A DR-FDIA method considering residual contamination under incomplete information

Abstract

The present application relates to the field of power system attack testing, and discloses a DR-FD IA method taking into account residual pollution under incomplete information, including the following steps: S1, select target measurement points and construct attack vectors; S2, select several points from the non-zero elements of the attack vector and set them to zero; S3, calculate the expected dimensionality reduction residual; S4, determine whether the conditions are met; S5, if the conditions are met, record the attack combination, continue to traverse all combinations under the number, if there is no combination that meets the conditions, increase the number of zeroing points and traverse again, if there is a combination that meets the conditions, traverse all combinations under the condition of zeroing number + 1 and enter S6; S6, output the attack combination with the largest residual norm of the zeroing element. The present invention expands the paradigm of the concealment of false data injection attacks. It only needs to master the local topological structure and line parameters to construct the attack vector within tens of milliseconds and mislead the DC / AC state estimation results at a very small attack cost.

Description

Technical Field

[0001] The invention relates to the technical field of power system attack testing, and in particular to a DR-FDIA method taking residual pollution into account under incomplete information. Background Art

[0002] Electricity is an important part of the lifeline of a city. With the rapid development of the Internet and the rapid advancement of the global digitalization process, the network security of the power system has become an important global issue. The power data acquisition and supervision (SCADA) system is an important technical means to support the safe and stable operation of the power grid. It carries out state estimation based on the real-time measurement data of the power grid, and detects, identifies, eliminates and corrects bad data to retain normal data for use by the dispatching center. Once the SCADA system is attacked by a network attack, it will cause the dispatching center to make wrong decisions, threaten the safety and stability of the power grid, cause economic losses, and even endanger the normal operation of social functions and the stability of people's lives.

[0003] False Data Injection Attack (FDIA) is a network attack technology for power SCADA systems. It injects false data into the uploaded measurement information to avoid the bad data detection link of state estimation, causing the dispatch center to misjudge the state of the power grid. It has the characteristics of good concealment, high flexibility, wide attack range, and strong destructive power. Existing FDIA research is mainly divided into two directions: attack modeling and detection. Among them, attack detection stands from the perspective of the defender and studies how to detect FDIA quickly and accurately; while attack modeling stands from the perspective of the attacker, excavating system business-level vulnerabilities, studying attack mechanisms, applicable conditions and optimal strategies, and is mainly divided into two research directions: optimal attack strategy and coordinated attack strategy.

[0004] The optimal attack strategy refers to the most effective attack plan designed by the attacker to achieve a certain goal (such as maximizing the attack effect, minimizing the cost, etc.) under specific conditions. Some studies have proposed the concepts of strong attack and weak attack, and established a minimum residual energy model to weigh the concealment and destructiveness of FDIA. Another study took the maximum operating cost of the power system as the objective function and constructed a two-level optimization model for the FDIA strategy. Another study took the overload of multiple lines as the goal and characterized the solution of the optimal FDIA as a single-layer mixed integer linear programming problem. However, the attack means and styles used under the optimal attack strategy are relatively simple, and the actual operation is difficult. Unlike the optimal attack strategy, the coordinated attack strategy uses multiple means (physical / network) to coordinate with false data injection to achieve the purpose of destroying the operation of the system. Some scholars have studied various coordinated attack scenarios such as the coordinated attack model of telesignaling and telemetry, the coordinated attack model of physical disconnection and measurement value, and the coordinated attack model of network parameters and measurement value, enriching the attack style of FDIA.

[0005] However, whether it is the optimal attack strategy or the coordinated attack strategy, the above studies all assume that the attacker, under the premise of mastering the complete network topology and line parameters, can directly avoid bad data detection by injecting false data and retain false data to mislead the dispatcher. This assumption has the following problems: the attack of false data directly avoiding bad data detection is difficult, costly, and unlikely to be implemented; in practice, it is often difficult for attackers to accurately obtain all the information of the target and can only master part of the network information.

[0006] It should be pointed out that if false data fails to escape bad data detection, but can induce residual contamination (i.e., bad data points cause other normal measurement residuals to exceed the threshold value and are mistakenly eliminated), it is still possible to be retained, thereby causing the dispatcher to make an erroneous operation. At this time, since the false data does not need to satisfy Kirchhoff's law, the attack cost (i.e., the number of measurements read and tampered) is smaller. However, there are few FDIA studies that consider residual contamination, and the incomplete information dilemma faced by attackers further exacerbates the difficulty of formulating attack strategies.

[0007] Some studies have begun to explore FDIA under incomplete information. These studies have revealed the attack mechanism of FDIA with incomplete information, proposed a heuristic algorithm for finding the optimal attack area, and expanded the scenario to the AC power flow model. Another study proposed a blind FDIA model based on principal component analysis, in which the attacker only needs measurement data from multiple sections to launch an attack. On this basis, a blind FDIA method based on matrix reconstruction and subspace estimation was proposed to enhance the robustness in measurement noise scenarios. However, these studies are all aimed at the attack mode of traditional FDIA and do not consider residual contamination. How to induce residual contamination and reduce the cost of false data attacks under incomplete information is a key issue that needs to be solved urgently.

[0008] In addition, the present invention also aims to provide new ideas for the defense of the power system by studying the attack mechanism of FDIA. By simulating possible attack methods, the power system can optimize and adjust its security defense measures in advance. Specifically, by understanding the attack mode, the defense system can improve the predictability of potential threats, optimize the existing bad data detection and identification methods, and enhance the robustness and stability of the system in the face of real attacks. This not only improves the safety and reliability of the power system, but also provides an important reference for the improvement of defense methods. Summary of the invention

[0009] In view of the shortcomings of the prior art, the present invention provides a DR-FDIA method that takes into account residual contamination under incomplete information, expanding the paradigm of the concealment of false data injection attacks. The attacker only needs to master the local topology and line parameters to construct an attack vector within tens of milliseconds and mislead the DC / AC state estimation results at a very low attack cost.

[0010] To achieve the above objectives, the present invention is implemented through the following technical solutions: A DR-FDIA method taking into account residual contamination under incomplete information, comprising the following steps:

[0011] S1. Select the target measurement point and construct the attack vector a according to the following formula;

[0012] a=Hc

[0013] Among them, a is the attack vector, H is the Jacobian matrix, and c is any non-zero vector.

[0014] Count the number of non-zero elements of the attack vector as d, set the counting variable k = 1, flag = 0;

[0015] S2, select dk-1 non-zero elements from the set and set them to zero;

[0016] S3, calculate the reduced dimension residual expectation E[r Ni ],in

[0017]

[0018] Among them, r Ni is the standardized residual, W is the residual sensitivity matrix, D = diag (WR) is the diagonal matrix, a D is the attack vector after dimensionality reduction;

[0019] S4. Determine whether the following conditions are met:

[0020]

[0021] Among them, R Aand R P Select the matrix for the rows;

[0022] S5. If the conditions are met, record the attack combination. Continue to traverse all combinations, and determine whether there is a combination that meets the conditions. Let k = k + 1, if there is a combination that meets the conditions, then set flag = flag + 1;

[0023] S6. If flag≠2, repeat steps S2 to S5; if flag=2, output the attack combination with the largest l1 norm of the zeroed element residual.

[0024] Preferably, the optimization algorithm used is a mechanism-driven sub-minimum attack cost solution optimization algorithm.

[0025] Preferably, the attack vector a D The construction includes the following steps:

[0026] Construct the Jacobian matrix H or the local Jacobian matrix H A ;

[0027] Construct attack vector a according to the formula a=Hc;

[0028] According to the designed mechanism-driven sub-minimum attack cost optimization algorithm, the attack vector a is formed by dimensionality reduction. D .

[0029] Preferably, the construction of the Jacobian matrix H or the local Jacobian matrix H A It is constructed by judging whether the complete network information is mastered. If the complete network information is mastered, the Jacobian matrix H is constructed. If the partial network information is mastered, H is constructed. A .

[0030] Preferably, the residual sensitivity matrix W is constructed as follows:

[0031] W=IH(H T R -1 H) -1 H T R -1

[0032] Among them, I is the identity matrix, H is the Jacobian matrix, and R is the measurement error variance matrix.

[0033] Preferably, the row selection matrix R A and R P is defined as:

[0034] and

[0035] Among them, |SA | and |S P | respectively represent S A and S P The size of the collection.

[0036] Preferably, the attack vector a D The construction also includes the following steps:

[0037] Set dk-1 non-zero elements in the attack vector a to zero, Combination of

[0038] Calculate the expected dimensionality reduction residual according to the formula

[0039] Determine whether the following formula is true:

[0040]

[0041] If true, the attack combination is recorded.

[0042] Preferably, the residual expectation calculation formula also includes:

[0043]

[0044] Where z is the measurement vector, z a is a vector containing false data D The measurement vector of .

[0045] Preferably, the judgment condition also includes:

[0046]

[0047] Among them, W A is the residual sensitivity matrix of the attack area, D A is the diagonal matrix of the attack area.

[0048] Preferably, the method further comprises optimizing the attack vector a output by an attack cost optimization search algorithm. D The optimization includes the following steps:

[0049] Select the number k of the FDIA injection bus and construct the attack vector a according to the formula a=Hc;

[0050] Count the number of non-zero elements d in the attack vector a, set the counting variable k = 1, flag = 0;

[0051] Set dk-1 non-zero elements in the attack vector a to zero, perform combination traversal, and calculate the expected dimensionality reduction residual;

[0052] Determine whether the attack conditions are met, and if so, record the attack combination.

[0053] Continue to iterate through all combinations, and determine whether there is a combination that meets the conditions. Let k = k + 1, if there is a combination that meets the conditions, then set flag = flag + 1;

[0054] If flag≠2, repeat the traversal process; if flag=2, output the attack combination with the largest l1 norm of the zeroed element residual.

[0055] The present invention provides a DR-FDIA method taking into account residual contamination under incomplete information. It has the following beneficial effects:

[0056] 1. This paper proposes a new network attack model that takes into account residual pollution under incomplete information, and proposes a dimensionality reduction FDIA model (DR-FDIA) for the standardized residual search method in the bad data identification link. The DR-FDIA model uses residual expectation inequality constraints and only requires a small number of false data points to achieve the attack effect. In addition, the construction principle of DR-FDIA under local network information is derived through topological partitioning and matrix transformation, and a mechanism-driven sub-minimum attack cost optimization algorithm is proposed.

[0057] 2. This invention expands the paradigm of the concealment of false data injection attacks. The attacker only needs to master the local topology and line parameters to construct an attack vector within tens of milliseconds, and mislead the DC / AC state estimation results at a very low attack cost, thereby undermining the safe, stable and economic operation of the power grid. At the same time, these studies provide important references for the improvement of defense measures and promote the improvement of the defense capabilities of the power system. BRIEF DESCRIPTION OF THE DRAWINGS

[0058] Figure 1 It is a schematic diagram of the method flow of the present invention;

[0059] Figure 2 It is a schematic diagram of the FDIA attack path of the present invention;

[0060] Figure 3 It is a bar chart schematic diagram of the attack success rate for bus 97 under different noise levels and test threshold values ​​of the present invention;

[0061] Figure 4 It is a schematic diagram comparing the attack success rates of various buses of IEEE 118 under the DC power flow model of the present invention;

[0062] Figure 5 It is a schematic diagram comparing the attack success rates on some buses of IEEE 118 under the AC power flow model of the present invention;

[0063] Figure 6 It is a schematic diagram of the comparison of attack costs of the IEEE 118-node system of the present invention. DETAILED DESCRIPTION

[0064] The following will be combined with the drawings in the specification of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0065] Please see attached Figure 1-Figure 2 , the present invention proposes a new network attack model that takes into account residual pollution under incomplete information, and proposes a dimensionality reduction false data injection attack (DR-FDIA) model for the standardized residual search method in the bad data identification link. The DR-FDIA model uses the residual expectation inequality constraint through the model, and only a small number of false data points are needed to achieve the attack effect. In addition, the construction principle of DR-FDIA under local network information is derived through topological partitioning and matrix transformation, and a mechanism-driven sub-minimum attack cost solution optimization algorithm is proposed. The following is a detailed description of the specific implementation method.

[0066] 1. State estimation and bad data detection and identification methods

[0067] In the high-voltage transmission network, the bus voltage is close to the rated voltage and the branch resistance is much smaller than the reactance. In order to simplify the calculation and ensure convergence, the system measurement equation usually adopts a linearized DC power flow model. The measurement equation is expressed as follows:

[0068] z=Hx+v (1)

[0069] Where z∈R m Represents the system measurement vector; H∈R m×n is the measurement Jacobian matrix; x∈R n represents the system state variable; v represents the mean value of 0 and the variance of σ 2 ∈R m The estimated value of the state variable can be solved by weighted least squares (WLS):

[0070]

[0071] In the formula, Represents the estimated value of the system state variable; R∈Rm×m represents the measurement error variance matrix, R -1 The traditional bad data detection determines the existence of bad data by comparing the Euclidean norm of the measurement residual with the detection threshold value τ.

[0072]

[0073] The bad data detector will trigger an alarm. Once bad data is detected, the system will enable the bad data identification link to find the specific location of the bad data. The theoretical basis for identifying bad data is the residual equation, which is expressed as

[0074] r=[IH(H T R -1 H) -1 H T R -1 ]v=Wv=Wz (4)

[0075] Where r is the residual vector, W is the residual sensitivity matrix, and I is the unit matrix.

[0076] Commonly used bad data identification methods include weighted residual search method (i.e., r w method) and the standardized residual search method (i.e., r N The basic idea is to remove the element with the largest absolute value of the residual vector. If the formula (3) is not satisfied, the element with the largest absolute value of the residual vector will continue to be calculated and removed until the formula (3) is satisfied.

[0077] 2. FDIA attack modeling ideas considering residual contamination

[0078] Traditional FDIA exploits the loophole of residual test and constructs the attack vector under the DC power flow model as shown in formula (5):

[0079] a=Hc (5)

[0080] where c∈R n is any non-zero vector.

[0081] At this time, residual detection cannot detect false data mixed in the measurement data, and attackers can tamper with the measurement values ​​and state variables to any value, threatening the safe and stable operation of the power system. Figure 2 Shown as a blue dotted box.

[0082] Although traditional FDIA has the advantages of high concealment and strong attack orientation, the number of tampered measurement values ​​is large, and the requirements for avoiding bad data detection are too strict, which brings certain difficulties to the specific implementation of FDIA. In fact, triggering bad data detection does not mean that the network attack has been discovered. Figure 2As shown, the detected bad data will enter the identification stage. If residual contamination occurs at this time, resulting in the false data not being eliminated in the end, the same effect of concealing the misleading state estimation results can be achieved.

[0083] Based on the above analysis, the present invention establishes a new FDIA model taking residual pollution into account. The basic idea is to calculate the S A The measurement of the collection injects false data, triggering the residual pollution removal S P Normal measurement of the collection, finally retaining S A A subset S R The measurement in , so as to achieve the attack effect, such as Figure 2 Shown as a purple dashed box.

[0084] In actual scenarios, it is difficult for attackers to obtain complete network information. How to construct effective attack vectors to induce residual pollution under incomplete information is a difficult problem. N The DR-FDIA model was constructed by this method, and the corresponding incomplete information modeling mechanism was explored, solving the problem of how to conceal a single false data with fewer measurement injection points.

[0085] 3. DR-FDIA Mechanism Analysis

[0086] The breakthrough of DR-FDIA mechanism analysis is the residual equation. The standardized residual equation is:

[0087]

[0088] In the formula, r N is the standardized residual, W N is the standardized residual sensitivity matrix, D = diag (WR) is a diagonal matrix, and its diagonal elements d ii is the variance of the corresponding residual component.

[0089] In r N Under the law, W N The column vector of is always diagonally dominant, that is, the standardized residual caused by a single bad data with a larger value at this measurement point must be the largest. Therefore, it is necessary to explore other attack methods that ensure that there are at least two false data injection points.

[0090] As can be seen from the above, the residual generated by the traditional FDIA satisfies formula (5) and can avoid bad data detection and identification. However, once a part of the non-zero elements in a are set to zero (which is equivalent to attack vector dimensionality reduction), the power balance will be broken, triggering bad data detection and identification. The measurement set with non-zero elements in a set to zero is denoted as S P , the remaining non-zero element measurement set is recorded as S A , S A The corresponding attack vector is denoted as aD As long as the residual vector r N In, S P The corresponding residual component is greater than S A The corresponding residual component can trigger the residual pollution phenomenon, which is the core idea of ​​DR-FDIA.

[0091] Next, we will derive and analyze the residual equation. Assume that the measurement vector z a Contains false data vector a D , from formula (4) and (6) we can get

[0092]

[0093] Finding the expectation of the above formula gives

[0094]

[0095] Since the residual caused by normal measurement error is expected to be 0, the main factors affecting the residual size are This one. Once S is satisfied A The maximum value of the residual component in is less than S P The maximum value of the residual component in will trigger the residual pollution phenomenon, which is more likely to cause S A The tampering measurement in is retained to achieve the attack effect. Its mathematical expression is

[0096]

[0097] In the formula, Represents the row selection matrix, retaining only W N Zhong and S A Measure the relevant rows. The meaning is similar and will not be repeated here.

[0098] In actual scenarios, the attacker faces the problem of how to construct vector a and select S while mastering local network information. A The present invention uses matrix theory to resolve the above difficulties and theoretically provides the conditions for launching DR-FDIA under incomplete information conditions.

[0099] It is easy to know that the Jacobian matrix of the DC power flow model can be written as:

[0100]

[0101] Where G represents the line admittance diagonal matrix, and A represents the branch-saving association matrix. Consider dividing the power grid into the attack area (subscript A) and the non-attack area (subscript N), then

[0102]

[0103] From the definition and properties of the branch correlation matrix, we can know that A NA =0, A AN There are non-zero elements only in the rows where the boundary nodes are located, which is approximately a zero matrix, so there is

[0104]

[0105] At this time, the Jacobian matrix H is approximately

[0106]

[0107] Formula (13) means that the attack area is approximately decoupled from the non-attack area, and the traditional FDIA can be launched on the bus in the attack area by the following formula:

[0108] a A =H A c A (14)

[0109] When the state variable error vector c in the attack area A Formula (14) is equivalent to Formula (5) only when there are non-zero elements at the non-boundary busbar. The successful launch of traditional FDIA under incomplete information conditions is a prior art and will not be described here.

[0110] Get the attack vector a under the local topology A Later, the next thing to solve is to convert a A Which non-zero elements in are set to zero, thus inducing the problem of residual pollution. Expanding formula (8) yields

[0111]

[0112] From formula (15), we can see that the expected size of the residual is related to a A The local residual sensitivity matrix W of the non-zero elements and corresponding attack areas (A) It is related to the linear combination of the corresponding elements in (that is, the sub-matrix composed of rows and columns corresponding to the attack area measurement values ​​extracted from the W matrix), but has nothing to do with the non-attack area elements corresponding to W.

[0113] The residual sensitivity matrix W constructed from the attack area information A The expression is

[0114]

[0115] Calculate W (A) With W A The difference matrix ΔW A Right now

[0116] ΔW A =W (A) -W A(17)

[0117] Analysis found that ΔW A The absolute value of most elements is less than 0.01. If we assume that ΔW A is a zero matrix, then W A ≈W (A) At this point, once satisfied

[0118]

[0119] It is considered that DR-FDIA has a high probability of being successfully launched. The meanings of the symbols in the formula are similar to those in formula (9) and will not be repeated here. Formula (18) is a solution to the problem of how to choose S under incomplete information. A Thus, the judgment conditions of DR-FDIA are constructed.

[0120] It is worth noting that once the bad data identification phase is entered, the program will run in a closed loop until formula (3) is satisfied. The attacker cannot make any changes to the data during the iteration process. Therefore, formula (9) or (18) is only used for the first execution of r N Although the first bad data identification is S A Measuring the evasion does not necessarily guarantee that it will be evaded in each subsequent identification, but it is a reasonable and effective heuristic method to avoid the complex task of analyzing the residual changes during the dynamic iteration. A Measurement, but as long as the state estimation converges, at least S A If there is one measurement in the attack, then in order to fit the measurement, the estimation result will be offset, but a certain attack purpose can still be achieved.

[0121] 4. DR-FDIA Optimization Scheme Based on Sub-Minimum Attack Cost

[0122] The present invention hopes to find the DR-FDIA attack scheme with the minimum cost. The optimization problem can be described as

[0123]

[0124] The meanings of the variables in the formula are the same as above and will not be repeated here.

[0125] This is an NP-hard nonlinear integer programming problem, which contains absolute value and infinite norm terms and is difficult to solve directly using a solver. To this end, the present invention designs a mechanism-driven DR-FDIA optimization algorithm, such as Figure 1 shown.

[0126] Note that due to the W NSome assumptions and approximations are made in the array, and there are interference factors such as measurement errors in actual scenarios, which may disrupt the residual sorting and cause the searched minimum cost DR-FDIA solution to fail.

[0127] Considering that DR-FDIA reduces the dimension of the attack vector a, the following rule exists: when satisfying formula (9) or (18), the more non-zero elements are retained, the fewer times bad data are identified, the greater the possibility of eliminating normal measurements, and the closer the state estimation result is to the tampered value. Therefore, in order to balance the attack cost and effect and ensure computational efficiency, the algorithm starts searching by retaining two non-zero elements. Once a feasible solution is found, an additional search is performed, that is, to find the sub-minimum cost attack solution.

[0128] Embodiment 1:

[0129] The embodiment of the present invention provides a DR-FDIA method taking into account residual contamination under incomplete information, comprising the following steps:

[0130] S1. Select the target measurement point and construct the attack vector a according to the following formula;

[0131] a=Hc

[0132] Among them, a is the attack vector, H is the Jacobian matrix, and c is any non-zero vector.

[0133] Count the number of non-zero elements of the attack vector as d, set the counting variable k = 1, flag = 0;

[0134] S2, select dk-1 non-zero elements from the set and set them to zero;

[0135] S3, calculate the reduced dimension residual expectation E[r Ni ],in

[0136]

[0137] Among them, r Ni is the standardized residual, W is the residual sensitivity matrix, D = diag (WR) is the diagonal matrix, a D is the attack vector after dimensionality reduction;

[0138] S4. Determine whether the following conditions are met:

[0139]

[0140] Among them, R A and R P Select the matrix for the rows;

[0141] S5. If the conditions are met, record the attack combination. Continue to traverse all combinations, and determine whether there is a combination that meets the conditions. Let k = k + 1, if there is a combination that meets the conditions, then set flag = flag + 1;

[0142] S6. If flag≠2, repeat steps S2 to S5; if flag=2, output the attack combination with the largest l1 norm of the zeroed element residual.

[0143] Through the above steps, the present invention provides a DR-FDIA method that can effectively induce residual pollution and implement false data injection attacks under incomplete information. This method can successfully induce residual pollution under incomplete information conditions by reasonably selecting and injecting false data, using graph theory search and residual expectation calculation, and ultimately achieve misleading of power system state estimation.

[0144] Embodiment 2:

[0145] The embodiment of the present invention provides a DR-FDIA attack cost optimization search algorithm based on mechanism drive and graph theory search, and the steps are as follows:

[0146] Step 1: Determine whether you have complete network information

[0147] If the complete network information is known, the Jacobian matrix H can be constructed;

[0148] If we have partial network information, we can only construct H A .

[0149] In this step, we first determine whether the attacker has complete power system network information. If the attacker has complete network information, he can construct the Jacobian matrix H of the entire system to conduct a comprehensive attack analysis. If he only has partial network information, he can only construct a partial Jacobian matrix H. A , perform attack analysis within a limited network scope.

[0150] Step 2: Select the number k of the FDIA injection bus and construct the attack vector a according to the following formula;

[0151] a=Hc

[0152] Among them, a is the attack vector, H is the Jacobian matrix, and c is any non-zero vector.

[0153] Count the number of non-zero elements of the attack vector as d, set the counting variable k = 1, flag = 0;

[0154] Step 3: Count the number of non-zero elements in the attack vector a, which is d in total, set the counting variable k=1, and return the flag flag=0.

[0155] In this step, the number of non-zero elements d in the attack vector a is counted. These non-zero elements represent the measurement points that need to be tampered. The counting variable k is initialized to 1 to record the number of current attack points, and the return flag flag is set to 0, indicating that the optimal attack combination has not been found.

[0156] Step 4: Set dk-1 non-zero elements in attack vector a to 0, for a total of combinations, let the counting variable count = 0, and the number of successfully implemented attack combinations ck = 0.

[0157] In this step, we start to gradually reduce the number of non-zero elements in the attack vector a. Set dk-1 non-zero elements to zero, and there are Initialize the counting variable count to 0, and record the number of successfully implemented attack combinations ck to 0.

[0158] Step 5: Calculate the expected dimensionality reduction residual according to formula (8) Judgment formula

[0159]

[0160] or

[0161]

[0162] Is it true? If it is true, go to step 6; otherwise, jump to step 7.

[0163] If any of the above formulas holds true, it is believed that DR-FDIA has a high probability of being successfully launched.

[0164] Step 6: Record the attack combination, the number of successfully implemented attack combinations ck=ck+1.

[0165] In this step, if the condition in step 5 is met, the attack combination is recorded, and the number of successfully implemented attack combinations ck is increased by 1.

[0166] Step 7: Counting variable count = count + 1.

[0167] In this step, the value of the counting variable count is increased to record the number of attack combinations currently traversed.

[0168] Step 8: Determine whether The attack combination traversal, that is, whether the counting variable count is equal to

[0169] If they are equal, go to step 9;

[0170] If not, jump to step 5.

[0171] In this step, it is determined whether all possible attack combinations have been traversed. If the counting variable count is equal to If all combinations have been traversed, execute step 9; otherwise, continue to jump to step 5 for the next traversal.

[0172] Step 9: Determine whether the number of successfully implemented attack combinations ck is equal to zero.

[0173] If it is equal to zero, the number of attack points of dimensionality reduction k = k + 1, and jump to step 4 and traverse again;

[0174] If not, set the number of attack points of dimensionality reduction k=k+1, and execute step 10 after re-traversing all combinations of k=k+1.

[0175] In this step, it is determined whether the number of successfully implemented attack combinations ck is zero. If ck is equal to zero, it means that no attack combination that meets the conditions is found, then the number of attack points i of the dimension reduction is increased, and a combination that meets the conditions is found after the number of attack points of the dimension reduction is increased; otherwise, after the number of attack points i of the dimension reduction is increased once and all combinations of the number of attack points i of the dimension reduction are traversed, step 10 is executed.

[0176] Step 10: Output the attack combination with the largest l1 norm of the residual error of zeroed elements.

[0177] In this step, the attack combination with the largest l1 norm of the zeroed element residual is output as the final optimized attack scheme. This attack combination can minimize the attack cost while maximizing the residual pollution effect, thus achieving misleading of the power system state estimation.

[0178] Through the above steps, the present invention provides a mechanism-driven DR-FDIA attack cost optimization search algorithm. The algorithm gradually reduces the number of non-zero elements of the attack vector, calculates and evaluates the attack effects of different combinations, and finally finds the optimal attack scheme. Under the condition of incomplete information, this method can effectively induce residual pollution and realize false data injection attack, providing a new research direction and technical means for power system network security.

[0179] Embodiment 3:

[0180] This embodiment provides an application of the DR-FDIA method based on incomplete information and taking residual contamination into account in the IEEE 118-node system, and verifies its effectiveness and superiority under different simulation parameter settings.

[0181] 1. Simulation parameter settings

[0182] 1) Example system and load data: This embodiment uses the improved IEEE 118 node system for simulation analysis. The simulation data selected the load data of the New York Independent System Operator (NYISO) on the 1st of each month in 2013, with a load section every 5 minutes, a total of 3456 load sections, from which 100 sections were randomly selected for simulation. The load data of each section was divided into 99 areas and connected to the IEEE 118 node system.

[0183] 2) Attack subgraph division: IEEE 118-node system bus 3-7, 11-13, bus 27, 28, 32, 114, 115, bus 83-90 and bus 76, 77, 80, 82, 94-97 constitute attack subgraphs respectively. Figure 1-4 ,All simulation calculations are performed in these four subgraphs.

[0184] 3) Measurement system parameter configuration: Since the standard deviations of the various measurements in the measurement error simulation are not much different, the standard deviations of all measurement noises are equal (i.e., R = I), and the value set is {0.005, 0.01, 0.05, 0.1, 0.5}, and the limit of bad data is ±3σ~±8σ. The bad data identification method of LN-FDIA adopts r w The default system measurement configuration is full measurement, and the reasonable upper limit of the measurement value is ±60% of the current load value of each load node. The calculated variables are all per-unit values.

[0185] 4) Attack parameter setting: In this embodiment, LN-FDIA with complete / incomplete network information (Complete / Incomplete information) is written as CLN-FDIA / ILN-FDIA. Assume that the attacker can only obtain the measurement information of one load section, and all attack vector amplitudes are ±50% of the target bus load value under the same load section. In addition, since the zero-injection power bus measurement is a virtual measurement with a zero error; and the active output measurement of the power plant is monitored in real time by the dispatch center, this embodiment assumes that the attacker cannot directly attack these buses.

[0186] 5) Simulation environment configuration: The relevant calculations are implemented in MATLAB software through the MATPOWER toolkit. The computer configuration is AMD Ryzen 74800H with Radeon Graphics CPU@2.90GHz and 16GB memory.

[0187] 2. Feasibility verification of attack model under DC power flow

[0188] The feasibility of the attack model is simulated and verified under the DC power flow model. Taking bus 97 as the attack target, the success rates of the two attack models under different noise levels and different test thresholds are calculated. Figure 4 As shown. The attack success rate is defined as the number of load sections where the target bus measurement estimation deviation exceeds 30% divided by the total number of load sections, the same below. Note that the definition of the attack success rate here is relatively strict. In actual simulations, almost all attack vectors trigger residual pollution. However, due to the interference of factors such as load fluctuations, measurement redundancy, inspection thresholds, and measurement noise, the estimation deviation fluctuates to a certain extent. If only the triggering of residual pollution is used as the criterion, the average attack success rate of all examples will be above 99%.

[0189] Depend on Figure 3 It can be seen that the success rate of the two attack models reaches 100% under most combinations of test thresholds and noise levels. When the measurement noise standard deviation is 0.5 and the test threshold is greater than ±6σ, the attack success rate is 0. This is because, under this combination of test threshold and noise level, even if no network attack is carried out, the state estimation program will detect and eliminate a large amount of bad data, and the injection of attack vectors will aggravate the residual pollution phenomenon, which ultimately makes the system unobservable, so the attack fails.

[0190] Since the current measuring instruments have high accuracy and relatively low noise levels, and the limit of bad data is usually above ±3σ to ±7σ, in order to simulate a more realistic measurement system, in subsequent simulation calculations, the inspection threshold value is selected as ±8σ, and the measurement noise standard deviation is fixed at 0.01.

[0191] This embodiment also attacks other buses in the four attack subgraphs. The results are as follows: Figure 5 As shown in Figure 2, for each bus 11, 84, 88 and 97, the success rates of the two DR-FDIA attack models are both as high as 100%.

[0192] 3. Feasibility verification of attack model under AC flow

[0193] AC power flow model is often used in actual power systems. In order to reflect the practical applicability of the model, this section uses the AC power flow state estimation program for simulation. The simulation results are shown in Figure 5 shown. Figure 5 The attack success rates of CDR-FDIA and IDR-FDIA on all buses are 100%. This is because the success of DR-FDIA attacks is closely related to a A Non-zero elements and W N Sub-matrix W corresponding to array active measurement (A)In high-voltage AC systems, the connection between active type measurement and voltage, and reactive type measurement and phase angle is weak, and active and reactive power can be linearly decoupled for calculation. Therefore, although DR-FDIA is constructed under the DC power flow model, it can still work in AC power flow state estimation.

[0194] 4. Computational efficiency comparison

[0195] In real-world scenarios, the frequency of data collection and uploading is very high. SCADA data is usually uploaded every 2 seconds or so, so the real-time nature of the attack is very important. Table 1 shows the average calculation time of the attack vectors of the two attack models for a single bus. Among them, the calculation time of IDR-FDIA is less than 0.05 seconds, which reflects the excellent real-time performance of the model and is suitable for large-scale example systems.

[0196] Table 1 Average computation time of attack vectors

[0197] Model CDR-FDIA IDR-FDIA Calculation time 20.193s 0.047s

[0198] 5. Comparison of attack costs

[0199] Attack cost is also one of the important indicators to measure whether the attack model is feasible. Figure 6 As shown in the figure, the attack costs of the two attack models are almost the same, and on average only no more than 4 measurement values ​​need to be tampered with, which is significantly lower than the attack cost of the traditional DC / AC power flow model FDIA (the average attack costs are 14 and 32 respectively), reflecting the significant advantage of the model of the present invention in saving attack resources.

[0200] This paper proposes a new network attack model that takes into account residual pollution under incomplete information, and proposes a dimensionality reduction FDIA model (DR-FDIA) for the standardized residual search method in the bad data identification link. The DR-FDIA model uses residual expectation inequality constraints and only requires a small number of false data points to achieve the attack effect. In addition, the construction principle of DR-FDIA under local network information is derived through topological partitioning and matrix transformation, and a mechanism-driven sub-minimum attack cost solution optimization algorithm is proposed.

[0201] The innovation of this invention is to expand the paradigm of the concealment of false data injection attacks. The attacker only needs to master the local topology and line parameters to construct an attack vector within tens of milliseconds, and mislead the DC / AC state estimation results at a very low attack cost, thereby destroying the safe, stable and economic operation of the power grid. At the same time, these studies provide important references for the improvement of defense measures and promote the improvement of the defense capabilities of the power system.

[0202] In summary, the present invention has demonstrated its effectiveness and superiority in different scenarios in simulation analysis, and has high practical application value and promotion prospects, especially in improving the security defense of power systems.

[0203] Although embodiments of the present invention have been shown and described, it will be appreciated by those skilled in the art that various changes, modifications, substitutions and variations may be made to the embodiments without departing from the principles and spirit of the present invention, and that the scope of the present invention is defined by the appended claims and their equivalents.

Claims

1. A DR-FDIA method taking into account residual contamination under incomplete information, characterized in that: The following steps are involved: S1. Select the target measurement point and construct the attack vector a according to the following formula: a=Hc Where a is the attack vector, H is the Jacobian matrix, and c is any non-zero vector; Count the number of non-zero elements of the attack vector as d, set the counting variable k = 1, flag = 0; S2, select dk-1 non-zero elements from the set and set them to zero; S3, calculate the reduced dimension residual expectation E[r Ni ],in Among them, r Ni is the standardized residual, W is the residual sensitivity matrix, D = diag (WR) is the diagonal matrix, a D is the attack vector after dimensionality reduction; S4. Determine whether the following conditions are met: Among them, R A and R P is a row selection matrix, the row selection matrix R A and R P is defined as: Among them, |S A | and |S P | respectively represent S A and S P The size of the collection; S5. If the conditions are met, record the attack vector combination of the current dk-1 zeroed elements and continue to traverse all combinations, determine whether there is a combination that meets the conditions, set k = k + 1, if there is a combination that meets the conditions, set flag = flag + 1; S6. If flag≠2, repeat steps S2 to S5; if flag=2, output the attack combination with the largest l1 norm of the zeroed element residual.

2. The DR-FDIA method taking into account residual contamination under incomplete information according to claim 1, characterized in that: The DR-FDIA attack scheme optimization algorithm based on sub-minimum attack cost is adopted.

3. The DR-FDIA method taking into account residual contamination under incomplete information according to claim 1, characterized in that: The attack vector a D The construction includes the following steps: Construct the Jacobian matrix H or the local Jacobian matrix H A .

4. The DR-FDIA method taking into account residual contamination under incomplete information according to claim 3, characterized in that: The Jacobian matrix H or the local Jacobian matrix H is constructed A It is constructed by judging whether the complete network information is mastered. If the complete network information is mastered, the Jacobian matrix H is constructed. If the partial network information is mastered, H is constructed. A .

5. The DR-FDIA method taking into account residual contamination under incomplete information according to claim 1, characterized in that: The construction formula of the residual sensitivity matrix W is: W=I-H(H T R -1 H) -1 H T R -1 Among them, I is the identity matrix, H is the Jacobian matrix, and R is the measurement error variance matrix.

6. The DR-FDIA method taking into account residual contamination under incomplete information according to claim 1, characterized in that: The attack vector a D The construction also includes the following steps: Set dk-1 non-zero elements in the attack vector a to zero, Combination of Calculate the expected dimensionality reduction residual according to the formula Determine whether the following formula is true: If established, the attack combination is recorded.

7. The DR-FDIA method taking into account residual contamination under incomplete information according to claim 1, characterized in that: The residual expectation calculation formula also includes: Where z is the measurement vector, z a is a vector containing false data D The measurement vector of .

8. The DR-FDIA method taking into account residual contamination under incomplete information according to claim 1, characterized in that: The judgment condition includes any one of the following two conditions being met: Among them, W A is the residual sensitivity matrix of the attack area, D A is the diagonal matrix of the attack area.

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