False data attack resilient method based on adaptive compensation droop coefficient

Abstract

The present application belongs to the technical field of resisting micro-grid network attack, and specifically discloses a false data attack resilience resisting method based on adaptive compensation droop coefficient, which comprises resisting frequency and voltage abnormality caused by network attack by increasing an adaptive compensation droop coefficient module. The network attack resisting method adopted by the present application only performs simple and quick adaptive compensation on the droop coefficient, does not directly change the original power distribution, performs detection and scaling functions on excessive network attack, and realizes controllability of the system by multiplying an attenuation function; when the size of the network attack is within the controllable range, the adaptive compensation can quickly and efficiently restore the frequency and voltage operating state in the micro-grid system.

Description

TECHNICAL FIELD

[0001] The present application relates to the field of resisting micro-grid network attack in information physical system, and particularly relates to a false data attack resilient resistance method based on adaptive compensation droop coefficient. BACKGROUND

[0002] False data injection attack is a typical network attack method, which can interfere with decision-making by destroying the data integrity of distributed communication network system, successfully avoid bad data detection mechanism, and achieve the purpose of endangering the security of power information physical system. When the micro-grid is connected to the grid, hackers can inject false signals, causing the secondary control compensation frequency or voltage to change, resulting in secondary control failure. In the face of micro-grid secondary control attack, the general resistance method includes event trigger mechanism, switching control and adaptive control, etc. In order to cut off the network attack on the secondary control, the secondary control can be actively dropped. For the system, it is equivalent to setting the original secondary control frequency compensation or voltage compensation to zero, but on the physical connection, the port still exists, so that the system still has the risk of further penetration attack under the primary droop control operation.

[0003] It should be noted that the information disclosed in the above background section is only used to strengthen the understanding of the background of the present application, and therefore can include information that does not constitute prior art known to those skilled in the art. SUMMARY

[0004] The purpose of the present application is to solve the technical problems existing in the background art. To this end, a false data attack resilient resistance method based on adaptive compensation droop coefficient is provided.

[0005] In order to achieve the above purpose, the technical scheme adopted by the present application is as follows:

[0006] The false data attack resilient resistance method based on adaptive compensation droop coefficient comprises the following steps:

[0007] Step S1: design frequency recovery control formula and voltage recovery control formula;

[0008] Step S2: convert the control formula of the output frequency recovery and the output voltage recovery of the distributed power supply into a matrix form;

[0009] Step S3: design the inclusive controller form of the distributed frequency recovery and voltage recovery of the communication time delay;

[0010] Step S4: use a consistency algorithm to divide the active power and the reactive power equally;

[0011] Step S5: set the false data injection attack running state of the distributed power supply, and add a detection module to analyze the sampling of the false data injection attack;

[0012] Step S6: setting a droop coefficient adaptive elastic control module to adaptively compensate the detected attack signal.

[0013] The following is a further defined technical solution of the application, for an inverter type island micro-grid composed of multiple distributed power supplies, each distributed power supply communicates with adjacent distributed power supplies to form a sparse communication network, and two distributed power supplies are selected to receive reference threshold signals, including upper limit of voltage reference value, lower limit of voltage reference value, upper limit of frequency reference value and lower limit of frequency reference value.

[0014] In order to realize active power sharing while clearly defining the stable value of the output frequency recovery of the distributed power supply, the inclusive algorithm is used to give the upper limit of the frequency reference value and the lower limit of the frequency reference value for two distributed power supplies for frequency recovery, and the frequency recovery control formula is represented as:

[0015]

[0016] In the formula, i represents the communication network node i, i.e. the i-th distributed power supply, j represents the communication network node j, i.e. the j-th distributed power supply, i and j are positive integers, S ωi is the frequency recovery control signal of the i-th distributed power supply, c ω is the frequency control gain, a ij represents the communication between the communication network node i and the communication network node j, N is the total number of distributed power supplies in the island micro-grid, N+1 represents the communication network node number of the upper limit of the reference value, N+2 represents the communication network node number of the lower limit of the reference value, ω oi is the output frequency of the i-th distributed power supply, ω oj is the output frequency of the j-th distributed power supply, ω ref,u is the upper limit of the frequency reference value, ω ref,l is the lower limit of the frequency reference value.

[0017] In order to realize reactive power sharing while clearly defining the stable value of the output voltage recovery of the distributed power supply, the inclusive algorithm is used to give the upper limit of the voltage reference value and the lower limit of the voltage reference value for two distributed power supplies for voltage recovery, and the voltage recovery control formula is represented as:

[0018]

[0019] In the formula, S vi is the voltage recovery control signal of the i-th distributed power supply, c v is the voltage control gain, v oi is the output voltage of the i-th distributed power supply, v ojThe output voltage of the jth distributed power supply is v ref,u The upper limit of the voltage reference value is v ref,l The lower limit of the voltage reference value is v

[0020] The frequency recovery control formula and the voltage recovery control formula are in matrix form, and are converted by the following steps:

[0021] Let ω o =[ω o1 ,...,ω oN ] T , ω ref =[ω ref,u ,ω ref,l ] T The frequency recovery control formula is written in matrix form:

[0022]

[0023] Let v o =[v o1 ,...,v oN ] T , v ref =[v ref,u ,v ref,l ] T The voltage recovery control formula is written in matrix form:

[0024]

[0025] In the formula, L1 and L2 are the first coefficient matrix and the second coefficient matrix extracted from the communication network Laplacian matrix block L, L1∈R N×N , L2∈R N×N , R represents the real number field, and N is the total number of distributed power supplies in the island microgrid.

[0026] The communication network Laplacian block matrix L is represented as:

[0027]

[0028] The following is a further limited technical solution of the application, because the distributed power supply has a time delay when transmitting information to the adjacent node in the communication network, it is converted into a distributed frequency recovery inclusive controller form containing communication time delay:

[0029]

[0030] The distributed voltage recovery inclusive controller form containing communication time delay is:

[0031]

[0032] In the formula, τ is a time delay, τ max is a communication time delay margin, λ k is a characteristic equation root of the kth distributed power supply.

[0033] The following is a further defined technical solution of the application, in the active power and reactive power sharing control of the island micro-grid elastic distributed control, the active power and the reactive power are shared by using a consistency algorithm:

[0034]

[0035] In the formula, S Pi is the active power recovery control signal of the ith distributed power supply, S Qi is the reactive power recovery control signal of the ith distributed power supply, c P is the active power control gain, c Q is the reactive power control gain, m Pi is the active droop coefficient of the ith distributed power supply, m Pj is the active droop coefficient of the jth distributed power supply, n Qi is the reactive droop coefficient of the ith distributed power supply, n Qj is the reactive droop coefficient of the jth distributed power supply, P i is the output active power of the ith distributed power supply, P j is the output active power of the jth distributed power supply, Q i is the output reactive power of the ith distributed power supply, Q j is the output reactive power of the jth distributed power supply.

[0036] The following is a further defined technical solution of the application, a false data injection attack detection module is introduced, the detection module is used for comparing the frequency and the voltage recovery control signal, and the comparison result is transmitted to the elastic control module; the elastic control module combines the active power and the reactive power recovery control signal with the frequency recovery control signal and the voltage recovery control signal, and is used for resisting the false data injection attack.

[0037] The following is a further defined technical solution of the application, the false data injection attack detection module adopts the following formula to carry out sampling analysis of the false data injection attack:

[0038]

[0039] Wherein, x p ∈R n , μ(t) ∈R m , y p ∈Rp represents state variables, input variables, measured output variables of the system respectively, t is a discrete time, ω(t) ∈ R l is an unknown input disturbance of the system at t, f a (t) ∈ R q represents a false data injection attack actuator signal at t, the false data injection attack actuator can tamper with the control signal received by the actuator during wireless transmission, f s (t) ∈ R h represents a false data injection attack sensor signal at t, the false data injection attack sensor can tamper with the measurement signal received by the controller during wireless transmission, A ∈ R n×n , B ∈ R n×m , C ∈ R n×l , F a ∈ R n×q , F s ∈ R p×h , D ∈ R p×n is a constant matrix of appropriate dimension.

[0040] The following is a further limited technical solution of the application, the false data injection attack detection module will carry out secondary control drop when detecting too large frequency and voltage recovery control signal, at this time, the state of the false data injection attack suffered is as follows:

[0041]

[0042] Wherein, y fi (t) and y Ei (t) are the output frequency and output voltage of the i-th inverter system at t, z f and z E are the rated frequency and rated voltage, m i and n i are both droop coefficients, P i (t) and Q i (t) are the output active power and reactive power at t, m f , n f are compensation droop coefficients, e ξ (t), e η (t) are the frequency attack and voltage attack at t.

[0043] The following is a further limited technical solution of the application, the compensation droop coefficients m f and n f of the elastic control module, the following formula is used to realize self-adaptation:

[0044]

[0045] Wherein, Pave and Q ave are the average values of the active power and the reactive power of each distributed power source, respectively, k mj and k nj are the droop control gains of the jth active power and the reactive power, a mj and a nj are the control gains of the jth active power and the reactive power, η i is the neighbor set of the distributed power source i.

[0046] The following is a further limited technical solution of the present application, in each control cycle, the external interference is detected, the calculation of the droop coefficient in the corresponding interval is triggered, and the value of the compensation droop coefficient is set. When the attack value is negative, it will be compensated to the stable value of the primary control, thereby suppressing the fluctuation of the microgrid caused by the false data injection attack, and restoring the voltage and frequency state in the microgrid. When the attack value is positive, it is compensated to the stable value of the secondary control, and the network attack is used to achieve the effect of the secondary control.

[0047] Compared with the prior art, the present application has the following technical effects:

[0048] The network attack resisting method adopted by the present application is only a simple and quick adaptive compensation of the droop coefficient, without directly changing the original power distribution. The detection scaling function is performed on the excessive network attack, and the controllability of the system is realized by multiplying the attenuation function. When the size of the network attack is within the controllable range, the adaptive compensation can quickly and efficiently restore the frequency and voltage operating state in the microgrid system.

[0049] The present application will be further described below in conjunction with the drawings and examples. BRIEF DESCRIPTION OF DRAWINGS

[0050] In order to more clearly illustrate the technical solutions in the embodiments of the present application or the prior art, the drawings needed to be used in the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present application, and other drawings can be obtained by those skilled in the art without creative labor on the basis of these drawings.

[0051] Figure 1 is a method step flow chart of the present application;

[0052] Figure 2 is a simplified structure diagram of the inverter system in parallel in the microgrid of the present application;

[0053] Figure 3 is a control block diagram of the adaptive compensation of the droop coefficient of the present application;

[0054] Figure 4A voltage operating state diagram of a system of the present application suffering from a network attack;

[0055] Figure 5 A network attack signal simulation diagram of the present application;

[0056] Figure 6 A bus voltage amplitude diagram of the present application using adaptive compensation of droop coefficients;

[0057] Figure 7 A bus voltage amplitude diagram using a traditional method;

[0058] Figure 8 A system frequency diagram of the present application using adaptive compensation of droop coefficients;

[0059] Figure 9 A system frequency diagram using a traditional method. DETAILED DESCRIPTION

[0060] In order to make the above objectives, features and advantages of the present application more apparent, specific embodiments of the present application will be described in detail below with reference to the accompanying drawings. In the following description, numerous specific details are set forth in order to provide a thorough understanding of the present application. However, the present application can be practiced in a number of different ways beyond the specific embodiments described herein and by persons skilled in the art without departing from the scope of the present application, and therefore the present application is not limited to the specific embodiments disclosed below.

[0061] As shown in Figures 1-9 , the embodiment provides a false data attack resilience method based on adaptive compensation of droop coefficients, and the specific steps are as follows:

[0062] Step S1: design a frequency recovery control formula and a voltage recovery control formula;

[0063] Step S2: convert the control formula of output frequency recovery and output voltage recovery of the distributed power supply into a matrix form;

[0064] Step S3: design an inclusive controller form of distributed frequency recovery and voltage recovery of communication time delay;

[0065] Step S4: use a consistency algorithm to divide the active power and the reactive power equally;

[0066] Step S5: set a false data injection attack operating state of the distributed power supply, and add a detection module to perform sampling analysis of the false data injection attack;

[0067] Step S6: set an adaptive resilience control module of droop coefficients, and perform adaptive compensation on the detected attack signal.

[0068] The island micro-grid adaptive distributed frequency and voltage recovery control method specifically comprises the following steps: for an inverter type island micro-grid composed of multiple distributed power sources, each distributed power source is in bidirectional communication with an adjacent distributed power source to form a sparse communication network, and optionally, two distributed power sources respectively receive reference threshold signals, which specifically comprise an upper limit of a voltage reference value, a lower limit of the voltage reference value, an upper limit of a frequency reference value and a lower limit of the frequency reference value.

[0069] In order to determine the stable value of the output frequency recovery of the distributed power source while achieving the active power sharing, the inclusive algorithm is used to give the upper limit of the frequency reference value and the lower limit of the frequency reference value for the two distributed power sources for frequency recovery, and the frequency recovery control formula is represented as follows:

[0070]

[0071] In the formula, i represents a communication network node i, i.e. the i-th distributed power source, j represents a communication network node j, i.e. the j-th distributed power source, i and j are positive integers, S ωi is a frequency recovery control signal of the i-th distributed power source, c ω is a frequency control gain, a ij represents the communication between the communication network node i and the communication network node j, N is the total number of distributed power sources in the island micro-grid, N+1 represents the serial number of the communication network node of the upper limit of the reference value, N+2 represents the serial number of the communication network node of the lower limit of the reference value, ω oi is the output frequency of the i-th distributed power source, ω oj is the output frequency of the j-th distributed power source, ω ref,u is the upper limit of the frequency reference value, ω ref,l is the lower limit of the frequency reference value.

[0072] In order to determine the stable value of the output voltage recovery of the distributed power source while achieving the reactive power sharing, the inclusive algorithm is used to give the upper limit of the voltage reference value and the lower limit of the voltage reference value for the two distributed power sources for voltage recovery, and the voltage recovery control formula is represented as follows:

[0073]

[0074] In the formula, S vi is a voltage recovery control signal of the i-th distributed power source, c v is a voltage control gain, v oi is the output voltage of the i-th distributed power source, v oj is the output voltage of the j-th distributed power source, v ref,u is the upper limit of the voltage reference value, v ref,l is the lower limit of the voltage reference value.

[0075] The frequency recovery control formula and the voltage recovery control formula adopt a matrix form, and are converted through the following steps;

[0076] Let ω o = [ω o1 ,...,ω oN ] T , ω ref = [ω ref,u ,ω ref,l ] T , and the frequency recovery control formula is written in a matrix form:

[0077]

[0078] Let v o = [v o1 ,...,v oN ] T , v ref = [v ref,u ,v ref,l ] T , and the voltage recovery control formula is written in a matrix form:

[0079]

[0080] In the formula, L1 and L2 are a first coefficient matrix and a second coefficient matrix extracted from a Laplace matrix block L of a communication network, L1∈R N×N , L2∈R N×N , R represents a real number field, and N is the total number of distributed power sources in an island micro-grid.

[0081] The communication network Laplace block matrix L is represented as:

[0082]

[0083] Since there is a time delay in the transmission of information from the distributed power source to the adjacent node in the communication network, the distributed frequency recovery inclusive controller form containing the communication time delay is converted as:

[0084]

[0085] The distributed voltage recovery inclusive controller form containing the communication time delay is:

[0086]

[0087] In the formula, τ is a delay time, τ max is a communication time delay margin, and λ k is a characteristic equation root of the kth distributed power source.

[0088] In the active power and reactive power sharing control of island micro-grid elastic distributed control, the active power and the reactive power are shared by using a consistency algorithm:

[0089]

[0090] In the formula, S Pi It is the active power recovery control signal of the i-th distributed power supply, S Qi It is the reactive power recovery control signal of the i-th distributed power supply, c P It is the active power control gain, c Q It is the reactive power control gain, m Pi It is the active droop coefficient of the i-th distributed power supply, m Pj It is the active droop coefficient of the j-th distributed power supply, n Qi It is the reactive droop coefficient of the i-th distributed power supply, n Qj It is the reactive droop coefficient of the j-th distributed power supply, P i It is the output active power of the i-th distributed power supply, P j It is the output active power of the j-th distributed power supply, Q i It is the output reactive power of the i-th distributed power supply, Q j It is the output reactive power of the j-th distributed power supply.

[0091] A detection module of false data injection attack is introduced, the detection module is used for comparing frequency and voltage recovery control signals, and the comparison result is transmitted to the elastic control module; the elastic control module combines the active power and the reactive power recovery control signal with the frequency recovery control signal and the voltage recovery control signal, and is used for resisting the false data injection attack.

[0092] Figure 2 It is a simplified structure diagram of the inverter system in parallel in the micro-grid of the application, in which the parallel of two inverters and the output impedance of the inverter are considered to be inductive, the power distribution algorithm of each inverter adopts the droop control method, and the generation of the power conversion control signal adopts the double-loop control method based on the PI controller. A detection module of false data injection attack is added to the existing droop control module, and the following formula is used for sampling analysis of the false data injection attack:

[0093]

[0094] In the formula, x p ∈R n , mu (t) ∈R m , y p ∈R p Respectively represent the state variable, input variable and measured output variable of the system, t is a discrete time, and omega (t) ∈Rl is the unknown input disturbance of the system at time t, f a (t)∈R q is the false data injection attack actuator signal at time t, the false data injection attack actuator can tamper with the control signal received by the actuator during wireless transmission, f s (t)∈R h is the false data injection attack sensor signal at time t, the false data injection attack sensor can tamper with the measurement signal received by the controller during wireless transmission, A∈R n×n , B∈R n×m , C∈R n×l , F a ∈R n×q , F s ∈R p×h , D∈R p×n is a constant matrix of appropriate dimension.

[0095] False data injection attack detection module, when detecting too large frequency and voltage recovery control signal will carry on the secondary control off, at this time suffered false data injection attack state as follows:

[0096]

[0097] Where, y fi (t) and y Ei (t) are the output frequency and output voltage of the ith inverter system at time t, z f and z E are the rated frequency and rated voltage, m i and n i are the droop coefficients, P i (t) and Q i (t) are the output active power and reactive power at time t, m f , n f are the compensation droop coefficients, e ξ (t), e η (t) are the frequency attack and voltage attack at time t.

[0098] The compensation droop coefficients m f and n f of the elastic control module, the following formula is used to realize self-adaption:

[0099]

[0100] Where, P ave and Q ave are the average values of the active power and reactive power of each distributed power supply, k mj and k nja is the droop control gain of the jth active power and reactive power mj a is the droop control gain of the jth active power and reactive power nj a is the control gain of the jth active power and reactive power i a is the neighbor set of the distributed power i.

[0101] In each control cycle, the external interference is detected, the calculation of the droop coefficient in the corresponding interval is triggered, and the value of the compensation droop coefficient is set. When the attack value is negative, it is compensated to the stable value of the primary control, thereby suppressing the fluctuation of the microgrid caused by the false data injection attack, and restoring the voltage and frequency state in the microgrid. When the attack value is positive, it is compensated to the stable value of the secondary control, and the network attack reaches the effect of the secondary control.

[0102] Figure 4 is the complete running state of the system, 0-0.5 seconds is the primary control running state of the system; 0.5-1.5 is the secondary control running state of the system; at 1.5 seconds, the system suffers from a network attack, and the system switches to control back to the primary control running at 1.55 seconds, but the communication port of the secondary control is modified to a constant or a periodic function variable, causing instability or even paralysis of the primary control.

[0103] A microgrid model of two parallel inverter systems is built, an adaptive compensation controller is designed and applied to the droop coefficient of the microgrid, the size of the false data injection attack is observed, and the running state of the microgrid using the traditional switching control method is compared. The droop control coefficient of the traditional method is fixed. The microgrid runs in island mode, the network attack signal source is injected at t=1.55 seconds, and the running state changes of the bus voltage amplitude and system frequency of the microgrid during this period are observed, wherein the power of the load is 20kW. In this embodiment, the amplitude is 0.27, the bias is 0.17, and the frequency is 4rad / s. The network attack signal simulation diagram of the present application is shown in Figure 5 The running state of the system, Figure 6 and Figure 8 are the bus voltage amplitude diagram and the system frequency diagram using the droop coefficient adaptive compensation of the present application, respectively. It can be seen that when the sine signal is positive, the system bus voltage amplitude and the system frequency size are maintained near the rated value of the secondary control (311V and 50Hz), and the difference is very small; when the sine signal is negative, the system bus voltage amplitude and the system frequency size are maintained near the rated value of the primary control (308V and 49.9Hz), and the difference is very small. In comparison, Figure 7 and Figure 9 are the bus voltage amplitude diagram and the system frequency diagram using the traditional method, respectively. It can be seen that the bus voltage amplitude and the system frequency size under the traditional method present obvious deviation from the rated value.

[0104] The above merely describes preferred embodiments of the present application, and is not intended to limit the present application in any form. Any person skilled in the art, without departing from the technical scheme of the present application, can make many possible changes and modifications to the technical scheme of the present application, or modify equivalent embodiments, by using the disclosed methods and technical contents. Therefore, any equivalent changes made according to the shape, structure and principle of the present application, without departing from the technical scheme of the present application, should be covered within the protection scope of the present application.

Claims

1. A method for resilient defense against spoofing attacks based on adaptive sagging coefficient compensation, characterized in that, Includes the following steps: Step S1: Design the frequency recovery control formula and the voltage recovery control formula; Step S2: Convert the control formulas for output frequency recovery and output voltage recovery of the distributed power source into matrix form; Step S3: Design a distributed frequency recovery and voltage recovery containment controller for communication delay; Step S4: Use a consensus algorithm to evenly distribute active power and reactive power; Step S5: Set the running status of the fake data injection attack for distributed power supply, and add a detection module to perform sampling and analysis of the fake data injection attack; Step S6: Set up the droop coefficient adaptive elastic control module to adaptively compensate for the detected attack signal; Compensation sag coefficient of elastic control module m f and n f The following formula is used to achieve adaptive behavior: in, P ave and Q ave These are the average active and reactive power values ​​for each distributed power source, respectively. k mj and k nj For the first j The droop control gain for both active and reactive power. a mj and a nj For the first j Control gains for active and reactive power, η i For distributed power sources i The set of neighbors; External interference is detected in each control cycle, triggering the calculation of the droop coefficient in the corresponding interval. The value of the compensation droop coefficient is set. When the attack value is negative, it is compensated to the stable value of the primary control, thereby suppressing the fluctuations caused by the microgrid's false data injection attack and restoring the voltage and frequency state in the microgrid. When the attack value is positive, it is compensated to the stable value of the secondary control, using network attacks to achieve the effect of secondary control.

2. The method for resilient defense against spoofing attacks based on adaptive compensation sagging coefficient as described in claim 1, characterized in that, For an inverter-type islanded microgrid composed of multiple distributed power sources, each distributed power source communicates bidirectionally with its neighboring distributed power sources to form a sparsely connected communication network. Any two distributed power sources can be randomly selected to receive reference threshold signals, which include the upper limit of voltage reference value, the lower limit of voltage reference value, the upper limit of frequency reference value, and the lower limit of frequency reference value. To achieve equal distribution of active power while determining the stable value of the output frequency recovery of distributed power sources, a frequency recovery control formula is used, based on the envelope algorithm, to provide upper and lower limits of frequency reference values ​​for two of the distributed power sources. The frequency recovery control formula is expressed as: In the formula: i Represents a communication network node i That is, the first i Taiwan distributed power supply, j Represents a communication network node j That is, the first j Taiwan distributed power supply, i and j All are positive integers. S ωi For the first i Frequency recovery control signal of distributed power source, c ω For frequency control gain, a ij Represents a communication network node i and communication network nodes j The communication status, N This represents the total number of distributed power sources in an isolated microgrid. N +1 indicates the communication network node sequence number of the upper limit of the reference value. N +2 represents the communication network node number of the lower limit of the reference value. ω oi For the first i The output frequency of the distributed power supply ω oj For the first j The output frequency of the distributed power supply ω ref,u This is the upper limit of the frequency reference value. ω ref,l This is the lower limit of the frequency reference value; To achieve reactive power equalization while determining the stable output voltage recovery value of the distributed power sources, a voltage reference upper limit and a voltage reference lower limit are given for two of the distributed power sources based on the envelope algorithm for voltage recovery. The voltage recovery control formula is expressed as: In the formula: S vi For the first i The voltage recovery control signal of the distributed power source. c v For voltage-controlled gain, v oi For the first i The output voltage of the distributed power supply v oj For the first j The output voltage of the distributed power supply v ref,u This is the upper limit of the voltage reference value. v ref,l This is the lower limit of the voltage reference value.

3. The method for resilient defense against spoofing attacks based on adaptive compensation sagging coefficient as described in claim 2, characterized in that, The frequency recovery control formula and voltage recovery control formula are in matrix form and are transformed through the following steps; make , , The frequency recovery control formula is written in matrix form: ； make , , The voltage recovery control formula is written in matrix form: ； In the formula: L 1. L 2 is a block composed of the Laplace matrix of the communication network. L The first coefficient matrix and the second coefficient matrix extracted from them L 1∈ R N×N , L 2∈ R N×N , R Represents the real number field. N This represents the total number of distributed power sources in an isolated microgrid. The communication network Laplace block matrix L Represented as: 。 4. The method for resilient defense against spoofing attacks based on adaptive compensation sagging coefficient as described in claim 3, characterized in that, Because there is a time delay in the transmission of information from distributed power sources to adjacent nodes in the communication network, it is transformed into a distributed frequency recovery containment controller form that includes communication delay: Distributed voltage recovery containment controller form with communication delay: In the formula: τ For the delay time, τ max For communication delay margin, λ k For the first k The characteristic equation root of a distributed power source.

5. The method for resilient defense against spoofing attacks based on adaptive compensation sagging coefficient as described in claim 3, characterized in that, In the flexible distributed control of islanded microgrids, active and reactive power are evenly distributed using a consensus algorithm: In the formula: S Pi For the first i The active power recovery control signal for the distributed power source. S Qi For the first i The reactive power recovery control signal of the distributed power source. c P For active power control gain, c Q For reactive power control gain, m Pi For the first i Active power droop factor of distributed power sources in Taiwan m Pj For the first j Active power droop factor of distributed power sources in Taiwan n Qi For the first i The reactive power droop factor of distributed power sources in Taiwan. n Qj For the first j The reactive power droop factor of distributed power sources in Taiwan. P i For the first i The output active power of the distributed power source. P j For the first j The output active power of the distributed power source. Q i For the first i The output reactive power of the distributed power source Q j For the first j The reactive power output of the distributed power source.

6. The method for resilient defense against spoofing attacks based on adaptive compensation sagging coefficient as described in claim 3, characterized in that, A detection module for false data injection attacks is introduced. The detection module compares the frequency and voltage recovery control signals and transmits the comparison result to the elastic control module. The elastic control module combines the active power and reactive power recovery control signals with the frequency recovery control signal and the voltage recovery control signal to resist false data injection attacks.

7. The method for resilient defense against spoofing attacks based on adaptive compensation sagging coefficient as described in claim 5, characterized in that, The fake data injection attack detection module uses the following formula to sample and analyze fake data injection attacks: in, x p ∈ R n μ ( t )∈ R m 、y p ∈ R p These represent the system's state variables, input variables, and measured output variables, respectively. t For discrete time intervals, ω ( t )∈ R l for t Unknown input disturbances to the system at any given time. f a ( t )∈ R q represent t The spoofed data injection attack can manipulate the executor's signals during wireless transmission. f s ( t )∈ R h represent t The injection of spoofed data into the sensor signal at any given moment can tamper with the measurement signal received by the controller during wireless transmission. A ∈ R n×n , B ∈ R n×m , C ∈ R n×l , F a ∈ R n×q , F s ∈ R p×h , D ∈ R p×n It is a constant matrix.

8. The method for resilient defense against spoofing attacks based on adaptive compensation sagging coefficient as described in claim 5, characterized in that, The fake data injection attack detection module will perform secondary control disconnection when it detects excessively high frequency and voltage recovery control signals. The state of the fake data injection attack under these circumstances is as follows: in, y fi ( t )and y Ei ( t ) are respectively t The first moment i The output frequency and output voltage of the inverter system z f and z E These are the rated frequency and rated voltage, respectively. m i and n i All are droop coefficients. P i ( t )and Q i ( t ) are respectively t The output active power and reactive power at any given time, m f , n f To compensate for the droop coefficient, e ξ ( t ), e η ( t )for t Frequency attacks and voltage attacks.

9. The method for resilient defense against spoofing attacks based on adaptive compensation sagging coefficient as described in claim 1, characterized in that, External interference is detected in each control cycle, triggering the calculation of the droop coefficient in the corresponding interval, and setting the value of the compensation droop coefficient. When the attack value is negative, it will be compensated to the stable value of the first control, thereby suppressing the fluctuations caused by the microgrid being attacked by false data injection, and restoring the voltage and frequency state in the microgrid. When the attack value is positive, it is compensated to the stable value of secondary control, thus achieving the effect of secondary control through network attacks.

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