Multiplicative false data injection attack iteration detection method
By establishing a state estimation model in a distributed power system and using iterative distributed Kalman filter detection technology, the accuracy problem of multiplicative false data injection attack detection in distributed systems is solved and more efficient detection performance is achieved.
Patent Information
- Application Number
- CN202411368275.0
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2024-09-29
- Publication Date
- 2025-01-21
- Estimated Expiration
- Not applicable · inactive patent
AI Technical Summary
In distributed power supply systems, it is difficult for the prior art to accurately detect multiplicative false data injection attacks, especially in the application of distributed Kalman filtering algorithms. The effect of using measurement prediction errors is insufficient, which affects detection performance.
An iterative detection method for multiplicative false data injection attacks is proposed. By establishing the state estimation measurement equation and state estimation model of the distributed power system, and using iterative distributed Kalman filter detection technology, the information in the measurement information is fully utilized to improve Detection accuracy.
This method can effectively improve the detection accuracy of multiplicative false data injection attacks in distributed systems, correct the attacked data, and obtain reasonable power system state estimation results.
Smart Images
Figure CN119337367A_ABST
Abstract
Description
Technical Field
[0001] The invention relates to the technical field of data attack detection, and in particular to an iterative detection method for multiplicative false data injection attacks. Background Art
[0002] With the mutual coupling between the information side and the physical side of the power system, the power system is developing towards intelligence, which is of great significance for real-time analysis and scientific decision-making of the power system. However, networked information transmission also increases the probability of the power system being attacked by cyber attacks. Currently, there are two main methods for detecting cyber attacks: data-driven and model-driven.
[0003] Data-driven detection methods do not involve system parameters and specific structures during application. They build a detection framework based on historical observation data and then analyze real-time data. This type of method only needs historical data to detect false data injection attacks (FDIA).
[0004] The model-driven detection method needs to use the power system parameters and topology to build a model and perform FDIA detection based on the model. The basic idea is to use various state estimation algorithms to obtain real-time estimated values, and then compare them with historical data or indicator functions. When the estimated residual or indicator function value is greater than a certain threshold, or the probability distribution of the current data does not meet the distribution of historical data, the data is considered to be false.
[0005] As the number of distributed power sources connected to the grid continues to increase, the measurement data in the power grid has gradually become more complex, uncertain, and changeable. This change makes it more complicated and challenging to accurately detect false data in distributed power systems. Most existing studies focus on additive FDIA, which is an overly simple attack construction method. The distributed Kalman filter algorithm is a suboptimal algorithm that does not fully utilize the measurement prediction error, which will affect the detection performance to a certain extent. Summary of the invention
[0006] The purpose of the present invention is to provide an iterative detection method for multiplicative false data injection attacks in order to improve the accuracy of detection of multiplicative false data injection attacks in distributed systems.
[0007] The purpose of the present invention can be achieved by the following technical solutions:
[0008] Compared with the prior art, the present invention has the following beneficial effects:
[0009] A multiplicative false data injection attack iterative detection method, the method comprising:
[0010] S1. Establish measurement equations and state estimation models for distributed power system state estimation;
[0011] S2. For the i-th sensor node of the system, obtain the actual quantity measurement, where the actual quantity measurement is the quantity measurement y without multiplicative false data injection attack. i,k Or actual volume measurement of multiplicative false data injection attacks
[0012] S3, based on actual quantity measurement, measurement equation and state estimation model, iterative distributed Kalman filter detection of multiplicative false data injection attack, the specific steps of S3 are:
[0013] A1. For a single sensor node i, assuming that the state estimate at time k-1 is known and the estimated error covariance P i,k-1|k-1 , calculate the state prediction and the prediction error covariance P i,k|k-1 ;
[0014] A2. Predict the quantity based on the state and the prediction error covariance P i,k|k-1 Get the initial state prediction and the initial state prediction error covariance Set the initial number of iterations s = 0;
[0015] A3. Calculate the measurement prediction of the sth iteration at time k The residual with the actual quantity measurement and update the detection function;
[0016] A4, judging whether the test function in the sth iteration exceeds the set threshold ε, if it exceeds the threshold, it can be judged that there is a multiplicative false data injection attack and an alarm operation is performed, and at the same time, the actual measurement containing the multiplicative false data injection attack is corrected by using the measurement prediction value, and then A5 is executed, otherwise A5 is directly executed;
[0017] A5. Calculate the state prediction value and prediction error covariance of the s+1th iteration. If the iteration termination condition is met, output the state estimation result. Otherwise, increase the number of iterations by 1 and return to A3.
[0018] Furthermore, the distributed power system includes a multi-sensor network physical model composed of N sensor nodes, node i only receives information from its neighboring nodes, and the topological structure of the sensor network is represented by an undirected connection graph G = {ε, ν}, ν = {1, 2, ..., N} is a node set, ε = {1, 2, ..., N} is an edge set, and N i={j∈ν:(i,j)∈ε} is the set of neighbor nodes of node i. When there is no multiplicative false data injection attack, the actual quantity measurement of each node i is:
[0019] y i,k =h(x k )+v i,k
[0020] where y i,k is the quantity measurement of the i-th sensor node at time k, including the active and reactive power injected by the node, and the active and reactive power flow on the line; k is the state quantity at time k, including the voltage amplitude and phase angle of the node; h(*) represents the nonlinear relationship between the power system quantity measurement and the state quantity, which is determined by the system parameters and the system topology; v i,k is the measurement noise of the i-th sensor node, which has a mean of 0 and a variance matrix of R i,k Gaussian distribution of
[0021] Where h(x n ) is:
[0022]
[0023] The measurement equation for the distributed power system state estimation is:
[0024]
[0025] Among them, P i,k , Q i,k P is the measurement of the injected active and reactive power of the power system at the node at time k; ij,k , Q ij,k is the active and reactive power flow on the lines between nodes of the power system at time k; V i,k is the voltage amplitude of the node in the power system at time k; θ ij,k is the phase angle difference between the nodes of the power system at time k; G ij , B ij , g ij , b ij ,y c Characterize the power system quantity and system parameters.
[0026] Furthermore, the state estimation model is:
[0027] x k =F(x k-1 )+q k-1
[0028] y i,k =h(x k )+v i,k
[0029] Among them, F represents the state quantity x at time k-1 k-1 State transfer function at adjacent moments; q k-1 is the system error, and its variance matrix is Q k-1 .
[0030] Furthermore, the actual amount of the multiplicative false data injection attack is measured as:
[0031]
[0032] in, is the measurement vector when the i-th node is attacked by multiplicative false data injection, M i,k is a non-zero multiplicative attack vector.
[0033] Furthermore, the state prediction quantity and the prediction error covariance P i,k|k-1 for:
[0034]
[0035] P i,k|k-1 =FP i,k-1|k-1 F T +Q k
[0036] Among them, F represents the state transfer function of the state quantity at adjacent moments, Q k Represents the variance matrix of the systematic error.
[0037] Furthermore, without multiplicative false data injection attack, the measurement prediction of the sth iteration at time k is calculated Residuals from actual measurements And update the detection function Specifically:
[0038]
[0039] in, For measurement prediction The quantity measurement y without multiplicative false data injection attack i,k The residual of
[0040] Calculate the measurement prediction of the sth iteration at time k when there is a multiplicative false data injection attack Residuals from actual measurements And update the detection function Specifically:
[0041]
[0042] Where H represents the Jacobian matrix, R i,k Indicates v i,k The variance of is: represents the state prediction of the sth iteration, represents the prediction error covariance of the sth iteration, is the measurement prediction error covariance of the sth iteration, Quantitative measurement of multiplicative false data injection attacks The residual.
[0043] Furthermore, the actual quantity measurement containing multiplicative false data injection attack is corrected specifically as follows:
[0044] The measurement prediction of the sth iteration As actual quantity measurement.
[0045] Furthermore, when there is no multiplicative false data injection attack, the process of calculating the state prediction quantity and prediction error covariance of the s+1th iteration is:
[0046]
[0047]
[0048] When there is a multiplicative false data injection attack, the process of calculating the state prediction quantity and prediction error covariance of the s+1th iteration is:
[0049]
[0050] in, represents the state prediction of the s+1th iteration, represents the prediction error covariance of the s+1th iteration.
[0051] Furthermore, when there is no multiplicative false data injection attack, the iteration termination condition is to satisfy the inequality:
[0052]
[0053] When a multiplicative false data injection attack is carried out, the iteration termination condition is to satisfy the inequality:
[0054]
[0055] in,
[0056]
[0057] If the inequality is satisfied, the measurement prediction error of the s+1 iteration is As the measured prediction error for the next iteration;
[0058] Or the iteration termination condition is reaching a maximum number of iterations.
[0059] Furthermore, the state estimation result is the state prediction value and the prediction error covariance when the iteration is terminated.
[0060] The present invention firstly establishes a distributed power system multiplicative false data injection attack model; then proposes an iterative detection method based on distributed Kalman filtering, which makes full use of the implicit information in the measurement information to improve the detection accuracy of the distributed system multiplicative false data injection attack, and then corrects the attacked data to obtain a reasonable power system state estimation result, thereby improving the accuracy of the detection of multiplicative false data injection attacks in the distributed system. BRIEF DESCRIPTION OF THE DRAWINGS
[0061] Figure 1 This is a comparison diagram of the voltage amplitude estimation errors of the two methods;
[0062] Figure 2 This is a comparison diagram of the voltage phase angle estimation error of the two methods;
[0063] Figure 3 Comparison chart of the two methods’ detection capabilities for multiplicative false data injection attacks;
[0064] Figure 4 It is a flow chart of the present invention. DETAILED DESCRIPTION
[0065] The present invention is described in detail below in conjunction with the accompanying drawings and specific embodiments. This embodiment is implemented based on the technical solution of the present invention, and provides a detailed implementation method and specific operation process, but the protection scope of the present invention is not limited to the following embodiments.
[0066] The present invention proposes an iterative detection method for multiplicative false data injection attack, the flow chart of which is as follows: Figure 4 As shown, the method comprises the following steps:
[0067] S1. Establish measurement equations and state estimation models for distributed power system state estimation;
[0068] S2. For the i-th sensor node of the system, obtain the actual quantity measurement, where the actual quantity measurement is the quantity measurement y without multiplicative false data injection attack. i,k Or actual volume measurement of multiplicative false data injection attacks
[0069] S3, based on the actual measurement, measurement equation and state estimation model, iterative distributed Kalman filter detection of multiplicative false data injection attack, the specific steps of S3 are:
[0070] A1. For a single sensor node i, assuming that the state estimate at time k-1 is known and the estimated error covariance P i,k-1|k-1 , calculate the state prediction and the prediction error covariance P i,k|k-1 ;
[0071] A2. Predict the quantity based on the state and the prediction error covariance P i,k|k-1 Get the initial state prediction and the initial state prediction error covariance Set the initial number of iterations s = 0;
[0072] A3. Calculate the measurement prediction of the sth iteration at time k The residual with the actual quantity measurement and update the detection function;
[0073] A4, judging whether the test function in the sth iteration exceeds the set threshold ε, if it exceeds the threshold, it can be judged that there is a multiplicative false data injection attack and an alarm operation is performed, and at the same time, the actual measurement containing the multiplicative false data injection attack is corrected by using the measurement prediction value, and then A5 is executed, otherwise A5 is directly executed;
[0074] A5. Calculate the state prediction value and prediction error covariance of the s+1th iteration. If the iteration termination condition is met, output the state estimation result. Otherwise, increase the number of iterations by 1 and return to A3.
[0075] The specific method is:
[0076] The measurement equation and state estimation model of distributed power system state estimation are established. The specific steps are as follows: Consider a multi-sensor network physical model composed of N sensor nodes. Node i only receives information from its neighboring nodes. The topological structure of the sensor network is represented by an undirected connection graph G = {ε, ν}. ν = {1,2,...,N} is a node set, ε = {1,2,...,N} is an edge set, and N i ={j∈ν:(i,j)∈ε} is the set of neighbor nodes of node i. For each node i, the measurement equation for power network state estimation can be described as:
[0077] y i,k =h(x k )+v i,k
[0078] In the formula, y i,k is the quantity measurement of the i-th sensor node at time k, including the active and reactive power injected by the node, and the active and reactive power flow on the line; kis the state quantity at time k, including the voltage amplitude and phase angle of the node; h(*) represents the nonlinear relationship between the power system quantity measurement and the state quantity, which is usually determined by the system parameters and the topological structure of the system; v i,k is the measurement noise of the i-th sensor node, which has a mean of 0 and a variance matrix of R i Gaussian distribution; system measurement usually has a certain degree of redundancy, that is, the measurement dimension is greater than the state dimension. The Jacobian matrix of h(x) is:
[0079]
[0080] The specific measurement equation is:
[0081]
[0082] Where P i,k , Q i,k P is the measurement of the injected active and reactive power of the power system at the node at time k; ij,k , Q ij,k is the active and reactive power flow on the lines between nodes of the power system at time k; V i,k is the voltage amplitude of the node in the power system at time k; θ ij,k is the phase angle difference between the nodes of the power system at time k; G ij , B ij , g ij , b ij ,y c Characterize the power system quantity and system parameters.
[0083] The nonlinear power system state estimation model can be expressed as:
[0084] x k =F(x k-1 )+q k-1
[0085] y i,k =h(x k )+v i,k
[0086] Where: F represents the state quantity x at time k-1 k-1 State transfer function at adjacent moments; q k-1 is the system error, and its variance matrix is Q k-1 .
[0087] For the i-th sensor node, the amount of multiplicative false data injection attack is measured as:
[0088]
[0089] In the formula, M is the measurement vector when the i-th node is attacked by multiplicative false data injection. i,k is a non-zero multiplicative attack vector.
[0090] The Jacobian matrix H of h(x) in the measurement equation includes the active power and reactive power of each branch, the active power and reactive power injected by each node, and the state variables to be determined, namely the voltage amplitude and phase angle of the node. The state quantity to be determined and the quantity measurement are reflected in a one-to-one correspondence in the Jacobian matrix. The present invention considers multiplicative false data injection attacks, by changing the power of each branch and node, and then changing the state variables.
[0091] Iterative distributed Kalman filter detection of multiplicative false data injection attack. When there is no multiplicative false data injection attack, the specific steps are as follows:
[0092] Distributed Kalman filtering uses multiple related sensors to jointly observe the same target and is executed independently on each sensor. For a single sensor node i, assuming that the state estimate at time k-1 is known and the estimated error covariance P i,k-1|k-1 , calculate the state prediction and prediction error covariance:
[0093]
[0094] According to the state prediction quantity above Obtain the iterative initial state prediction quantity, according to the state prediction error covariance P in (1) i,k+1|k Get the iterative initial state prediction error covariance:
[0095]
[0096] Calculate the measurement prediction for the sth iteration at time k Residuals from actual measurements And update the detection function
[0097]
[0098]
[0099] Determine whether the test function in each iteration exceeds the set threshold ε. If it exceeds the threshold, it can be determined that there is a multiplicative false data injection attack and an alarm operation is performed. At the same time, the actual measurement containing multiplicative FDIA is corrected using the measurement prediction value to facilitate the next iteration:
[0100]
[0101] If the above formula is not true, it means that this iteration has not detected a multiplicative false data injection attack, and the state prediction value can be updated, as shown in step (4); if the above formula is true, it means that this iteration has detected a multiplicative false data injection attack, so the actual measurement containing the multiplicative false data injection attack needs to be corrected as follows:
[0102]
[0103] Calculate the state prediction and error covariance for the s+1th iteration:
[0104]
[0105] Determine whether the following iteration stop conditions are met. If they are met, output the final state estimate and error covariance. If not, return to step (3) for the next iteration detection:
[0106]
[0107] The number of iterations or the termination condition is very important for the estimation effect of iterative distributed Kalman filtering. Therefore, the iteration termination condition adopts the maximum likelihood surface control. When the estimated state continues to approach the likelihood surface, the iteration continues. Once it is far away from the likelihood surface, the iteration stops. That is, the inequality in (5) is used as the iteration termination condition. When the inequality in (5) holds or the number of iterations reaches the preset maximum number of iterations, the iteration is terminated, and the state estimation result is finally output:
[0108]
[0109] According to the above steps, the iterative detection process of the distributed Kalman filter is used to detect the multiplicative false data injection attack of the power system through multiple chi-square tests, which can effectively improve the performance of multiplicative false data injection attack detection in the distributed system.
[0110] When there is a multiplicative false data injection attack, the specific steps are as follows:
[0111] Parts A1 and A2 are the same as those without the multiplicative false data injection attack, and the measurement prediction for the sth iteration at time k is calculated. Residuals from actual measurements And update the detection function Specifically:
[0112]
[0113] Where H represents the Jacobian matrix, R i,k Indicates v i,k The variance of is: represents the state prediction of the sth iteration, represents the prediction error covariance of the sth iteration, is the measurement prediction error covariance of the sth iteration, Quantitative measurement of multiplicative false data injection attacks The residual.
[0114] The process of calculating the state prediction and prediction error covariance for the s+1th iteration is:
[0115]
[0116]
[0117] in, represents the state prediction of the s+1th iteration, represents the prediction error covariance of the s+1th iteration.
[0118] When there is no multiplicative false data injection attack, the iteration termination condition is to satisfy the inequality:
[0119]
[0120] The following simulation experiment is conducted. The proposed method is compared with the existing detection method based on distributed Kalman filtering through simulation experiments. In the experiment, a multiplicative attack is injected at time 20. The simulation results are shown in the figure below. Figures 1 to 3 As shown in Table 1. Figures 1 to 3 It can be seen that the iterative distributed Kalman filtering (IDKF) multiplicative false data injection attack detection algorithm has better final state estimation effect than the existing detection algorithm based on the distributed Kalman filtering algorithm. As can be seen from Table 1, the detection algorithm based on the distributed Kalman filtering cannot detect the multiplicative false data at the 20th moment. The iterative detection algorithm proposed in the present invention can accurately and timely detect the multiplicative false data injection attack at the 20th moment. This is mainly because the measurement data at different moments will undergo multiple multiplicative false data injection attack detections in the latter's iterative process. The results show that the multiplicative false data injection attack was successfully detected after two iterations at the 20th moment. This processing method improves the accuracy of multiplicative false data injection attack detection.
[0121] The present invention firstly establishes a distributed power system multiplicative false data injection attack model; then proposes an iterative detection method based on distributed Kalman filtering, which makes full use of the implicit information in the measurement information to improve the detection accuracy of the distributed system multiplicative false data injection attack, and then corrects the attacked data to obtain a reasonable power system state estimation result, thereby improving the accuracy of the detection of multiplicative false data injection attacks in the distributed system.
[0122] The present invention establishes a distributed power system multiplicative false data injection attack detection model; then proposes an iterative detection method based on a distributed Kalman filter algorithm (DKF, Distributed Kalman Filter), which makes full use of the implicit information in the measurement information to improve the detection accuracy of the distributed system multiplicative false data injection attack, and then corrects the attacked data to obtain a reasonable power system state estimation result, thereby improving the accuracy and real-time performance of the multiplicative false data injection attack detection.
[0123] The preferred specific embodiments of the present invention are described in detail above. It should be understood that a person skilled in the art can make many modifications and changes based on the concept of the present invention without creative work. Therefore, any technical solution that can be obtained by a person skilled in the art through logical analysis, reasoning or limited experiments based on the concept of the present invention on the basis of the prior art should be within the scope of protection determined by the claims.
Claims
1. A multiplicative false data injection attack iterative detection method, characterized in that: The method comprises: S1. Establish measurement equations and state estimation models for distributed power system state estimation; S2. For the i-th sensor node of the system, obtain the actual quantity measurement, where the actual quantity measurement is the quantity measurement y without multiplicative false data injection attack. i,k Or actual volume measurement of multiplicative false data injection attacks S3, based on actual quantity measurement, measurement equation and state estimation model, iterative distributed Kalman filter detection of multiplicative false data injection attack, the specific steps of S3 are: A1. For a single sensor node i, assuming that the state estimate at time k-1 is known and the estimated error covariance P i,k-1|k-1 , calculate the state prediction and the prediction error covariance P i,k|k-1 ; A2. Predict the quantity based on the state and the prediction error covariance P i,k|k-1 Get the initial state prediction and the initial state prediction error covariance Set the initial number of iterations s = 0; A3. Calculate the measurement prediction of the sth iteration at time k The residual with the actual quantity measurement and update the detection function; A4, judging whether the test function in the sth iteration exceeds the set threshold ε, if it exceeds the threshold, it can be judged that there is a multiplicative false data injection attack and an alarm operation is performed, and at the same time, the actual measurement containing the multiplicative false data injection attack is corrected by using the measurement prediction value, and then A5 is executed, otherwise A5 is directly executed; A5. Calculate the state prediction value and prediction error covariance of the s+1th iteration. If the iteration termination condition is met, output the state estimation result. Otherwise, increase the number of iterations by 1 and return to A3.
2. The iterative detection method for multiplicative false data injection attack according to claim 1, characterized in that: The distributed power system includes a multi-sensor network physical model composed of N sensor nodes. Node i only receives information from its neighboring nodes. The topological structure of the sensor network is represented by an undirected connection graph G = {ε, ν}, ν = {1, 2, ..., N} is a node set, ε = {1, 2, ..., N} is an edge set, and N i ={j∈ν:(i,j)∈ε} is the set of neighbor nodes of node i. When there is no multiplicative false data injection attack, the actual quantity measurement of each node i is: y i,k =h(x k )+v i,k where y i,k is the quantity measurement of the i-th sensor node at time k, including the active and reactive power injected by the node, and the active and reactive power flow on the line; k is the state quantity at time k, including the voltage amplitude and phase angle of the node; h(*) represents the nonlinear relationship between the power system quantity measurement and the state quantity, which is determined by the system parameters and the system topology; v i,k is the measurement noise of the i-th sensor node, which has a mean of 0 and a variance matrix of R i,k Gaussian distribution of Where h(x n ) is: The measurement equation for the distributed power system state estimation is: Among them, P i,k , Q i,k P is the measurement of the injected active and reactive power of the power system at the node at time k; ij,k , Q ij,k is the active and reactive power flow on the lines between nodes of the power system at time k; V i,k is the voltage amplitude of the node in the power system at time k; θ ij,k is the phase angle difference between the nodes of the power system at time k; G ij , B ij , g ij , b ij ,y c Characterize the power system quantity and system parameters.
3. The iterative detection method for multiplicative false data injection attack according to claim 2 is characterized in that: The state estimation model is: x k =F(x k-1 )+q k-1 y i,k =h(x k )+v i,k Among them, F represents the state quantity x at time k-1 k-1 State transfer function at adjacent moments; q k-1 is the system error, and its variance matrix is Q k-1 .
4. The iterative detection method for multiplicative false data injection attack according to claim 3 is characterized in that: The actual amount of the multiplicative false data injection attack is measured as: in, is the measurement vector when the i-th node is attacked by multiplicative false data injection, M i,k is a non-zero multiplicative attack vector.
5. The iterative detection method for multiplicative false data injection attack according to claim 4 is characterized in that: The state prediction and the prediction error covariance P i,k|k-1 for: P i,k|k-1 =FP i,k-1|k-1 F T +Q k Among them, F represents the state transfer function of the state quantity at adjacent moments, Q k Represents the variance matrix of the systematic error.
6. The iterative detection method for multiplicative false data injection attack according to claim 5, characterized in that: When there is no multiplicative false data injection attack, calculate the measurement prediction of the sth iteration at time k Residuals from actual measurements And update the detection function Specifically: in, For measurement prediction The quantity measurement y without multiplicative false data injection attack i,k The residual of Calculate the measurement prediction of the sth iteration at time k when there is a multiplicative false data injection attack Residuals from actual measurements And update the detection function Specifically: Where H represents the Jacobian matrix, R i,k Indicates v i,k The variance of is: represents the state prediction of the sth iteration, represents the prediction error covariance of the sth iteration, is the measurement prediction error covariance of the sth iteration, Quantitative measurement of multiplicative false data injection attacks The residual.
7. The iterative detection method for multiplicative false data injection attack according to claim 6, characterized in that: The correction of the actual quantity measurement containing multiplicative false data injection attack is specifically as follows: The measurement prediction of the sth iteration As actual quantity measurement.
8. The iterative detection method for multiplicative false data injection attack according to claim 7, characterized in that: When there is no multiplicative false data injection attack, the process of calculating the state prediction quantity and prediction error covariance of the s+1th iteration is: When there is a multiplicative false data injection attack, the process of calculating the state prediction quantity and prediction error covariance of the s+1th iteration is: in, represents the state prediction of the s+1th iteration, represents the prediction error covariance of the s+1th iteration.
9. The iterative detection method for multiplicative false data injection attack according to claim 8, characterized in that: When there is no multiplicative false data injection attack, the iteration termination condition is to satisfy the inequality: When a multiplicative false data injection attack is carried out, the iteration termination condition is to satisfy the inequality: in, If the inequality is satisfied, the measurement prediction error of the s+1 iteration is As the measured prediction error for the next iteration; Or the iteration termination condition is reaching a maximum number of iterations.
10. The iterative detection method for multiplicative false data injection attack according to claim 9, characterized in that: The state estimation result is the state prediction value and the prediction error covariance when the iteration ends.