FDI attack-oriented distributed security and stability control method for DC microgrid

Abstract

The invention discloses an FDI attack-oriented distributed security and stability control method for a direct-current micro-grid, and relates to the field of micro-grid control, and the method comprises the steps: achieving a control target according to different time scales based on a hierarchical control architecture of the direct-current micro-grid, constructing a distributed power generation unit model, defining the dynamic states of a primary controller and a secondary controller, and designing an FDI attack model; under the bounded FDI attack, a safety-critical secondary controller is developed based on a robust CBF; the CLF is constructed in combination with the conditions of voltage balance and current balance to ensure that the DC micro-grid can recover to a stable state after attack, so that the stability of the system is maintained; and solving a new secondary controller meeting robust CBF and CLF constraints by adopting a quadratic programming method. According to the technical scheme provided by the invention, the distributed secondary control target of the DC micro-grid can still be realized even under the FDI attack, and the safety and stability of the DC micro-grid when facing the FDI attack from a communication network are improved.

Description

Technical Field

[0001] The present invention relates to the technical field of microgrid control, and particularly to a distributed security and stability control method for a DC microgrid against FDI attacks. Background Art

[0002] Due to its efficient power management, easy control, and compatibility with modern DC loads, DC microgrids have been widely applied in fields such as renewable energy integration, electric vehicle charging stations, and data centers. However, the commonly used hierarchical control structure in DC microgrids integrates the communication network layer, local control layer, and physical device layer through communication channels, making DC microgrids vulnerable to network attacks and intrusions. In particular, the communication-dependent secondary control structure implemented through distributed control makes DC microgrids face a greater risk of network attacks, which may disrupt power balance, reduce operating stability, and even lead to serious system failures. Existing resilience control methods in DC microgrids mainly consider from the perspective of stabilizing the system state, which ensures that the trajectories of DC microgrid states (such as voltage and current) can converge to the equilibrium point after being attacked, but do not consider the instantaneous security issues of the system, such as transient voltage overshoot that may damage the load. Summary of the Invention

[0003] The purpose of the present invention is to propose a distributed security and stability control method for a DC microgrid against FDI attacks in view of the deficiencies of the prior art.

[0004] The purpose of the present invention is achieved through the following technical solutions: A distributed security and stability control method for a DC microgrid against FDI attacks, comprising:

[0005] S1. Based on the hierarchical control architecture of the DC microgrid, achieve control objectives according to different time scales, construct a DGU unit model, define the dynamics of the primary and secondary controllers, where the control frequency of the secondary controller is lower than that of the primary controller and a distributed control scheme is adopted, and construct an FDI attack model for the secondary control communication link;

[0006] S2. Construct a CBF-constrained safety set, and then construct the conditions constrained by CBF according to the upper limit of the attack vector amplitude and time limit in the attack model to ensure within the safety set specified by CBF;

[0007] S3. Construct a CLF constraint according to the steady-state expressions for achieving voltage balance and current sharing in the DC microgrid, so that the DC microgrid system can restore a stable state after being attacked;

[0008] S4. According to the constructed robust CBF and CLF constraints, obtain a new secondary controller based on dynamic constraint optimization; use the new secondary controller for distributed security and stability control against FDI attacks.

[0009] Furthermore, the DGU unit model specifically includes:

[0010] Based on the hierarchical control architecture of the DC microgrid, a sub-DGU model is constructed:

[0011]

[0012] where V i is the voltage of the DGU at the point of common coupling, I l =(V i -V j ) / R l is the line current, where R l is the resistance of the line, V ti is the control input of the transformer, I ti is the output current of the DGU, I Li is the load current; R ti , L ti and C ti are the resistance, inductance and capacitance parameters of the converter respectively, represents the edge connecting the DGU, represents a set of N DGUs.

[0013] Furthermore, the dynamics of the primary and secondary controllers include:

[0014] V ti =u i +g i ψ i ;

[0015] where u i =k 1,i V i +k 2,i I i +k 3,i v i is the primary controller; where k 1,i , k 2,i and k 3,i represent the gains of the feedback control; ψ i is the secondary controller, whose control frequency is lower than that of the primary control. The secondary control adopts a distributed control scheme, and its dynamics are:

[0016]

[0017] where is the rated current corresponding to DGU i, is the set of neighbors in the communication network of DGU i, and τ represents the time delay of the secondary control relative to the primary control.

[0018] Furthermore, the FDI attack model for the secondary control communication link includes:

[0019]

[0020] wherein, is the output current of DGU i after being attacked, φ i,j is the attack vector injected by the adversary, and β i,j (t - t a ) is a step function that activates the attack at t = t a .

[0021] Furthermore, the construction of the CBF constraint safety set includes:

[0022] Construct the safety set for each DGU i: The load needs to satisfy the safety constraint: Thus, the safety set is constructed as:

[0023]

[0024] In the formula, h i,1 = V i - V i , V i is the voltage of the DGU at the point of common coupling, V i and are the upper and lower limits of V i ; The set ensures safety within the framework of set invariance, ensuring that the state of the system always remains within the predefined safety set.

[0025] Furthermore, the CBF constraint includes:

[0026] Construct the CBF of relative degree 2 by recursively defining the CBF of relative degree 2 for each DGU i: B li and B hi respectively represent the CBFs defined based on the lower and upper bounds of the load voltage, and B li and B hi are respectively:

[0027] B li = I ti + ξ i - G pi V i

[0028]

[0029] Construct the new safety set as:

[0030]

[0031] In the formula, is the coupling term between DGU i and its neighbor nodes; represents the edge connecting the DGUs, represents a set of N DGUs; is used to express the relationship between the DGUs and the edges. The element indicates that DGU i is the source of edge l; indicates that DGU i is the sink of edge l;

[0032] Satisfy the conditions of the CBF and guarantee the forward invariance of the sets and to ensure that the DC microgrid system is within the safety set specified by the CBF.

[0033] Furthermore, the construction process of the CLF constraint includes:

[0034] Let represent the stable state of each DGU, and the steady-state error is expressed as Construct the CLF:

[0035]

[0036] where γ i = θ 3,i - θ 1,i θ 2,i ,

[0037] Furthermore, construct the CLF constraint as:

[0038]

[0039] where and k 1,i 、k 2,i and k 3,i represent the gains of the feedback control in the primary controller; C ti is the capacitance parameter of the converter, and L ti is the inductance parameter of the converter.

[0040] Furthermore, the new secondary controller specifically obtained based on the constructed robust CBF and CLF constraints through dynamic constraint optimization is:

[0041] Modify the nominal secondary controller ψ i in the least invasive way while ensuring safety, stability, and real-time feasibility, to obtain the following QP-based optimization problem:

[0042]

[0043] Among them, δ i is the slack variable, and p i represents the penalty coefficient; solving this optimization problem using QP yields a new secondary controller; V i is the voltage of the DGU at the point of common coupling, R ti is the resistance of the converter,, i is the coupling term between the DGU i and its neighboring nodes, and li is the adjustment parameter of the class function in the CBF ;

[0044] In addition, the time delay τ of the secondary control needs to satisfy τ < τ ref to ensure the convergence of the system, where τ ref = π / (2λ max (L c )) is the maximum delay margin for an undirected graph network to converge.

[0045] On the other hand, a distributed security and stability control device for a DC microgrid against FDI attacks is also provided, including a memory and one or more processors. Executable code is stored in the memory, and when the processor executes the executable code, the distributed security and stability control method for a DC microgrid against FDI attacks as described above is implemented.

[0046] On the other hand, a computer-readable storage medium is also provided, on which a program is stored. When the program is executed by a processor, the distributed security and stability control method for a DC microgrid against FDI attacks as described above is implemented.

[0047] Advantages of the present invention: Compared with the existing elastic control methods in DC microgrids, more are considered from the perspective of stabilizing the system state. The present invention considers the instantaneous state security of the DC microgrid, and designs an elastic distributed secondary controller based on a robust CBF for the microgrid under bounded FDI attacks. This strategy not only complies with the delay margin constraint related to secondary control communication, but also ensures the security of the DC microgrid by implementing strict transient security conditions. In addition, by analyzing the voltage balance and current sharing conditions, the present invention constructs a CLF based on the equilibrium point to ensure that the DC microgrid can return to a stable state after an attack, thereby maintaining the stability of the system. Description of the Drawings

[0048] Figure 1 is a schematic diagram of the hierarchical control structure of the DC microgrid provided by the embodiment of the present invention;

[0049] Figure 2is the voltage and current response diagram of the DC microgrid provided by the embodiment of the present invention when the attack vector is φ 2,3 = 1.8 under resilient control and without resilient control;

[0050] Figure 3 is the voltage and current response diagram of the DC microgrid provided by the embodiment of the present invention when the attack vector is φ 2,3 = 3.3 under resilient control and without resilient control;

[0051] Figure 4 is the heat map composed of the voltage V i and the safety boundary B li and B hi ;

[0052] Figure 5 is the schematic diagram of the device of the present invention;

[0053] Figure 6 is the schematic diagram of the method flow of the present invention. Detailed implementation manners

[0054] To better understand the technical solution of the present application, the embodiments of the present application will be described in detail below with reference to the accompanying drawings.

[0055] It should be clear that the described embodiments are only a part of the embodiments of the present application, rather than all of the embodiments. All other embodiments obtained by those of ordinary skill in the art based on the embodiments in the present application without creative efforts shall fall within the protection scope of the present application.

[0056] The embodiment of the present invention provides a distributed security and stability control method for a DC microgrid facing FDI attacks. The method includes steps such as DGU and attack modeling, designing a robust control barrier function (CBF) constraint, designing a control Lyapunov function (CLF) constraint based on the equilibrium point, solving a dynamic constraint optimization problem, and experimental verification. The process is as Figure 6 shown. The specific implementation manners of each step will be elaborated below.

[0057] Step 1: DGU and attack modeling. Figure 1 is the schematic diagram of the hierarchical control structure of the DC microgrid of the present invention. Based on the hierarchical control architecture of the DC microgrid, the control objectives are achieved according to different time scales, a DGU model is constructed, the dynamics of the primary and secondary controllers are defined, and an FDI attack model is designed. Figure 1 The electrical network in the DCmG shown in is represented as an undirected graph where represents a set of N DGUs, andij Connect the source node DGU i to the sink node DGU j, indexed by l ∈ {1,..., M}, where M = |ε el |. Define the incidence matrix where the element indicates that DGU i is the source of edge l; if indicates that DGU i is the sink of edge l. The communication network is represented by the graph where is the set of nodes corresponding to the DGUs, and ε c represents the communication links.

[0058] Based on the hierarchical control architecture of the DC microgrid, construct the DGU model:

[0059]

[0060] In Equation (1), V i is the voltage of the DGU at the point of common coupling, I l = (V i - V j ) / R l is the line current, where R l is the resistance of the line, V ti is the control input of the transformer, I ti is the output current of the DGU, I Li is the load current. R ti , L ti and C ti are the resistance, inductance, and capacitance parameters of the converter, respectively.

[0061] Define the dynamics of the primary and secondary controllers at different time scales:

[0062] V ti = u i + g i ψ i ; (2)

[0063] In Equation (2), u i = k 1,i V i + k 2,i I i + k 3,i v i is the primary controller, where k 1,i , k 2,i and k 3,i represent the gains of the feedback control respectively; g i is the control coefficient of the secondary control, ψ i is the secondary controller, whose control frequency is lower than that of the primary control. The secondary control adopts a distributed control scheme, and its dynamics are:

[0064]

[0065] In Equation (3), is the rated current corresponding to DGU i, is the set of neighbors in the communication network of DGU i, and τ represents the time delay of the secondary control relative to the primary control.

[0066] Combining (1)-(3), the closed-loop expression of the DGU model is:

[0067]

[0068] The FDI attack of the attacker against the communication link of the secondary control is modeled as:

[0069]

[0070] In Equation (4), is the output current of DGU i after being attacked, φ i,j is the attack vector injected by the opponent, and β i,j (t - t a ) is a step function that activates the attack at t = t a .

[0071] Step 2: Design a robust CBF constraint.

[0072] Step 2.1, construct the safety set for each DGU i: The load needs to satisfy the safety constraint: Thus, construct the safety set:

[0073]

[0074] h in Equation (5) i,1 = V i - V i , The set can ensure safety within the framework of set invariance, guaranteeing that the state of the system always remains within the predefined safety set.

[0075] Step 2.2, construct a CBF with a relative degree of 1: The present invention uses a robust CBF as a method to adjust the existing secondary controller to ensure that the system state remains within the range of the predefined safety set over time. Let b li = V i - V i and be set as candidate CBFs. Differentiating b li and b hi yields:

[0076]

[0077] In Equation (6), is the coupling term between DGU i and its neighbor nodes, and Y Li is the load conductance. Since there is no explicit relationship between the derivative of the CBF and the secondary controller, it is necessary to design a CBF with a relative degree of 2.

[0078] Let By choosing as type of function, satisfying the conditions of the CBF requires which is equivalent to:

[0079]

[0080] Similarly, is equivalent to

[0081]

[0082] Step 2.3, construct a CBF with a relative degree of 2: By recursively defining the CBF with a relative degree of 2 for each DGU i, where B li and B hi represent the CBFs defined based on the lower and upper bounds of the load voltage respectively, and B li and B hi are respectively:

[0083] B li = I ti + ξ i - G pi V i

[0084]

[0085] Construct a new safety set as:

[0086]

[0087] Select and as type of function, where η li > 0 and η hi < 0 are adjustment parameters. Due to the attacker being restricted by the attack resources, the amplitude of the attack vector injected by the attacker has an upper bound, that is, |φ i,j | is bounded; and the attack vector can only be injected within a limited time. Then there exists a constant upper bound ω ij > 0 such that where Γ represents the duration of the attack. Therefore, the conditions of the CBF are satisfied Equivalent to:

[0088]

[0089] Similarly, is equivalent to

[0090]

[0091] By and ensuring the forward invariance of the set to further ensure the forward invariance of and ensure that the DC microgrid system is within the safety set specified by CBF.

[0092] Step 3: Design the CLF constraints.

[0093] Step 3.1 Derive the steady-state expressions for the DC microgrid to achieve voltage balance and current sharing: The compact set of the complete dynamics of the DC microgrid can be expressed as follows:

[0094]

[0095] where and In addition, V, I t , v, V ref , ψ, θ1, θ2, θ3, θ4 are the vector forms of the PCC voltage, filter output current, integrator state, load current, load power, reference voltage, secondary controller, and intermediate parameter θ 1,i , θ 2,i , θ 3,i , θ 4,i respectively, and the matrices R, C t , Y L are the diagonal matrices collecting the electrical parameters R L , C ti and Y Li respectively. The steady-state solution of the microgrid system (1) needs to satisfy:

[0096]

[0097] In Equation (8), L c is the Laplacian matrix of the communication network graph G c , is the vector of rated currents.

[0098] Step 3.2, construct the CLF according to the steady-state solution expression of the DC microgrid and the conditions of voltage balance and current sharing. The specific steps are as follows:

[0099] According to formula (8), the expression of the steady-state component of system (7) is derived as:

[0100]

[0101]

[0102] Then, according to (9) and (10), the equilibrium state of each DGU can be obtained. According to (11) and (12), the equilibrium state and The dynamics of each DGUi can be written as:

[0103]

[0104] In formula (13), B i = [0, θ 4,i , 0] T And

[0105] Let represent the stable state of each DGU, and the steady-state error can be expressed as Then, a CLF can be constructed:

[0106]

[0107] where γ i = θ 3,i - θ 1,i θ 2,i , Furthermore, the CLF constraint is constructed as:

[0108]

[0109] where and

[0110] Step 4: Solve the dynamic constraint optimization problem. To modify the nominal secondary controller ψ i in the least invasive way while ensuring safety, stability, and real-time feasibility, we obtain the following quadratic programming (QP)-based optimization problem:

[0111]

[0112] where δ i is a slack variable introduced to prevent the CLF constraint from being too conservative, and p i represents the penalty coefficient. Solving this optimization problem using QP gives a new secondary controller. In addition, the time delay τ of the secondary control needs to satisfy τ < τref to ensure the convergence of the system, where τ ref = π / (2λ max (L c )) is the maximum delay margin for an undirected graph network to converge.

[0113] Step 5: Experimental verification. The feasibility and robustness of the resilient distributed control strategy for a DC microgrid against FDI attacks based on robust CBF-CLF are verified through a hardware experimental platform. Specifically, a DC microgrid composed of four DGUs has been constructed for communication and computing constraints. Data transmission is achieved through Raspberry Pi units, which establish TCP / IP Modbus communication links to simulate the communication network of the DC microgrid. Modbus TCP / IP communication runs between the server and the client. To collect information from other DGUs, each controller sets up its own server for clients to access. In addition, the clients accessing its server can update the data stored there. It should be noted that the hardware-in-the-loop experimental platform and the Raspberry Pi controllers are set within the same subnet. In the real-time simulation system, each DGU collects its local state information and sends the data to the target controller through the channel assigned to its corresponding ID. Communication between the controllers allows sharing of local information, thus enabling the distributed resilient secondary control algorithm. Finally, the secondary control signal is sent back to the corresponding DGUs in the hardware-in-the-loop experimental platform through the specified channel.

[0114] Using the controller designed by the method of the present invention, the safe range of the DC microgrid load is set to [47.5V, 48.5V]. Figure 2 is and Figure 3 respectively show the voltage and current responses of the DC microgrid after being subjected to FDI attacks under the influence of a single attack vector φ 2,3 = 1.8 and multiple attack vectors φ 2,3 = 2.8, and φ 4,1 = 1.5. The left subplots in both figures show the system performance without the resilient controller. Without resilient control, the voltage rapidly deviates from its stable value after the attack is activated and cannot recover to the original balance. The current sharing is also disturbed, and the current fluctuates significantly, indicating that the system loses its load current sharing ability. In contrast, the right subplots show the effect of the resilient controller. With the resilient controller, despite the interference caused by the attack, the voltage can quickly recover to the safe range and remain stable. Similarly, the current achieves a current sharing distribution after minor fluctuations, ensuring the normal operation of the system. In Figure 3 , as the attack intensity increases and multiple link attacks occur, the deviation from the balance becomes more severe, but the resilient controller still effectively mitigates the impact of the attack, keeping the voltage and current stable near the equilibrium point.Figure 4 It includes four sub - figures, each sub - figure representing a DGU and containing two heat maps corresponding to B li and B hi The relationship with voltage V i The horizontal axis represents B li or B hi values under specific control boundaries, while the vertical axis represents the voltage V of each DGU i . The color intensity reflects the frequency distribution of data in each interval. It can be clearly seen from the figure that the voltage distribution remains within the interior of the safety set corresponding to the CBF with a relative degree of 1 and a relative degree of 2 defined. In addition, the voltage is concentrated near the steady state, indicating that the system can maintain good stability even under attacks.

[0115] The specific parameters of different DGUs in this embodiment are shown in the following table:

[0116]

[0117]

[0118] Corresponding to the foregoing embodiment of a distributed security and stability control method for a DC micro - grid facing FDI attacks, the present invention also provides an embodiment of a distributed security and stability control device for a DC micro - grid facing FDI attacks.

[0119] See Figure 5 An embodiment of a distributed security and stability control device for a DC micro - grid facing FDI attacks provided by an embodiment of the present invention includes a memory and one or more processors. Executable code is stored in the memory. When the processor executes the executable code, it is used to implement a distributed security and stability control method for a DC micro - grid facing FDI attacks in the foregoing embodiment.

[0120] An embodiment of a distributed security and stability control device for a DC micro - grid facing FDI attacks provided by the present invention can be applied to any device with data - processing capabilities. Such a device with data - processing capabilities can be a device or apparatus such as a computer. The device embodiment can be implemented by software, or by hardware, or by a combination of software and hardware. Taking software implementation as an example, as a logically - defined device, it is formed by the processor of any device with data - processing capabilities reading the corresponding computer program instructions in the non - volatile memory into the memory for operation. From a hardware perspective, as Figure 5 shown, it is a hardware structure diagram of any device with data - processing capabilities where a distributed security and stability control device for a DC micro - grid facing FDI attacks provided by the present invention is located. Except for Figure 5In addition to the processor, memory, network interface, and non-volatile memory shown, any device with data processing capabilities where the device in the embodiment is located may generally include other hardware according to the actual functions of the device with data processing capabilities, which will not be elaborated herein.

[0121] For the specific implementation process of the functions and roles of each unit in the above device, please refer to the implementation process of the corresponding steps in the above method, which will not be elaborated herein.

[0122] For the device embodiment, since it basically corresponds to the method embodiment, the relevant parts can be referred to the partial description of the method embodiment. The device embodiments described above are only illustrative. The units described as separate components may or may not be physically separated, and the components shown as units may or may not be physical units, that is, they may be located in one place or distributed to multiple network units. Some or all of the modules can be selected according to actual needs to achieve the purpose of the solution of the present invention. Those of ordinary skill in the art can understand and implement it without creative efforts.

[0123] The embodiment of the present invention also provides a computer-readable storage medium, on which a program is stored. When the program is executed by a processor, it implements a distributed security and stability control method for a DC microgrid facing FDI attacks in the above embodiment.

[0124] The computer-readable storage medium may be an internal storage unit of any device with data processing capabilities described in any of the foregoing embodiments, such as a hard disk or memory. The computer-readable storage medium may also be an external storage device of any device with data processing capabilities, such as a plug-in hard disk, a Smart Media Card (SMC), an SD card, a Flash Card, etc. equipped on the device. Further, the computer-readable storage medium may also include both an internal storage unit and an external storage device of any device with data processing capabilities. The computer-readable storage medium is used to store the computer program and other programs and data required by the device with data processing capabilities, and can also be used to temporarily store the data that has been output or will be output.

[0125] The present invention also provides a computer program product, including a computer program. When the computer program is executed by a processor, it implements the distributed security and stability control method for a DC microgrid facing FDI attacks described above.

[0126] Other embodiments of the present application will be readily contemplated by those skilled in the art upon consideration of the specification and practice of the disclosure herein. The present application is intended to cover any variations, uses, or adaptations of the present application, which follow the general principles of the present application and include known common general knowledge or conventional technical means in the technical field not disclosed in the present application. The specification and examples are only illustrative, and the true scope and spirit of the present application are pointed out by the claims.

[0127] It should be understood that the above general description and the following detailed description are only exemplary and explanatory, and cannot limit the present application. The present application is not limited to the exact structures already described and shown in the drawings, and various modifications and changes can be made without departing from its scope. The scope of the present application is only limited by the appended claims.

Claims

1. A distributed security and stability control method for a DC microgrid against FDI attacks, characterized in that, Including: S1. A hierarchical control architecture for a DC microgrid, achieving control objectives according to different time scales, constructing a DGU unit model, defining the dynamics of primary and secondary controllers, where the control frequency of the secondary controller is lower than that of the primary controller and a distributed control scheme is adopted, and constructing an FDI attack model for the secondary control communication link; S2. Constructing a CBF-constrained safety set, and then constructing the conditions of the CBF constraint according to the upper limit of the attack vector amplitude and the time limit in the attack model to ensure being within the safety set specified by the CBF; S3. Constructing a CLF constraint according to the steady-state expressions for voltage balance and current sharing in the DC microgrid, so that the DC microgrid system can recover to a stable state after being attacked; S4. According to the constructed robust CBF and CLF constraints, obtaining a new secondary controller through dynamic constraint optimization; using the new secondary controller for distributed security and stability control against FDI attacks.

2. A distributed security and stability control method for a DC microgrid facing FDI attacks according to claim 1, characterized in that, The DGU unit model specifically includes: Based on the hierarchical control architecture of the DC microgrid, constructing a sub-DGU model: Wherein, V i is the voltage of the DGU at the point of common coupling, I l =(V i -V j ) / R l is the line current, where R l is the resistance of the line, V ti is the control input of the transformer, I ti is the output current of the DGU, I Li is the load current; R ti , L ti and C ti are the resistance, inductance and capacitance parameters of the converter respectively, represents the edge connecting the DGU, represents a set of N DGUs.

3. A distributed security and stability control method for a DC microgrid facing FDI attacks according to claim 1, characterized in that, The dynamics of the primary and secondary controllers Including: V ti = u i + g i ψ i ; where u i = k 1,i V i + k 2,i I i + k 3,i v i is the primary controller; where k 1,i , k 2,i and k 3,i represent the gains of feedback control; ψ i is the secondary controller, whose control frequency is lower than that of the primary control, and g i is the control coefficient of the secondary control; the secondary control adopts a distributed control scheme, and its dynamics are: wherein, is the rated current corresponding to DGU i, is the set of neighbors in the communication network of DGU i, and τ represents the time delay of the secondary control relative to the primary control.

4. A distributed security and stability control method for a DC microgrid facing FDI attacks according to claim 1, characterized in that The FDI attack model for the secondary control communication link includes: Wherein, is the output current of DGU i after being attacked, and φ i,j is the attack vector injected by the adversary, and β i,j (t - t a ) is a step function that activates the attack at t = t a .

5. A distributed security and stability control method for a DC microgrid against FDI attacks according to claim 1, characterized in that The construction of the CBF-constrained safety set includes: Construct the security set for each DGU i: The load needs to satisfy the security constraints: Construct the security set from this: In the formula V i is the voltage of the DGU at the point of common coupling V i and are the upper and lower limits of V i ; The set Ensures safety within the framework of set invariance, guaranteeing that the state of the system always remains within a predefined safe set 6. A distributed security and stability control method for a DC microgrid facing FDI attacks according to claim 5, characterized in that The CBF constraint includes: Construct the CBF with relative degree 2 by recursively defining each DGU i's CBF with relative degree 2: B li and B hi respectively represent the CBFs defined based on the lower and upper bounds of the load voltage. B li and B hi are respectively: Constructing a new safety set as: In the formula, is the coupling term between DGU i and its neighbor nodes; represents the edge connecting the DGU, represents a set of N DGUs; is used to express the relationship between the DGU and the edge. The element indicates that DGU i is the source of edge l; indicates that DGU i is the sink of edge l; Conditions satisfying CBF and guarantee the set and to be forward invariant, ensuring that the DC microgrid system is within the safety set specified by the CBF.

7. A distributed security and stability control method for a DC microgrid facing FDI attacks according to claim 1, characterized in that, The construction process of the CLF constraint includes: Let represent the steady state of each DGU, and the steady state error is expressed as Construct the CLF: where γ i = θ 3,i - θ 1,i θ 2,i , Furthermore, constructing the CLF constraint as: Among them and k 1,i 、k 2,i and k 3,i represent the gains of the feedback control in the primary controller; C ti is the capacitance parameter of the converter, and L ti is the inductance parameter of the converter.

8. A distributed security and stability control method for a DC microgrid facing FDI attacks according to claim 7, characterized in that, The obtaining of the new secondary controller through dynamic constraint optimization according to the constructed robust CBF and CLF constraints is specifically: Modify the nominal secondary controller ψ in a minimally invasive manner while ensuring safety, stability, and real-time feasibility i , and obtain the following QP-based optimization problem: where, δ i is the slack variable, p i represents the penalty coefficient; solving this optimization problem using QP yields a new secondary controller; V i is the voltage of the DGU at the point of common coupling, R ti is the resistance of the converter, i is the coupling term between DGU i and its neighboring nodes, li is the tuning parameter of the type function in the CBF; g i is the control coefficient of the secondary control, ω ij > 0 represents a constant upper bound; In addition, the time delay τ of the secondary control needs to satisfy τ < τ ref to ensure the convergence of the system, where τ ref = π / (2λ max (L c )) is the maximum delay margin for the convergence of an undirected graph network.

9. A distributed security and stability control device for a DC microgrid against FDI attacks, comprising a memory and one or more processors, wherein executable code is stored in the memory, characterized in that, When the processor executes the executable code, it implements a distributed security and stability control method for a DC microgrid against FDI attacks as described in any one of claims 1-8.

10. A computer-readable storage medium having a program stored thereon, characterized in that, When the program is executed by the processor, it implements a distributed security and stability control method for a DC microgrid against FDI attacks as described in any one of claims 1-8.

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