Intermediate variable-based estimation method of DC micro-grid T-S fuzzy system under FDI attack

Abstract

The invention discloses an intermediate variable-based estimation method for a DC micro-grid T-S fuzzy system under FDI attack, and the method comprises the following steps: firstly, giving a nonlinear DC micro-grid system with a constant power load under T-S attack; obtaining a T-S fuzzy model of the system through a fan-shaped nonlinear method; designing an intermediate variable and an intermediate observer; finally, designing and solving an intermediate observation gain through a matrix inequality; and assigning the observation gain to the loop. According to the method, the uncertainty of the parameters of the direct-current micro-grid system can be completely reduced on a nonlinear system.

Description

Technical Field

[0001] The present invention belongs to the technical field of power system observer design, and more specifically, relates to an estimation method based on intermediate variables for a TS fuzzy system of a DC microgrid under FDI attack. Background Art

[0002] Due to the openness and vulnerability of communication networks, power systems face the threat of cyber attacks. Typically, typical cyber attacks include denial of service (DoS) attacks, delay attacks, and false data injection (FDI) attacks, where FDI attacks tamper with power system data, causing power outages or even system blackouts.

[0003] Since FDI attacks are somewhat concealed, how to ensure the reliability of the power system under FDI attacks is of great significance.

[0004] With the development of power systems and the use of energy storage devices, more and more nonlinear characteristics appear in power systems. Among the related research topics of DC microgrids, the control and stability of DC microgrids with constant power loads (CPL) have attracted a lot of attention. The study of constant power loads in DC microgrids is crucial for marine power grids, automotive and spacecraft applications, and induction motor drives. From the existing technology, technicians use current distribution to stabilize the entire DC microgrid, while the negative impedance characteristics of constant power may make the entire system unstable. Due to the nonlinear characteristics of DC microgrids with constant power loads, the TS fuzzy method can better approximate nonlinear dynamics, providing an important way to study nonlinear systems. The design of observers based on TS fuzzy models has very important practical significance.

[0005] At present, the TS fuzzy model can approximate nonlinear dynamics well and has become an important approach in the field of nonlinear research. In particular, the fuzzy control gain theory based on parallel compensation (PDC) and linear matrix inequality (LMI) techniques has made linear control theory widely used in nonlinear system control. However, in the study of attack signal estimation of nonlinear systems under network attacks, the real-time estimation of FDI attacks and system states has not been well achieved simultaneously.

[0006] Therefore, a new estimation method based on intermediate variables for TS fuzzy system of DC microgrid under FDI attack is urgently needed. Summary of the invention

[0007] The present invention proposes an estimation method based on intermediate variables for TS fuzzy system of DC microgrid under FDI attack. Specifically, an intermediate variable is introduced and an intermediate estimator is constructed to estimate the state of the system and FDI attack at the same time, which meets the requirements of accuracy and real-time performance in practical applications.

[0008] In order to solve at least one of the above technical problems, according to one aspect of the present invention, a method for estimating a TS fuzzy system of a DC microgrid under FDI attack based on intermediate variables is provided, comprising the following steps:

[0009] Step 1, given a nonlinear DC microgrid system with a constant power supply load under FDI attack;

[0010] Step 2, obtaining the TS fuzzy model of the DC microgrid;

[0011] Step 3, design the intermediate estimator;

[0012] Step 4: Design and solve the intermediate estimator gain through matrix inequality to realize the estimation of the TS fuzzy system of the DC microgrid based on intermediate variables under FDI attack.

[0013] Furthermore, step 1 is specifically: studying the properties of a DC power supply and a single constant power load;

[0014] The dynamic equation of the tributary link when the RLC filter is connected in series with the jth constant power load system is as follows:

[0015]

[0016] Where P j is the jth constant power supply load, i L,j , v C,j are the inductor current and capacitor voltage of the jth constant power supply load, C j is the input capacitance of the jth constant power supply load, V dc is the DC power supply, r L,j , L j are the line resistance and filter inductance of the jth constant power supply load; for the balance point [i L0,j v C0,j ], constant power P j The following constraints must be met:

[0017]

[0018] P max,j is the maximum power of the jth constant power supply load. By ensuring that the Jacobian matrix of formula (1) is Hurwitz and has negative real roots, it is ensured that there is a practical operable point;

[0019] Considering the voltage source connected to the ESS through the RLC filter, the ESS is represented by the current source ies, then the state space is represented as follows:

[0020]

[0021] Among them, C s is the output capacitance of the source converter, L s , r s are the line resistance and filter inductance in the ESS, i L,s , v C,s are the inductor current and capacitor voltage in the ESS, i es is the injected current.

[0022] By changing formula (1) and formula (3), a dynamic system with an equilibrium point located at the origin is obtained through the Lyapunov stability analysis method, as follows:

[0023]

[0024] The state space expression given multiple constant power loads is as follows:

[0025]

[0026] Where j = {1, 2, ..., Q}, s = Q + 1 1 represents the state of the DC source filter; x j =[i L,j v C,j ] T and x s =[i L,s v C,s ] T are the states of the jth constant power load filter and the DC source filter, respectively, and:

[0027]

[0028] The source subsystem can be described as:

[0029]

[0030] in,

[0031] Assuming that the current point coordinates are transformed and the current of the energy storage system becomes the control input and FDI attack, the entire DC microgrid system is rewritten, and its equilibrium point is at the origin, in the following form:

[0032]

[0033] in and

[0034]

[0035] h=[h1,…,h Q ]T and

[0036] Furthermore, in step 2, the equivalent TS fuzzy model of the nonlinear system is systematically calculated by using the sector nonlinear method to obtain the local matrix and TS fuzzy membership function, which are specifically:

[0037] The multiple constant power DC microgrids are equivalent to an equivalent constant power microgrid system by nonlinear modeling of this system;

[0038] For a given area Calculate sectors and Make

[0039]

[0040] By transforming the sector inequality Convert to min-max inequality get:

[0041]

[0042] Based on the sector nonlinear method, consider:

[0043]

[0044] Solving equation (10) yields the membership functions M1 and M2;

[0045]

[0046] Substituting (10) into (8), considering FDI attack, the equivalent TS fuzzy model is:

[0047]

[0048] Where i = 1, 2, the FDI attack signal is denoted as a y (t),B wj represents the grid disturbance, u(t) represents the system input, and the output is the corresponding system state and actuator attack C j =I 4×4 ;

[0049]

[0050]

[0051] 4. The method according to claim 3, characterized in that step 3 specifically comprises: Then formula (12) becomes:

[0052]

[0053] in Next, design the intermediate variables:

[0054]

[0055] where μ j Based on the intermediate variable (14) and formula (13), the intermediate observer is obtained:

[0056]

[0057] in, is the estimated value of z(t),τ(t).

[0058] Furthermore, step 4 is specifically as follows:

[0059] first

[0060] definition According to formulas (13) and (15),

[0061] get:

[0062]

[0063] Proof According to the Lyapunov stability criterion, the constructor V(t) is as follows:

[0064]

[0065] So

[0066]

[0067] because

[0068]

[0069]

[0070] So

[0071]

[0072] definition Then substituting into formula (17) we can get:

[0073]

[0074] in:

[0075]

[0076]

[0077] on the other hand:

[0078]

[0079] Then from (18) and (19) we can get

[0080]

[0081] in

[0082]

[0083] In order to determine the stable interval of the system state, the following set is introduced:

[0084]

[0085] So:

[0086]

[0087] Conclusion

[0088] Just solve the matrix:

[0089]

[0090] Where * represents a symmetric element, P represents the positive definite matrix to be solved, and H represents the matrix to be solved:

[0091]

[0092]

[0093] Get P1, P2, H then the estimator gain L = P -1 H can be calculated.

[0094] According to another aspect of the present invention, a computer-readable storage medium is provided, on which a computer program is stored, and when the program is executed by a processor, the steps of the estimation method based on intermediate variables of the TS fuzzy system of a DC microgrid under FDI attack of the present invention are implemented.

[0095] According to another aspect of the present invention, a computer device is provided, comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein when the processor executes the program, the steps of the estimation method based on intermediate variables for the TS fuzzy system of a DC microgrid under FDI attack of the present invention are implemented.

[0096] Compared with the existing technology, the above method of the present invention has the following beneficial effects: the TS fuzzy model proposed by the present invention can completely accommodate the uncertainty of the parameters of the DC microgrid system on the nonlinear system. Secondly, the design of the intermediate estimator can be well free from the restriction of the observer matching condition, and the real-time estimation of the system state and FDI attack can be realized. BRIEF DESCRIPTION OF THE DRAWINGS

[0097] In order to more clearly illustrate the technical solutions of the embodiments of the present invention, the drawings of the embodiments will be briefly introduced below. Obviously, the drawings in the following description only relate to some embodiments of the present invention, but are not intended to limit the present invention.

[0098] Figure 1 It represents the overall architecture diagram of the present invention.

[0099] Figure 2 A simplified model schematic diagram showing a DC power supply, a power converter and a j-th CPL in Embodiment 1 of the present invention;

[0100] Figure 3 A simplified model schematic diagram showing the energy storage system in Embodiment 1 of the present invention;

[0101] Figure 4 A flow chart of the method of the present invention is shown. DETAILED DESCRIPTION

[0102] To make the purpose, technical solution and advantages of the embodiments of the present invention clearer, the technical solution of the embodiments of the present invention will be described clearly and completely in conjunction with the accompanying drawings of the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of them.

[0103] Unless otherwise defined, technical or scientific terms used herein shall have the same meaning as commonly understood by one of ordinary skill in the art to which the invention belongs.

[0104] Embodiment 1:

[0105] like Figure 1-4 As shown, the present invention proposes an estimation method based on intermediate variables for the TS fuzzy system of a DC microgrid under FDI attack, comprising the following steps:

[0106] Step 1, given a nonlinear DC microgrid system with a constant power supply load under FDI attack;

[0107] Step 2, obtaining the TS fuzzy model of the DC microgrid;

[0108] Step 3, design the intermediate estimator;

[0109] Step 4, design and solve the intermediate estimator gain through matrix inequality to realize the estimation of the DC microgrid TS fuzzy system based on intermediate variables under FDI attack;

[0110] Step 1, Figure 1 It includes several constant power loads (CPLs), DC power supplies, and energy storage systems (ESSs). Figure 1 Build a dynamic model of a DC microgrid.

[0111] In order to obtain the dynamics of a DC microgrid with multiple constant power loads, we first study the properties of the DC power source and a single constant power load such as Figure 2 As shown. Then the dynamic equation of the tributary link when the RLC filter is connected in series with the jth constant power load system is as follows:

[0112]

[0113] Where P j is the jth constant power supply load; for the balance point [i L0,j v C0,j ], constant power P j The following constraints must be met:

[0114]

[0115] By ensuring that the Jacobian matrix of equation (1) is Hurwitz and has negative real roots, it can be ensured that there are actual operable points.

[0116] Consider a voltage source connected to an ESS through an RLC filter. The ESS is represented by a current source ies, as Figure 3 As shown, the state space is expressed as follows:

[0117]

[0118] By changing formula (1) and formula (3), a dynamic system with an equilibrium point located at the origin can be obtained, which can be analyzed by Lyapunov stability analysis method, as follows:

[0119]

[0120] The state space expression given multiple constant power loads is as follows:

[0121]

[0122] Where j = {1, 2, ..., Q}, s = Q + 1 1 represents the state of the DC source filter. j =[i L,j c C,j ]T and x s =[i L,s c C,s ] T are the states of the jth constant power load filter and the DC source filter, respectively, and:

[0123]

[0124] The source subsystem can be described as:

[0125]

[0126] in,

[0127] Assuming that the current point coordinates are transformed and the current of the energy storage system becomes the control input and FDI attack, the entire DC microgrid system is rewritten, and its equilibrium point is at the origin, in the following form:

[0128]

[0129] in and

[0130]

[0131] h=[h1,…,h Q ] T and

[0132] Step 2. In the past DC microgrid TS fuzzy model, the linear controller can only guarantee the local stability near the working point. The TS fuzzy model designed by the nonlinear controller can guarantee the semi-global stability of the system and ensure the dynamic stability of the DC microgrid with constant power load.

[0133] The equivalent TS fuzzy model of the nonlinear system is systematically calculated by deploying the so-called sector nonlinear method, and the local matrix and TS fuzzy membership functions are obtained.

[0134] The multiple constant power DC microgrids are equivalent to an equivalent constant power microgrid system, and the nonlinear modeling of this system is performed. Sectors can be calculated and Make

[0135] By transforming the sector inequality Convert to min-max inequality get:

[0136]

[0137] Based on the sector nonlinear method, consider:

[0138]

[0139] Solving equation (10) yields the membership functions M1 and M2;

[0140]

[0141] Substituting (10) into (8), considering FDI attack, the equivalent TS fuzzy model is:

[0142]

[0143] Where i = 1, 2, the FDI attack signal is denoted as a y (t),B wj represents the grid disturbance, u(t) represents the system input, and the output is the corresponding system state and actuator attack C j =I 4×4 .

[0144]

[0145]

[0146] Step 3. Design the intermediate observer of the DC microgrid with multiple constant power loads. First, we need to design the intermediate variables

[0147] make Then formula (12) can be transformed into:

[0148]

[0149] in Next, design the intermediate variables:

[0150]

[0151] where μ j yes

[0152] Based on the intermediate variable (14) and formula (13), we can obtain the intermediate observer

[0153]

[0154] in, is the estimated value of z(t),τ(t).

[0155] Step 4. Design and solve the intermediate observer gain through matrix inequality, and finally estimate the fault through the intermediate observer.

[0156] first

[0157] definition From formula (13) and (15), we can get:

[0159]

[0160] Evidence According to the Lyapunov stability criterion, we construct the function V(t) as follows:

[0161]

[0162] So

[0163]

[0164] because

[0165]

[0166] So

[0167]

[0168]

[0169] We define Then substituting into formula (17) we can get:

[0170]

[0171] in:

[0172]

[0173] on the other hand:

[0174]

[0175] Then from (18) and (19) we can get

[0176]

[0177] in

[0178]

[0179] In order to determine the stable interval of the system state, we introduce the following set:

[0180]

[0181] So:

[0182]

[0183] It can be concluded that

[0184] We just need to solve the matrix:

[0185]

[0186] Where * represents a symmetric element, P represents the positive definite matrix to be solved, and H represents the matrix to be solved

[0187]

[0188] Get P1, P2, H then the estimator gain L = P -1 H can be calculated.

[0189] Through the above steps, an estimator based on intermediate variables for the TS fuzzy system of the DC microgrid under FDI attack can be designed. The estimator can accurately estimate the state of the system and the FDI attack in real time to ensure the stability and safety of the system. In addition, the switching fuzzy model predictive control (MPC) is introduced. The information of some key points of the system's membership function can be updated in time, and the value obtained at each moment is optimal. Compared with the previous method, the curve converges faster, the conservative performance of the system is better, and the computational burden of the online optimization problem is reduced.

[0190] Embodiment 2:

[0191] The computer-readable storage medium of this embodiment stores a computer program thereon, and when the program is executed by a processor, the steps in the estimation method based on intermediate variables for the TS fuzzy system of a DC microgrid under FDI attack of Example 1 are implemented.

[0192] The computer-readable storage medium of this embodiment may be an internal storage unit of the terminal, such as a hard disk or memory of the terminal; the computer-readable storage medium of this embodiment may also be an external storage device of the terminal, such as a plug-in hard disk, a smart memory card, a secure digital card, a flash memory card, etc. equipped on the terminal; further, the computer-readable storage medium may also include both an internal storage unit of the terminal and an external storage device.

[0193] The computer-readable storage medium of this embodiment is used to store computer programs and other programs and data required by the terminal. The computer-readable storage medium can also be used to temporarily store data that has been output or is to be output.

[0194] Embodiment 3:

[0195] The computer device of this embodiment includes a memory, a processor, and a computer program stored in the memory and executable on the processor. When the processor executes the program, the steps of the estimation method based on intermediate variables for the TS fuzzy system of a DC microgrid under FDI attack in Example 1 are implemented.

[0196] In this embodiment, the processor may be a central processing unit, or other general-purpose processors, digital signal processors, application-specific integrated circuits, readily available programmable gate arrays or other programmable logic devices, discrete gate or transistor logic devices, discrete hardware components, etc. The general-purpose processor may be a microprocessor or the processor may also be any conventional processor, etc. The memory may include a read-only memory and a random access memory, and provide instructions and data to the processor. A portion of the memory may also include a non-volatile random access memory. For example, the memory may also store information about the device type.

[0197] Those skilled in the art will appreciate that the disclosed content of the embodiments may be provided as methods, systems, or computer program products. Therefore, the present solution may adopt the form of hardware embodiments, software embodiments, or embodiments combining software and hardware. Moreover, the present solution may adopt the form of a computer program product implemented on one or more computer-usable storage media (including but not limited to disk storage and optical storage, etc.) containing computer-usable program codes.

[0198] The present solution is described with reference to the flowchart and / or block diagram of the method and computer program product according to the embodiment of the present solution. It should be understood that each process and / or block in the flowchart and / or block diagram, as well as the combination of the processes and / or blocks in the flowchart and / or block diagram, can be implemented by computer program instructions; these computer program instructions can be provided to a processor of a general-purpose computer, a special-purpose computer, an embedded processor or other programmable data processing device to generate a machine, so that the instructions executed by the processor of the computer or other programmable data processing device generate instructions for implementing the processes in the flowchart and / or block diagram. Figure 1 A process or multiple processes and / or boxes Figure 1 A device that provides the functions specified in a block or multiple blocks.

[0199] These computer program instructions may also be stored in a computer readable memory capable of directing a computer or other programmable data processing device to operate in a specific manner, so that the instructions stored in the computer readable memory produce an article of manufacture including an instruction device, which implements the process Figure 1 A process or multiple processes and / or boxes Figure 1 A function specified in one or more boxes.

[0200] These computer program instructions can also be loaded onto a computer or other programmable data processing device so that a series of operating steps are executed on the computer or other programmable device to produce a computer-implemented process, thereby providing instructions for implementing the process. Figure 1 A process or multiple processes and / or boxes Figure 1 A step that specifies a function in one or more boxes.

[0201] Those skilled in the art can understand that all or part of the processes in the above-mentioned embodiments can be implemented by instructing the relevant hardware through a computer program, and the program can be stored in a computer-readable storage medium, and when the program is executed, it can include the processes of the embodiments of the above-mentioned methods. The storage medium can be a disk, an optical disk, a read-only memory (ROM) or a random access memory (RAM), etc.

[0202] The examples described in the present invention are merely descriptions of the preferred implementation modes of the present invention, and are not intended to limit the concept and scope of the present invention. Without departing from the design concept of the present invention, various modifications and improvements made to the technical solutions of the present invention by engineers and technicians in this field should all fall within the protection scope of the present invention.

Claims

1. An estimation method based on intermediate variables for TS fuzzy system of DC microgrid under FDI attack, characterized in that: The steps include: Step 1, given a nonlinear DC microgrid system with a constant power supply load under FDI attack; Step 2, obtaining the TS fuzzy model of the DC microgrid; Step 3, design the intermediate estimator; Step 4: Design and solve the intermediate estimator gain through matrix inequality to realize the estimation of the TS fuzzy system of the DC microgrid based on intermediate variables under FDI attack.

2. The method according to claim 1, characterized in that: Step 1 is specifically: studying the properties of a DC power source and a single constant power load; The dynamic equation of the tributary link when the RLC filter is connected in series with the jth constant power load system is as follows: Where P j is the jth constant power supply load, i L,j , v C,j are the inductor current and capacitor voltage of the jth constant power supply load, C j is the input capacitance of the jth constant power supply load, V dc is the DC power supply, r L,j , L j are the line resistance and filter inductance of the jth constant power supply load; for the balance point [i L0,j v C0,j ], constant power P j The following constraints must be met: P max,j is the maximum power of the jth constant power supply load. By ensuring that the Jacobian matrix of formula (1) is Hurwitz and has negative real roots, it is ensured that there is a practical operable point; Considering the voltage source connected to the ESS through the RLC filter, the ESS is represented by the current source ies, then the state space is represented as follows: Among them, C s is the output capacitance of the source converter, L s , r s are the line resistance and filter inductance in the ESS, i L,s , v C,s are the inductor current and capacitor voltage in the ESS, i es is the injected current. By changing formula (1) and formula (3), a dynamic system with an equilibrium point located at the origin is obtained through the Lyapunov stability analysis method, as follows: The state space expression given multiple constant power loads is as follows: Where j = {1, 2, ..., Q}, s = Q + 1 1 represents the state of the DC source filter; x j =[i L,j v C,j ] T and x s =[i L,s v C,s ] T are the states of the jth constant power load filter and the DC source filter, respectively, and: The source subsystem can be described as: in, Assuming that the current point coordinates are transformed and the current of the energy storage system becomes the control input and FDI attack, the entire DC microgrid system is rewritten, and its equilibrium point is at the origin, in the following form: in and h=[h1,…,h Q ] T and 3. The method according to claim 2, characterized in that In step 2, the equivalent TS fuzzy model of the nonlinear system is systematically calculated by using the sector nonlinear method to obtain the local matrix and TS fuzzy membership function, which are specifically: The multiple constant power DC microgrids are equivalent to an equivalent constant power microgrid system by nonlinear modeling of this system; For a given area Calculate sectors and Make By transforming the sector inequality Convert to min-max inequality get: Based on the sector nonlinear method, consider: Solving equation (10) yields the membership functions M1 and M2; Substituting (10) into (8), considering FDI attack, the equivalent TS fuzzy model is: Where i = 1, 2, the FDI attack signal is denoted as a y (t),B wj represents the grid disturbance, u(t) represents the system input, and the output is the corresponding system state and actuator attack C j =I 4×4 ; 4. The method according to claim 3, characterized in that Step 3 is as follows: Then formula (12) becomes: in Next, design the intermediate variables: where μ j Based on the intermediate variable (14) and formula (13), the intermediate observer is obtained: in, is the estimated value of z(t),τ(t).

5. The method according to claim 4, characterized in that Step 4 is as follows: first definition From formula (13) and (15), we can get: Proof According to the Lyapunov stability criterion, the constructor V(t) is as follows: So because So definition Then substituting into formula (17) we can get: in: on the other hand: Then from (18) and (19) we can get in In order to determine the stable interval of the system state, the following set is introduced: So: Conclusion Just solve the matrix: Where * represents a symmetric element, P represents the positive definite matrix to be solved, and H represents the matrix to be solved: Get P1, P2, H then the estimator gain L = P -1 H can be calculated.

6. A computer-readable storage medium having a computer program stored thereon, characterized in that: When the program is executed by a processor, the steps in the estimation method based on intermediate variables for the TS fuzzy system of a DC microgrid under FDI attack as described in any one of claims 1 to 5 are implemented.

7. A computer device comprising a memory, a processor and a computer program stored in the memory and executable on the processor, characterized in that: When the processor executes the program, the steps in the estimation method based on intermediate variables for the TS fuzzy system of a DC microgrid under FDI attack as described in any one of claims 1 to 5 are implemented.

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