Distributed security and stability control method for DC microgrid against FDI attacks

Abstract

The present invention discloses a distributed security and stability control method for a DC microgrid against FDI attacks, which relates to the field of microgrid control. The method includes: achieving control objectives according to different time scales based on a hierarchical control architecture of the DC microgrid, constructing a distributed generation unit model, defining the dynamics of primary and secondary controllers, and designing an FDI attack model; developing a safety-critical secondary controller based on a robust CBF under bounded FDI attacks; constructing a CLF by combining voltage and current balance conditions to ensure that the DC microgrid can return to a stable state after the attack, thereby maintaining system stability; and using a quadratic programming method to solve a new secondary controller that meets the robust CBF and CLF constraints. The technical solution of the present invention can still achieve the distributed secondary control objectives of the DC microgrid even under FDI attacks, thereby improving the security and stability of the DC microgrid when facing FDI attacks from the communication network.

Description

Technical Field

[0001] The present invention relates to the field of microgrid control technology, and in particular to a distributed security and stability control method for a direct current microgrid resistant to FDI attacks. Background Art

[0002] DC microgrids have been widely used in areas such as renewable energy integration, electric vehicle charging stations, and data centers due to their efficient power management, ease of control, and compatibility with modern DC loads. However, the hierarchical control structure commonly used in DC microgrids integrates the communication network layer, local control layer, and physical device layer through communication channels, making DC microgrids vulnerable to cyberattacks and intrusions. In particular, the communication-dependent secondary control structure implemented through distributed control exposes DC microgrids to a greater risk of cyberattacks, which can disrupt power balance, reduce operational stability, and even lead to severe system failures. Existing resilient control methods in DC microgrids primarily focus on stabilizing the system state. This ensures that the trajectory of the DC microgrid state (such as voltage and current) converges to an equilibrium point after an attack, but does not consider transient system security issues, such as the potential for transient voltage overshoots to cause load breakdown. Summary of the Invention

[0003] The present invention aims to address the deficiencies of the existing technology and propose a distributed security and stability control method for DC microgrids against FDI attacks.

[0004] The object of the present invention is achieved through the following technical solution: 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, control objectives are achieved according to different time scales. A DGU unit model is constructed, and the dynamics of the primary and secondary controllers are defined. The control frequency of the secondary controller is lower than that of the primary controller and a distributed control scheme is adopted. An FDI attack model targeting the secondary control communication link is constructed.

[0006] S2. Construct a CBF constrained security set, and then construct the CBF constraint conditions based on the upper limit of the attack vector amplitude and the time limit in the attack model to ensure that it is within the security set specified by the CBF;

[0007] S3. Construct CLF constraints based on the steady-state expression of voltage balance and current sharing achieved by the DC microgrid, so that the DC microgrid system can recover to a stable state after being attacked.

[0008] S4. According to the constructed robust CBF and CLF constraints, a new two-level controller is obtained based on dynamic constraint optimization. The new two-level controller is used to perform distributed security and stability control against FDI attacks.

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

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

[0011]

[0012] Where, is the voltage of the DGU at the point of common coupling, is the line current, where is the resistance of the line, is the control input of the transformer, is the output current of the DGU, is the load current; 、 and are the resistance, inductance and capacitance parameters of the converter, represents the edge connecting DGU, Represents a group A DGU.

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

[0014] ;

[0015] Where, is the primary controller; 、 and represents the gain of feedback control; It is a 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, Corresponds to DGU Rated current, For DGU The set of neighbors in the communication network, Indicates the time delay of secondary control relative to primary control.

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

[0019] ;

[0020] Where, DGU was attacked The output current, is the attack vector injected by the adversary, is a step function, Activate the attack.

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

[0022] Build each DGU Security set: The payload needs to meet the security constraints: , and thus construct a safe set:

[0023]

[0024] In the formula , ; is the voltage of the DGU at the point of common coupling, and for The upper and lower limits of Security is ensured within the framework of set invariance, ensuring that the state of the system always remains within a predefined safe set.

[0025] Furthermore, the CBF constraints include:

[0026] By recursively defining each DGU CBF of relative degree 2 Construct a CBF of relative degree 2: and They represent the CBF defined based on the lower and upper bounds of the load voltage, and They are:

[0027] ,

[0028] .

[0029] Construct a new security set as:

[0030] .

[0031] Where, For DGU and the coupling terms between neighboring nodes; represents the edge connecting DGU, Represents a group DGU; Used to express the relationship between DGU and edge, element Indicates DGU It's the edge source; Indicates DGU It's the edge The exchange;

[0032] Meet the CBF conditions and Guaranteed Collection and The forward invariance of ensures that the DC microgrid system is within the safety set specified by CBF.

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

[0034] make represents the steady state of each DGU, and the steady-state error is expressed as , construct CLF:

[0035] ,

[0036] in , ;

[0037] Then, the CLF constraint is constructed as:

[0038]

[0039] in and , , , , 、 and represents the gain of feedback control in the primary controller; is the capacitance parameter of the converter, is the inductance parameter of the converter.

[0040] Furthermore, the new two-stage controller obtained by solving the robust CBF and CLF constraints based on the dynamic constraint optimization is specifically:

[0041] Modify the nominal secondary controller in a minimally invasive manner while ensuring safety, stability, and real-time feasibility , we get the following QP-based optimization problem:

[0042]

[0043] in, is the slack variable, represents the penalty coefficient; QP is used to solve this optimization problem to obtain a new two-stage controller; is the voltage of the DGU at the point of common coupling, , is the resistance of the converter, For DGU and the coupling terms between neighboring nodes, For CBF Tuning parameters of class functions;

[0044] In addition, the time delay of the secondary control Needs to be satisfied To ensure the convergence of the system, is the maximum delay margin within which an undirected graph network can converge.

[0045] On the other hand, a distributed security and stability control device for a DC microgrid against FDI attacks is also provided, comprising a memory and one or more processors, wherein the memory stores executable code, and when the processor executes the executable code, the distributed security and stability control method for a DC microgrid against FDI attacks 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 facing FDI attacks is implemented.

[0047] Beneficial effects of the present invention: Compared with the existing elastic control methods in DC microgrids, the present invention is more considered from the perspective of stabilizing the system state. The present invention takes into account the transient state security of the DC microgrid, and designs a resilient distributed secondary controller based on robust CBF under bounded FDI attacks. This strategy not only complies with the delay margin constraints related to secondary control communications, but also ensures the security of the DC microgrid by enforcing strict transient safety conditions. In addition, by analyzing the voltage balance and current sharing conditions, the present invention constructs a CLF based on the balance point to ensure that the DC microgrid can return to a stable state after the attack, thereby maintaining the stability of the system. BRIEF DESCRIPTION OF THE DRAWINGS

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

[0049] Figure 2 The embodiment of the present invention provides an attack vector of Voltage and current response diagram of the DC microgrid with and without elastic control;

[0050] Figure 3 The embodiment of the present invention provides an attack vector of Voltage and current response diagram of the DC microgrid with and without elastic control;

[0051] Figure 4 The voltage provided by the embodiment of the present invention is and safety boundaries as well as Heat map of the composition;

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

[0053] Figure 6 It is a schematic flow chart of the method of the present invention. DETAILED DESCRIPTION

[0054] In order to better understand the technical solution of the present application, the embodiments of the present application are described in detail below with reference to the accompanying drawings.

[0055] It should be clear that the embodiments described are only part of the embodiments of this application, not all of the embodiments. Based on the embodiments in this application, all other embodiments obtained by ordinary technicians in this field without making creative work are within the scope of protection of this application.

[0056] The embodiment of the present invention provides a distributed security and stability control method for DC microgrids facing FDI attacks, which includes the following steps: DGU and attack modeling, designing robust control barrier function (CBF) constraints, designing equilibrium point-based control Lyapunov function (CLF) constraints, solving dynamic constraint optimization problems, experimental verification, etc. The process is as follows: Figure 6 The following describes in detail the specific implementation of each step.

[0057] Step 1: DGU and attack modeling. Figure 1 This is a 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, 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 ,in Represents a group DGUs, and Indicates the connections between these DGUs edges (power lines). Each edge The source node DGU Connect to sink node DGU , and by Index, where . Define the incidence matrix , where the elements Indicates DGU It's the edge source; if Indicates DGU It's the edge The communication network is shown in Figure 1. Indicates that is the node set corresponding to DGU, Indicates a communication link.

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

[0059] (1)

[0060] In formula (1), is the voltage of the DGU at the point of common coupling, is the line current, where is the resistance of the line, is the control input of the transformer, is the output current of the DGU, is the load current. 、 and 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] ; (2)

[0063] In formula (2), is the primary controller, where 、 and They represent the gains of feedback control respectively; is the control coefficient of the secondary control, It is a 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] ; (3)

[0065] In formula (3), Corresponds to DGU Rated current, For DGU The set of neighbors in the communication network, Indicates the time delay of secondary control relative to primary control.

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

[0067]

[0068] The attacker’s FDI attack on the secondary controlled communication link is modeled as:

[0069] ; (4)

[0070] In formula (4), DGU was attacked The output current, is the attack vector injected by the adversary, is a step function, Activate the attack.

[0071] Step 2: Design robust CBF constraints.

[0072] Step 2.1, construct each DGU Security set: The payload needs to meet the security constraints: , and thus construct a safe set:

[0073] (5)

[0074] In formula (5) , .gather Security can be ensured within the framework of set invariance, ensuring that the state of the system always remains within a predefined safe set.

[0075] Step 2.2, constructing a CBF with a relative degree of 1: The present invention uses a robust CBF as a method to adjust the existing two-level controller to ensure that the system state remains within the predefined safety set over time. and Set as candidate CBF. and Taking the derivative, we can get:

[0076] . (6)

[0077] In formula (6), For DGU and the coupling terms between neighboring nodes, is the load conductance. Since there is no clear relationship between the derivative of CBF and the secondary controller, it is necessary to design a CBF with a relative degree of 2.

[0078] make , by selecting As Class function, meeting the CBF conditional requirements , which is equivalent to:

[0079] ;

[0080] Similarly, Equivalent to

[0081] .

[0082] Step 2.3, construct a CBF with relative degree 2: recursively define each DGU The relative degree of CBF is 2, where and They represent the CBF defined based on the lower and upper bounds of the load voltage, respectively. and They are:

[0083] ,

[0084] .

[0085] Construct a new security set as:

[0086] .

[0087] Select and As Class function, where and is the adjustment parameter. Since the attacker is limited by the attack resources, the attack vector amplitude injected by the attacker has an upper bound, that is, is bounded; and the attack vector can only be injected within a limited time. Then there is a constant upper bound , making ,in Indicates the duration of the attack. Therefore, the CBF condition is met , which is equivalent to:

[0088] ,

[0089] Similarly, Equivalent to

[0090] .

[0091] pass and Guaranteed Collection The forward invariance of The forward invariance of ensures that the DC microgrid system is within the safety set specified by CBF.

[0092] Step 3: Design CLF constraints.

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

[0094] (7)

[0095] in, , , , , , and .also, 、 、 、 、 、 、 、 、 、 、 They are PCC voltage, filter output current, integrator state, load current, load power, reference voltage, secondary controller and intermediate parameters. 、 、 、 The vector form of the matrix 、 、 Collect electrical parameters 、 and The diagonal matrix of the microgrid system (1) needs to satisfy the following steady-state solution:

[0096] (8)

[0097] In formula (8), Communication network diagram The Laplace matrix of is the vector of rated current.

[0098] In step 3.2, based on the DC microgrid steady-state solution expression and the voltage balance and current sharing conditions, construct the CLF. The specific steps are as follows:

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

[0100] , (9)

[0101] , (10)

[0102] , (11)

[0103] . (12)

[0104] Then, according to (9) and (10), the equilibrium state of each DGU can be obtained 、 , according to (11) and (12), the equilibrium state and Each DGU The dynamics can be written as:

[0105] , (13)

[0106] In formula (13), , , as well as .

[0107] make represents the steady state of each DGU, and the steady-state error can be expressed as , you can construct a CLF:

[0108] ,

[0109] in , . Then, the CLF constraint is constructed as:

[0110]

[0111] in and .

[0112] Step 4: Solve the dynamic constrained optimization problem. In order to modify the nominal secondary controller in a minimally invasive manner while ensuring safety, stability, and real-time feasibility , we get the following optimization problem based on quadratic programming (QP):

[0113]

[0114] in, To prevent the CLF constraint from being too conservative, slack variables are introduced. represents the penalty coefficient. QP is used to solve this optimization problem to obtain a new two-stage controller. In addition, the time delay of the two-stage control Needs to be satisfied To ensure the convergence of the system, is the maximum delay margin within which an undirected graph network can converge.

[0115] Step 5: Experimental Verification. The feasibility and robustness of the resilient distributed control strategy for a DC microgrid based on robust CBF-CLF in response to FDI attacks were verified using a hardware experimentation platform. Specifically, a DC microgrid consisting of four DGUs was constructed for communication and computational constraints. Data transmission was implemented using a Raspberry Pi unit, which established a TCP / IP Modbus communication link to simulate the DC microgrid's communication network. Modbus TCP / IP communication operates between a server and a client. To collect information from other DGUs, each controller sets up its own server for client access. Furthermore, clients accessing its server can update the data stored there. Notably, the hardware-in-the-loop experimentation platform and the Raspberry Pi controllers are set up within the same subnet. In the real-time simulation system, each DGU collects its local state information and sends this data to the target controller via a channel assigned to its corresponding ID. Communication between controllers allows the sharing of local information, thereby implementing a distributed resilient secondary control algorithm. Finally, the secondary control signals are sent back to the corresponding DGU in the hardware-in-the-loop experimentation platform via a designated channel.

[0116] The controller designed by the method of the present invention sets the safety range of the DC microgrid load to . Figure 2 Yes and Figure 3 Shown respectively in single attack vector and multiple attack vectors ,as well as The voltage and current responses of the DC microgrid after being attacked by FDI under the influence of . The left sub-graphs in both figures show the system performance without a resilient controller. Without resilient control, the voltage quickly deviates from its stable value after the attack is activated and cannot return to the original balance. The current sharing is also disturbed, and the current fluctuates significantly, indicating that the system has lost its load sharing capability. In contrast, the sub-graph on the right shows the effect of the resilient controller. With the resilient controller, the voltage can quickly return to a safe range and remain stable despite the disturbance caused by the attack. Similarly, the current achieves a current sharing distribution after a small fluctuation, ensuring the normal operation of the system. Figure 3 In the ,case of attack intensity increases and is accompanied by multiple link attacks, the deviation from the ,balance becomes more serious, but the elastic controller still ,effectively mitigates the impact of the attack and stabilizes the voltage and ,current near the equilibrium point. Figure 4 It includes four sub-graphs, each representing a DGU, and contains two heat maps corresponding to and With voltage The horizontal axis represents the relationship between or The vertical axis represents the voltage of each DGU. The color intensity reflects the frequency distribution of the data within each interval. It is clear from the figure that the voltage distribution remains within the safe set corresponding to the defined CBFs of relative degree 1 and relative degree 2. In addition, the voltage is concentrated near the steady state, indicating that the system can maintain good stability even under attack.

[0117] The specific parameters of different DGUs in this embodiment are shown in the following table:

[0118]

[0119] Corresponding to the aforementioned embodiment of a distributed security and stability control method for a DC microgrid against FDI attacks, the present invention also provides an embodiment of a distributed security and stability control device for a DC microgrid against FDI attacks.

[0120] See also Figure 5 An embodiment of the present invention provides a distributed security and stability control device for a DC microgrid against FDI attacks, comprising a memory and one or more processors. The memory stores executable code. When the processor executes the executable code, it is used to implement a distributed security and stability control method for a DC microgrid against FDI attacks in the above embodiment.

[0121] The embodiment of the distributed security and stability control device for a DC microgrid against FDI attacks provided by the present invention can be applied to any device with data processing capabilities, and the device with data processing capabilities can be a device or apparatus such as a computer. The device embodiment can be implemented through software, or through hardware or a combination of software and hardware. Taking software implementation as an example, as a device in a logical sense, it is formed by the processor of any device with data processing capabilities in which it is located reading the corresponding computer program instructions in the non-volatile memory into the memory for execution. From the hardware level, if Figure 5 As shown, it is a hardware structure diagram of a distributed security and stability control device for a DC microgrid facing FDI attacks provided by the present invention, in which any device with data processing capability is located. Figure 5 In addition to the processor, memory, network interface, and non-volatile memory shown, any device with data processing capabilities in which the apparatus in the embodiment is located may also include other hardware, generally based on the actual functions of the device with data processing capabilities, which will not be described in detail.

[0122] The implementation process of the functions and effects of each unit in the above-mentioned device is specifically described in the implementation process of the corresponding steps in the above-mentioned method, and will not be repeated here.

[0123] For the device embodiments, since they basically correspond to the method embodiments, the relevant parts can be referred to the partial description of the method embodiments. The device embodiments described above are only exemplary, wherein 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 across multiple network units. Some or all of the modules can be selected according to actual needs to achieve the purpose of the present invention. Those of ordinary skill in the art can understand and implement the present invention without making any creative efforts.

[0124] An embodiment of the present invention further provides a computer-readable storage medium having a program stored thereon. When the program is executed by a processor, the distributed security and stability control method for a DC microgrid against FDI attacks in the above embodiment is implemented.

[0125] The computer-readable storage medium may be an internal storage unit of any device with data processing capabilities described in any of the aforementioned 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. Furthermore, 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 any device with data processing capabilities, and may also be used to temporarily store data that has been output or is to be output.

[0126] 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.

[0127] Those skilled in the art will readily appreciate other embodiments of the present application after considering the specification and practicing the contents disclosed herein. This application is intended to cover any variations, uses, or adaptations of the present application that follow the general principles of the present application and include common knowledge or customary techniques in the art not disclosed herein. The description and examples are to be considered merely as exemplary, and the true scope and spirit of the present application are indicated by the claims.

[0128] It should be understood that the above general description and the detailed description that follows are exemplary and explanatory only and do not limit the present application. The present application is not limited to the precise structure described above and shown in the accompanying drawings, and various modifications and changes may be made without departing from the scope of the present application. The scope of the present application is limited only by the appended claims.

Claims

1. A distributed security and stability control method for DC microgrids against FDI attacks, characterized by: include: S1. Based on the hierarchical control architecture of the DC microgrid, control objectives are achieved according to different time scales. A DGU unit model is constructed, and the dynamics of the primary and secondary controllers are defined. The control frequency of the secondary controller is lower than that of the primary controller and a distributed control scheme is adopted. An FDI attack model targeting the secondary control communication link is constructed. The DGU unit model specifically includes: Based on the hierarchical control architecture of DC microgrid, a DGU model is constructed: ； Where, is the voltage of the DGU at the point of common coupling, is the line current, where is the resistance of the line, is the control input of the transformer, is the output current of the DGU, is the load current; 、 and are the resistance, inductance and capacitance parameters of the converter, represents the edge connecting DGU, Represents a group DGU; FDI attack models targeting secondary control communication links include: ； Where, DGU was attacked The output current, is the attack vector injected by the adversary, is a step function, Activate the attack when S2. Construct a CBF constrained security set, and then construct the CBF constraint conditions based on the upper limit of the attack vector amplitude and the time limit in the attack model to ensure that it is within the security set specified by the CBF; S3. Construct CLF constraints based on the steady-state expression of voltage balance and current sharing achieved by 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, a new two-level controller is obtained based on dynamic constraint optimization. The new two-level controller is used to perform distributed security and stability control against FDI attacks.

2. The distributed security and stability control method for a DC microgrid against FDI attacks according to claim 1 is characterized in that: The dynamics of the primary and secondary controllers include: ； Where, is the primary controller; 、 and represents the gain of feedback control; It is a secondary controller, and its control frequency is lower than the primary control. is the control coefficient of the secondary control; the secondary control adopts a distributed control scheme, and its dynamics is: ； Where, Corresponds to DGU Rated current, For DGU The set of neighbors in the communication network, Indicates the time delay of secondary control relative to primary control.

3. The distributed security and stability control method for a DC microgrid against FDI attacks according to claim 1 is characterized in that: The construction of the CBF constraint safety set includes: Build each DGU Security set: The payload needs to meet the security constraints: , and thus construct a safe set: In the formula , ; is the voltage of the DGU at the point of common coupling, and for The upper and lower limits of Security is ensured within the framework of set invariance, ensuring that the state of the system always remains within a predefined safe set.

4. The distributed security and stability control method for a DC microgrid against FDI attacks according to claim 3 is characterized in that: The CBF constraints include: By recursively defining each DGU CBF of relative degree 2 Construct a CBF of relative degree 2: and They represent the CBF defined based on the lower and upper bounds of the load voltage, and They are: ， . Construct a new security set as: . Where, For DGU and the coupling terms between neighboring nodes; represents the edge connecting DGU, Represents a group DGU; Used to express the relationship between DGU and edge, element Indicates DGU It's the edge source; Indicates DGU It's the edge The exchange; Meeting the CBF requirements and Guaranteed Collection and The forward invariance of ensures that the DC microgrid system is within the safety set specified by CBF.

5. The distributed security and stability control method for a DC microgrid against FDI attacks according to claim 1 is characterized in that: The construction process of the CLF constraint includes: make represents the steady state of each DGU, and the steady-state error is expressed as , construct CLF: ， in , ; Then, the CLF constraint is constructed as: in and , , , , 、 and represents the gain of feedback control in the primary controller; is the capacitance parameter of the converter, is the inductance parameter of the converter.

6. The distributed security and stability control method for a DC microgrid against FDI attacks according to claim 5 is characterized in that: According to the robust CBF and CLF constraints constructed, the new two-stage controller is obtained based on the dynamic constraint optimization solution: Modify the nominal secondary controller in a minimally invasive manner while ensuring safety, stability, and real-time feasibility , we get the following QP-based optimization problem: ； in, is the slack variable, represents the penalty coefficient; QP is used to solve this optimization problem to obtain a new two-stage controller; is the voltage of the DGU at the point of common coupling, , is the resistance of the converter, For DGU and the coupling terms between neighboring nodes, For CBF Tuning parameters of class functions; is the control coefficient of the secondary control, represents the upper bound of a constant; In addition, the time delay of the secondary control Needs to be satisfied To ensure the convergence of the system, is the maximum delay margin within which an undirected graph network can converge.

7. A distributed security and stability control device for a DC microgrid against FDI attacks, comprising a memory and one or more processors, wherein the memory stores executable code, characterized in that: When the processor executes the executable code, a distributed security and stability control method for a DC microgrid against FDI attacks according to any one of claims 1 to 6 is implemented.

8. A computer-readable storage medium having a program stored thereon, characterized in that: When the program is executed by a processor, a distributed security and stability control method for a DC microgrid against FDI attacks according to any one of claims 1 to 6 is implemented.

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