A Method for Detecting Single-Phase High-Impedance Grounding Faults in Distribution Networks Based on Phasor Measurement

Abstract

The present invention proposes a method for detecting single-phase high-resistance grounding faults in a distribution network based on full phasor measurement. Through the analysis of the line state space, the deterministic functional relationships between phase voltage, phase current and unbalanced current are deduced, and a calculation method for the monitored quantity approximately equal to the fault current is constructed. The coefficients are solved using the measurement data during the fault-free operation of the system, and the current monitored quantity is calculated using the obtained coefficients, thereby realizing fault detection and line selection. The present invention is applicable to point-to-point direct supply dedicated lines, significantly improving the early detection ability of high-resistance grounding faults and providing a new technical means for ensuring the power supply reliability of important loads.

Description

Technical Field

[0001] The present invention relates to the technical field of distribution network detection, and specifically to a method for detecting single-phase high-impedance grounding faults in a distribution network based on full phasor measurement. Background Technique

[0002] With the accelerating advancement of the intelligent upgrade of China's manufacturing industry, the in-depth application of artificial intelligence technology, and the transformation of transportation electrification, the medium-voltage distribution network presents the dual characteristics of a sharp increase in large-capacity and highly sensitive loads and the large-scale access of centralized and distributed energy. The number of dedicated lines directly from the substation to users has increased rapidly. The reliable operation of such lines is directly related to the stability of core industrial production capacity, the continuity of power supply for critical infrastructure, and the new energy consumption efficiency.

[0003] The distribution line passes through a complex environment and is prone to high-impedance grounding faults (HIF) such as wire touching trees and human electric shock. Especially when the grounding fault transition resistance is greater than 10 kΩ, the fault electrical quantity characteristics are weak and it is difficult to be detected by existing equipment, which may lead to major safety accidents such as fires and casualties, or the spread of faults may lead to serious power outages. To ensure the reliability of dedicated line power supply, it is necessary to detect and dispose of high-impedance grounding faults such as wire touching trees early, which requires the relay protection system to have sensitive single-phase high-impedance grounding fault monitoring capabilities. In addition, high-impedance grounding faults belong to weak asymmetric faults, and the unbalanced current generated by factors such as line non-transposition and non-full-phase power supply in the actual distribution network adds difficulty to fault detection and becomes one of the main interference factors for high-impedance grounding fault detection.

[0004] Existing HIF detection methods are mainly divided into transient methods, steady-state methods, and AI methods. Based on the distortion and irregularity of the transient time-domain zero-sequence current waveform, the existing technology realizes the quantification of signal fluctuations through the non-linear analysis of the waveform and then uses mathematical morphology to enhance the fault characteristics to achieve HIF detection. However, when the distortion of the fault signal is extremely small, the sensitivity decreases. In order to better capture the transient characteristics, some scholars use the harmonic components of HIF for detection, but it is prone to failure in the nonlinear load switching scenario. In the existing technology, there is also the use of differential energy detection of positive-sequence current components to reduce the influence of nonlinear loads, but it is limited in application for situations such as unbalanced operation. Although the existing technology combines the traveling wave method with the energy mutation to construct an HIF criterion to solve the confusion of normal transient disturbances, its applicability in actual different systems still needs to be verified. Summary of the Invention

[0005] To solve the above technical problems, the present invention proposes a method for detecting single-phase high-impedance grounding faults in a distribution network based on full phasor measurement, including the following steps:

[0006] The full phasor at the line outlet without a fault and the zero-sequence current There is a functional relationship with the monitored quantity as follows:

[0007] ;

[0008] Wherein, K is a 6×1 complex coefficient vector;

[0009] When the line is operating normally without a fault, let , and use at least 6 sets of measured values of the full-phase and zero-sequence currents to solve the complex coefficient vector K;

[0010] After completing the solution of K, use the real-time measured values of the full-phase and zero-sequence currents and the calculated complex coefficient vector K to calculate the current monitored quantity in real time ;

[0011] Determine whether the current monitored quantity is located in the protection action area. If so, determine that a fault exists and execute the protection action.

[0012] In the preferred embodiment, when the line is fault-free, the phase-to-ground currents of each phase are:

[0013] ;

[0014] Wherein, the three-phase phase-to-ground voltage vector at the outlet of Line1 is , the three-phase current vector is , is the full length of Line1, is the phase-to-ground current of each phase, i = A, B, C; A, B, C represent three phases, is the phase-to-ground admittance matrix of Line1, the unit length impedance matrix of Line1 is Z, and the propagation constant is ;

[0015] Since the zero-sequence current is the sum of the phase-to-ground currents of each of the three-phase lines :

[0016] ;

[0017] Therefore, there is a fixed functional relationship between the full-phase quantity and the zero-sequence current at the line outlet when there is no fault:

[0018] ;

[0019] The monitored quantity is:

[0020] ;

[0021] ​When there is no fault, there is .

[0022] In the preferred embodiment, the zero-sequence current when solving the single-phase grounding fault is:

[0023] If there is a single-phase grounding fault with a shunt admittance of Y f at point l of phase A, the line is divided into two sections, 0~l f and l f ~l, and the solution process for the first section is as follows: f ~l for solution. The solution process for the first section is as follows:

[0024] ;

[0025] ;

[0026] where the superscript (1) or (2) represents the first or second section of the line, is the three-phase current and voltage at the beginning of the second section; the three-phase current vector of the first section of the line is , and the three-phase current vector of the second section of the line is ;

[0027] The three-phase shunt capacitance current is calculated according to the following formula :

[0028] ;

[0029] , are the three-phase shunt voltage vectors at a distance x from the Line1 outlet in the first and second sections of the line respectively;

[0030] For a specific fault, there is also a definite functional relationship between the full vector at the line outlet and the zero-sequence current:

[0031] ;

[0032] If the function obtained during no-fault is still used to solve , then during the fault, there is , and is approximately equal to the fault current.

[0033] In the preferred embodiment, linearized dimensionality reduction is used for solution, and a monitoring quantity equation is constructed:

[0034] Solve for and of the complex coefficient matrices M and N:

[0035] ;

[0036] ;

[0037] Among them is a 3-order matrix, the impedance admittance matrix is a 3-order square matrix, both M and N are 3-order matrices, then:

[0038] ;

[0039] ;

[0040] Among them and are the elements in the i-th row and j-th column of M and N respectively, and represent the j-th element of the vector;

[0041] After arrangement, we get:

[0042] ;

[0043] Then it is simplified to: ;

[0044] With the load fluctuation and line switching during the normal operation of the system, after obtaining at least 6 groups of different and , solve the complex coefficient vector K under the normal operation of the system, and construct the measured quantity equation:

[0045] .

[0046] In the preferred embodiment, the measured quantity calculated under the fault-free condition is approximately equal to 0;

[0047] During single-phase ground fault, the calculated measured quantity is approximately equal to the fault current;

[0048] The influence of the consistency measurement deviation of voltage transformers and current transformers and the direct measurement or three-phase synthesis acquisition method of zero-sequence current on the calculation error of the measured quantity is negligible.

[0049] Compared with the prior art, the present invention has the following beneficial technical effects:

[0050] The present invention uses state space theory to propose a high-resistance grounding fault detection method for distribution networks based on full phasor measurement. Compared with the sensitivity upper limit of traditional zero-sequence current protection in the order of 10 kΩ, the theoretical upper limit of the detection sensitivity of this method is increased to the order of several hundred kΩ, and it is independent of the system grounding method, and has self-adaptability under different line and load parameters, which can greatly improve the system's ability to observe line faults, and can be used for sensitive detection and early elimination of high-hazard and high-risk faults or hidden dangers such as personnel electric shock, tree faults, and cable insulation damage, and greatly improve the prevention ability of electrical line accidents for point-to-point direct supply dedicated lines and the power supply reliability of important sensitive loads.

[0051] The method proposed by the present invention has theoretical completeness and shows extremely high detection sensitivity in digital simulation, but it lacks actual engineering verification. To ensure reliability, in actual application scenarios, the action threshold can be set according to safety requirements, such as the 30 mA threshold for ensuring personal safety in live working scenarios and the 200 mA threshold for preventing fires in the case of wire-touching-tree faults, etc. Description of the Drawings

[0052] Figure 1 is the unbalanced current analysis model for the medium-voltage distribution system;

[0053] Figure 2 is the medium-voltage distribution network simulation model;

[0054] Figure 3 is the simulation result of the fault line;

[0055] Figure 4 is the simulation result of the non-fault line. Detailed Implementation Manner

[0056] Next, the technical solutions in the embodiments of the present invention will be clearly and completely described in conjunction with the accompanying drawings in the embodiments of the present invention. Obviously, the described embodiments are only a part of the embodiments of the present invention, rather than all the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those of ordinary skill in the art without creative efforts shall fall within the protection scope of the present invention.

[0057] 1. When there is no fault on the line, there is a fixed complex linear relationship between the unbalanced current in the running state of the line and the full phasor at the line outlet. The complex coefficient vector K in this relationship is obtained by solving the state space;

[0058] Using the zero-sequence current in the running state of the line , to solve for K.

[0059] Given an analysis system as Figure 1 shown, taking Line1 as the research object therein, for simplicity of analysis, it is assumed that the line parameters are uniform. Since the range and speed of changes in parameters such as the structure and material of the line over time are extremely small, the per-unit-length impedance matrix Z and admittance matrix Y of the line are regarded as constants.

[0060] Define the three-phase ground voltage vector and the three-phase current vector at a distance x from the outlet of Line1 as

[0061] (1);

[0062] (2);

[0063] where the subscript 1 represents Line1, and A, B, and C represent three phases. The line state variables at a distance x from the starting end of the line are:

[0064] (3);

[0065] Then the state equation at a distance x is:

[0066] (4);

[0067] where A is the system matrix:

[0068] (5);

[0069] The analytical solution of Equation (4) is:

[0070] (6);

[0071] For expand at x = 0:

[0072] (7);

[0073] where I is the 6th-order identity matrix.

[0074] Substitute Equation (5) and simplify to get

[0075] (8);

[0076] It is in the form of a series expansion of hyperbolic functions, that is:

[0077] (9);

[0078] where the propagation constant .

[0079] Then the phase voltage at x is:

[0080] (10);

[0081] Then the three-phase line-to-ground currents for the entire line are:

[0082] (11);

[0083] where l is the total length of Line1, is the Line1 line-to-ground admittance matrix:

[0084] (12);

[0085] where is the line-to-ground admittance of each phase, and after simplification:

[0086] (13);

[0087] where are the respective earth currents, and except for the phase voltage at the line outlet on the right side of the formula, and the phase current is the others are all 3D constant complex coefficient matrices determined by the line parameters, indicating that there is a fixed functional relationship between the earth currents of each phase and the phase voltage and phase current at the line outlet.

[0088] Zero-sequence current has the physical meaning of the current in the loop formed by the line and the earth, and is independent of the phase current. Therefore, the zero-sequence current is actually the sum of the earth currents of each phase of the three-phase line, that is:

[0089] (14);

[0090] It can be seen from equations (13) and (14) that under the condition of fixed line parameters, there is a definite functional relationship between the full vector at the line outlet without a fault and the zero-sequence current. Denote this relationship as:

[0091] (15);

[0092] Define the monitored quantity:

[0093] (16);

[0094] Then, without a fault, there is .

[0095] 2. When there is a single-phase ground fault on the line, the unbalanced current in the zero-sequence current can be calculated using the full-phase vector at the line outlet, and the difference between the zero-sequence current and the calculated unbalanced current is not zero.

[0096] If there is a single-phase ground fault with a ground admittance of Y f at the l f of phase A, divide the line into two sections: 0~l f and l f ~l for solution.

[0097] The solution process of the first section is similar to the previous part, except that the line length changes from l to l f , and we get:

[0098] (17);

[0099] (18);

[0100] where the superscript (1) or (2) represents the first or second section of the line, , As the boundary conditions for the solution in the second paragraph. After obtaining , , the three-phase capacitance current to ground can be calculated by the following formula:

[0101] (19);

[0102] Furthermore, it can be known that for a specific fault, there is also a definite non-linear function relationship between the full vector at the line outlet and the zero-sequence current.

[0103] (20);

[0104] If the function f obtained under fault-free conditions is still used to solve , since , there is .

[0105] Comparing the results of the first part and this part, it is easy to see that using the measurement of phase voltage and phase current to compensate for the unbalanced capacitance current in the zero-sequence current, and then realizing the detection of single-phase grounding faults, has basic feasibility in principle.

[0106] 3. Perform linearized dimensionality reduction suitable for engineering applications according to the parameter structure, and construct a six-dimensional constant complex coefficient linear calculation equation for the monitored quantity.

[0107] It can be seen from equation (13) that the key to the problem lies in solving the complex coefficient matrices and of and .

[0108] From the definition of , it is easy to know that is a 3-order matrix, and the other impedance admittance matrices are also 3-order square matrices. Therefore, both M and N are 3-order matrices.

[0109] Equation (13) is rewritten as:

[0110] (21);

[0111] Then equation (14) is:

[0112] (22);

[0113] Where , are the elements in the i-th row and j-th column of M and N respectively, , The superscript j represents the j-th element of the vector.

[0114] After further arrangement:

[0115] (23);

[0116] It can be seen that the coefficients of the phase voltage and phase current are the sums of the corresponding columns in the constant complex coefficient matrices M and N, and are still a constant complex coefficient. When solving, it is not necessary to calculate all 18 matrix elements. Therefore, equation (23) is simplified to:

[0117] (24);

[0118] where K is a 6×1 complex coefficient vector.

[0119] When obtaining at least 6 different and later, the complex coefficient vector K under normal system operation can be solved, and then the monitoring quantity equation can be constructed:

[0120] (25);

[0121] 4. The monitoring quantity is approximately equal to the fault grounding current for the fault line and almost zero for the non-fault line.

[0122] Equation (25) gives the calculation formula of the monitoring quantity , but its physical meaning is still not clear, which is not conducive to setting the action threshold. In this embodiment, its physical meaning is analyzed.

[0123] It is easy to obtain from the expansion formulas of the hyperbolic sine and cosine functions:

[0124] (26);

[0125] (27);

[0126] Given a typical propagation constant of the distribution line , it has the following characteristics: the modulus of the diagonal elements is about 0.03, and the modulus of the non-diagonal elements is about -0.005 to -0.012. If the line length is short (l < 30 km), the error introduced by taking only the first term values in equations (26) and (27) is not greater than 0.5%. Therefore, both take the first term and substitute it into equation (13) to get:

[0127] (28);

[0128] where , represent the admittance and impedance of the whole line.

[0129] It can be seen that in this approximate calculation, the influence of the earth current and the inter-phase circulating current on the phase current is ignored. The current of the entire line is regarded as the same, and the phase voltage is linearly related to the distance. At this time, the above formula has a clear physical meaning. The first term represents the current generated by the phase voltage at the line outlet on the earth admittance of the entire line, and the second term represents the current generated by half of the line voltage drop on the earth admittance of the entire line. This formula is derived from the line state space, and the condition for its establishment is only that the line parameters are constant, regardless of the source-load state at both ends of the line, the line power flow direction, the system neutral point grounding method, etc.

[0130] Since the line parameters change slowly and the fluctuation range is extremely small, 、 can be regarded as constants. Therefore, under the fault-free state, this formula and formula (25) are valid for any phase voltage and phase current.

[0131] When there is a high-resistance grounding fault in phase A where the fault current is much smaller than the line load current, the phase voltage at the line outlet becomes due to the fault. The phase voltage of each phase is still approximately linearly distributed with the distance, and the phase current of each phase is approximately unchanged. Then formula (25) becomes:

[0132] (29);

[0133] The second term is the unbalanced earth capacitance current of the non-fault phase assuming the system is operating normally in the 、 state. And from the definition of zero-sequence current, it can be known that . And is actually the unbalanced current the sum of this non-fault component and the fault grounding current this fault component. Since the fault current is much smaller than the load current, its influence on the second term of formula (29) is small. In addition, the physical meaning of the second term of formula (29) is the earth current generated by the line voltage drop, which is different by one or more orders of magnitude compared with the first term. Therefore, the non-fault component under the fault state is approximately equal to the unbalanced current 、 when the system is operating normally in the state. In summary, it can be obtained that the calculated monitored quantity is approximately equal to the fault current, that is:

[0134] (30);

[0135] 5. The influence of the measurement consistency deviation on the calculation accuracy can be ignored.

[0136] In the previous analysis, the phase voltage, phase current, and zero-sequence current are all accurate values. In practical applications, the measurement errors introduced by the transformers are inevitable. In this chapter, the influence of measurement errors on the method will be analyzed.

[0137] Assume that the ratios of the measured vectors to the true vectors of the three-phase voltage and current transformers 、 、 、 、 、 are the diagonal elements of the diagonal matrix e, and the ratio of the measured vector to the actual vector of the zero-sequence current transformer is , then the measured values are and . When solving for K in a fault-free system, is 0, and the measured zero-sequence current is the unbalanced current with measurement errors , then there is:

[0138] (31);

[0139] After a fault, there is:

[0140] (32);

[0141] where is the full-phase vector at the line outlet after the fault.

[0142] As can be seen from the previous analysis, the sum of the first two terms in the above formula is always 0, and since is close to 1, so there is

[0143] (33);

[0144] Considering the scenario of synthesizing the zero-sequence current from three-phase currents, the measured zero-sequence current is . When there is no fault, there is:

[0145] (34);

[0146] After a fault, there is:

[0147] (35);

[0148] Similar to Equation (33), obviously there is:

[0149] (36);

[0150] That is, when using three-phase currents to synthesize the zero-sequence current, the influence on the calculation error of the monitored quantity is extremely small.

[0151] In summary, the influence of the measurement error of the mutual inductor and the zero-sequence current measurement method on the calculation error of the monitored quantity can be ignored.

[0152] 6. Full-phasor unbalance compensation high-resistance grounding fault detection process and verification

[0153] Based on the above analysis, a full-phasor unbalance compensation high-resistance grounding fault detection method is constructed, and its basic process is as follows:

[0154] a) When there is no fault on the line, let , substitute the measured values of phase voltage, phase current, and zero-sequence current into Equation (25) to calculate the complex coefficient vector K;

[0155] b) After calculating the complex coefficient vector K, calculate the current monitored quantity in real time according to Equation (25);

[0156] c) Determine whether is located in the action area. If so, execute corresponding actions such as alarm, tripping, etc.

[0157] To verify the correctness of this method, a medium-voltage distribution system with n outgoing lines as shown in Figure 2 is established using Matlab / Simulink. Z NG is the neutral grounding impedance. Three lines (Line1 and Line2 are overhead lines, and Line3 is a cable) are simulated with a π model containing unbalanced line parameters, and other lines are simulated in the lumped form of unbalanced three-phase shunt capacitances .

[0158] By changing , adjust the total capacitive current of the system to be less than 30 A, is set to open circuit to simulate a neutral ungrounded system. A grounding resistance with a resistance value of R f is connected to phase A of Line 1 to simulate a grounding fault. The three-phase loads of each outgoing line are independently set for the three-phase load and single-phase load power supply scenarios respectively. The three-phase load scenario accounts for 70%, and random values are assigned according to the requirements that the unbalanced capacity does not exceed 10% and the power factor is not less than 0.9 to simulate the three-phase load fluctuation. The single-phase power supply scenario accounts for 30%, and the power supply phase load capacity and its power factor are randomly determined. Solve the phase voltage, phase current, and zero-sequence current at the outlets of the 3 lines in the phase domain.

[0159] By setting different R f resistance values, different fault transition resistance conditions are simulated. The simulation is carried out in groups, and each group of simulations is for R fThey are respectively set to 10 GΩ, 60 kΩ, 40 kΩ, 20 kΩ, 10 kΩ, 5 kΩ, 3 kΩ, 2 kΩ, and 1 kΩ, with a total of 9 groups. For each group, 3 lines are set with different random capacities, and 3 lines are respectively given unbalanced three-phase loads within the unbalance tolerance requirement range for 100 simulations.

[0160] To simulate the measurement error of the mutual inductor in the actual application scenario, a fixed proportion deviation is added to the simulation data. The accuracy requirement of a 0.2-level mutual inductor is that the measured amplitude error is not higher than 0.2%, and the angle error does not exceed 2 minutes. To simulate the worst measurement conditions, the simulation is carried out according to a measurement error not higher than 1%. The specific method is to generate a random angle vector with an amplitude from -0.01 to 0.01 and superimpose it on the 1 vector to form a measurement error simulation vector. Each phase voltage, phase current, and zero-sequence current corresponds to a measurement error simulation vector, and its simulation value is multiplied by the corresponding error simulation vector to simulate the inherent measurement error of each mutual inductor.

[0161] After calculating K using the noise-added data of the non-faulty group, the monitor values of each outgoing line in each fault resistance scenario are calculated using the obtained K and the noise-added data.

[0162] Taking R f = 10 GΩ simulation group as the system non-faulty group, the complex coefficient vector K of each line is calculated by the least squares method, and then the monitor value of the corresponding line is solved according to equation (25). Repeat the simulation 10 times, and take the one with the largest fluctuation range of the zero-sequence current. Compare the accurate value of the fault current, the measured value of the monitor, and the measured value of the zero-sequence current. As Figure 3 、 4 shown, where Figure 3 in (a)-(f) are the simulation results when the fault resistance of the faulty line is 10 GΩ, 60 kΩ, 20 kΩ, 10 kΩ, 5 kΩ, and 2 kΩ, Figure 4 in (a)-(f) are the simulation results when the fault resistance of the non-faulty line is 10 GΩ, 60 kΩ, 20 kΩ, 10 kΩ, 5 kΩ, and 2 kΩ.

[0163] From Figure 3 in (a), Figure 4 in (a)-(f) of the simulation results, it can be seen that when the simulated system is operating normally, under the influence of unbalanced line parameters and unbalanced loads, the amplitude of the line zero-sequence current (all unbalanced currents) can reach about 0.7 A magnitude, and the fluctuation range of the amplitude can reach about 0.5 A magnitude. For systems or lines with a greater degree of unbalance, these two amplitudes may be larger, which is consistent with on-site experience.

[0164] Perform data processing according to the method proposed by the present invention. Calculate K using the phase voltage and phase current under normal operation of this line, and then calculate the monitored quantity according to Equation (25). For all groups of the fault-free line and all groups of the non-faulty lines, it does not exceed 1 mA. During a fault, compared with the error does not exceed 30 mA, and this error increases as the fault resistance decreases and only appears in the 2 kΩ group.

[0165] Conduct more groups of simulations to test the applicability of the method under different grounding systems and scenarios of synthesizing zero-sequence current from three-phase currents. Change Adjust the total capacitive current of the system to about 50 A, Set it as an arc suppression coil with overcompensation of 8% to simulate a resonant grounding system. Change all three lines to cable lines and change Adjust the total capacitive current of the system to about 120 A, Set it as a 10 Ω resistor to simulate a small-resistance grounding system. Increase the fixed measurement error of the current transformer to a random value within 1% to simulate harsh measurement conditions. Still conduct simulations in the same way as in the previous part. Conduct 10 simulations for each of the three grounding methods and take the set of results with the largest average relative error. Among all the simulation results, the amplitude of the monitored quantity of the non-faulty line is less than 1 mA, and the relative error amplitude and the maximum absolute error of the monitored quantity of the faulty line compared with the fault current are shown in Table 1.

[0166] It can be seen from the simulation results that when there is imbalance in the system itself, the amplitude of the zero-sequence current without a fault is not 0, and the amplitude of the zero-sequence current may decrease when a single-phase grounding fault occurs. If the zero-sequence current is obtained by synthesizing three-phase currents, the consistency deviation of the current transformer leads to the measured zero-sequence current amplitude being greater than the true zero-sequence current amplitude. Assume that the maximum amplitude of the unbalanced current during normal operation of the system reaches 2 A, and the maximum range of amplitude fluctuation is 1 A. Then the former limits the upper limit of the fault transition resistance tolerance of the zero-sequence amplitude over-limit detection method to about 3 kΩ, and the latter limits the upper limit of the fault transition resistance tolerance of the sudden change detection method to about 6 kΩ.

[0167] In the case of serious consistency deviation in the measurement accuracy of the current transformer, the method of the present invention can still effectively compensate for the unbalanced current introduced by line parameters and load imbalance. The absolute error between the obtained monitored quantity and the actual fault current is at the mA level. Therefore, when setting the fault detection threshold based on the monitored quantity, it is no longer necessary to consider the fluctuation range of the unbalanced current, but to consider the maximum fluctuation range of the calculation error of the monitored quantity relative to the fault current. The theoretical upper limit of the fault transition resistance tolerance can reach several hundred kΩ.

[0168] Since the average relative error of the monitored quantity compared to the actual fault current is less than 0.7%, and the maximum error is less than 1%, it can be considered that the calculated monitored quantity is the fault current. Considering the line selection scenario, since the calculation of the monitored quantity only depends on the status of this line, when a fault occurs on a non - this line or unbalanced load on this line causes three - phase imbalance of the system, the amplitude of the monitored quantity is not higher than 1 mA. Therefore, by determining with a very small threshold (such as 10 mA), it can be determined whether this line is a fault line without comparing with other lines.

[0169] Table 1 Simulation results of the error of the monitored quantity under different scenarios

[0170]

[0171] In Table 1, Inf represents the non - fault group, and - represents meaningless.

[0172] The all - phasor unbalanced compensation high - resistance grounding fault detection method proposed by the present invention based on the state - space theory. Compared with the sensitivity upper limit of about 10 kΩ of the traditional zero - sequence current protection, the theoretical upper limit of the detection sensitivity of this method is increased to several hundred kΩ, and it is independent of the system grounding method. It can greatly improve the system's ability to observe line faults, and can be used for sensitive detection and early elimination of high - risk faults or hidden dangers such as personal electric shock, tree faults, and cable insulation damage, greatly improving the prevention ability of electrical line accidents for point - to - point direct - supply dedicated lines and the power supply reliability of important sensitive loads.

[0173] For those skilled in the art, it is obvious that the present invention is not limited to the details of the above - mentioned exemplary embodiments, and can be implemented in other specific forms without departing from the spirit or basic characteristics of the present invention. Therefore, the embodiments should be regarded as exemplary and non - restrictive. The scope of the present invention is defined by the appended claims rather than the above description. Therefore, all changes falling within the meaning and scope of the equivalent elements of the claims are intended to be included in the present invention. Any reference signs in the claims should not be regarded as limiting the claimed rights.

Claims

1. A method for detecting single-phase high-resistance grounding faults in a distribution network based on full phasor measurement, characterized in that, It includes the following steps: Full phasor at the line outlet when there is no fault , zero-sequence current and the monitored quantity There is a functional relationship as follows: ； Among them, K is a 6×1 complex coefficient vector; When the line operates normally without faults, let , and use the measured values of at least 6 groups of different positive-sequence phasors and zero-sequence currents to solve the complex coefficient vector K; After the solution of K is completed, the current monitored quantity is calculated in real time by using the real-time measured values of the full phasor and zero-sequence current and the calculated complex coefficient vector K ; Determine the current monitored quantity Whether it is located in the protection action area. If so, determine that a fault exists and execute the protection action; When there is no fault in the line, the current of each phase to the ground is: ； Among them, the three-phase line-to-ground voltage vectors at the exit of Line1 are , and the three-phase current vectors are , is the total length of Line1, is the line-to-ground current of each phase, i = A, B, C; A, B, and C represent the three phases, is the line-to-ground admittance matrix of Line1, the impedance matrix per unit length of Line1 is Z, and the propagation constant is ; Due to the zero-sequence current which is the sum of the respective line-to-ground currents of the three-phase lines as follows: ； Therefore, the full phasor at the line outlet when there is no fault and the zero-sequence current have a fixed functional relationship: ； Monitoring quantity is as follows: ； When there is no fault ; Solve the zero-sequence current during single-phase ground fault: If there is a single-phase grounding fault with a shunt admittance to ground of Y at point A-phase l f , the line is divided into two sections, 0~l f and l f ~l, for solution. The solution process for the first section is as follows: f ​ ； where the superscripts (1) or (2) represent the first or second section of the line, is the three-phase current and voltage at the start of the second section; the three-phase current vectors of the first section of the line are , and the three-phase current vectors of the second section of the line are ; calculate the three-phase capacitive current to ground according to the following formula : ； and are the three-phase line-to-ground voltage vectors at a distance x from the Line1 outlet in the first and second line segments, respectively. For a specific fault, there is also a definite functional relationship between the full vector at the line outlet and the zero-sequence current: ； If the function obtained under fault-free conditions is still used for solution , then under fault conditions, there is , and is approximately equal to the fault current; Use linearized dimensionality reduction to solve and construct the monitored quantity equation: Solve and for the complex coefficient matrices M and N: ； wherein is a third-order matrix. The impedance admittance matrix is a third-order square matrix. Both M and N are third-order matrices, then: ； Among them and are the elements in the \(i\)-th row and \(j\)-th column of \(M\) and \(N\) respectively, and represents the \(j\)-th element of the vector; After arrangement, we get: ； Then it simplifies to: ; With the load fluctuations and line switching during the normal operation of the system, obtain at least 6 different and After that, solve the complex coefficient vector K under the normal operation of the system and construct the monitoring quantity equation: 。 2. The single-phase high-resistance grounding fault detection method for a distribution network based on all-phase measurement according to claim 1, wherein The monitored quantity calculated under no-fault condition is approximately equal to 0; During single-phase ground fault, the monitored quantity calculated is approximately equal to the fault current; The influence of the consistency measurement deviation of the voltage transformer and current transformer and the direct measurement or three-phase synthesis acquisition method of the zero-sequence current on the calculation error of the monitored quantity is negligible.

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