Power distribution network two-stage fault positioning method and device based on synchronous phasor measurement

Abstract

The invention provides a power distribution network two-stage fault positioning method and device based on synchronous phasor measurement. The method comprises the steps of obtaining network topology before a fault, voltage phasor measurement data before and after the fault and three-phase active and reactive power injection pseudo measurement of all unbalanced nodes; constructing a virtual current fault positioning model, enumerating each line which may have a fault, solving the fault positioning model to obtain first matching index values, performing ascending sorting on all the first matching index values, and 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 a node with the highest matching degree as an end point of the fault line, and determining the fault line and a fault accurate position by using other hardware-based methods after one end point of the fault line is obtained; according to the invention, high fault positioning precision can be realized under the condition of limited [mu] PMU.

Description

Technical Field

[0001] The present invention relates to the technical field of distribution network, and in particular to a two-stage fault location method and device for distribution network based on synchronous phasor measurement. Background Art

[0002] The distribution network is closely connected to users and is a key link in ensuring reliable power supply to users. However, the distribution network has a complex structure, a harsh operating environment, and a high probability of faults. If the faults are not handled in a timely manner, it will seriously affect the reliable power supply to users. Fault handling includes fault location, isolation, and power supply restoration. Fault location is the basis of fault isolation and power supply restoration, and is of great significance to the safe and reliable operation of the distribution network. However, the three-phase imbalance and insufficient measurement configuration of the distribution network make it difficult to directly apply the fault location method of the transmission network.

[0003] Existing distribution network fault location methods can be roughly divided into: impedance-based methods, traveling wave-based methods, data-driven methods, methods based on fault flow calculation or state estimation (SE), and methods based on sparse optimization.

[0004] The traditional impedance-based method is simple to implement, but due to the complex structure of the distribution network and the large number of branches, the fault may be located to other adjacent branches; the algorithm based on voltage sag can be regarded as an impedance method, which uses the transfer impedance matrix and the measured voltage deviation to estimate the fault current and match the fault point, but this method requires a large number of measurement equipment and is only applicable to constant impedance loads; the traveling wave-based method locates the fault through the arrival time of the fault reflection wave and is not affected by network parameters, fault type and operating mode. However, this method relies on high-sampling rate measurement equipment, and the branches and transformers in the system will reduce the accuracy; data-driven methods include various technologies from signal processing to artificial intelligence. By fully approximating nonlinear problems, the limitations of driving technology are overcome, but such methods require a large amount of fault data for training, have poor interpretability, and cannot adapt to changes in network topology.

[0005] Based on the method of fault power flow calculation / SE matching, the fault current is injected into the suspicious node, the power flow calculation / SE is performed, the system state quantity in the fault steady state is obtained, and the voltage estimation value is compared with the measured value to select the node with the largest matching degree; however, this type of method has a large amount of calculation and is slow.

[0006] In view of the above problems, it is necessary to study an efficient fault location method based on two-stage model matching, which can achieve higher fault location accuracy with limited micro-phasor measurement units and improve the overall calculation speed. Summary of the invention

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

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

[0009] Construct a virtual current fault location model, enumerate each line that may have a fault, and solve the fault location model to obtain a first matching index value, sort all first matching index values ​​in ascending order, and select the first u lines to construct a candidate fault line set;

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

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

[0012] Define virtual current:

[0013] I v =YΔV (17)

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

[0015] Take out the rows and columns corresponding to the balanced nodes in the matrix and vector in (9), (9) can be rewritten as:

[0016]

[0017] Where: is the virtual complex current injection vector at the balance node 1; ΔV1 is the complex voltage difference vector at the balance node 1; Y 11 is the positive sequence self-admittance at the balancing node 1; Y 12 , Y 21 is the positive sequence series admittance of line 1-2; Y is the remaining node admittance matrix after removing the balance node related parts from the positive sequence node admittance matrix; I v is the virtual complex current injection vector except the balancing node 1; Δ V is the complex voltage difference vector between the fault and before the fault except for the balancing node 1;

[0018] Only the unbalanced nodes are retained, then equation (9) becomes:

[0019] I v = Y Δ V (19)

[0020] Construct the unknown virtual current vector I v Linear observation model associated with voltage phasor measurement changes:

[0021] Δ V = ZI v +η (20)

[0022] Where: η is the error value;

[0023] Extract the configuration voltage phasor measurement n o The rows corresponding to the nodes are:

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

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

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

[0027] The linear least squares method is used to solve the linear regression problem (15) to obtain the first matching index value; for a specific fault line l, the calculation formula of the first matching index value is:

[0028]

[0029] Where: For Z o The submatrix consisting of two columns corresponding to the lth line in ; MI is the matching index value; is the optimal solution of the following least squares model:

[0030]

[0031] Furthermore, when performing nonlinear fault state estimation SE on the associated nodes of the 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] Where: J(x) is the objective function; is the measurement vector; is the measurement error vector, is the covariance matrix of e; h(·) is the nonlinear measurement function vector; is the state variable vector, including the real and imaginary parts of the three-phase complex voltages at nodes other than the balanced nodes:

[0034] Let the first-order derivative of the objective function be 0, and use Taylor expansion to linearize it at the initial point x0, and we get:

[0035]

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

[0037] Where: H is the Jacobian matrix; is the partial derivative of the objective function; Δx is the change of the state quantity;

[0038] Starting from the initial point x0, the Gauss-Newton method is used to solve (24). The modified equation at the kth 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] Where: Δx (k) is the change in state quantity at the kth iteration; x (k) is the state quantity at the kth iteration;

[0041] After converting the node injection power measurement into the node injection current measurement, the Jacobian matrix becomes a constant matrix. After the Jacobian matrix is ​​constantized, the modified equation (25) of the kth 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 the candidate fault line, the load model needs to be considered in the iterative process of fault state estimation. In each iteration, the load is corrected according to the node voltage obtained in the previous iteration, as shown in the following formula:

[0044]

[0045] Where: are the node i at the kth iteration. Phase active and reactive loads, if there is no distributed generation at node i, then are the node i’s Phase active and reactive load; is the value of node i at the kth iteration Phase voltage; is the rated phase voltage of the distribution system; α1, β1, and γ1 are the coefficients of the constant power, constant current, and constant impedance parts of the active load respectively; α 2 , β2, and γ2 are the coefficients of the constant power, constant current, and constant impedance parts of the reactive load, respectively.

[0046] Furthermore, when the nonlinear fault state of the associated nodes of the candidate fault line is estimated, the fault point current needs to be compensated and injected into the assumed virtual fault point. In the kth iteration, the fault current can be calculated by the following formula:

[0047]

[0048] Where: are the three-phase complex injection currents of the root node, fault point f, and node i at the kth iteration respectively.

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

[0050]

[0051] Where: Estimate values ​​for state variables; are the terminal node i Measured value and estimated value of phase voltage amplitude; Ω end is the set of all terminal nodes;

[0052] After calculating the second matching index values ​​of all candidate fault points, select the node with the lowest second matching index value as an endpoint of the fault 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 faulty node, and voltage amplitude measurement needs to be configured at each end node.

[0055] A two-stage fault location device for distribution network based on synchronous phasor measurement, comprising:

[0056] A data acquisition module is used to obtain the network topology before the fault, the voltage phase measurement data before and after the fault, and the three-phase active and reactive power injection pseudo-measurements of all unbalanced nodes;

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

[0058] The fault line and fault precise location determination module is used to perform nonlinear fault state estimation SE on all associated nodes of the candidate fault line in turn, 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 for storing one or more programs,

[0062] Wherein, 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 network based on synchronous phasor measurement as described above.

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

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

[0065] The present invention is based on a sparse optimization method. When measurement information is insufficient, the fault location success rate of selecting the top-1 line is low; however, by relaxing the standard, the method of screening the top-u lines can significantly improve the success rate of fault line screening, thereby greatly reducing the search space of the second-stage SE matching; through the two-stage fault location method, under different load models, fault types, μPMU measurement and pseudo-measurement error levels and high-resistance faults, a higher fault location accuracy can be achieved under limited μPMU conditions; in addition, the fault line screening method based on linear model matching proposed in the present invention has an extremely fast calculation speed, and at the same time, the two-stage method uses the candidate fault nodes screened out in the first stage as the search space, and the overall calculation speed is about 5 times faster than that of using only the second stage. BRIEF DESCRIPTION OF THE DRAWINGS

[0066] The technical solution of the present invention will be further described in detail below in conjunction with the accompanying drawings and embodiments, but it should be understood that these drawings are designed only for explanation purposes and are not intended to limit the scope of the present invention. In addition, unless otherwise specified, these drawings are intended only to conceptually illustrate the structural configurations described herein and are not necessarily drawn to scale.

[0067] Figure 1 A flow chart of a two-stage fault location method for a distribution network based on synchronized phasor measurement provided by an embodiment of the present invention;

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

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

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

[0071] Figure 5 The top-6 success rates under different measurement errors provided in Example 2 of the present invention;

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

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

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

[0075] Fig. 9 The success rate (ZIP load) of the two-stage fault location method provided in Example 2 of the present invention. DETAILED DESCRIPTION

[0076] In order to make the purpose, technical scheme and advantages of the implementation of the present invention clearer, the technical scheme in the embodiment of the present invention will be described in more detail below in conjunction with the drawings in the embodiment of the present invention. In the drawings, the same or similar reference numerals throughout represent the same or similar elements or elements with the same or similar functions. The described embodiments are part of the embodiments of the present invention, not all of the embodiments. The embodiments described below with reference to the drawings are exemplary and are intended to be used to explain the present invention, and should not be construed as limitations on the present invention. Based on the embodiments in the present invention, all other embodiments obtained by ordinary technicians in this field without making creative work are within the scope of protection of the present invention.

[0077] The embodiments of the present invention are described in detail below with reference to the accompanying drawings.

[0078] Example 1

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

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

[0081] Construct a virtual current fault location model, enumerate each line that may have a fault, and solve the fault location model to obtain a first matching index value, sort all first matching index values ​​in ascending order, and select the first u lines to construct a candidate fault line set;

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

[0083] Specifically, when constructing a virtual current fault location model, first establish a virtual current model:

[0084] For a b For an unbalanced distribution network with 10 nodes, the network equation based on the three-phase node admittance matrix is:

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

[0086] Where: is the three-phase complex current injection vector; is the three-phase complex voltage vector; is the three-phase node admittance matrix.

[0087] Since all types of faults have positive sequence components, the fault location adopts the positive sequence network equation based on the positive sequence node admittance matrix:

[0088] I=YV (34)

[0089] Where: It is the positive sequence complex current injection vector before the fault; is the positive sequence complex voltage vector before the fault; is the positive sequence node admittance matrix before the fault.

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

[0091]

[0092] Where: I k is the positive sequence complex injection current of node k before the fault; V k is the positive sequence complex voltage of node k before the fault; Y kk , Y ki are the positive sequence self-admittance and mutual-admittance respectively; y ki is the positive sequence series admittance of line ki; y k is the positive sequence shunt admittance and load admittance of node k; Ω b is the set of all nodes; is the set of neighbor nodes of node k.

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

[0094]

[0095] Where: is the three-phase complex current injection vector before the fault at node k; is the three-sequence complex injection current before the fault at node k; The three-phase complex voltage vector before the fault at node k; is the three-sequence complex voltage vector before the fault at node k; is the three-phase node admittance matrix before the fault at node k; is 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 endpoints m of the faulted line 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 section 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 endpoints n of the faulted line before and during the fault can also be derived.

[0104] For any node k other than the two endpoints of the faulted 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: is the virtual complex current injection vector; ΔV=V′-V is the complex voltage difference vector during the fault and before the fault.

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

[0110]

[0111] Where: is the virtual complex current injection vector at node m; is the virtual complex current injection vector at node m; y ni is 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) shows that the virtual injection current of any node k except the nodes at both ends of the fault line and the unbalanced nodes is zero:

[0113]

[0114] Where: is the virtual complex current injection 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 only two non-zero elements in can determine the faulty line.

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

[0117]

[0118] Where: is the virtual complex current injection vector at the balance node 1; ΔV1 is the complex voltage difference vector at the balance node 1; Y 11 is the positive sequence self-admittance at the balancing node 1; Y 12 , Y 21 is the positive sequence series admittance of line 1-2; Yis the remaining node admittance matrix after removing the balance node related parts from the positive sequence node admittance matrix; I v is the virtual complex current injection vector except the balancing node 1; Δ V is the complex voltage difference vector between the fault and before the fault except the balancing node 1.

[0119] Only the unbalanced nodes are retained, then equation (9) becomes:

[0120] I v = Y Δ V (45)

[0121] Construct the unknown virtual current vector I v Linear observation model associated with voltage phasor measurement changes:

[0122] Δ V = ZI v +η (46)

[0123] Where: η is the error value;

[0124] Extract the configuration voltage phasor measurement n o The rows corresponding to the nodes are:

[0125] Δ V o = Z o I v +η o (47)

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

[0127] In actual distribution networks, in most cases, the fault occurs only on one line, that is, 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 the sparse learning algorithm:

[0128]

[0129] Where: 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 of enumerating each line that may fail, solving the fault location model, obtaining the first matching index value, sorting all the first matching index values ​​in ascending order, and selecting the first u lines to construct the candidate fault line set is as follows:

[0131] The sparse optimization model (16) can be quickly solved using existing sparse learning algorithms. However, the regularization term in the model results in only suboptimal solutions. In addition, if the regularization parameter is not selected appropriately, the accuracy of fault location is difficult to guarantee, and the regularization parameter determination method based on cross-validation is computationally intensive.

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

[0133]

[0134] Where: For Z o The submatrix consisting of two columns corresponding to the lth line in ; MI is the matching index value; is the optimal solution of the following least squares model:

[0135]

[0136] Since the variable dimension of each matching index calculation is only 2, the calculation speed is extremely fast and suitable for online applications; however, in a distribution network with insufficient measurement configuration, the line with the smallest matching index value is likely not the actual fault line. Therefore, this embodiment sorts the MI vectors in ascending order and selects the first u lines to construct a set of candidate fault lines. According to statistical theory, when the measurement error obeys a Gaussian distribution, the least squares and maximum likelihood estimation are equivalent. At this time, even if the first matching index value of the real fault line is not the smallest, it will be ranked in the front, which theoretically guarantees the effectiveness of the proposed strategy of selecting the first u lines.

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

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

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

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

[0141] Where: is the measurement vector; is the measurement error vector, is the covariance matrix of e; h(·) is the nonlinear measurement function vector; is the state variable vector, including the real and imaginary parts of the three-phase complex voltages at nodes other than the balanced nodes:

[0142]

[0143] Where: are the real and imaginary parts of the three-phase complex voltage at node i respectively;

[0144] Establish SE model based on WLS estimation criterion:

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

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

[0147] Let the first-order derivative of the objective function be 0, and use Taylor expansion to linearize it at the initial point x0, and we get:

[0148]

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

[0150] Where: H is the Jacobian matrix; is the partial derivative of the objective function; Δx is the change of the state quantity;

[0151] Starting from the initial point x0, the Gauss-Newton method is used to solve (24). The modified equation at the kth 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] Where: Δx (k) is the change in state quantity at the kth iteration; x (k) is the state quantity at the kth iteration.

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

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

[0156]

[0157] Where: are the node i at the kth iteration. The real and imaginary parts of the phase injected current; are the node i at the kth iteration. Phase active and reactive power pseudo-measurements, these measurements will change according to the current node voltage value in each iteration, and the specific formula depends on the node load model (see equation (27)); are the node i at the kth iteration. Real and imaginary parts of phase complex voltage;

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

[0159]

[0160] Where: is the series conductance of line ik; is the series susceptance of line ik.

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

[0162] After the Jacobian matrix is ​​constantized, the modified equation (25) for the kth iteration becomes:

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

[0164] In addition, the load model needs to be considered during the fault SE iteration process. After a fault occurs, the power consumed by the load will change with the node voltage, especially when the transition resistance is very small, the load model is very different from before the fault. SE can essentially be regarded as a nonlinear fit of the state variable to the measurement, so the state cannot be directly fitted to the node injection power measurement before the fault, but in each iteration, the load should be corrected according to the node voltage obtained in the previous iteration, as shown in the following formula:

[0165]

[0166] Where: are the node i at the kth iteration. Phase active and reactive loads, if there is no distributed generation at node i, then are the node i’s Phase active and reactive load; is the value of node i at the kth iteration Phase voltage; is the rated phase voltage of the distribution system; α1, β1, and γ1 are the coefficients of the constant power, constant current, and constant impedance parts of the active load, respectively; α2, β2, and γ2 are the coefficients of the constant power, constant current, and constant impedance parts of the reactive load, respectively.

[0167] Compared with the SE in normal operation, the faulty SE needs to compensate the fault point current and inject it 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 kth iteration, the fault current can be calculated as follows:

[0168]

[0169] Where: are the three-phase complex injection currents of the root node, fault point f, and node i at the kth 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 faulty node. Therefore, the voltage amplitude measurement should be configured at the end node of each branch line. The voltage amplitude measurement can be measured by a smart meter and transmitted to the control center at a lower frequency, or triggered only when a fault is detected. The matching index of the 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] Where: Estimate values ​​for state variables; are the terminal node i Measured value and estimated value of phase voltage amplitude; Ω end is the set of all terminal nodes.

[0173] Since the weights of voltage amplitude measurement and power pseudo-measurement are quite different, in order to avoid the disparity in the weights of the two types of measurements resulting in one type of measurement residual dominating the matching index and the characteristics of the other type of measurement residual being masked, the influence of measurement weight is not considered in the matching index.

[0174] After calculating the matching index values ​​of all candidate fault points, select the node with the lowest matching index value as an endpoint of the fault 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 reasons are 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 faulty 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 node i voltage estimate close to the measured value, 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 part of the path from the root node to node i, and the estimated voltage value of node i tends to be greater than the measured value. At this time, the SE algorithm will increase the pseudo-measurement residual to reduce the voltage amplitude measurement residual of node i, so as to minimize the total objective function value. In other words, high pseudo-measurement residual is the price that must be paid for accurate fitting of 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), so it can be distinguished 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 point of the faulty line, other hardware-based methods (such as the traveling wave method) can be further used to determine the faulty line and the precise location of the fault.

[0182] Example 2

[0183] In this section, an unbalanced 33-bus distribution system is used to test the proposed method, and the block sparse Bayesian learning (BSBL) algorithm is used to solve (14) to compare with the proposed method.

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

[0185] For voltage amplitude measurement and active and reactive power pseudo-measurement, the relative measurement error is superimposed on the true value according to the following formula:

[0186]

[0187] Where: V i 、V i,true are the measured value and true value of the voltage amplitude of the i-th node respectively; P i , P i,true are the measured value and true value of the active power injected into the i-th node respectively; Q i , Q i,true are the measured value and true value of reactive power injected into the i-th node respectively; randn(0,1 2 ) is the standard Gaussian distribution; e V 、e P They are the relative measurement error percentages of all voltage amplitude measurements and power measurements respectively.

[0188] For voltage phase angle measurement, the absolute measurement error is superimposed on its true value according to the following formula:

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

[0190] Where: θ i ,θ i,true are the measured value and true value of the voltage phase angle of the ith node respectively; e θ is the standard deviation of the measurement error of all voltage phase angles.

[0191] Three single-phase photovoltaic power sources with a total capacity of 800kW are added to nodes 12 and 29 respectively. When the system is operating normally, photovoltaic power generation equipment usually operates in maximum power point tracking mode; when the system fails, the system voltage reduction will affect the photovoltaic output, which is related to the control strategy of the photovoltaic inverter. In this test, the PVSystem component control strategy in OpenDSS is used, and the photovoltaic output changes according to the voltage amplitude of the photovoltaic node:

[0192]

[0193] Where: is the node i at the kth iteration The photovoltaic output active power of the phase; For node i The active power output before the PV fault on the phase.

[0194] First, the first phase was tested, including tests with different numbers of μPMUs and different μPMU measurement error levels;

[0195] Test results with different μPMU numbers:

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

[0197] Table 1 μPMU configuration for 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, as the number of μPMUs increases, the success rate of faulty line screening increases. However, if the line with the minimum matching index value is selected as the final result in each test, the success rate is less than 30% even if 8 μPMUs are configured due to insufficient measurement information; if the selection criteria are relaxed and the top-6 of MI is selected, the success rate can be close to 100%, that is, the correct faulty line always falls in the top-6 of MI, thereby greatly reducing the search space of SE matching in the second stage, proving the effectiveness of the proposed method. In contrast, the BSBL algorithm performs poorly, and the success rate of faulty line screening is less than 60% even when 8 μPMUs are configured; in addition, selecting top-k from the BSBL algorithm results is not helpful in improving the success rate, because this type of algorithm will set most of the elements of the solution vector to zero, making the sorting invalid.

[0201] The success rate of the screening method based on linear model matching 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. Figure 4 It can be seen that the success rate is slightly lower than that of the constant impedance load, but it can be improved by selecting more lines with high matching index values. For example, when 6 μPMUs are configured and top-6 is selected, the success rate of fault line screening can reach 95%. In contrast, the BSBL algorithm has a positioning success rate of less than 50% even when 8 μPMUs are configured, which is only slightly better than the proposed method when top-1 is selected.

[0202] Test of different μPMU measurement error levels:

[0203] Considering two load models, constant impedance load and ZIP load, the proposed screening algorithm based on linear model matching is tested under different μPMU measurement error levels. Five μPMUs are configured at nodes 8, 13, 19, 23, and 29, as shown in Table 1. Five levels of fault resistance are set, which are random numbers between 0~100Ω, 0~200Ω, 0~300Ω, 0~400Ω, and 0~500Ω; 10 μPMU measurement error levels are designed, as shown in Table 2.

[0204] Table 2 Different μPMU measurement error levels

[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 top-6 fault line screening of the linear model matching method under different μPMU measurement error levels is demonstrated. As can be seen from the figure, as the measurement error increases, the success rate of fault line screening decreases to a certain extent. However, even in the 0-500Ω high-resistance fault test with a high error level and weak fault characteristics, the success rate of the algorithm is still not less than 80%. In addition, since the virtual current-based fault location model is derived under the assumption of a constant impedance load, the success rate under the ZIP load is slightly lower than that under the constant impedance load, but the success rate remains above 75%.

[0207] Then the second phase of testing:

[0208] Considering two load models, constant impedance load and ZIP load, the fault location method based on SE matching is tested. According to Table 1, 5 μPMUs are configured at nodes 8, 13, 19, 23, and 29 respectively. V Set to 0.016%, voltage phase angle measurement θ Set to 0.0033°, the voltage amplitude of the end nodes 18, 22, 25, and 33 is measured. V The error level of pseudo measurement is set to 0.1%, and there are 10 levels of pseudo measurement error, namely 5%, 10%, 15%, 20%, 25%, 30%, 35%, 40%, 45%, and 50%. The fault resistance is set to 5 levels, namely 0~100Ω, 0~200Ω, 0~300Ω, 0~400Ω, and random numbers between 0~500Ω. In the test, as long as any end of the fault line can be identified, the fault location is considered successful; at the same time, the short circuit calculation (SC) matching method based on pseudo measurement is compared with the SE matching method.

[0209] The success rate of fault location based on SE / SC matching method under constant impedance load is as follows: Figure 6 As shown in the figure, as the pseudo-measurement error increases, the fault location success rate of the two methods decreases to a certain extent. When the pseudo-measurement error and the fault resistance are both small, the fault location success rate of the SC matching method is slightly higher than that of the SE matching method; and when the pseudo-measurement error and the fault resistance are large, the fault location success rate of the SE matching method is much higher than that of 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 fault location success rate of the SE matching method is still higher than 90%, while the fault location success rate of the SC matching method is only 70%.

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

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

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

[0213] The fault location success rates based on the two-stage method under constant impedance load and ZIP load are as follows: Figure 8 , Fig. 9 As shown in the figure, the fault location success rate of the two-stage method is generally very close to that of the SE matching method alone. As long as the top-6 lines screened out in the first stage include the real fault line, the final result depends only on the effectiveness of the SE matching method in the second stage; at the same time, even if the top-6 lines screened out in the first stage miss the real fault line, the second stage may still identify one end node of the fault line, resulting in the final success rate of the two-stage method being higher than the success rate of the first stage, as shown in Fig. 9 This is because the judgment criteria for successful fault location in the two stages are different: in the first stage, screening out the real fault line is considered successful; while in the second stage, the judgment criteria are more relaxed, as long as any end node of the fault line is identified, the fault location is considered successful. Therefore, even if the fault line is missed in the first stage, it is still possible to identify one end node of the real fault line in the second stage.

[0214] In addition, the CPU calculation time was 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, i.e., the proposed fault line screening method based on linear model matching, is extremely fast in calculation, because the variable dimension of each matching index calculation is only 2; the second stage, i.e., the method based on SE matching, is very time-consuming, because it is necessary to perform iterative nonlinear SE on all unbalanced nodes as candidate fault nodes, which is very computationally intensive; in the two-stage method, by using the endpoints of the six candidate fault lines screened in the first stage as candidate fault nodes, the number of nonlinear SEs required is significantly reduced, and its calculation speed is about 5 times faster than that of using only the second stage, so it is very suitable for practical applications.

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

[0217] method Stage 1 Stage 2only 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 for solving a virtual current fault location model is proposed. The matching index values ​​of all lines are sorted, and the top-u is selected to construct a set of candidate fault lines. Then, the associated nodes of the candidate lines are fault SE, and the nodes with the highest matching degree are selected to further determine the fault line and its precise location. Various fault types, load models, and high-resistance fault scenarios are simulated and tested in a typical three-phase unbalanced distribution network to verify the effectiveness of the proposed method.

[0219] Example 3

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

[0221] A data acquisition module is used to obtain the network topology before the fault, the voltage phase measurement data before and after the fault, and the three-phase active and reactive power injection pseudo-measurements of all unbalanced nodes;

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

[0223] The fault line and fault precise location determination module is used to perform nonlinear fault state estimation SE on all associated nodes of the candidate fault line in turn, 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 for storing one or more programs,

[0227] Among them, 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 network based on synchronous phasor measurement in this embodiment; it should be noted that the computing device may include but is not limited to a processing unit and a storage unit; those skilled in the art can understand that the computing device including a processing unit and a storage unit does not constitute a limitation on the computing device, and may include more components, or a combination of certain components, or different components. For example, the computing device may also include input and output devices, network access devices, buses, etc.

[0228] A computer-readable storage medium having a non-volatile program code executable by a processor, wherein when the computer program is executed by the processor, the steps of the two-stage fault location method for a distribution network based on synchronous phasor measurement in this embodiment are implemented; it should be noted that the readable storage medium can be, for example, but not limited to, an electrical, magnetic, optical, electromagnetic, infrared, or semiconductor system, device or device, or any combination of the above; the program contained on the readable medium can be transmitted using any appropriate medium, including, but not limited to wireless, wired, optical cable, RF, etc., or any suitable combination of the above. For example, the program code for performing the operation of the present invention can be written in any combination of one or more programming languages, including object-oriented programming languages ​​such as Java, C++, etc., and also conventional procedural programming languages ​​such as C language or similar programming languages. The program code can be executed entirely on a user computing device, partially on a user device, as an independent software package, or entirely on a remote computing device or server. In cases involving a remote computing device, the remote computing device may be connected to the user computing device through any type of network, including a local area network (LAN) or a wide area network (WAN), or may be connected to an external computing device (e.g., through the Internet using an Internet service provider).

[0229] Finally, it should be pointed out that the above embodiments are only used to illustrate the technical solutions of the present invention, rather than to limit them. Although the present invention has been described in detail with reference to the above embodiments, a person skilled in the art should understand that the technical solutions described in the above embodiments can still be modified, or some of the technical features can be replaced by equivalents; and these modifications or replacements do not make the essence of the corresponding technical solutions 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 network based on synchronized phasor measurement, characterized in that: The steps include: Obtain the network topology before the fault, voltage phasor measurement data before and after the fault, and three-phase active and reactive power injection pseudo-measurements of all unbalanced nodes; Construct a virtual current fault location model, enumerate each line that may have a fault, and solve the fault location model to obtain a first matching index value, sort all first matching index values ​​in ascending order, and select the first u lines to construct a candidate fault line set; Nonlinear fault state estimation SE is performed on all associated nodes of the candidate fault line in turn, and the node with the highest matching degree is selected as the fault line endpoint. After obtaining an endpoint of the fault line, other hardware-based methods are used to determine the fault line and the precise location of the fault.

2. The distribution network topology tracking method based on finite synchronized phasor measurement according to claim 1 is characterized in that: The method for constructing a virtual current fault location model is: Define virtual current: I v =YΔV (1) Where: is the virtual complex current injection vector; ΔV=V′-V is the complex voltage difference vector between the fault and before the fault; is the positive sequence node admittance matrix before the fault; the virtual injection currents of nodes m and n at both ends of the fault line are not zero, and the virtual injection currents of any node k except the nodes at both ends of the fault line and the unbalanced nodes are all zero; Take out the rows and columns corresponding to the balanced nodes in the matrix and vector in (9), (9) can be rewritten as: Where: is the virtual complex current injection vector at the balance node 1; ΔV1 is the complex voltage difference vector at the balance node 1; Y 11 is the positive sequence self-admittance at the balancing node 1; Y 12 , Y 21 is the positive sequence series admittance of line 1-2; Y is the remaining node admittance matrix after removing the balance node related parts from the positive sequence node admittance matrix; I v is the virtual complex current injection vector except the balancing node 1; Δ V is the complex voltage difference vector between the fault and before the fault except for the balancing node 1; Only the unbalanced nodes are retained, then equation (9) becomes: I v = Y D V (3) Construct the unknown virtual current vector I v Linear observation model associated with voltage phasor measurement changes: D V = ZI v +n (4) Where: η is the error value; Extract the configuration voltage phasor measurement n o The rows corresponding to the nodes are: D V o = Z o I v +n o (5) Where: subscript o represents the row corresponding to the observable node.

3. The distribution network topology tracking method based on finite synchronized phasor measurement according to claim 2 is characterized in that: The method for solving the fault location model is: The linear least squares method is used to solve the linear regression problem (15) to obtain the first matching index value; for a specific fault line l, the calculation formula of the first matching index value is: Where: For Z o The submatrix consisting of two columns corresponding to the lth line in ; MI is the matching index value; is the optimal solution of the following least squares model:

4. The distribution network topology tracking method based on finite synchronized phasor measurement according to claim 1 is characterized in that: When performing nonlinear fault state estimation SE on the associated nodes of the candidate fault line, a state estimation SE model is established based on the weighted least squares WLS estimation criterion: minJ(x)=[zh(x)] T R -1 [zh(x)] (8) Where: J(x) is the objective function; is the measurement vector; is the measurement error vector, is the covariance matrix of e; h(·) is the nonlinear measurement function vector; is the state variable vector, including the real and imaginary parts of the three-phase complex voltages at nodes other than the balanced nodes: Let the first-order derivative of the objective function be 0, and use Taylor expansion to linearize it at the initial point x0, and we get: -H T (x0)R -1 [zh(x0)-H(x0)·Δx]=0 (10) Where: H is the Jacobian matrix; To find the partial derivative of the objective function; Δx is the change of state quantity; Starting from the initial point x0, the Gauss-Newton method is used to solve (24). The modified equation at the kth iteration is: Δx (k) =[H T (x (k) )R -1 H(x (k) )] -1 H T (x (k) )R -1 [z-h(x (k) )] (11) Where: Δx (k) is the change in state quantity at the kth iteration; x (k) is the state quantity at the kth iteration; After converting the node injection power measurement into the node injection current measurement, the Jacobian matrix becomes a constant matrix. After the Jacobian matrix is ​​constantized, the modified equation (25) of the kth iteration becomes: Δx (k) =[H T R -1 H] -1 H T R -1 [z-h(x (k) )] (12)。 5. The distribution network topology tracking method based on finite synchronized phasor measurement according to claim 1 is characterized in that: When performing nonlinear fault state estimation on the associated nodes of the candidate fault line, the load model needs to be considered in the fault state estimation iteration process. In each iteration, the load is corrected according to the node voltage obtained in the previous iteration, as shown in the following formula: Where: are the node i at the kth iteration. Phase active and reactive loads, if there is no distributed generation at node i, then are the node i’s Phase active and reactive load; is the value of node i at the kth iteration Phase voltage; is the rated phase voltage of the distribution system; α1, β1, and γ1 are the coefficients of the constant power, constant current, and constant impedance parts of the active load, respectively; α2, β2, and γ2 are the coefficients of the constant power, constant current, and constant impedance parts of the reactive load, respectively.

6. The distribution network topology tracking method based on finite synchronized phasor measurement according to claim 1 is characterized in that: When performing nonlinear fault state estimation on the associated nodes of the candidate fault line, the fault point current needs to be compensated and injected into the assumed virtual fault point. In the kth iteration, the fault current can be calculated as follows: Where: are the three-phase complex injection currents of the root node, fault point f, and node i at the kth iteration respectively.

7. The distribution network topology tracking method based on finite synchronized phasor measurement according to claim 1 is characterized in that: The second matching index value of the candidate fault node i is composed of the state estimation measurement residual vector and the L1 norm of the terminal node voltage amplitude measurement residual vector composition: Where: Estimate values ​​for state variables; are the terminal node i Measured value and estimated value of phase voltage amplitude; Ω end is the set of all terminal nodes; After calculating the second matching index values ​​of all candidate fault points, select the node with the lowest second matching index value as an endpoint of the fault line:

8. The distribution network topology tracking method based on finite synchronized phasor measurement according to claim 1 is characterized in that: When there is no voltage amplitude measurement at the downstream nodes of the fault point, the matching method based on fault state estimation cannot identify the faulty node, and voltage amplitude measurement needs to be configured at each end node.

9. A two-stage fault location device for distribution network based on synchronous phasor measurement, characterized in that: include: A data acquisition module is used to obtain the network topology before the fault, the voltage phase measurement data before and after the fault, and the three-phase active and reactive power injection pseudo-measurements of all unbalanced nodes; A candidate fault line set construction module is used to construct a virtual current fault location model, enumerate each line that may have a fault, and solve the fault location model to obtain a first matching index value, sort all first matching index values ​​in ascending order, and select the first u lines to construct a candidate fault line set; The fault line and fault precise location determination module is used to perform nonlinear fault state estimation SE on all associated nodes of the candidate fault line in turn, 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.

10. A computing device, characterized in that: include: one or more processing units; A storage unit for storing 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 execute the method as described in any one of claims 1 to 8.

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