A spoofing attack and defense method based on graph neural network parameter estimation priority

Abstract

This invention discloses a spoofing data injection attack and defense method based on graph neural network parameter estimation priority, belonging to the field of power system network security technology. During power grid operation, dynamic disturbances are applied to the parameters of target branches. The topology of the main grid and distribution network is constructed as a single graph structure. A first graph neural network is used to jointly learn measurement features and predict the parameters of each branch after the disturbance. An attack vector is generated based on the set of target branches, the target measurement set, and the parameter prediction results. The attack vector is embedded into the full measurement space, and state estimation is performed in combination with the parameter prediction results to obtain the residual statistics and state estimation offset features after the attack. The post-attack measurement vector, offset features, residual statistics, and parameter prediction results are concatenated into a node input feature vector, which is input into a second graph neural network to output the attack probability of each branch, and the set of attacked branches is obtained by filtering. This invention achieves rapid estimation of branch parameters under dynamic disturbances and accurate location of attack branches.

Description

Technical Field

[0001] This invention belongs to the field of power system network security technology, specifically involving a method for attacking and defending against fake data injection based on graph neural network parameter estimation priority. Background Technology

[0002] With the continuous development of information technology, the informatization and intelligence of power system networks are constantly improving. However, existing information technologies still have unavoidable vulnerabilities, which makes the security of power system networks more vulnerable to cyberattacks. For example, as one of the most threatening cyberattacks, False Data Injection (FDI) attacks can mislead and exploit state estimation results to maliciously tamper with measurement data without being detected by malicious data detectors. Its stealth often causes significant harm to power system networks. Therefore, the attack and defense issues related to power system network measurement data have become one of the important research directions in the field of power system network security in the current information age.

[0003] To enhance the defense capabilities of power system networks against spoofing attacks, researchers have proposed Moving Target Defense (MTD) strategies in recent years. These methods periodically perturb line parameters, making it difficult for attackers to accurately obtain the true system model, thus increasing the difficulty of constructing attack vectors. The core assumption of existing MTD methods is that attackers cannot obtain the newly changed parameters in a timely manner. This determines the effectiveness of MTD, and since attackers cannot directly obtain the newly changed branch parameters required to construct a spoofing data injection (FDI) attack, this assumption holds true in most practical situations. Typically, attackers use methods such as independent component analysis, subspace estimation, principal component analysis, and matrix reconstruction to infer the newly changed branch parameters from large amounts of online and offline measurement data. Due to the need for numerous measurements, the inference process in these methods usually takes several hours, preventing attackers from obtaining the newly changed branch parameters in a timely manner, thereby ensuring the effectiveness of MTD.

[0004] However, with the improvement of computing power and data processing capabilities, intelligent attack methods based on big data analysis are constantly evolving, challenging the above assumptions in complex scenarios with dynamically changing parameters. In recent years, technologies have proposed FDI blind attack methods based on unsupervised learning. This method can extract measurement features corresponding to the current parameters from mixed measurements, thereby improving the stealth of the attack. However, this type of method still has two drawbacks: first, the process of constructing the attack still requires a large number of measurements to infer the parameters, so it may not be timely enough in the scenario of defending against MTD for moving targets with small switching cycles; second, it is difficult to uniformly model the measurement requirements and attacks in real time, making it difficult to meet the needs of rapid attack and defense analysis under complex operating conditions.

[0005] Furthermore, as the coupling between the main grid and distribution network deepens, power system networks at different voltage levels exhibit significant differences in topology, operation mode, and measurement types. Traditional attack and defense methods typically target only a single power system network level, making it difficult to effectively characterize the interrelationships between multi-level power system networks, thus limiting system parameter estimation and attack capabilities. In the complex environment of dynamic defense strategies, existing methods generally suffer from strong dependence on system branch parameter acquisition, low parameter estimation efficiency, and difficulty in accurately locating attack branches, making it difficult to simultaneously meet the requirements of attack concealment, detection reliability, and real-time performance. Summary of the Invention

[0006] The purpose of this invention is to provide a method that can uniformly characterize the correlation between the topology of the main grid side and the distribution grid side and multi-element measurements under the conditions of dynamic changes in system parameters and collaborative operation of multi-level power system networks (grids), and realize rapid estimation of system parameters and identification of attack branches, so as to reduce the dependence on measurement completeness and long-term data windows, and improve the real-time response capability and reliability of power grid security analysis and collaborative defense under complex operating environments.

[0007] This invention provides a spoofing injection attack and defense method based on graph neural network parameter estimation priority. It constructs an adjacency matrix based on the unified graph structure of the main and distribution networks in the power grid, and a node feature matrix composed of the measurement features of each branch of the power grid. The adjacency matrix and the node feature matrix are jointly input into a trained first graph neural network to predict the parameters of each branch after a disturbance. The branches after the disturbance refer to the branches in the power grid after a moving target defense disturbance is applied to the power grid. In the attack vector construction stage, an attack vector is generated based on the set of attack target branches, the set of target measurements, and the predicted parameters of each branch after the disturbance. The attack vector is then embedded into the full measurement space to form the attack vector. The measured vector after the attack is combined with the predicted parameters of each branch after the disturbance to solve for the state estimation, thus obtaining the post-attack state estimate. The post-attack residual statistics are calculated. The offset feature between the post-attack state estimate and the pre-attack state estimate is calculated to obtain the state estimate offset feature. Based on the graph structure, the post-attack measured vector, the state estimate offset feature, the post-attack residual statistics, and the predicted parameters of each branch after the disturbance are concatenated to form a node fusion feature vector, which is input into a pre-trained second graph neural network. The output is the attack probability of each branch in the power grid. The attack probability of each branch in the power grid is filtered according to a preset threshold to obtain the set of attacked branches. The parameters of each branch after the disturbance include branch conductance and branch susceptance.

[0008] Based on a graph structure with power grid branches as nodes, the periodic measurement features, state estimation offset features, residual statistical features, and predicted parameters of each branch after disturbance are aligned by timestamps. These are then aggregated to the corresponding branch nodes according to the correlation mapping between measurements and branches, and concatenated with the state estimation offset features, residual statistical features, and predicted parameters of each branch after disturbance in a preset order to form a node input feature vector. Maintaining the same topological connectivity as during the training phase, and updating edge weights based on the predicted parameters of each branch after disturbance, a periodic graph input sample is constructed to characterize the topological propagation relationship of anomalies between branches and the coupling characteristics of parameter disturbances under attack. This graph input sample is then input into a second graph neural network that has been pre-trained offline. Through neighborhood feature aggregation and high-order topological information extraction under the graph structure, the fusion expression of anomaly features of each branch of the power grid is achieved, outputting the attack probability or attack score corresponding to each branch. Finally, by aggregating the attack probabilities of all branches of the power grid, the existence determination result of the attack across the entire network is obtained.

[0009] The attack probability of each branch of the power grid is filtered according to a preset threshold to obtain a set of attacked branches. Consistency correction is then performed on the set of attacked branches based on the grid topology connectivity constraints, prioritizing branches that are topologically connected, have a high attack probability, and meet preset similarity criteria. Finally, the set of attacked branches and its confidence level are determined, with the confidence level calculated from the branch attack probability. The second graph neural network is trained offline using normal operation samples and attack samples, with branch attack labels and grid-wide attack presence labels as supervisory signals. During online operation, when the chi-square detection does not trigger an alarm but the preset location trigger condition is met, the second graph neural network accepts the graph structure input corresponding to the current moving target defense MTD cycle and outputs the attack probability of each branch.

[0010] Furthermore, applying moving target defense disturbances to the power grid specifically involves: actively and periodically changing the parameters of the target branch through a controllable series compensation device; the target branch refers to the branch selected to be subjected to moving target defense dynamic disturbances. Applying moving target defense disturbances to the power grid causes the electrical characteristics of the power grid to change over time, thereby disrupting the system model established by the attacker based on historical data and improving the power grid's defense capability against false data injection attacks.

[0011] Furthermore, the measurement characteristics include active power at the starting end, reactive power at the starting end, active power at the ending end, reactive power at the ending end, voltage amplitude at the starting end, and voltage amplitude at the ending end.

[0012] Furthermore, the training process of the first graph neural network is as follows: The measurement characteristics of each branch of the power grid are used as node features in a graph structure. Each branch includes main grid-side branches and distribution grid-side branches. Branch parameters are used as label data, including parameters of branches without moving target defense disturbances and parameters of branches with moving target defense disturbances. The first graph neural network is trained using mean absolute error or mean square error as the loss function. Specifically, using branch parameters as label data involves: applying a maximum-minimum normalization method to the distribution grid-side branch parameters to perform scaling transformation, obtaining normalized distribution grid-side label data, which, together with the main grid-side label data, constructs training samples and inputs them into the first graph neural network. The first graph neural network outputs predicted branch parameters after disturbance, including both distribution grid-side and main grid-side disturbance parameters. Inverse normalization is then performed on the predicted distribution grid-side disturbance parameters to restore their actual numerical range.

[0013] To address the issues of frequent changes in branch parameters and slow update speed of traditional analytical identification in MTD (Moving Target Defense) scenarios, this invention unifies the topological relationships between the main grid and distribution network sides into a single graph structure. The measurement features of branch nodes on both the main grid and distribution network sides are jointly input into a first graph neural network for joint learning and prediction. In the pre-training phase, measurement data for each target branch are first read and aligned. Given the small differences in conductance and susceptance parameters corresponding to the distribution network measurement data, to avoid weakening of distribution side features due to scale differences during joint training between the main grid and distribution network sides, this invention performs scale transformation on the distribution network side conductance and susceptance parameters using a maximum-minimum normalization method before training the first graph neural network. The normalized distribution side label data and the main grid side label data are then used to construct training samples, which are input into the first graph neural network. Pre-defined measurement features are used as node input features, and branch parameter labels are used as supervision signals, with the mean absolute error (MAE) or mean square error (MSE) as the loss function. After the first graph neural network is trained, the time-aligned joint measurement data of the main grid side and distribution grid side within each moving target defense MTD cycle are constructed into a periodic graph input in the same graph structure organization method as the training phase, and input into the first graph neural network that has been trained offline. The output parameter prediction results are then processed by inverse normalization of the conductance and susceptance parameters predicted by the distribution grid side to restore their actual numerical range.

[0014] Furthermore, to address the challenges of rapidly determining attack target branches and target measurements in complex MTD (Moving Target Defense) scenarios, and the difficulty in timely incorporating perturbation parameters into the attack construction model, a candidate attack region search model is constructed using the power grid topology, measurement set, and predicted parameters of each branch after perturbation as inputs. This model is designed to satisfy both power grid topology connectivity and measurement observability constraints, thereby determining the set of attack target branches and their corresponding target measurement sets. The method for obtaining the set of attack target branches is as follows: Step S1, Initialization: Let the current bus set be... Only the central bus is included, and the candidate branch set O is initialized to empty; Step S2, update the candidate branch set O and expand the bus: Get the current bus set The branches connected to each busbar are denoted as the branch set. and set up the branch paths Add to the candidate branch set O, and simultaneously add the branch set The busbar at the other end of the branch in the middle serves as the newly extended busbar; Step S3, Boundary busbar determination: Check whether each newly extended bus meets the power injection conditions; If a power generation unit or load injection exists on the newly extended bus, the power injection condition is met, the bus is marked as a boundary bus, and the search for new branches from that bus is stopped. If there are no generating units or load injections on the newly extended bus, the power injection condition is not met. The bus is then marked as an internal node, and the current bus set is updated using the buses marked as internal nodes. ; Return to steps S2-S3 to continue updating the candidate branch set O and expanding the bus. When all the newly expanded buses meet the power injection condition, stop the search. At this time, the candidate branch set O is the final candidate set of attack target branches. From the candidate set of attack target branches, select the branch combination that satisfies the condition that the state offset can be realized and has the smallest number of parameters of each branch after the required estimation of the perturbation as the set of attack target branches; The target measurement set refers to the set of measurement features of the attack target branch in the attack target branch set.

[0015] Furthermore, the attack target branch set, the target measurement set, and the predicted parameters of each branch after perturbation are jointly input into the attack vector construction model to generate an attack vector that satisfies the state estimation concealment condition and measurement configuration constraints. The attack vector constructed within the measurement subspace corresponding to the target measurement set... Represented as: ; in, This represents a measurement function constructed based on an AC power flow model. Represents the state variables of the power grid system. This represents the predicted parameter values ​​for each branch within the set of attack target branches after defensive perturbations to moving targets. This indicates the expected system state offset.

[0016] Furthermore, after embedding the attack vector into the full measurement space, a post-attack measurement vector is formed. This vector is then combined with the predicted parameters of each branch after the perturbation to perform state estimation, yielding the post-attack state estimate. Specifically: The attack vector is embedded into the full measurement space. ;in, This represents the measurement vector after the attack. This represents the full vector measurement before the attack. The attack vector is represented; a weighted least squares criterion is used to measure the noise covariance matrix. Using weights, solve for the post-attack state estimation. Let the objective function be... for: ; ; in, This represents a measurement function constructed based on an AC power flow model. For the state variables of the power grid system, This represents the set of independent variables that minimize the objective function.

[0017] Furthermore, the post-attack residual statistics are expressed as: ; in, This represents the residual statistics after the attack. This represents the measurement vector after the attack. This represents a measurement function constructed based on an AC power flow model. This represents the predicted parameter values ​​for each branch within the set of attack target branches after defensive perturbations to moving targets. This indicates the state estimate after the attack.

[0018] Furthermore, the attack vector satisfies the state estimation concealment condition, specifically by constructing the chi-square detection residual statistic. , is represented as: ; in, Represents the measurement noise covariance matrix. This represents the residual statistics after the attack; residual statistics Compared with the preset chi-square detection threshold, when the residual statistic If the attack vector does not exceed the preset chi-square detection threshold, the state estimation concealment condition is met, and the attack vector is determined not to have triggered a chi-square detection alarm. Otherwise, the attack vector is determined to have been detected, and an alarm is triggered. The chi-square detection threshold is determined based on a preset saliency level and detection degrees of freedom.

[0019] Beneficial Effects: This invention addresses the challenges of dynamic changes in branch parameters in power system networks under Moving Target Defense (MTD) perturbation scenarios. By constructing a graph model, it estimates branch parameters after MTD disturbances and analyzes and protects against anomalous data injection. To address the issues of rapid branch parameter changes and the difficulty of real-time adaptation using traditional parameter update methods in complex MTD scenarios, this invention introduces a first graph neural network for branch parameter prediction, enabling rapid estimation of branch parameters after disturbances. Traditional methods in MTD scenarios often rely on analytical identification, iterative estimation, or updates based on fixed model parameters. These methods suffer from long computation times, poor adaptability to frequent disturbances, and difficulty in timely estimating the current true network parameter state. This leads to mismatches between the branch parameters used in subsequent attack construction and detection analysis and the actual branch parameters of the power grid. To address the aforementioned shortcomings, this invention constructs a graph structure input from the power grid topology and measurement characteristics. It utilizes a first-graph neural network to predict the parameters of each branch after a disturbance, enabling the branch parameter estimation process to explicitly leverage the topological coupling relationships between branches and the disturbance propagation characteristics. This allows for faster acquisition of branch parameter results consistent with the current power grid state, even in complex scenarios with frequent MTD switching. By introducing a first-graph neural network model to jointly model the power grid topology and measurement characteristics, this invention enhances the ability to represent system parameter changes under complex disturbance defense environments, thus providing a new technical approach for power grid security protection. This method improves the timeliness and consistency of parameter updates and provides reliable parameter support for subsequent attack vector construction, detection verification, and attack branch location.

[0020] To address the problems of insufficient feature utilization and limited generalization ability caused by the fragmented and separate training of parameter estimation on the main grid and distribution network sides in traditional methods, this invention adopts a collaborative training mechanism for the main grid and distribution network sides. This is beneficial for improving the stability and adaptability of the parameter prediction model under different voltage levels and topologies. Existing methods typically model and train the main grid and distribution network sides separately during parameter estimation, making it difficult to utilize the correlation information between the two sides in terms of topology, measurement patterns, and disturbance response within a unified framework. This is especially problematic when there are significant differences in measurement scales and inconsistent sample distributions, leading to poor model generalization ability and weak adaptability to complex disturbance scenarios. To address these shortcomings, this invention introduces a collaborative mechanism between the main grid and distribution network sides during the first graph neural network training stage. By using a unified graph modeling framework, it jointly utilizes the topology and measurement data of the main grid and distribution network sides for parameter learning, and performs scale processing on the distribution network side parameters to reduce the impact of data distribution differences at different voltage levels on the training process. Compared to separate training methods for the main grid side and the distribution network side, this invention is beneficial to improving the prediction accuracy, robustness and generalization ability of the model in scenarios with multiple topologies, multiple disturbance modes and different voltage levels.

[0021] To address the shortcomings of traditional methods for locating FDI (Fulfilled Direct Injection) branches in attacks, such as insufficient utilization of topological coupling relationships and limited accuracy and timeliness in scenarios involving dynamic disturbances during Mobile Target Defense (MTD) attacks, this invention utilizes a second graph neural network to identify and locate attacked branches. This approach more effectively identifies the propagation and coupling characteristics of attacks between branches. Traditional attack detection and localization methods often rely on single-time residual statistics, threshold discrimination, or local rule matching, typically focusing on determining whether anomalies exist in the power grid. However, their ability to accurately identify attacked branches is significantly limited. Even when attacked branches are identified and located, it is often difficult to fully utilize the correlation between the power grid topology, state estimation offset information, and multi-source anomaly features. This is especially true when network parameters change dynamically due to MTD disturbances during MTD attacks, where the localization results are easily affected by parameter time lags and disturbance switching. To address this deficiency, this invention, after the power grid has been attacked and no anomalies have been detected and verified, comprehensively utilizes post-attack measurement features, state estimation offset information, detection statistics, and post-disturbance branch parameter information to construct a graph structure identification input for the current disturbance cycle, and then employs a second graph neural network for attack branch localization. This method can integrate branch neighborhood information and high-order topological relationships in a graph structure to achieve rapid identification and localization of attacked branches, which is beneficial to improving the accuracy and robustness of abnormal branch identification in complex scenarios.

[0022] To address the problems of inconsistencies in evaluation results caused by the separation of attack construction, detection verification, and attack localization in existing technologies, and the lack of unified parameter benchmarks, this invention systematically proposes an integrated power grid attack and defense mechanism based on graph neural networks for mobile target defense against MTD disturbances. Traditional solutions typically focus only on attack vector construction or identification of attacked branches, lacking a systematic design under the same parameter benchmark and framework. In the scenario of mobile target defense against dynamic MTD disturbances, this separated processing can easily lead to inconsistencies between the parameters used in attack construction, the parameters used in state estimation, and the information on which the localization model is based, thus affecting the stealth of the attack construction and the comparability of the defense evaluation. To address this deficiency, this invention organically links the steps of mobile target defense against MTD disturbances, branch parameter prediction, attack target selection and attack vector construction, and attack branch identification and localization, forming a closed-loop pipeline for mobile target defense against MTD disturbances. This allows attack construction, detection verification, and localization to operate collaboratively under a unified post-disturbance parameter benchmark, effectively improving the consistency of attack effect evaluation and the collaborative capability of detection and localization.

[0023] To address the issue of insufficient robustness of models under complex measurement conditions, the data construction and graph sample generation methods of this invention possess good adaptability to complex scenarios, which is beneficial for improving stability in practical applications. Traditional data processing methods often employ tabular, single-point, or local feature inputs, making it difficult to systematically represent the topological relationships between branches. Furthermore, they are not well-suited to real-world anomalies such as measurement noise, missing features, and node failures. To overcome these shortcomings, this invention employs a branch-level graph structure data construction method, reorganizing the branch measurement features at each moving target defense MTD cycle time into a graph sample sequence. During the training and testing phases, scenarios involving noise disturbances, missing features, or missing nodes are introduced for robust training and evaluation. This enhances the model's adaptability under complex measurement conditions, providing a more robust and effective data processing and organization method for optimizing power grid attack detection and defense strategies. Attached Figure Description

[0024] Figure 1 This is a flowchart of the state estimation process; Figure 2 This is a spurious parameter estimation map under MTD perturbation in moving target defense; Figure 3 The second figure is a schematic diagram of neural network parameter identification. Detailed Implementation

[0025] The present invention provides a spoofing attack and defense method based on graph neural network parameter estimation priority, such as... Figure 1 As shown, before constructing the attack vector, the parameters of each branch after the disturbance are predicted based on the graph neural network first, so as to ensure that the branch parameters used in the attack construction are consistent with the current power grid state. For the scenarios of coordinated operation of the main grid and distribution network and MTD parameter disturbance of moving target defense, the first graph neural network is used to quickly estimate the conductance and susceptance parameters of each branch. During the training phase, the samples of the main grid side and the distribution network side are trained together to improve the generalization across voltage levels. During the operation phase, the topology identification of the second graph neural network is used to output the judgment result of whether each branch of the power grid has been attacked.

[0026] Specifically, the spoofing injection attack and defense method based on graph neural network parameter estimation priority of the present invention includes the following steps: Step 1: Collect measurement data and construct the graph structure Collect operational measurement data and topology information of branches and their associated buses in the power grid, and construct graph structure input features for branch parameter prediction, attack vector construction and abnormal branch identification; In this specific embodiment, the simulation data of the IEEE 14-node power grid's Moving Target Defense (MTD) is selected as the implementation object. The MTD simulation data includes historical measurement datasets without MTD disturbances and time-series measurement datasets after MTD disturbances are applied. The time-series measurement datasets include a directory organized into 120 cycles, each cycle corresponding to a MTD configuration cycle, containing 96 time steps, corresponding to a 15-minute sampling interval within a day. Each cycle directory includes at least CSV files for each branch, including the starting active power, starting reactive power, ending active power, ending reactive power, starting voltage amplitude, and ending voltage amplitude. Each CSV file is indexed by a timestamp. This embodiment uses branches as the modeling object, reads the branch and IEEE 14-node line topology relationships in the power grid, aligns the measurement data within the same cycle by timestamp, and organizes them into periodic samples according to the MTD operation cycle.

[0027] A graph structure is constructed based on the power grid topology, specifically, as follows: Figure 2 As shown, the power grid branches are the nodes in the graph structure. The associated bus of the branch is used to determine the connection relationship between the branches. The periodic measurement data is mapped to the node features according to the branches to form a node feature matrix. Based on the topology between the branches in the IEEE 14 line system, the adjacency relationship matrix is ​​constructed. Finally, the node feature matrix and the adjacency matrix are combined to form the input sample of the first graph neural network to characterize the branch coupling relationship, power flow transmission relationship and disturbance propagation characteristics.

[0028] Step 2: Apply moving target defense MTD disturbance In the power grid, a branch is selected as the target branch for applying dynamic disturbances to defend against moving targets. During the normal operation of the power grid, dynamic disturbances to defend against moving targets are applied to the target branch to form a network configuration that changes over time, thereby compressing the effective time window for attackers to construct attack models based on historical measurements.

[0029] A Flexible AC Transmission System (FACTS) device is used to simulate the Moving Target Defense (MTD) strategy, dynamically changing the conductance and susceptance values ​​of the target branch. Specifically, a Controllable Series Compensator (TCSC) is used to dynamically adjust the parameters of the target branch. The TCSC affects the reactance of the target branch by changing the degree of series compensation, thereby dynamically changing the impedance characteristics of the target branch and quickly disabling the attack vector constructed by the attacker based on old data. In this embodiment, records of each disturbance are read from the disturbance data log file obtained through simulation. The disturbance record includes at least the timestamp of parameter change, the number of the disturbed branch, the branch selection strategy, and the reactance values ​​before and after the disturbance, as shown in Table 1.

[0030] Table 1 Example of a disturbance data log file

[0031] Step 3: Use the first graph neural network to predict branch parameters in a collaborative manner between the main grid side and the distribution network side. In this embodiment, a simulation is performed based on the IEEE 14 power grid topology. A power grid containing 15 branches is constructed, and each branch is mapped to a node in the graph structure, with node numbers ranging from 0 to 14. An edge connection index (edge_index) of the graph is pre-constructed based on the power grid topology connection relationship to represent the topology connection relationship between branches and the propagation path of measurement influence. The adjacency matrix A is obtained based on the edge connection index (edge_index).

[0032] Furthermore, each node corresponds to a branch, and 6-dimensional measurement features are extracted for that node in each operating cycle, namely, active power at the starting end, reactive power at the starting end, active power at the ending end, reactive power at the ending end, voltage amplitude at the starting end, and voltage amplitude at the ending end. The predicted target parameters are branch conductance target_g or branch susceptance target_b, and the label type is set manually during training as the corresponding supervision signal.

[0033] Read the measurement data files corresponding to 15 branches. Each measurement data file contains six-dimensional measurement features aligned to time at each time step. Extract the measurement features of the six dimensions as the input features of the nodes. Read the true values ​​of branch conductance and branch susceptance corresponding to each branch as supervision labels. There are a total of 11,520 data records in the dataset. Take the first 80% of the records to form training samples. The dataset includes historical measurement datasets and time-series measurement datasets after applying moving target defense MTD perturbation.

[0034] Stack the 15 node features of each timestamp t in node order to form a node feature matrix. The target parameters corresponding to the same timestamp are stacked in node order to form a label vector: Furthermore, ( edge_index The data is encapsulated as a graph sample data Data, and the training sample set is obtained by traversing all time steps. The training sample set is then serialized and stored as train for subsequent steps.

[0035] To simulate measurement noise and missing data, the input node features are perturbed and enhanced: on the one hand, Gaussian noise is superimposed on the features of randomly selected samples; on the other hand, the feature dimensions of the node features are set to zero proportionally to improve the adaptability of the first graph neural network to anomaly detection and missing data measurement.

[0036] Further, the training and prediction results of the first graph neural network are output. First, a graph convolutional neural network is used to aggregate neighborhood information of node features. This graph convolutional neural network includes at least one layer of graph convolutional structure, and multiple layers can be stacked to achieve a deep representation of the power grid topology and node features. Specifically, let the adjacency matrix of the graph be... Adding a self-loop yields: ; Correspondence matrix , is represented as: ; in, Represents the identity matrix. This represents the adjacency matrix after adding self-loops. Represents a node With nodes Self-connection and adjacency relationships; The process of a Graph Convolutional Network (GCN) can be represented as follows: ; in, This represents the sigmoid activation function. , This represents the input variable of the sigmoid activation function. This is the weight matrix. ; , represents the node feature matrix output by the graph convolutional neural network. This represents a 6x6 real matrix. This represents a real matrix with 15 rows and 6 columns. Represents a node The hidden feature representation; express transpose, Representing the adjacency matrix The correspondence matrix, This represents the node feature matrix input to the graph convolutional neural network; The node implicit representations with fused topological coupling information are obtained. Subsequently, two fully connected layers are applied to each of the 15 nodes, followed by Sigmoid activation. The predicted values ​​of the parameters of each branch after perturbation are then output, forming a set of parameter prediction results for the 15 branches. ; ; ; in, This represents the shared weight parameters in the first fully connected layer mapping. This represents the shared weight parameters in the second-layer fully connected mapping. Indicates 1 row A 6-column real matrix This represents the bias parameters of the first fully connected layer mapping. This represents the bias parameters of the second-layer fully connected mapping. Represents a node The intermediate features after the first fully connected layer mapping, Represents a node The value after the second fully connected layer mapping represents the node in this invention. Predicted values ​​of the corresponding branch parameters; Training the objective function, for the first element in a batch Nodes in each sample The tag is The predicted result is Then the node Mean square error for: ; in, This represents the batch sample index during the training of the first graph neural network. This represents the batch size when training the first neural network.

[0037] The first graph shows the average of the overall training loss of the neural network over the mean squared errors of the 15 nodes: ; in, This represents the overall training loss function of the neural network in the first graph.

[0038] Table 2 shows examples of input node features and branch parameter prediction results for some nodes at different time steps. The input node features include active power at the starting end, reactive power at the starting end, active power at the ending end, reactive power at the ending end, voltage amplitude at the starting end, and voltage amplitude at the ending end; the supervision labels are the true values ​​of branch conductance (target_g) and branch susceptance (target_b); the prediction results (predict_g, predict_b) are the branch parameter estimates output by the neural network in the first graph.

[0039] Table 2. Examples of prediction results for node characteristics and branch parameters

[0040] Step 4: Selecting attack paths and constructing attack vectors First, a heuristic topology search method is used to determine the set of attack target branches and the set of their corresponding target measurements, and then an attack vector that satisfies the concealment constraint is constructed.

[0041] Specifically, first, any busbar is set as the central busbar. According to the power grid topology, the buses are expanded outward layer by layer to obtain the boundary buses. All branches electrically connected to the central busbar and the expanded buses are searched to form a candidate branch set. The search process is as follows: (1) Initialization Let the current bus set be... Only the central bus is included, and the candidate branch set O is initialized to empty; (2) Update the candidate branch set O and expand the bus. Get the current bus set The branches connected to each busbar are denoted as the branch set. and set up the branch paths Add to the candidate branch set O, and simultaneously add the branch set The busbar at the other end of the branch serves as the newly extended busbar; (3) Boundary busbar determination Check whether each newly extended bus meets the power injection conditions; If a power generation unit or load injection exists on the newly extended bus, the power injection condition is met, the bus is marked as a boundary bus, and the search for new branches from that bus is stopped. If there are no generating units or load injections on the newly extended bus, the power injection condition is not met. The bus is then marked as an internal node, and the current bus set is updated using the buses marked as internal nodes. ; Return (2) Continue to update the candidate branch set O and expand the bus. When all the newly expanded buses meet the power injection condition, stop the search. At this time, the candidate branch set O is the final attack target branch candidate set. Define the boundary busbar The change in active power injection is The change in reactive power injection is , and the boundary busbar Connected nodes The power flow changes are respectively the active power changes. and reactive power change Other adjacent branch roads The tidal current changes are respectively and , Indicates the boundary busbar Connecting branch roads The change in active power, Indicates the boundary busbar Connecting branch roads The change in reactive power; Then the boundary busbar The following power balance relationship is satisfied: ; ; in, Indicates the boundary busbar A set of connected branches. When the boundary bus... When load injection exists, the power balance constraint mentioned above is satisfied by adjusting the injection amount at this bus, thus stopping further expansion in this direction; when the boundary bus... In the absence of power injection, to maintain consistency of the measurement functions before and after the attack, the power flow measurements of other branches connected to it are further modified. Therefore, branches connected to this boundary bus are still included in the candidate attack region. Through the above-described bus expansion process and boundary bus determination, a set of candidate branches is obtained.

[0042] From the candidate branch set, select the branch combination that satisfies the condition for state shift realization and has the smallest number of branch parameters after the required estimation of perturbation as the attack target branch set. And determine the corresponding target measurement set based on the correlation between branches and measurement items. .

[0043] Construct the attack vector, input the prediction results of the periodic branch parameters of the current moving target's defense against MTD disturbances, and set the attack target branch set. The predicted values ​​of parameters for each branch after the internal moving target defense disturbance are denoted as: Target measurement set The measurement vector within is denoted as Local AC measurement functions constructed based on the AC power flow model within the target measurement subspace. Let the current state variables of the power grid system be... This includes the voltage amplitude and phase angle of each bus, with a preset desired state offset of [value missing]. Then the attack vector within the target measurement subspace is: ; Satisfying the condition for realizable state offset means that the selection of the attack target branch set must guarantee the existence of a state offset vector. This makes the state offset vector The determined attack vector The system state that can be constructed and attacked. It is physically feasible.

[0044] Step 5: Inject attack vectors and perform chi-square detection The constructed attack vector is injected into the original measurement vector, and the stealth of the constructed attack vector is verified by the AC state estimation and chi-square detection module. Specifically, firstly, based on the index position of the target measurement set in the full measurement space, the attack vector is... Full vector measurement before embedding attack In the process, the measurement vector after the attack is formed. , is represented as: .

[0045] Furthermore, the post-attack measurement vector Input the AC state estimation model and combine it with the prediction results of the periodic branch parameters of the MTD disturbance in the moving target defense. State estimation is performed. The state estimation uses the weighted least squares method to measure the noise covariance matrix. As weights, construct the objective function: ; And obtain the post-attack state estimate. Furthermore, the residual vector after the attack is calculated. , is represented as: ; And construct a chi-square detection residual statistic based on the residual vector. , is represented as: ; residual statistics The residual statistic is compared with a preset chi-square detection threshold. If the residual statistic is less than the preset chi-square detection threshold, it is determined that the constructed attack vector has not triggered a chi-square detection alarm; otherwise, it is determined that the constructed attack vector has been detected and an alarm is triggered.

[0046] Furthermore, to ensure that the state estimation processes before and after the attack are compared under the same parameter benchmark, the full measurement vector before the attack is used as the basis. Prediction results of periodic branch parameters for MTD disturbance in moving target defense The same communication state estimation method as the post-attack state estimation is used to solve the problem, and the pre-attack state estimation result is obtained. Specifically, the pre-attack state estimation results The following formula can be used to obtain: ; in, This represents the full vector measurement before the attack. This indicates the predicted parameters of each branch after the moving target defense disturbance. This represents the AC measurement function based on the predicted parameters of each branch after the disturbance, where Σ represents the measurement noise covariance matrix. This represents the set of independent variables that minimize the objective function.

[0047] Furthermore, the post-attack state estimation Compared with pre-attack state estimation The difference is used to construct the state estimation offset feature, which is expressed as: ; in, This represents the state estimation offset feature.

[0048] Step 6: Identification and Localization of Attack Paths First, based on the branch graph structure constructed in step 1, the normal operation samples and attack samples are uniformly organized into graph input samples, where graph nodes correspond to all branches in the power grid, and the connection relationship between nodes is determined by the topological relationship between branches. For each training sample, the measurement features after the attack, state estimation offset information, residual statistics information, and branch parameter information after the disturbance are aligned according to the timestamp, and then collected to the corresponding branch nodes according to the correlation mapping relationship between the measurement data and the branches. Further, the periodic measurement features after the attack, state estimation offset features, residual statistics features, and branch parameter features after the disturbance are concatenated in a preset order to form a timestamp. Time node fusion feature vector The node fusion feature matrix of the current sample can be constructed from the node fusion feature vectors of all branches: ; in, express transpose, This represents the total number of branch nodes. This represents the dimension of the fused features input to a single node.

[0049] Regarding graph topological relationships, This is a branch-level weighted adjacency matrix, whose elements... Used to characterize nodes With nodes The strength of topological coupling between them.

[0050] Furthermore, based on the branch-level weighted adjacency matrix Construct degree matrix , is represented as: ; ; in, Represents a node The degree; And construct the normalized Laplace matrix , is represented as: ; in, Represents an M-dimensional identity matrix. Normalized Laplacian matrix. Used to characterize the local connectivity and global topology in a branch-level graph structure.

[0051] Furthermore, such as Figure 3 As shown, a second graph neural network based on ARMA graph filters is used to perform neighborhood propagation and topology aggregation on branch-level anomaly features. The node fusion feature matrix is ​​then used. Input the ARMA graph filter layer. For the first-order ARMA recursive formula, its propagation process can be expressed as: ; in, Indicates the first The hidden layer output after the next iteration. and These are the filter coefficients. The expression is represented by the normalized Laplace matrix. The modified Laplacian matrix obtained by translation transformation can be expanded into a trainable form with a fixed number of steps T to facilitate neural network training: ; in, , , These are the parameters to be learned.

[0052] Furthermore, in this specific embodiment, the second graph neural network includes two layers of ARMA graph filters, namely a first layer of ARMA graph filters and a second layer of ARMA graph filters; to enhance feature representation capabilities, the second layer of ARMA graph filters is further... The output of the first-layer ARMA graph filter is obtained by averaging and aggregating the parallel first-order ARMA graph filter recursive blocks: ; in, This represents the output of the first-layer ARMA graph filter. Indicates the first layer The output of an ARMA recursive block after T iterations.

[0053] Then the output of the first layer ARMA graph filter Input second-layer ARMA graph filter: ; in, Indicates the second layer An ARMA recursive block with Given the input and the output after T iterations, The output of the second-layer ARMA graph filter is the higher-order topological representation of the branch.

[0054] Furthermore, the obtained higher-order topological representation of the branches is input into a fully connected mapping layer, which outputs the attack probability corresponding to each branch: ; in, , Represents a node The predicted probability of being attacked. and For output layer parameters, This represents the Sigmoid activation function. This represents the overall network attack existence determination result obtained by aggregating the attack probabilities of each branch, where the maximum value aggregation method is used, i.e.: ; Furthermore, during the training phase, the attacked power grid samples and normal samples are input uniformly, and the labels of the real attack branches are recorded as follows: , Represents a node The corresponding branch in this sample is the actual branch that was attacked. This indicates that no attack has occurred. Since one or more attack branches may exist simultaneously, the attack localization task is treated as a multi-label classification problem, and a binary cross-entropy loss function is used for supervised training of the second graph neural network. ; in, This represents the overall training loss function of the neural network in the second graph.

[0055] This invention proposes a rapid prediction method for branch conductance and susceptance parameters after MTD (Moving Target Defense) disturbances based on graph neural networks. This method uses power grid branches as graph nodes and constructs a graph topology based on shared buses or electrical connections between branches. Branch measurement features and the power grid topology are input into a first graph neural network. Through graph convolution operations and nonlinear mapping, the method achieves rapid prediction of the conductance and susceptance parameters of the target branch after being subjected to MTD disturbances. This replaces traditional prediction methods that rely on analytical modeling and iterative identification, improving the real-time performance and accuracy of parameter acquisition in complex scenarios with frequent MTD disturbances.

[0056] A collaborative training mechanism for the main grid and distribution network sides is proposed. This mechanism integrates the branches of the main grid and distribution network sides into the same graph learning framework for joint modeling and parameter learning. By constructing a unified graph representation across voltage levels, setting a shared feature extraction structure for the main grid and distribution network sides, and combining distribution network parameter label normalization processing and hierarchical output mapping mechanism, the mechanism solves the training instability problem caused by the differences between the main grid and distribution network sides in terms of topological scale, measurement distribution and parameter magnitude. This improves the overall accuracy and generalization ability of branch parameter prediction in the collaborative scenario of the main grid and distribution network sides.

[0057] A fictitious data injection (FDI) attack defense mechanism based on graph neural network topology identification is proposed. This mechanism utilizes post-attack measurement features, state estimation offsets, chi-square residual statistics, and parameter prediction results after moving target (MTD) disturbance defense to construct a graph input sample for the current operating cycle. A second graph neural network is then used to characterize the propagation relationships of power flow anomalies, topological coupling relationships, and the correlation of parameter disturbances, outputting the identification results of the attacked branches. This combination forms an integrated power grid security protection technology solution encompassing power grid parameter prediction, collaborative training on the main grid and distribution grid sides, and FDI attack identification and defense.

Claims

1. A spoofing injection attack and defense method based on graph neural network parameter estimation priority, characterized in that, An adjacency matrix is ​​constructed based on the unified graph structure of the main and distribution networks in the power grid. The measurement characteristics of each branch of the power grid constitute a node feature matrix. The adjacency matrix and the node feature matrix are input into a pre-trained first graph neural network to predict the parameters of each branch after the disturbance. The branches after the disturbance refer to each branch in the power grid after the moving target defense disturbance is applied to the power grid. During the attack vector construction phase, an attack vector is generated based on the attack target branch set, the target measurement set, and the predicted parameters of each branch after perturbation. After embedding the attack vector into the full measurement space, the post-attack measurement vector is formed. Combined with the prediction results of the parameters of each branch after the perturbation, the state estimation is solved to obtain the post-attack state estimate and the post-attack residual statistics are calculated. Calculate the offset features between the post-attack state estimate and the pre-attack state estimate to obtain the state estimate offset features; Based on the graph structure, the measurement vector after the attack, the state estimation offset feature, the residual statistics after the attack, and the predicted parameters of each branch after the disturbance are concatenated to form a node fusion feature vector, which is input into a pre-trained second graph neural network to output the attack probability of each branch in the power grid. The attack probability of each branch in the power grid is then filtered according to a preset threshold to obtain the set of attacked branches.

2. The method for attacking and defending against fake data injection according to claim 1, characterized in that, The parameters of each branch after the disturbance include branch conductance and branch susceptance.

3. The method for attacking and defending against fake data injection according to claim 1, characterized in that, Applying moving target defense disturbances to the power grid involves: actively and periodically changing the parameters of the target branch through a controllable series compensation device; The target branch refers to the branch selected to apply dynamic disturbances for mobile target defense.

4. The method for attacking and defending against fake data injection according to claim 1, characterized in that, The measurement characteristics include active power at the starting end, reactive power at the starting end, active power at the ending end, reactive power at the ending end, voltage amplitude at the starting end, and voltage amplitude at the ending end.

5. The method for attacking and defending against fake data injection according to claim 1, characterized in that, The training process of the first neural network is as follows: The measurement characteristics of each branch of the power grid are used as the node features of the graph structure. Each branch of the power grid includes the main grid side branch and the distribution network side branch. The parameters of each branch are used as the label data. The parameters of each branch include the parameters of the branch without moving target defense disturbance and the parameters of the branch with moving target defense disturbance. The mean absolute error or mean square error is used as the loss function to train the first graph neural network. The method of using branch parameters as label data specifically involves: performing scaling transformation on the distribution network side branch parameters of the power grid using the maximum-minimum value normalization method to obtain normalized distribution network side label data, which, together with the main grid side label data of the power grid, constructs training samples and inputs them into the first graph neural network. The neural network outputs the predicted parameters of each branch after the disturbance. These parameters include those of the distribution network side and the main grid side. The predicted parameters of the distribution network side are then subjected to inverse normalization to restore the actual numerical range.

6. The method for attacking and defending against fake data injection according to claim 1, characterized in that, The method for obtaining the set of attack target branches includes the following steps: Step S1, Initialization: Let the current bus set be... Only the central bus is included, and the candidate branch set O is initialized to empty; Step S2, update the candidate branch set O and expand the bus: Get the current bus set The branches connected to each busbar are denoted as the branch set. and set up the branch paths Add to the candidate branch set O, and simultaneously add the branch set The busbar at the other end of the branch in the middle serves as the newly extended busbar; Step S3, Boundary busbar determination: Check whether each newly extended bus meets the power injection conditions; If a power generation unit or load injection exists on the newly extended bus, the power injection condition is met, the bus is marked as a boundary bus, and the search for new branches from that bus is stopped. If there are no generating units or load injections on the newly extended bus, the power injection condition is not met. The bus is then marked as an internal node, and the current bus set is updated using the buses marked as internal nodes. ; Return to steps S2-S3 to continue updating the candidate branch set O and expanding the bus. When all the newly expanded buses meet the power injection condition, stop the search. At this time, the candidate branch set O is the final candidate set of attack target branches. From the candidate set of attack target branches, select the branch combination that satisfies the condition that the state offset can be realized and has the smallest number of parameters of each branch after the required estimation of the perturbation as the set of attack target branches; The target measurement set refers to the set of measurement features of the attack target branch in the attack target branch set.

7. The method for attacking and defending against fake data injection according to claim 1, characterized in that, The attack vector is represented as follows: in, Represents the attack vector. This represents a measurement function constructed based on an AC power flow model. Represents the state variables of the power grid system. This represents the predicted parameter values ​​for each branch within the set of attack target branches after defensive perturbations to moving targets. This indicates the expected system state offset.

8. The method for attacking and defending against fake data injection according to claim 1, characterized in that, After embedding the attack vector into the full measurement space, a post-attack measurement vector is formed. Combined with the predicted parameters of each branch after perturbation, a state estimation is performed to obtain the post-attack state estimate, specifically: The attack vector is embedded into the full measurement space. ;in, This represents the measurement vector after the attack. This represents the full vector measurement before the attack. Indicates the attack vector; The weighted least squares criterion is used to measure the noise covariance matrix. Using weights, solve for the post-attack state estimation. Let the objective function be... for: in, This represents a measurement function constructed based on an AC power flow model. This represents the predicted parameter values ​​for each branch within the set of attack target branches after defensive perturbations to moving targets. For the state variables of the power grid system, This represents the set of independent variables that minimize the objective function.

9. The method for attacking and defending against fake data injection according to claim 1, characterized in that, The post-attack residual statistics are expressed as follows: in, This represents the residual statistics after the attack. This represents the measurement vector after the attack. This represents a measurement function constructed based on an AC power flow model. This represents the predicted parameter values ​​for each branch within the set of attack target branches after defensive perturbations to moving targets. This indicates the state estimate after the attack.

10. The method for attacking and defending against fake data injection according to claim 1, characterized in that, The attack vector satisfies the state estimation concealment condition, specifically: Constructing chi-square test residual statistics , represented as: in, Represents the measurement noise covariance matrix. This represents the residual statistics after the attack; residual statistics Compared with the preset chi-square detection threshold, when the residual statistic If the value does not exceed the preset chi-square detection threshold, then the state estimation concealment condition is met.

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