A false data injection attack under power system frequency control method and device

Abstract

The application discloses a power system frequency control method and device under a false data injection attack, and the method is characterized in that: a graph topology structure and a weight adjacency matrix are constructed, then a dynamic coupling graph model is constructed, and a degree matrix and a graph Laplacian matrix are calculated; a graph filter is constructed relying on the graph Laplacian matrix, a system physical dynamic and a false data injection attack component are separated in a spectral domain, and real state and attack residual estimation values are obtained in combination with sparse observation data; estimated results are used to compensate frequency measurement values, compensated frequency deviations are obtained, a preset performance controller is activated through a linear variable parameter condition, frequency transient behavior is constrained, and a control instruction is output; frequency state deviations of adjacent regions are calculated according to the compensated frequency deviations of each region, a distributed consistency coordination protocol is designed to generate a synchronous compensation signal, and global frequency collaborative control is realized. The application solves the problems of being easily misled and fixed control gain lacking adaptive adjustment in the prior art.

Description

Technical Field

[0001] This invention relates to the field of power system frequency control technology, specifically to a method and apparatus for power system frequency control under a false data injection attack. Background Technology

[0002] With the large-scale grid connection of new energy sources and the increasing interconnectivity of regional power grids, the frequency stability characteristics of multi-regional power systems are becoming increasingly complex, and system operation faces greater uncertainty and dynamic coupling characteristics. Load frequency control, as a core means of ensuring active power balance and frequency stability in the power grid, combines inter-regional coordinated regulation with local control to achieve frequency deviation suppression and rational allocation of tie-line power. Meanwhile, the deep integration of power cyber-physical systems has led to a high degree of openness in measurement, communication, and control. False data injection attacks, by tampering with remote measurement signals and misleading control decisions, have become a significant threat to the safe and stable operation of frequency control systems. Existing research largely relies on graph signal processing, state estimation, and distributed cooperative control methods to achieve state awareness and robust control under attack conditions, providing technical support for frequency security control in complex operating situations.

[0003] Existing frequency control methods for resisting attacks still have significant shortcomings. Conventional control strategies often employ fixed-gain structures, making it difficult to balance transient response speed and steady-state control accuracy in response to frequency deviations, and lacking adaptive adjustment mechanisms when approaching performance boundaries. Some pre-defined performance control methods do not incorporate linear variable parameter design into their gain scheduling strategies, failing to achieve smooth switching based on system operating states, and are prone to overcontrolling and steady-state oscillations under small disturbances. Furthermore, existing distributed cooperative control methods often rely directly on local measurements and information from neighboring regions for consistent iteration, failing to fully consider the reliability of frequency deviations after attack compensation, and lacking organic coordination with local pre-defined performance controllers. This makes it difficult to simultaneously satisfy multi-region frequency synchronization constraints and dynamic performance constraints under spoofed data injection attack scenarios, resulting in a trade-off between control robustness and transient quality.

[0004] Therefore, there is an urgent need for a power system frequency control method under false data injection attacks to solve the problems of susceptibility to misleading and fixed control gain lacking adaptive adjustment in existing technologies. Summary of the Invention

[0005] To address these issues, the present invention provides a power system frequency control method and apparatus under false data injection attacks, which solves the problems of existing multi-regional power system frequency control being easily misled under false data injection attacks, fixed control gain lacking adaptive adjustment, difficulty in balancing transient performance and steady-state accuracy, and insufficient distributed coordination and local control coordination.

[0006] To achieve the above objectives, the present invention provides the following technical solution: a power system frequency control method under a false data injection attack, characterized in that it includes: Based on the physical interconnection topology of a multi-regional power system and the state-space model of load frequency control, each control region is defined as a graph vertex, and the dynamic coupling relationship between regions is defined as a graph edge, forming a graph topology. The dynamic coupling strength of the graph vertices is quantified using the Frobenius norm of system matrix partitioning to obtain a weighted adjacency matrix. Based on the graph topology and the weighted adjacency matrix, a dynamic coupling graph model of the multi-regional power system is constructed. The degree matrix is ​​calculated based on the weighted adjacency matrix. The graph Laplace matrix is ​​calculated based on the weighted adjacency matrix and the degree matrix. A graph filter is constructed based on the graph Laplacian matrix; the graph filter is used to separate the physical dynamics of the system from the spurious data injection attack components in the spectral domain to obtain the separation result; based on the separation result and sparse observation data, the system's true state and attack residual estimation results are obtained. Based on the actual state of the system and the attack residual estimation results, attack compensation is performed on the frequency measurement values ​​to obtain compensated frequency deviation information; based on the compensated frequency deviation information, a preset performance controller is activated through linear variable parameter conditions; the preset performance controller constrains the transient behavior of frequency deviation and outputs preset performance control commands. Based on the compensated frequency deviation of each region, frequency state deviation information between adjacent regions is calculated; based on the preset performance control command and the frequency state deviation information, a distributed consistency coordination protocol is designed and a frequency synchronization compensation signal is generated to realize the frequency collaborative control of the entire power system in multiple regions.

[0007] As a preferred scheme for power system frequency control under false data injection attacks, in the process of quantifying the dynamic coupling strength of the graph vertices based on the Frobenius norm of system matrix partitioning, the expression for the dynamic coupling weight between adjacent graph vertices is: ; In the formula, The dynamic coupling weights between regions i and j; and These are the block matrices representing the corresponding regions in the system state matrix; q is the Frobenius norm; p and q are the row and column indices of the matrix elements, respectively. The expressions for the degree matrix and the graph Laplacian matrix are as follows: ; ; In the formula, D is the degree matrix; Let be the degree value of region i; N is the total number of regions. is the weighted adjacency matrix; L is the graph Laplacian matrix; j is the region index.

[0008] As a preferred scheme for power system frequency control under spoofing data injection attacks, the expression of the graph filter is: ; In the formula, g(λ) is the spectral response function; Adjust the filter parameters; G is the eigenvalue of the graph Laplacian matrix; G is the graph filter; Q is the eigenvector matrix obtained by the spectral decomposition of the graph Laplacian matrix; Q T is the transpose of the eigenvector matrix; N is the total number of control areas in the multi-regional power system; The formula for calculating the true state of the system is: ; In the formula, The system represents the actual state; G is the graph filter. This is sparse observation data; The formula for calculating the attack residual estimation result is as follows: ; In the formula, This is the result of the attack residual estimation.

[0009] As a preferred scheme for power system frequency control under a spoofing data injection attack, the expression for the compensated frequency deviation information is: ; In the formula, This provides the frequency deviation information for the i-th region after compensation. This represents the original frequency measurement value for the i-th region; This represents the attack residual estimation result for the i-th region; During the process of activating the preset performance controller based on the compensated frequency deviation information and the linear variable parameter condition, a gain saturation mechanism is introduced to control the preset performance controller. When the absolute value of the normalized error is less than the activation threshold, the system is determined to be operating in the steady-state region, and the preset performance controller adopts a low-gain linear control mode. When the absolute value of the normalized error is not less than the activation threshold, the system enters the transient region, triggering the preset performance control enhancement mechanism. By adaptively increasing the control gain, the system frequency deviation is ensured to meet the preset performance constraint requirements. The conditional activation function expression for the linear variable parameter condition is: ; ; In the formula, Conditionally activate the adaptive gain function; The normalized error signal for the i-th region; The conditional activation threshold; This is the saturation threshold; This is the maximum gain amplification factor; This is the performance envelope function; The frequency deviation of the i-th control region; The expression for the state-space model of the preset performance controller is: ; In the formula, Let be the state derivative of the PPC subsystem in region i; The state vector of the PPC subsystem; The system matrix is ​​a linear variable parameter system; For scheduling parameters; The input matrix; For control input; Here is the perturbation matrix; For disturbance terms; This refers to the output of the PPC subsystem. This is the output matrix; Injecting attack items into fake data; This refers to the noise measurement term.

[0010] As a preferred embodiment of a power system frequency control method under a false data injection attack, the expression of the preset performance control command is: ; In the formula, This refers to the local preset performance control instructions for the i-th region; , These are the proportional gain and integral gain, which are dynamically adjusted according to the scheduling parameters and normalization error, respectively. This is for the comprehensive testing volume of emergency resection in the region; , It is the linearly variable parameter fundamental gain matrix.

[0011] As a preferred scheme for power system frequency control under a false data injection attack, the formula for calculating the frequency state deviation information between adjacent regions is as follows: ; In the formula, This refers to the frequency state deviation information between the i-th region and the j-th region; The compensated frequency deviation for the i-th region; The frequency deviation after compensation in the j-th region; The expression for the frequency synchronization compensation signal is: ; In the formula, This is the final overall control command for the i-th region; These are distributed consistency coordination and control instructions. For damping control commands; The set of regions adjacent to region i; For linearly variable parameter damping gain.

[0012] This invention also provides a power system frequency control device under a fake data injection attack, employing the above-mentioned power system frequency control method under a fake data injection attack, including: A module for constructing a dynamic coupled graph model and obtaining the graph Laplace matrix is ​​used to construct a graph topology based on the physical interconnection topology of a multi-regional power system and the load frequency control state space model. Each control region is defined as a graph vertex, and the dynamic coupling relationships between regions are defined as graph edges. The module quantifies the dynamic coupling strength of the graph vertices using the Frobenius norm of system matrix partitioning to obtain a weighted adjacency matrix. Based on the graph topology and the weighted adjacency matrix, a dynamic coupled graph model of the multi-regional power system is constructed. The degree matrix is ​​calculated based on the weighted adjacency matrix. Finally, the graph Laplace matrix is ​​calculated based on the weighted adjacency matrix and the degree matrix. The graph filter construction and processing module is used to construct a graph filter based on the graph Laplacian matrix; separate the system's physical dynamics and spurious data injection attack components in the spectral domain using the graph filter to obtain the separation result; and obtain the system's true state and attack residual estimation results based on the separation result and sparse observation data. The preset performance controller activation and command output module is used to perform attack compensation on the frequency measurement value based on the actual state of the system and the attack residual estimation result to obtain the compensated frequency deviation information; activate the preset performance controller through linear variable parameter conditions based on the compensated frequency deviation information; constrain the transient behavior of frequency deviation through the preset performance controller and output the preset performance control command. The frequency synchronization compensation signal generation module is used to calculate the frequency state deviation information between adjacent regions based on the compensated frequency deviation of each region; and to design a distributed consistency coordination protocol and generate a frequency synchronization compensation signal based on the preset performance control command and the frequency state deviation information, so as to realize the frequency collaborative control of the entire power system in multiple regions.

[0013] As a preferred solution for power system frequency control devices under false data injection attacks, in the module for constructing the dynamic coupling graph model and obtaining the graph Laplacian matrix, during the process of quantifying the dynamic coupling strength of the graph vertices based on the Frobenius norm of system matrix partitioning, the expression for the dynamic coupling weight between adjacent graph vertices is: ; In the formula, The dynamic coupling weights between regions i and j; and These are the block matrices representing the corresponding regions in the system state matrix; q is the Frobenius norm; p and q are the row and column indices of the matrix elements, respectively. The expressions for the degree matrix and the graph Laplacian matrix are as follows: ; ; In the formula, D is the degree matrix; Let be the degree value of region i; N is the total number of regions. is the weighted adjacency matrix; L is the graph Laplacian matrix; j is the region index.

[0014] As a preferred solution for power system frequency control devices under false data injection attacks, the graph filter construction and processing module contains the following expression for the graph filter: ; In the formula, g(λ) is the spectral response function; Adjust the filter parameters; G is the eigenvalue of the graph Laplacian matrix; G is the graph filter; Q is the eigenvector matrix obtained by the spectral decomposition of the graph Laplacian matrix; Q T is the transpose of the eigenvector matrix; N is the total number of control areas in the multi-regional power system; The formula for calculating the true state of the system is: ; In the formula, The system represents the actual state; G is the graph filter. This is sparse observation data; The formula for calculating the attack residual estimation result is as follows: ; In the formula, This is the result of the attack residual estimation.

[0015] As a preferred solution for a power system frequency control device under a false data injection attack, the expression for the compensated frequency deviation information in the preset performance controller activation and command output module is as follows: ; In the formula, This provides the frequency deviation information for the i-th region after compensation. This represents the original frequency measurement value for the i-th region; This represents the attack residual estimation result for the i-th region; During the process of activating the preset performance controller based on the compensated frequency deviation information and the linear variable parameter condition, a gain saturation mechanism is introduced to control the preset performance controller. When the absolute value of the normalized error is less than the activation threshold, the system is determined to be operating in the steady-state region, and the preset performance controller adopts a low-gain linear control mode. When the absolute value of the normalized error is not less than the activation threshold, the system enters the transient region, triggering the preset performance control enhancement mechanism. By adaptively increasing the control gain, the system frequency deviation is ensured to meet the preset performance constraint requirements. The conditional activation function expression for the linear variable parameter condition is: ; ; In the formula, Conditionally activate the adaptive gain function; The normalized error signal for the i-th region; The conditional activation threshold; This is the saturation threshold; This is the maximum gain amplification factor; This is the performance envelope function; The frequency deviation of the i-th control region; The expression for the state-space model of the preset performance controller is:

[0016] In the formula, Let be the state derivative of the PPC subsystem in region i; The state vector of the PPC subsystem; The system matrix is ​​a linear variable parameter system; For scheduling parameters; The input matrix; For control input; Here is the perturbation matrix; For disturbance terms; This refers to the output of the PPC subsystem. This is the output matrix; Injecting attack items into fake data; This refers to the noise measurement term.

[0017] As a preferred solution for a power system frequency control device under a false data injection attack, the expression of the preset performance control command in the preset performance controller activation and command output module is as follows: ; In the formula, This refers to the local preset performance control instructions for the i-th region; , These are the proportional gain and integral gain, which are dynamically adjusted according to the scheduling parameters and normalization error, respectively. This is for the comprehensive testing volume of emergency resection in the region; , It is the linearly variable parameter fundamental gain matrix.

[0018] As a preferred solution for a power system frequency control device under a false data injection attack, the calculation formula for the frequency state deviation information between adjacent regions in the frequency synchronization compensation signal generation module is as follows: ; In the formula, This refers to the frequency state deviation information between the i-th region and the j-th region; The compensated frequency deviation for the i-th region; The frequency deviation after compensation in the j-th region; The expression for the frequency synchronization compensation signal is: ; In the formula, This is the final overall control command for the i-th region; These are distributed consistency coordination and control instructions. For damping control commands; The set of regions adjacent to region i; For linearly variable parameter damping gain.

[0019] The present invention has the following advantages: First, by separating attack components through graph filters and performing frequency measurement compensation, the impact of spoofing attacks on the frequency control loop can be weakened, thereby improving the system's operational stability under attack scenarios.

[0020] Second, by adopting a gain adaptive mechanism driven by normalized error, the control action can be adjusted according to the frequency deviation state, thus better balancing the transient constraints and steady-state operation of the system.

[0021] Third, combining local preset performance control with distributed collaborative control can both suppress frequency deviation in a single region and achieve frequency synchronization in multiple regions, thereby improving the overall control effect of the interconnected power grid.

[0022] Fourth, the linear variable parameter control structure is adopted, which adapts to the dynamic changes of the system, making the control strategy more adaptable and conducive to maintaining the stable operation of the power grid frequency under complex operating conditions. Attached Figure Description

[0023] To more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings in the following description are merely exemplary, and those skilled in the art can derive other embodiments based on the provided drawings without creative effort.

[0024] The structures, proportions, sizes, etc. illustrated in this specification are only for the purpose of assisting those skilled in the art in understanding and reading the content disclosed herein, and are not intended to limit the conditions under which the present invention can be implemented. Therefore, they have no substantial technical significance. Any modifications to the structure, changes in the proportions, or adjustments to the size, without affecting the effects and objectives that the present invention can produce, should still fall within the scope of the technical content disclosed in the present invention.

[0025] Figure 1 This is a flowchart illustrating a power system frequency control method under a false data injection attack, as provided in Embodiment 1 of the present invention. Figure 2 This is a schematic diagram illustrating the specific implementation process of a power system frequency control method under a false data injection attack provided in Embodiment 1 of the present invention; Figure 3 This is a schematic diagram of the three-region system structure used in the test system in one possible embodiment of Embodiment 1 of the present invention; Figure 4 This is a schematic diagram of the performance curve under FDIA in one possible embodiment provided in Embodiment 1 of the present invention; Figure 5 This is a schematic diagram of the architecture of a power system frequency control device under a false data injection attack, as provided in Embodiment 2 of the present invention. Detailed Implementation

[0026] The following specific embodiments illustrate the implementation of the present invention. Those skilled in the art can easily understand other advantages and effects of the present invention from the content disclosed in this specification. Obviously, the described embodiments are only some, not all, of the embodiments of the present invention. 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.

[0027] Example 1 See Figure 1 and Figure 2 Embodiment 1 of the present invention provides a method for frequency control of a power system under a false data injection attack, comprising the following steps: S1. Based on the physical interconnection topology of a multi-regional power system and the state-space model of load frequency control, each control region is defined as a graph vertex, and the dynamic coupling relationship between regions is defined as a graph edge, forming a graph topology. The dynamic coupling strength of the graph vertices is quantified based on the Frobenius norm of system matrix partitioning to obtain a weighted adjacency matrix. Based on the graph topology and the weighted adjacency matrix, a dynamic coupling graph model of the multi-regional power system is constructed. The degree matrix is ​​calculated based on the weighted adjacency matrix. The graph Laplace matrix is ​​calculated based on the weighted adjacency matrix and the degree matrix. S2. Construct a graph filter based on the graph Laplacian matrix; separate the system's physical dynamics and spurious data injection attack components in the spectral domain using the graph filter to obtain the separation result; obtain the system's true state and attack residual estimation results based on the separation result and sparse observation data. S3. Based on the actual state of the system and the attack residual estimation result, attack compensation is performed on the frequency measurement value to obtain the compensated frequency deviation information; based on the compensated frequency deviation information, a preset performance controller is activated through linear variable parameter conditions; the preset performance controller is used to constrain the transient behavior of frequency deviation and output a preset performance control command. S4. Based on the compensated frequency deviation of each region, calculate the frequency state deviation information between adjacent regions; based on the preset performance control command and the frequency state deviation information, design a distributed consistency coordination protocol and generate a frequency synchronization compensation signal to realize the frequency collaborative control of the entire power system in multiple regions.

[0028] In this embodiment, in step S1, the transfer function model of the LFC system in region i includes the governor, turbine, load, synchronous generator, and tie-line power at the physical layer, as well as the LFC center and communication network at the network layer. The dynamics of the LFC system in region i are as follows: ; In the formula, Δf i ΔPgi ΔX gi ΔP tiei A CEi These represent the frequency deviation, generator mechanical input deviation, governor deviation, tie-line power deviation between regions i and j, and region control error, respectively, in the power system.

[0029] set up , u i and Let the state vector, output vector, control input, and load disturbance of region i be represented respectively. Then, the state-space model of the attacked LFC system is obtained: ; ; ; ; ; ; ; ; ; in, ;

[0030] In the formula, Let be the rotor inertia time constant of the generator in the i-th region; Let be the load damping coefficient for region i; Let be the time constant of the steam turbine in the i-th region; Let be the time constant of the speed controller in the i-th region; Let be the droop coefficient of the speed governor in the i-th region; Let be the synchronization power coefficient of the tie line between region i and its neighboring region j; Let be the frequency deviation coefficient for the i-th region.

[0031] In this embodiment, in step S1, based on the physical interconnection topology of the multi-regional power system and the load frequency control state space model, each control region is defined as a graph vertex, and the dynamic coupling relationship between regions is defined as a graph edge, forming a graph topology. The dynamic coupling strength of the graph vertices is quantified based on the Frobenius norm of system matrix partitioning to obtain a weighted adjacency matrix. Based on the graph topology and the weighted adjacency matrix, a dynamic coupling graph model of the multi-regional power system is constructed. The degree matrix is ​​calculated based on the weighted adjacency matrix. The graph Laplace matrix is ​​calculated based on the weighted adjacency matrix and the degree matrix.

[0032] Specifically, combining the physical wiring topology and load frequency control state-space model of a multi-region interconnected power system, each independent control region in the system is abstracted as a vertex in a graph structure, and the power interaction and dynamic coupling relationship between regions formed by tie lines is abstracted as an edge in the graph structure, thus constructing a basic graph topology that can represent the interconnection relationship of the system. To more realistically reflect the degree of dynamic correlation between regions, the Frobenius norm after system matrix block partitioning is used to quantify the strength of dynamic coupling between each vertex, and the quantization result is used as the edge weight assignment, thereby obtaining a weighted adjacency matrix that can reflect the degree of dynamic correlation between regions. Based on the graph topology and the weighted adjacency matrix, a dynamic coupling graph model adapted to the multi-region power system is constructed, enabling it to represent the spatial structure and dynamic characteristics of the system. The degree matrix is ​​calculated based on the sum of the connection weights of each vertex in the weighted adjacency matrix, and the graph Laplacian matrix is ​​solved by combining the weighted adjacency matrix and the degree matrix, providing a mathematical basis for graph filtering operations and signal spectral domain separation.

[0033] This study considers an interconnected power system consisting of N control areas. While physical connections are defined by tie lines, a dynamic coupling diagram for the communication layer is defined to capture deeper dynamic interactions. .

[0034] Vertex set Each node i corresponds to a control region. Global state This is a stack of local states. Communication between neighbors only involves exchanging partial state information.

[0035] It is a set of edges, representing communication links connecting different control regions. An edge is defined if and only if there is a direct dynamic coupling between region i and region j. exist.

[0036] To quantify the dynamic coupling strength between regions i and j, the system matrix is ​​used. Constructing the weight matrix using the block norm .

[0037] The coupling between regions i and j in A is not only reflected in Blocks are also reflected in The effect of a block is bidirectional, but the strength may be asymmetrical. Therefore, a symmetric, synthetic coupling strength is defined. Vertices are defined. and Dynamic coupling weights between for: ; In the formula, The dynamic coupling weights between regions i and j; and These are the block matrices representing the corresponding regions in the system state matrix; q is the Frobenius norm; p and q are the row and column indices of the matrix elements, respectively. In the LFC model, and It is very sparse, therefore this essentially quantifies the geometric mean strength of the bidirectional frequency coupling. For i=j, let =0. This yields a symmetric weighted adjacency matrix. .

[0038] In this embodiment, the degree matrix is ​​calculated and the graph Laplacian matrix is ​​established as follows: ; ; In the formula, D is the degree matrix; Let be the degree value of region i; N is the total number of regions. is the weighted adjacency matrix; L is the graph Laplacian matrix; j is the region index.

[0039] L is a real symmetric positive semi-definite matrix. Its eigenvectors Q define the Fourier basis of the graph, and its eigenvalues... Graph frequencies are defined. Eigenvalue decomposition is performed on L: ; Calculate the eigenvalues ​​of the graph Laplacian matrix L And sorted in ascending order .

[0040] In this embodiment, in step S2, a graph filter is constructed based on the graph Laplacian matrix; the graph filter is used to separate the physical dynamics of the system from the spurious data injection attack components in the spectral domain to obtain the separation result; based on the separation result and sparse observation data, the system's true state and attack residual estimation results are obtained.

[0041] Specifically, utilizing the spectral domain characteristics of the graph Laplacian matrix obtained in step S1, a graph filter suitable for dynamic signal processing in power systems is constructed. This filter can decompose and process the system observation signal in the graph frequency domain. Since the inherent physical dynamic signal of the system and the spoofed data injection attack signal have significant distribution differences in the graph spectral domain, the graph filter can separate the mixed observation signal contaminated by the attack into two parts: one part is the physical dynamic component reflecting the true operating law of the system, and the other part is the spoofed data attack component formed by malicious tampering, thus achieving effective separation of the two types of signals. Based on the signal separation, combined with the observation data provided by the sparsely arranged measurement devices in the system, a state reconstruction and attack quantity fitting method is used to estimate the operating state of the system that is not directly observed. Simultaneously, the amplitude and distribution of the attack signal are approximated, ultimately obtaining the true system state unaffected by spoofed data interference, as well as the attack residual estimation result that can be used for subsequent control compensation and correction. This eliminates the adverse effects of the attack on frequency measurement and state perception at the signal level.

[0042] Covert attacks distort the distribution of system dynamics in the graph domain. Therefore, a graph filter G is designed to amplify this distortion for detection. The spectral response function g(λ) is designed, and the graph filter matrix is ​​constructed as follows: ; In the formula, g(λ) is the spectral response function; Adjust the filter parameters; G is the eigenvalue of the graph Laplacian matrix; G is the graph filter; Q is the eigenvector matrix obtained by the spectral decomposition of the graph Laplacian matrix; Q T is the transpose of the eigenvector matrix; N is the total number of control areas in the multi-regional power system.

[0043] In this embodiment, the formula for calculating the true state of the system is: ; In the formula, The system represents the actual state; G is the graph filter. This is sparse observation data; The formula for calculating the attack residual estimation result is as follows: ; In the formula, This is the result of the attack residual estimation.

[0044] In this embodiment, in step S3, based on the actual state of the system and the attack residual estimation result, the frequency measurement value is compensated for the attack to obtain the compensated frequency deviation information; based on the compensated frequency deviation information, the preset performance controller is activated by the linear variable parameter condition; the preset performance controller constrains the transient behavior of the frequency deviation and outputs the preset performance control command.

[0045] Specifically, the attack residual estimate obtained in step S2 is used as a correction value to perform a subtraction compensation operation on the original frequency measurement value, eliminating the superimposed spurious attack components and restoring the compensated frequency deviation information that reflects the true operating condition of the system. Based on this compensated frequency deviation, the normalized error is calculated in conjunction with the preset performance envelope function. The normalized error is used as the basis for scheduling and activation of the linear variable parameter preset performance controller. The controller triggers the corresponding gain adjustment rule according to the interval in which the normalized error is located. The controller adopts a proportional-integral control law, combined with the linear variable parameter base gain and adaptive adjustment coefficient, to constrain transient indicators such as frequency deviation overshoot and settling time, while outputting corresponding local preset performance control commands, providing a local control basis for subsequent coordinated control.

[0046] The expression for the compensated frequency deviation information is as follows: ; In the formula, This provides the frequency deviation information for the i-th region after compensation. This represents the original frequency measurement value for the i-th region; This represents the attack residual estimation result for the i-th region.

[0047] In this embodiment, during the process of activating the preset performance controller based on the compensated frequency deviation information and the linear variable parameter condition, a gain saturation mechanism is introduced to control the preset performance controller. When the absolute value of the normalized error is less than the activation threshold, the system is determined to be operating in the steady-state region, and the preset performance controller adopts a low-gain linear control mode. When the absolute value of the normalized error is not less than the activation threshold, the system enters the transient region, triggering the preset performance control enhancement mechanism. By adaptively increasing the control gain, the system frequency deviation is ensured to meet the preset performance constraint requirements.

[0048] The conditional activation function expression for the linear variable parameter condition is: ; ; In the formula, Conditionally activate the adaptive gain function; The normalized error signal for the i-th region; The conditional activation threshold; This is the saturation threshold; This is the maximum gain amplification factor; This is the performance envelope function; Let be the frequency deviation of the i-th control region.

[0049] In this embodiment, let , , The dynamic model of the preset performance controller can be described as follows: (The states, disturbances, and measurement outputs are used for the PPC, respectively.) ; ; In the formula, Let be the state derivative of the PPC subsystem in region i; The state vector of the PPC subsystem; The system matrix is ​​a linear variable parameter system; The scheduling parameters are an uncertain parameter vector containing the inertial constant and damping coefficient; The input matrix; For control input; Here is the perturbation matrix; For disturbance terms; This refers to the output of the PPC subsystem. This is the output matrix; Injecting attack items into fake data; This refers to the noise measurement term.

[0050] In this embodiment, due to frequency measurement The controller may be vulnerable to FDIA and uses attack estimation provided by the Graph Signal Processing (GSP) module. The measurements are compensated to obtain a frequency estimate for the controller: ; The local control gain adopts an LPV base gain and conditional activation enhancement structure, and the expression of the preset performance control command is: ; In the formula, This refers to the local preset performance control instructions for the i-th region; , These are the proportional gain and integral gain, which are dynamically adjusted according to the scheduling parameters and normalization error, respectively. This is for the comprehensive testing volume of emergency resection in the region; , It is the linearly variable parameter fundamental gain matrix.

[0051] In this embodiment, in step S4, frequency state deviation information between adjacent regions is calculated based on the compensated frequency deviation of each region; based on the preset performance control command and the frequency state deviation information, a distributed consistency coordination protocol is designed and a frequency synchronization compensation signal is generated to realize the frequency collaborative control of the entire power system in multiple regions.

[0052] Specifically, the reliable frequency deviation of each region after attack compensation is extracted. For adjacent regions with direct interconnection, the difference in frequency deviation after compensation is calculated. This difference is the frequency state deviation information that characterizes the degree of frequency imbalance between regions.

[0053] The formula for calculating the frequency state deviation information between adjacent regions is as follows: ; In the formula, This refers to the frequency state deviation information between the i-th region and the j-th region; The compensated frequency deviation for the i-th region; The frequency deviation after compensation in region j.

[0054] Based on the frequency state deviation, a distributed consistency coordination protocol is designed. By performing a weighted summation of the frequency state deviations of adjacent regions, a coordination control term capable of driving regional frequencies towards consistency is constructed. This coordination control term is used as a frequency synchronization compensation signal and superimposed and fused with the local preset performance control command obtained in step S3 to form a total control signal that takes into account both local frequency constraints and inter-regional coordination. Each region performs iterative consistency adjustment through distributed information interaction, gradually reducing the frequency differences between regions. Ultimately, under the premise of resisting false data injection attacks, the coordinated and stable operation of the entire network frequency of the multi-regional interconnected power system is achieved.

[0055] The expression for the frequency synchronization compensation signal is as follows: ; In the formula, This is the final overall control command for the i-th region; These are distributed consistency coordination and control instructions. For damping control commands; The set of regions adjacent to region i; For linearly variable parameter damping gain.

[0056] In one possible implementation, a verification example is provided as follows: The test system uses a three-zone LFC system to illustrate the feasibility and superiority of the GSP scheme, such as... Figure 3As shown. The measured values ​​sent to the controller are used as attack targets. By injecting false data and tampering with the measurement signals, the attacker can choose to attack any of the three regions. First, the effectiveness of the proposed strategy in defending against FDI attacks was verified. Then, in MATLAB 2024b, the controller for the three-region LFC system was designed using YALMIP and SeDuMi. Detailed system parameters are shown in Table 1. The hardware configuration includes an Intel Core Ultra 5 225F processor (base frequency 3.3 GHz) and an RT-LABOP5600 real-time emulator.

[0057] Table 1 Parameters of the Three-Region Power System

[0058] In this example, the GSP method essentially relies on reliable information from unattacked regions to reconstruct the state of attacked regions. Therefore, the fewer healthy nodes there are, the more limited the topological redundancy available for state recovery becomes, making the estimation task more challenging. Based on this, this invention employs a three-region interconnected system and implements FDIA on one of the regions. The system is in an extreme condition of 'low redundancy observation', with a total simulation duration of 30 seconds. The attack scenario is set as follows: at 2 seconds, region 1 experiences a 0.01 pu perturbation; during system recovery, at 3 seconds, it suffers a 0.01 pu step FDI attack, while the measurement channel exhibits Gaussian noise with a standard deviation of 0.5 MHz. In the simulation of frequency control under a 30-second network attack in the study area, FDIA detection was performed using detection statistics. The proposed method showed good detection performance under four different attack types. It achieved 100% detection for step attacks, 94.2% for ramp attacks, and over 80% for sinusoidal attacks. The lowest detection rate (72.7%) was observed for random attacks due to the random perturbation of the attack quantity. Regarding estimation performance, the ramp FDIA estimation error was the smallest at 1.644 × 10⁻³ p.u., the random attack estimation error was the largest at 2.866 × 10⁻³ p.u., and the step attack estimation error was the smallest at 17.5%. Despite significant differences in the three test scenarios under parameter uncertainty and FDIA, the proposed pre-defined performance control method still achieved asymptotic stability of ACE.

[0059] To visually demonstrate the frequency control effect of this invention under parameter uncertainty and FDIA, such as Figure 4 As shown, this is a comparison curve of the system frequency response and ACE change.

[0060] Depend on Figure 4As can be seen, despite the significant differences among the three test scenarios, the present invention can still achieve asymptotic stability of ACE, effectively constrain transient fluctuations in frequency deviation, and ensure multi-region frequency coordination and synchronization.

[0061] The results of this example verify that the present invention can suppress the impact of false data injection attacks through graph theory detection, strictly constrain frequency transient performance and ensure coordinated operation in multiple regions under the low inertia scenario of new energy, and has good engineering feasibility and application value.

[0062] The application scenarios of this invention are as follows: In scenarios where multi-regional interconnected power systems are subjected to false data injection attacks and the system experiences complex operating conditions such as low inertia of new energy sources and load disturbances, this invention effectively suppresses the interference of attacks on frequency control by combining graph signal processing to separate attack components, attack compensation, and adaptive variable gain control, thereby ensuring system frequency stability and multi-regional coordinated operation.

[0063] In scenarios where sparsely distributed measurement devices and a small number of healthy nodes in multi-regional power systems make state estimation and attack detection difficult, this invention relies on dynamic coupling graph models and graph filtering techniques to reconstruct the true state of the system using limited reliable topology information, thereby achieving effective detection and suppression of attacks.

[0064] In scenarios where multi-regional interconnected power grids need to balance local frequency constraints with network-wide coordinated control, and face parameter uncertainties and external disturbances, this invention constrains transient frequency deviation behavior through the combination of local preset performance control and distributed consistency coordination protocol, thereby achieving frequency synchronization in various regions and improving system operational stability.

[0065] In scenarios where power information and physical systems are highly integrated, and where false data injection attacks can easily tamper with frequency measurement signals and mislead control decisions, this invention eliminates the impact of attacks by estimating attack residuals and compensating for frequencies. At the same time, it adapts to dynamic changes in the system through a linear variable parameter activation mechanism, demonstrating good engineering feasibility.

[0066] It should be noted that the method of this disclosure embodiment can be executed by a single device, such as a computer or server. The method of this embodiment can also be applied to a distributed scenario, where multiple devices cooperate to complete the task. In such a distributed scenario, one of these devices may execute only one or more steps of the method of this disclosure embodiment, and the multiple devices will interact with each other to complete the method described.

[0067] It should be noted that the above description describes some embodiments of this disclosure. Other embodiments are within the scope of the appended claims. In some cases, the actions or steps recorded in the claims can be performed in a different order than that shown in the above embodiments and still achieve the desired result. Furthermore, the processes depicted in the drawings do not necessarily require a specific or sequential order to achieve the desired result. In some embodiments, multitasking and parallel processing are also possible or may be advantageous.

[0068] Example 2

[0069] See Figure 5 Embodiment 2 of the present invention also provides a power system frequency control device under a false data injection attack, comprising: The module 001 for constructing a dynamic coupled graph model and obtaining the graph Laplace matrix is ​​used to construct a graph topology based on the physical interconnection topology of a multi-regional power system and the load frequency control state space model. It defines each control region as a graph vertex and the dynamic coupling relationship between regions as graph edges. Based on the Frobenius norm of system matrix partitioning, it quantifies the dynamic coupling strength of the graph vertices to obtain a weighted adjacency matrix. Based on the graph topology and the weighted adjacency matrix, it constructs a dynamic coupled graph model of the multi-regional power system. It calculates the degree matrix based on the weighted adjacency matrix and calculates the graph Laplace matrix based on the weighted adjacency matrix and the degree matrix. The graph filter construction and processing module 002 is used to construct a graph filter based on the graph Laplacian matrix; separate the system's physical dynamics and spurious data injection attack components in the spectral domain using the graph filter to obtain the separation result; and obtain the system's true state and attack residual estimation results based on the separation result and sparse observation data. The preset performance controller activation and command output module 003 is used to perform attack compensation on the frequency measurement value based on the actual state of the system and the attack residual estimation result to obtain the compensated frequency deviation information; based on the compensated frequency deviation information, activate the preset performance controller through linear variable parameter conditions; constrain the transient behavior of frequency deviation through the preset performance controller and output the preset performance control command. The frequency synchronization compensation signal generation module 004 is used to calculate the frequency state deviation information between adjacent regions based on the compensated frequency deviation of each region; and to design a distributed consistency coordination protocol and generate a frequency synchronization compensation signal based on the preset performance control command and the frequency state deviation information, so as to realize the frequency collaborative control of the entire power system in multiple regions.

[0070] In this embodiment, in the dynamic coupling graph model construction and graph Laplacian matrix acquisition module 001, during the process of quantifying the dynamic coupling strength of the graph vertices based on the Frobenius norm of system matrix partitioning, the expression for the dynamic coupling weight between adjacent graph vertices is: ; In the formula, The dynamic coupling weights between regions i and j; and These are the block matrices representing the corresponding regions in the system state matrix; q is the Frobenius norm; p and q are the row and column indices of the matrix elements, respectively. The expressions for the degree matrix and the graph Laplacian matrix are as follows: ; ; In the formula, D is the degree matrix; Let be the degree value of region i; N is the total number of regions. is the weighted adjacency matrix; L is the graph Laplacian matrix; j is the region index.

[0071] In this embodiment, in the graph filter construction and processing module 002, the expression of the graph filter is: ; In the formula, g(λ) is the spectral response function; Adjust the filter parameters; G is the eigenvalue of the graph Laplacian matrix; G is the graph filter; Q is the eigenvector matrix obtained by the spectral decomposition of the graph Laplacian matrix; Q T is the transpose of the eigenvector matrix; N is the total number of control areas in the multi-regional power system; The formula for calculating the true state of the system is: ; In the formula, The system represents the actual state; G is the graph filter. This is sparse observation data; The formula for calculating the attack residual estimation result is as follows: ; In the formula, This is the result of the attack residual estimation.

[0072] In this embodiment, the expression for the compensated frequency deviation information in the preset performance controller activation and command output module 003 is as follows: ; In the formula, This provides the frequency deviation information for the i-th region after compensation. This represents the original frequency measurement value for the i-th region; This represents the attack residual estimation result for the i-th region; During the process of activating the preset performance controller based on the compensated frequency deviation information and the linear variable parameter condition, a gain saturation mechanism is introduced to control the preset performance controller. When the absolute value of the normalized error is less than the activation threshold, the system is determined to be operating in the steady-state region, and the preset performance controller adopts a low-gain linear control mode. When the absolute value of the normalized error is not less than the activation threshold, the system enters the transient region, triggering the preset performance control enhancement mechanism. By adaptively increasing the control gain, the system frequency deviation is ensured to meet the preset performance constraint requirements. The conditional activation function expression for the linear variable parameter condition is: ; ; In the formula, Conditionally activate the adaptive gain function; The normalized error signal for the i-th region; The conditional activation threshold; The saturation threshold; This is the maximum gain amplification factor; This is the performance envelope function; The frequency deviation of the i-th control region; The expression for the state-space model of the preset performance controller is: ; In the formula, Let be the state derivative of the PPC subsystem in region i; This is the state vector of the PPC subsystem; The system matrix is ​​a linear variable parameter system; For scheduling parameters; The input matrix; For control input; Here is the perturbation matrix; For disturbance terms; This refers to the output of the PPC subsystem. This is the output matrix; Injecting attack items into fake data; This refers to the noise measurement term.

[0073] In this embodiment, in the preset performance controller activation and instruction output module 003, the expression of the preset performance control instruction is: ; In the formula, This refers to the local preset performance control instructions for the i-th region; , These are the proportional gain and integral gain, which are dynamically adjusted according to the scheduling parameters and normalization error, respectively. This is for the comprehensive testing volume of emergency resection in the region; , It is the linearly variable parameter fundamental gain matrix.

[0074] In this embodiment, the formula for calculating the frequency state deviation information between adjacent regions in the frequency synchronization compensation signal generation module 004 is as follows: ; In the formula, This refers to the frequency state deviation information between the i-th region and the j-th region; The compensated frequency deviation for the i-th region; The frequency deviation after compensation in the j-th region; The expression for the frequency synchronization compensation signal is: ; In the formula, This is the final overall control command for the i-th region; These are distributed consistency coordination and control instructions. For damping control commands; The set of regions adjacent to region i; For linearly variable parameter damping gain.

[0075] It should be noted that the information interaction and execution process between the modules of the above system are based on the same concept as the method embodiment in Embodiment 1 of this application, and the resulting technical effects are the same as those in the method embodiment of this application. For details, please refer to the description in the method embodiment shown above in this application, and it will not be repeated here.

[0076] Example 3

[0077] Embodiment 3 of the present invention provides a non-transitory computer-readable storage medium storing program code for a power system frequency control method under a false data injection attack. The program code includes instructions for executing the power system frequency control method under a false data injection attack according to Embodiment 1 or any possible implementation thereof.

[0078] Computer-readable storage media can be any available medium that a computer can access, or a data storage device such as a server or data center that integrates one or more available media. The available medium can be magnetic media (e.g., floppy disks, hard disks, magnetic tapes), optical media (e.g., DVDs), or semiconductor media (e.g., solid-state drives (SSDs)).

[0079] Example 4

[0080] Embodiment 4 of the present invention provides an electronic device, including: a memory and a processor; The processor and the memory communicate with each other via a bus; the memory stores program instructions that can be executed by the processor, and the processor can execute the frequency control method for a power system under a false data injection attack according to Embodiment 1 or any possible implementation thereof by calling the program instructions.

[0081] Specifically, a processor can be implemented in hardware or software. When implemented in hardware, the processor can be a logic circuit, an integrated circuit, etc. When implemented in software, the processor can be a general-purpose processor that reads software code stored in memory. This memory can be integrated into the processor or located outside the processor and exist independently.

[0082] In the above embodiments, implementation can be achieved, in whole or in part, through software, hardware, firmware, or any combination thereof. When implemented in software, it can be implemented, in whole or in part, as a computer program product. The computer program product includes one or more computer instructions. When the computer program instructions are loaded and executed on a computer, all or part of the processes or functions described in the embodiments of the present invention are generated. The computer can be a general-purpose computer, a special-purpose computer, a computer network, or other programmable system. The computer instructions can be stored in a computer-readable storage medium or transmitted from one computer-readable storage medium to another. For example, the computer instructions can be transmitted from one website, computer, server, or data center to another via wired (e.g., coaxial cable, fiber optic, digital subscriber line (DSL)) or wireless (e.g., infrared, wireless, microwave, etc.) means.

[0083] It is obvious to those skilled in the art that the modules or steps of the present invention described above can be implemented using general-purpose computing systems. They can be centralized on a single computing system or distributed across a network of multiple computing systems. Optionally, they can be implemented using program code executable by a computing system, thereby storing them in a storage system for execution by the computing system. In some cases, the steps shown or described can be performed in a different order than those presented herein, or they can be fabricated as separate integrated circuit modules, or multiple modules or steps can be fabricated as a single integrated circuit module. Thus, the present invention is not limited to any particular combination of hardware and software.

[0084] Although the present invention has been described in detail above with general descriptions and specific embodiments, modifications or improvements can be made to it, which will be obvious to those skilled in the art. Therefore, all such modifications or improvements made without departing from the spirit of the present invention fall within the scope of protection claimed by the present invention.

Claims

1. A method for frequency control of a power system under a false data injection attack, characterized in that, include: Based on the physical interconnection topology of a multi-regional power system and the state space model of load frequency control, each control region is defined as a graph vertex and the dynamic coupling relationship between regions is defined as a graph edge, forming a graph topology. The dynamic coupling strength of the graph vertices is quantified based on the Frobenius norm of system matrix partitioning to obtain the weighted adjacency matrix. Based on the graph topology and the weighted adjacency matrix, a dynamic coupled graph model of a multi-regional power system is constructed. The degree matrix is ​​calculated based on the weighted adjacency matrix. The graph Laplacian matrix is ​​calculated based on the weighted adjacency matrix and the degree matrix. Construct a graph filter based on the graph Laplacian matrix; The graph filter is used to separate the system's physical dynamics from the spoof data injection attack components in the spectral domain to obtain the separation result; Based on the separation results and sparse observation data, the system's true state and attack residual estimation results are obtained; Based on the actual state of the system and the attack residual estimation results, attack compensation is performed on the frequency measurement values ​​to obtain the compensated frequency deviation information. Based on the compensated frequency deviation information, a preset performance controller is activated by a linear variable parameter condition; the preset performance controller constrains the transient behavior of the frequency deviation and outputs a preset performance control command. Based on the compensated frequency deviation of each region, frequency state deviation information between adjacent regions is calculated; based on the preset performance control command and the frequency state deviation information, a distributed consistency coordination protocol is designed and a frequency synchronization compensation signal is generated to realize the frequency collaborative control of the entire power system in multiple regions.

2. The power system frequency control method under a false data injection attack according to claim 1, characterized in that, In the process of quantifying the dynamic coupling strength of the graph vertices based on system matrix block Frobenius norm, the expression for the dynamic coupling weight between adjacent graph vertices is: ； In the formula, The dynamic coupling weights between regions i and j; and These are the block matrices representing the corresponding regions in the system state matrix; q is the Frobenius norm; p and q are the row and column indices of the matrix elements, respectively. The expressions for the degree matrix and the graph Laplacian matrix are as follows: ； ； In the formula, D is the degree matrix; Let be the degree value of region i; N is the total number of regions. is the weighted adjacency matrix; L is the graph Laplacian matrix; j is the region index.

3. The power system frequency control method under a false data injection attack according to claim 2, characterized in that, The expression for the graph filter is: ； In the formula, g(λ) is the spectral response function; Adjust the filter parameters; Let G be the eigenvalues ​​of the graph Laplacian matrix; G be the graph filter; and Q be the eigenvector matrix obtained by the spectral decomposition of the graph Laplacian matrix. Q T is the transpose of the eigenvector matrix; N is the total number of control areas in the multi-regional power system; The formula for calculating the true state of the system is: ； In the formula, The system represents the actual state; G is the graph filter. This is sparse observation data; The formula for calculating the attack residual estimation result is as follows: ； In the formula, This is the result of the attack residual estimation.

4. The power system frequency control method under a false data injection attack according to claim 3, characterized in that, The expression for the compensated frequency deviation information is: ； In the formula, This provides the frequency deviation information for the i-th region after compensation. This represents the original frequency measurement value for the i-th region; This represents the attack residual estimation result for the i-th region; During the process of activating the preset performance controller based on the compensated frequency deviation information and the linear variable parameter condition, a gain saturation mechanism is introduced to control the preset performance controller. When the absolute value of the normalized error is less than the activation threshold, the system is determined to be operating in the steady-state region, and the preset performance controller adopts a low-gain linear control mode. When the absolute value of the normalized error is not less than the activation threshold, the system enters the transient region, triggering the preset performance control enhancement mechanism. By adaptively increasing the control gain, the system frequency deviation is ensured to meet the preset performance constraint requirements. The conditional activation function expression for the linear variable parameter condition is: ； ； In the formula, Conditionally activate the adaptive gain function; The normalized error signal for the i-th region; The conditional activation threshold; The saturation threshold; This is the maximum gain amplification factor; This is the performance envelope function; The frequency deviation of the i-th control region; The expression for the state-space model of the preset performance controller is: ； In the formula, Let be the state derivative of the PPC subsystem in region i; This is the state vector of the PPC subsystem; The system matrix is ​​a linear variable parameter system; For scheduling parameters; The input matrix; For control input; Here is the perturbation matrix; For disturbance terms; This refers to the output of the PPC subsystem. This is the output matrix; Injecting attack items into fake data; This refers to the noise measurement term.

5. A power system frequency control method under a false data injection attack according to claim 4, characterized in that, The expression for the preset performance control instruction is: ； In the formula, This refers to the local preset performance control instructions for the i-th region; , These are the proportional gain and integral gain, which are dynamically adjusted according to the scheduling parameters and normalization error, respectively. This is for the comprehensive testing volume of emergency resection in the region; , It is the linearly variable parameter fundamental gain matrix.

6. A power system frequency control method under a false data injection attack according to claim 5, characterized in that, The formula for calculating the frequency state deviation information between adjacent regions is: ； In the formula, This refers to the frequency state deviation information between the i-th region and the j-th region; The compensated frequency deviation for the i-th region; The frequency deviation after compensation in the j-th region; The expression for the frequency synchronization compensation signal is: ； In the formula, This is the final overall control command for the i-th region; These are distributed consistency coordination and control instructions. For damping control commands; The set of regions adjacent to region i; For linearly variable parameter damping gain.

7. A power system frequency control device under a spoofing data injection attack, employing the power system frequency control method under a spoofing data injection attack as described in any one of claims 1-6, characterized in that, include: The module for constructing a dynamic coupled graph model and obtaining the graph Laplace matrix is ​​used to define each control region as a graph vertex and the dynamic coupling relationship between regions as a graph edge based on the physical interconnection topology of a multi-regional power system and the load frequency control state space model, thereby forming a graph topology structure; the module quantifies the dynamic coupling strength of the graph vertices based on the Frobenius norm of system matrix partitioning to obtain the weighted adjacency matrix; Based on the graph topology and the weighted adjacency matrix, a dynamic coupled graph model of a multi-regional power system is constructed. The degree matrix is ​​calculated based on the weighted adjacency matrix. The graph Laplacian matrix is ​​calculated based on the weighted adjacency matrix and the degree matrix. The graph filter construction and processing module is used to construct a graph filter based on the graph Laplacian matrix. The graph filter is used to separate the system's physical dynamics from the spoof data injection attack components in the spectral domain to obtain the separation result; Based on the separation results and sparse observation data, the system's true state and attack residual estimation results are obtained; The preset performance controller activation and command output module is used to perform attack compensation on the frequency measurement value based on the actual state of the system and the attack residual estimation result to obtain the compensated frequency deviation information; activate the preset performance controller through linear variable parameter conditions based on the compensated frequency deviation information; constrain the transient behavior of frequency deviation through the preset performance controller and output the preset performance control command. The frequency synchronization compensation signal generation module is used to calculate the frequency state deviation information between adjacent regions based on the compensated frequency deviation of each region; and to design a distributed consistency coordination protocol and generate a frequency synchronization compensation signal based on the preset performance control command and the frequency state deviation information, so as to realize the frequency collaborative control of the entire power system in multiple regions.

8. A power system frequency control device under a false data injection attack according to claim 7, characterized in that, In the module for constructing the dynamic coupled graph model and obtaining the graph Laplacian matrix, during the process of quantifying the dynamic coupling strength of the graph vertices based on the Frobenius norm of system matrix partitioning, the expression for the dynamic coupling weight between adjacent graph vertices is: ； In the formula, The dynamic coupling weights between regions i and j; and These are the block matrices representing the corresponding regions in the system state matrix; q is the Frobenius norm; p and q are the row and column indices of the matrix elements, respectively. The expressions for the degree matrix and the graph Laplacian matrix are as follows: ； ； In the formula, D is the degree matrix; Let be the degree value of region i; N is the total number of regions. is the weighted adjacency matrix; L is the graph Laplacian matrix; j is the region index.

9. A power system frequency control device under a false data injection attack according to claim 8, characterized in that, In the graph filter construction and processing module, the expression of the graph filter is: ； In the formula, g(λ) is the spectral response function; Adjust the filter parameters; G is the eigenvalue of the graph Laplacian matrix; G is the graph filter; Q is the eigenvector matrix obtained by the spectral decomposition of the graph Laplacian matrix; Q T is the transpose of the eigenvector matrix; N is the total number of control areas in the multi-regional power system; The formula for calculating the true state of the system is: ； In the formula, The system represents the actual state; G is the graph filter. This is sparse observation data; The formula for calculating the attack residual estimation result is as follows: ； In the formula, This is the result of the attack residual estimation.

10. A power system frequency control device under a false data injection attack according to claim 9, characterized in that, In the preset performance controller activation and command output module, the expression for the compensated frequency deviation information is: ； In the formula, This provides the frequency deviation information for the i-th region after compensation. This represents the original frequency measurement value for the i-th region; This represents the attack residual estimation result for the i-th region; During the process of activating the preset performance controller based on the compensated frequency deviation information and the linear variable parameter condition, a gain saturation mechanism is introduced to control the preset performance controller. When the absolute value of the normalized error is less than the activation threshold, the system is determined to be operating in the steady-state region, and the preset performance controller adopts a low-gain linear control mode. When the absolute value of the normalized error is not less than the activation threshold, the system enters the transient region, triggering the preset performance control enhancement mechanism. By adaptively increasing the control gain, the system frequency deviation is ensured to meet the preset performance constraint requirements. The conditional activation function expression for the linear variable parameter condition is: ； ； In the formula, Conditionally activate the adaptive gain function; The normalized error signal for the i-th region; The conditional activation threshold; The saturation threshold; This is the maximum gain amplification factor; This is the performance envelope function; The frequency deviation of the i-th control region; The expression for the state-space model of the preset performance controller is: ； In the formula, Let be the state derivative of the PPC subsystem in region i; This is the state vector of the PPC subsystem; The system matrix is ​​a linear variable parameter system; For scheduling parameters; The input matrix; For control input; Here is the perturbation matrix; For disturbance terms; This refers to the output of the PPC subsystem. This is the output matrix; Injecting attack items into fake data; For measuring noise; In the preset performance controller activation and instruction output module, the expression of the preset performance control instruction is: ； In the formula, This refers to the local preset performance control instructions for the i-th region; , These are the proportional gain and integral gain, which are dynamically adjusted according to the scheduling parameters and normalization error, respectively. This is for the comprehensive testing volume of emergency resection in the region; , The fundamental gain matrix is ​​a linear variable parameter matrix; In the frequency synchronization compensation signal generation module, the formula for calculating the frequency state deviation information between adjacent regions is as follows: ； In the formula, This refers to the frequency state deviation information between the i-th region and the j-th region; The compensated frequency deviation for the i-th region; The frequency deviation after compensation in the j-th region; The expression for the frequency synchronization compensation signal is: ； In the formula, This is the final overall control command for the i-th region; These are distributed consistency coordination and control instructions. For damping control commands; The set of regions adjacent to region i; For linearly variable parameter damping gain.

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