltage power consumption network, it is often difficult to directly define its noise, but through the analysis of a large amount of noise data, some rules are also summarized.The noise in a low-voltage power network often has the characteristics of periodicity, continuity, randomness and variability.However, for a specific power consumption place, in a certain power consumption period, the types and quantities of power loads are relatively stable, and their power sources are also relatively fixed.Based on the comprehensive analysis of the above noise characteristics, it is completely reasonable to assume that the noise is stable in a certain power consumption period where the same electric field is located.Under this assumption, the frequency spectrum of a noise signal and its time domain signal can be obtained by direct acquisition and frequency spectrum analysis of the current signal in the power cable (filtering out normal working current).As shown in Figure 2, the current high-frequency noise signal obtained by filtering two current signals collected within 15 min before and after an office scene is displayed.It is not difficult to find that in this office scene, the current high-frequency noise at two adjacent moments is very similar and consistent, which shows that it is reasonable and feasible to assume that the noise is stable in a certain power consumption period in which the same electric field is located.
not difficult to find that in this office scene, the current high-frequency noise at two a cent moments is very similar and consistent, which shows that it is reasonable and feas to assume that the noise is stable in a certain power consumption period in which same electric field is located.On the premise that the noise signal itself or its spectrum can be obtained, the curr signal can be denoised by wavelet threshold denoising, filtering and spectral subtract The spectral subtraction method is not only ideal in dealing with broadband super posed noise but also simple in implementation and stable in effect.Therefore, this sche will realize the noise reduction of the measured current signal based on spectral subt tion to improve the performance of the fault arc detection algorithm.

Noise Reduction Method of Current Based on Spectral Subtraction
Spectral subtraction is a noise reduction algorithm that originated from the field speech recognition [22,23], which contains the most intuitive idea of noise reduction: spectrum of noisy speech signal MINUS the spectrum of noise signal is the spectrum clean signal.The premise of its realization is to assume that the noise signal is locally sta additive noise independent of pure speech signals.Classical spectral subtraction subtra the power spectrum of the estimated noise from the power spectrum of the speech sig and sets the negative value generated in this process to zero to obtain a new power sp trum.Finally, the new power spectrum is recombined with the phase of the original sig to reconstruct the time waveform and complete the denoising of the speech signal.T method is simple and easy to implement, but in the process of noise reduction by spec subtraction, the noise may be overestimated, resulting in a negative difference in the p cess of subtracting the estimated noise power spectrum from the power spectrum of no speech signal.Although setting a negative value to zero is simple and straightforward, result is a single and small peak in the reconstructed signal's spectrum, which is tra formed into the time domain and referred to as "music noise" [24].
In order to solve the problem of "music noise" caused by classical spectral subt tion, some scholars put forward an improved spectral subtraction [23], and its spec principle and formula are as follows:  On the premise that the noise signal itself or its spectrum can be obtained, the current signal can be denoised by wavelet threshold denoising, filtering and spectral subtraction.The spectral subtraction method is not only ideal in dealing with broadband superimposed noise but also simple in implementation and stable in effect.Therefore, this scheme will realize the noise reduction of the measured current signal based on spectral subtraction to improve the performance of the fault arc detection algorithm.

Noise Reduction Method of Current Based on Spectral Subtraction
Spectral subtraction is a noise reduction algorithm that originated from the field of speech recognition [22,23], which contains the most intuitive idea of noise reduction: the spectrum of noisy speech signal MINUS the spectrum of noise signal is the spectrum of clean signal.The premise of its realization is to assume that the noise signal is locally stable additive noise independent of pure speech signals.Classical spectral subtraction subtracts the power spectrum of the estimated noise from the power spectrum of the speech signal and sets the negative value generated in this process to zero to obtain a new power spectrum.Finally, the new power spectrum is recombined with the phase of the original signal to reconstruct the time waveform and complete the denoising of the speech signal.This method is simple and easy to implement, but in the process of noise reduction by spectral subtraction, the noise may be overestimated, resulting in a negative difference in the process of subtracting the estimated noise power spectrum from the power spectrum of noisy speech signal.Although setting a negative value to zero is simple and straightforward, the result is a single and small peak in the reconstructed signal's spectrum, which is transformed into the time domain and referred to as "music noise" [24].
In order to solve the problem of "music noise" caused by classical spectral subtraction, some scholars put forward an improved spectral subtraction [23], and its specific principle and formula are as follows: Here, the premise of Equation ( 1) is that |Y i (ω)| 2 − α|D i (ω)| 2 > 0, otherwise |S i (ω)| 2 will satisfy Equation (2).In Formula (2), α is called the over-reduction factor, and its value range is α ≥ 1. Increasing the value of α can subtract more noise components from the power spectrum of noisy speech.The reduction of noise components can improve the signal-to-noise ratio of the output signal, make the amplitude of residual noise smaller, and have a good suppression effect on "music noise".In Equation (2), β is the lower spectral limit coefficient, and its value range is 0 ≤ β ≤ 1, which can keep a few but necessary additive noise components in the spectrum of the denoised signal, and its purpose is to artificially fill a small part of background noise in the denoised "pure" speech signal in order to reduce the signal burr phenomenon.The effect is to weaken the residual "music noise" through the masking characteristics of human hearing; secondly, residual "music noise" can have a soothing effect on hearing, reduce the perception of "music noise" by the human ear and, to some extent, increase the acceptability of speech signals.
The key to the realization of current signal denoising technology based on spectral subtraction is to reasonably estimate the noise and its spectrum.In the field of arc fault detection, it is no longer feasible to obtain noise signals by directly filtering the lowfrequency components of current because the characteristic frequency band caused by arc faults is highly coincident with the noise frequency band.Therefore, ways to reasonably evaluate the power consumption noise under the condition of uncertain arc faults in the environment has become the key to improving the accuracy of real-time detection of arc faults in power lines.This requires a targeted study of the disturbance law of an arc fault to the current signal.With this problem, we study the line current and its wavelet coefficient under the same resistive load and different arc burning.Comparing Figures 3 and 4 carefully, it is not difficult to find that the current distortion caused by an arc fault is easily drowned out by background noise for a relatively weak arc, but with the enhancement of the arc combustion degree, the current distortion caused by an arc fault is less and less disturbed by background noise, and its characteristics become more and more obvious.
Electronics 2023, 12, x FOR PEER REVIEW 5 Here, the premise of Equation ( 1) is that |  ()| 2 − |  ()| 2 > 0, otherwise |  ( will satisfy Equation (2).In formula (2),  is called the over-reduction factor, and its v range is  ≥ 1. Increasing the value of  can subtract more noise components from power spectrum of noisy speech.The reduction of noise components can improve the nal-to-noise ratio of the output signal, make the amplitude of residual noise smaller, have a good suppression effect on "music noise".In Equation ( 2),  is the lower spe limit coefficient, and its value range is 0 ≤  ≤ 1, which can keep a few but neces additive noise components in the spectrum of the denoised signal, and its purpose artificially fill a small part of background noise in the denoised "pure" speech sign order to reduce the signal burr phenomenon.The effect is to weaken the residual "m noise" through the masking characteristics of human hearing; secondly, residual "m noise" can have a soothing effect on hearing, reduce the perception of "music noise the human ear and, to some extent, increase the acceptability of speech signals.
The key to the realization of current signal denoising technology based on spe subtraction is to reasonably estimate the noise and its spectrum.In the field of arc detection, it is no longer feasible to obtain noise signals by directly filtering the low quency components of current because the characteristic frequency band caused by faults is highly coincident with the noise frequency band.Therefore, ways to reason evaluate the power consumption noise under the condition of uncertain arc faults in environment has become the key to improving the accuracy of real-time detection o faults in power lines.This requires a targeted study of the disturbance law of an arc to the current signal.With this problem, we study the line current and its wavelet co cient under the same resistive load and different arc burning.Comparing Figures 3 a carefully, it is not difficult to find that the current distortion caused by an arc fault is e drowned out by background noise for a relatively weak arc, but with the enhanceme the arc combustion degree, the current distortion caused by an arc fault is less and disturbed by background noise, and its characteristics become more and more obvio   of wa detail coefficient of each layer of current signal; and (4) judging whether an arc fault o in the line according to the threshold conditions of each characteristic quantity.Com hensive analysis of the characteristics of the multi-load circuit series fault arc dete method and spectral subtraction shows that: (1) low-frequency noise will not affec results of the fault arc detection algorithm; (2) the background noise easily affects the sitivity of the fault arc detection algorithm, but when the arc fault is obvious, the fau detection algorithm can identify it; (3) if there is no fault arc in the line, the backgr noise in the higher frequency band can be obtained by filtering the low frequency co nents in the current signal.Therefore, the current without fault arc information can be identified by the m load circuit series fault arc detection system identification, and then the normal wo signal can be filtered out to form the reference background noise.Further, the refe noise can just be used as the estimation noise of the current signal denoising system b on spectral subtraction (as shown in Figure 5).On the one hand, taking the current s without fault arc detection for three seconds as the reference current can greatly re the risk of misjudging the fault current as normal current, and even if the fault curre The realization process of the multi-load circuit series fault arc detection method designed in our laboratory is as follows: (1) collecting line current signal x(t) on the main road in real time through high-precision current transformer; (2) carrying out four-layer wavelet transform on the current signal x(t) by using the db4 wavelet base to obtain the wavelet detail coefficient F i,j of each layer of x(t); (3) calculating kurtosis j=1 |Fi,j| and peak factor of wavelet detail coefficient of each layer of current signal; and (4) judging whether an arc fault occurs in the line according to the threshold conditions of each characteristic quantity.Comprehensive analysis of the characteristics of the multi-load circuit series fault arc detection method and spectral subtraction shows that: (1) low-frequency noise will not affect the results of the fault arc detection algorithm; (2) the background noise easily affects the sensitivity of the fault arc detection algorithm, but when the arc fault is obvious, the fault arc detection algorithm can identify it; (3) if there is no fault arc in the line, the background noise in the higher frequency band can be obtained by filtering the low frequency components in the current signal.Therefore, the current without fault arc information can be identified by the multi-load circuit series fault arc detection system identification, and then the normal working signal can be filtered out to form the reference background noise.Further, the reference noise can just be used as the estimation noise of the current signal denoising system based on spectral subtraction (as shown in Figure 5).On the one hand, taking the current signal without fault arc detection for three seconds as the reference current can greatly reduce the risk of misjudging the fault current as normal current, and even if the fault current in a second is misjudged as normal current, it can be averaged by the reference current power spectrum.On the other hand, the scheme combines the current signal denoising algorithm with the arc fault detection algorithm, which can update the background noise in real time and make the noise estimation of the power network more accurate by the current signal denoising system based on spectral subtraction.Specifically, noise signals in power lines can be obtained by the following steps: a second is misjudged as normal current, it can be averaged by the reference current power spectrum.On the other hand, the scheme combines the current signal denoising algorithm with the arc fault detection algorithm, which can update the background noise in real time and make the noise estimation of the power network more accurate by the current signal denoising system based on spectral subtraction.Specifically, noise signals in power lines can be obtained by the following steps: Step 1: using high-precision current transformer coils to collect current signals from the user's distribution line at a sampling frequency of 409.6 kHz, with a current collection time of 1 s each time, forming a sampling current (); Step 2: transmitting the sampling current () to a multi-load loop series fault arc detection system to judge whether a series fault arc occurs in the line; Step 3: if the judgment result is that the line is in a fault state, an alarm message is sent externally; if it is judged that the line is in a normal state, repeat steps 1 and 2; Step 4: if the multi-load loop series fault arc detection system determines the current signals collected for 3 s as normal current, set the current signals collected in the last 1 s as reference signals  1 (),  2 () and  3 (); Step 5: Fourier transform  1 () ,  2 () and  3 () , respectively, to generate frequency domain signals  1 () ,  2 () and  3 () .Considering that noise with lower frequency will not interfere with the results of the fault arc detection algorithm, a high-pass filter is designed to filter out the signal components with frequencies less than 1 kHz in  1 ′ () ,  2 ′ () and  3 ′ () . 1 ′ () ,  2 ′ () and  3 ′ () are generated, and the noise signals  1 () ,  2 () and  3 () in the higher frequency band are generated by inverse Fourier transform.
In this case, the noise power spectrum can be estimated by calculating the average of the power spectra of  1 (),  2 () and  3 ().Next, only by setting reasonable parameters  and  , the current signal can be denoised by spectral subtraction.Finally, in this scheme, we set the over-reduction factor to  = 1.2 and the spectral lower limit coefficient to  = 0.05 to complete the current signal noise reduction in the field of arc fault detection.Step 1: using high-precision current transformer coils to collect current signals from the user's distribution line at a sampling frequency of 409.6 kHz, with a current collection time of 1 s each time, forming a sampling current x(n); Step 2: transmitting the sampling current x(n) to a multi-load loop series fault arc detection system to judge whether a series fault arc occurs in the line; Step 3: if the judgment result is that the line is in a fault state, an alarm message is sent externally; if it is judged that the line is in a normal state, repeat steps 1 and 2; Step 4: if the multi-load loop series fault arc detection system determines the current signals collected for 3 s as normal current, set the current signals collected in the last 1 s as reference signals X 1 (n), X 2 (n) and X 3 (n); Step 5: Fourier transform X 1 (n), X 2 (n) and X 3 (n), respectively, to generate frequency domain signals ζ 1 (n), ζ 2 (n) and ζ 3 (n).Considering that noise with lower frequency will not interfere with the results of the fault arc detection algorithm, a high-pass filter is designed to filter out the signal components with frequencies less than 1 kHz in n) and ζ 3 (n) are generated, and the noise signals σ 1 (t), σ 2 (t) and σ 3 (t) in the higher frequency band are generated by inverse Fourier transform.
In this case, the noise power spectrum can be estimated by calculating the average of the power spectra of σ 1 (t), σ 2 (t) and σ 3 (t).Next, only by setting reasonable parameters α and β, the current signal can be denoised by spectral subtraction.Finally, in this scheme, we set the over-reduction factor to α = 1.2 and the spectral lower limit coefficient to β = 0.05 to complete the current signal noise reduction in the field of arc fault detection.

Experimental Verification and Discussion
As shown in Figure 6, according to Article 42.1.3of the ANSI/UL 1699 "Fault Arc Circuit Breakers" standard, an arc is generated based on experimental circuits and arc generation devices.Provide 220 V and 50 Hz AC voltage to the arc generator.In the experiment, the circuit current is changed by changing the load type or quantity.In order to verify the noise reduction effect of the current signal noise reduction algorithm based on spectral subtraction, the electric load is designated as an incandescent lamp or air conditioner.During the experiment, the normal current without an arc fault in the line was collected before the carbon electrode was separated from the copper electrode, and then the electrode was gradually separated to generate an arc and collect the fault current.

Experimental Verification and Discussion
As shown in Figure 6, according to Article 42.1.3of the ANSI/UL 1699 "Fault Arc Circuit Breakers" standard, an arc is generated based on experimental circuits and arc generation devices.Provide 220 V and 50 Hz AC voltage to the arc generator.In the experiment, the circuit current is changed by changing the load type or quantity.In order to verify the noise reduction effect of the current signal noise reduction algorithm based on spectral subtraction, the electric load is designated as an incandescent lamp or air conditioner.During the experiment, the normal current without an arc fault in the line was collected before the carbon electrode was separated from the copper electrode, and then the electrode was gradually separated to generate an arc and collect the fault current.Figures 7 and 8 show the influence of the current signal denoising algorithm based on spectral subtraction on the normal current and fault current characteristics of incandescent lamps and vacuum cleaners, respectively.Comparing Figure 7a with Figure 8a, it is not difficult to find that before the current signal is denoised, the characteristic values of both incandescent lamp current and vacuum cleaner current are basically concentrated Figures 7 and 8 show the influence of the current signal denoising algorithm based on spectral subtraction on the normal current and fault current characteristics of incandescent lamps and vacuum cleaners, respectively.Comparing Figure 7a with Figure 8a, it is not difficult to find that before the current signal is denoised, the characteristic values of both incandescent lamp current and vacuum cleaner current are basically concentrated around 3, which shows that although the working hours of incandescent lamp and vacuum cleaner are different, their background noise is approximately Gaussian distribution, which once again proves that the assumption that the line noise signal is stable in the same power consumption period in the same place is reasonable.Moreover, after noise reduction, the characteristic value of normal current will be reduced to 1.5, which is also consistent with theoretical expectations.This can ensure that the weak arc fault will not be drowned by the line noise.around 3, which shows that although the working hours of incandescent lamp and vacuum cleaner are different, their background noise is approximately Gaussian distribution, which once again proves that the assumption that the line noise signal is stable in the same power consumption period in the same place is reasonable.Moreover, after noise reduction, the characteristic value of normal current will be reduced to 1.5, which is also consistent with theoretical expectations.This can ensure that the weak arc fault will not be drowned by the line noise.On this basis, the power spectrum of the power line noise signal can be estimated by capturing the reference current signal, and then the noise signal in the line current can be On this basis, the power spectrum of the power line noise signal can be estimated by capturing the reference current signal, and then the noise signal in the line current can be well suppressed by using the current signal denoising system based on spectrum subtraction method, and when the line has a fault arc, the noise reduction system will not destroy the characteristics of the arc fault.It is verified that the noise reduction algorithm can greatly improve the sensitivity of the original multi-load circuit series fault arc detection algorithm to the line arc fault on the basis of the unchanged reliability of fault arc identification.

Conclusions
This study first delved into the sources and characteristics of noise in power lines and, combined with the characteristics of various types of noise, proposed the assumption that the noise signal is stable within a certain power cycle in the same power field.Further analysis of power source noise and arc fault interference signals indicates that although power source noise may mask the fault arc interference signal, the multi-load circuit series fault arc detection algorithm can still effectively identify fault arcs in the circuit when the fault arc lasts for a long time or burns fiercely.The inspiration of this result is that the multi-load circuit series arc fault detection algorithm can filter out current signals without fault arc information, forming a reference current.By filtering out the components below 1 kHz in the reference current signal, a higher frequency band background noise signal can be constructed.
Under the premise that background noise can be pre-obtained or effectively estimated, using spectral subtraction to denoise the target signal is the simplest, most convenient and most effective method.Therefore, in subsequent research, this scheme proposes a current signal-denoising technology based on spectral subtraction and provides a detailed introduction to its implementation method.The experimental results show that the noise reduction method and the multi-load circuit series arc fault detection algorithm complement each other, greatly expanding the applicability of the original detection algorithm and enabling the fault arc protection device to issue accurate and reliable actions in any environment.

Figure 2 .
Figure 2. Background noise carried in the current signal of an office scene at different times: the d in Figure (a) comes from the current signal collected near 12 o'clock on 1 May 2023 in an office sc the data in Figure (b) comes from the current signal collected near 12:15 on 1 May 2023 in this o scene. or

Figure 2 .
Figure 2. Background noise carried in the current signal of an office scene at different times: the data in Figure (a) comes from the current signal collected near 12 o'clock on 1 May 2023 in an office scene; the data in Figure (b) comes from the current signal collected near 12:15 on 1 May 2023 in this office scene.

Figure 3 .Figure 3 .
Figure 3. Arc fault current and its wavelet coefficient under resistive load.(a) Resistive curren under weak arc fault, (b) The first layer wavelet detail coefficient of resistive current under we Figure 3. Arc fault current and its wavelet coefficient under resistive load.(a) Resistive current under weak arc fault, (b) The first layer wavelet detail coefficient of resistive current under weak arc fault, (c) Second-layer wavelet detail coefficient of resistive current under weak arc fault, (d) Third-layer wavelet detail coefficient of resistive current under weak arc fault.

Figure 4 .
Figure 4. Arc fault current and its wavelet coefficient under resistive load.(a) Resistive curren under severe arc fault, (b) The first layer wavelet detail coefficient of resistive current under s arc fault, (c) Second-layer wavelet detail coefficient of resistive current under severe arc fault, Third-layer wavelet detail coefficient of resistive current under severe arc fault.The realization process of the multi-load circuit series fault arc detection metho signed in our laboratory is as follows: (1) collecting line current signal () on the road in real time through high-precision current transformer; (2) carrying out fourwavelet transform on the current signal () by using the db4 wavelet base to obtai wavelet detail coefficient  , of each layer of () ; (3) calculating kurtosis

Figure 4 .
Figure 4. Arc fault current and its wavelet coefficient under resistive load.(a) Resistive current under severe arc fault, (b) The first layer wavelet detail coefficient of resistive current under severe arc fault, (c) Second-layer wavelet detail coefficient of resistive current under severe arc fault, (d) Third-layer wavelet detail coefficient of resistive current under severe arc fault.

Figure 5 .
Figure 5. Fusion scheme of current signal denoising and the fault arc detection algorithm.

Figure 5 .
Figure 5. Fusion scheme of current signal denoising and the fault arc detection algorithm.

Figure 6 .
Figure 6.Arc generator and experimental circuit.(a) Structure diagram of the ANSI/UL 1699 arc generator, (b) Experimental circuit diagram, (c) Photo of real experimental facilities.

Figure 6 .
Figure 6.Arc generator and experimental circuit.(a) Structure diagram of the ANSI/UL 1699 arc generator, (b) Experimental circuit diagram, (c) Photo of real experimental facilities.

Figure 7 .
Figure 7. Influence of the current signal denoising algorithm based on spectral subtraction on current characteristics of incandescent lamps.(a) Characteristics of incandescent lamp current before and after noise reduction under normal conditions, (b) Characteristics of incandescent lamp current before and after noise reduction under arc occurrence.

Figure 7 .
Figure 7. Influence of the current signal denoising algorithm based on spectral subtraction on current characteristics of incandescent lamps.(a) Characteristics of incandescent lamp current before and after noise reduction under normal conditions, (b) Characteristics of incandescent lamp current before and after noise reduction under arc occurrence.

Figure 8 .
Figure 8. Influence of the current signal denoising algorithm based on spectral subtraction on current characteristics of vacuum cleaners.(a) Characteristics of vacuum cleaner current before and after noise reduction under normal conditions, (b) Characteristics of vacuum cleaner current before and after noise reduction under arc occurrence.

Figure 8 .
Figure 8. Influence of the current signal denoising algorithm based on spectral subtraction on current characteristics of vacuum cleaners.(a) Characteristics of vacuum cleaner current before and after noise reduction under normal conditions, (b) Characteristics of vacuum cleaner current before and after noise reduction under arc occurrence.