Distributed power supply FDIA detection method based on multi-resolution morphological gradient
By adopting multi-resolution morphological gradient technology in distributed power system, a false data injection attack model and extracting attack detection signal characteristics are solved, and FDIA attack detection problem in distributed power system is achieved efficient and accurate attack detection and position.
Patent Information
- Application Number
- CN202411518267.X
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2024-10-29
- Publication Date
- 2025-02-07
AI Technical Summary
In distributed power systems, false data injection attacks (FDIA) cause unstable microgrid operation, and existing detection methods are difficult to achieve efficient, accurate and real-time attack detection.
A distributed power supply FDIA detection method based on multi-resolution morphological gradient is adopted to establish a false data injection attack model, an attack detection signal is constructed, and a multi-resolution morphological gradient is used to extract the detection signal to determine whether the attack occurs.
It realizes rapid and accurate detection of FDIA attacks, can locate the location of the attack and the tampered data type, distinguish system load disturbances and FDIA attacks, and has good economic and engineering application value.
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Figure CN119402252A_ABST
Abstract
Description
Technical Field
[0001] The present invention relates to the field of network security technology, and in particular to a distributed power supply FDIA detection method based on multi-resolution morphological gradient. Background Art
[0002] Distributed power generation technologies such as photovoltaics and wind power are playing an increasingly important role in building a green, clean and efficient new power system. In the context of a large number of distributed generation (DG) connected to the new power system, its secondary control mode mainly includes centralized control, decentralized control and distributed control, among which distributed control is becoming more and more popular due to its flexibility and scalability.
[0003] In the distributed control architecture, adjacent DGs usually rely on sparse communication networks to achieve information interaction. The state of the communication network will directly affect the dynamic performance and operational stability of the microgrid. However, with the widespread application of public wireless communication technologies such as 5G and Wi-Fi in the field of microgrid communication, their open communication environment makes system information interaction extremely vulnerable to malicious network attacks, and the operational safety of microgrids needs to be paid attention to. False Data Injection Attack (FDIA) is a common type of network attack in power grids. The attacker first uses advanced computer information technology to penetrate the communication network, and then tamper with the important state quantity interaction information between DGs to make the secondary coordinated control target of the microgrid invalid, causing the system operation to deviate from the set working point or even cause system instability. Considering the plug-and-play requirements of DG for attack detection flexibility and real-time control, it is necessary to further study efficient, accurate, and real-time attack detection methods to ensure the actual needs of DG system operation safety. Summary of the invention
[0004] In order to solve the above technical problems, the present invention provides a distributed power supply FDIA detection method based on multi-resolution morphological gradient, comprising the following steps:
[0005] S1. Based on the interactive information of the secondary coordination control layer between distributed power sources, a false data injection attack model for reactive power sharing state quantity and average voltage observation state quantity is established;
[0006] S2. Analyze the impact of false data injection attacks on the consistency of system reactive power sharing and average voltage observations, and construct attack detection signals for each distributed power source based on local information of distributed power sources and neighbor interaction information;
[0007] S3. Use multi-resolution morphological gradient to extract features of attack detection signals, and determine whether a false data injection attack occurs by comparing the size relationship between the calculated value and the detection threshold.
[0008] The technical solution further defined in the present invention is:
[0009] Furthermore, in step S1, the false data injection attack model for the reactive power sharing state quantity and the average voltage observation state quantity is as follows:
[0010]
[0011] in, and Indicates that the communication link is attacked from node DG j Send to neighbor node DG i False information; Q j Respectively represent the jth distributed generation DG j The true values of reactive power and average voltage observables; and They represent the false data injection attack signals launched by the attacker on the communication link, and their physical meanings are respectively injecting interactive information Q j and The false value in; t represents time; o j and τ j are symbolic functions, respectively used to represent the mutual information Q j and Whether it is attacked by false data injection.
[0012] As described above, in the distributed power FDIA detection method based on multi-resolution morphological gradient, in step S2, the impact of false data injection attack on the consistency of system reactive power sharing and average voltage observation values is analyzed, where the reactive power sharing deviation between distributed power sources is expressed as:
[0013]
[0014] Among them, n i (i=1, 2, ...) represents the i-th distributed generation DG i The corresponding voltage control droop coefficient, n j Denotes the jth distributed generation DG i The corresponding voltage control droop coefficient, N i Denotes distributed generation DG i The set of neighbor nodes, Q i Indicates DG i Output reactive power, Q j Indicates DG i Neighbor node DG j The output reactive power of DG i The neighbor node number of Represents the reactive information sharing communication topology G Q The corresponding adjacency matrix element, C Q Represents the reactive power coupling coefficient;
[0015] The weighted average voltage observer of each distributed power source is expressed as:
[0016]
[0017] in, represents the weighted average voltage observation value of each distributed power source, U i Indicates DG i Corresponding to the output voltage of the inverter, Indicates DG i The true value of the average voltage observable, Denotes the voltage observation information sharing communication topology G U The corresponding adjacency matrix element, C E represents the voltage coupling coefficient that meets the stability requirements of the control system, Indicates DG i With neighbor node DG j The accumulation of voltage observation errors between the two.
[0018] As described above, in the distributed power FDIA detection method based on multi-resolution morphological gradient, in step S2, the secondary coordinated control strategy of the voltage between distributed power sources is as follows:
[0019]
[0020] Among them, U ni Indicates the nominal voltage value, K vi represents the voltage control coefficient; u i Represents the secondary voltage regulation term, K i Represents the integral coefficient of the controller, β i Represents the weight coefficient of reactive power sharing and voltage recovery, U ref Indicates the reference value of the system rated voltage;
[0021] When DG i and DG j When the communication link between them is attacked by false data injection, it will cause deviations in the secondary coordination control target, and eventually cause the output voltage of each distributed power source to exceed the safe range. At this time, DG i The secondary control instructions are updated as follows:
[0022]
[0023] By taking the derivative of the above formula (7), we get:
[0024]
[0025] in, and They represent the false data injection attack signals launched by the attacker on the communication link, and their physical meanings are respectively injecting interactive information Q j and False value in o j and τ j are symbolic functions, respectively used to represent the mutual information Q j and Whether it is attacked by false data injection; the impact of false data injection attack on the consistency of reactive power sharing and average voltage observation values of distributed power sources in the system is measured by and express.
[0026] As described above, in the distributed power FDIA detection method based on multi-resolution morphological gradient, in step S2, the attack detection signal of each distributed power source is constructed based on the local information of the distributed power source and the interactive information of the neighbors. or If a false data injection attack occurs, the impact of the attack will be directly reflected in the amount of controlled information. and Therefore, in any distributed power source, an attack detection signal suitable for the secondary coordinated control of voltage between distributed power sources described in equations (3) to (6) is constructed as follows:
[0027]
[0028] Among them, G Q Represents the communication topology of reactive power sharing, G U Represents the communication topology of voltage observation.
[0029] As described above, in the distributed power FDIA detection method based on multi-resolution morphological gradient, in step S3, the multi-resolution morphological gradient is used to inject the false data of each distributed power source in the system into the attack detection signal Ω i Processing is performed, where the multi-resolution morphological gradient is expressed as follows:
[0030]
[0031]
[0032] in, represents the multiresolution morphological gradient, ω represents the analysis level of the multiresolution morphological gradient, and s represents a variable flat structure element with different origin positions.
[0033] As described above, in the distributed power FDIA detection method based on multi-resolution morphological gradient, in step S3, a variable flat structure element s with different origin positions is defined as follows:
[0034] S + ={S1, S2, ..., S l-1 , S l } (13)
[0035] S - ={ S1 , S2,…,S l-1 , S l} (14)
[0036] Among them, l represents the step size.
[0037] As described above, in the distributed power FDIA detection method based on multi-resolution morphological gradient, in step S3, the analysis level of the multi-resolution morphological gradient is ω=2, and a linear structure element is used to inject a false data attack detection signal Ω i Perform calculation processing.
[0038] As described above, in the distributed power FDIA detection method based on multi-resolution morphological gradient, in step S3, a linear structure element is used to inject false data into the attack detection signal Ω i The result of the operation is compared with the set threshold. If it exceeds the threshold, it means that the corresponding distributed power source has been attacked by false data injection, as described below:
[0039]
[0040] in, and Respectively represent the corresponding DG i Attack Detection Signal and The multi-resolution morphological gradient values obtained after processing, and the corresponding detection thresholds are and When the multi-resolution morphological gradient value exceeds the corresponding detection threshold, it means that the node DG j To neighbor node DG i The communication link of DG j Transmit to DG i The data is tampered by false data injection.
[0041] As described above, in the distributed power FDIA detection method based on multi-resolution morphological gradient, in step S3, the detection threshold and Set them to 0.5 and 0.3 respectively.
[0042] The beneficial effects of the present invention are:
[0043] In the present invention, based on the system interaction information and local measurement information, a real-time attack detection signal that can effectively characterize the impact of FDIAs is constructed, and the attack detection signal is secondary processed using multi-resolution morphological gradient to extract the mutation characteristics of the measured signal; this method determines whether an FDI attack occurs by comparing the size relationship between the calculated value and the detection threshold, locates the DG position attacked by FDI in the system, and determines the type of tampered data, thereby effectively distinguishing between system load disturbances and FDI attacks, without the need to set up additional physical devices, and can be directly embedded in the system secondary controller to realize real-time detection of FDIAs, with good economic efficiency and engineering application value. BRIEF DESCRIPTION OF THE DRAWINGS
[0044] Figure 1 It is a schematic diagram of the overall process of the present invention;
[0045] Figure 2 Schematic diagram of a 5DG simulation system used in an embodiment of the present invention;
[0046] Figure 3 A schematic diagram of the communication network topology used by the test system in an embodiment of the present invention;
[0047] Figure 4 Schematic diagram of the operating status of the test system in different time periods according to an embodiment of the present invention;
[0048] Figure 5 is the attack detection signal in the embodiment of the present invention The morphological gradient value obtained after processing Schematic diagram, where a to e are the morphological gradient values of DG1 to DG5 respectively to Schematic diagram;
[0049] Figure 6 is the attack detection signal in the embodiment of the present invention The morphological gradient value obtained after processing Schematic diagram, where a to e are the morphological gradient values of DG1 to DG5 respectively to Schematic diagram. DETAILED DESCRIPTION
[0050] The present embodiment provides a distributed power FDIA detection method based on multi-resolution morphological gradient, which is used to quickly and accurately detect whether each distributed power (Distributed Generation, DG) is attacked by false data injection (False Data Injection, FDI) during information interaction, and determine the type of tampered data, such as Figure 1 As shown, the following steps are included:
[0051] S1. Based on the interactive information of the secondary coordination control layer between distributed power sources, a false data injection attack model for reactive power sharing state quantity and average voltage observation state quantity is established, as shown in the following formula:
[0052]
[0053] in, and Indicates that the communication link is attacked from node DG j Send to neighbor node DG i False information; Q j and Respectively represent the jth distributed generation DG j The true values of reactive power and average voltage observables; and They represent the false data injection attack signals launched by the attacker on the communication link, and their physical meanings are respectively injecting interactive information Q j and The false value in the signal can be either an arbitrary constant or a mathematical function designed by the attacker; t represents time; o j and τ j are symbolic functions, respectively used to represent the mutual information Q j and Whether it is attacked by false data injection.
[0054] S2. Analyze the impact of false data injection attacks on the consistency of system reactive power sharing and average voltage observations, and construct attack detection signals for each distributed power source based on the local information of the distributed power source and the neighbor interaction information.
[0055] The reactive power sharing deviation between distributed power sources is expressed as:
[0056]
[0057] Among them, n i (i=1, 2, ...) represents the i-th distributed generation DG i The corresponding voltage control droop coefficient, n j Denotes the jth distributed generation DGi The corresponding voltage control droop coefficient, N i Denotes distributed generation DG i The set of neighbor nodes, Q i Indicates DG i Output reactive power, Q j Indicates DG i Neighbor node DG j The output reactive power of DG i The neighbor node number of Represents the reactive information sharing communication topology G Q The corresponding adjacency matrix element, C Q It represents the reactive power coupling coefficient that meets the stability requirements of the control system.
[0058] The weighted average voltage observer of each distributed power source is expressed as:
[0059]
[0060] in, represents the weighted average voltage observation value of each distributed power source, U i Indicates DG i Corresponding to the output voltage of the inverter, Indicates DG i The true value of the average voltage observable, Denotes the voltage observation information sharing communication topology G U The corresponding adjacency matrix element, C E represents the voltage coupling coefficient that meets the stability requirements of the control system, Indicates DG i With neighbor node DG j The accumulation of voltage observation errors between the two.
[0061] Accordingly, the secondary coordinated control strategy of voltage between distributed power sources is as follows:
[0062]
[0063] Among them, U ni Indicates the nominal voltage value, K vi represents the voltage control coefficient; u i Represents the secondary voltage regulation term, K i Represents the integral coefficient of the controller, β i Represents the weight coefficient of reactive power sharing and voltage recovery, U ref Indicates the reference value of the system rated voltage.
[0064] When DG i and DG jWhen the communication link between them is attacked by false data injection, it will cause deviations in the secondary coordination control target, and eventually cause the output voltage of each distributed power source to exceed the safe range. At this time, DG i The secondary control instructions are updated as follows:
[0065]
[0066] By taking the derivative of the above formula (7), we get:
[0067]
[0068] in, and They represent the false data injection attack signals launched by the attacker on the communication link, and their physical meanings are respectively injecting interactive information Q j and False value in o j and τ j are symbolic functions, respectively used to represent the mutual information Q j and Whether it is attacked by false data injection; the impact of false data injection attack on the consistency of reactive power sharing and average voltage observation values of distributed power sources in the system is measured by and express.
[0069] Based on the local information of distributed power sources and the interactive information of neighbors, the attack detection signal of each distributed power source is constructed. Once the interactive information in the system ( or ) is attacked by false data injection, the impact of the attack will be directly reflected in the amount of control information and Therefore, the attack detection signal applicable to the secondary coordinated control of voltage between distributed power sources described in equations (3) to (6) can be constructed in any distributed power source as follows:
[0070]
[0071] Among them, G Q Represents the communication topology of reactive power sharing, G U Represents the communication topology of voltage observation.
[0072] S3. Use multi-resolution morphological gradient to extract features of attack detection signals, and determine whether a false data injection attack occurs by comparing the size relationship between the calculated value and the detection threshold.
[0073] The multi-resolution morphological gradient is used to inject false data into the detection signal Ω of each distributed power source in the system. iProcessing is performed, where the multi-resolution morphological gradient is expressed as follows:
[0074]
[0075]
[0076] in, Represents the multi-resolution morphological gradient; ω represents the analysis level of the multi-resolution morphological gradient. In this embodiment, ω=2, which is essentially to suppress the basic dynamic characteristics of the signal and enhance the key characteristics of the signal mutation; s represents a variable flat structure element with different origin positions.
[0077] A variable flat structure element s with different origin positions is defined as follows:
[0078] S + ={S1, S2, ..., S l-1 , S l } (13)
[0079] S - ={ S1 , S2,…,S l-1 ,s l} (14)
[0080] Among them, l represents the step size.
[0081] Linear structural elements will be used to inject false data into the attack detection signal Ω i The result of the operation is compared with the set threshold. If it exceeds the threshold, it means that the corresponding distributed power source has been attacked by false data injection, as described below:
[0082]
[0083] in, and Respectively represent the corresponding DG i Attack Detection Signal and The multi-resolution morphological gradient values obtained after processing, and the corresponding detection thresholds are and The two detection thresholds can be estimated through a large number of experiments and experience. When the multi-resolution morphological gradient value exceeds the corresponding detection threshold, it means that the node DG j To neighbor node DG i The communication link of DG j Transmit to DG i The data is tampered by false data injection.
[0084] Applying the method of this embodiment to practice, the simulation system is as follows: Figure 2 As shown, it consists of 5 distributed power sources, all of which are connected to the voltage bus through their respective connection impedances, and all carry local loads; the rated active and reactive capacities of the 5 distributed power sources are not equal, and the common-end load adopts an impedance load; according to the distributed power supply FDIA detection method based on multi-resolution morphological gradient of this embodiment, a system simulation model is built based on the MATLAB R2020a / Simulink platform to verify the control effect of the method of this embodiment.
[0085] like Figure 3 As shown in the figure, it is a schematic diagram of the communication network topology used in the embodiment of the present invention. When the system runs to 6s, the communication links from DG2 to DG1, DG3 and DG5 are all affected by FDIAs, that is, the voltage observation value information in the data packet sent by DG2 to DG1, DG3 and DG5 and were tampered with and Among them, the malicious attacker injects G U The false signal is satisfy and In addition, in this example, DG2 is Q Transmit reactive power information to DG2 At 5 seconds, it was tampered with satisfy
[0086] like Figure 4 As shown in the figure, it is a schematic diagram of the operating status of the test system in different time periods. In the period from 0 to 1s, the DG in the test system only performs local control, the secondary coordinated voltage control strategy is put into use at 1.5s, the external load disturbance is connected at 3s, and the G Q Suffering from FDI attack 1, 6s moment G U Under FDI attack 2, the attack detection mechanism is in working state from 0 to 8 seconds.
[0087] like Figure 5 As shown in Figures a to e, they are attack detection signals The morphological gradient value obtained after processing Setting G Q Detection Threshold is 0.5 (obtained from empirical testing), Figure 5 In Figure c The value at 5s is much larger than that of other DGs and is approximately equal to 3.6, indicating that the reactive power sharing interaction information received by DG3 at 5s has been injected with false data; the simulation results show that the method of this embodiment can be used to locate the position of the DG attacked by FDI in the system and determine the type of tampered data.
[0088] like Figure 6 As shown in Figures a to e, they are attack detection signals The morphological gradient value obtained after processing Setting G U Detection Threshold is 0.3 (obtained from empirical testing), Figure 6 In Figures a, c, and e, and The values at 6s are approximately equal to 60, which is much larger than and It shows that the average voltage observation interaction information received by DG1, DG3 and DG5 at 6s has been injected with false data; the simulation results show that the method of this embodiment can be used to locate the position of the DG attacked by FDI in the system and determine the type of tampered data.
[0089] The technical problem to be solved by this embodiment is that when the system communication network is attacked by FDI, it is necessary to consider how to construct the attack detection signal of each DG based on the local information of DG and the interaction information of neighbors, and how to use multi-resolution morphological gradients to extract features of the attack detection signal, so as to effectively determine the location of the FDI attack and the type of data that has been tampered with, so as to provide a guarantee for improving the stability of system operation.
[0090] The method of this embodiment is based on system interaction information and local measurement information, constructs a real-time attack detection signal that can effectively characterize the impact of FDIAs, and uses multi-resolution morphological gradients to perform secondary processing on the attack detection signal to extract the mutation characteristics of the measured signal; this method determines whether an FDI attack has occurred by comparing the size relationship between the calculated value and the detection threshold, locates the position of the DG attacked by FDI in the system, and determines the type of tampered data, thereby effectively distinguishing between system load disturbances and FDIAs. No additional physical device is required, and it can be directly embedded in the system secondary controller to realize real-time detection of FDIAs, which has good economic efficiency and engineering application value.
[0091] In addition to the above embodiments, the present invention may also have other implementation modes. Any technical solution formed by equivalent replacement or equivalent transformation falls within the protection scope required by the present invention.
Claims
1. A distributed power supply FDIA detection method based on multi-resolution morphological gradient, characterized by: The following steps are involved: S1. Based on the interactive information of the secondary coordination control layer between distributed power sources, a false data injection attack model for reactive power sharing state quantity and average voltage observation state quantity is established; S2. Analyze the impact of false data injection attacks on the consistency of system reactive power sharing and average voltage observations, and construct attack detection signals for each distributed power source based on local information of distributed power sources and neighbor interaction information; S3. Use multi-resolution morphological gradient to extract features of attack detection signals, and determine whether a false data injection attack occurs by comparing the size relationship between the calculated value and the detection threshold.
2. The distributed power supply FDIA detection method based on multi-resolution morphological gradient according to claim 1 is characterized in that: In step S1, the false data injection attack model for the reactive power sharing state quantity and the average voltage observation state quantity is as follows: in, and Indicates that the communication link is attacked from node DG j Send to neighbor node DG i False information; Q j and Respectively represent the jth distributed generation DG j The true values of reactive power and average voltage observables; and They represent the false data injection attack signals launched by the attacker on the communication link, and their physical meanings are respectively injecting interactive information Q j and The false value in; t represents time; o j and τ j are symbolic functions, respectively used to represent the mutual information Q j and Whether it is attacked by false data injection.
3. The distributed power supply FDIA detection method based on multi-resolution morphological gradient according to claim 1 is characterized in that: In step S2, the influence of false data injection attack on the consistency of reactive power sharing and average voltage observation value of the system is analyzed, wherein the reactive power sharing deviation between distributed power sources is expressed as: Among them, n i (i=1, 2, ...) represents the i-th distributed generation DG i The corresponding voltage control droop coefficient, n j Denotes the jth distributed generation DG i The corresponding voltage control droop coefficient, N i Denotes distributed generation DG i The set of neighbor nodes, Q i Indicates DG i Output reactive power, Q j Indicates DG i Neighbor node DG j The output reactive power of DG i The neighbor node number of Represents the reactive information sharing communication topology G Q The corresponding adjacency matrix element, C Q Represents the reactive power coupling coefficient; The weighted average voltage observer of each distributed power source is expressed as: in, represents the weighted average voltage observation value of each distributed power source, U i Indicates DG i Corresponding to the output voltage of the inverter, Indicates DG i The true value of the average voltage observable, Denotes the voltage observation information sharing communication topology G U The corresponding adjacency matrix element, C E represents the voltage coupling coefficient that meets the stability requirements of the control system, Indicates DG i With neighbor node DG j The accumulation of voltage observation errors between the two.
4. The distributed power supply FDIA detection method based on multi-resolution morphological gradient according to claim 3 is characterized in that: In step S2, the secondary coordinated control strategy of the voltage between distributed power sources is as follows: Among them, U ni Indicates the nominal voltage value, K vi represents the voltage control coefficient; u i Represents the secondary voltage regulation term, K i Represents the integral coefficient of the controller, β i Represents the weight coefficient of reactive power sharing and voltage recovery, U ref Indicates the reference value of the system rated voltage; When DG i and DG j When the communication link between them is attacked by false data injection, it will cause deviations in the secondary coordination control target, and eventually cause the output voltage of each distributed power source to exceed the safe range. At this time, DG i The secondary control instructions are updated as follows: By taking the derivative of the above formula (7), we get: in, and They represent the false data injection attack signals launched by the attacker on the communication link, and their physical meanings are respectively injecting interactive information Q j and False value in o j and τ j are symbolic functions, respectively used to represent the mutual information Q j and Whether it is attacked by false data injection; the impact of false data injection attack on the consistency of reactive power sharing and average voltage observation values of distributed power sources in the system is measured by and express.
5. The distributed power supply FDIA detection method based on multi-resolution morphological gradient according to claim 4 is characterized in that: In step S2, an attack detection signal of each distributed power source is constructed based on the local information of the distributed power source and the interactive information of the neighbors. or If a false data injection attack occurs, the impact of the attack will be directly reflected in the amount of controlled information. and Therefore, in any distributed power source, an attack detection signal suitable for the secondary coordinated control of voltage between distributed power sources described in equations (3) to (6) is constructed as follows: Among them, G Q Represents the communication topology of reactive power sharing, G U Represents the communication topology of voltage observation.
6. The distributed power supply FDIA detection method based on multi-resolution morphological gradient according to claim 1 is characterized in that: In step S3, a multi-resolution morphological gradient is used to inject a false data attack detection signal Ω into each distributed power source in the system. i Processing is performed, where the multi-resolution morphological gradient is expressed as follows: in, represents the multiresolution morphological gradient, ω represents the analysis level of the multiresolution morphological gradient, and s represents a variable flat structure element with different origin positions.
7. The distributed power supply FDIA detection method based on multi-resolution morphological gradient according to claim 6 is characterized in that: In step S3, the variable flat structure element s with different origin positions is defined as follows: s + ={s1,s2,…,s l-1 , s l } (13) s - ={ s1 ,s2…,s l-1 ,s l } (14) Among them, l represents the step size.
8. The distributed power supply FDIA detection method based on multi-resolution morphological gradient according to claim 6 is characterized in that: In step S3, the analysis level of the multi-resolution morphological gradient is ω=2, and a linear structure element is used to inject an attack detection signal Ω into the false data. i Perform calculation processing.
9. The distributed power supply FDIA detection method based on multi-resolution morphological gradient according to claim 8 is characterized in that: In step S3, a linear structure element is used to inject the false data into the attack detection signal Ω i The result of the operation is compared with the set threshold. If it exceeds the threshold, it means that the corresponding distributed power source has been attacked by false data injection, as described below: in, and Respectively represent the corresponding DG i Attack Detection Signal and The multi-resolution morphological gradient values obtained after processing, and the corresponding detection thresholds are and When the multi-resolution morphological gradient value exceeds the corresponding detection threshold, it means that the node DG j To neighbor node DG i The communication link of DG j Transmit to DG i The data is tampered by false data injection.
10. The distributed power supply FDIA detection method based on multi-resolution morphological gradient according to claim 9 is characterized in that: In step S3, the detection threshold and Set them to 0.5 and 0.3 respectively.