Distribution network fault positioning method based on particle filter algorithm multi-information fusion

Abstract

A distribution network fault positioning method based on particle filter algorithm multi-information fusion comprises the following steps: extracting transient information, and extracting a transient zero-sequence current high-frequency component by using discrete wavelet transform; calculating a similar entropy and a skewness coefficient of a transient zero-sequence current high-frequency component of each measurement point to obtain a respective corresponding initial fault section position; fusing the two preliminary fault section positions by using a particle filtering algorithm to obtain a fault section position; determining head and tail fault steady-state zero-sequence voltage and power of the fault section; and cutting a fault section, obtaining the zero-sequence voltage and power of a next cutting point by using a particle filter algorithm, carrying out iterative cutting until a threshold condition is met, and outputting a fault position. According to the method, transient zero-sequence current high-frequency components and steady-state zero-sequence voltage power serve as fault characteristic quantities, and the fault positioning function under the conditions of different fault positions, fault closing angles and white noise interference of the active distribution network is achieved.

Description

Technical Field

[0001] The present invention relates to the technical field of distribution network fault location, and in particular to a distribution network fault location method based on multi-information fusion of a particle filtering algorithm. Background Art

[0002] Distributed power sources have become the core component of the new generation of distribution networks due to their flexible power supply, green and low-carbon features. The traditional single-end distribution network forms an active distribution network with the continuous access of distributed power sources. Due to the volatility and randomness of the output of distributed power sources, the fault equivalent circuits and parameters of the active distribution network are complex and changeable, which not only further weakens the fault characteristics, but also makes it difficult to accurately locate the fault section with a single fault characteristic.

[0003] At present, there are three main fault location methods: impedance method, traveling wave method, and signal injection method. The impedance method can be divided into two types: single-ended method and double-ended method. The disadvantage of the impedance ranging method is that when a branch appears on the fault line, the impedance equation no longer holds, so the impedance method is not applicable to complex lines. The advantage of the traveling wave method is that the ranging accuracy is high, but measuring the fault traveling wave requires special recording equipment. The signal injection method can inject different signals according to the characteristics of the system, which is more flexible to use, but it requires matching signal generation equipment and signal collection equipment, so the cost is relatively high. Summary of the invention

[0004] In view of the problem that inaccurate fault positioning is prone to occur when using a single fault characteristic quantity for fault positioning, the present invention provides a distribution network fault positioning method based on multi-information fusion of a particle filtering algorithm, aiming to solve the problem that inaccurate fault positioning is prone to occur when a single fault characteristic quantity is used. The transient zero-sequence current high-frequency component and the steady-state zero-sequence voltage power are used as fault characteristic quantities to realize the fault positioning function under different fault positions, fault closing angles, and white noise interference conditions of the active distribution network.

[0005] The technical solution adopted by the present invention is:

[0006] The distribution network fault location method based on multi-information fusion of particle filtering algorithm includes the following steps:

[0007] Step 1: Extract transient information and use discrete wavelet transform to extract the high-frequency component of transient zero-sequence current;

[0008] Step 2: Calculate the similarity entropy and skewness coefficient of the transient zero-sequence current high-frequency component at each measuring point to obtain the corresponding preliminary fault section position;

[0009] Step 3: Use the particle filter algorithm to fuse the two preliminary fault section locations to obtain the fault section location;

[0010] Step 4: Determine the steady-state zero-sequence voltage and power of the first and last faults in the fault section;

[0011] Step 5: Cut the fault section, use the particle filter algorithm to obtain the zero-sequence voltage and power of the next cutting point, iterate the cutting until the threshold condition is met, and output the fault location.

[0012] In step 1, the short-circuit fault must have a continuous steady-state process when using steady-state fault information for fault location, which is difficult to apply to the neutral point grounding system through arc suppression coil. The discrete wavelet transform (DWT) is used to introduce transient information to improve the positioning accuracy. The wavelet basis function Perform translation and scaling to obtain the mother wavelet function coefficient W φ (a,τ), as shown in formula (1):

[0013]

[0014] Among them, a>0 is the scale factor, which reflects the change of the wavelet basis function itself; τ is the parameter reflecting the translation, which indicates the time domain position of the wavelet basis function in the signal; t is the starting time of the signal data window to be analyzed after the short circuit fault; φ a,τ (t) is the mother wavelet function.

[0015] Then, the mother wavelet function is inner-producted with the signal to be analyzed x(t) to obtain the wavelet coefficient W of the signal to be analyzed. a,τ , as shown in formula (2):

[0016] Wa, τ = <x(t),φa, τ (t)>=W(a,τ) (2);

[0017] in, <x(t),φ a,τ (t)> represents the inner product of the signal to be analyzed and the mother wavelet function; W(a,τ) represents that the wavelet coefficient of the signal to be analyzed is a function of a and τ.

[0018] At this time, the transient component X(t) of the signal to be analyzed is as shown in formula (3):

[0019]

[0020] Substituting the intercepted zero-sequence current data window into equations (1), (2), and (3), the extracted transient zero-sequence current high-frequency component can be obtained as shown in equation (4):

[0021]

[0022] The step 2 comprises the following steps:

[0023] S2.1: Based on the transient zero-sequence current high-frequency component extracted in step 1, the random variable X = {x1, x2, ..., x n}、Y={y1,y2,…,y n} is the transient zero-sequence current state of any two measuring points of the fault line; p(X=i)(i=1,2,…,n), p(Y=i)(i=1,2,…,n) are the corresponding probabilities of each measuring point. The relative entropy between any two measuring points of the fault line is calculated as shown in formula (5):

[0024]

[0025] Among them, D(X||Y) represents the relative entropy value of state X relative to state Y; D(Y||X) represents the relative entropy value of state Y relative to state X; p(x i ) represents the probability of the fault line measurement point X = i; p(y i ) represents the probability of faulty line measurement point Y=i.

[0026] Finally, the relative entropy matrix is ​​formed as shown in formula (6).

[0027]

[0028] Where D represents the relative entropy matrix of any two measurement points of the fault line; that is, the matrix D a , D d The elements in the matrix D b , D c The elements in the middle are obviously smaller. Based on this, the fault section location (m, n) can be preliminarily determined;

[0029] D a Indicates the matrix D whose element values ​​are obviously smaller and located in the upper left corner; D b Indicates the matrix D with obviously larger element values ​​and located in the upper right corner; D c Denotes the matrix with obviously larger element values ​​in D and located in the lower left corner; D d Represents the matrix D whose element values ​​are obviously smaller and located in the lower right corner.

[0030] D(1||1) represents the relative entropy of measurement point 1 relative to measurement point 1; D(m||1) represents the relative entropy of measurement point m relative to measurement point 1; D(1m) represents the relative entropy of measurement point 1 relative to measurement point m; D(m||m) represents the relative entropy of measurement point m relative to measurement point m; D(n||1) represents the relative entropy of measurement point n relative to measurement point 1; D(k||1) represents the relative entropy of measurement point k relative to measurement point 1; D(n||m) represents the relative entropy of measurement point n relative to measurement point m; D(k||m) represents the relative entropy of measurement point k relative to measurement point m ; D(1n) represents the relative entropy of measurement point 1 relative to measurement point n; D(m||n) represents the relative entropy of measurement point m relative to measurement point n; D(1k) represents the relative entropy of measurement point 1 relative to measurement point k; D(m||k) represents the relative entropy of measurement point m relative to measurement point k; D(n||n) represents the relative entropy of measurement point n relative to measurement point n; D(k||n) represents the relative entropy of measurement point k relative to measurement point n; D(n||k) represents the relative entropy of measurement point n relative to measurement point k; D(k||k) represents the relative entropy of measurement point k relative to measurement point k. S2.2: Calculate the skewness coefficient of the transient component, as shown in formula (7):

[0031]

[0032] Among them, S represents the skewness coefficient; x i Represents the i-th value of the sequence to be analyzed; represents the average value of the sequence to be analyzed; n represents the number of values ​​in the sequence to be analyzed.

[0033] The size of the skewness coefficient reflects the degree of asymmetry of the data distribution. When the skewness coefficient is greater than zero, it means that the data distribution is skewed to the right, that is, there are more items with larger values; when the skewness coefficient is less than zero, it means that the data distribution is skewed to the left, that is, there are more items with smaller values. The larger the absolute value of the skewness coefficient, the more obvious the skewness of the data. In practical applications, the distribution characteristics of the data can be judged by observing the data distribution graph or using the skewness coefficient for quantitative analysis.

[0034] S2.3: Obtain two preliminary fault section locations through two transient fault information, namely, matrix D a , D d The elements in the matrix D b , D c The elements in the figure are obviously smaller. Based on this, the fault section location (m,n) can be preliminarily determined; m represents the fault line measurement point m; n represents the fault line measurement point n;

[0035] From formula (7), we can get the skewness coefficient of each measuring point of the fault line as S = {S1, S2, ..., S m ,Sn ,…,S q}, S1, S2, …, Sm represent the skewness coefficients of the fault line measurement points 1, 2, …, m respectively; S n ,…,S q They respectively represent the skewness coefficients of the fault line measurement points n, ..., q.

[0036] If the skewness coefficients from measuring point 1 to measuring point m are all less than zero, and the skewness coefficients from measuring point n to measuring point q are all greater than zero, it can be preliminarily determined that the fault section is (m, n).

[0037] In step 3, in order to improve the accuracy of fault section location, a particle filter algorithm is introduced to correct the preliminary fault section location result obtained by the relative entropy coefficient after preprocessing, and obtain the final fault section location. The particle filter algorithm process includes the following steps:

[0038] Step 3.1: Assume the system state model equation and observation model equation as shown in equations (8) and (9):

[0039] x t =f(x t-1 )+Q t (8);

[0040] y t =h(x t )+R t (9);

[0041] Among them, x t ,y t represents a random variable, f(·) and h(·) are functions of the variable x; t is the number of iterations; f(x t-1 ) means f(x t ) before iteration, the function of variable x; Q t Represents the predicted noise; R t represents the noise of the observation.

[0042] Step 3.2: According to the system model of equation (8), the state of each particle is predicted to obtain the particle sample at the next moment. The prediction equation is as follows:

[0043]

[0044] Where n represents the total number of particles; represents the i-th particle; represents the prediction weight of the i-th particle; δ(·) represents the Dirac function; f t - (x) represents the particle sample at the next moment; x represents the predicted variable; The unit impulse representing the difference between the current particle sample and the i-th particle.

[0045] Step 3.3: According to the observation model and observation data, calculate the weight of each particle and perform normalization. The weight represents the consistency between each particle and the observation data. The update equation is shown in equation (11):

[0046]

[0047] in, represents the weight of the i-th particle; f t + (x) represents the posterior probability density of variable X; η represents the inverse of the sum of the weights of the i-th particle; represents the prediction weight of the i-th particle; n represents the total number of particles; f R [y t -h(x)] represents the observation noise probability density.

[0048] Bring the above particle filter algorithm process into the distribution network measurement data;

[0049] First, the skewness coefficient positioning results of each measurement point in the distribution network after skewness coefficient preprocessing are initialized by particles to obtain represents the i-th particle at the t-th step, i∈(1,k), k is the total number of measurement points in the distribution network, represents the i-th particle at the measurement point m at the t-th step; represents the i-th particle at the measurement point n at the t-th step.

[0050] Assign initial weight values ​​to particles Then predict and generate samples at time t represents the particle sample before particle initialization; Q represents the noise during prediction.

[0051] And calculate the corresponding weight value of the particle at time t: as shown in formula (12)

[0052]

[0053] Among them, f t - (P) represents the weight value corresponding to the particle at time t; represents the weight value before particle initialization; P represents the sample at time t after particle initialization; P t -(i) represents the sample at time t generated after prediction; δ(PP t -(i) ) represents the pulse difference between the sample particle after initialization and the predicted one; k represents the total number of measurement points in the distribution network.

[0054] Then, the result obtained by formula (12) is used as the observation quantity to correct the relative entropy coefficient fault location result after distribution network preprocessing according to formula (13).

[0055]

[0056] Among them, f t + (P) represents the sample corrected after particle prediction; f W (P t -P t - ) represents the difference between the particle weight value after the relative entropy coefficient positioning result and the particle weight value before the prediction at time t; P t Represents the relative entropy coefficient positioning result particle initialization sample; P t - Represents the particle weight value before the relative entropy coefficient positioning result prediction; η represents the inverse of the sum of the weights of the i-th particle.

[0057] Final resampling: Assume that the particle at step t is P t =[P t 1 ,P t 2 ,…,P t i ,…,P t k ], P t 1 ,P t 2 ,…,P t i ,…,P t k They represent the particle samples at measurement points 1, 2, ..., k respectively.

[0058] P t i The next step of particles generated after iteration is When detected The weight value When it is less than the set threshold ζ, a random number j from 1 to k is generated, and P t i =P t i , and iterate again This process repeats until In step 4, since the transformer connected to the DG has a delta connection, the impact of the DG on the zero-sequence component can be ignored. The zero-sequence current and voltage distribution of the infinitesimal interval in the fault section of the active distribution network is as follows: Figure 2 As shown. Among them, U 0(K) , U 0(K+1)is the zero-sequence voltage at the beginning and end of the Kth infinite interval in the upstream section of the fault; U 0(I) , U 0(I+1) is the zero-sequence voltage at the beginning and end of the Ith infinite interval in the downstream section of the fault; I 0(K) ,I 0(I) is the zero-sequence current flowing through the wireless cell K and I; L0, R0, C0, G0 are the zero-sequence inductance, resistance, capacitance, and conductance per unit length of the line; the voltage U on the left and right sides of the fault point 0(K+1) , U 0(I) Satisfying formula (14):

[0059] U 0(K+1) =U 0(K) +I 0(K) Z0

[0060] U 0(I) =U 0(I+1) +I 0(I) Z0 (14);

[0061] Z0=R0+jωL0

[0062] Wherein, Z0 represents the line zero-sequence impedance; ω represents the angular frequency.

[0063] From formula (14), the zero-sequence voltage amplitude distribution of the fault section can be obtained as follows: Figure 3 As shown in Figure 1, the zero-sequence voltage amplitude at the fault point is the largest. Based on the differential idea, the fault section (m, n) is divided into infinite sub-intervals, U 0(st) , U 0(ed) is the zero-sequence voltage at the beginning and end of the sub-interval.

[0064] At this time, the calculation of the fault point position is transformed into seeking the sub-interval with the highest zero-sequence voltage amplitude. When the left and right sides of the sub-interval are infinitely close, the interval can be regarded as the point where the fault occurs.

[0065] In step 5, the final fault section is cut based on the iterative algorithm and particle filtering principle:

[0066] Define the flow from the head end to the end as the forward direction, and the flow from the end end to the head end as the reverse direction. Assuming that the fault section (m, n) is known, it is cut as follows Figure 4 As shown. Among them: S m is the zero-sequence power at the head end of the fault section, V m is the zero-sequence voltage at the head end of the fault section, S n is the zero-sequence power at the end of the fault section, V nis the zero-sequence voltage at the end of the fault section; △V1 is the positive zero-sequence lateral voltage drop of the mk section, δV1 is the positive zero-sequence longitudinal voltage drop of the mk section, △S1 is the positive zero-sequence power loss of the mk section; △V2 is the positive zero-sequence lateral voltage drop of the In section, δV2 is the positive zero-sequence longitudinal voltage drop of the In section, △S2 is the positive zero-sequence power loss of the In section; △V2′ is the reverse zero-sequence lateral voltage drop of the kI section, δV2′ is the reverse zero-sequence longitudinal voltage drop of the kI section, △S2′ is the reverse zero-sequence power loss of the kI section; △V3 is the reverse zero-sequence lateral voltage drop of the In section, δV is the reverse zero-sequence longitudinal voltage drop of the In section, △S3 is the reverse zero-sequence power loss of the In section; R+jX is the line zero-sequence impedance corresponding to the cut section.

[0067] Extract the zero-sequence voltage and power at both ends of the fault section. At this time, forward calculation is performed to calculate the zero-sequence voltage V of the finite number of cutting points k and I in the fault section (m, n). k 、V I , the first and last zero-sequence voltage and power of the next cutting point are obtained through the forward iterative method as shown in equations (15), (16), and (17):

[0068]

[0069] Among them, P m Indicates the active power at the measuring point m; Q m Represents the reactive power at the measuring point m; V m Represents the voltage at the measuring point m; P k Indicates the active power at the measuring point k; Q k Represents the reactive power at the measuring point k; V k represents the voltage at the measuring point k; R represents the resistance between the measuring points m and k; X represents the reactance between the measuring points m and k.

[0070]

[0071] Reverse calculation is performed to calculate the zero-sequence voltage of a finite number of cut points k and I in the fault section (m, n), as shown in equations (18), (19), and (20):

[0072]

[0073] Among them, P I ′ represents the active power at point I during reverse calculation; Q I ′ represents the reactive power at point I during reverse calculation; V I ' shows the voltage at point I when reverse calculation is performed.

[0074]

[0075] Wherein, δV3 represents the longitudinal voltage drop of the In segment.

[0076]

[0077] Among them, V I ′ represents the voltage at point I during reverse calculation; V k ′ represents the voltage at point k during reverse calculation.

[0078] The forward and reverse results of each cutting of the fault section are fused using the particle filter algorithm to obtain the power and voltage information of the next cutting point; then the iterative cutting is continued until the precise location of the fault is obtained.

[0079] The present invention provides a distribution network fault location method based on multi-information fusion of particle filtering algorithm, and the technical effects are as follows:

[0080] 1) The present invention proposes a fault location method that combines transient information and steady-state information, which makes up for the fault location limitation brought by a single amount of fault information and improves the accuracy of fault location.

[0081] 2) The present invention utilizes the particle filter algorithm to perform information fusion, thereby increasing the utilization rate of the fault characteristic quantity with obvious fault characteristics, and is beneficial to the identification of system fault points.

[0082] 3) In order to solve the problem that a single fault characteristic quantity cannot correctly reflect the fault location, this method proposes a particle filter algorithm multi-information fusion model based on multiple fault characteristic quantities. The transient zero-sequence current high-frequency component and steady-state zero-sequence voltage are used as fault characteristic quantities, and the particle filter algorithm model is used to perform multi-information fusion to obtain the fault location.

[0083] 4) The present invention proposes a new method for applying multi-information fusion based on particle filtering algorithm in fault location, using the relative entropy and skewness coefficient of the high-frequency component of zero-sequence current as fault characteristic quantities for locating the fault section; using the particle filtering algorithm to fuse the two transient high-frequency component information to obtain the fault section position; using the zero-sequence voltage of the fault section as the fault characteristic quantity, using forward iteration and particle filtering algorithm fusion to obtain the steady-state zero-sequence voltage and power distribution, thereby achieving effective and accurate fault location of the active distribution network. BRIEF DESCRIPTION OF THE DRAWINGS

[0084] The present invention will be further described below in conjunction with the accompanying drawings and embodiments:

[0085] Figure 1 Fault location flowchart

[0086] Figure 2 Schematic diagram of zero-sequence current and voltage distribution between infinitesimal intervals in the fault section.

[0087] Figure 3 Schematic diagram of zero-sequence voltage amplitude distribution in the fault section.

[0088] Figure 4 This is a schematic diagram of the cutting point distribution in the fault section.

[0089] Figure 5 Schematic diagram of the active distribution network system model.

[0090] Figure 6 This is a schematic diagram of transient information when there is a fault on the upstream side of the DG.

[0091] Figure 7 Schematic diagram of particle weight iteration fault precise positioning when a fault occurs on the upstream side of a DG.

[0092] Figure 8 This is a schematic diagram of transient information when a fault occurs between two DGs.

[0093] Fig. 9 Schematic diagram of particle weight iteration fault precise positioning when a fault occurs between two DGs.

[0094] Fig.10 This is a schematic diagram of transient information when a fault occurs on the downstream side of the DG.

[0095] Fig.11 Schematic diagram of particle weight iteration fault accurate positioning when fault occurs on the downstream side of DG.

[0096] Fig.12 This is a schematic diagram of transient information when the fault closing angle is 60°.

[0097] Fig.13 Schematic diagram of accurate fault location using particle weight iteration when the fault closing angle is 60°.

[0098] Fig.14 This is a schematic diagram of transient information when there is a fault on the upstream side of the DG with 25dB white noise.

[0099] Fig.15 Schematic diagram of particle weight iteration fault accurate positioning when there is a fault on the upstream side of the 25dB white noise DG. DETAILED DESCRIPTION

[0100] A new method for fault location in distribution network based on multi-information fusion of particle filter model. Aiming at the problem that a single fault feature quantity cannot correctly reflect the fault location, this method proposes a multi-information fusion model of particle filter algorithm based on multi-fault feature quantities, takes transient zero-sequence current high-frequency component and steady-state zero-sequence voltage as fault feature quantities, and uses particle filter algorithm model to fuse multi-information to obtain the fault location.

[0101] This method extracts the high-frequency component of transient zero-sequence current after the fault through discrete wavelet transform; defines the similarity entropy and skewness coefficient of the high-frequency component of transient zero-sequence current to obtain the preliminary fault section; realizes the fusion of similarity entropy and skewness coefficient information based on the multi-information fusion model of particle filter algorithm to obtain the location of the fault section; adopts the forward iteration method to cut the fault section, and uses particle filter to fuse the weights of zero-sequence voltage and power at the cutting point at different fault times to obtain the zero-sequence voltage and power at the next cutting point, until the threshold is met and the cutting is stopped to obtain the fault point location. The flow chart of this method is as follows Figure 1 As shown, the principle is simple, the fault location speed is fast, and it is easy to implement, and it can be well applied to active distribution networks.

[0102] The following steps are involved:

[0103] Step 1. Transient information extraction:

[0104] Through formula (2), the wavelet coefficient of the zero-sequence current signal I0(t) can be obtained by taking the inner product with the mother wavelet function, as shown below:

[0105] W a,τ = <I0(t),φ a,τ (t)>=W(a,τ) (2);

[0106] Using the wavelet coefficients obtained by equation (2), the zero-sequence current signal I0(t) can be expressed as

[0107]

[0108] Since the Daubechies wavelet family (dbN) has better wavelet expansion performance, the boundary distortion caused by energy concentration can be controlled by adjusting the support length. Therefore, the present invention adopts the Daubechies wavelet as the wavelet basis function.

[0109] Step 2. Preprocessing of transient information:

[0110] 1) Similarity entropy calculation: The transient zero-sequence current of each measuring point corresponding to the fault line is taken as a measurement system, and the transient zero-sequence current state of any two measuring points of the fault line is expressed by random variables X = {x1, x2, ..., x n}、Y={y1,y2,…,y n}, the corresponding probability is p(X=i)(i=1,2,…,n), p(Y=i)(i=1,2,…,n), the entropy of the transient zero-sequence current at the above two measurement points is defined as follows

[0111]

[0112] In order to highlight the trend and size of the relative entropy value change, the absolute value is used for calculation. The relative entropy value of state X relative to state Y D(X||Y) and the relative entropy value of state Y relative to state X D(Y||X) are as follows:

[0113]

[0114] Assuming that the fault line has k measurement points and the fault section is (m, n), the fault line measurement system contains k different states. The relative entropy value of each measurement point state relative to the k states is calculated to form the following matrix.

[0115]

[0116] The transient zero-sequence current waveforms of the measurement points located upstream and downstream of the fault are consistent, and the relative entropy value is small; conversely, the relative entropy value is large; that is, the matrix D a , D d The elements in the matrix D b , D c The elements in the middle are obviously smaller. Based on this, the fault section location (m, n) can be preliminarily determined.

[0117] 2) Calculation of skewness coefficient: The transient zero-sequence current state at any point of the fault line is expressed as a random variable X = {x1, x2, …, x n} indicates that if the faulty line has a total of q measurement points, its skewness coefficient is calculated as follows.

[0118]

[0119] The peak of the transient zero-mode current sampling value frequency distribution upstream of the fault point is on the right, the long tail is on the left side of the mode, and the data obeys the negative skew distribution, S < 0; the peak of the transient zero-mode current sampling value frequency distribution in the non-fault section is on the left, the long tail is on the right side of the mode, and the data obeys the positive skew distribution, S > 0. From formula (30), the skew coefficient of each measurement point of the fault line can be obtained as S = {S1, S2, ..., S m ,S n ,…,S q If the skewness coefficients from measurement point 1 to measurement point m are all less than zero, and the skewness coefficients from measurement point n to measurement point q are all greater than zero, it can be preliminarily determined that the fault section is (m, n).

[0120] Step 3. Steady-state information analysis:

[0121] Extract the zero-sequence voltage and power at both ends of the fault section. At this time, forward calculation is performed to calculate the zero-sequence voltage V of the finite number of cutting points k and I in the fault section (m, n). k 、V I , as shown in equations (15), (16), and (17):

[0122]

[0123] Reverse calculation is performed to calculate the zero-sequence voltage of a finite number of cutting points k and I in the fault section (m, n), as shown in equations (18), (19), and (20):

[0124]

[0125] The forward and reverse results of each cutting of the fault section are fused using the particle filter algorithm to obtain the power and voltage information of the next cutting point; then the iterative cutting is continued until the precise location of the fault is obtained.

[0126] Step 4. Locate the fault section:

[0127] 1) Definition of particle filter algorithm parameters. The present invention uses the density of particles after particle filtering to analyze the fault location results and presents the fault location process in a 3D graph, where the X and Y axes are the fault measurement points n1, n2, ..., n s , Z is the fault precise location coefficient r, which is defined as follows

[0128]

[0129] Among them, l mn is the line length of the fault section, l f The distance between the fault point and the measuring point near the bus outlet in the fault section is n m The line length, l m is the measuring point n m The line length from the busbar outlet.

[0130] The segment positioning result in the particle filter information fusion is displayed in the XY plane projection. When the particle projection falling into a certain grid p in the XY plane is the densest, the segment corresponding to the grid p is the fault segment. In order to measure the density of particle projection in the XY plane, the present invention defines the plane density N p , which is defined as follows

[0131]

[0132] Where N1 is the number of particle projections falling into the XY plane grid p, S p is the area of ​​the grid p in the XY plane.

[0133] Subsequent work will continue to incorporate other information and display the results in XZ plane projection. The particles whose projection falls on the XZ plane and have the highest linear density on the Z axis are considered as failure points. The linear density is defined as follows

[0134]

[0135] Where, l is the preset unit length of the Z axis, l = l th , N2 is the number of particle projections that fall into the XZ plane after the first projection of the particle filter, and then the second projection is made on the Z axis on this basis and falls into the line segment l.

[0136] 2) Initialization: Initialize the skewness coefficient positioning results of each measurement point in the distribution network after skewness coefficient preprocessing to obtain particles represents the i-th particle at the t-th step, i∈(1,k), k is the total number of measurement points in the distribution network. Assign the particle an initial weight value

[0137] 3) Prediction, generating samples at time t And calculate the corresponding weight value of the particle at time t: as shown in formula (12)

[0138]

[0139] 4) Update, using the result obtained by formula (12) as the observation quantity, the relative entropy coefficient fault location result after distribution network preprocessing is corrected according to formula (13).

[0140]

[0141] (5) Resampling: Assume that the particle at step t is P t =[P t 1 ,P t 2 ,…,P t i ,…,P t k ], P t i The next step of particles generated after iteration is When detected The weight value When it is less than the set threshold ζ, a random number j from 1 to k is generated, and P t i =P t i , and iterate again This process repeats until

[0142] (6) Calculate the plane density, stop resampling, and calculate the particle projection plane density N on the XY plane p , the plane density N p The largest segment is regarded as the faulty segment and the result is output.

[0143] Step 5. Accurately locate the fault:

[0144] (1) Obtain the fault section (m, n) of k groups of faults at the time of the fault 4 power frequency cycles after the fault time i The zero-sequence power and voltage at the beginning and end, that is, S m(t) ={S m(1) ,S m(2) ,…,S m(k)}、V m(t) , S n(t) 、V n(t) , at this time, the number of iterations i = 0;

[0145] (2) Assume that the number of sub-intervals obtained in each iteration is N, the total number of iterations is K, and the length of the fault section is l mn , then at the i-th iteration

[0146] (3) S m(t) 、V m(t) Substitute into equations (15), (16), and (17) to calculate the power and voltage S of the next cutting point m+1 at different times for the m point k group: m+1(t) 、V m+1(t) ; S n(t) 、V n(t) Substitute into equations (18), (19), and (20) to calculate the power and voltage S′ at the cutting point n-1 on point n: n-1(t) , V′ n-1(t) ; Use the particle filter algorithm to filter out the zero-sequence power and voltage at the fault time with larger particle weights in the forward and reverse cutting process to obtain a new fault interval (m, n) i+1 .

[0147] (4) Set the new fault interval (m,n) i+1 Continue cutting iteration and particle filter algorithm screening until l mn ≤l th , l th A threshold is set for the iteration interval. At this time, the fault interval can be regarded as a fault point and output, ending the iteration.

[0148] Simulation verification:

[0149] In order to verify the fault location method proposed in the present invention (hereinafter referred to as the location method), the PSCAD / EMTDC simulation platform was used to build the following Figure 5 The active distribution network model shown. The left side is the system power supply; each measurement point is a 5km overhead line, with a total of 19 measurement points, and fault location verification is performed under different fault locations, different fault closing angles, and noise fault scenarios.

[0150] 1) Simulation verification of fault location on the upstream side of DG: The fault is set upstream of the two DGs, between measurement points 4 and 5, and 3906m away from measurement point 4; take A phase single-phase grounding fault, fault closing angle is 0°, white noise 0dB as an example, the fault time is set to 0.1s, and lasts for 0.2s. Read the zero-sequence current of each monitoring point after the fault occurs, calculate its high-frequency zero-sequence current relative entropy and skewness coefficient; use the particle filter algorithm to fuse transient information to obtain the fault section location; extract the zero-sequence voltage at the beginning and end of the fault section, and iterate the power to cut to obtain the fault location. The simulation results are shown as follows Figure 6 , Figure 7 shown.

[0151] Depend on Figure 6 It can be seen that the different colored dotted lines in the high-frequency component of zero-sequence current indicate the measurement points 1-4 upstream of the fault, and the different colored solid lines indicate the measurement points 5-12 downstream of the fault; the waveform of the high-frequency component of zero-sequence current on the upstream side of the fault point is consistent, and the relative entropy value is small, while the waveform of the high-frequency component of zero-sequence current on the downstream side of the fault point is consistent, and the relative entropy value is large; it can be preliminarily obtained that the fault section is (4,5). In the frequency distribution diagram of the high-frequency component of zero-sequence current, the black, red, blue, and green columns indicate the measurement points 1-4 upstream of the fault, and the other color columns indicate the measurement points 5-12 downstream of the fault. Fig.10 It can be seen that the frequency distribution peak of measurement point 1 close to the busbar is on the right side, and the long tail is on the left side of the mode, which conforms to the negative skewed distribution, and the skewness coefficient is less than zero. The same is true for measurement points 2, 3, and 4. The frequency distribution peak of measurement points 5-12 in the non-fault section on the downstream side of the fault is on the left side, and the long tail is on the right side of the mode, which conforms to the positive skewed distribution, and the skewness coefficient is greater than zero. The skewness coefficients between measurement points 4 and 5 have different signs, and it can be preliminarily obtained that the fault section is (4,5).

[0152] Depend on Figure 7 It can be seen that using the fault transient information as follows Figure 6 The particle filter algorithm information fusion process shown in the figure fuses the above preliminary segment positioning results to obtain the fault segment (4,5) and iterate the cutting point to obtain the following: Figure 7 The particle weight iteration fault is accurately located when the upstream fault is shown. Among them, the X and Y axes represent the measurement points of the section, and the Z axis represents the accurate positioning coefficient; first, the fault section positioning result is projected on the XY plane, as shown by the green triangle, and the density of each grid plane is calculated. The fault section corresponding to the maximum plane density is (4,5); further, the accurate positioning result is projected on the XZ plane, and the linear density on the Z axis is calculated. The accurate positioning coefficient of the fault point corresponding to the maximum linear density is r=0.7745. The calculation shows that the fault point is located in the section (4,5), 3872.3m away from the measurement point 4, and the absolute positioning error is 33.7m.

[0153] 2) Fault location simulation verification between two DGs: The fault is set between the two DGs, between measurement points 7 and 8, and 2818.5m away from measurement point 7; take A phase single-phase grounding fault, fault closing angle is 0°, white noise 0dB as an example, the fault time is set to 0.1s and lasts for 0.2s. The simulation results are shown as follows Figure 8 , Fig. 9 shown.

[0154] The transient component of fault information is as follows: Figure 8 As shown. Figure 8 It can be seen that the waveform of the high-frequency component of the zero-sequence current of measuring points 1-7 is consistent, and the relative entropy value is small. The waveform of the high-frequency component of the zero-sequence current of measuring points 8-12 is consistent, and the relative entropy value is large; the fault section can be preliminarily obtained as (7, 8); the peak of the frequency distribution of measuring points 1-7 is on the right, and the long tail is on the left side of the mode, which conforms to the negative skewed distribution, and the skewness coefficient is less than zero. The peak of the frequency distribution of measuring points 8-12 is on the left, and the long tail is on the right side of the mode, which conforms to the positive skewed distribution, and the skewness coefficient is greater than zero; the skewness coefficients between measuring points 7 and 8 are of different signs, and the fault section can be preliminarily obtained as (7, 8).

[0155] The above preliminary segment location results are fused to obtain the fault segment (7,8). The cutting point is iterated in the fault segment (7,8) to obtain Fig. 9 When the fault occurs between the two DGs shown in the figure, the particle weight iteration fault is accurately located. The plane density of each grid is calculated, and the fault section corresponding to the maximum plane density is (7,8); the accurate positioning result is further projected on the XZ plane, and the linear density on the Z axis is calculated to obtain the accurate positioning coefficient of the fault point corresponding to the maximum linear density r=0.5694. The calculated fault point is located in the section (7,8), 2847.06m away from the measurement point 7, and the absolute positioning error is 28.56m.

[0156] 3) Simulation verification of fault location on the downstream side of DG: The fault is set on the downstream side of the two DGs, between measurement points 10 and 11, and 1598m away from measurement point 10; take A phase single-phase grounding fault, fault closing angle 60°, and white noise 0dB as an example. The fault time is set to 0.1s and lasts for 0.2s. The simulation results are shown as follows Fig.10 , Fig.11 shown.

[0157] Depend on Fig.10It can be seen that the waveform of the high-frequency component of the zero-sequence current of measuring points 1-10 is consistent, and the relative entropy value is small. The waveform of the high-frequency component of the zero-sequence current of measuring points 11 and 12 is consistent, and the relative entropy value is large; the fault section can be preliminarily obtained as (10, 11); the peak of the frequency distribution of measuring points 1-10 is on the right, and the long tail is on the left side of the mode, which conforms to the negative skewed distribution, and the skewness coefficient is less than zero. The peak of the frequency distribution of measuring points 11 and 12 is on the left, and the long tail is on the right side of the mode, which conforms to the positive skewed distribution, and the skewness coefficient is greater than zero; the skewness coefficients between measuring points 10 and 11 are of different signs, and the fault section can be preliminarily obtained as (10, 11).

[0158] The above preliminary segment location results are fused to obtain the fault segment (10,11). The cutting point is iterated in the fault segment (10,11) to obtain Fig.11 The particle weight iteration fault is accurately located when the fault occurs on the downstream side of the DG shown in the figure. The plane density of each grid is calculated, and the fault section corresponding to the maximum plane density is (10,11); the accurate positioning result is further projected on the XZ plane, and the linear density on the Z axis is calculated to obtain the accurate positioning coefficient of the fault point corresponding to the maximum linear density r=0.3269. The calculated fault point is located in the section (10,11), 1634.27m away from the measurement point 7, and the absolute positioning error is 36.27m.

[0159] 4) Fault closing angle 60° simulation verification: The fault is set upstream of the two DGs, between measurement points 4 and 5, and 3906m away from measurement point 4; taking the A-phase single-phase grounding fault as an example, the fault closing angle is 60°, and the white noise is 0dB. Set the ABC three-phase symmetrical fault between measurement points 10 and 11 as an example. The fault occurs at 0.02s. The simulation results are shown as follows Fig.12 , Fig.13 shown. Fig.12 Analysis and Figure 6 The same, no further elaboration is required.

[0160] The particle weight iteration fault accurate positioning at 60° closing angle is as follows Fig.13 As shown in the figure, the accurate positioning coefficient of the fault point is r=0.7904, and the calculated fault point is located in section (4,5), 3951.8m away from the measuring point 4, and the absolute positioning error is 45.8m.

[0161] 3) Adaptive simulation verification under the influence of white noise: The fault is set upstream of DG, between measurement points 4 and 5, and 3906m away from measurement point 4; take phase A single-phase grounding as an example. The fault closing angle is 0°, and 25dB Gaussian white noise is added. The simulation results are shown as follows Fig.14 , Fig.15 shown.

[0162] Depend on Fig.14It can be seen that under the influence of 25dB Gaussian white noise, the transient component of the fault information has a power frequency periodic waveform distortion at the beginning of the intercepted data window, but according to the waveform of the high-frequency component of the zero-sequence current and its frequency distribution at this time, it can still be preliminarily obtained that the fault section is (4,5).

[0163] Particle weight iteration fault accurate positioning under 25dB white noise Fig.15 As shown in the figure, the accurate positioning coefficient of the fault point corresponding to the maximum linear density is r = 0.7907, and the calculated fault point is located in section (4,5), 3953.7m away from the measuring point 4, and the absolute positioning error is 47.7m.

Claims

1. A distribution network fault location method based on multi-information fusion of particle filter algorithm, characterized by The following steps are involved: Step 1: Extract transient information and use discrete wavelet transform to extract the high-frequency component of transient zero-sequence current; Step 2: Calculate the similarity entropy and skewness coefficient of the transient zero-sequence current high-frequency component of each measuring point to obtain the corresponding preliminary fault section position; Step 3: Use the particle filter algorithm to fuse the two preliminary fault section locations to obtain the fault section location; Step 4: Determine the steady-state zero-sequence voltage and power of the first and last faults in the fault section; Step 5: Cut the fault section, use the particle filter algorithm to obtain the zero-sequence voltage and power of the next cutting point, iterate the cutting until the threshold condition is met, and output the fault location.

2. According to claim 1, the method for locating distribution network faults based on multi-information fusion of particle filtering algorithm is characterized by: In step 1, the transient information is introduced by using discrete wavelet transform (DWT) to transform the wavelet basis function Perform translation and scaling to obtain the mother wavelet function coefficient W φ (a,τ), as shown in formula (1): Among them, a>0 is the scale factor, which reflects the change of the wavelet basis function itself; τ is the parameter reflecting the translation, which indicates the time domain position of the wavelet basis function in the signal; t is the starting time of the signal data window to be analyzed after the short circuit fault; φ a,τ (t) is the mother wavelet function; Then, the mother wavelet function is inner-producted with the signal to be analyzed x(t) to obtain the wavelet coefficient W of the signal to be analyzed. a,τ , as shown in formula (2): W a,τ =<x(t),φ a,τ (t)>=W(a,τ)(2); in, <x(t),φ a,τ (t)> represents the inner product of the signal to be analyzed and the mother wavelet function; W(a,τ) represents that the wavelet coefficient of the signal to be analyzed is a function of a and τ; At this time, the transient component X(t) of the signal to be analyzed is as shown in formula (3): Substituting the intercepted zero-sequence current data window into equations (1), (2), and (3), the extracted transient zero-sequence current high-frequency component can be obtained as shown in equation (4):

3. The distribution network fault location method based on multi-information fusion of particle filtering algorithm according to claim 1 is characterized in that: The step 2 comprises the following steps: S2.1: Based on the transient zero-sequence current high-frequency component extracted in step 1, the random variable X = {x1, x2, ..., x n }、Y={y1,y2,…,y n } is the transient zero-sequence current state of any two measuring points of the fault line; the relative entropy between any two measuring points of the fault line is calculated, as shown in formula (5): Among them, D(X||Y) represents the relative entropy value of state X relative to state Y; D(Y||X) represents the relative entropy value of state Y relative to state X; p(x i ) represents the probability of the fault line measurement point X = i; p(y i ) represents the probability of the faulty line measurement point Y=i; Finally, the relative entropy matrix is ​​formed as shown in formula (6): Where D represents the relative entropy matrix of any two measurement points of the fault line; that is, the matrix D a , D d The elements in the matrix D b , D c The middle element is obviously smaller; based on this, the fault section location (m, n) can be preliminarily determined; D a Indicates the matrix D whose element values ​​are obviously smaller and located in the upper left corner; D b Indicates the matrix D with obviously larger element values ​​and located in the upper right corner; D c Denotes the matrix with obviously larger element values ​​in D and located in the lower left corner; D d It represents the matrix with obviously smaller element values ​​in matrix D and located in the lower right corner; D(1||1) represents the relative entropy of measurement point 1 relative to measurement point 1; D(m||1) represents the relative entropy of measurement point m relative to measurement point 1; D(1||) represents the relative entropy of measurement point 1 relative to measurement point m; D(m||m) represents the relative entropy of measurement point m relative to measurement point m; D(n||1) represents the relative entropy of measurement point n relative to measurement point 1; D(k||1) represents the relative entropy of measurement point k relative to measurement point 1; D(n||m) represents the relative entropy of measurement point n relative to measurement point m; D(k||m) represents the relative entropy of measurement point k relative to measurement point m; D(1||n) represents the relative entropy of measurement point 1 relative to measurement point n; D(m||n) represents the relative entropy of measurement point m relative to measurement point m. relative entropy to measurement point n; D(1||k) represents the relative entropy of measurement point 1 relative to measurement point k; D(m||k) represents the relative entropy of measurement point m relative to measurement point k; D(n||n) represents the relative entropy of measurement point n relative to measurement point n; D(k||n) represents the relative entropy of measurement point k relative to measurement point n; D(n||k) represents the relative entropy of measurement point n relative to measurement point k; D(k||k) represents the relative entropy of measurement point k relative to measurement point k; S2.2: Calculate the skewness coefficient of the transient component, as shown in formula (7): Among them, S represents the skewness coefficient; x i Represents the i-th value of the sequence to be analyzed; represents the average value of the sequence to be analyzed; n represents the number of values ​​in the sequence to be analyzed; S2.3: Obtain two preliminary fault section locations through two transient fault information, namely, matrix D a , D d The elements in the matrix D b , D c The middle element is obviously smaller; based on this, the fault section location (m, n) can be preliminarily determined; From formula (7), we can get the skewness coefficient of each measuring point of the fault line as S = {S1, S2, ..., S m ,S n ,…,S q },S1,S2,…,S m They represent the skewness coefficients of the fault line measurement points 1, 2, ..., m respectively; S n ,…,S q They represent the skewness coefficients of the fault line measurement points n, ..., q respectively; If the skewness coefficients from measuring point 1 to measuring point m are all less than zero, and the skewness coefficients from measuring point n to measuring point q are all greater than zero, it can be preliminarily determined that the fault section is (m, n).

4. The distribution network fault location method based on multi-information fusion of particle filtering algorithm according to claim 2 is characterized in that: The size of the skewness coefficient reflects the degree of asymmetry of the data distribution; when the skewness coefficient is greater than zero, it means that the data distribution is skewed to the right, that is, there are more items with larger values; when the skewness coefficient is less than zero, it means that the data distribution is skewed to the left, that is, there are more items with smaller values; the larger the absolute value of the skewness coefficient, the more obvious the skewness of the data; the distribution characteristics of the data can be judged through data distribution graphs or quantitative analysis using the skewness coefficient.

5. The distribution network fault location method based on multi-information fusion of particle filtering algorithm according to claim 1 is characterized by: In step 3, a particle filter algorithm is introduced to correct the preliminary fault section location result obtained by the relative entropy coefficient using the skewness coefficient location result after preprocessing to obtain the final fault section location; The particle filter algorithm process includes the following steps: Step 3.1: Assume the system state model equation and observation model equation as shown in equations (8) and (9): x t =f(x t-1 )+Q t (8); y t =h(x t )+R t (9); Among them, x t ,y t represents a random variable, f(·) and h(·) are functions of the variable x; t is the number of iterations; f(x t-1 ) means f(x t ) before iteration, the function of variable x; Q t Represents the predicted noise; R t represents the noise of the observation; Step 3.2: According to the system model of equation (8), the state of each particle is predicted to obtain the particle sample at the next moment. The prediction equation is as follows: Where n represents the total number of particles; represents the i-th particle; represents the prediction weight of the ith particle; δ(·) represents the Dirac function; represents the particle sample at the next moment; x represents the predicted variable; The unit impulse representing the difference between the current particle sample and the i-th particle; Step 3.3: According to the observation model and observation data, the weight of each particle is calculated and normalized; the weight represents the consistency between each particle and the observation data. The update equation is shown in formula (11): in, represents the weight of the i-th particle; represents the posterior probability density of variable X; η represents the inverse of the weight sum of the i-th particle; represents the prediction weight of the i-th particle; n represents the total number of particles; f R [y t -h(x)] represents the observation noise probability density; Bring the above particle filter algorithm process into the distribution network measurement data; First, the skewness coefficient positioning results of each measurement point in the distribution network after skewness coefficient preprocessing are initialized by particles to obtain represents the i-th particle at the t-th step, i∈(1,k), k is the total number of measurement points in the distribution network, represents the i-th particle at the measurement point m at the t-th step; represents the i-th particle at the measurement point n at the t-th step; Assign initial weight values ​​to particles Then predict and generate samples at time t represents the particle sample before particle initialization; Q represents the noise during prediction; And calculate the corresponding weight value of the particle at time t: as shown in formula (12) in, Indicates the weight value corresponding to the particle at time t; represents the weight value before particle initialization; P represents the sample at time t after particle initialization; Represents the sample at time t generated after prediction; represents the pulse of the difference between the sample particle after initialization and the predicted one; k represents the total number of measurement points in the distribution network; Then update, use the result obtained by formula (12) as the observation quantity to correct the relative entropy coefficient fault location result after distribution network preprocessing according to formula (13); in, represents the samples corrected after particle prediction; Represents the difference between the particle weight value after and before the prediction of the relative entropy coefficient positioning result at time t; P t Represents the relative entropy coefficient positioning result particle initialization sample; Represents the particle weight value before the relative entropy coefficient positioning result prediction; η represents the inverse of the sum of the weights of the i-th particle; Final resampling: Assume that the particle at step t is represent the particle samples at measurement points 1, 2, …, k respectively; P t i The next step of particles generated after iteration is When detected The weight value When it is less than the set threshold ζ, a random number j from 1 to k is generated, and Re-iterate and generate This process repeats until 6. The distribution network fault location method based on multi-information fusion of particle filter algorithm according to claim 1 is characterized by: In step 4, since the transformer connected to the DG has a delta connection, the influence of the DG on the zero-sequence component can be ignored; U0 ( K ) , U 0(K+1) is the zero-sequence voltage at the beginning and end of the Kth infinite interval in the upstream section of the fault; U 0( I ) , U 0(I+1) is the zero-sequence voltage at the beginning and end of the Ith infinite interval in the downstream section of the fault; I 0(K) ,I 0(I) is the zero-sequence current flowing through the wireless cell K and I; L0, R0, C0, G0 are the zero-sequence inductance, resistance, capacitance, and conductance per unit length of the line; the voltage U on the left and right sides of the fault point 0(K+1) , U 0(I) Satisfying formula (14): U 0(K+1) =U 0(K) +I 0(K) Z0 U 0(I) =U 0(I+1) +I 0(I) Z0 (14); Z0=R0+jωL0 Wherein, Z0 represents the zero-sequence impedance of the line; ω represents the angular frequency; From formula (14), we can get the zero-sequence voltage amplitude distribution of the fault section. The zero-sequence voltage amplitude of the fault point is the largest. Divide the fault section (m, n) into infinite sub-intervals, U 0(st) , U 0(ed) is the zero-sequence voltage at the beginning and end of the sub-interval.

7. The distribution network fault location method based on multi-information fusion of particle filter algorithm according to claim 1 is characterized by: In step 5, the final fault section is cut based on the iterative algorithm and particle filtering principle: Define the flow from the head end to the end as the forward direction, and the flow from the end end to the head end as the reverse direction. Assume that the fault section (m, n) is known, where: S m is the zero-sequence power at the head end of the fault section, V m is the zero-sequence voltage at the head end of the fault section, S n is the zero-sequence power at the end of the fault section, V n is the zero-sequence voltage at the end of the fault section; △V1 is the positive zero-sequence lateral voltage drop of the mk section, δV1 is the positive zero-sequence longitudinal voltage drop of the mk section, △S1 is the positive zero-sequence power loss of the mk section; △V2 is the positive zero-sequence lateral voltage drop of the In section, δV2 is the positive zero-sequence longitudinal voltage drop of the In section, △S2 is the positive zero-sequence power loss of the In section; △V2′ is the reverse zero-sequence lateral voltage drop of the kI section, δV2′ is the reverse zero-sequence longitudinal voltage drop of the kI section, △S2′ is the reverse zero-sequence power loss of the kI section; △V3 is the reverse zero-sequence lateral voltage drop of the In section, δV is the reverse zero-sequence longitudinal voltage drop of the In section, and △S3 is the reverse zero-sequence power loss of the In section; R+jX is the zero-sequence impedance of the line corresponding to the cut section; Extract the zero-sequence voltage and power at both ends of the fault section; at this time, forward calculate the zero-sequence voltage V of the finite cutting points k and I in the fault section (m, n) k 、V I , the first and last zero-sequence voltage and power of the next cutting point are obtained through the forward iterative method as shown in equations (15), (16), and (17): Among them, P m Indicates the active power at the measuring point m; Q m Represents the reactive power at the measuring point m; V m Represents the voltage at the measuring point m; P k Indicates the active power at the measuring point k; Q k Represents the reactive power at the measuring point k; V k represents the voltage at the measuring point k; R represents the resistance between the measuring points m and k; X represents the reactance between the measuring points m and k; Reverse calculation is performed to calculate the zero-sequence voltage of a finite number of cut points k and I in the fault section (m, n), as shown in equations (18), (19), and (20): Among them, P I ′ represents the active power at point I during reverse calculation; Q I ′ represents the reactive power at point I during reverse calculation; V I ' represents the voltage at point I during reverse calculation; Among them, δV3 represents the longitudinal voltage drop of the In segment; Among them, V I ′ represents the voltage at point I during reverse calculation; V k ′ represents the voltage at point k during reverse calculation; The forward and reverse results of each cutting of the fault section are fused using the particle filter algorithm to obtain the power and voltage information of the next cutting point; then the iterative cutting is continued until the precise location of the fault is obtained.

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