Arc fault identification method for low voltage distribution lines based on harmonic characteristic distance measurement

Abstract

A method for identifying arc faults in low-voltage distribution lines based on harmonic characteristic distance measurement belongs to the field of electrical engineering measurement technology. It is characterized by comprising the following steps: step 1, constructing a reference vector; step 2, constructing a harmonic factor characteristic vector and a harmonic initial phase angle characteristic vector; step 3, normalizing the harmonic initial phase angle; step 4, decentralizing the normalized harmonic initial phase angle; step 5, calculating the Euclidean distance; step 6, constructing a classification plane to classify fault and non-fault differential voltages. In this method for identifying arc faults in low-voltage distribution lines based on harmonic characteristic distance measurement, the similarity between the differential voltage waveform and the square wave is used to identify whether the waveform contains a fault arc voltage to identify the fault, which can overcome the interference of the line voltage drop on the identification of the differential waveform type, and is still effective under the premise of considering the existence of the line voltage drop, and has the advantage of strong line voltage drop resistance.

Description

Technical Field

[0001] A method for identifying arc faults in low-voltage power distribution lines based on harmonic characteristic distance measurement belongs to the technical field of electrical engineering measurement. Background Art

[0002] In low-voltage power distribution systems, fires caused by electrical lines account for more than 50% of electrical fires each year. Even if electrical fires caused by power plugs are not considered, the proportion is still more than 40%. Among the fires caused by electrical lines, series arc faults caused by loose terminals, insulation damage, and conductor damage in low-voltage distribution lines are currently one of the most difficult line faults to detect. When a series arc fault occurs, its fault current is smaller than the line load current, and conventional line protection devices (circuit breakers, residual current protectors) cannot protect it. From the waveform characteristics, it is difficult to distinguish the series arc fault current from the load current of the nonlinear load.

[0003] At present, the detection methods for series arc faults in low-voltage distribution lines are divided into two categories:

[0004] (1) Detection method based on fault current characteristics. This type of method is currently the most studied at home and abroad. Its basic detection idea is to use the harmonic characteristics, singularity characteristics and random characteristics of the fault current in the time domain or transform domain for detection. In addition, in recent years, there have been methods that use artificial intelligence technology to fuse two or more of the above characteristics to achieve fault identification.

[0005] The idea of ​​series arc fault detection based on fault current is that when a series arc fault occurs in the line, the fault current will show typical fault characteristics of "zero rest", high-frequency harmonics, and increased current change rate. These characteristics are applicable to linear loads; but there are a large number of nonlinear loads below the side load, such as computers (switching voltage), microwave ovens (magnetrons), vacuum cleaners (series motors), etc., and with the popularization of power electronic equipment, the number of nonlinear loads is gradually increasing. The normal load current of these nonlinear loads may also show "zero rest", high-frequency harmonics, and increased current change rate. Therefore, the use of current "zero rest", high-frequency harmonics, and increased current change rate is prone to misjudgment of faults. In recent years, although many detection methods have emerged that use artificial intelligence technology to fuse multiple current features, the effectiveness of these methods depends on the number of load types used for training. At present, although there are products for arc detection on the market, such as AFCI or AFD, in actual applications, the detection accuracy of these products is not high.

[0006] (2) Detection method based on fault voltage characteristics. Specifically, the following research is included:

[0007] 1) The literature “Load-end arc fault voltage detection and morphological wavelet identification” extracts the fault arc characteristics by wavelet decomposition of the load-end voltage.

[0008] 2) The document “Research on low voltage arc fault identification method based on EMD and ELM” uses empirical mode decomposition to extract load end fault characteristics.

[0009] The methods mentioned in the above two documents essentially use the waveform distortion caused by the arc voltage starting and breaking phase angle at the fault point to detect the fault. However, this feature is affected by the load type and line parameters, and is difficult to distinguish from normal voltage distortion.

[0010] 3) The document "Predicting Series Fault Arc Using Load Terminal Voltage" uses wavelet packets to decompose the load terminal voltage and uses the prediction residual of the extreme learning machine to extract the fault arc characteristics. The actual detection effect of the technical solution disclosed in this document depends on the number of types of training loads.

[0011] 4) The document "Series Fault Arc Detection Method Based on Load-End Voltage Analysis" proposes an upstream line fault detection method based on the differential mean of adjacent voltage waveforms at the load end. This method assumes that the adjacent cycle voltage waveforms at the load end have large differences when a fault occurs. In actual faults, the fault voltage cycles at the load end may also have high similarities, and the accuracy of this method is less than ideal. For the detection method based on the load-side voltage, since the arc burning voltage is 10-20V and the equivalent impedance of the load is much larger than the line impedance, the fault voltage characteristics are mainly reflected in the load-side voltage after the fault point. The actual load-side voltage is around 220V, so the proportion of the fault arc voltage information on the load-side voltage is less than 10%. Therefore, the sensitivity of fault detection using the load-side voltage alone is also low, and it is difficult to extract complete fault information using the load-side voltage. The current detection method can only use the load-side voltage distortion caused by arc initiation for detection. This feature is easily affected by the load type and line parameters, and it is difficult to distinguish it from normal voltage distortion.

[0012] For fault detection, the ideal detection method should be able to establish a relatively unified fault detection criterion and have a high detection sensitivity. Since the fault current characteristics are easily affected by the load type and are difficult to distinguish from the load current of nonlinear loads, it is very difficult to implement detection using fault current. When an arc fault occurs, the arc voltage at the fault point is approximately in the shape of a square wave, and this feature is little affected by the load type, that is, regardless of whether it is a linear or nonlinear load, the arc voltage at the fault point is approximately in the shape of a square wave. Therefore, identifying whether there is a fault arc voltage in the line can establish a relatively unified fault detection criterion. In response to this problem, a Chinese patent with application number 202110457409.6 and patent name "A series arc detection method for low-voltage distribution networks" discloses a voltage differential detection method after synchronous data sampling of the monitoring points installed on the monitored line. The basic principle of this method is to differentiate the synchronous cyclic signal of the monitoring point, and identify whether the differential signal has the characteristics of the fault arc voltage to identify whether there is a series arc fault in the line. From the perspective of detection sensitivity, if a series arc fault occurs in the line to be monitored, the main component of the differential voltage is the arc voltage, so this method has the highest detection sensitivity. However, this method does not consider the impact of the voltage drop in the actual line on the differential voltage recognition effect. For low-voltage distribution lines, the line voltage drop can reach 5% of the rated voltage, which is about 11V at 230V. Since the effective value of the fault arc voltage is 10-20V, when the line to be monitored is long, the line voltage drop can reach a level similar to the arc voltage. At this time, the line voltage drop will make the method disclosed in this patent application no longer effective. Summary of the invention

[0013] The technical problem to be solved by the present invention is: to overcome the shortcomings of the prior art and provide a method for identifying fault arcs in low-voltage distribution lines based on harmonic characteristic distance measurement, which utilizes the similarity between the differential voltage waveform and the square wave to identify whether the waveform contains a fault arc voltage to identify the fault, and can overcome the interference of the line voltage drop on the identification of the differential waveform type, that is, it is still effective under the premise of considering the existence of the line voltage drop, so that the method has the advantage of strong resistance to line voltage drop, and can therefore be used for fault monitoring of longer lines, with higher engineering value.

[0014] The technical solution adopted by the present invention to solve the technical problem is: the method for identifying arc faults in low-voltage distribution lines based on harmonic characteristic distance measurement is characterized by comprising the following steps:

[0015] Step 1: Use the harmonic factors of the odd harmonics of the square wave to construct a reference vector H ref and the initial phase angle to construct the reference vector P ref ;

[0016] Step 2: Extract a frequency data S from the differential recording data x , calculate S x The harmonic factor and initial phase angle of the harmonic factor are used to construct the harmonic factor eigenvector H x and harmonic initial phase angle eigenvector P x ;

[0017] Step 3, normalizing the initial phase angle of the harmonics;

[0018] Step 4, decentralize the normalized harmonic initial phase angle;

[0019] Step 5: Calculate the Euclidean distance D between the harmonic factor feature vector and the reference vector H , calculate the Euclidean distance D between the decentralized initial phase angle eigenvector and the reference vector P ;

[0020] Step 6: Use the Euclidean distance D between the harmonic factor feature vector and the reference vector H , the Euclidean distance D between the initial phase angle eigenvector and the reference vector P , a dividing area between fault and non-fault data is constructed to classify the fault and non-fault differential voltages.

[0021] Preferably, in step 1, the odd-order harmonics of the square wave are the 3rd, 5th and 7th harmonics of the square wave respectively.

[0022] Preferably, in step 2, the harmonic factor characteristic vector H x and harmonic initial phase angle eigenvector P x They are

[0023]

[0024] Where: Respectively represent the frequency data S x The nth harmonic factor and initial phase angle of the signal.

[0025] Preferably, in step 5, the Euclidean distance D between the harmonic factor feature vector and the reference vector is H , the decentralized initial phase angle eigenvector The Euclidean distance D from the reference vector P They are:

[0026]

[0027] in, Respectively represent the 3rd, 5th, and 7th harmonic factors of the waveform to be identified; They respectively represent the initial phase angles of the 3rd, 5th, and 7th harmonics after the waveform to be identified is decentralized.

[0028] Preferably, in step 6, a boundary area between fault and non-fault data is constructed according to the characteristic distribution of the fault differential voltage, and α and β are used as boundary thresholds. The classification strategy is as follows:

[0029]

[0030] Where α and β are the set thresholds for fault detection.

[0031] Preferably, in step 1, the harmonic factor reference vector H of the 3rd, 5th and 7th harmonics of the square wave is used. ref and the initial phase angle to construct the reference vector P ref They are:

[0032]

[0033] Preferably, in step 1, the formula for normalizing the initial phase angle of the harmonic is:

[0034]

[0035] Where: is the normalized initial phase angle of harmonics, It is the normalized power frequency and initial phase angle of each harmonic obtained by FFT decomposition.

[0036] Preferably, in step 1, the formula for decentralizing the normalized harmonic initial phase angle is:

[0037]

[0038] Where: is the initial phase angle of the decentralized harmonic.

[0039] Compared with the prior art, the present invention has the following beneficial effects:

[0040] In this low-voltage distribution line fault arc identification method based on harmonic characteristic distance measurement, the similarity between the differential voltage waveform and the square wave is used to identify whether the waveform contains a fault arc voltage to identify the fault. This can overcome the interference of the line voltage drop on the differential waveform type identification, that is, under the premise of considering the existence of the line voltage drop, the method is still effective, so that the method has the advantage of strong resistance to line voltage drop, and therefore can be used for fault monitoring of longer lines, with higher engineering value.

[0041] Since the fault arc voltage is generally greater than or similar to the normal voltage drop of the line, the method of using the waveform characteristics of the differential voltage to identify whether there is a series arc fault in the line has a high detection sensitivity.

[0042] The method of integrating the 3rd, 5th, and 7th harmonic factors of differential voltage and the initial phase angle characteristics highlights the main characteristics of the arc square wave, eliminates the power frequency interference in the arc square wave, and weakens the high-frequency difference interference of arc voltages of different types of loads. It has the characteristics of strong versatility. BRIEF DESCRIPTION OF THE DRAWINGS

[0043] Figure 1 The figure is a flow chart of the fault arc identification method for low-voltage distribution lines based on harmonic characteristic distance measurement.

[0044] Figure 2 It is the equivalent circuit of series arc fault.

[0045] Figure 3 This is the voltage and current waveform of the electric heater fault.

[0046] Figure 4 This is the voltage and current waveform of the induction cooker fault.

[0047] Figure 5 The voltage and current waveforms of microwave oven fault.

[0048] Figure 6 This is the voltage and current waveform of the vacuum cleaner fault.

[0049] Figure 7 This is the voltage and current waveform of computer failure.

[0050] Figure 8 The harmonic order-harmonic factor curves of five types of loads before and after faults.

[0051] Fig. 9 The harmonic order-initial phase angle curves of five types of loads before and after faults.

[0052] Fig.10 The harmonic order-initial phase angle curves before and after the fault for five types of load decentralization.

[0053] Fig.11 It is a two-dimensional distribution diagram of harmonic factor and initial phase angle distance. DETAILED DESCRIPTION

[0054] Figures 1 to 11 The best embodiment of the present invention is shown below in conjunction with the attached Figures 1 to 11 The present invention is further described.

[0055] like Figure 1 As shown, the method for identifying arc faults in low-voltage distribution lines based on harmonic characteristic distance measurement includes the following steps:

[0056] Step 1, construct a reference vector;

[0057] The reference vector H is constructed using the harmonic factors of the 3rd, 5th, and 7th harmonics of the square wave. refand the initial phase angle to construct the reference vector P ref .

[0058] The Fourier series expansion of a periodic square wave signal s(t) with an amplitude of A, an initial phase angle of θ, and a fundamental frequency of ω is:

[0059]

[0060] It can be seen from the above formula that the ideal square wave contains only 1, 3, 5, ... odd harmonic components, the amplitude of each odd harmonic is proportional to the inverse of its harmonic order, and the initial phase angle of each odd harmonic is proportional to its harmonic order.

[0061] Reference Figure 3 to Figure 7 The arc voltage waveform and fault current waveform of the fault point of common linear loads (electric heaters) and nonlinear loads (induction cookers, microwave ovens, vacuum cleaners, computers) are shown. From the current waveform, the fault current waveforms of each load are very different. The fault current waveforms are mostly based on the load current waveform with zero break, high-frequency noise and other characteristics. However, since the nonlinear load current itself may have zero break, high-frequency noise and other characteristics, the current detection method is more difficult. Observe the arc voltage waveform of each load. From the common characteristics of each waveform, the main contour of the arc voltage of different loads is approximately a square wave with an arc voltage of 15 to 20V, where Figure 7 Computers are switching power supply loads. Since the switching power supply load current has a long "zero rest" time, the current is too small to maintain a stable arc during this process. Therefore, the arc voltage of this process shows high-frequency oscillation characteristics, but from the low-frequency contour of its arc voltage, it still conforms to the approximate square wave characteristics. From the difference in the characteristics of each waveform, Figure 3 , Figure 4 , Figure 6 There are obvious arcing and arcing peaks. Figure 5 There is no such feature. The reason is that the inductance component of the microwave oven load is relatively large, and the energy storage of the inductor to supplement the energy in the arc starting and arc extinction stages weakens this feature. Figure 7 There is a long-term high-frequency oscillation feature; in addition, there are differences in the rising (falling) rate of the half-wave change of each arc voltage. Figure 3 The resistive load changes along the sine form. Figures 4 to 7 The resistance and inductance of the nonlinear load change edge should be higher than Figure 3 The above-mentioned differences in arcing and arcing peaks, high-frequency oscillations, and rates of change edges all correspond to the high-frequency components of the arc voltage. It can be seen that if the difference characteristics of the arc voltage are ignored, it is feasible to extract its main low-frequency common characteristics to characterize the existence of the arc voltage.

[0062] In such Figure 2In the series arc fault equivalent circuit shown in the figure, when a series arc fault occurs in the line, it is approximately equivalent to inserting a voltage source u in series at the fault point. arc (t), M and N in the figure are the upstream and downstream monitoring points of the line respectively, u arc (t) represents the arc voltage, R (R1, R2), L (L1, L2) represent the line impedance, R L , L L Indicates the load. In case of a fault, the differential voltage appears as a normal line impedance voltage drop u z (t) and arc voltage u arc The sum of (t), the differential voltage is expressed as:

[0063]

[0064] Among them, u M (t) represents the voltage at the upstream monitoring point of the line, u N (t) represents the voltage at the monitoring point downstream of the line, R1 represents the resistance of the upstream line, R2 represents the resistance of the downstream line, L1 represents the inductance of the upstream line, L2 represents the inductance of the downstream line, u z (t) represents the normal line impedance voltage drop, u arc (t) represents the arc voltage.

[0065] In actual systems, the change in differential voltage amplitude caused by a series arc fault may be similar to that caused by a normal load change. It is difficult to distinguish between a fault and a normal operating state based solely on the change in differential voltage amplitude. Therefore, it is necessary to comprehensively utilize waveform characteristic information such as the amplitude and harmonic content of the differential voltage to identify faults in order to improve the reliability of fault detection.

[0066] Arc voltage u arc (t) The waveform is approximately a square wave, and the line voltage drop u generated by the load current z (t) is similar to the load current waveform. The line voltage drop waveform of a linear load is close to a sine wave, and its harmonic content is very small, generally not exceeding 5%; the line voltage drop of a nonlinear load is mostly manifested as a superposition of low-order harmonics or a triangular wave shape near the peak of the power supply, and its voltage drop waveform peak generally appears near the peak of the power supply voltage rather than near the zero point, which is significantly different from a square wave. Therefore, fault detection can be achieved by identifying whether the waveform has square wave characteristics.

[0067] Using the harmonic factor reference vector H of the 3rd, 5th, and 7th harmonics of the square wave ref and the initial phase angle to construct the reference vector P ref They are:

[0068]

[0069] Step 2, constructing the harmonic factor eigenvector and the harmonic initial phase angle eigenvector;

[0070] Extract a cycle data S from the differential recording data x , calculate S x The harmonic factor and initial phase angle of the harmonic factor are used to construct the harmonic factor eigenvector H x and harmonic initial phase angle eigenvector P x ,in:

[0071]

[0072] Where: Respectively represent S x The nth harmonic factor and initial phase angle of the signal.

[0073] Step 3, normalizing the initial phase angle of the harmonics;

[0074] Since the actual interception S x The initial phase angle can be any angle, and the harmonic initial phase angle needs to be normalized:

[0075]

[0076] Where: is the normalized initial phase angle of harmonics, It is the normalized power frequency and initial phase angle of each harmonic obtained by FFT decomposition.

[0077] Step 4, decentralize the normalized harmonic initial phase angle;

[0078] Since the arc-off-arcing rising edge of the actual arc voltage is not an ideal transition edge, there may be errors in the calculation of the fundamental initial phase angle, resulting in an overall deviation of the normalized harmonic initial phase angle from the square wave. The normalized harmonic initial phase angle needs to be decentralized:

[0079]

[0080] Where: is the initial phase angle of the decentralized harmonic.

[0081] Step 5: Calculate the Euclidean distance between the harmonic factor eigenvector and the reference vector, and calculate the decentralized initial phase angle eigenvector Euclidean distance to a reference vector;

[0082] Calculate the harmonic factor eigenvector H respectively x With the reference vector H ref The Euclidean distance and the decentralized initial phase angle eigenvector With reference vector P ref The Euclidean distance of:

[0083]

[0084] in, Respectively represent the 3rd, 5th, and 7th harmonic factors of the waveform to be identified; They respectively represent the initial phase angles of the 3rd, 5th, and 7th harmonics after the waveform to be identified is decentralized.

[0085] The Euclidean distance reflects the waveform S x The similarity with the square wave, the smaller the Euclidean distance, the higher the similarity with the square wave.

[0086] Step 6, constructing a boundary area between fault and non-fault data to classify the fault and non-fault differential voltages;

[0087] Due to the use of D H and D P Two-dimensional features, based on the characteristic distribution of fault differential voltage, the boundary area between fault and non-fault data is constructed, with α and β as the boundary thresholds. The classification strategy is as follows:

[0088]

[0089] Among them: α, β are the set thresholds for fault detection.

[0090] In summary, the waveform characteristics can be described by the amplitude and phase angle of the harmonic content it contains. The main components of the square wave are 1st to 7th odd harmonics, among which the 3rd, 5th and 7th harmonics account for more than 60% of the total harmonic content outside the power frequency. In order to highlight the square wave characteristics and eliminate the influence of the power frequency components, the present invention discloses a series arc fault detection method based on the 3rd, 5th and 7th harmonic parameters of the differential voltage and the square wave similarity measurement. The method integrates the harmonic factors of the 3rd, 5th and 7th harmonics of the differential voltage and the composite characteristics of the initial phase angle of the harmonics to construct a comprehensive criterion. When the detected waveform characteristics meet the square wave characteristics, it is considered that a series arc fault has occurred.

[0091] Further references Figures 8 to 10 , five loads (electric heater, induction cooker, microwave oven, vacuum cleaner, computer) are given at 100m, 4mm 2 The harmonic order-harmonic factor curve before and after the fault on the PVC line, the harmonic order-initial phase angle curve, and the harmonic order-initial phase angle curve after decentralization. Figure 8 The odd harmonic factors of each waveform, except for the microwave oven, before and after the fault of other loads are significantly different from those of the square wave. The microwave oven has a large amount of harmonic components in the load current, which leads to a large voltage drop and voltage distortion, and its harmonic factor is close to that of the square wave. Fig. 9is the normalized initial phase angle of odd harmonics. Except for the induction cooker, the initial phase angles of odd harmonics of other loads showed great randomness before the fault, but were basically in a straight line after the fault. Affected by the normalization error of the initial phase angle, the initial phase angles of each harmonic are offset from the square wave as a whole. Fig.10 ,After decentralization, the initial phase angles of the harmonics after the fault fluctuate around the square wave, and the fault characteristics are more obvious.

[0092] It can be seen that both odd harmonic factor and initial phase angle can reflect the existence of fault arc voltage, but relying on a single feature will lead to misjudgment. In order to effectively characterize the fault characteristics, it is necessary to combine the two features. Fig.11 It is a two-dimensional distribution diagram of the harmonic factor and the initial phase angle distance of the harmonic before and after the above load fault. Fig.11 From the perspective of the two-dimensional distance feature plane distribution, the two-dimensional feature distribution before and after the fault has an obvious boundary plane, which can be used to achieve the binary classification of fault voltage drop and normal line voltage drop. For example, α=0.25, β=50° can be used as the recognition threshold of the fault waveform. When it meets and When , the waveform is a fault waveform containing arc voltage, indicating that there is a series arc fault in the monitored line; when or When , it indicates that the waveform is not an arc fault waveform, indicating that there is no series arc fault in the monitored line.

[0093] The above is only a preferred embodiment of the present invention, and does not limit the present invention in other forms. Any technician familiar with the profession may use the above disclosed technical content to change or modify it into an equivalent embodiment with equivalent changes. However, any simple modification, equivalent change and modification made to the above embodiment according to the technical essence of the present invention without departing from the technical solution of the present invention still belongs to the protection scope of the technical solution of the present invention.

Claims

1. A method for identifying arc faults in low-voltage distribution lines based on harmonic characteristic distance measurement, characterized in that: The steps include: Step 1: Use the harmonic factors of the odd harmonics of the square wave to construct a reference vector H ref and the initial phase angle to construct the reference vector P ref ; Step 2: Extract a frequency data S from the differential recording data x , calculate S x The harmonic factor and initial phase angle of the harmonic factor are used to construct the harmonic factor eigenvector H x and harmonic initial phase angle eigenvector P x ; Step 3, normalizing the initial phase angle of the harmonics; Step 4, decentralize the normalized harmonic initial phase angle; Step 5: Calculate the Euclidean distance D between the harmonic factor feature vector and the reference vector H , calculate the Euclidean distance D between the decentralized initial phase angle eigenvector and the reference vector P ; Step 6: Use the Euclidean distance D between the harmonic factor feature vector and the reference vector H , the Euclidean distance D between the initial phase angle eigenvector and the reference vector P , a dividing area between fault and non-fault data is constructed to classify the fault and non-fault differential voltages.

2. The method for identifying arc faults in low-voltage distribution lines based on harmonic characteristic distance measurement according to claim 1 is characterized in that: In step 1, the odd harmonics of the square wave are the 3rd, 5th and 7th harmonics of the square wave respectively.

3. The method for identifying arc faults in low-voltage distribution lines based on harmonic characteristic distance measurement according to claim 2 is characterized in that: In step 2, the harmonic factor eigenvector H x and harmonic initial phase angle eigenvector P x They are Where: Respectively represent the frequency data S x The nth harmonic factor and initial phase angle of the signal.

4. The method for identifying arc faults in low-voltage distribution lines based on harmonic characteristic distance measurement according to claim 3 is characterized in that: In step 5, the Euclidean distance D between the harmonic factor feature vector and the reference vector H , the decentralized initial phase angle eigenvector The Euclidean distance D from the reference vector P They are: in, Respectively represent the 3rd, 5th, and 7th harmonic factors of the waveform to be identified; They respectively represent the initial phase angles of the 3rd, 5th, and 7th harmonics after the waveform to be identified is decentralized.

5. The method for identifying arc faults in low-voltage distribution lines based on harmonic characteristic distance measurement according to claim 4 is characterized in that: In step 6, a boundary area between fault and non-fault data is constructed according to the characteristic distribution of the fault differential voltage, and α and β are used as boundary thresholds. The classification strategy is as follows: Where α and β are the set thresholds for fault detection.

6. The method for identifying arc faults in low-voltage distribution lines based on harmonic characteristic distance measurement according to claim 2 is characterized in that: In step 1, the harmonic factor reference vector H of the 3rd, 5th, and 7th harmonics of the square wave is used. ref and the initial phase angle to construct the reference vector P ref They are:

7. The method for identifying arc faults in low-voltage distribution lines based on harmonic characteristic distance measurement according to claim 1 is characterized in that: In step 1, the formula for normalizing the initial phase angle of the harmonic is: Where: is the normalized initial phase angle of harmonics, It is the normalized power frequency and initial phase angle of each harmonic obtained by FFT decomposition.

8. The method for identifying arc faults in low-voltage distribution lines based on harmonic characteristic distance measurement according to claim 7 is characterized in that: In the step 1, the formula for decentralizing the normalized harmonic initial phase angle is: Where: is the initial phase angle of the decentralized harmonic.

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