Low-current grounding system single-phase grounding fault diagnosis method based on low-voltage side measurement

Abstract

The invention discloses a low-current grounding system single-phase grounding fault diagnosis method based on low-voltage side measurement. The method comprises the following steps that electrical quantity information is collected in a sensor of a low-voltage measurement system; carrying out phase-mode transformation by adopting Karnaul transformation, and extracting transient voltage characteristics; using an improved Prony algorithm to extract the main frequency characteristic component; and determining a fault line selection and a fault section according to the process. According to the method, cloud side end cooperative diagnosis is comprehensively utilized, low-voltage side measurement information is fully used, and the medium-voltage side single-phase earth fault is diagnosed. The method comprises the following steps of: acquiring measured voltage information of a low-voltage side, removing electromagnetic coupling among three phases through Karnaul transformation, obtaining transient voltage characteristics of a line mode by utilizing derivation, extracting a main frequency component based on an improved Prony algorithm, obtaining a corresponding single-phase earth fault diagnosis criterion, and achieving the effects of detecting and positioning a single-phase earth fault of a medium-voltage side.

Description

Technical Field

[0001] The present invention belongs to the field of abnormal condition detection of low-voltage distribution networks, and particularly relates to a single-phase grounding fault diagnosis method for a small-current grounding system based on low-voltage side measurement. Background Art

[0002] With the progress of society and the continuous improvement of the economic development level, the power demand also continues to rise. Users in all walks of life have put forward higher requirements for the existing power supply reliability and stable power quality. As the last link of the power system, the normal and stable operation of the distribution network is directly related to the user's power consumption experience and is in a very important position. According to the different neutral grounding methods, the power system can be divided into two types: a large-current grounding system and a small-current grounding system. Among them, the small-current grounding system usually adopts the method of non-effective grounding of the neutral point, including direct grounding of the neutral point and grounding of the neutral point through an arc suppression coil, and is usually applied to the distribution network below 66 kV. When a fault occurs in the distribution system, due to the small-current grounding method, the generated fault current signal is weak. The most common fault mode is single-phase grounding fault, which accounts for about 80% of the total number of faults. Its fault current is weak and difficult to detect. However, it usually also generates overvoltage, etc., which causes damage to the insulation of the distribution network system and equipment. When the system operates in a fault state, there may also be impact accidents, even threatening personal safety. Therefore, fault line identification and fault point location are of great significance for maintaining the safe and reliable operation of the power system. Nowadays, the methods for detecting single-phase grounding faults in small-current systems can generally be divided into three categories: based on injected signals, based on steady-state characteristics, and based on transient characteristics. Among them, the method based on injected signals is to externally apply a DC signal to one end of the neutral point of the voltage transformer after determining the grounded phase. Since the DC signal only exists in the fault line, a signal detector is used to track the signal to determine the fault line; the method based on steady-state characteristics uses steady-state characteristics for fault line selection, such as identifying the fault line based on characteristics such as zero-sequence current, zero-sequence voltage amplitude, zero-sequence admittance, and power detection. However, the current of the grounded fault line is small, and signal interference will occur during line switching, etc. At the same time, affected by different neutral grounding methods, excessive resistance, etc., the accuracy of fault line selection based on steady-state characteristics for fault identification is relatively low; the method based on transient characteristics has relatively rich signal characteristics during the transient process when a grounding fault occurs in the distribution network, and its amplitude is usually large, but the duration is short, and there are certain requirements for the detection frequency. It usually includes analysis methods such as the first half-wave method, transient energy method, and wavelet transform method. Summary of the Invention

[0003] The present invention is proposed to solve the problems existing in the prior art, and its purpose is to provide a single-phase grounding fault diagnosis method for a small-current grounding system based on low-voltage side measurement.

[0004] The technical solution of the present invention is: a single-phase grounding fault diagnosis method for a small current grounding system based on low-voltage side measurement, including the following steps:

[0005] A. Collect electrical quantity information in the sensors of the low-voltage measurement system;

[0006] B. Perform phase-mode transformation using the Karrenbauer transformation to extract transient voltage characteristics;

[0007] C. Use the improved Prony algorithm to extract the main frequency characteristic components;

[0008] D. Determine the fault line selection and fault section according to the process.

[0009] Furthermore, in step A, collecting electrical quantity information in the sensors of the low-voltage measurement system, the specific process is as follows:

[0010] The low-voltage sensor continuously monitors the voltage signal, and provides assistance and support for the detection and location of single-phase grounding faults on the medium-voltage side by means of data analysis of the low-voltage side measurement system.

[0011] Furthermore, in step B, performing phase-mode transformation using the Karrenbauer transformation to extract transient voltage characteristics, the specific process is as follows:

[0012] First, perform the Karrenbauer transformation;

[0013] Then, based on the Karrenbauer transformation, establish a composite mode network diagram;

[0014] Finally, extract the transient voltage characteristics.

[0015] Furthermore, in step C, using the improved Prony algorithm to extract the main frequency characteristic components, the specific process is as follows:

[0016] First, obtain the amplitude, phase angle, frequency, and attenuation factor information through the Prony algorithm;

[0017] Then, calculate the mean square error result to determine the order of the Prony algorithm and improve the fitting effect.

[0018] Furthermore, in step D, determining the fault line selection and fault section according to the process, the specific process is as follows:

[0019] First, compare the obtained main frequency characteristic components with a preset threshold. If it exceeds the preset threshold, upload the information;

[0020] Then, determine the feeder where the single-phase grounding fault occurs based on the uploaded information;

[0021] Finally, determine the fault section based on the amplitude of the main frequency characteristic components.

[0022] Furthermore, the feeder with a single-phase grounding fault is determined based on the uploaded information, and the specific process is as follows:

[0023] Compare and analyze the uploaded information from different low-voltage sensors. When the average amplitude of the main frequency components of the low-voltage sensors of a certain feeder is much greater than that of other feeders, it is considered that a single-phase grounding fault has occurred on this feeder.

[0024] Furthermore, the fault section is determined based on the amplitude of the main frequency characteristic component, and the specific process is as follows:

[0025] Compare the amplitudes of the main frequency components of the low-voltage measurement points on the faulty line. The fault section is located between the two distribution transformers with the highest amplitudes of the main frequency components among the adjacent two distribution transformers.

[0026] Furthermore, the Karrenbauer transformation is performed, and the specific process is as follows:

[0027] First, transform the three-phase system into a 0-mode system, a 1-mode system, and a 2-mode system through the Karrenbauer transformation;

[0028] Then, obtain the voltage and current expressions of the 0-mode system, the 1-mode system, and the 2-mode system.

[0029] Furthermore, the transient voltage characteristics are extracted, and the specific process is as follows:

[0030] First, at the starting moment of the transient process, regardless of the grounding method, the composite equivalent capacitance in the power system affects the transient current of the composite mode network, and then determines the distribution of the transient voltage;

[0031] Then, when a single-phase grounding fault occurs, the distribution network outgoing lines in the power system are relatively short, and the capacitive reactances to the ground of each outgoing line are not very different, making the transient voltage values of the non-faulty lines small; while the transient voltage value of the faulty line depends on all the capacitive reactances to the ground of the entire system, and the value is much larger than that corresponding to a single non-faulty line, thus serving as the basis for selecting the faulty line.

[0032] The beneficial effects of the present invention are as follows:

[0033] The present invention comprehensively utilizes cloud-edge-end collaborative diagnosis, fully uses the low-voltage side measurement information, and diagnoses the single-phase grounding fault on the medium-voltage side. Collect the low-voltage side measured voltage information, remove the electromagnetic coupling between the three phases through the Karrenbauer transformation, utilize the derived line-mode transient voltage characteristics, extract the main frequency components based on the improved Prony algorithm, and obtain the corresponding single-phase grounding fault diagnosis criterion, achieving the effects of detecting and locating the single-phase grounding fault on the medium-voltage side. Description of the Drawings

[0034] Figure 1 is the composite mode network diagram of the present invention;

[0035] Figure 2 is the 1-mode transient voltage distribution diagram of single-phase grounding fault of the present invention;

[0036] Figure 3 is the flow chart of single-phase grounding fault detection of the present invention;

[0037] Figure 4 is the experimental model diagram in the research materials of the present invention. Detailed implementation manners

[0038] Hereinafter, the present invention will be described in detail with reference to the drawings and embodiments:

[0039] As Figures 1 to 4 shown, the single-phase grounding fault diagnosis method for a small current grounding system based on low-voltage side measurement includes the following steps:

[0040] A. Collect electrical quantity information in the sensors of the low-voltage measurement system;

[0041] B. Perform phase-mode transformation using the Karrenbauer transformation to extract transient voltage characteristics;

[0042] C. Use the improved Prony algorithm to extract the main frequency characteristic components;

[0043] D. Determine the fault line selection and fault section according to the process.

[0044] Step A collects electrical quantity information in the sensors of the low-voltage measurement system, and the specific process is as follows:

[0045] The low-voltage sensors continuously monitor the voltage signals, and provide assistance and support for the detection and location of single-phase grounding faults on the medium-voltage side by means of data analysis of the low-voltage side measurement system.

[0046] Step B performs phase-mode transformation using the Karrenbauer transformation to extract transient voltage characteristics, and the specific process is as follows:

[0047] First, perform the Karrenbauer transformation;

[0048] Then, based on the Karrenbauer transformation, establish a composite mode network diagram;

[0049] Finally, extract the transient voltage characteristics.

[0050] Step C uses the improved Prony algorithm to extract the main frequency characteristic components, and the specific process is as follows:

[0051] First, obtain the amplitude, phase angle, frequency, and attenuation factor information through the Prony algorithm;

[0052] Then, calculate the mean square error result to determine the order of the Prony algorithm and improve the fitting effect.

[0053] Step D determines the faulty line selection and the faulty section according to the process, and the specific process is as follows:

[0054] First, compare the obtained main frequency characteristic components with the preset threshold. If it exceeds the preset threshold, upload the information.

[0055] Then, determine the feeder with a single-phase grounding fault based on the uploaded information.

[0056] Finally, determine the faulty section based on the amplitude of the main frequency characteristic components.

[0057] Determine the feeder with a single-phase grounding fault based on the uploaded information, and the specific process is as follows:

[0058] Compare and analyze the uploaded information from different low-voltage sensors. When the average amplitude of the main frequency components of the low-voltage sensors of a certain feeder is much greater than that of other feeders, it is considered that a single-phase grounding fault has occurred on this feeder.

[0059] Determine the faulty section based on the amplitude of the main frequency characteristic components, and the specific process is as follows:

[0060] Compare the amplitudes of the main frequency components of the low-voltage measurement points on the faulty line. The faulty section is located between the two distribution transformers with the highest amplitudes of the main frequency components among the adjacent two distribution transformers.

[0061] Perform the Karrenbauer transformation, and the specific process is as follows:

[0062] First, transform the three-phase system into a 0-mode system, a 1-mode system, and a 2-mode system through the Karrenbauer transformation.

[0063] Then, obtain the voltage and current expressions of the 0-mode system, the 1-mode system, and the 2-mode system.

[0064] Extract the transient voltage characteristics, and the specific process is as follows:

[0065] First, at the starting moment of the transient process, regardless of the grounding method, the composite equivalent capacitance in the power system affects the transient current of the composite mode network, and then determines the distribution of the transient voltage.

[0066] Then, when a single-phase grounding fault occurs, the distribution network outgoing lines in the power system are relatively short, and the capacitance to the ground of each outgoing line has little difference, making the transient voltage value of the non-faulty line small; while the transient voltage value of the faulty line depends on all the capacitances to the ground of the entire system, and the value is much larger than that corresponding to a single non-faulty line, thus serving as the basis for selecting the faulty line.

[0067] Specifically, in step A, electrical quantity information is collected by the sensors of the low-voltage measurement system. With the increasingly improved low-voltage measurement system device, a large number of intelligent distribution transformer terminals can be deployed, enabling sufficient information to be collected, enhancing the ability of distribution network situation awareness. By analyzing the data of the low-voltage side measurement system, it provides assistance and support for the detection and location of single-phase grounding faults on the medium-voltage side. At the same time, no additional specific equipment needs to be invested on the medium-voltage side, reducing equipment investment and operation and maintenance management costs.

[0068] Specifically, in step B, the Karrenbauer transformation is a method of transforming the three-phase voltage and current in the power system into moduli through phase-mode transformation. Through this transformation, the electromagnetic coupling between the three phases can be eliminated. The Karrenbauer transformation has many applications in improving the accuracy of fault location and the utilization rate of power grid information, and has good robustness. By the Karrenbauer transformation, the three-phase system is transformed into a 0-mode, 1-mode, and 2-mode system. The specific transformation method is as follows:

[0069] First, at any point on the uniform three-phase transmission line, the voltage U and current I satisfy the following equations

[0070]

[0071] where U and I are the phase voltages and phase currents in the frequency domain respectively, x is the distance on the line from the measurement point; Z and Y are the series impedance and shunt admittance matrices of the line per unit length.

[0072] Then, through substitution transformation, the following formula can be obtained:

[0073]

[0074] Since there is electromagnetic coupling between the three-phase lines, the basic equations and wave equations of each phase are not independent, and it is very difficult to solve directly. The essence of the phase-mode transformation is to use the eigenvector matrix of the sparse matrix ZY or YZ as the mode transformation matrix, and diagonalize the matrices ZY, YZ, Z, and Y at the same time, so as to convert the mutually coupled phase-domain equations into uncoupled mode-domain equations. The phase-mode transformation matrix T m is a constant matrix independent of the specific line parameters. Using T m is as follows:

[0075]

[0076] Its inverse matrix is:

[0077]

[0078] Then the corresponding 0-mode, 1-mode, and 2-mode voltage and current are shown in the following formulas:

[0079]

[0080] Among them, \(i\) 0 , \(i\) 1 , \(i\) 2 are respectively the zero-mode component, first-mode component, and second-mode component of the current. \(i\) a , \(i\) b , \(i\) c are respectively the current components of phases A, B, and C of the current. \(u\) 0 , \(u\) 1 , \(u\) 2 are respectively the zero-mode component, first-mode component, and second-mode component of the voltage. \(u\) a , \(u\) b , \(u\) c are respectively the voltage components of phases A, B, and C of the voltage.

[0081] Specifically, in the complex-mode network diagram, the first-mode component and the second-mode component are collectively referred to as the line-mode components, which respectively form loops between phases AB and AC. The parameters are the same as those of the positive-sequence loop in the unbalanced component analysis. The zero-mode component forms a loop through the three-phase conductors and the ground, so it is the same as the zero-sequence loop parameters.

[0082] Specifically, in step B, based on the Karrenbauer transformation, a complex-mode network diagram is established, as Figure 1 shown. \(u\) k (t) is the power supply voltage. \(u\) 0 , \(u\) 1 , \(u\) 2 are respectively the zero-mode component, first-mode component, and second-mode component of the voltage. \(i\) 0 , \(i\) 1 , \(i\) 2 are respectively the zero-mode component, first-mode component, and second-mode component of the current. \(R\) g is the grounding resistance. \(L\) LK is the inductance of the zero-sequence reactor. \(L\) and \(R\) respectively correspond to the inductance and resistance on the corresponding branch. \(C\) 0 is the zero-mode distributed capacitance of the busbar and the power supply behind it.

[0083] Specifically, the transient voltage characteristics are extracted in step B as follows:

[0084] At the initial moment of the transient process, regardless of the grounding method, the composite equivalent capacitance in the power system affects the transient current of the complex-mode network, and thus determines the distribution of the transient voltage. Therefore, when a single-phase grounding fault occurs, the distribution network outgoing lines in the power system are relatively short, and the capacitance to the ground of each outgoing line varies little, making the transient voltage value of the non-faulty line small; while the transient voltage value of the faulty line depends on the capacitance to the ground of the entire system, and the value is much larger than that corresponding to a single non-faulty line. This rule can be used as the basis for selecting the faulty line.

[0085] Taking the first-mode component as an example, from Figure 1And Figure 2 It can be known that on the entire faulty line, the voltages at the fault point, the beginning of the line, and the end of the line are respectively:

[0086]

[0087] Among them, R 1 and L 1 are the resistance and inductance on the 1-mode line, R s and L s are the resistance and inductance on the power supply side, R e and L e are the resistance and inductance on the load side, and i 1 is the current on the 1-mode line.

[0088] Figure 2 is a schematic diagram of the distribution of the 1-mode voltage component of a single-phase grounding fault. According to Kirchhoff's voltage law, the voltages U sm and U em on both sides of the fault point are respectively:

[0089]

[0090] Among them, j is the imaginary unit, ω is the system angular frequency, and m is the number of measurement points from the fault point; U sm is the voltage at the mth measurement point from the fault point on the power supply side, U em is the voltage at the mth measurement point from the fault point on the load side, R sk and L sk are respectively the resistance and inductance of the kth section on the power supply side; R ek and L ek are respectively the resistance and inductance of the kth section on the load side; R sz , L sz are the total resistance and inductance from the fault point to the power supply side; R ez , L ez are the total resistance and inductance from the fault point to the load side.

[0091] It can be seen from the above formula that on the faulty line, the voltage value corresponding to the fault point is the highest. As the distance increases, the corresponding voltage value will decrease. Based on this rule as the basis for fault point location, the data of the measurement points on the low-voltage side are compared and analyzed to determine the location section where the fault point is located.

[0092] Specifically, the line-mode transient voltage signal caused by a fault in step C is a combination of sine functions with different frequencies, amplitudes, and exponential decays. However, there is a transient main frequency component among them, and its amplitude determines the amplitude of the line-mode transient voltage signal. By improving the Prony algorithm to extract the main frequency component, more reliable information than the amplitude of the line-mode transient voltage signal can be provided, thereby improving the robustness of fault detection.

[0093] The Prony algorithm is a time series analysis method for signal processing. Its essential idea is to represent a signal as a linear combination of a set of exponential functions and estimate the parameters of the model through a linear regression method. It is suitable for analyzing dynamically changing signals and has been widely applied in many fields such as radar, seismology, and speech processing. It can efficiently estimate information such as the frequency, amplitude, phase, and decay factor of a signal. Its implementation steps are as follows:

[0094] First, use the exponential function as the mathematical model of the algorithm:

[0095]

[0096] b i =A i exp(jθ i )(11)

[0097] z i =exp[(-α i +j2πf i )Δt] (12)

[0098]

[0099] In the above formula, k = (1, 2,..., N - 1) is the number of sampling points; y(kΔt) represents the measured signal; η(kΔt) is the system noise; is the fitting signal; i = (1, 2,..., p) is the amplitude; p is the model order; θ is the phase angle; α is the decay factor; Δt represents the sampling interval, A is the amplitude, f is the frequency, and j is the imaginary unit.

[0100] Then, by solving it, the corresponding amplitude, phase angle, frequency, and decay factor information can be obtained:

[0101]

[0102] Finally, this method is very sensitive to the influence of noise, and the determination of its modal terms is inaccurate, which may lead to digital overflow. To improve the fitting effect, the order p' of the algorithm is determined by calculating the mean square error result.

[0103]

[0104] In formula (15), C can be set as a constant, or the maximum value of the input data can be taken, and the optimal order with the minimum mean square error can be selected.

[0105] Specifically, in the implementation of step D, the low-voltage sensor continuously monitors the voltage signal and calculates the line-mode transient component and its main frequency component on-site. When the amplitude of its main frequency component is detected to exceed the preset threshold for two consecutive cycles, the result is uploaded to the cloud master station, and the cloud master station will compare the information from different low-voltage sensors for collaborative analysis to determine the faulty line and location. The process is as Figure 4 shown as follows:

[0106] d1. The low-voltage sensor continuously monitors the on-site voltage signal.

[0107] d2. The low-voltage sensor obtains the line-mode transient voltage component through phase-mode transformation and calculates the main frequency component through the improved Prony algorithm; when the amplitude of the main frequency component is detected to exceed the preset threshold, the result is uploaded to the cloud master station.

[0108] d3. The cloud master station compares and analyzes the messages from different low-voltage sensors to collaboratively determine the faulty line and location. When the average amplitude of the main frequency components of the low-voltage sensors of a certain feeder is much greater than that of other feeders, it is considered that a single-phase grounding fault has occurred in this feeder.

[0109] d4. Compare the amplitudes of the main frequency components of the low-voltage measurement points on the faulty line. The faulty section is between two adjacent distribution transformers, between the two distribution transformers with the highest amplitudes of the main frequency components.

[0110] d5. The cloud master station notifies the relevant personnel of the faulty feeder and the faulty location section.

[0111] Example 1

[0112] A system with three 10 kV feeders is used as the experimental object, which is equipped with multiple distribution transformers. L1 is selected as the faulty line, and the line between transformers 1 and 2 is used as the faulty section. Experiments are carried out for different cases of arc suppression coil grounding, non-grounding, and fault resistances of 0, 10, and 100. The experimental results are shown in Table 1.

[0113] Table 1 Experimental Results

[0114]

[0115] As can be seen from Table 1, the amplitude of the main frequency component of the faulty line is significantly greater than that of the main frequency components of other branches. Through this, the faulty line can be clearly judged. On the faulty line, the amplitudes of the main frequency components measured at the low voltage of Distribution Transformers 1 and 2 are relatively the highest. It can be judged that the single-phase grounding fault occurs between Distribution Transformers 1 and 2. Under the conditions of changing the grounding method and the fault resistance, the method proposed in the present invention is still applicable and has good robustness.

[0116] Although the present invention has been described above in conjunction with the accompanying drawings, the present invention is not limited to the above specific embodiments. The above specific embodiments are merely illustrative rather than restrictive. Under the inspiration of the present invention, those of ordinary skill in the art can also make many variations without departing from the purpose of the present invention, and these all fall within the protection scope of the present invention.

Claims

1. A single-phase grounding fault diagnosis method for a small current grounding system based on low-voltage side measurement, characterized in that: The following steps are involved: A. Collect electrical quantity information from sensors in low-voltage measurement systems; B. Use Karenbauer transformation to perform phase mode transformation and extract transient voltage characteristics; C. Use the improved Prony algorithm to extract the main frequency characteristic components; D. Determine the fault line selection and fault section based on the process.

2. The single-phase grounding fault diagnosis method of a small current grounding system based on low-voltage side measurement according to claim 1 is characterized in that: Step A collects electrical quantity information from the sensor of the low-voltage measurement system. The specific process is as follows: The low-voltage sensor continuously monitors the voltage signal and uses the data analysis of the low-voltage side measurement system to provide assistance and support for the detection and location of single-phase grounding faults on the medium-voltage side.

3. The single-phase grounding fault diagnosis method of a small current grounding system based on low-voltage side measurement according to claim 1 is characterized in that: Step B uses Karenbauer transformation to perform phase mode transformation and extract transient voltage characteristics. The specific process is as follows: First, perform the Karenbauer transformation; Then, based on the Karenbauer transformation, a composite module network graph is established; Finally, the transient voltage characteristics are extracted.

4. The single-phase grounding fault diagnosis method of a small current grounding system based on low-voltage side measurement according to claim 1 is characterized in that: Step C uses the improved Prony algorithm to extract the main frequency characteristic components. The specific process is as follows: First, the amplitude, phase angle, frequency, and attenuation factor information are obtained through the Prony algorithm; Then, the mean square error results were calculated to determine the order of the Prony algorithm to improve the fitting effect.

5. The single-phase grounding fault diagnosis method of a small current grounding system based on low-voltage side measurement according to claim 1 is characterized in that: Step D determines the fault line selection and fault section according to the process. The specific process is as follows: First, the main frequency characteristic component obtained is compared with a preset threshold, and if it exceeds the preset threshold, the information is uploaded; Then, the feeder where the single-phase grounding fault occurs is determined based on the uploaded information; Finally, the fault section is determined based on the amplitude of the main frequency characteristic component.

6. The single-phase grounding fault diagnosis method of a small current grounding system based on low-voltage side measurement according to claim 5 is characterized in that: Based on the uploaded information, it is determined that a single-phase grounding fault has occurred in the feeder. The specific process is as follows: The uploaded information from different low-voltage sensors is compared and analyzed. When the average amplitude of the main frequency components of the low-voltage sensors of a certain feeder is much larger than that of other feeders, it is considered that a single-phase grounding fault has occurred in the feeder.

7. The single-phase grounding fault diagnosis method of a small current grounding system based on low-voltage side measurement according to claim 5 is characterized in that: Based on the amplitude of the main frequency characteristic component, the fault section is determined. The specific process is as follows: By comparing the amplitudes of the main frequency components of each low-voltage measuring point on the faulty line, the fault section is located between two adjacent distribution transformers, between the two distribution transformers with the highest amplitude of the main frequency components.

8. The single-phase grounding fault diagnosis method of a small current grounding system based on low-voltage side measurement according to claim 3 is characterized in that: Carry out Karenbauer transformation, the specific process is as follows: Firstly, the three-phase system is transformed into a 0-mode system, a 1-mode system, and a 2-mode system through Karenbauer transformation; Then, the voltage and current expressions of the 0-mode system, the 1-mode system, and the 2-mode system are obtained.

9. The single-phase grounding fault diagnosis method of a small current grounding system based on low-voltage side measurement according to claim 3 is characterized in that: Extract transient voltage features. The specific process is as follows: First, at the beginning of the transient process, without being restricted by the grounding method, the composite equivalent capacitance in the power system affects the transient current of the composite mode network, and then determines the distribution of the transient voltage; Then, when a single-phase grounding fault occurs, the distribution network outgoing lines in the power system are relatively short, and the capacitance to ground of each outgoing line is not much different, which makes the transient voltage value of the non-fault line smaller; while the transient voltage value of the faulty line depends on all the capacitance to ground of the entire system, and the value is much larger than the value corresponding to a single non-faulty line, thus serving as the basis for selecting the faulty line.

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