A power system false data attack method based on signal space projection method

Abstract

The application discloses a power system false data attack method based on a signal space projection method, and the method steps comprise the following steps: S1, a traditional false data injection attack-defense double-layer model is established; S2, considering the concealment of false data, a signal offset two norm inequality constraint is established; S3, a signal space projection method is proposed, the two norm inequality constraint is projected to the Jacobian matrix column space and the left null space for linearization, and then the solution is obtained through a convex optimization method, in the aspect of the false data injection attack of the power system, the FDI attack mode for guaranteeing that the false data escapes various test methods by adding the two norm constraint is simulated, meanwhile, the signal space projection method is proposed, the two norm inequality constraint is projected onto the hyperplane of each space first, and then is projected onto each singular unit vector, so that the high-dimensional vector two norm constraint is simplified, and the solution of the constraint model is accelerated, and reference is provided for power system information security.

Description

Technical Field

[0001] This invention relates to the field of power cyber-physical systems technology, specifically a method for attacking spoofed data in power systems based on signal spatial projection. Background Technology

[0002] The development of smart grids has enhanced the communication and control capabilities of the power industry and brought significant economic benefits to society. However, so-called cybersecurity vulnerabilities have also attracted increasing attention. Supervisory Control and Data Acquisition (SCADA) systems transmit measurement values, status information, and circuit breaker signals to Remote Terminal Units (RTUs). Because these signals rely on communication and network technologies, they are vulnerable to cybersecurity attacks. Recent research indicates that attackers can compromise measurement data collected by SCADA systems through RTUs, heterogeneous communication networks, or control center office LANs. As the information source for the control center, an attack on the SCADA system can affect the results of status estimations and further mislead the operation and control functions of the Energy Management System (EMS), leading to catastrophic consequences.

[0003] False data injection (FDI) attacks are a type of cyberattack that exploits the state estimation capabilities of SCADA systems. With the development of smart grids, these attacks are receiving increasing attention. Attackers manipulate measurement data from just a few meters away, distorting the state estimation results and posing a threat to grid security. Therefore, protecting systems from FDI attacks is crucial.

[0004] Existing research on fictitious data injection (FDI) attacks mainly considers two layers of constraints: maximizing the cost at the attack level and minimizing the operating cost at the system level. However, this dual constraint does not address the issue of attacks with large amplitudes being easily detected by the system, and the solution to the L2 norm inequality constraint is based on traditional methods. Summary of the Invention

[0005] The purpose of this invention is to address the vulnerability of existing smart grids to network attacks, which fail to consider the large-scale attacks that are easily detected by the system, thus posing a certain threat to grid security. Therefore, this invention proposes a method for attacking false data in power systems based on the signal spatial projection method.

[0006] The objective of this invention can be achieved through the following technical solution: a method for attacking spoofed data in a power system based on signal spatial projection, comprising:

[0007] S1: Establishment of a false data injection model: By analyzing the damage of false data injection to the operation of the power system through a dual-bus system, a two-layer model of false data injection attack and defense is established.

[0008] S2: Establishment of signal offset L2 inequality constraint: Set the distance between the original measurement vector and the measurement vector after the attack to be less than R, and establish the signal offset L2 inequality;

[0009] S3: Based on the established signal offset L2 inequality constraint, project the signal onto the column space and left null space of the Jacobian matrix using the signal space projection method; specifically:

[0010] The hypersphere formed by the vector 2-norm constraint is first projected onto the column space Col(H) and the left null space Null(H). T On the hyperplane;

[0011] The projection vectors of the measurement vectors Z and Z0 onto the column space Col(H) are the measurement estimation vectors, and their projections onto the left null space Null(H) are the measurement estimation vectors. T The projection vector on the plane is the measurement residual vector;

[0012] The column space and the left null space are spanned by the first r left singular value vectors and the last mr left singular value vectors of matrix H, respectively, i.e., Col(H) = span{u1, u2, ..., u}. r}, Null(H)=span{u r+1 u r+2 , ..., u m};

[0013] Next, project the projection vectors of Z and Z0 on the hyperplane onto each singular value vector to complete the line projection. After projecting Z and Z0, the projection is linearized in the column space as follows: Where i∈{1,2,……,r}; P is the projection matrix, P=H(H T WH) -1 H T W; if W = I, then P = H(H) T H) -1 H T ;

[0014] The constraints in the left null space are simplified linearized to |P i KZ|≤r, i∈{r+1,r+2,……,m}, where K=IP, (IP)Z is the measurement residual; P i For line projection matrix,

[0015] As a preferred embodiment of the present invention, the establishment of the two-layer model for fake data injection attack-defense specifically includes:

[0016] S11: Set the objective functions for the upper and lower layers of the two-layer model;

[0017] S12: Set basic constraints: Limit attack resources, generator output, load shedding, and line transmission capacity to a preset range;

[0018] S13: Set system power flow constraints: Add line power flow constraints so that the power system power flow is satisfied after spurious data injection.

[0019] In a preferred embodiment of the present invention, the power flow satisfaction after the injection of false data is obtained through calculation, specifically including:

[0020] Formula 1:

[0021] Equation 2: -τD d ≤ΔD d ≤τD d ;

[0022] Equation 3: ΔPL=-SF·KD·ΔD;

[0023] Equation 4: PL = SF·KP·P - SF·KD·(D + ΔD - S);

[0024] In the formula, ΔD d The decision variable is the one constrained by the attack layer, i.e., the algebraic sum of all substation attack data is zero; τ is the value of each load ΔD. d / D d The maximum value is to limit the attack range of the substation load data to τ; Equations 1, 2 and 3 are constraints of the attack layer, and Equation 4 is a constraint of the defense layer.

[0025] In a preferred embodiment of the present invention, the signal offset L2 norm inequality constraint is obtained by calculation, specifically including: ||Z-Z0||2≤R; where Z0=Hx+e is the real-time measurement vector of the system, H is the m*n dimensional system Jacobian matrix, x is the state vector, e is the measurement error vector, Z is the measurement vector of the system after being attacked, and R is the signal offset.

[0026] Compared with the prior art, the beneficial effects of the present invention are:

[0027] 1. In the context of the convergence of information and network technologies and the vulnerability of power systems to network attacks, this invention proposes a novel fake data injection attack mechanism that improves concealment by adding a signal offset L2 norm inequality constraint, providing a reference for information security in power systems.

[0028] 2. This invention proposes a signal space projection method, which first projects the supersphere formed by the vector L2 norm constraint onto the hyperplane of each space, and then onto each singular value vector, thereby simplifying the high-dimensional vector L2 norm constraint and linearizing it;

[0029] 3. This invention is beneficial for accelerating the solution of L2 norm inequality constraints while ensuring a certain level of accuracy. In large systems, due to the high vector dimension, the computation of planning solutions containing L2 norm constraints is slow. By using spatial projection to transform the hypersphere into inequality constraints on a straight line, the direct expansion of the norm can be avoided, thereby accelerating the solution speed. Attached Figure Description

[0030] To facilitate understanding by those skilled in the art, the present invention will be further described below with reference to the accompanying drawings.

[0031] Figure 1 This is a flowchart illustrating the implementation of the fake data attack based on the signal spatial projection method of this invention.

[0032] Figure 2 This diagram illustrates the principle of the signal space projection method in a specific application of the present invention. Detailed Implementation

[0033] The technical solution of the present invention will be clearly and completely described below with reference to the embodiments. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0034] Please see Figure 1 As shown, a method for attacking spoofed data in power systems based on signal spatial projection, used in the IEEE 39-node power cyber-physical system, includes:

[0035] S1: Analyze the damage to power system operation caused by spoofing through a simple dual-bus system, and establish a two-layer attack-defense model for spoofing data injection, specifically:

[0036] S11: Set the objective functions for the upper and lower layers of the two-layer model: Consider the different meanings represented by the upper and lower layers, namely, the goal of maximizing cost at the attack level and the goal of minimizing operating cost at the system level; under the condition of limited attack resources, the upper layer represents the attacker and determines the attack vector to be injected in order to maximize the operating cost of the system; the lower layer represents the optimal response of SCED to the error state estimation that has been successfully manipulated by the attack vector determined by the upper layer.

[0037] The objective function of the upper layer (attack layer) is The objective function of the lower layer (defense layer) is With P g and S d As a variable. and The solution to the lower-level objective function, i.e. Where cg For the power generation cost of generator g, cs d For the unloading cost of load d, P g S is the power output of generator g. d The unloaded load is the load d.

[0038] Attack resource constraints are limited to Generator output constraint is The load reduction constraint is 0 ≤ S d ≤D d +ΔD d The line transmission power constraint is Where b represents the attack resource. Let g be the minimum power output of generator g. D represents the maximum power output of generator g. d Let ΔD be the actual load value of load d. d PL injects load variations into the load d to attack the load variation. l For line transmission power, This represents the maximum transmission power of the power transmission line.

[0039] S12: Set basic constraints: Limit attack resources, generator output, load shedding, and line transmission capacity within a certain range to ensure the rationality of the model;

[0040] S13: Set system power flow constraints: Add line power flow constraints to ensure that the power system power flow is still satisfied after the injection of false data, thus ensuring that the attack is not detected; satisfy the constraints that allow the injection of false data to evade system monitoring, specifically calculated according to the following formula:

[0041]

[0042] -τD d ≤ΔD d ≤τD d

[0043] ΔPL=-SF·KD·ΔD

[0044] PL=SF·KP·P-SF·KD·(D+ΔD-S)

[0045] In the formula, ΔD d These are decision variables constrained by the attack layer. The attack is guaranteed to be a load redistribution attack, meaning the algebraic sum of all substation attack data is zero; τ is the load ΔD for each substation. d / D dThe maximum value of τ is used to limit the attack amplitude of substation load data to within τ, thereby ensuring the rationality of the attacked data. Equations 1, 2, and 3 are constraints of the attack layer, while Equation 4 is a constraint of the defense layer. Equations 3 and 4 ensure that the line power flow is still satisfied after the injection of false data, thus ensuring that the attack is not detected.

[0046] S2: Considering the concealment of false data, a signal offset L2 inequality constraint is established. The signal offset L2 inequality constraint is established by setting the distance between the original measurement vector and the measurement vector after the attack to be less than R. To solve the problem that the large change amplitude of false data is easily detected by the system, the signal offset L2 inequality constraint is introduced, specifically calculated according to the following formula: ΔZ=[ΔPL,KD·ΔD], Z=Z0+ΔZ, ||Z-Z0||2≤R, where Z0=Hx+e is the real-time measurement vector of the system, which is also the center point of the normal data, i.e., the center data, H is the m*n dimensional system Jacobian matrix, x is the state vector, e is the measurement error vector, Z is the measurement vector of the system after the attack, and R is the signal offset. This constraint allows the injected false data to evade various detection methods, improving the concealment of false data.

[0047] S3: Set system power flow constraints: Add line power flow constraints to ensure that the power system power flow is still satisfied after the injection of spoofed data, thus ensuring that the attack is not detected; based on the established signal offset L2 inequality constraints, linearize them using the signal space projection method, and then solve them using convex optimization methods, specifically:

[0048] By projecting the excess sphere formed by the vector 2-norm constraint onto the hyperplanes of each space, and then onto each singular value vector, we can avoid directly solving for the norm expansion, thus speeding up the solution. The projection is first onto the column space Col(H) and the left null space Null(H). T On the hyperplane of ), the projection vectors of the measurement vectors Z and Z0 onto Col(H) are the measurement estimation vectors, and in Null(H) T The projection vector onto the matrix is ​​the measurement residual vector. The column space (signal space) and the left null space (noise space) are spanned by the first r left singular value vectors and the last mr left singular value vectors of matrix H, respectively, i.e., Col(H) = span{u1, u2, ..., u...}. r}, Null(H)=span{u r+1 ,u r+2 ,...,u m Then, the projection vectors of Z and Z0 on the hyperplane are projected onto each singular value vector to complete the line projection, thereby simplifying the L2 norm constraint of the high-dimensional vector and accelerating the solution of the L2 norm constraint.

[0049] Constrained linearization in column space: After projecting Z and Z0, the linearization in column space is achieved as follows: i∈{1,2,...,r}, where P is the projection matrix, and P=H(H T WH) -1 H T If W = I, then P = H(H) T H) -1 H T P i For line projection matrix,

[0050] Noise threshold determination in the left null space: Since the noise threshold is small, i.e., the measurement vector is in the noise space Null(H) T The magnitude of the projection vector on the surface is small, and Col(H)⊥Null(H) T Therefore, the measurement vector is close to the signal space Col(H) (if there is no noise, the measurement signal falls in Col(H)). Thus, the constraints in the left null space can be simply linearized to P. i KZ≤r, i∈{r+1,r+2,...,m}. Where K=IP, (IP)Z is the measurement residual, and P... i For line projection matrix, Taking three-dimensional space as an example, such as Figure 2 As shown, u1 and u2 are singular unit vectors spanning a column space, u3 is a singular unit vector spanning a left null space, and ΔZ is the attack vector. and These are the projection vectors of Z and Z0 in the column space, respectively.

[0051] To verify the effectiveness of this invention, a simulated spoofing attack was conducted using the IEEE 39-node power cyber-physical system as an example. Generator parameters are shown in Table 1. The load attack range τ = 50%, the load offloading cost cs = $100 / MWh, the number of attack resources b = 50, and baseMVA = 100. Simulation was performed using Python 3.9, and the comparison results between the signal space projection algorithm and the direct L2 constraint are shown in Table 2.

[0052] Table 1 Generator Parameters of the IEEE 39-Block System

[0053]

[0054] Table 2 Comparison results of signal space projection algorithm and direct L2 constraint

[0055]

[0056] As shown in Table 2, the signal space projection algorithm proposed in this invention can linearize the L2 inequality constraint, significantly accelerating the solution speed compared to traditional L2 inequality constraints. The algorithm proposed in this invention can provide a reference for simplifying L2 inequality constraints in other scenarios.

[0057] The preferred embodiments of the present invention disclosed above are merely illustrative of the invention. These preferred embodiments do not exhaustively describe all details, nor do they limit the invention to specific implementations. Clearly, many modifications and variations can be made based on the content of this specification. This specification selects and specifically describes these embodiments to better explain the principles and practical applications of the invention, thereby enabling those skilled in the art to better understand and utilize the invention. The invention is limited only by the claims and their full scope and equivalents.

Claims

1. A power system false data attack method based on signal space projection method, characterized in that, The method comprises: S1: false data injection model establishment: analyzing the damage of false data injection to power system operation through a double bus system, and establishing a false data injection attack-defense double-layer model; S2: signal offset two norm inequality constraint establishment: the distance between the original measurement vector and the measurement vector after the attack is less than R, and a signal offset two norm inequality is established; R is a signal offset degree; S3: according to the established signal offset two norm inequality constraint, a signal space projection method is used to project it to the column space and left null space of the Jacobian matrix; specifically: The hyper-sphere formed by the vector two-norm constraint is first projected onto the hyper-planes of the column space Col(H) and the left null space Null(H T ) of H, where H is the m*n dimensional system Jacobian matrix. The projection of the measurement vector Z and Z0 onto the column space Col(H) is the measurement estimate vector, and the projection onto the left null space Null(H T ) is the measurement residual vector. The column space and the left null space of H are spanned by the first r left singular vectors and the last m-r left singular vectors of H, respectively, i.e., Col(H) = span{u1, u2,..., ur}, Null(H) = span{u r} r+1 , r+2 u m m-r}, respectively. The projection vectors of Z and Z0 on the hyperplane are projected to each singular value vector, completing line projection, and Z and Z0 are projected and linearized in the column space as follows: where i∈{1,2,……,r}; P is a projection matrix, P=H(H T WH) -1 H T W; if W=I, then P=H(H T H) -1 H T ; The constraints in the left null space are simply linearized as |P i KZ|≤r, i∈{r+1, r+2, …, m}, where, K=I-P, (I-P)Z is the measurement residual; P i is the line projection matrix, .

2. The false data attacks method of power system based on signal subspace projection method according to claim 1, characterized in that, The specific establishment of the false data injection attack-defense double-layer model comprises: S11: setting the objective functions of the upper and lower layers of the double-layer model; the objective function of the upper layer is , and the objective function of the lower layer is , taking and as variables, and as the solution of the lower layer objective function, that is, ; wherein c g is the power generation cost of the generator g, cs d is the load shedding cost of the load d, P g is the power generation power of the generator g, and S d is the load shedding load of the load d; S12: Set basic constraints: Limit attack resources, generator output, load shedding, and line transmission power within preset ranges; attack resources are limited to... The generator output constraint is The load reduction constraint is The line transmission power constraint is Where b represents the attack resource. For generator Minimum power output, D represents the maximum power output of generator g. d The actual load value of load d. The load variation is injected into the load d to perform the attack. PL is a load variation for load injection attacks. l For line transmission power, This represents the maximum transmission power of the power transmission line. S13: setting system power flow constraints: adding line power flow constraints so that the false data injection satisfies the power system power flow.

3. The false data attacks method of power system based on signal subspace projection method according to claim 2, characterized in that, The false data injection after meeting the power system flow is obtained by calculation, and specifically includes: ​ Formula II: ; Formula Three: ; Formula Four: ; wherein, is the decision variable of attack layer constraint, i.e., all substation attack data algebraic sum is zero; τ is the maximum value of each load , i.e., the attack amplitude of substation load data is limited to τ; formula one, formula two and formula three are all attack layer constraints, and formula four is a defense layer constraint.

4. The false data attacks method of power system based on signal subspace projection method according to claim 1, characterized in that, The signal offset two norm inequality constraint is calculated, and specifically includes: , , ; in the formula, Z0=Hx+e is a real-time measurement vector of the system, x is a state vector, e is a measurement error vector, and Z is a measurement vector of the system after being attacked.

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