Two-stage fault location method and device for distribution network based on synchronous phasor measurement

Abstract

The application provides a power distribution network two-stage fault locating method and device based on synchronous phasor measurement, comprising the following steps: acquiring network topology before fault, voltage phasor measurement data before and after fault and three-phase active and reactive power injection pseudo measurement of all unbalanced nodes; constructing a virtual current fault locating model, enumerating each possible fault line, solving the fault locating model, obtaining a first matching index value, sorting all first matching index values in ascending order, selecting the first u lines to construct a candidate fault line set; performing nonlinear fault state estimation (SE) on all associated nodes of the candidate fault line in sequence, selecting the node with the highest matching degree as the fault line endpoint, and obtaining one endpoint of the fault line; and determining the fault line and the accurate fault position by using other hardware-based methods; the application can realize high fault locating accuracy under the condition of limited muPMU.

Description

Technical Field

[0001] This invention relates to the field of power distribution network technology, and in particular to a two-stage fault location method and device for power distribution networks based on synchronous phasor measurement. Background Technology

[0002] The distribution network is closely connected to users and is a crucial link in ensuring reliable power supply. However, the distribution network has a complex structure, operates in a harsh environment, and has a high probability of faults. If faults are not handled promptly, they can seriously affect the reliable power supply to users. Fault handling includes fault location, isolation, and power restoration, among which fault location is the foundation for fault isolation and power restoration, and is of great significance for the safe and reliable operation of the distribution network. However, the distribution network suffers from three-phase imbalance and insufficient measurement configuration, making it difficult to directly apply fault location methods used in transmission networks.

[0003] Existing methods for fault location in distribution networks can be broadly categorized into: impedance-based methods, traveling wave-based methods, data-driven methods, fault power flow calculation or state estimation (SE) methods, and sparse optimization-based methods.

[0004] Traditional impedance-based methods are simple to implement, but due to the complexity of distribution network structures and the large number of branches, they may mislead users into locating faults in adjacent branches. Voltage sag-based algorithms can be considered a type of impedance method, using the transferred impedance matrix and measured voltage deviation to estimate the fault current and match the fault point. However, this method requires a large number of measurement devices and is only applicable to constant impedance loads. Traveling wave-based methods locate faults by the arrival time of the reflected fault wave, unaffected by network parameters, fault type, or operating mode. However, this method relies on high-sampling-rate measurement devices, and the presence of branches and transformers in the system reduces accuracy. Data-driven methods encompass various techniques from signal processing to artificial intelligence, overcoming the limitations of driving techniques by sufficiently approximating nonlinear problems. However, these methods require large amounts of fault data for training, have poor interpretability, and cannot adapt to changes in network topology.

[0005] The fault power flow calculation / SE matching method injects fault current into suspected nodes, performs power flow calculation / SE, calculates the system state variables at fault steady state, compares the voltage estimate with the measured value, and selects the node with the highest matching degree; however, this type of method has a large computational load and is relatively slow.

[0006] To address the aforementioned issues, it is necessary to research an efficient fault location method based on two-stage model matching. This method can achieve high fault location accuracy with limited micro phasor measurement units and improves the overall calculation speed. Summary of the Invention

[0007] The two-stage fault location method for distribution networks based on synchronous phasor measurement includes the following steps:

[0008] Acquire the network topology before the fault, voltage phasor measurement data before and after the fault, and pseudo-measurements of three-phase active and reactive power injection at all unbalanced nodes;

[0009] A virtual current fault location model is constructed, each line that may be faulty is enumerated, and the fault location model is solved to obtain the first matching index value. All first matching index values ​​are sorted in ascending order, and the top u lines are selected to construct a candidate fault line set.

[0010] Nonlinear fault state estimation (SE) is performed sequentially on all associated nodes of the candidate faulty line. The node with the highest matching degree is selected as the endpoint of the faulty line. After obtaining an endpoint of the faulty line, other hardware-based methods are used to determine the faulty line and the precise location of the fault.

[0011] Furthermore, the method for constructing the virtual current fault location model is as follows:

[0012] Define virtual current:

[0013] I v =YΔV (17)

[0014] In the formula: The virtual complex current injection vector; ΔV = V′ - V is the complex voltage difference vector between the fault and the fault state; The positive-sequence node admittance matrix before the fault; the virtual injection currents of nodes m and n at both ends of the faulted line are not zero, and the virtual injection current of any node k except for the nodes at both ends of the faulted line and unbalanced nodes is zero.

[0015] By extracting the rows and columns corresponding to the balance nodes from the matrices and vectors in (9), (9) can be rewritten as:

[0016]

[0017] In the formula: Y is the virtual complex current injection vector at slack node 1; ΔV1 is the complex voltage difference vector at slack node 1; 11 Y is the positive-sequence self-admittance at equilibrium node 1; 12 Y 21 This is the positive-sequence series admittance of line 1-2; Y This is the remaining node admittance matrix after removing the relevant part of the equilibrium node from the positive-order node admittance matrix; I v The virtual complex current injection vector excluding equilibrium node 1; Δ V The complex voltage difference vector between the fault and the fault state, excluding the balancing node 1.

[0018] If only the non-equilibrium nodes are retained, then equation (9) becomes:

[0019] I v = Y Δ V (19)

[0020] Constructing the unknown virtual current vector I v Linear observation model associated with changes in voltage phasor measurements:

[0021] Δ V = ZI v +η (20)

[0022] In the formula: η is the error value;

[0023] Extract the configuration voltage phasor measurement n o Rows corresponding to each node:

[0024] Δ V o = Z o I v +η o (twenty one)

[0025] In the formula: the subscript o represents the row corresponding to the observable node.

[0026] Furthermore, the method for solving the fault location model is as follows:

[0027] The first matching index value is obtained by solving the linear regression problem using the linear least squares method (15); for a specific faulty line l, the formula for calculating the first matching index value is:

[0028]

[0029] In the formula: From Z o The submatrix consists of the two columns corresponding to the l-th line; MI is the matching index value. The optimal solution for the following least squares model is:

[0030]

[0031] Furthermore, when performing nonlinear fault state estimation (SE) for the associated nodes of candidate faulty lines, a state estimation SE model is established based on the weighted least squares (WLS) estimation criterion:

[0032] minJ(x)=[zh(x)] T R -1 [zh(x)] (24)

[0033] In the formula: J(x) is the objective function; For measurement vectors; For the measurement error vector, Let be the covariance matrix of e; h(·) is the vector of nonlinear measurement functions; This is a state variable vector, including the real and imaginary parts of the three-phase complex voltages at nodes other than the slack node:

[0034] Setting the first derivative of the objective function to 0, and linearizing it using Taylor expansion at the initial point x0, we get:

[0035]

[0036] -H T (x0)R -1 [zh(x0)-H(x0)·Δx]=0 (26)

[0037] In the formula: H is the Jacobian matrix; To obtain the partial derivative of the objective function; Δx is the change in the state variables;

[0038] Starting from the initial point x0, the Gauss-Newton method is used to solve (24). The corrected equation for the k-th iteration is:

[0039] Δx (k) =[H T (x (k) )R -1 H(x (k) )] -1 H T (x (k) )R -1 [zh(x (k) (27)

[0040] In the formula: Δx (k) x represents the change in state variables during the k-th iteration; (k) This refers to the state variables at the k-th iteration.

[0041] After converting the node injection power measurement to the node injection current measurement, the Jacobian matrix becomes a constant matrix. After the Jacobian matrix is ​​constant, the correction equation (25) for the k-th iteration becomes:

[0042] Δx (k) =[H T R -1 H] -1 H T R-1 [zh(x (k) (28).

[0043] Furthermore, when performing nonlinear fault state estimation on the associated nodes of candidate faulty lines, the load model needs to be considered during the fault state estimation iteration process. In each iteration, the load is corrected based on the node voltage obtained in the previous iteration, as shown in the following formula:

[0044]

[0045] In the formula: These are the values ​​of node i at the k-th iteration. For both active and reactive loads, if there is no distributed power source at node i, then These are the nodes i before the fault. Active and reactive loads; For node i in the k-th iteration Phase voltage; α is the rated phase voltage of the power distribution system; α1, β1, and γ1 are the coefficients of the constant power, constant current, and constant impedance components of the active load, respectively; α 2 β2 and γ2 are the coefficients of the constant power, constant current and constant impedance components of the reactive load, respectively.

[0046] Furthermore, when performing nonlinear fault state estimation on the associated nodes of the candidate faulty line, the fault point current needs to be compensated and injected into the assumed virtual fault point. In the k-th iteration, the fault current can be calculated by the following formula:

[0047]

[0048] In the formula: These are the three-phase complex injection currents at the root node, fault point f, and node i during the k-th iteration, respectively.

[0049] Furthermore, the second matching index value of candidate fault node i consists of two parts: the L1 norm of the state estimation measurement residual vector and the terminal node voltage magnitude measurement residual vector.

[0050]

[0051] In the formula: These are estimates of the state variables; These are the end nodes i respectively Measured and estimated values ​​of phase voltage amplitude; Ω end It is the set of all end nodes;

[0052] After calculating the second matching index value for all candidate fault points, the node with the lowest second matching index value is selected as an endpoint of the faulty line:

[0053]

[0054] Furthermore, when there is no voltage amplitude measurement at the downstream node of the fault point, the matching method based on fault state estimation cannot identify the fault node, and voltage amplitude measurement needs to be configured at each end node.

[0055] A two-stage fault location device for distribution networks based on synchronous phasor measurement includes:

[0056] The data acquisition module is used to acquire the network topology before the fault, the voltage phasor measurement data before and after the fault, and the pseudo-measurement of the three-phase active and reactive power injection of all unbalanced nodes.

[0057] The candidate fault line set construction module is used to construct a virtual current fault location model, enumerate each line that may be faulty, solve the fault location model, obtain the first matching index value, sort all the first matching index values ​​in ascending order, and select the top u lines to construct the candidate fault line set.

[0058] The fault line and precise fault location determination module is used to perform nonlinear fault state estimation (SE) on all associated nodes of the candidate fault line in sequence, select the node with the highest matching degree as the fault line endpoint, and after obtaining an endpoint of the fault line, use other hardware-based methods to determine the fault line and the precise fault location.

[0059] A computing device, comprising:

[0060] One or more processing units;

[0061] A storage unit is used to store one or more programs.

[0062] When the one or more programs are executed by the one or more processing units, the one or more processing units execute the two-stage fault location method for distribution networks based on synchronous phasor measurement as described above.

[0063] A computer-readable storage medium having processor-executable non-volatile program code, wherein when the computer program is executed by the processor, it implements the steps of the two-stage fault location method for distribution networks based on synchronous phasor measurement as described above.

[0064] The advantages and positive effects of this invention are:

[0065] This invention, based on a sparse optimization method, finds that selecting the top-1 lines results in a low success rate for fault location when measurement information is insufficient. However, by relaxing the criteria and selecting the top-u lines, the success rate of fault line selection can be significantly improved, thereby greatly reducing the search space for the second-stage SE matching. Through the two-stage fault location method, high fault location accuracy can be achieved with limited μPMU under different load models, fault types, μPMU measurement and pseudo-measurement error levels, and high-resistance faults. Furthermore, the fault line selection method based on linear model matching proposed in this invention has extremely fast computation speed, and the two-stage method uses the candidate fault nodes selected in the first stage as the search space, making the overall computation speed about 5 times faster than using only the second stage. Attached Figure Description

[0066] The technical solution of the present invention will be further described in detail below with reference to the accompanying drawings and embodiments. However, it should be understood that these drawings are designed for illustrative purposes only and are not intended to limit the scope of the present invention. Furthermore, unless specifically indicated, these drawings are intended only to conceptually illustrate the structural construction described herein and are not necessarily drawn to scale.

[0067] Figure 1 This is a flowchart of a two-stage fault location method for distribution networks based on synchronous phasor measurement provided in an embodiment of the present invention.

[0068] Figure 2 This is a 33-node distribution network provided in Embodiment 2 of the present invention;

[0069] Figure 3 The success rate (constant impedance load) of the screening method based on linear model matching provided in Embodiment 2 of the present invention;

[0070] Figure 4 The success rate (ZIP load) of the screening method based on linear model matching provided in Embodiment 2 of the present invention;

[0071] Figure 5 This refers to the top-6 success rate under different measurement errors provided in Embodiment 2 of the present invention.

[0072] Figure 6 The success rate of fault location based on SE / SC matching (constant impedance load) provided in Embodiment 2 of the present invention;

[0073] Figure 7 The fault location success rate (ZIP load) based on SE / SC matching provided in Embodiment 2 of the present invention;

[0074] Figure 8 The success rate of the two-stage fault location method provided in Embodiment 2 of the present invention (constant impedance load);

[0075] Figure 9 The success rate (ZIP load) of the two-stage fault location method provided in Embodiment 2 of the present invention. Detailed Implementation

[0076] To make the objectives, technical solutions, and advantages of this invention clearer, the technical solutions of the embodiments of this invention will be described in more detail below with reference to the accompanying drawings. In the drawings, the same or similar reference numerals denote the same or similar elements or elements having the same or similar functions throughout. The described embodiments are some, but not all, embodiments of this invention. The embodiments described below with reference to the accompanying drawings are exemplary and intended to explain this invention, and should not be construed as limiting the invention. All other embodiments obtained by those skilled in the art based on the embodiments of this invention without creative effort are within the scope of protection of this invention.

[0077] The embodiments of the present invention will now be described in detail with reference to the accompanying drawings.

[0078] Example 1

[0079] This embodiment provides a two-stage fault location method for distribution networks based on synchronous phasor measurement, including the following steps:

[0080] Acquire the network topology before the fault, voltage phasor measurement data before and after the fault, and pseudo-measurements of three-phase active and reactive power injection at all unbalanced nodes;

[0081] A virtual current fault location model is constructed, each line that may be faulty is enumerated, and the fault location model is solved to obtain the first matching index value. All first matching index values ​​are sorted in ascending order, and the top u lines are selected to construct a candidate fault line set.

[0082] Nonlinear fault state estimation (SE) is performed sequentially on all associated nodes of the candidate faulty line. The node with the highest matching degree is selected as the endpoint of the faulty line. After obtaining an endpoint of the faulty line, other hardware-based methods (such as the traveling wave method) are used to determine the faulty line and the precise location of the fault.

[0083] Specifically, when constructing a virtual current fault location model, the virtual current model is first established:

[0084] For a given n b For an unbalanced distribution network with n nodes, the network equation based on the three-phase node admittance matrix is ​​as follows:

[0085] I abc =Y abc V abc (33)

[0086] In the formula: For the injection vector of three-phase complex current; It is a three-phase complex voltage vector; This is the admittance matrix of the three-phase nodes.

[0087] Since all types of faults have positive-sequence components, fault localization employs a positive-sequence network equation based on the positive-sequence node admittance matrix:

[0088] I = YV (34)

[0089] In the formula: Inject vectors into the positive-sequence complex current prior to the fault; This is the positive-sequence complex voltage vector before the fault. This is the admittance matrix of the positive sequence nodes before the fault.

[0090] Assuming all loads in the system are constant impedance loads, then the pre-fault positive sequence injection complex current of all unbalanced nodes k in (2) is:

[0091]

[0092] In the formula: I k V is the positive-sequence re-injection current at node k before the fault; k Y is the positive-sequence complex voltage of node k before the fault; kk Y ki These are positive-order self-admittance and mutual admittance, respectively; y ki Let y be the positive-sequence series admittance of line ki; k Ω represents the positive-sequence parallel admittance and load admittance of node k; b For the set of all nodes; Let k be the set of neighboring nodes.

[0093] The elements corresponding to node k in I, V, and Y can be obtained through the Fortescue transformation:

[0094]

[0095] In the formula: The three-phase complex current injection vector before the fault at node k; The three-sequence re-injection current before the fault at node k; The three-phase complex voltage vector before the fault at node k; The three-sequence complex voltage vector before the fault at node k; Let be the three-phase node admittance matrix before the fault at node k; Let be the three-order node admittance matrix before the fault at node k; and:

[0096]

[0097] When a fault occurs on line m-n and the fault enters the steady state, the positive-sequence network equation based on the positive-sequence nodal admittance matrix still holds:

[0098] I′ = Y′V′ (38)

[0099] Where: is the positive-sequence complex current injection vector in the fault; is the positive-sequence complex voltage vector in the fault; is the positive-sequence nodal admittance matrix in the fault.

[0100] According to (2) and (6), the complex injection currents at the fault line endpoints m before and during the fault are:

[0101]

[0102] Where: V m is the positive-sequence complex voltage of node m before the fault; V i is the positive-sequence complex voltage of node m before the fault; V n is the positive-sequence complex voltage of node n before the fault; I′ m is the positive-sequence complex injection current of node m during the fault; V m ′ is the positive-sequence complex voltage of node m during the fault; V i ′ is the positive-sequence complex voltage of node i during the fault; V f ′ is the positive-sequence complex voltage of node f during the fault; V n ′ is the positive-sequence complex voltage of node n during the fault; is the set of adjacent nodes of node m except node n; 0 < c < 1 is the ratio of the length of the m-f segment to the m-n line; y mi is the positive-sequence series admittance of line m-i; y mn is the positive-sequence series admittance of line m-n; y mf is the positive-sequence series admittance of line m-f.

[0103] Similarly, the complex injection currents at the fault line endpoint n before and during the fault can also be derived.

[0104] For any node k except the two endpoints of the fault line and the swing node, its complex injection currents before and during the fault are:

[0105]

[0106] Define the virtual current:

[0107] I v = YΔV (41)

[0108] Where: The virtual complex current injection vector; ΔV = V′ - V is the complex voltage difference vector between the fault and the fault state.

[0109] Subtracting the two equations in (7), we can see that the virtual injection currents at nodes m and n at both ends of the faulty line are not zero:

[0110]

[0111] In the formula: Inject a vector into the virtual complex current at node m; Inject the virtual complex current vector at node m; y ni The positive-sequence series admittance of line mi; ΔV m =V m '-V m ;ΔV i =V i '-V i ;ΔV n =V n '-V n .

[0112] Subtracting the two equations in (8), we can see that the virtual injection current at any node k, except for the nodes at both ends of the faulty line and the unbalanced node, is zero:

[0113]

[0114] In the formula: Inject the virtual complex current vector at node m; ΔV k =V k '-V k .

[0115] In summary, the sparse virtual current vector I in (9) is reconstructed using the observed voltage differences before and during the fault. v Based on I v The faulty circuit can be identified by the two non-zero elements in the data.

[0116] When determining the fault location model, the rows and columns corresponding to the equilibrium nodes in the matrix and vector in (9) are extracted, and (9) can be rewritten as:

[0117]

[0118] In the formula: Y is the virtual complex current injection vector at slack node 1; ΔV1 is the complex voltage difference vector at slack node 1; 11 Y is the positive-sequence self-admittance at equilibrium node 1; 12 Y 21 This is the positive-sequence series admittance of line 1-2; YThis is the remaining node admittance matrix after removing the relevant part of the equilibrium node from the positive-order node admittance matrix; I v The virtual complex current injection vector excluding equilibrium node 1; Δ V It is the complex voltage difference vector between the fault and the fault state excluding the balancing node 1.

[0119] If only the non-equilibrium nodes are retained, then equation (9) becomes:

[0120] I v = Y Δ V (45)

[0121] Constructing the unknown virtual current vector I v Linear observation model associated with changes in voltage phasor measurements:

[0122] Δ V = ZI v +η (46)

[0123] In the formula: η is the error value;

[0124] Extract the configuration voltage phasor measurement n o Rows corresponding to each node:

[0125] Δ V o = Z o I v +η o (47)

[0126] In the formula: the subscript o represents the row corresponding to the observable node.

[0127] In actual power distribution networks, in most cases, a fault occurs on only one line, i.e., I. v It is very sparse, with only two non-zero elements corresponding to the nodes at both ends of the faulty line. Therefore, based on the linear regression model shown in Equation (15), the fault location problem can be transformed into the following sparse vector recovery problem with L1 norm, and solved using a sparse learning algorithm:

[0128]

[0129] In the formula: the superscript H is the conjugate transpose symbol; λ is the regularization parameter; This is the optimal solution for the sparse optimization model.

[0130] The method for enumerating each potentially faulty line and solving the fault location model to obtain the first matching index value, sorting all the first matching index values ​​in ascending order, and selecting the top u lines to construct a candidate faulty line set is as follows:

[0131] The sparse optimization model (16) can be solved quickly using existing sparse learning algorithms. However, the regularization term in the model leads to only suboptimal solutions. Furthermore, if the regularization parameter is not selected appropriately, the fault location accuracy is difficult to guarantee, and the regularization parameter determination method based on cross-validation has a large computational load.

[0132] The exhaustive search method is particularly suitable for fault location problems in actual distribution networks where, in most cases, faults occur on only one line. The exhaustive method enumerates each possible faulty line l and uses the linear least squares method to solve a linear regression problem (15) to obtain the matching index value. Specifically, for a specific faulty line l, the formula for calculating the matching index is:

[0133]

[0134] In the formula: From Z o The submatrix consists of the two columns corresponding to the l-th line; MI is the matching index value. The optimal solution for the following least squares model is:

[0135]

[0136] Since the variable dimension for each matching index calculation is only 2, the calculation speed is extremely fast, making it suitable for online applications. However, in distribution networks with insufficient measurement configuration, the line with the smallest matching index value may not be the actual faulty line. Therefore, this embodiment sorts the MI vectors in ascending order and selects the top u lines to construct a candidate faulty line set. According to statistical theory, when the measurement error follows a Gaussian distribution, least squares and maximum likelihood estimation are equivalent. In this case, even if the first matching index value of the actual faulty line is not the smallest, it will still rank high, theoretically guaranteeing the effectiveness of the proposed strategy of selecting the top u lines.

[0137] The specific method for sequentially performing nonlinear fault state estimation (SE) on all associated nodes of the candidate faulty line and selecting the node with the highest matching degree as the endpoint of the faulty line is as follows:

[0138] like Figure 1As shown, in the second stage, nonlinear fault state estimation (SE) is performed on all nodes of the u candidate lines, and the node with the highest matching degree is selected as the fault line endpoint. Since the fast screening and sorting method based on linear model matching was adopted in the first stage, the computational amount of SE matching can be greatly reduced and the fault location accuracy can be improved. In this embodiment, SE based on weighted least squares (WLS) is used to calculate the matching index value of each candidate node. The principle is briefly introduced as follows.

[0139] For a distribution network with m measurements, its measurement model is:

[0140] z = h(x) + e (51)

[0141] In the formula: For measurement vectors; For the measurement error vector, Let be the covariance matrix of e; h(·) is the vector of nonlinear measurement functions; This is a state variable vector, including the real and imaginary parts of the three-phase complex voltages at nodes other than the slack node:

[0142]

[0143] In the formula: These are the real and imaginary parts of the three-phase complex voltage at node i, respectively.

[0144] Establishing an SE model based on the WLS estimation criterion:

[0145] minJ(x)=[zh(x)] T R -1 [zh(x)] (53)

[0146] In the formula: J(x) is the objective function.

[0147] Setting the first derivative of the objective function to 0, and linearizing it using Taylor expansion at the initial point x0, we get:

[0148]

[0149] -H T (x0)R -1 [zh(x0)-H(x0)·Δx]=0 (55)

[0150] In the formula: H is the Jacobian matrix; To obtain the partial derivative of the objective function; Δx is the change in the state variables;

[0151] Starting from the initial point x0, the Gauss-Newton method is used to solve (24). The corrected equation for the k-th iteration is:

[0152] Δx (k) =[H T (x (k) )R -1 H(x (k) )] -1 H T (x (k) )R -1 [zh(x (k) (56)

[0153] In the formula: Δx (k) x represents the change in state variables during the k-th iteration; (k) This is the state variable at the k-th iteration.

[0154] Fault state estimation (SE) uses the following two types of measurements:

[0155] (1) Pseudo-measurements of three-phase active and reactive power injection at all unbalanced nodes; these measurements can be provided by the results of SE before the fault, and in each iteration, they need to be converted into equivalent node injection complex current measurements using the following formula:

[0156]

[0157] In the formula: These are the values ​​of node i at the k-th iteration. The real and imaginary parts of the phase injection current; These are the values ​​of node i at the k-th iteration. The active and reactive power pseudo-measurements are based on the current node voltage value in each iteration. The specific formula depends on the node load model (see equation (27)). These are the values ​​of node i at the k-th iteration. Real and imaginary parts of the phase complex voltage;

[0158] After converting node injected power measurement to node injected current measurement, the Jacobian matrix becomes a constant matrix, and the measurement equation is:

[0159]

[0160] In the formula: For the series conductance of line ik; The series susceptance of line ik.

[0161] (2) Measurement of three-phase complex voltage of μPMU node under fault steady state; Although the three-phase complex voltage of all adjacent nodes of μPMU node can also be calculated from the branch complex current provided by μPMU, this paper assumes that μPMU can only provide the three-phase complex voltage of the node where it is located.

[0162] After constantizing the Jacobian matrix, the corrected equation (25) for the k-th iteration becomes:

[0163] Δx (k) =[H T R -1 H] -1 H T R -1 [zh(x (k) (59)

[0164] Furthermore, the load model needs to be considered during the fault SE iteration process. After a fault occurs, the power consumed by the load changes with the node voltage, especially when the transition resistance is very small, the load model is significantly different from that before the fault. SE can essentially be regarded as a nonlinear fit of the state variables to the measurement. Therefore, the state cannot be directly fitted to the node injected power measurement before the fault. Instead, in each iteration, the load should be corrected based on the node voltage obtained in the previous iteration, as shown in the following equation:

[0165]

[0166] In the formula: These are the values ​​of node i at the k-th iteration. For both active and reactive loads, if there is no distributed power source at node i, then These are the nodes i before the fault. Active and reactive loads; For node i in the k-th iteration Phase voltage; α1, β1, and γ1 are the coefficients of the constant power, constant current, and constant impedance components of the active load, respectively; α2, β2, and γ2 are the coefficients of the constant power, constant current, and constant impedance components of the reactive load, respectively.

[0167] Compared to a normally operating SE, a fault SE requires compensation for the fault point current, which is then injected into the assumed virtual fault point. Therefore, a μPMU needs to be configured at the root node to monitor the three-phase complex current. In the k-th iteration, the fault current can be calculated using the following formula:

[0168]

[0169] In the formula: These are the three-phase complex injection currents at the root node, fault point f, and node i during the k-th iteration, respectively.

[0170] When there is no voltage amplitude measurement at the downstream node of the fault point, the SE-based matching method cannot identify the fault node. Therefore, voltage amplitude measurement should be configured at the end node of each branch line. The voltage amplitude measurement can be obtained through smart meters and transmitted to the control center at a low frequency, or the transmission can be triggered only when a fault is detected. The matching index of candidate fault node i consists of two parts: the state estimation measurement residual vector and the L1 norm of the end node voltage amplitude measurement residual vector.

[0171]

[0172] In the formula: These are estimates of the state variables; These are the end nodes i respectively Measured and estimated values ​​of phase voltage amplitude; Ω end It is the set of all end nodes.

[0173] Because the weights of voltage amplitude measurement and power pseudo-measurement differ significantly, the influence of measurement weights is not considered in the matching index to avoid one type of measurement residual dominating the matching index while the characteristics of the other type of measurement residual are masked due to the large difference in the weights of the two types of measurement.

[0174] After calculating the matching index values ​​for all candidate fault points, the node with the lowest matching index value is selected as an endpoint of the faulty line:

[0175]

[0176] If there is no voltage amplitude measurement downstream of the fault point, the fault location method based on SE matching will fail. The reason is analyzed as follows:

[0177] If node i is configured with voltage amplitude measurement, and the fault point is downstream of node i, then:

[0178] (1) If the assumed fault node is downstream of node i, the compensated fault current will always flow through the path from the root node to node i. No matter which downstream node is assumed to have a fault, the SE algorithm can easily make the voltage estimate of node i close to the measured value, thus making it impossible to distinguish which downstream node has a fault.

[0179] (2) If the assumed fault node is upstream of node i, the compensated fault current only flows through a portion of the path from the root node to node i. The estimated voltage value of node i will tend to be greater than the measured value. In this case, the SE algorithm will increase the pseudo-measurement residual to reduce the voltage amplitude measurement residual of node i, so as to minimize the overall objective function value. In other words, a high pseudo-measurement residual is the price that must be paid for accurately fitting the voltage amplitude measurement, and the farther the assumed fault node is from the fault point, the greater the price (the first item of the matching index) required. Therefore, it is possible to distinguish which upstream node is the real fault node.

[0180] Therefore, in order to monitor the entire distribution network, voltage amplitude measurement should be configured at each end node.

[0181] After obtaining one end of the faulty line, other hardware-based methods (such as the traveling wave method) can be used to determine the faulty line and its precise location.

[0182] Example 2

[0183] This section uses an unbalanced 33-node power distribution system to test the proposed method, and uses the Block Sparse Bayesian Learning (BSBL) algorithm to solve (14) for comparison with the proposed method.

[0184] The 33-node system was expanded into an unbalanced system with three-phase unbalanced loads. Each node was configured with a single-phase load, and the active and reactive load values ​​were set to random numbers within the ranges of 60–200 kW and 20–100 kVar, respectively. The neutral point of the root node was directly grounded. OpenDSS was used to simulate 10 types of faults and applied to 31 lines excluding lines 1-2. The fault types included single-phase ground faults (A, B, C), two-phase ground faults (AB, BC, AC), two-phase faults (AB, BC, AC), and three-phase faults (ABC), totaling 310 faults. The distance from each fault point to the starting node of the line was randomly set to 10%–90% of the total line length.

[0185] For voltage amplitude measurements and pseudo-measurements of active and reactive power, the relative measurement error is added to the true value using the following formula:

[0186]

[0187] In the formula: V i V i,true These are the measured value and the true value of the voltage amplitude at the i-th node, respectively; P i P i,true Q represents the measured value and the true value of the active power injected into the i-th node, respectively; i Q i,true Let randn(0,1) be the measured value and the true value of the reactive power injected into the i-th node, respectively. 2 ) is a standard Gaussian distribution; e V e P These represent the percentage of relative measurement error for all voltage amplitude measurements and power measurements.

[0188] For voltage phase angle measurements, the absolute measurement error is added to the true value using the following formula:

[0189] θ i =θ i,true +randn(0,1 2 )eθ (65)

[0190] In the formula: θ i θ i,true These are the measured and true values ​​of the voltage phase angle at the i-th node, respectively; e θ It is the standard deviation of the measurement error for all voltage phase angles.

[0191] Three single-phase photovoltaic (PV) power sources with a total capacity of 800kW were added to nodes 12 and 29, respectively. During normal system operation, the PV power generation equipment typically operates in maximum power point tracking (MPPT) mode. When a system fault occurs, the reduced system voltage affects the PV output, which is specifically related to the control strategy of the PV inverter. In this test, the PVSystem element control strategy in OpenDSS was used, and the PV output varied according to the voltage amplitude of the PV nodes.

[0192]

[0193] In the formula: At node i during the k-th iteration The active power output of the photovoltaic phase; For node i The active power output before the photovoltaic failure on the phase.

[0194] First, the first phase of testing was conducted, including testing with different numbers of μPMUs and testing with different μPMU measurement error levels.

[0195] Test results with different numbers of μPMUs:

[0196] Considering both constant impedance load and ZIP load models, the proposed linear model matching-based screening algorithm was tested for different numbers of μPMUs. The voltage amplitude measurement of the μPMUs was e. V Set to 0.016%, voltage phase angle measurement e θ Set to 0.0033°, the voltage amplitude measured at terminal nodes 18, 22, 25, and 33 is e. V The value was set to 0.1%, and the fault resistance was set to a random number between 0 and 100 Ω. μPMU configuration schemes with different numbers were obtained using MATLAB's built-in genetic algorithm, with the success rate of all 310 fault location tests used as the fitness function of the genetic algorithm. The obtained μPMU configuration schemes are shown in Table 1.

[0197] Table 1 μPMU Configuration of the 33-Node System

[0198]

[0199]

[0200] The success rate of the screening method based on linear model matching under constant impedance load is as follows: Figure 3 As shown in the figure, the success rate of fault line screening increases with the increase of the number of μPMUs. However, if the line with the smallest matching index value is selected as the final result in each test, the success rate is less than 30% even with 8 μPMUs due to insufficient measurement information. If the selection criteria are relaxed to select the top-6 of the MI, the success rate can approach 100%, meaning that the correct fault line always falls in the top-6 of the MI, thus greatly reducing the search space for SE matching in the second stage and proving the effectiveness of the proposed method. In contrast, the BSBL algorithm performs poorly, with a fault line screening success rate of less than 60% even with 8 μPMUs. Furthermore, selecting the top-k from the BSBL algorithm results does not help improve the success rate because this type of algorithm sets most elements of the solution vector to zero, thus invalidating the sorting.

[0201] The success rate of the linear model matching-based screening method under ZIP load is as follows: Figure 4 As shown, α1, β1, γ1 and α2, β2, γ2 are all set to 0.4, 0.3, 0.3. From Figure 4 It can be seen that the success rate is slightly lower compared to the constant impedance load, but this can be improved by selecting more lines with high matching index values. For example, when configuring 6 μPMUs and selecting the top-6, the success rate of fault line screening can reach 95%. In contrast, the BSBL algorithm has a location success rate of less than 50% even when configuring 8 μPMUs, only slightly better than the proposed method when selecting the top-1.

[0202] Testing of different μPMU measurement error levels:

[0203] Considering both constant impedance load and ZIP load models, the proposed linear model matching-based screening algorithm was tested under different μPMU measurement error levels. Five μPMUs were configured at nodes 8, 13, 19, 23, and 29, as shown in Table 1. Five levels of fault resistance were set, consisting of random numbers between 0–100Ω, 0–200Ω, 0–300Ω, 0–400Ω, and 0–500Ω. Ten μPMU measurement error levels were designed, as shown in Table 2.

[0204] Table 2. Measurement error levels for different μPMUs

[0205] plan <![CDATA[e V / and θ ]]> plan <![CDATA[e V / and θ ]]> 1 0.01％ / 0.001° 6 0.06％ / 0.006° 2 0.02％ / 0.002° 7 0.07％ / 0.007° 3 0.03％ / 0.003° 8 0.08％ / 0.008° 4 0.04％ / 0.004° 9 0.09％ / 0.009° 5 0.05％ / 0.005° 10 0.010％ / 0.0010°

[0206] Figure 5The success rate of the linear model matching method in identifying the top-6 faulty lines under different μPMU measurement error levels is shown in the figure. As can be seen from the figure, the success rate of faulty line selection decreases to some extent with increasing measurement error. However, even in the 0–500Ω high-resistance fault test with high error levels and weak fault characteristics, the success rate of this algorithm is still no less than 80%. Furthermore, since the fault location model based on virtual current is derived under the assumption of constant impedance load, the success rate under ZIP load is slightly lower than that under constant impedance load, but it still remains above 75%.

[0207] Next, the second phase of testing will be conducted:

[0208] The fault location method based on SE matching was tested, considering both constant impedance load and ZIP load models. According to Table 1, five μPMUs were configured at nodes 8, 13, 19, 23, and 29. The voltage amplitude of the μPMUs was measured... V Set to 0.016%, voltage phase angle measurement e θ Set to 0.0033°, the voltage amplitude measured at terminal nodes 18, 22, 25, and 33 is e. V The pseudo-measurement error level is set to 0.1%, with 10 levels: 5%, 10%, 15%, 20%, 25%, 30%, 35%, 40%, 45%, and 50%. The fault resistance is set to 5 levels: random numbers between 0-100Ω, 0-200Ω, 0-300Ω, 0-400Ω, and 0-500Ω. During testing, successful fault location is considered achieved as long as any endpoint of the faulty line can be identified. Simultaneously, a short-circuit (SC) matching method based on pseudo-measurement is compared with the SE matching method.

[0209] The success rate of fault location based on the SE / SC matching method under constant impedance load is as follows: Figure 6 As shown in the figure, the success rate of fault location decreases to some extent with the increase of pseudo-measurement error. When both the pseudo-measurement error and the fault resistance are small, the success rate of fault location using the SC matching method is slightly higher than that using the SE matching method; however, when both the pseudo-measurement error and the fault resistance are large, the success rate of fault location using the SE matching method is much higher than that using the SC matching method. For example, when the pseudo-measurement error is 20% and the fault resistance is a random number between 0 and 500Ω, the success rate of fault location using the SE matching method is still higher than 90%, while the success rate of fault location using the SC matching method is only 70%.

[0210] The success rate of fault location based on the SE / SC matching method under ZIP load is as follows: Figure 7 As shown, the obtained test results are consistent with... Figure 6 Very similar, it can be concluded that... Figure 6The same conclusion is reached: when the pseudo-measurement error and the fault resistance are large, the success rate of fault location based on the SE matching method is much higher than that based on the SC matching method.

[0211] Finally, a two-stage comprehensive test will be conducted:

[0212] The overall performance of the proposed two-stage fault location method was tested. The first stage was fault line screening based on linear model matching, and the second stage was fault location based on SE matching. The test environment was exactly the same as that of the second stage test, but in the second stage SE matching, only the associated nodes of the top-6 lines in the first stage were used as candidate fault nodes.

[0213] The success rates of fault location based on the two-stage method under constant impedance load and ZIP load are as follows: Figure 8 , Figure 9 As shown in the figure, the overall success rate of fault location using the two-stage method is very close to that of the SE matching method alone. As long as the top-6 routes selected in the first stage include the truly faulty routes, the final result depends solely on the effectiveness of the SE matching method in the second stage. Furthermore, even if the top-6 routes selected in the first stage miss the truly faulty routes, the second stage may still identify one end node of the faulty route, thus leading to a higher final success rate for the two-stage method compared to the first stage. Figure 9 As shown. This is because the criteria for successful fault location differ between the two stages: in the first stage, identifying the actual faulty line is considered successful; while in the second stage, the criteria are more lenient, and identifying any node at either end of the faulty line is considered successful fault location. Therefore, even if a faulty line is missed in the first stage, it is still possible to identify a node at the end of the actual faulty line in the second stage.

[0214] In addition, CPU computation time was also tested:

[0215] Table 3 shows the average CPU time required for a single fault location test when using different methods. It can be seen that the first stage, the proposed fault line screening method based on linear model matching, is extremely fast because the variable dimension for each matching index calculation is only 2. The second stage, the SE-based matching method, is very time-consuming because it requires iterative nonlinear SE calculations on all unbalanced nodes as candidate fault nodes, resulting in a large computational load. In the two-stage method, by using the endpoints of the six candidate fault lines selected in the first stage as candidate fault nodes, the required number of nonlinear SE calculations is significantly reduced, and its computational speed is about 5 times faster than using only the second stage, making it very suitable for practical applications.

[0216] Table 3 Comparison of CPU time for different fault location methods

[0217] method Stage 1 Stage 2 only Two-stage (top-6) time 2.3ms 1.5s 0.3s

[0218] This embodiment proposes an efficient fault location method based on two-stage model matching. First, a linear model matching algorithm is proposed to solve the virtual current-based fault location model. The matching index values ​​of all lines are sorted, and the top-u values ​​are selected to construct a candidate fault line set. Then, fault SE (Search Engine Analysis) is performed on the associated nodes of the candidate lines to filter out the nodes with the highest matching degree, which are used to further determine the fault line and its precise location. Simulation tests were conducted on a typical three-phase unbalanced distribution network with various fault types, load models, and high-resistance fault scenarios, verifying the effectiveness of the proposed method.

[0219] Example 3

[0220] This embodiment provides a two-stage fault location device for distribution networks based on synchronous phasor measurement, including:

[0221] The data acquisition module is used to acquire the network topology before the fault, the voltage phasor measurement data before and after the fault, and the pseudo-measurement of the three-phase active and reactive power injection of all unbalanced nodes.

[0222] The candidate fault line set construction module is used to construct a virtual current fault location model, enumerate each line that may be faulty, solve the fault location model, obtain the first matching index value, sort all the first matching index values ​​in ascending order, and select the top u lines to construct the candidate fault line set.

[0223] The fault line and precise fault location determination module is used to perform nonlinear fault state estimation (SE) on all associated nodes of the candidate fault line in sequence, select the node with the highest matching degree as the fault line endpoint, and after obtaining an endpoint of the fault line, use other hardware-based methods (such as the traveling wave method) to determine the fault line and the precise fault location.

[0224] A computing device is also provided, comprising:

[0225] One or more processing units;

[0226] A storage unit is used to store one or more programs.

[0227] When the one or more programs are executed by the one or more processing units, the one or more processing units execute the two-stage fault location method for distribution networks based on synchronous phasor measurement in this embodiment. It should be noted that the computing device may include, but is not limited to, processing units and storage units. Those skilled in the art will understand that the inclusion of processing units and storage units in the computing device does not constitute a limitation on the computing device. It may include more components, or combine certain components, or different components. For example, the computing device may also include input / output devices, network access devices, buses, etc.

[0228] A computer-readable storage medium having processor-executable non-volatile program code, wherein the computer program, when executed by a processor, implements the steps of the two-stage fault location method for distribution networks based on synchronous phasor measurement in this embodiment. It should be noted that the readable storage medium can be, for example, but not limited to, electrical, magnetic, optical, electromagnetic, infrared, or semiconductor systems, devices, or any combination thereof. The program contained on the readable medium can be transmitted using any suitable medium, including, but not limited to, wireless, wired, optical fiber, RF, etc., or any suitable combination thereof. For example, the program code for performing the operations of this invention can be written in any combination of one or more programming languages, including object-oriented programming languages ​​such as Java, C++, etc., and conventional procedural programming languages ​​such as C or similar programming languages. The program code can be executed entirely on a user's computing device, partially on a user's device, as a standalone software package, or entirely on a remote computing device or server. In cases involving remote computing devices, the remote computing devices can be connected to the user's computing device via any type of network—including a local area network (LAN) or a wide area network (WAN), or they can be connected to an external computing device (e.g., via the Internet using an Internet service provider).

[0229] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, and not to limit them. Although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some of the technical features; and these modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the embodiments of the present invention.

Claims

1. A two-stage fault location method for distribution networks based on synchronous phasor measurement, characterized in that, Includes the following steps: Acquire the network topology before the fault, voltage phasor measurement data before and after the fault, and pseudo-measurements of three-phase active and reactive power injection at all unbalanced nodes; A virtual current fault location model is constructed, each line that may be faulty is enumerated, and the fault location model is solved to obtain the first matching index value. All first matching index values ​​are sorted in ascending order, and the top u lines are selected to construct a candidate fault line set. Nonlinear fault state estimation (SE) is performed sequentially on all associated nodes of the candidate faulty line. The node with the highest matching degree is selected as the endpoint of the faulty line. After obtaining an endpoint of the faulty line, other hardware-based methods are used to determine the faulty line and the precise location of the fault. The method for constructing a virtual current fault location model is as follows: Define virtual current: ； In the formula: Let n be the virtual complex current injection vector. b This represents the total number of network nodes. This is the complex voltage difference vector between the fault and the voltage before the fault. The positive-sequence node admittance matrix before the fault; the virtual injection currents of nodes m and n at both ends of the faulted line are not zero, and the virtual injection current of any node k except for the nodes at both ends of the faulted line and unbalanced nodes is zero. By extracting the rows and columns corresponding to the equilibrium nodes from the matrix and vector in (1), (1) can be rewritten as: ； In the formula: The virtual complex current injection vector at equilibrium node 1; This is the complex voltage difference vector at equilibrium node 1; The positive-sequence self-admittance at equilibrium node 1; , This is the positive-sequence series admittance of line 1-2; This is the remaining node admittance matrix after removing the relevant part of the equilibrium node from the positive-order node admittance matrix; The virtual complex current injection vector excluding the equilibration node 1; The complex voltage difference vector between the fault and the fault state, excluding the balancing node 1. If only the non-equilibrium nodes are retained, then equation (1) becomes: ； Constructing an unknown virtual current vector Linear observation model associated with changes in voltage phasor measurements: ； In the formula: ; This is the error value; Extract the configuration voltage phasor measurement n o Rows corresponding to each node: ； In the formula: the subscript o represents the row corresponding to the observable node; The method for solving the fault location model is as follows: The first matching index value is obtained by solving the linear regression problem using the linear least squares method (5); for a specific faulty line l, the formula for calculating the first matching index value is: ； In the formula: From The submatrix consisting of the two columns corresponding to the l-th line; To match the indicator value; , It is the optimal solution for the following least squares model. , It is a virtual complex current column vector Elements at the locations of the nodes at both ends of line l: ； When performing nonlinear fault state estimation (SE) on the associated nodes of candidate faulty lines, the fault point current needs to be compensated and injected into the assumed virtual fault point. In the k-th iteration, the fault current can be calculated by the following formula: ； In the formula: These are the three-phase complex injection currents at the root node, fault point f, and node i during the k-th iteration, respectively.

2. The two-stage fault location method for distribution networks based on synchronous phasor measurement according to claim 1, characterized in that, When performing nonlinear fault state estimation (SE) for associated nodes of candidate faulty lines, a state estimation SE model is established based on the weighted least squares (WLS) estimation criterion: ； In the formula: The objective function is... For measurement vectors; For the measurement error vector, Let be the covariance matrix of e; h(·) is the vector of nonlinear measurement functions; This is a state variable vector, including the real and imaginary parts of the three-phase complex voltages at nodes other than the slack node: Setting the first derivative of the objective function to 0, and linearizing it using Taylor expansion at the initial point x0, we get: ； ； In the formula: It is a Jacobian matrix; To find the partial derivatives of the objective function; The change in state quantity; Starting from the initial point x0, the Gauss-Newton method is used to solve (10). The corrected equation for the kth iteration is: ； In the formula: This represents the change in state variables during the k-th iteration. This refers to the state variables at the k-th iteration. After converting the node injection power measurement to the node injection current measurement, the Jacobian matrix becomes a constant matrix. After the Jacobian matrix is ​​constant, the modified equation (11) for the k-th iteration becomes: 。 3. The two-stage fault location method for distribution networks based on synchronous phasor measurement according to claim 1, characterized in that, When performing nonlinear fault state estimation (SE) on the associated nodes of a candidate faulty line, the load model needs to be considered during the SE iteration process. In each iteration, the load is corrected based on the node voltage obtained in the previous iteration, as shown in the following formula: ； In the formula: These are the values ​​of node i at the k-th iteration. For both active and reactive loads, if there is no distributed power source at node i, then , ; , These are the nodes i before the fault. Active and reactive loads; For node i in the k-th iteration Phase voltage; The rated phase voltage of the power distribution system; These are the coefficients for the constant power, constant current, and constant impedance components of the active load, respectively. These are the coefficients for the constant power, constant current, and constant impedance components of the reactive load, respectively.

4. The two-stage fault location method for distribution networks based on synchronous phasor measurement according to claim 1, characterized in that, The second matching index value of candidate fault node c consists of two parts: the L1 norm of the state estimation measurement residual vector and the terminal node voltage magnitude measurement residual vector. composition: ； In the formula: These are estimates of the state variables; These are the end nodes d respectively Measured and estimated values ​​of phase voltage amplitude; It is the set of all end nodes; After calculating the second matching index value for all candidate fault points, the node with the lowest second matching index value is selected as an endpoint of the faulty line: 。 5. The two-stage fault location method for distribution networks based on synchronous phasor measurement according to claim 1, characterized in that, When there is no voltage amplitude measurement at the downstream node of the fault point, the matching method based on fault state estimation cannot identify the fault node, and voltage amplitude measurement needs to be configured at each end node.

6. A two-stage fault location device for distribution networks based on synchronous phasor measurement, used to implement the two-stage fault location method for distribution networks based on synchronous phasor measurement as described in any one of claims 1-5, characterized in that, include: The data acquisition module is used to acquire the network topology before the fault, the voltage phasor measurement data before and after the fault, and the pseudo-measurement of the three-phase active and reactive power injection of all unbalanced nodes. The candidate fault line set construction module is used to construct a virtual current fault location model, enumerate each line that may be faulty, solve the fault location model, obtain the first matching index value, sort all the first matching index values ​​in ascending order, and select the top u lines to construct the candidate fault line set. The fault line and precise fault location determination module is used to perform nonlinear fault state estimation (SE) on all associated nodes of the candidate fault line in sequence, select the node with the highest matching degree as the fault line endpoint, and after obtaining an endpoint of the fault line, use other hardware-based methods to determine the fault line and the precise fault location.

7. A computing device, characterized in that: include: One or more processing units; A storage unit is used to store one or more programs. Wherein, when the one or more programs are executed by the one or more processing units, the one or more processing units perform the method as described in any one of claims 1 to 5.

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