Flexible power distribution network fault positioning method and system based on three-phase robust state estimation

Abstract

The invention belongs to the field of power distribution networks, and provides a flexible power distribution network fault positioning method and system based on three-phase robust state estimation.The method comprises the steps that firstly, a fault state estimation model based on measurement transformation is constructed by means of node injection pseudo measurement generated by real-time voltage phasor measurement after a fault and state estimation before the fault; the false measurement is injected into the flexible switch instantaneous locking correction node when the fault is considered; secondly, establishing a quadratic-constant generalized maximum likelihood estimation model, solving by using an iterative variable weight least square algorithm to realize real-time measurement weight self-adaption, and inhibiting pollution of bad data to an estimation result after delaying the real-time measurement weight to be adjusted to the first iteration; and thirdly, providing a fault positioning algorithm based on fault state estimation matching, performing fault state estimation on each candidate node, designing a matching index which comprehensively considers multi-source measurement weight difference and a measurement position, and determining a fault position by comparing the matching degree of each candidate node.

Description

Technical Field

[0001] The present invention belongs to the technical field of distribution networks, and particularly relates to a flexible distribution network fault location method and system based on three-phase robust state estimation. Background Technique

[0002] The statements in this part only provide background technical information related to the present invention and do not necessarily constitute prior art.

[0003] The distribution network is the last link of power transmission and is a key infrastructure for maintaining reliable power supply to end users. However, the complex structure and harsh operating environment of the distribution network lead to a higher probability of distribution network faults compared with the transmission system. If the faults are not handled in time, it will seriously affect the reliable power supply to the user side. Therefore, it is very important to solve the faults in time. Fault handling includes fault location, fault isolation, and power supply restoration. Accurate fault location is the basis for fault isolation and power supply restoration. Due to the three-phase unbalanced structure of the distribution network and insufficient measurement configuration, the traditional fault location methods in transmission lines are not applicable, so the requirements for algorithms are more stringent.

[0004] The fault location methods of the distribution network are mainly divided into three categories: methods based on measurement signals, methods based on injected signals, and methods based on artificial intelligence. Among them, the measurement signal methods include methods based on steady-state measurement signals, traveling wave methods, methods based on transient measurement signals, harmonic methods, etc. Although the methods based on measurement signals are systematic in theory, they have many limitations in practical applications, such as the requirement for network-wide observability and the performance degradation problems under the penetration of distributed energy and network parameter changes. The methods based on signal injection avoid some of the limitations of measurement requirements, but they show operational sensitivity to the impedance characteristics of faults and require a large amount of configuration costs. The methods based on artificial intelligence, although having potential in fault identification, also have the following problems in actual deployment: 1) relying on a large amount of training data and the limited representativeness of the fault data set; 2) being very sensitive to topological changes; 3) being a "black box" calculation inside and having poor interpretability.

[0005] In recent years, μPMU devices with high precision and high sampling rate have been gradually applied to distribution systems, creating conditions for accurate fault location in distribution networks. μPMU usually obtains synchronous signals from the GPS / Beidou system and provides time-aligned voltage and current phasor measurements during faults, which greatly improves the observability of the distribution network under fault scenarios. In the prior art, a dual-objective optimization framework is proposed to configure μPMU devices by minimizing the installation cost and maximizing the observability of fault location through the ε-constraint method and mixed-integer linear programming. By analyzing voltage deviation and impedance parameters, a literature proposes an online fault tracking method based on iterative support detection. However, this method actually relies on sufficient μPMU coverage, while the number of installed devices in the actual system is limited, thus affecting the accuracy of fault location. To solve the problem of limited number of μPMU configurations in fault location, the fault location method based on SE has unique advantages. There is also a literature proposing a distribution network fault location method based on SE, which identifies the fault location by setting virtual fault points and performing fault SE. However, it still requires a comprehensive configuration of μPMU at each node of the system. Introducing the pseudo-measurement of node injection power enhances the observability of three-phase unbalanced systems and reduces the configuration requirements for μPMU.

[0006] Existing measurement-based methods ignore the impact of measurement anomalies. Under fault conditions, measurement data is subject to various interferences such as time synchronization errors and electromagnetic noise under large short-circuit currents, resulting in non-Gaussian outliers in the measurement data, which violates the assumption that traditional SE measurement errors follow a Gaussian distribution, and further leads to the deterioration of SE results. When the system is operating normally, the voltage values of each node are close to 1.0 p.u., so gross error filtering can be achieved through threshold checking in the data preprocessing stage. However, during a fault, due to the fault type, fault location, and the size and location of the fault resistance, the voltage drop caused by the fault current cannot be predicted, and it is impossible to determine whether the voltage limit violation is a real fault response or a measurement anomaly. Therefore, traditional data preprocessing methods cannot reliably eliminate contaminated measurement data and are difficult to distinguish real fault responses from measurement distortions. Summary of the Invention

[0007] To solve the above problems, the present invention proposes a flexible distribution network fault location method and system based on three-phase robust state estimation. The present invention has extremely low amplitude sensitivity to bad data and exhibits good stability regardless of the severity of the bad data.

[0008] According to some embodiments, the first solution of the present invention provides a flexible distribution network fault location method based on three-phase robust state estimation, adopting the following technical solutions:

[0009] The flexible distribution network fault location method based on three-phase robust state estimation includes:

[0010] Obtain real-time voltage phasor measurements after a fault and pseudo measurements of node injections before the fault;

[0011] Based on the pseudo measurements of node injections and real-time voltage phasor measurements, after delaying the weight adjustment of the real-time voltage phasor measurements until after the first iteration, iteratively solve the three-phase robust fault state estimation model and output the fault state estimation results;

[0012] Take all load nodes as the candidate fault node set, perform iterative solution of the three-phase robust fault state estimation model for each candidate fault node, and calculate the matching index values of the candidate fault nodes according to the solution results;

[0013] Divide all adjacent lines of the candidate fault node with the minimum matching index value into multi-line lines of equal length, use the division points of the adjacent lines as virtual fault nodes, and re-locate the fault for all virtual fault nodes to determine the exact fault location.

[0014] Further, the three-phase robust fault state estimation model is specifically:

[0015]

[0016] Where: r i = z i - h i (x) is the residual of the i-th measurement; is the measurement column vector, m is the number of measurements; h(x) is the measurement function column vector; ρ(·) is the quadratic-constant (QC) penalty function.

[0017] Further, the iterative solution of the three-phase robust fault state estimation model based on the pseudo measurements of node injections and real-time voltage phasor measurements, after delaying the weight adjustment of the real-time voltage phasor measurements until after the first iteration, is specifically:

[0018] Based on the input network model, pseudo measurements of node injections before the fault, real-time voltage phasor measurements, and the assumed fault nodes;

[0019] For flexible switch nodes, subtract the flexible switch injection pseudo measurements from the pseudo measurements of node injections before the fault;

[0020] Start with a flat voltage, and the iteration number k = 1;

[0021] According to the current voltage estimation value, correct the pseudo measurements of PV injection power and the pseudo measurements of load node injection power;

[0022] Calculate the fault current and superimpose it on the pseudo measurements of the injection current of the assumed fault nodes;

[0023] Calculate the residual vector and update the weights of the phasor measurement values;

[0024] Update the state variables. When k = 1, use the corrected node injection pseudo-measurement for update; when k > 1, use the corrected node injection pseudo-measurement and the real-time voltage phasor measurement for update;

[0025] Until the algorithm converges, output the fault state estimation result.

[0026] Furthermore, the state variables are updated by the following formula:

[0027] Δx (k) =[H T Φ(x (k) )H] -1 H T Φ(x (k) )[z - h(x (k) )];

[0028] Where, is the measurement column vector, m is the number of measurements; h(x (k) ) is the measurement function column vector at the k-th iteration; x (k) is the three-phase state vector at the k-th iteration, H is the measurement Jacobian matrix; Φ is the weight factor matrix.

[0029] Furthermore, calculate the matching index value of the candidate fault node according to the solution result, specifically:

[0030]

[0031] In the formula: is the estimated value of the state variable; is the measurement column vector, m is the number of measurements; is the measurement function column vector of the estimated value of the state variable; the norm is defined as are respectively the measured value and the estimated value of the phase voltage amplitude of each feeder end node i; Ω end is the set of feeder end nodes.

[0032] Furthermore, re-perform fault location for all virtual fault nodes to determine the exact fault location, specifically:

[0033] Perform iterative solution of the three-phase robust fault state estimation model for each virtual fault node in turn, and calculate the matching index value of the virtual fault node according to the solution result;

[0034] Determine the exact fault location with the virtual fault node having the minimum matching index value.

[0035] According to some embodiments, the second solution of the present invention provides a flexible distribution network fault location system based on three-phase robust state estimation, adopting the following technical solution:

[0036] A flexible distribution network fault location system based on three-phase robust state estimation, comprising:

[0037] A data acquisition module, configured to acquire real-time voltage phasor measurements after a fault and node injection pseudo-measurements before the fault;

[0038] A fault state estimation module solving module, configured to iteratively solve a three-phase robust fault state estimation model based on node injection pseudo-measurements and real-time voltage phasor measurements, and output a fault state estimation result after adjusting the weight of the delayed real-time voltage phasor measurements until the first iteration;

[0039] A candidate fault point screening module, configured to use all load nodes as a candidate fault node set, perform iterative solution of the three-phase robust fault state estimation model for each candidate fault node, and calculate the matching index value of the candidate fault node according to the solution result;

[0040] An accurate fault location module, configured to divide all adjacent lines of the candidate fault node with the minimum matching index value into multi-line lines of equal length, use the division points of the adjacent lines as virtual fault nodes, re-perform fault location for all virtual fault nodes, and determine the accurate fault location.

[0041] According to some embodiments, the third solution of the present invention provides a computer-readable storage medium.

[0042] A computer-readable storage medium, on which a computer program is stored, and when the program is executed by a processor, it implements the steps in the flexible distribution network fault location method based on three-phase robust state estimation described in the first aspect above.

[0043] According to some embodiments, the fourth solution of the present invention provides a computer device.

[0044] A computer device, comprising a memory, a processor, and a computer program stored on the memory and executable on the processor, and when the processor executes the program, it implements the steps in the flexible distribution network fault location method based on three-phase robust state estimation described in the first aspect above.

[0045] According to some embodiments, the fifth aspect of the present invention provides a computer program product or a computer program.

[0046] The present invention provides a computer program product or a computer program, which includes computer instructions stored in a computer-readable storage medium. The processor of the computer device reads the computer instructions from the computer-readable storage medium and executes the computer instructions, so that the computer device executes the steps in the flexible distribution network fault location method based on three-phase robust state estimation as described in the first aspect above.

[0047] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0048] The present invention proposes a flexible distribution network fault location method based on three-phase robust state estimation. First, a fault state estimation model based on measurement transformation is constructed by using the real-time voltage phasor measurement after the fault and the node injection pseudo-measurement generated by the SE before the fault, and the node injection pseudo-measurement is corrected by considering the instantaneous locking of the flexible switch during the fault. Secondly, a quadratic-constant type generalized maximum likelihood estimation model is established, and the iterative variable-weight least squares algorithm is used to solve the problem to realize the adaptive adjustment of the real-time measurement weight. Thirdly, a fault location algorithm based on the matching of the fault SE is proposed, and the fault SE is executed for each candidate node. A matching index considering the weight difference of multi-source measurements and the measurement position is designed, and the fault location is determined by comparing the matching degrees of each candidate node. Finally, simulation tests are carried out on a 33-node unbalanced distribution network to verify the effectiveness of the proposed method under conditions such as strong pseudo-measurement noise, high fault resistance, and serious bad data. Description of the Drawings

[0049] The specification drawings forming a part of the present invention are used to provide a further understanding of the present invention. The schematic embodiments of the present invention and their descriptions are used to explain the present invention and do not constitute an improper limitation of the present invention.

[0050] Figure 1 It is a flowchart of the flexible distribution network fault location method based on three-phase robust state estimation according to the embodiment of the present invention;

[0051] Figure 2 It is a flowchart of the fault location method based on fault state estimation according to the embodiment of the present invention;

[0052] Figure 3 It is a flowchart of the fault state estimation algorithm according to the embodiment of the present invention;

[0053] Figure 4 It is a diagram of the 33-node system according to the embodiment of the present invention;

[0054] Figure 5 It is a comparison chart of the matching index values of the fault location methods based on the traditional SE and the robust SE at different nodes according to the embodiment of the present invention;

[0055] Figure 6 It is a comparison chart of multi-scenario comprehensive test results of the fault location methods based on traditional SE and robust SE without bad data described in the embodiments of the present invention;

[0056] Figure 7 It is a comparison chart of multi-scenario comprehensive test results of the fault location methods based on traditional SE and robust SE under 25% - 35% bad data described in the embodiments of the present invention;

[0057] Figure 8 It is a comparison chart of multi-scenario comprehensive test results of the fault location methods based on traditional SE and robust SE under 45% - 55% bad data described in the embodiments of the present invention;

[0058] Figure 9 It is a comparison chart of multi-scenario comprehensive test results of the fault location methods based on traditional SE and robust SE under 75% - 85% bad data described in the embodiments of the present invention. Detailed implementation manners

[0059] The present invention will be further described below in conjunction with the accompanying drawings and embodiments.

[0060] It should be noted that the following detailed descriptions are all illustrative and are intended to provide further explanations of the present invention. Unless otherwise specified, all technical and scientific terms used herein have the same meaning as commonly understood by those of ordinary skill in the technical field to which the present invention belongs.

[0061] It should be noted that the terms used herein are only for describing specific implementation manners and are not intended to limit the exemplary embodiments according to the present invention. As used herein, unless the context clearly indicates otherwise, the singular forms are also intended to include the plural forms. In addition, it should be understood that when the terms "comprise" and / or "include" are used in this specification, they indicate the presence of features, steps, operations, devices, components, and / or combinations thereof.

[0062] Without conflict, the embodiments in the present invention and the features in the embodiments can be combined with each other.

[0063] Embodiment 1

[0064] As Figure 1As shown in the figure, this embodiment provides a flexible distribution network fault location method based on three-phase robust state estimation. This embodiment takes the application of this method to a server as an example. It can be understood that this method can also be applied to a terminal, and can also be applied to a system including a terminal and a server, and is realized through the interaction between the terminal and the server. The server can be an independent physical server, or a server cluster or distributed system composed of multiple physical servers, or a cloud server that provides basic cloud computing services such as cloud services, cloud databases, cloud computing, cloud functions, cloud storage, network servers, cloud communications, middleware services, domain name services, security services CDN, and big data and artificial intelligence platforms. The terminal can be a smart phone, a tablet computer, a laptop computer, a desktop computer, a smart speaker, a smart watch, etc., but is not limited thereto. The terminal and the server can be directly or indirectly connected through wired or wireless communication methods, and this application does not make any restrictions here. In this embodiment, the method includes the following steps:

[0065] Obtain the real-time voltage phasor measurement after the fault and the pseudo-measurement of the node injection before the fault;

[0066] Based on the pseudo-measurement of the node injection and the real-time voltage phasor measurement, after adjusting the weight of the real-time voltage phasor measurement to the first iteration, iteratively solve the three-phase robust fault state estimation model, and output the fault state estimation result;

[0067] Take all load nodes as the candidate fault node set, perform iterative solution of the three-phase robust fault state estimation model for each candidate fault node, and calculate the matching index value of the candidate fault node according to the solution result;

[0068] Divide all adjacent lines of the candidate fault node with the smallest matching index value into multi-line lines of equal length, use the division points of the adjacent lines as virtual fault nodes, re-perform fault location for all virtual fault nodes, and determine the exact fault location.

[0069] Accurate fault location is crucial for reliable power supply in distribution networks. However, due to the unknown fault location, fault type, and fault resistance magnitude, it is difficult for traditional methods to distinguish true fault responses from measurement distortions. Therefore, this embodiment proposes a fault location method for flexible distribution networks based on three-phase robust state estimation. First, a fault state estimation model based on measurement transformation is constructed using the real-time voltage phasor measurements after the fault and the node injection pseudo-measurements generated by the pre-fault state estimation, and the node injection pseudo-measurements are corrected considering the instantaneous locking of flexible switches during the fault; second, a quadratic-constant generalized maximum likelihood estimation model is established, and the iterative variable-weight least squares algorithm is used to solve for real-time measurement weight adaptation, and the weight of the delayed real-time measurement is adjusted after the first iteration to suppress the contamination of the estimation results by bad data; third, a fault location algorithm based on fault state estimation matching is proposed, fault state estimation is performed on each candidate node, a matching index that comprehensively considers the weight differences of multi-source measurements and the measurement positions is designed, and the fault location is determined by comparing the matching degrees of each candidate node. Finally, simulation tests are carried out on a 33-node unbalanced distribution network to verify the effectiveness of the proposed method under conditions such as strong pseudo-measurement noise, high fault resistance, and severe bad data.

[0070] Specifically, the method described in this embodiment includes:

[0071] S1: Fault state estimation of three-phase unbalanced flexible distribution networks

[0072] S1.1: Three-phase state estimation based on measurement transformation

[0073] For a three-phase distribution network with n nodes, its measurement model is:

[0074] z = h(x) + e (1);

[0075] Where: is the measurement column vector, m is the number of measurements; h(x) is the measurement function column vector; e is the measurement error vector, is the three-phase state vector in the rectangular coordinate system, including the real and imaginary parts of the three-phase voltages of each node except the slack node (numbered 1):

[0076]

[0077] Where: are the real and imaginary part column vectors of the three-phase voltages of node i, respectively.

[0078] An SE model is established based on the weighted least squares estimation criterion:

[0079] J(x) = [z - h(x)] T R -1 [z - h(x)] (3);

[0080] Where: is the measurement error covariance matrix.

[0081] Let the first-order derivative of the objective function be 0:

[0082]

[0083] Where: H(x) is the Jacobian matrix of the measurement equation with respect to the state variable, that is

[0084] The Gauss-Newton method is used to iteratively solve the nonlinear equation group (4). The k-th iteration correction equation of the state vector is:

[0085] Δx (k) =[H T (x (k) )R -1 H(x (k) )] -1 H T (x (k) )R -1 [zh(x (k) )](5);

[0086] Where: Δx (k) =x (k+1) -x (k) , is the state variable correction value of the kth iteration; H(x (k) ) is the measurement Jacobian matrix of the kth iteration.

[0087] There are two types of measurements used for faulty SE:

[0088] 1) The pseudo-measurement of injected power of all unbalanced nodes can be given by the real-time SE before the fault. When a short circuit fault occurs in the flexible distribution system, the soft open point (SOP) is considered to be instantly locked after detecting the fault. Therefore, the pseudo-measurement of injected power of the node before the fault needs to be subtracted from the injected power before the fault:

[0089]

[0090] Where: are respectively used for the faulty SE at node i Phase active and reactive power injection pseudo-measurement; They are respectively the nodes i provided by SE before the failure Phase active and reactive power injection pseudo-measurement; are respectively the SOP injected into node i before the fault Phase active and reactive power.

[0091] Since H(x(k) ) Each iteration requires reconstruction and involves a large amount of computation. Therefore, in each iteration, the injected power measurement of the node is transformed into an equivalent injected complex current measurement, so that the measurement Jacobian matrix becomes a constant matrix:

[0092]

[0093] In the formula: are respectively the real and imaginary parts of the pseudo-measurement of the phase current injection current at node i; are respectively the real and imaginary parts of the phase voltage at node i at the k-th iteration.

[0094] The three-phase injected complex current measurement function after measurement transformation is:

[0095]

[0096] In the formula: are respectively the three-phase conductance and susceptance matrices of branch i-k; is the three-phase injected complex current vector of node i; are respectively the real and imaginary parts of; j 2 =-1.

[0097] 2) Configure the real-time complex voltage measurement of μPMU nodes. These measurement values can be directly used in SE calculations.

[0098] After changing H(x (k) ) into a constant matrix, Equation (5) becomes:

[0099] Δx (k) =[H T R -1 H] -1 H T R -1 [z - h(x (k) )](9);

[0100] Use Equation (9) as the k-th iteration correction equation for the final state vector.

[0101] S1.2: Correction of PV node injection pseudo-measurement under fault

[0102] In the distribution system, PV usually adopts maximum power point tracking control to maximize power output. However, when a fault occurs, the voltage drop caused by the fault current will also cause changes in PV power output, and the actual power output depends on the implemented control strategy. When the voltage drop is within a certain range, the PV power output can be maintained; if the voltage continues to drop and the PV has low voltage ride-through capability, the PV power output is approximately quadratic proportional to the voltage amplitude:

[0103]

[0104] Where: P, P f are the active power outputs of the PV node before and during the fault, respectively; V f is the voltage magnitude of the PV node during the fault; V N is the rated voltage of the system; η is the coefficient reflecting the constant power ability of the PV.

[0105] Therefore, the injected pseudo-measurements of the PV node before the fault cannot be directly applied to the SE during the fault. So in each iteration of the SE, the injected power pseudo-measurements of this node need to be corrected according to the magnitude of the voltage of the current PV node:

[0106]

[0107] Where: is the phase injected active power of the PV node i at the k-th iteration; is the phase voltage magnitude of the PV node i at the k-th iteration.

[0108] S1.3: Correction of the injected pseudo-measurements of the load node under the fault

[0109] The composite load of the load node generally adopts the ZIP model. In addition to the need to correct the node injection power of the SOP node, the change in the power consumed by the load caused by the voltage drop of the feeder due to the occurrence of the fault also needs to be considered. Therefore, the injected pseudo-measurements of the load node before the fault cannot be directly applied to the SE during the fault. So in each iteration of the SE, the injected power pseudo-measurements of this node need to be dynamically corrected according to the magnitude of the current voltage of the node:

[0110]

[0111] Where: are the phase injected active and reactive powers of the load node i at the k-th iteration, respectively; α, β, and γ are the coefficients of the constant impedance, constant current, and constant power parts in the load, respectively, and α + β + γ = 1.

[0112] S1.4: Fault current compensation for the ground fault

[0113] Another difference between SE under fault scenarios and traditional SE is related to the grounding characteristics of the system. In a system with effectively grounded neutral points, when a grounding fault occurs at a certain node, since a loop is formed through the earth at the grounding point, a fault current will be generated at the grounding point, thereby changing the network current distribution. Therefore, a μPMU can be configured at the root node to monitor the total complex current phasor of the fault feeder. Then, in each iteration of SE, the fault node injection current is calculated by subtracting the load currents of all nodes from the root node current and superimposed on the original injection current pseudo-measurement at the fault point:

[0114]

[0115] Where: is the phase current phasor of the fault point f at the k-th iteration; is the phase current phasor of the root node at the k-th iteration.

[0116] Since the fault type is unknown when the fault occurs, the fault current of each phase can be calculated separately. For example, when a phase A grounding fault occurs, the fault currents of phases B and C gradually approach zero during the iteration process, and it can be determined that the fault phase is phase A. In this way, the proposed method can not only identify the fault type but also make the algorithm unaffected by the transition resistance.

[0117] S2: Fault location based on three-phase robust fault state estimation

[0118] As mentioned above, two types of measurement data are used in SE: μPMU measurements and pseudo-measurements. The pseudo-measurement values are derived from the SE results before the fault and can be considered free of gross errors. Under fault conditions, due to factors such as time synchronization errors and electromagnetic interference under large short-circuit currents, the real-time μPMU measurements may exhibit non-Gaussian anomalies, violating the Gaussian distribution error assumption of traditional SE and leading to serious errors in the SE results. When the system is operating normally, the voltages of all nodes are close to 1.0 p.u., and obvious bad data can be directly screened out during the data preprocessing stage. However, when a short-circuit fault occurs in the system, it will cause a voltage drop in the system, and there will be nodes with voltages far lower than 1.0 p.u. Due to the fault type, fault location, and the size and location of the fault resistance, the voltage drop caused by the fault current cannot be predicted, and it is impossible to determine whether the voltage violation is a real fault response or a measurement anomaly. Therefore, in this section, a method based on three-phase robust SE is proposed to achieve reliable fault location.

[0119] S2.1: Three-phase robust fault state estimation model

[0120] Robust estimation has three properties:

[0121] 1) Efficiency: Under the assumed measurement model, the estimation should be optimal or close to optimal.

[0122] 2) Stability: When there are minor deviations between the actual measurement model and the assumed model, the estimation is less affected.

[0123] 3) Crash resistance: When there are severe deviations between the actual measurement model and the assumed model, the estimation is not affected by crashes.

[0124] Adopt the quadratic-constant generalized maximum likelihood estimation (M-estimation) criterion to construct a robust estimation model as follows:

[0125]

[0126] Where: r i = z i - h i (x) is the residual of the i-th measurement; ρ(·) is the quadratic-constant (QC) penalty function:

[0127]

[0128] Where: λ is the adjustment parameter.

[0129] Use the IRLS algorithm to solve this model. Let the first-order partial derivative of the objective function be zero, and we get:

[0130]

[0131] Where: Φ(r) = diag(φ(r i )) is the weight factor matrix; is the residual vector; W = R -1 is the initial weight matrix; the first-order derivative of the penalty function and the weight factor φ(r i ) are given by the following formula:

[0132]

[0133] Use the Gauss-Newton method to iteratively solve the nonlinear equations (16). The correction equation of the state vector at the k-th iteration is as follows:

[0134] Δx (k) = [H T Φ(x (k) )H] -1 H T Φ(x (k) )[z - h(x (k) )](18);

[0135] Among them, is the measurement column vector, m is the number of measurements; h(x (k) ) is the measurement function column vector at the k-th iteration; x(k) is the three-phase state vector at the k-th iteration, H is the measurement Jacobian matrix; Φ is the weight factor matrix.

[0136] The weight factor of μPMU measurement is dynamically updated during the iteration process, and the relationship between r i and λ is rejudged before each iteration, and the weight is adjusted, while the weight factor of the pseudo-measurement always remains 1. In this way, the influence of bad data can be resisted.

[0137] The flow chart of the robust SE algorithm for fault adaptation is as Figure 3 shown. It should be noted that considering the low measurement redundancy of the distribution network, an additional strategy is implemented in the algorithm: in the first iteration of SE, only the pseudo-measurement is used to update the state variables, and the μPMU measurement values are only involved in the calculation in subsequent iterations. If bad data participates in the calculation in the first iteration, it may cause the bad data to dominate the residual distribution, and due to the low measurement redundancy, the situation cannot be reversed in subsequent iterations, but the normal data will be offset instead, and finally the algorithm will lose the ability to resist bad data. The specific robust SE algorithm is as follows:

[0138] Based on the input electrical network model, pre-fault node injection pseudo-measurements, real-time voltage phasor measurements, and candidate fault nodes;

[0139] For flexible switch nodes, subtract the flexible switch injection pseudo-measurement from the pre-fault node injection power pseudo-measurement;

[0140] Start with voltage flat, and the iteration number k = 1;

[0141] According to the current voltage estimate, correct the PV injection power pseudo-measurement and the load node injection power pseudo-measurement;

[0142] Calculate the fault current according to formula (13) and superimpose it on the injection current pseudo-measurement of the candidate fault node;

[0143] Calculate the residual vector and update the phasor measurement value weight according to formula (15);

[0144] Update the state variables according to formula (17). When k = 1, use the modified node injection pseudo-measurement for update; when k > 1, use the modified node injection pseudo-measurement and the real-time voltage phasor measurement for update;

[0145] Until the algorithm converges, output the fault state estimation result.

[0146] S2.2: Fault location based on robust SE

[0147] Short-circuit faults occurring at different locations and of different types in the distribution network will result in different voltage distributions in the system. Based on this, fault location and fault type identification can be realized. The steps are as follows:

[0148] 1) Take all load nodes as the candidate fault node set;

[0149] 2) Perform three-phase robust fault SE for each candidate fault node, and in each iteration, inject the calculated fault current into the candidate fault node;

[0150] 3) After the three-phase robust fault SE converges, calculate the matching index value.

[0151] Repeat this process until all nodes in the candidate fault node set are traversed.

[0152] The matching index of candidate fault node i consists of the following two items:

[0153]

[0154] Where: is the estimated value of the state variable; the norm is defined as are the measured value and estimated value of the phase voltage amplitude at the end node i of each feeder respectively; Ω end is the set of end nodes of the feeders.

[0155] The explanations of the two parameters in the above formula are as follows:

[0156] 1) The first item is the L2 norm of the measurement residual vector (excluding bad data with a weight factor of 0). Since there is a large difference in the weights of voltage amplitude measurements and pseudo-measurements, in order to avoid a certain type of measurement residual in the matching index dominating and masking the characteristics of the other type of measurement residual, the influence of the initial weight matrix W is not considered in the index.

[0157] 2) As Figure 1 shown, the second item is the L1 norm of the phasor of the voltage amplitude measurement residual at the end nodes of each branch of the feeder. Since these voltage amplitude measurements from low-cost smart meters have a non-linear relationship with the state variables, if they participate in the SE calculation, the Jacobian matrix cannot be kept constant, so they are only used for residual matching. If μPMUs are configured at these nodes, they can directly participate in the SE calculation, and in this case, this item can be omitted to simplify the index formula.

[0158] After calculating the matching indexes of all candidate fault points, select the node with the lowest matching index value which is an end point of the fault branch.

[0159]

[0160] According to the accuracy requirement, this node All adjacent lines are divided into multiple segments of equal length, and the division points of the adjacent lines are used as virtual fault nodes; for the division of adjacent lines, according to the actual requirements for fault location accuracy, for example, the fault location accuracy is 100m, this node has three adjacent lines. One is 300m with 2 division points; one is 200m with 1 division point; one is 100m with 0 division points; all the division points on these three adjacent lines are used as virtual fault nodes.

[0161] For all virtual fault nodes, re - execute the above - mentioned fault location method, and determine the exact fault location based on the virtual fault node with the minimum matching index value.

[0162] S2.3: Measurement Configuration

[0163] If there is no voltage magnitude measurement configured downstream of the fault point, the fault location method based on SE will fail. Therefore, voltage magnitude measurement devices should be installed at the end nodes of each feeder in the distribution network. The specific reason analysis is as follows:

[0164] 1) When there is a voltage magnitude measurement at the upstream node i of the fault, no matter which node downstream the fault is assumed to occur at, the compensated fault current will start from the root node and flow through node i. Therefore, for the fault SE calculation at any downstream node, the calculated voltage magnitude values at node i are almost equal, and it is impossible to distinguish which specific location downstream has a fault.

[0165] 2) When there is a voltage magnitude measurement at the downstream node i of the fault, considering different positions as candidate fault points and performing fault SE, the compensated current flowing from the root node to node i in each fault SE is different, that is, the estimated voltage magnitude values at node i obtained from each fault SE are different. Therefore, from all the calculation results, the calculation scenario that is closest and most matched to the measurement provided by SM can be selected to determine the fault location.

[0166] Simulation Verification

[0167] Specifically, the proposed fault location method is tested in a 33 - node distribution system with a rated voltage of 12.66 kV.

[0168] Such as Figure 4As shown in the figure, the standard 33-node system is expanded into a three-phase unbalanced network. Among them, two PV power generation devices are added at nodes 12 and 29, and all loads are set as constant impedance loads. Nodes 18 and 33 are flexibly interconnected through SOP. Six μPMUs are configured at nodes 1, 6, 14, 20, 24, and 30, and pseudo-measurements are adopted at all nodes except the slack node. The output range of single-phase loads is set from 60 kW + j20 kVar to 200 kW + j100 kVar. The transformer at the root node is set with effectively grounded neutral point. Power flow data is obtained through simulation in OpenDSS, the maximum number of iterations of SE is set to 20, and the convergence criterion is max(Δx) < 0.1.

[0169] Typical scenario test

[0170] To verify the performance of the fault location method based on SE in typical scenarios, an AB-phase ground short-circuit fault with a fault resistance of 10 Ω is set at node 24. All measurement values are generated by superimposing Gaussian errors on the true power flow values. The relative errors of pseudo-measurements, voltage amplitude measurements, and current amplitude measurements are set to 5%, 0.0016%, and 0.4% respectively; the absolute errors of voltage and current phase angle measurements are set to 0.001 rad and 0.0058 rad. β in the robust SE is set to 100.

[0171] To verify the robustness of the proposed fault location method based on robust SE, a μPMU device (except node 1) is randomly selected, and the three-phase voltage amplitude measurement values are set to 45% - 55% of the true values, so as to generate 6 bad data including real and imaginary parts, and the fault location algorithm based on robust SE is used for calculation to verify its resistance to bad data. For comparison, traditional SE is used for calculation in the scenario with bad data.

[0172] The matching index values obtained by the two methods at the candidate nodes are as Figure 5 shown. The results show that the robust SE method obtains the minimum matching index value at node 24, accurately identifies the true fault location, and at the same time resists the influence of bad data; in contrast, the matching index values calculated by the traditional SE method at different nodes are seriously interfered by bad data, with large offsets and unable to complete fault location.

[0173] Comprehensive multi-scenario test

[0174] This section conducts a detailed multi-scenario test on the line fault location ability of the proposed algorithm. Except for line 1-2, 10 different fault types are simulated on the remaining 31 lines: single-phase grounding faults (A-G, B-G, C-G), two-phase grounding faults (AB-G, BC-G, AC-G), two-phase faults (AB, BC, AC), and three-phase faults (ABC), totaling 310 fault scenarios. The fault locations are set to be randomly distributed within the range of 10% to 90% of the length of each line, and three different fault resistance levels of 0 to 100 Ω, 0 to 200 Ω, and 0 to 500 Ω are tested. The relative error of the pseudo-measurement is divided into 10 levels and varies within the range of 5% to 50%.

[0175] To test the robustness of the proposed fault location algorithm based on robust SE, the three-phase voltage amplitudes measured by a randomly selected μPMU are scaled to 25% - 35%, 45% - 55%, and 75% - 85% of the true values to simulate bad data. For the 310 fault scenarios, node identification is used as the success criterion, that is, the algorithm is required to identify any adjacent node of the line where the fault occurs. For example, for a fault occurring at the 75% position on line 6-7, as long as either node 6 or node 7 is identified, the fault location is considered successful.

[0176] The test results are as Figure 6 、 Figure 7 、 Figure 8 and Figure 9 shown. Under the ideal condition without bad data, the fault location methods based on traditional SE and robust SE have very similar success rates, and the performance of both decreases as the pseudo-measurement error increases. In the scenario with bad data, the fault location method based on traditional SE completely fails and cannot identify the fault location; in contrast, the fault location method based on robust SE still maintains a high level of accuracy. Even in the scenarios with a pseudo-measurement error of 20%, a high-resistance fault close to 200 Ω, and the presence of 6 bad data, the fault location success rate can still reach 90%. And the proposed method is extremely insensitive to the amplitude of bad data. Regardless of the severity of the bad data (0.35 - 0.85 times the true value), it shows good stability, verifying the robust ability of the proposed fault location method.

[0177] To overcome the problem that traditional methods are difficult to distinguish real fault responses from measurement distortions due to unknown fault locations, fault types, and fault resistance magnitudes, this embodiment proposes a fault location method for flexible distribution networks based on three-phase robust state estimation. Using the real-time voltage phasor measurements after a fault and the node injection pseudo-measurements generated by the pre-fault state estimation, a quadratic-constant type generalized maximum likelihood estimation model is constructed, and an iterative variable-weight least squares algorithm is used to solve for real-time measurement weight adaption. On this basis, a fault location algorithm based on fault state estimation matching is proposed, and a matching index that comprehensively considers the weight differences of multi-source measurements and measurement locations is designed. Through simulations on a 33-node unbalanced distribution network, the effectiveness of the algorithm is verified, and the following conclusions are drawn:

[0178] 1) Under ideal conditions without bad data, the fault location method based on robust SE and the fault location method based on traditional SE exhibit similar performance;

[0179] 2) In scenarios with severe bad data, the fault location method based on robust SE can still maintain a high accuracy rate, while the fault location method based on traditional SE completely fails;

[0180] 3) The proposed fault location method based on robust SE is extremely insensitive to the amplitude of bad data and exhibits good stability regardless of the severity of the bad data.

[0181] Embodiment 2

[0182] This embodiment provides a fault location system for flexible distribution networks based on three-phase robust state estimation, including:

[0183] A data acquisition module configured to acquire real-time voltage phasor measurements after a fault and node injection pseudo-measurements before the fault;

[0184] A fault state estimation module solving module configured to iteratively solve a three-phase robust fault state estimation model based on the node injection pseudo-measurements and real-time voltage phasor measurements, and output a fault state estimation result after adjusting the weight of the delayed real-time voltage phasor measurements until the first iteration;

[0185] A candidate fault point screening module configured to use all load nodes as a candidate fault node set, perform iterative solution of the three-phase robust fault state estimation model for each candidate fault node, and calculate the matching index value of the candidate fault node according to the solution result;

[0186] An accurate fault location module configured to divide all adjacent lines of the candidate fault node with the smallest matching index value into multi-line lines of equal length, use the division points of the adjacent lines as virtual fault nodes, and re-perform fault location for all virtual fault nodes to determine the accurate fault location.

[0187] The examples and application scenarios implemented by the above modules and corresponding steps are the same, but are not limited to the content disclosed in the first embodiment above. It should be noted that the above modules, as part of a system, can be executed in a computer system such as a set of computer-executable instructions.

[0188] In the above embodiments, the descriptions of each embodiment have their own emphases. For parts not detailed in a certain embodiment, reference can be made to the relevant descriptions of other embodiments.

[0189] The proposed system can be implemented in other ways. For example, the system embodiments described above are merely illustrative. For example, the division of the above modules is only a logical function division. In actual implementation, there can be other division methods. For example, multiple modules can be combined or integrated into another system, or some features can be ignored or not executed.

[0190] Embodiment Three

[0191] This embodiment provides a computer-readable storage medium, on which a computer program is stored. When the program is executed by a processor, it implements the steps in the flexible distribution network fault location method based on three-phase robust state estimation as described in the first embodiment above.

[0192] Embodiment Four

[0193] This embodiment provides a computer device, including a memory, a processor, and a computer program stored on the memory and executable on the processor. When the processor executes the program, it implements the steps in the flexible distribution network fault location method based on three-phase robust state estimation as described in the first embodiment above.

[0194] Embodiment Five

[0195] This embodiment provides a computer program product or a computer program. The computer program product or the computer program includes computer instructions, and the computer instructions are stored in a computer-readable storage medium. The processor of the computer device reads the computer instructions from the computer-readable storage medium, and the processor executes the computer instructions, so that the computer device executes the steps in the flexible distribution network fault location method based on three-phase robust state estimation as described in the first embodiment above.

[0196] Those skilled in the art should understand that the embodiments of the present invention can be provided as methods, systems, or computer program products. Therefore, the present invention can adopt the form of hardware embodiments, software embodiments, or embodiments combining software and hardware aspects. Moreover, the present invention can adopt the form of a computer program product implemented on one or more computer-usable storage media (including but not limited to disk memories and optical memories, etc.) containing computer-usable program code.

[0197] The present invention is described with reference to the flowcharts and / or block diagrams of methods, apparatuses (systems), and computer program products according to embodiments of the present invention. It should be understood that each flow and / or block in the flowchart and / or block diagram, and the combination of flows and / or blocks in the flowchart and / or block diagram, can be implemented by computer program instructions. These computer program instructions can be provided to the processor of a general-purpose computer, a special-purpose computer, an embedded processor, or other programmable data processing devices to generate a machine, such that the instructions executed by the processor of the computer or other programmable data processing devices produce means for implementing the functions specified in one flow Figure 1 one flow or multiple flows and / or blocks Figure 1 or multiple blocks.

[0198] These computer program instructions can also be stored in a computer-readable memory that can direct a computer or other programmable data processing device to work in a specific manner, such that the instructions stored in the computer-readable memory produce a manufactured article including instruction means that implement the functions specified in one flow Figure 1 one flow or multiple flows and / or blocks Figure 1 or multiple blocks.

[0199] These computer program instructions can also be loaded onto a computer or other programmable data processing device, such that a series of operation steps are executed on the computer or other programmable device to generate a computer-implemented process, and thus the instructions executed on the computer or other programmable device provide steps for implementing the functions specified in one flow Figure 1 one flow or multiple flows and / or blocks Figure 1 or multiple blocks.

[0200] Those of ordinary skill in the art can understand that to implement all or part of the processes in the above-described embodiment methods, it can be completed by instructing relevant hardware through a computer program. The program can be stored in a computer-readable storage medium. When the program is executed, it can include the processes of the embodiments of the above-described methods. Among them, the storage medium can be a magnetic disk, an optical disk, a read-only memory (ROM), or a random access memory (RAM), etc.

[0201] Although the specific implementation manners of the present invention are described above in conjunction with the accompanying drawings, it is not a limitation on the protection scope of the present invention. Those skilled in the art should understand that based on the technical solutions of the present invention, various modifications or deformations that can be made by those skilled in the art without creative efforts are still within the protection scope of the present invention.

Claims

1. A fault location method for flexible distribution network based on three-phase robust state estimation, characterized in that Including: Obtaining real-time voltage phasor measurements after a fault and pseudo measurements of node injections before the fault; Based on the pseudo measurements of node injections and real-time voltage phasor measurements, by delaying the weight adjustment of the real-time voltage phasor measurements until after the first iteration, iteratively solving the three-phase robust fault state estimation model and outputting the fault state estimation result; Taking all load nodes as the candidate fault node set, performing iterative solution of the three-phase robust fault state estimation model for each candidate fault node, and calculating the matching index value of the candidate fault node according to the solution result; Dividing all adjacent lines of the candidate fault node with the minimum matching index value into multi-line lines of equal length, taking the division points of the adjacent lines as virtual fault nodes, and re-performing fault location for all virtual fault nodes to determine the exact fault location.

2. The fault location method for a flexible distribution network based on three-phase robust state estimation according to claim 1, characterized in that, The three-phase robust fault state estimation model is specifically: Where: r i = z i - h i is the residual of the i-th measurement; is the measurement column vector, m is the number of measurements; h(x) is the measurement function column vector; ρ(·) is a quadratic-constant (QC) penalty function.

3. The fault location method for flexible distribution network based on three-phase robust state estimation according to claim 1, characterized in that Based on the pseudo measurements of node injections and real-time voltage phasor measurements, by delaying the weight adjustment of the real-time voltage phasor measurements until after the first iteration, iteratively solving the three-phase robust fault state estimation model is specifically: Based on the input network model, pseudo measurements of node injections before the fault, real-time voltage phasor measurements, and assumed fault nodes; For flexible switching nodes, subtracting the flexible switch injection pseudo measurement from the pseudo measurement of the node injection power before the fault; Starting with voltage flat start, the iteration number k = 1; According to the current voltage estimation value, correcting the pseudo measurements of PV injection power and load node injection power; Calculating the fault current and superimposing it on the pseudo measurement of the injection current of the assumed fault node; Calculating the residual vector and updating the weight of the phasor measurement value; Updating the state variables, using the corrected pseudo measurement of node injection for updating when k = 1; when k > 1, using the corrected pseudo measurement of node injection and real-time voltage phasor measurements for updating; Until the algorithm converges, outputting the fault state estimation result.

4. The fault location method for flexible distribution network based on three-phase robust state estimation according to claim 3, wherein The state variables are updated by the following formula: Δx (k) = [H T Φ(x (k) )H] -1 H T Φ(x (k) )[z - h(x (k) )]; wherein, is the measurement column vector, m is the number of measurements; h(x (k) ) is the measurement function column vector at the k-th iteration; x (k) is the three-phase state vector at the k-th iteration, H is the measurement Jacobian matrix; Φ is the weight factor matrix.

5. The fault location method for a flexible distribution network based on three-phase robust state estimation according to claim 1, characterized in that The calculating the matching index value of the candidate fault node according to the solution result is specifically: Wherein: is the estimated value of the state variable; is the measurement column vector, and m is the number of measurements; is the measurement function column vector of the estimated value of the state variable; the norm is defined as are respectively the measured value and the estimated value of the phase voltage amplitude of each feeder end node i; Ω end is the set of feeder end nodes.

6. The fault location method for a flexible distribution network based on three-phase robust state estimation according to claim 1, wherein, The re-performing fault location for all virtual fault nodes to determine the exact fault location is specifically: Sequentially performing iterative solution of the three-phase robust fault state estimation model for each virtual fault node, and calculating the matching index value of the virtual fault node according to the solution result; Determining the exact fault location with the virtual fault node having the minimum matching index value.

7. A flexible distribution network fault location system based on three-phase robust state estimation, characterized in that, Including: A data acquisition module configured to obtain real-time voltage phasor measurements after a fault and pseudo measurements of node injections before the fault; A fault state estimation module solving module configured to, based on the pseudo measurements of node injections and real-time voltage phasor measurements, by delaying the weight adjustment of the real-time voltage phasor measurements until after the first iteration, iteratively solve the three-phase robust fault state estimation model and output the fault state estimation result; A candidate fault point screening module configured to take all load nodes as the candidate fault node set, perform iterative solution of the three-phase robust fault state estimation model for each candidate fault node, and calculate the matching index value of the candidate fault node according to the solution result; The precise fault location module is configured to divide all adjacent lines of the candidate fault node with the smallest matching index value into multi-line lines of equal length, use the division points of the adjacent lines as virtual fault nodes, re-perform fault location on all virtual fault nodes, and determine the precise fault location.

8. A computer-readable storage medium having a computer program stored thereon, characterized in that, When the program is executed by a processor, it implements the steps in the flexible distribution network fault location method based on three-phase robust state estimation described in any one of claims 1-6.

9. A computer device, comprising a memory, a processor, and a computer program stored on the memory and executable on the processor, characterized in that, When the processor executes the program, it implements the steps in the flexible distribution network fault location method based on three-phase robust state estimation described in any one of claims 1-6.

10. A computer program product, characterized in that, The computer program product includes a computer program, and when the computer program is executed by a processor, it implements the steps in the flexible distribution network fault location method based on three-phase robust state estimation described in any one of claims 1-6.

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