A Defense Method for Topological Collaborative False Data Attacks in Power Grid States

Abstract

The present invention discloses a defense method for collaborative false data attacks on power grid state topology, which is based on spatio-temporal multi-modal neural network for collaborative false data attack defense on power grid, and includes the following steps: 1. Use the residual detection method to filter out bad data, and then use a detection model composed of a graph autoencoder and a residual neural network to detect and locate data attacks; 2. Construct a prediction model based on spatio-temporal features to predict corresponding telemetry data based on a possible set of tele-signals; 3. Use the N-k search method to input the telemetry and tele-signal combinations into the above detection model, and use the detected data as the true value. The present invention improves the defect that traditional methods are not suitable for collaborative FDIA scenarios. The defense strategy has stronger robustness against the situation where the topological structure is tampered with, enhances the power grid's ability to defend against collaborative FDIA, and meets the practical requirements of the industry for collaborative FDIA defense.

Description

Technical Field

[0001] The present invention belongs to the technical field of power system operation safety maintenance, and particularly relates to a defense method for collaborative false data attacks in power grid state topology. Background Art

[0002] At present, the power system has developed into a cyber-physical power system (CPPS) with deep coupling between the information system and the physical system. There are a large number of communication nodes in the CPPS, and the vulnerabilities of these nodes have led to frequent network attack events against the CPPS. Among various types of network attacks, the false data injection attack (FDIA) has attracted wide attention in the academic and industrial fields due to its strong concealment and great destructiveness. After continuous development, the FDIA has become a collaborative FDIA that simultaneously tamper with the system's electrical quantities (i.e., telemetry) and topological information (i.e., telecontrol). This attack can cause partial unobservability of the system. The information about the current system operation state held by the power grid dispatching center will be significantly less than that of the attacker under a large-scale FDIA. This is the defense scenario under asymmetric information. In view of this, constructing a systematic defense strategy for FDIA under this asymmetric information is of great significance for the safe operation of the power system.

[0003] At present, the systematic defense of FDIA in the power system is still a difficult problem worldwide. Although there are dozens of research papers on this problem at home and abroad, there is still no mature solution for FDIA in the industrial field. From the existing literature on FDIA defense strategies, it can be found that these research works have two deficiencies: 1. The detection and location methods are all based on the complete observability of the system topology, that is, the case where the Jacobian matrix of state estimation is known, and there is little research on the defense scenario with low system observability caused by attacks. 2. The recovery methods also mostly focus on the recovery of telemetry or telecontrol data, and there is little research based on the unobservability of both. Therefore, it is necessary to propose a systematic defense strategy that can reduce the impact of collaborative FIDA and play a greater defense role when dealing with collaborative FDIA under information asymmetry.

[0004] The FDIA defense strategy of the present invention is divided into three stages: detection, location, and recovery. The construction difficulty lies in how to detect two different modalities of data, telemetry and telecontrol, under asymmetric information, and how to determine the operating conditions of the unobservable area. To address these challenges, the present invention proposes a systematic defense strategy based on multi-modal deep learning, aiming to ensure the observability of the power grid and the ability to resist FDIA under information asymmetry conditions, and enhance the stability during the operation of the power grid. Summary of the Invention

[0005] The technical problem to be solved by the present invention is that it is difficult to detect the collaborative FDIA measurement data and it is difficult to restore the safe operation state under the condition that a large area of the power grid is unobservable. A method for defending against false data attacks in power grid state topology collaboration is provided. The present invention improves the defect that the topological information error is not considered in the previous traditional methods. The defense strategy has stronger robustness against the situation where the topological structure is tampered with, enhances the ability of the power grid to defend against collaborative FDIA, and meets the practical requirements of the industry for collaborative FDIA defense.

[0006] To achieve the above object, the present invention adopts the following technical solutions:

[0007] A method for defending against false data attacks in power grid state topology collaboration according to the present invention includes the following steps:

[0008] (1) Use the residual detection method to filter out bad data, and then use the detection model to detect the data to determine the attacked measurement data: Use the residual detection method to detect the network topology and telemetry data, filter out the bad data generated by physical network operation failures, equipment measurement errors, and communication system noises in the data, so that only the real data and the false data tampered by collaborative FDIA are retained in the system; then send the telemetry and telecommunication signals together into the detection model for detection, identify the attacked buses and branches, and determine the attacked area;

[0009] (2) Construct a prediction model based on spatio-temporal features to predict the corresponding telemetry data based on the possible set of telecommunication signals: Establish a spatio-temporal feature prediction model based on a spatio-temporal neural network. The spatio-temporal feature prediction model based on a spatio-temporal neural network includes a historical feature processing module and an existing feature processing module; The spatio-temporal feature prediction model based on a spatio-temporal neural network predicts the corresponding telemetry data according to the historical topological structure, and then sends the telemetry and telecommunication signals together into the above detection model for detection. If the detection is passed, the data recovery is completed; if the detection is not passed, go to the next step;

[0010] (3) Use the N-k search method to input the combination of telemetry and telecommunication signals into the prediction model based on spatio-temporal features, and use the data passing the detection as the true value: Speculate the possible topological structures according to the historical topological information of the unobservable area, then predict the telemetry data corresponding to the possible topological structures, send the combination of telemetry and telecommunication signals into the detection model, and screen out the correct data combination.

[0011] The detection model is constructed using a Graph Auto-Encoder (GAE) and Residual Neural Networks (ResNet). The attack detection process is shown as follows:

[0012] V = GAE(A, X)

[0013]

[0014] In the formula, V represents the extracted topological feature, A represents the adjacency matrix, X represents the node feature, and z represents the telemetry data; represents the feature fusion operation; the detection model outputs a set of {0,1} labels, indicating that the corresponding measurement is under attack, and the attacked area of the power grid is determined based on these labels.

[0015] The prediction model based on spatio-temporal features is constructed as follows:

[0016] Use the Graph Autoencoder (GAE) and the Long Short-Term Memory neural network (LSTM) to construct a spatio-temporal feature prediction model based on a spatio-temporal neural network, simply referred to as Bi-GAE-LSTM; the Bi-GAE-LSTM model includes a historical feature processing module and an existing feature processing module. In a power system with n buses and b branches, the attacked area includes n a buses and b a branches, the input is and the output is The Bi-GAE-LSTM model is shown as follows:

[0017] V n = σ(WA p X n )

[0018]

[0019]

[0020] In the formula, A t is the normalized adjacency matrix, that is, the graph convolution kernel, which is obtained from the topological structure corresponding to the historical measurement data; A p represents the normalized adjacency matrix obtained from the current topological structure, which is related to the possible topological structures of the unobservable regions; W, W h1 , W h2 represent weight matrices; σ represents the activation function; LSTM represents the Long Short-Term Memory neural network layer; V n represents the spatial features extracted from the existing observable measurement data; V h represents the temporal features extracted from the historical measurements; represents the feature fusion operation; FC represents the fully connected layer; M represents the final prediction result, that is, the restored measurement data.

[0021] The σ selects the ReLU function.

[0022] The residual detection method described above filters out the bad data in the data generated by physical network operation failures, device measurement errors, and communication system noise based on the two-norm threshold detection with a given threshold size. The detection follows the formula:

[0023] ||r a || = ||z a -Hx a ||

[0024] = ||z + a - H(x + c)||

[0025] = ||z - Hx|| < τ

[0026] where τ is a constant threshold, r a is the residual vector, z a is the attacked telemetry data, H is the Jacobian matrix of state estimation, x a is the attacked state variable, z is the normal telemetry data; a is the attack vector, x is the state variable, and c is the vector causing the state variable error.

[0027] The target searched by the N-k search method is represented by the following formula:

[0028] min Σ|Hc|

[0029] s.t. |Hc| = De(A p , M p )

[0030]

[0031] where |Hc| represents the number of attacked measurements detected; De represents the detection model proposed in Chapter 3; A p represents a possible topological structure; M p represents the measurement data restored according to the topological structure A p in accordance with Equation (4.6); represents the set of possible topological structures, which is related to the topology of the unknown area.

[0032] The search process of the N-k search method is as follows:

[0033] (1) Determine the unknown area and generate the set of all topological structures of the unknown area;

[0034] (2) According to the prediction model proposed above, restore the telemetry data corresponding to each possible topological structure;

[0035] (3) Send each group of topological structures and telemetry data into the detection model for detection to obtain a group of data that safely passes the detection model;

[0036] (4) Use the security data as the pseudo-measurement of the unknown area to complete data recovery.

[0037] The described historical feature module consists of a GAE and a long short-term memory neural network.

[0038] The described existing feature module uses GAE to extract the measurement and topological features of the observable area.

[0039] The described collaborative FDIA is established as follows:

[0040] Establish a linear state estimation model as:

[0041] z = Hx + e

[0042] Where z is the telemetry quantity, H represents the Jacobian matrix of the topology, x is the state quantity, and e is the error in the state quantity, which will inevitably occur during the data acquisition process;

[0043] Construct an attack vector according to the principle of the improved collaborative FDIA:

[0044] (1) The attacker intercepts the telemetry and telecontrol data and tampers with a part, and sends the tampered version to the dispatching center, as shown in the following formula:

[0045]

[0046]

[0047] Where s represents the telecontrol data, b ∈ {0, 1} d represents the modification of the telecontrol data; z represents the telemetry data, and a(z) represents the telemetry attack vector; after the attack, the topological information will change. In order to cover up the change of the topological information, the attacker will construct an attack vector based on the forged topological structure. The construction rule of the telemetry data attack vector conforms to the description of the following formula:

[0048]

[0049] a(z) = (H' - H)(H T H) -1 H T z

[0050] Where H' represents the H matrix after modifying the topology, H represents the H matrix before modification, Col(H) is the column space of H, z a represents the telemetry data injected by the topology maintenance attack, a(z) represents the attack vector; H T is the transpose matrix of H;

[0051] (2) An optimized strategy for constructing attack vectors is proposed to minimize the number of measurements that need to be attacked by collaborative FDIA to achieve a specific attack range. Therefore, the attack vector optimization strategy can be expressed by the following formula:

[0052] min||c||1

[0053] s.t.|Hc|≥Q

[0054]

[0055] Q=∑ob i -∑n ij

[0056] In the formula, |Hc| represents the measured value under attack. Through the inequality constraint, it is ensured that it is greater than or equal to the preset attack range Q. min||c||1 is the objective function to be solved, that is, the minimum number of attack nodes. During the optimization process, |Hc| will gradually decrease to the value closest to Q. ob i represents the observability of node i, represents the number of measurements adjacent to node i, n i represents the number of measurements of node i itself. Since the measurements of adjacent nodes will be double-counted during the calculation, the double-counted number ∑n needs to be subtracted when calculating the attack range Q ij .

[0057] Compared with the prior art, the present invention has the following beneficial effects:

[0058] (1) The present invention solves the problem that the measurement data of collaborative FDIA is difficult to detect.

[0059] (2) The present invention does not rely on very strong scenario assumptions, can be applied to various problems caused by FDIA, has a wide application range, and has good industrial practicability.

[0060] (3) The present invention can maximize the restoration of power grid data under the condition of large-scale unobservability of the power grid, enhancing the self-healing ability of the power grid.

[0061] (4) The present invention has stronger robustness against the situation where the topological structure is tampered with, can enhance the power grid's ability to defend against collaborative FDIA, and meets the practical requirements of the industry for collaborative FDIA defense.

[0062] (5) The present invention has extremely strong fitting ability for the training set and can accurately predict the telemetry data in unknown areas.

[0063] (6) The detection method of the present invention has high detection accuracy: strong detection ability, and can effectively detect collaborative FDIA under different topological structures.

[0064] (7) The higher the prediction accuracy of the prediction method of the present invention, the closer the predicted value is to the actual measurement data, and the average relative error is within 5%.

[0065] (8) The present invention uses GAE to obtain an encoder suitable for feature extraction tasks, avoiding interference from randomly assigned initial weights to topological feature extraction. Training GAE with sample data of multiple topological situations can give appropriate weights to important features and has good adaptability to different topological structures.

[0066] (9) The present invention uses ResNet as a classifier to implement a deep neural network structure, which performs better than general neural networks in classification tasks, can greatly improve the efficiency of subsequent detection, reduce the workload and difficulty of false data identification, and thus improve the accuracy of false data discrimination. BRIEF DESCRIPTION OF THE DRAWINGS

[0067] Figure 1 is a flowchart of a method for defending against collaborative false data attacks on power grid state topology according to the present invention;

[0068] Figure 2 is a schematic diagram of a graph convolution kernel;

[0069] Figure 3 is a schematic diagram of a residual block;

[0070] Figure 4 is a structure diagram of a prediction model;

[0071] Figure 5 is a schematic diagram of a long short-term memory neural network;

[0072] Figure 6 is a schematic diagram of N-k search;

[0073] Figure 7 is the training situation of a detection model;

[0074] Figure 8 is a curve graph of the training loss of a prediction model;

[0075] Figure 9 is a graph of collaborative attack detection results;

[0076] Figure 10 is a comparison graph of predicted values and actual values.

[0077] Figure 11 is a topological graph of the IEEE-9 node system. DETAILED DESCRIPTION OF THE INVENTION

[0078] In order to more clearly understand the above objects, features and advantages of the present invention, the technical solutions of the present invention will be further described in detail below.

[0079] A method for defending against false data injection attacks in power grid state topology collaboration. First, a collaborative FDIA model is established to generate attacked telemetry and telecontrol data. The attack is divided into two steps. In the first step, the telemetry and telecontrol of specific lines in the power system are tampered with, causing the wrong Jacobian matrix to be used in the power grid state estimation process. In the second step, the attack strategy is improved by generating an attack vector through an optimization method to widely modify the telemetry data on buses and branches. The attacked telemetry and telecontrol are saved as the data to be detected in the power grid.

[0080] Specifically as follows:

[0081] In the power system, the relationship between the measured value and the state variable is shown in Equation (1):

[0082] z = Hx + e (1)

[0083] Where: z is the telemetry, H represents the Jacobian matrix of the topology, x is the state quantity, and e is the error in the state quantity.

[0084] Assume that a set of state variables x minimizes the measurement error, then this set of state variables is the optimal state quantity, and in the DC state estimation model, it can be solved by Equation (2.2):

[0085] minJ(x) = [z - Hx] T R -1 [z - Hx] (2)

[0086] And the estimation result Is given by Equation (3):

[0087]

[0088] Where R is a diagonal matrix with diagonal elements equal to σ i -2 σ i Is the measurement error of the i-th bus. Is the estimated state quantity. H T Is the transpose of the H matrix, R -1 Is the inverse matrix of R.

[0089] After obtaining the estimated state quantity, an attack vector can be constructed according to the principle of collaborative FDIA. The attacker intercepts the telemetry and telecontrol data and tampers with a part of it, and sends the tampered version to the dispatching center, as shown in the following formula:

[0090]

[0091] In the formula, s represents the telecontrol data, b ∈ {0, 1} dIndicates the modification of telemetry signals; z represents telemetry data, and a(z) represents the telemetry attack vector. After the attack, the topological information will change. To cover up the change in topological information, the attacker will construct the attack vector based on the forged topological structure. The construction rule of the telemetry data attack vector conforms to the description of the following formula:

[0092]

[0093] In the formula, H' represents the H matrix after modifying the topology, H represents the H matrix before modification, and Col(H) is the column space of H. z a represents the telemetry data injected by the topology maintenance attack, a(z) represents the attack vector; H T is the transpose matrix of H.

[0094] Keep the telemetry estimation value, telemetry signal, and state quantity estimation value after the attack as the data to be detected by FDIA.

[0095] After establishing the collaborative FDIA and generating the attacked telemetry and telemetry signal data, the following defenses are carried out:

[0096] (1) Use the residual detection method to filter out bad data, and then use the detection model to detect the data to determine the attacked measurement data: Use the traditional power grid method to detect the network topology and telemetry data, filter out the bad data generated by physical network operation failures, equipment measurement errors, and communication system noise in the data, so that only the real data and the false data tampered by FDIA are retained in the system. Then send the telemetry and telemetry signals together into the detection model constructed based on GAE and ResNet to detect, identify the attacked buses and branches, and determine the attacked area. Specifically as follows:

[0097] Generally speaking, due to physical network operation failures, equipment measurement errors, and communication system noise, the power system telemetry measurement data will always have contaminated bad data. To reduce the workload and difficulty of false data discrimination, the present invention first uses residual detection to filter out the bad data in the measurement data, and filters out the bad data generated by physical network operation failures, equipment measurement errors, and communication system noise in the data based on the two-norm threshold detection with a given threshold size. Its detection follows the formula:

[0098]

[0099] Among them, τ is a constant threshold; r a is the residual vector, z a is the attacked telemetry data, z is the normal telemetry data; a is the attack vector; H is the Jacobian matrix of state estimation; x a is the attacked state variable, x is the state variable, and c is the vector causing the state variable error.

[0100] However, the false measurements generated using the above collaborative FDIA strategy can be detected through residuals, so an additional detection model is required for detection. In the detection model, GAE is used to extract topological features. The difference between GAE and a general autoencoder is that in the encoder part, a Graph Convolutional Neural network (GCN) is used, which can extract non-Euclidean space graph features that cannot be processed by traditional autoencoders. As Figure 2 shown, GCN aggregates the features of adjacent nodes through the graph convolutional kernel defined by Equation (7).

[0101]

[0102] In the formula, D = diag(d1, d2, …, d n ) is the degree matrix corresponding to the system topology, and the diagonal element d n represents the number of adjacent nodes of the nth node. is the sum of the adjacency matrix A and the identity matrix I N . A t is a symmetrically normalized adjacency matrix.

[0103] The aggregated features are restored through the graph decoder defined by Equation (8).

[0104] X' = ReLU(FC(Z)) (8)

[0105] In the formula, X' represents the reconstructed node features, FC represents the fully connected layer, and Z represents the aggregated features. ReLU is the activation function.

[0106] The main purpose of using GAE is to obtain an encoder suitable for the feature extraction task and avoid interference from randomly assigned initial weights to topological feature extraction. The present invention uses sample data of multiple topological situations to train GAE, which can give appropriate weights to important features and has good adaptability to different topological structures.

[0107] After extracting topological features using the above topological feature extractor, a classifier that can learn features and map them to the output is also required. The present invention uses ResNet as the classifier. The characteristic of ResNet is the design of residual blocks, as Figure 3 shown. ResNet realizes a deep neural network structure through the design of residual blocks and performs better than general neural networks in classification tasks. The structure of ResNet is represented by the following formula:[[]]

[0108]

[0109] In the formula, FC is the fully connected layer. x L is the feature passed to the Lth residual block, which is always equal to xL-1 。W is the weight matrix of the convolutional layer, and i is the convolutional layer number. F represents the residual block function. x i and W i are the input features and the weight matrix of the i-th layer respectively.

[0110] This step of the present invention can greatly improve the efficiency of subsequent detection, reduce the workload and difficulty of false data identification, and thus improve the accuracy of false data discrimination.

[0111] (2) Construct a prediction model based on spatio-temporal features to restore the true telemetry of the system: The prediction model includes a historical feature processing module and an existing feature processing module. The historical feature module consists of a GAE and a Long Short-Term Memory (LSTM) neural network, which extracts the features of historical measurement data and topological information; while the existing feature module uses a GAE to extract the measurement and topological features of the observable region. The model can predict the corresponding telemetry data according to the historical topological structure, and then send the telemetry and telecontrol signals into the above detection model for detection. If the detection is passed, the data restoration is completed; if the detection is not passed, it enters step (3). Specifically as follows:

[0112] Use a GAE and an LSTM to construct a prediction model of spatio-temporal features, simply referred to as Bi-GAE-LSTM. As Figure 5 shown, the Bi-GAE-LSTM model includes a historical feature processing module and an existing feature processing module. The historical feature module consists of a GAE and an LSTM, which extracts the features of historical measurement data and topological information; while the existing feature module uses a GCN to extract the measurement and topological features of the observable region. The model can predict the corresponding telemetry data according to the given topological structure.

[0113] As known from Figure 5 , the input of the LSTM includes the current moment feature, the hidden state of the previous moment, and the memory state vector of the previous moment. The control of the forget gate and the candidate gate is used to select the length of the memory time scale.

[0114] The control method of the forget gate is shown in the following formula:

[0115] f t =σ(W f ×[h t-1 ,x t +b f ) (10)

[0116] The calculation method of the input gate is shown in the following formula:

[0117] i t =σ(W i ×[h t-1 ,xt +b i ) (11)

[0118] The calculation method of the candidate gate is as shown in the following formula:

[0119] C' t = tanh(W c × [h t-1 , x t +b c ) (12)

[0120] The calculation method of how to retain and forget features is as shown in the following formula:

[0121] C t = f t × C t-1 + i t × C' t (13)

[0122] Finally, the calculation method of the output gate is as shown in the following formula:

[0123]

[0124] In the formula, σ is the activation function, tanh is the hyperbolic tangent function, which is also used as the activation function. h t-1 represents the hidden state at time t - 1, that is, the feature map obtained through the hidden layer. [h t-1 , x t is the feature concatenation operation, f t , i t , O t are the outputs of the forget gate, memory gate and output gate respectively, C' t represents the candidate memory neuron, C t , C t-1 are the outputs of the controlled memory neurons at time t and t - 1 respectively; W f , W i , W c , W O are the weight matrices of each gate respectively, b f , b i , b c , b O are the error vectors of each gate respectively, h t is the hidden state at time t, which is used as the input for the next moment.

[0125] Suppose in a power system with n buses and b branches, the attack area contains n a buses and b a branches, then the input is The output is In this case, the model is as follows:

[0126]

[0127] In the formula, V n represents the spatial features extracted from the existing observable measurement data; σ represents the activation function, and ReLU is selected; A p represents the normalized adjacency matrix obtained from the current topological structure, which is related to the possible topological structures of the unobservable regions; X n is the existing node feature; V h represents the temporal features extracted from the historical measurements; represents the feature fusion operation; A t is the normalized adjacency matrix, that is, the graph convolution kernel, obtained from the topological structure corresponding to the historical measurement data; X h is the historical node feature; W represents the weight matrix of the graph convolution layer; W h1 represents the weight matrix of the first hidden layer in the LSTM, W h2 represents the weight matrix of the second hidden layer in the LSTM; LSTM represents the long short-term memory neural network layer; FC represents the fully connected layer; M represents the final prediction result, that is, the restored measurement data.

[0128] Take the topological structure at the moment before the attack as the basic topology, and use Bi-GAE-LSTM to predict the telemetry data of the unobservable (attack) region according to this topology. Then combine this telemetry and telecommunication data and send it into the above detection model for detection. Check the detection result. If the detection shows passing, the data recovery ends; if the detection shows non-passing, go to step (3).

[0129] (3) Restore the telecommunication data using the N-k search method based on the above prediction model and detection model. Speculate on the possible topological structures according to the historical topological information of the unobservable region, then predict the telemetry data corresponding to the possible topological structures, and send the telemetry and telecommunication combination into the detection model to screen out the correct data combination.

[0130] Restore the telecommunication data using the N-k search method based on the above prediction model and detection model. Speculate on the possible topological structures according to the historical topological information of the unobservable region. An attack may cause some branches in the power grid to stop working. Therefore, the set of possible topological structures includes the topological information of N-1, N-2 to N-k, and the maximum value of k is the total number of lines in the unobservable region.

[0131] The N-k search is to find the combinations that can pass the detection model. The search target can be expressed by the following formula:

[0132]

[0133] Among them, |Hc| represents the number of measured values detected to be attacked; De represents the detection model proposed in Equation (9); A p represents a possible topological structure; M p represents the measured data restored according to the topological structure A p , and the restoration method is based on Equation (13); represents a set composed of possible topological structures, which is related to the topology of the unknown area.

[0134] The specific search process is as follows:

[0135] (1) Determine the unknown area and generate a set of all topological structures of the unknown area;

[0136] (2) According to the prediction model proposed above, restore the telemetry data corresponding to each possible topological structure;

[0137] (3) Send each group of topological structures and telemetry data into the detection model for detection to obtain a set of data that safely passes the detection model;

[0138] (4) Use the safe data as the pseudo-measured values of the unknown area to complete data recovery.

[0139] It should be noted that due to the built-in positioning function of the GAE-ResNet detection model, the N-k search process can be optimized, and its optimization method is as Figure 6 shown. If the topological label of the detection model is 0, the system is attacked by a general FDIA. At this time, only the telemetry data needs to be restored. The detection model can also determine the scenario of a single-line topology attack. If a single-line topology attack is found, only the working state of that line needs to be reversed; for the collaborative attack area, the search can also start from the N-1 topological structure.

[0140] Case Analysis

[0141] The following will be described separately from the following five parts: example selection, training situation of the model, accuracy of the detection model, accuracy of the prediction model, and example of the systematic defense strategy.

[0142] The present invention has been tested on the IEEE-9, IEEE-57, and IEEE-118 node test systems, and the effectiveness of the defense strategy proposed by the present invention has been verified.

[0143] Training Situation of the Model

[0144] In the IEEE-9 node test system, after about 900 iterations of training, the model tends to converge. The results are as Figure 7As shown in the figure. It can be seen from the figure that during the entire training process, the accuracy rate increased from about 60% to about 94%, while the error decreased from 1.4 to nearly 0, and the overall trend showed a normal convergence phenomenon. And every 100 iterations, the accuracy rate will drop significantly. This is because after 100 iterations, the data of the next batch will be replaced for training. The topological structure of each batch is different, so the accuracy rate of the model will drop significantly. However, this drop amplitude decreases with the increase of the training set batches, and the drop amplitude is close to 0 after hundreds of iterations. Therefore, it shows that the trained model has strong robustness to topological structure changes. Tests were carried out on the IEEE-57 and IEEE-118 node test systems, which are consistent with the test results in the IEEE-9 node test system.

[0145] Figure 8 represents the loss function of the prediction model. The loss curve in the figure is the training set loss curve of the Bi-GAE-LSTM model on the IEEE-118 node test system, and the loss function is MSELoss(). It can be seen that the model converges after 50 iterations, and the MSE of the training set quickly decreases from 0.12 to about 0.001. This shows that the model has extremely strong fitting ability for the training set and can accurately predict the telemetry data in the unknown area. Tests were carried out on the IEEE-9 and IEEE-57 node test systems, which are similar to the test results in the IEEE-118 node test system.

[0146] Detection accuracy of the model

[0147] Table 1 shows the detection accuracy indicators of the 118-node system.

[0148] Table 1

[0149]

[0150] The present invention selects the Convolutional Neural network (CNN) and the Densely Connected Convolutional Networks (DenseNet) as classifiers, and builds a comparison between GAE-CNN, GAE-DenseNet and the model GAE-ResNet of the present invention to verify the influence of model depth on performance. In the selection of the main classifier ResNet, an 18-layer structure (abbreviated as ResNet18) was tested, and the model of the present invention is represented by GAE-ResNet18.

[0151] It can be seen from Table 1 that GAE-ResNet18 is the best method for detecting collaborative FDIA. Compared with GAE-CNN and CNN, the multi-modal detection method has an average improvement of about 10% in various indicators compared with the single-modal detection method. Compared with GAE-CNN, GAE-ResNet18 has a significant improvement in all indicators, indicating that the detection ability of ResNet is much stronger than that of CNN. Tests were carried out on the IEEE-9 and IEEE-57 node test systems, which are consistent with the test results in the IEEE-118 node test system. The improvement of GAE-ResNet in terms of modality and depth enables it to effectively detect collaborative FDIA under different topologies.

[0152] The accuracy of the prediction model

[0153] Table 2 shows the prediction accuracy indicators of the prediction model.

[0154] Table 2

[0155]

[0156] The present invention uses a GAE-LSTM model without an existing feature module, a double-layer LSTM model combining a random forest and LSTM, and a standard LSTM model for comparison.

[0157] It can be seen from Table 2 that the Bi-GAE-LSTM of the present invention uses a prediction method that aggregates historical features and existing features, and its prediction accuracy exceeds that of the prediction method that only uses historical features. The Mean Squared Error (MSE) and the Mean Absolute Percentage Error (MAPE) both represent the error between the prediction result and the correct measurement value. The closer such indicators are to 0, the stronger the model's prediction ability. It can be concluded from Table 2 that on the IEEE-118 node test system, the MAPE and MSE of the LSTM model are 0.0566 and 2.3411% respectively, while these two indicators in Bi-GAE-LSTM are 0.0024 and 0.2375% respectively, indicating that the error has decreased significantly. Similarly, in the IEEE-57 and IEEE-9 node test systems, the same trend is presented. The more fully the known historical data and existing data are mined, the higher the prediction accuracy of the model. The GAE-LSTM with topological information has a higher prediction accuracy compared to the LSTM that only uses measurement data, and the Bi-GAE-LSTM that aggregates historical features and existing features also has a significant increase in prediction accuracy compared to the GAE-LSTM that only uses historical features. Therefore, the Bi-GAE-LSTM model is a very effective method for telemetry data recovery when the power grid suffers from collaborative FDIA.

[0158] Accuracy of the prediction model

[0159] To illustrate the practical application of the present invention, the IEEE 9-bus system is taken as an example to show the operation process of the systematic defense strategy. Figure 10 It represents the collaborative attack detection result. The topology label shows that the topology structure has been tampered with. Therefore, the attack scenario is established as collaborative FDIA, and the attacked areas are determined as buses (1, 4, 5) and branches (1, 2). This attacked area is set as the unobservable area, and data restoration and detection are carried out. It can be determined from the label that branch (1, 2) is the collaborative FDIA attack area. Therefore, the topology subset consists of the topology structures of N-1 and N-2. The determined set of topologies with possible line breaks is [(1), (2), (1, 2)], which contains a total of three topology structures. The corresponding telemetry data of the topology is generated and sent into the detection model. The detection results are shown in Table 3:

[0160] Table 3

[0161]

[0162] As can be seen from Table 3, the telemetry and telecontrol joint restoration strategy can identify the correct topology. In the topology subset (2), the topology label is zero, and the alarm number of the measurement label is also zero, indicating that the set of telemetry and telecontrol data corresponding to this subset can pass the joint detection. After the topology information of topology subsets (1) and (1, 2) and their corresponding telemetry data are sent into the detection model for detection, the topology labels both alarm, and the alarm numbers of the measurement labels are 3 and 5 respectively, and they cannot pass the joint detection. This shows that the method can find the correct combination of telemetry and telecontrol.

[0163] To further illustrate the effect of the present invention, the telemetry data in the correct combination is compared with the actual telemetry data, and the comparison results are as Figure 10 shown. Analyzing the active power of buses (1, 4, 5) and branches (1, 2) corresponding to the unobservable area (i.e., Figure 10 the measurements corresponding to the numbers in it), it can be seen that the predicted values are very close to the actual measurement data, and the average error is within 10 MW. If the error is divided by the actual value as the relative error, the average relative error in the unknown area is within 5%. This proves that the telemetry data prediction method proposed in this paper has high accuracy in predicting telemetry data. It should be noted that for the telemetry data in the known area, there are also some deviations between the predicted values and the actual measured values, but they are still very close and within the allowable error range. Therefore, in actual use, the existing telemetry data or the predicted values can be used in the known area.

Claims

1. A defense method for collaborative false data attack in power grid state topology, characterized in that, It includes the following steps: (1) Use the residual detection method to filter out bad data, and then use the detection model to detect the data to determine the attacked measurement data: Use the residual detection method to detect the network topology and telemetry data, filter out the bad data generated by physical network operation failures, device measurement errors, and communication system noises in the data, so that only the real data and the false data tampered by collaborative FDIA are retained in the system; then send the telemetry and telecommunication signals together into the detection model for detection, identify the attacked buses and branches, and determine the attacked area; (2) Construct a prediction model based on spatio-temporal features to predict the corresponding telemetry data based on the possible set of telecommunication signals: Establish a prediction model based on spatio-temporal features, and the prediction model based on spatio-temporal features includes a historical feature processing module and an existing feature processing module; The prediction model based on spatio-temporal features predicts the corresponding telemetry data according to the historical topology structure, and then sends the telemetry and telecommunication signals together into the above detection model for detection. If the detection is passed, the data recovery is completed; if the detection is not passed, go to the next step; (3) Use the N-k search method to input the combination of telemetry and telecommunication signals into the prediction model based on spatio-temporal features, and use the data that passes the detection as the true value: Speculate the possible topology structures according to the historical topology information of the unobservable area, then predict the telemetry data corresponding to the possible topology structures, send the combination of telemetry and telecommunication signals into the detection model, and screen out the correct data combination.

2. The power grid state topology collaborative false data attack defense method according to claim 1, wherein The detection model is constructed using a graph autoencoder and a residual neural network, and the attack detection process is shown as follows: V = GAE(A, X) Wherein, V is the extracted topological feature, A represents the adjacency matrix, X is the node feature, and z is the telemetry data; represents the feature fusion operation; the detection model outputs a set of {0, 1} labels indicating that the corresponding measurement is under attack, and the attacked area of the power grid is determined based on these labels.

3. The power grid state topology collaborative false data attack defense method according to claim 1, characterized in that The prediction model based on spatio-temporal features is constructed according to the following method: Build a prediction model based on spatio-temporal features using GAE and long short-term memory neural network, abbreviated as Bi-GAE-LSTM; the Bi-GAE-LSTM model includes a historical feature processing module and an existing feature processing module. In a power system with n buses and b branches, the attack area includes n a buses and b a branches, the input is the output is The Bi-GAE-LSTM model is shown as follows: V n = σ(WA p X n ) where, A t is the normalized adjacency matrix, i.e., the graph convolution kernel, obtained from the topological structure corresponding to historical measurement data; A p represents the normalized adjacency matrix obtained from the current topological structure, which is related to the possible topological structure of the unobservable region; W, W h1 , W h2 represent weight matrices; σ represents the activation function; LSTM represents the long short-term memory neural network layer; V n represents the spatial features extracted from the existing observable measurement data; V h represents the time features extracted from historical measurements; represents the feature fusion operation; FC represents the fully connected layer; M represents the final prediction result, i.e., the restored measurement data; X n is the existing node feature; X h is the historical node feature.

4. The method for defending against false data attacks in grid state topology collaboration according to claim 3, characterized in that The σ is the ReLU function.

5. The power grid state topology collaborative false data attack defense method according to claim 1, characterized in that For the residual detection method, the detection follows the formula: ||r a || = ||z a -Hx a || = ||z + a - H(x + c)|| = ||z - Hx|| < τ where τ is a constant threshold, r a is the residual vector, z a is the attacked telemetry data, H is the Jacobian matrix of the state estimation, x a is the attacked state variable, z is the normal telemetry data; a is the attack vector, x is the state variable, and c is the vector that causes the error of the state variable.

6. The power grid state topology collaborative false data attack defense method according to claim 1, wherein The search target of the N-k search method is represented by the following formula: min Σ|Hc| s.t. |Hc| = De(A p , M p ) Among them, |Hc| represents the number of measured values detected to be attacked; De represents the proposed detection model; A p represents a possible topological structure; M p represents the measured data restored according to the topological structure A p ; represents a set composed of possible topological structures, which is related to the topology of the unknown area.

7. The power grid state topology collaborative false data attack defense method according to claim 1, characterized in that The search process of the N-k search method is as follows: (1) Determine the unknown area and generate the set of all topology structures of the unknown area; (2) According to the prediction model based on spatio-temporal features, restore the telemetry data corresponding to each possible topology structure; (3) Send each group of topology structures and telemetry data into the detection model for detection to obtain a group of data that safely passes the detection model; (4) Use the safe data as the pseudo-measurement of the unknown area to complete the data recovery.

8. The power grid state topology collaborative false data attack defense method according to claim 1, wherein The historical feature module consists of a GAE and a long short-term memory neural network.

9. The power grid state topology collaborative false data attack defense method according to claim 1, wherein The existing feature module uses a GAE to extract the measurement and topology features of the observable area.

10. The power grid state topology collaborative false data attack defense method according to claim 1, characterized in that, The collaborative FDIA is established according to the following method: Establish a linear state estimation model as: z = Hx + e In the formula, z is the normal telemetry data, H is the Jacobian matrix of state estimation, x is the state variable, and e is the error in the state quantity, which will inevitably occur during the data acquisition process; Construct an attack vector according to the principle of the improved collaborative FDIA: (1) The attacker intercepts the telemetry and telecommunication data and tampers with a part of it, and sends the tampered version to the dispatching center, as shown in the following formula: Where s represents the remote signaling data and b ∈ {0, 1} d represents the modification of the remote signaling data; z is the normal telemetry data, and a(z) represents the telemetry attack vector; after the attack, the topology information will change. To cover up the change in the topology information, the attacker will construct the attack vector based on the forged topology structure. The construction rule of the telemetry data attack vector conforms to the description of the following formula: a(z) = (H' - H)(H T H) -1 H T z where H' represents the H matrix after modifying the topology, H is the Jacobian matrix of state estimation, Col(H) is the column space of H, z a is the attacked telemetry data, and a(z) represents the telemetry attack vector; H T is the transpose matrix of H; (2) An optimization strategy for attack vector construction is proposed to minimize the number of measurements that need to be attacked by the collaborative FDIA to achieve a specific attack range. Therefore, the attack vector optimization strategy can be expressed by the following formula: min||c||1 s.t.|Hc|≥Q Q = ∑ob i - ∑n ij Where, |Hc| represents the measured value under attack. Through inequality constraints, it is ensured that it is greater than or equal to the preset attack range Q. min||c||1 is the objective function to be solved, that is, the number of attack nodes is minimized. During the optimization process, |Hc| will gradually decrease to the value closest to Q, ob i represents the observability of node i, represents the number of measurements adjacent to node i, n i represents the number of measurements of node i itself. Since the measurements of adjacent nodes will be double-counted during the calculation, the double-counted number Σn needs to be subtracted when calculating the attack range Q ij .

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