A robust state estimation method for improving reliability of power distribution network voltage sag monitoring

Abstract

This invention discloses a robust state estimation method for improving the reliability of voltage sag monitoring in distribution networks. The method involves acquiring the distribution network topology, branch parameters, and voltage sag records of monitored nodes; establishing a node impedance matrix and calculating the equivalent electrical distance; constructing an adaptive weighted graph based on node structural characteristics and voltage sag statistical similarity; dividing nodes into communities using spectral clustering; establishing an adaptive interactive field model based on equivalent electrical distance, community coupling relationships, and node credibility; constructing state estimation equations for unmonitored nodes; building an anomaly data identification model based on the residuals between measured and estimated values ​​of monitored nodes; updating node weights based on a robust loss function and an adaptive residual threshold; introducing the updated node weights into the state estimation equations; and establishing and solving a robust state estimation optimization model that incorporates community consistency, graph structure, and interactive field estimation consistency constraints to obtain the voltage sag state estimation results for unmonitored nodes.

Description

Technical Field

[0001] This invention relates to a robust state estimation method for improving the reliability of voltage sag monitoring in distribution networks, and relates to the field of power quality monitoring technology for distribution networks. Background Technology

[0002] Voltage sags are a common power quality disturbance, typically caused by short-circuit faults, sudden load changes, or the starting of large motors. Voltage sags can lead to the shutdown of sensitive equipment, instability in control systems, and interruptions in industrial production, resulting in significant economic losses. Therefore, accurately assessing the voltage sag levels at each node in the distribution network is crucial for power quality management, fault analysis, and operational decision-making.

[0003] Existing voltage sag state estimation methods based on network structures can, to some extent, overcome the dependence of traditional methods on the optimal configuration of monitoring devices and improve the state estimation capability under incomplete monitoring schemes. However, the following problems still exist in practical applications:

[0004] First, monitoring data may be affected by noise interference, communication errors and abnormal records during the collection and transmission process, resulting in insufficient reliability of some monitoring data. If it is directly used for state estimation, it will introduce systematic bias.

[0005] Second, existing methods lack an effective suppression mechanism for outlier data when using monitoring node data to build state estimation models. Outliers can easily participate directly in the estimation calculation, thus affecting the accuracy of the state estimation results for unmonitored nodes.

[0006] Third, in complex operating scenarios, existing methods do not adequately consider the differences in monitoring data quality and fail to distinguish the reliability of data from different monitoring nodes, which can easily lead to a decrease in the stability and reliability of state estimation results.

[0007] Therefore, there is an urgent need to propose a new method for estimating the voltage sag state of distribution networks. Under the condition of limited monitoring nodes, this method can not only utilize the distribution network structure information to estimate the voltage sag state of unmonitored nodes, but also effectively suppress the influence of abnormal monitoring data on the estimation results, thereby improving the reliability of distribution network voltage sag monitoring. Summary of the Invention

[0008] The present invention provides a robust state estimation method for improving the reliability of voltage sag monitoring in distribution networks in order to solve the problems existing in the prior art.

[0009] The technical solutions adopted in this invention are as follows:

[0010] A robust state estimation method for improving the reliability of voltage sag monitoring in distribution networks includes the following steps:

[0011] S1: Obtain the network topology, branch parameters, and voltage sag records of monitoring nodes of the distribution network, establish the node admittance matrix of the distribution network, and obtain the node impedance matrix based on the node admittance matrix.

[0012] S2: Calculate the equivalent electrical distance between nodes based on the node impedance matrix, and construct an adaptive weighted graph of nodes by combining node structural characteristics and voltage sag statistical similarity to characterize the propagation correlation of voltage sag between distribution network nodes;

[0013] S3: Construct a graph Laplacian matrix based on the node adaptive weighted graph, and divide the distribution network nodes into communities using the spectral clustering method to obtain multiple node communities;

[0014] S4: Based on the equivalent electrical distance between monitored and unmonitored nodes, node community coupling relationship, node credibility, and voltage sag record data of monitored nodes, construct an adaptive interactive field model and voltage sag state estimation equation for unmonitored nodes;

[0015] S5: Construct an abnormal data identification model based on the residual between the measured and estimated values ​​of the voltage sag at the monitoring node. Update the confidence weight of the monitoring node based on the robust loss function and the adaptive residual threshold to suppress abnormal data and obtain the updated node weight.

[0016] S6: Introduce the updated node weights into the adaptive interactive field model to obtain the weighted voltage sag state estimation results for unmonitored nodes; combine community consistency constraints, graph structure constraints, and interactive field estimation consistency constraints to establish a robust state estimation optimization model; solve the robust state estimation optimization model to obtain the voltage sag state estimation results for unmonitored nodes.

[0017] Furthermore, in S2, the node With nodes The equivalent electrical distance between them is calculated based on the node impedance matrix and is expressed as:

[0018] ,

[0019] in, , They are nodes With nodes The self-impedance term, For nodes With nodes The mutual impedance terms between them.

[0020] Furthermore, in S2, the node structure features include adjacency scale index, propagation efficiency index, and power support capability index.

[0021] node Adjacency size index Represented as:

[0022] ,

[0023] in, For nodes The number of adjacent nodes, For nodes The set of directly connected adjacent nodes;

[0024] node propagation efficiency index Represented as:

[0025] ,

[0026] in, The total number of distribution network nodes. For a set of nodes, For nodes To the node The shortest equivalent electrical distance;

[0027] node Power supply support capability indicators Represented as:

[0028] ,

[0029] in, This is the set of nodes that are directly connected to the power supply node.

[0030] Furthermore, in S2, the association weights between nodes are calculated based on the equivalent electrical distance between nodes, the similarity of node structural features, and the statistical similarity of node voltage sags, and a node weighted adjacency matrix is ​​constructed.

[0031] node With nodes Statistical similarity of voltage sags between Calculated based on the statistical eigenvector of node voltage sag, and expressed as:

[0032] ,

[0033] in, and They are nodes and The statistical feature vector of voltage sag within a preset statistical time window To prevent extremely small positive numbers with a denominator of zero;

[0034] node With nodes Structural feature similarity between Represented as:

[0035] ,

[0036] in, , They are nodes and The structural feature vector consists of normalized adjacency size index, propagation efficiency index, and power support capability index. This is a scale parameter for structural feature similarity;

[0037] The elements of the weighted adjacency matrix of the nodes are represented as follows:

[0038]

[0039] in, For nodes With nodes The equivalent electrical distance between them , and The adaptive weighting coefficients satisfy the following conditions: .

[0040] Furthermore, in S3, the degree matrix D and the graph Laplacian matrix are constructed based on the node weighted adjacency matrix. The graph Laplacian matrix is ​​subjected to eigenvalue decomposition, and the node community is divided using spectral clustering.

[0041] Furthermore, in S4, let the set of monitoring nodes be... The set of unmonitored nodes is Monitoring nodes Initial credibility weight Determined based on prior quality evaluation information from the monitoring device, and expressed as:

[0042] ,

[0043] in, , To monitor the accuracy indicators of the device, For data integrity rate, This represents the proportion of historical outlier data. , , The weighting coefficients are satisfied. , As the minimum confidence weight, when there is no prior quality evaluation information for the monitoring device, let ;

[0044] node Community and node Community coupling coefficient between the communities Determined based on the average inter-community association strength, expressed as:

[0045] ,

[0046] in, The average strength of association between communities. The minimum community coupling coefficient;

[0047] node Local propagation scale parameters Based on the adaptive determination of node structure characteristics, it is represented as follows:

[0048] ,

[0049] in, Based on the basic scale of communication, , , These are the normalized adjacency size index, propagation efficiency index, and power support capability index, respectively. , and This is the adjustment coefficient.

[0050] Furthermore, an estimation equation for the voltage sag state of unmonitored nodes is established based on an adaptive interactive field model; for unmonitored nodes... Monitoring nodes For unmonitored nodes Initial interaction field coefficients Represented as:

[0051] ,

[0052] The initial interaction field coefficients are normalized to obtain the monitoring nodes. For unmonitored nodes Normalized propagation weight :

[0053] ,

[0054] Unmonitored Nodes Initial voltage sag state estimate Represented as:

[0055] ,

[0056] in, For monitoring nodes The measured voltage sag statistics;

[0057] The initial state estimation equations for all unmonitored nodes are written in matrix form:

[0058] ,

[0059] in, This is the initial voltage sag state estimation vector for unmonitored nodes. This is the statistical vector of the measured voltage sag at the monitoring node. For normalized propagation weights The initial propagation weight matrix is ​​formed.

[0060] Furthermore, in S5, the estimated voltage sag statistic of the monitoring node itself is calculated using the leave-one interactive field estimation method, and an abnormal data identification model is constructed based on the residual between the measured value and the estimated value of the monitoring node.

[0061] For monitoring nodes Monitoring nodes For monitoring nodes Leave-one interaction field coefficient Represented as:

[0062] ,

[0063] The leave-one-out interaction field coefficients are normalized to obtain the monitoring node. For monitoring nodes Leave-one propagation weight :

[0064] ,

[0065] Monitoring nodes Estimated voltage sag statistic Represented as:

[0066] ,

[0067] Monitoring nodes residual Represented as:

[0068] ,

[0069] Construct a robust loss function based on the residuals. Its expression is:

[0070] ,

[0071] in, For monitoring nodes The adaptive residual threshold is expressed as:

[0072] ,

[0073] in, The minimum residual threshold, The basic threshold adjustment coefficient, For nodes Statistical consistency indicators of the community , The weighting coefficients are satisfied. .

[0074] Furthermore, the confidence weights of the monitoring nodes are updated based on the robust loss function and the adaptive residual threshold to obtain the updated node weights. :

[0075] ,

[0076] The updated node weights are introduced into the adaptive interaction field model for unmonitored nodes. Monitoring nodes For unmonitored nodes Updated interaction field coefficients Represented as:

[0077] ,

[0078] The updated interaction field coefficients are normalized to obtain the monitoring nodes. For unmonitored nodes Update propagation weight :

[0079] ,

[0080] Unmonitored Nodes Weighted voltage sag estimate Represented as:

[0081] ,

[0082] The weighted state estimation equations for all unmonitored nodes are written in matrix form:

[0083] ,

[0084] in, This is the weighted voltage sag state estimation vector for unmonitored nodes. To update the propagation weight The weighted propagation weight matrix is ​​formed.

[0085] Furthermore, in S6, the updated node weights are introduced into the robust state estimation optimization model, and the voltage sag state of unmonitored nodes is solved by combining community consensus constraints, graph structure constraints and interaction field estimation consensus constraints.

[0086] Let the voltage sag state vector of the unmonitored node to be determined be... ,in Unmonitored nodes Estimate the voltage sag state to be determined; construct the voltage sag state vector of all nodes. ,in:

[0087] ,

[0088] The objective function of the robust state estimation optimization model is expressed as:

[0089] ,

[0090] in, For the number of node communities, For the first The weighted variance of voltage sag statistics within each node community. For monitoring nodes robust loss function, Let Laplacian matrix be the graph constructed from the adaptive weighted graph. This is the weighted voltage sag state estimation vector for unmonitored nodes. , , , It is a non-negative balance coefficient;

[0091] Let the first Each node community is The set of monitoring nodes is The set of unmonitored nodes is Then the first Weighted average of voltage sag statistics within each node community Represented as:

[0092] ,

[0093] No. The weighted variance of voltage sag statistics within each node community Represented as:

[0094] ,

[0095] The robust state estimation optimization model satisfies the following constraints:

[0096] ,

[0097] By solving the robust state estimation optimization model, the voltage sag state estimation results of unmonitored nodes within a preset statistical time window are obtained.

[0098] Furthermore, the robust state estimation optimization model is solved using any one of the following algorithms: genetic algorithm, particle swarm optimization algorithm, differential evolution algorithm, sequential quadratic programming algorithm, or improved least squares algorithm. During the solution process, the weighted voltage sag state estimation vector of the unmonitored node is used as the initial estimation result or reference constraint term, and the voltage sag state vector of the unmonitored node is obtained through iterative optimization. And the voltage sag state vector of the unmonitored node to be determined As the voltage sag state estimation result of unmonitored nodes in the distribution network within a preset statistical time window; the voltage sag state estimation result includes the number of voltage sags, sag severity index or voltage sag performance index.

[0099] The present invention has the following beneficial effects:

[0100] (1) This invention performs state estimation based on a complex network model of the distribution network, without requiring the monitoring scheme to meet strict optimal observability conditions, and is applicable to scenarios where the monitoring device is not optimally configured in actual engineering. Under the condition of limited monitoring nodes, this invention can effectively utilize the distribution network topology information and impedance parameter information to estimate the voltage sag state of unmonitored nodes.

[0101] (2) Based on the traditional node partitioning method based on structural features, this invention further constructs an adaptive weighted graph by combining the statistical similarity of voltage sags between nodes, and realizes node community partitioning through spectral clustering. Compared with the simple index-weighted grouping method, this method can more accurately characterize the propagation correlation and statistical similarity between nodes, thereby improving the adaptability of the community partitioning results to the voltage sag propagation law.

[0102] (3) This invention constructs an adaptive interactive field model that considers community coupling relationships and node credibility. Compared with the traditional interactive field model that establishes propagation relationships based solely on equivalent electrical distance, this invention can simultaneously reflect the differences in data quality between monitoring nodes, the differences in propagation impact between communities to which nodes belong, and the modulation effect of local structural features of nodes on the propagation range, thereby improving the accuracy of state propagation modeling between monitoring nodes and unmonitored nodes.

[0103] (4) This invention introduces a robust loss function, an adaptive residual threshold, and a dynamic weight update mechanism in the state estimation process, and further incorporates community consistency constraints and graph structure constraints into the robust state estimation optimization model. Compared with traditional residual weighted or ordinary least squares estimation methods, this invention can effectively suppress the influence of abnormal monitoring data, noise interference, and communication errors on the state estimation results, and improve the accuracy, stability, and robustness of voltage sag state estimation for unmonitored nodes.

[0104] (5) This invention can assess the global voltage sag state of the distribution network under limited monitoring conditions, and is applicable to online monitoring, operation assessment and operation and maintenance decision support of the power quality of the distribution network. At the same time, the adaptive weighted graph modeling, spectral clustering community partitioning, adaptive interactive field modeling and robust joint optimization method proposed in this invention have good scalability and can provide effective technical support for voltage sag monitoring and analysis in complex distribution network scenarios. Attached Figure Description

[0105] Figure 1 This is a flowchart of the state estimation method for improving the reliability of voltage sag monitoring in distribution networks, as described in this invention.

[0106] Figure 2 This is a schematic diagram of the power distribution network testing system used in an embodiment of the present invention.

[0107] Figure 3 This is a schematic diagram of the distribution network node community division results in an embodiment of the present invention.

[0108] Figure 4 This is a comparison chart of the node voltage sag state estimation results under disturbance conditions in this embodiment. Detailed Implementation

[0109] The invention will now be further described with reference to the accompanying drawings.

[0110] This invention discloses a robust state estimation method for improving the reliability of voltage sag monitoring in distribution networks. The overall process is as follows: Figure 1 As shown, this embodiment uses the IEEE 30-node test system as the test object for the distribution network. The network topology and node connection relationships of the test system are as follows: Figure 2 As shown. The test system includes multiple bus nodes, branch connections, power supply nodes, and transformer branches, and can be used to verify the ability of the method of the present invention to estimate the voltage sag state of unmonitored nodes under conditions of limited monitoring nodes. Figure 3 This is a schematic diagram of the distribution network node community division results in this embodiment. Figure 4 This is a comparison chart showing the estimation results of node voltage sag states under disturbance conditions. The invention will now be described in further detail.

[0111] In this embodiment, the network topology information, branch parameters, and voltage sag records of some monitoring nodes of the distribution network testing system are first acquired. The network topology information includes node connection relationships, branch connection methods, and power node locations. The branch parameters include line impedance parameters and transformer branch parameters. The voltage sag records of the monitoring nodes include the number of voltage sags, voltage sag severity indicators, or voltage sag performance indicators for each monitoring node within a preset statistical time window.

[0112] After obtaining the distribution network topology information and branch parameters, the node admittance matrix of the test system is established, and the node impedance matrix is ​​further calculated. Preferably, the node impedance matrix is ​​denoted as... Its elements This represents the impedance coupling relationship between node i and node j. The node impedance matrix is ​​used for subsequent calculation of the equivalent electrical distance between nodes.

[0113] The equivalent electrical distance between any two nodes is calculated using the node impedance matrix. The equivalent electrical distance between node i and node j is expressed as:

[0114] ,

[0115] in, Represents a node With nodes The voltage difference between nodes, Represents a node Injected current at the location;

[0116] Based on the node impedance matrix, the equivalent electrical distance is expressed as:

[0117] ,

[0118] in, and Representing nodes respectively With nodes The self-impedance term, Represents a node With nodes The mutual impedance terms between them.

[0119] The above formula yields the equivalent electrical distance matrix between all network nodes, which is used to characterize the propagation relationship of voltage sags between network nodes.

[0120] After obtaining the equivalent electrical distance matrix, construct the structural characteristic index of voltage sag propagation. The structural characteristic index includes at least the adjacency scale index, propagation efficiency index, and power supply support capability index.

[0121] Among them, nodes Adjacency size index for:

[0122] ,

[0123] in, For nodes The number of adjacent nodes, For nodes The set of directly connected adjacent nodes.

[0124] node propagation efficiency index Represented as:

[0125] ,

[0126] in, The total number of distribution network nodes. For a set of nodes, For nodes To the node The shortest equivalent electrical distance.

[0127] node Power supply support capability indicators Represented as:

[0128] ,

[0129] in, For a set of nodes directly connected to the power source, the adjacency size index, propagation efficiency index, and power support capability index are used to characterize the ability of a node to be affected by voltage dip propagation from different perspectives.

[0130] After normalizing the adjacency scale, propagation efficiency, and power support capacity indices, an adaptive weighted graph is constructed by combining the statistical similarity of voltage sags between nodes. This adaptive weighted graph comprehensively characterizes the degree of correlation between nodes in terms of voltage sag propagation paths, local structural attributes, and sag statistical behavior.

[0131] Specifically, nodes are constructed within a preset statistical time window. Voltage sag statistical eigenvector:

[0132] ,

[0133] in, This represents the number of voltage dips after normalization. This represents the severity index of the normalized voltage sag. This represents the normalized voltage sag performance index.

[0134] node With nodes Statistical similarity of voltage sags between Represented as:

[0135] ,

[0136] in, and They are nodes and The statistical feature vector of voltage sag within a preset statistical time window To prevent extremely small positive numbers with a denominator of zero.

[0137] To quantify the similarity of local structural features among nodes, a node model is constructed. Structural feature vectors:

[0138] ,

[0139] in, , , These represent the normalized adjacency size index, propagation efficiency index, and power support capability index, respectively.

[0140] node With nodes Structural feature similarity between Represented as:

[0141] ,

[0142] in, This is the scale parameter for structural feature similarity.

[0143] The elements of the weighted adjacency matrix are represented as follows:

[0144] ,

[0145] in, Represents a node With nodes The equivalent electrical distance between them Represents a node With nodes Statistical similarity of voltage sags between them Represents a node With nodes Structural feature similarity between them , and The adaptive weighting coefficients satisfy the following conditions: .

[0146] Construct the degree matrix D based on the node weighted adjacency matrix, with its diagonal elements... Represented as:

[0147] ,

[0148] Further construct the graph Laplacian matrix L:

[0149] .

[0150] The graph Laplacian matrix is ​​subjected to eigenvalue decomposition, and the top k eigenvectors are extracted to form a clustering feature space. Spectral clustering is then used to divide the distribution network nodes into communities, resulting in multiple node communities. This approach allows nodes within the same community to exhibit higher similarity in voltage sag propagation characteristics and statistical behavior, thereby providing more reasonable structural prior information for estimating the voltage sag state of unmonitored nodes.

[0151] Based on the constructed adaptive weighted graph of nodes, eigenvalue decomposition of the graph Laplacian matrix is ​​performed, and spectral clustering is used to complete node community partitioning. The resulting community partitioning results are as follows: Figure 3 As shown. Preferably, in this embodiment, the IEEE 30-node test system can be divided into multiple communities.

[0152] In this embodiment, some nodes are designated as monitoring nodes, while the remaining nodes are designated as unmonitored nodes. Preferably, referring to the benchmark example, nodes 2, 6, 9, 18, and 25 are selected as monitoring nodes, and the remaining nodes are designated as unmonitored nodes. Of course, in practical applications, the number and location of monitoring nodes are not limited to the above settings.

[0153] Let the set of monitoring nodes be... The set of unmonitored nodes is Before constructing the adaptive interaction field model, the monitoring nodes are first determined. Initial credibility weight Community coupling coefficient between the communities to which the nodes belong and the local propagation scale parameter of node i .

[0154] When prior quality evaluation information for the monitoring device exists, the prior data quality index of monitoring node i Represented as:

[0155] ,

[0156] in, To monitor the accuracy indicators of the device, For data integrity rate, This represents the proportion of historical outlier data. , , Let be the weight coefficient, and satisfy... .

[0157] Monitoring nodes Initial credibility weight Represented as:

[0158] ,

[0159] in, As the minimum credibility weight, To prevent extremely small positive numbers with a denominator of zero, when no prior quality evaluation information for the monitoring device exists, let... .

[0160] Set nodes The community it belongs to is ,node The community it belongs to is Then the community coupling coefficient Determined based on the average correlation strength between communities. For any two communities and Its average correlation strength Represented as:

[0161] ,

[0162] in, For nodes in an adaptive weighted graph With nodes The correlation weights between them and Representing communities and community The number of nodes within.

[0163] Community Coupling Coefficient Represented as:

[0164] ,

[0165] in, This is the minimum community coupling coefficient.

[0166] Local propagation scale parameters The node structure is adaptively determined based on its characteristics, and its expression is:

[0167] ,

[0168] in, Based on the basic scale of communication, Represents a node The normalized value of the adjacency size index. Represents a node The normalized value of the propagation efficiency index. Represents a node The power supply support capability index is a normalized value. , and This is the adjustment coefficient.

[0169] As can be seen from the above formula, the node credibility weight Used to characterize the impact of monitoring node data quality on propagation modeling results; community coupling coefficient Used to characterize the differences in propagation impact among different node communities; local propagation scale parameter It is used to reflect the modulation effect of local structural features of a node on the propagation range of a voltage sag.

[0170] Based on the aforementioned initial credibility weights, community coupling coefficients, and local propagation scale parameters, the node... For nodes Initial adaptive interactive potential function Represented as:

[0171] ,

[0172] in, Indicates monitoring node The measured voltage sag statistics, Represents a node With nodes The equivalent electrical distance between them Represents a node Credibility weight, Represents a node The local propagation scale parameters, Represents a node Community and node Community coupling coefficient between the communities to which they belong.

[0173] The adaptive interactive field model is used to characterize the influence of monitored nodes on unmonitored nodes during the voltage sag propagation process. Based on the adaptive interactive field model, the voltage sag state estimation equation for unmonitored nodes is established. For any unmonitored node... Monitoring nodes For unmonitored nodes Initial interaction field coefficients Represented as:

[0174] ,

[0175] in, Indicates monitoring node The initial credibility weight, Represents a node With nodes The equivalent electrical distance between them Represents a node The local propagation scale parameters, Represents a node Community and node Community coupling coefficient between the communities they belong to Used to characterize the intensity of the propagation influence of monitored node i on unmonitored node j.

[0176] The initial interaction field coefficients are normalized to obtain the monitoring nodes. For unmonitored nodes Normalized propagation weight :

[0177] ,

[0178] in, To prevent extremely small positive numbers with a denominator of zero.

[0179] Unmonitored Nodes Initial voltage sag state estimate Represented as:

[0180] ,

[0181] in, Indicates monitoring node The measured voltage sag statistics;

[0182] Furthermore, the initial state estimation equations for all unmonitored nodes are written in matrix form:

[0183] ,

[0184] in, This is the initial voltage sag state estimation vector for unmonitored nodes. This is the statistical vector of the measured voltage sag at the monitoring node. For normalized propagation weights The initial propagation weight matrix is ​​formed.

[0185] To improve the ability of the state estimation process to suppress abnormal monitoring data, an abnormal data identification model is further constructed based on the residual between the measured and estimated values ​​of the monitoring nodes, and an abnormal data suppression mechanism is established based on the robust loss function and the adaptive residual threshold.

[0186] Specifically, the estimated voltage sag statistic for the monitoring node itself is calculated using the leave-one-out interactive field estimation method. For the monitoring node... Monitoring nodes Leave-one-out interaction field coefficients for monitoring node i Represented as:

[0187] ,

[0188] in, Indicates monitoring node The initial credibility weight, Represents a node Community and node Community coupling coefficient between the communities they belong to Represents a node With nodes The equivalent electrical distance between them Represents a node The local propagation scale parameter.

[0189] The coefficients of the leave-one-out interactive field are normalized to obtain the monitoring node. For monitoring nodes Leave-one propagation weight :

[0190] ,

[0191] Monitoring nodes Estimated voltage sag statistic Represented as:

[0192] ,

[0193] in, Indicates monitoring node The measured voltage sag statistics;

[0194] Monitoring nodes residual Represented as:

[0195] ,

[0196] in, Indicates monitoring node The measured voltage sag statistics, This indicates the monitoring nodes obtained using leave-one-out interactive field estimation. The estimated voltage sag statistics.

[0197] Construct a robust loss function based on the residuals. Its expression is:

[0198] ,

[0199] in, For monitoring nodes The adaptive residual threshold.

[0200] The robust loss function is used to characterize the degree of influence of abnormal residuals on the state estimation results and to provide a basis for subsequent node weight updates.

[0201] Adaptive residual threshold The initial credibility weight of the monitoring node and the statistical consistency index of the community to which the node belongs are determined, and its expression is:

[0202] ,

[0203] in, The minimum residual threshold, The basic threshold adjustment coefficient, For monitoring nodes The initial credibility weight, For nodes Statistical consistency indicators of the community , The weighting coefficients are satisfied. .

[0204] As can be seen from the above expression, the higher the node credibility and the stronger the statistical consistency within the community, the more reasonable the anomaly detection threshold of the corresponding node, thereby improving the adaptability of the anomaly identification results to the actual monitoring scenario.

[0205] Let the community to which node i belongs be . The set of monitoring nodes within this community is as follows:

[0206] ,

[0207] Then community Mean of voltage sag statistics at internal monitoring nodes Represented as:

[0208] ,

[0209] Community Dispersion of voltage sag statistics at internal monitoring nodes Represented as:

[0210] ,

[0211] node Statistical consistency indicators of the community Represented as:

[0212] ,

[0213] in, , The larger the value, the more likely it is to be a node. The more consistent the voltage sag statistics of monitoring nodes within the same community, the better.

[0214] The confidence weights of the monitoring nodes are updated based on the robust loss function and the adaptive residual threshold, resulting in the updated node weights. The residual weighting function for monitoring node i Represented as:

[0215] ,

[0216] in, To monitor the residual of node i, For monitoring nodes Adaptive residual threshold, To prevent extremely small positive numbers with a denominator of zero.

[0217] Monitoring nodes Node weights updated by robust loss function Represented as:

[0218] ,

[0219] The node weights updated by the robust loss function are introduced into the adaptive interaction field model to obtain the weighted interaction field state estimation relationship. For unmonitored nodes... Monitoring nodes Update the interaction field coefficients for unmonitored node j Represented as:

[0220] ,

[0221] in, Indicates monitoring node The node weights after robust update Represents a node Community and node Community coupling coefficient between the communities they belong to Represents a node With nodes The equivalent electrical distance between them Represents a node Local propagation scale parameters;

[0222] The updated interaction field coefficients are normalized to obtain the monitoring nodes. For unmonitored nodes Update propagation weight :

[0223] ,

[0224] Unmonitored Nodes Weighted voltage sag estimate Represented as:

[0225]

[0226] in, Indicates monitoring node The measured voltage sag statistics;

[0227] The weighted state estimation equations for all unmonitored nodes are written in matrix form:

[0228] ,

[0229] in, This is the weighted voltage sag state estimation vector for unmonitored nodes. This is the statistical vector of the measured voltage sag at the monitoring node. To update the propagation weight The weighted propagation weight matrix is ​​formed.

[0230] To obtain the optimal state estimation result, a robust state estimation optimization model is constructed. Let the state vector of the voltage sag at the unmonitored node be:

[0231] ,

[0232] in, Indicates unmonitored nodes The estimated value of the voltage sag state to be determined;

[0233] Construct the full node voltage sag state vector ,in:

[0234] ,

[0235] in, For monitoring nodes The measured voltage sag statistics, Unmonitored nodes The estimated value of the voltage sag state to be determined;

[0236] The objective function of the robust state estimation optimization model is expressed as:

[0237] ,

[0238] in, For the number of node communities, For the first The weighted variance of voltage sag statistics within each node community. For monitoring nodes robust loss function, The graph Laplacian matrix constructed from the adaptive weighted graph, This is the weighted voltage sag state estimation vector for unmonitored nodes. , , , It is a non-negative balance coefficient.

[0239] The objective function consists of four terms: the first term constrains the consistency of voltage sag statistics among nodes within the same community; the second term suppresses the interference of abnormal measurement data on the state estimation results; the third term utilizes graph structure information to maintain the smoothness and coordination of the state distribution of nodes across the network; and the fourth term maintains the consistency between the interaction field estimation results and the optimization solution results.

[0240] Let the first Each node community is The set of monitoring nodes is as follows:

[0241] ,

[0242] The set of unmonitored nodes is:

[0243] ,

[0244] Then the first Weighted average of voltage sag statistics within each node community Represented as:

[0245] ,

[0246] No. The weighted variance of voltage sag statistics within each node community Represented as:

[0247] ,

[0248] in, For monitoring nodes The node weights after robust update.

[0249] The robust state estimation optimization model satisfies the following constraints:

[0250] ,

[0251] in, This is used to ensure that the voltage sag statistics of unmonitored nodes are non-negative. Used to ensure that node weight updates are effective This is used to ensure effective propagation coupling between communities. Used to ensure the validity of local propagation scale parameters;

[0252] Based on the above constraints, an optimization algorithm is used to solve the robust state estimation optimization model. Preferably, a genetic algorithm, particle swarm optimization algorithm, differential evolution algorithm, sequential quadratic programming algorithm, or improved least squares algorithm can be used to solve the robust state estimation optimization model.

[0253] During the solution process, the weighted voltage sag state estimation vector of the unmonitored node is used. As an initial estimation result or reference constraint, the voltage sag state vector of the unmonitored node to be determined is obtained through iterative optimization. And the voltage sag state vector of the unmonitored node to be determined This serves as the voltage sag state estimation result for unmonitored nodes in the distribution network within a preset statistical time window. The voltage sag state estimation result includes the number of voltage sags, sag severity index, or voltage sag performance index.

[0254] Figure 4 A comparison chart showing the node voltage sag state estimation results of the IEEE 30-node system under disturbance conditions in this embodiment is presented. Figure 4 In the graph, the horizontal axis represents the node number, and the vertical axis represents the voltage sag monitoring value; the legend shows the actual value, the proposed method, and the traditional method, respectively. In this embodiment, nodes 2, 6, 9, 18, and 25 are monitored nodes, and the remaining nodes are unmonitored nodes. During the verification process of this embodiment, disturbances or outliers were introduced into the monitoring data of some monitoring nodes to simulate noise interference, communication errors, or abnormal recording scenarios that may occur during voltage sag monitoring. Figure 4 It can be seen that, under the above-mentioned limited monitoring node configuration and disturbance conditions, the proposed method, through adaptive weighted graph modeling, spectral clustering community partitioning, adaptive interactive field propagation modeling, and robust joint optimization, obtains estimation results that are generally closer to the true value curve. In contrast, the traditional method shows significant deviations from the true value at some nodes. This indicates that the method of the present invention can effectively suppress the influence of abnormal data, improve the accuracy and stability of node voltage sag estimation, and thus enhance the reliability of distribution network voltage sag monitoring.

[0255] During the verification process of the embodiments, disturbances or outliers can be introduced into the monitoring data of some monitoring nodes to simulate noise interference, communication errors, or abnormal recording scenarios, thereby further verifying the effectiveness of the abnormal data identification and adaptive weighting mechanism in this invention. In this case, the method of this invention can still reduce the impact of abnormal data on the state estimation results of unmonitored nodes through residual identification and dynamic weight reduction processing.

[0256] As can be seen from the above embodiments, the method of the present invention can still effectively utilize the distribution network structure information and limited monitoring data to make robust estimation of the voltage sag state of unmonitored nodes, even when the number of monitoring nodes is limited, the monitoring scheme does not meet the optimal observability conditions, and the monitoring data contains noise or outliers, thereby improving the reliability of distribution network voltage sag monitoring.

[0257] The above description is only a preferred embodiment of the present invention. It should be noted that those skilled in the art can make several improvements without departing from the principle of the present invention, and these improvements should also be considered within the scope of protection of the present invention.

Claims

1. A robust state estimation method for improving the reliability of voltage sag monitoring in distribution networks, characterized in that: Includes the following steps: S1: Obtain the network topology, branch parameters, and voltage sag records of monitoring nodes of the distribution network, establish the node admittance matrix of the distribution network, and obtain the node impedance matrix based on the node admittance matrix. S2: Calculate the equivalent electrical distance between nodes based on the node impedance matrix, and construct an adaptive weighted graph of nodes by combining node structural characteristics and voltage sag statistical similarity to characterize the propagation correlation of voltage sag between distribution network nodes; S3: Construct a graph Laplacian matrix based on the node adaptive weighted graph, and divide the distribution network nodes into communities using the spectral clustering method to obtain multiple node communities; S4: Based on the equivalent electrical distance between monitored and unmonitored nodes, node community coupling relationship, node credibility, and voltage sag record data of monitored nodes, construct an adaptive interactive field model and voltage sag state estimation equation for unmonitored nodes; S5: Construct an abnormal data identification model based on the residual between the measured and estimated values ​​of the voltage sag at the monitoring node. Update the confidence weight of the monitoring node based on the robust loss function and the adaptive residual threshold to suppress abnormal data and obtain the updated node weight. S6: Introduce the updated node weights into the adaptive interactive field model to obtain the weighted voltage sag state estimation results for unmonitored nodes; By combining community consistency constraints, graph structure constraints, and interaction field estimation consistency constraints, a robust state estimation optimization model is established; by solving the robust state estimation optimization model, the voltage sag state estimation results of unmonitored nodes are obtained.

2. The robust state estimation method for improving the reliability of voltage sag monitoring in distribution networks as described in claim 1, characterized in that: In S2, node With nodes The equivalent electrical distance between them is calculated based on the node impedance matrix and is expressed as: ， in, , They are nodes With nodes The self-impedance term, For nodes With nodes The mutual impedance terms between them.

3. The robust state estimation method for improving the reliability of voltage sag monitoring in distribution networks as described in claim 1, characterized in that: In S2, the node structure features include adjacency scale index, propagation efficiency index, and power support capability index. node Adjacency size index Represented as: ， in, For nodes The number of adjacent nodes, For nodes The set of directly connected adjacent nodes; node propagation efficiency index Represented as: ， in, The total number of distribution network nodes. For a set of nodes, For nodes To the node The shortest equivalent electrical distance; node Power supply support capability indicators Represented as: ， in, This is the set of nodes that are directly connected to the power supply node.

4. The robust state estimation method for improving the reliability of voltage sag monitoring in distribution networks as described in claim 1 or 3, characterized in that: In S2, the association weights between nodes are calculated based on the equivalent electrical distance between nodes, the similarity of node structural features, and the statistical similarity of node voltage sags, and a node weighted adjacency matrix is ​​constructed. node With nodes Statistical similarity of voltage sags between Calculated based on the statistical eigenvector of node voltage sag, and expressed as: ， in, and They are nodes and The statistical feature vector of voltage sag within a preset statistical time window To prevent extremely small positive numbers with a denominator of zero; node With nodes Structural feature similarity between Represented as: ， in, , They are nodes and The structural feature vector consists of normalized adjacency size index, propagation efficiency index, and power support capability index. This is a scale parameter for structural feature similarity; The elements of the weighted adjacency matrix of the nodes are represented as follows:

5. Among them, For nodes With nodes The equivalent electrical distance between them , and The adaptive weighting coefficients satisfy the following conditions: .

6. The robust state estimation method for improving the reliability of voltage sag monitoring in distribution networks as described in claim 4, characterized in that: In S3, the degree matrix D and the graph Laplacian matrix are constructed based on the node weighted adjacency matrix. The graph Laplacian matrix is ​​subjected to eigenvalue decomposition, and the node community is divided using spectral clustering.

7. The robust state estimation method for improving the reliability of voltage sag monitoring in distribution networks as described in claim 1, characterized in that: In S4, let the set of monitoring nodes be... The set of unmonitored nodes is Monitoring nodes Initial credibility weight Determined based on prior quality evaluation information from the monitoring device, and expressed as: ， in, , To monitor the accuracy indicators of the device, For data integrity rate, This represents the proportion of historical outlier data. , , The weighting coefficients are satisfied. , As the minimum confidence weight, when there is no prior quality evaluation information for the monitoring device, let ; node Community and node Community coupling coefficient between the communities Determined based on the average inter-community association strength, expressed as: ， in, The average strength of association between communities. The minimum community coupling coefficient; node Local propagation scale parameters Based on the adaptive determination of node structure characteristics, it is represented as follows: ， in, Based on the basic scale of communication, , , These are the normalized adjacency size index, propagation efficiency index, and power support capability index, respectively. , and This is the adjustment coefficient.

8. The robust state estimation method for improving the reliability of voltage sag monitoring in distribution networks as described in claim 6, characterized in that: An equation for estimating the voltage sag state of unmonitored nodes is established based on an adaptive interactive field model; for unmonitored nodes... Monitoring nodes For unmonitored nodes Initial interaction field coefficients Represented as: ， The initial interaction field coefficients are normalized to obtain the monitoring nodes. For unmonitored nodes Normalized propagation weight : ， Unmonitored Nodes Initial voltage sag state estimate Represented as: ， in, For monitoring nodes The measured voltage sag statistics; The initial state estimation equations for all unmonitored nodes are written in matrix form: ， in, This is the initial voltage sag state estimation vector for unmonitored nodes. This is the statistical vector of the measured voltage sag at the monitoring node. For normalized propagation weights The initial propagation weight matrix is ​​formed.

9. The robust state estimation method for improving the reliability of voltage sag monitoring in distribution networks as described in claim 1, characterized in that: In S5, the leave-one interactive field estimation method is used to calculate the estimated voltage sag statistic of the monitoring node itself, and an abnormal data identification model is constructed based on the residual between the measured value and the estimated value of the monitoring node. For monitoring nodes Monitoring nodes For monitoring nodes Leave-one interaction field coefficient Represented as: ， The leave-one-out interaction field coefficients are normalized to obtain the monitoring node. For monitoring nodes Leave-one propagation weight : ， Monitoring nodes Estimated voltage sag statistic Represented as: ， Monitoring nodes residual Represented as: ， Construct a robust loss function based on the residuals. Its expression is: ， in, For monitoring nodes The adaptive residual threshold is expressed as: ， in, The minimum residual threshold, The basic threshold adjustment coefficient, For nodes Statistical consistency indicators of the community , The weighting coefficients are satisfied. .

10. The robust state estimation method for improving the reliability of voltage sag monitoring in distribution networks as described in claim 8, characterized in that: The confidence weights of the monitoring nodes are updated based on the robust loss function and the adaptive residual threshold to obtain the updated node weights. : ， The updated node weights are introduced into the adaptive interaction field model for unmonitored nodes. Monitoring nodes For unmonitored nodes Updated interaction field coefficients Represented as: ， The updated interaction field coefficients are normalized to obtain the monitoring nodes. For unmonitored nodes Update propagation weight : ， Unmonitored Nodes Weighted voltage sag estimate Represented as: ， The weighted state estimation equations for all unmonitored nodes are written in matrix form: ， in, This is the weighted voltage sag state estimation vector for unmonitored nodes. To update the propagation weight The weighted propagation weight matrix is ​​formed.

11. The robust state estimation method for improving the reliability of voltage sag monitoring in distribution networks as described in claim 9, characterized in that: In S6, the updated node weights are introduced into the robust state estimation optimization model, and the voltage sag state of unmonitored nodes is solved by combining community consensus constraints, graph structure constraints and interaction field estimation consensus constraints. Let the voltage sag state vector of the unmonitored node to be determined be... ,in Unmonitored nodes The estimated value of the voltage sag state to be determined; Construct the full node voltage sag state vector ,in: ， The objective function of the robust state estimation optimization model is expressed as: ， in, For the number of node communities, For the first The weighted variance of voltage sag statistics within each node community. For monitoring nodes robust loss function, Let Laplacian matrix be the graph constructed from the adaptive weighted graph. This is the weighted voltage sag state estimation vector for unmonitored nodes. , , , It is a non-negative balance coefficient; Let the first Each node community is The set of monitoring nodes is The set of unmonitored nodes is Then the first Weighted average of voltage sag statistics within each node community Represented as: ， No. The weighted variance of voltage sag statistics within each node community Represented as: ， The robust state estimation optimization model satisfies the following constraints: ， By solving the robust state estimation optimization model, the voltage sag state estimation results of unmonitored nodes within a preset statistical time window are obtained.

12. The robust state estimation method for improving the reliability of voltage sag monitoring in distribution networks as described in claim 10, characterized in that: The robust state estimation optimization model is solved using any one of the following algorithms: genetic algorithm, particle swarm optimization algorithm, differential evolution algorithm, sequential quadratic programming algorithm, or improved least squares algorithm. During the solution process, the weighted voltage sag state estimation vector of the unmonitored nodes is used as the initial estimation result or reference constraint term, and the voltage sag state vector of the unmonitored nodes is obtained through iterative optimization. And the voltage sag state vector of the unmonitored node to be determined As the voltage sag state estimation result of unmonitored nodes in the distribution network within a preset statistical time window; the voltage sag state estimation result includes the number of voltage sags, sag severity index or voltage sag performance index.

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