CN114421499A - Attack reconstruction and elastic control method of multi-region load frequency system - Google Patents

Attack reconstruction and elastic control method of multi-region load frequency system Download PDF

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CN114421499A
CN114421499A CN202210107628.6A CN202210107628A CN114421499A CN 114421499 A CN114421499 A CN 114421499A CN 202210107628 A CN202210107628 A CN 202210107628A CN 114421499 A CN114421499 A CN 114421499A
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attack
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CN114421499B (en
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陈小莉
曹杰
岳东
刘金良
胡松林
赵玮
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Nanjing University of Finance and Economics
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    • H—ELECTRICITY
    • H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02J—CIRCUIT ARRANGEMENTS OR SYSTEMS FOR SUPPLYING OR DISTRIBUTING ELECTRIC POWER; SYSTEMS FOR STORING ELECTRIC ENERGY
    • H02J3/00—Circuit arrangements for ac mains or ac distribution networks
    • H02J3/24—Arrangements for preventing or reducing oscillations of power in networks
    • H02J3/241—The oscillation concerning frequency
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    • H—ELECTRICITY
    • H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02J—CIRCUIT ARRANGEMENTS OR SYSTEMS FOR SUPPLYING OR DISTRIBUTING ELECTRIC POWER; SYSTEMS FOR STORING ELECTRIC ENERGY
    • H02J3/00—Circuit arrangements for ac mains or ac distribution networks
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Abstract

The invention discloses an attack reconstruction and elastic control method of a multi-region load frequency system, wherein the method comprises the following steps of S1: establishing a load frequency control mathematical model of a multi-region power system under the condition of no network attack; s2: establishing mathematical models of DoS attack and FDI attack; s3: constructing mathematical models of a state observer and an attack observer, jointly estimating the system state and the FDI attack, considering the influence of the system state and the FDI attack, and constructing a controller with attack compensation; s4: considering the influence of DoS attack and FDI attack, and establishing a mathematical model for controlling the load frequency of the multi-region power system under hybrid attack; s5: designed to satisfy H∞Obtaining a controller gain matrix K, a state observer gain matrix G and an attack observation matrix G with an attack compensation function according to the controller design criterion of the multi-region power system load frequency control system with performance indexesA gain matrix L. The control method provided by the invention ensures stable, safe and reliable operation of the frequency of the multi-region power system under the DoS and FDI mixed attack.

Description

Attack reconstruction and elastic control method of multi-region load frequency system
Technical Field
The invention relates to the technical field of design of controllers of a multi-region power system, in particular to an attack reconstruction and elastic control method of a multi-region load frequency system.
Background
In recent years, modern power systems have become larger in scale, and a large-scale multi-area power system in which several area power systems are connected to each other is formed, and in order to ensure power supply quality and stabilize frequencies between areas, a load frequency control technique is applied thereto. With the development of new intelligent devices and network communication technologies, the traditional power system is gradually developed into an intelligent power grid, so that the efficiency, sustainability and reliability of the whole power system are greatly improved; however, the application of the communication network and the development of the advanced information technology make the multi-region power system easily suffer from malicious network attacks, so it is of great significance to research how the multi-region power system guarantees the stability and the security of the system under the malicious network attacks.
In practice, multi-area power systems face many load fluctuations and frequency deviation problems, and load frequency control is an important means to maintain grid frequency stability, and thus becomes a potential target for many attackers. In an attacked load frequency control system, DoS (noise-of-Service) attack and fdi (false Date injection) attack are two most common network attacks, wherein the DoS attack interferes with transmission of system information in a communication network to cause delay and loss of data packets, even deteriorates system performance, and prevents normal operation of a power system; FDI attacks disturb normal control decisions by injecting false information instead of real information. In the current technology, most of studies are directed to single attacks, but no effective processing mode has been found for hybrid attacks, for example, patent application CN113555873A discloses a composite frequency control method for a multi-region interconnected power system under a denial of service attack, which is directed to a load frequency control method for a multi-region power system only under DoS attack, and when an FDI attack is encountered, the system may be unstable, and thus a fault occurs. Therefore, how to handle DoS attacks and/or FDI attacks occurring in the load frequency control system is crucial.
Disclosure of Invention
In order to solve the technical problems, the invention provides an attack reconstruction and elastic control method for a multi-region load frequency system, which solves the problem that the multi-region power system cannot stably operate under the condition of external malicious attack.
The attack reconstruction and elastic control method of the multi-region load frequency system comprises the following steps:
s1: establishing a load frequency control mathematical model of a multi-region power system under the condition of no network attack;
s2: establishing mathematical models of DoS attack and FDI attack;
s3: constructing mathematical models of a state observer and an attack observer, jointly estimating the system state and the FDI attack, considering the influence of the system state and the FDI attack, and constructing a controller with attack compensation;
s4: considering the influence of DoS attack and FDI attack, and establishing a mathematical model for controlling the load frequency of the multi-region power system under hybrid attack;
s5: designed to satisfy H∞And obtaining a controller gain matrix K, a state observer gain matrix G and an attack observer gain matrix L with attack compensation according to the multi-region power system load frequency control criterion of the performance index.
Further, in step S1, a linear model is used to represent the system approaching the normal operating point, and first, the following mathematical model is obtained:
Figure BDA0003493910000000021
in which s is a complex number,. DELTA.fiIs a frequency deviation of the i-th area,
Figure BDA0003493910000000022
is the link power of the i-th zone,
Figure BDA0003493910000000023
the mechanical output deviation of the generator in the i-th zone,
Figure BDA0003493910000000024
deviation of valve position in i-th area, ACEiIs a control error of the i-th area,
Figure BDA0003493910000000025
is the load disturbance deviation of the i-th area, MiIs the generator moment of inertia of the i-th region, DiIs the generator damping coefficient of the i-th zone,
Figure BDA0003493910000000026
is the turbine time constant of the i-th region, TijThe link synchronization coefficients of the ith area and the jth area,
Figure BDA0003493910000000027
is the governor time constant of the i-th region, RiFor the i-th zone of reduced rotational speed, betaiIs a frequency deviation factor of the i-th region, aiUnknown attack FDI attack signals for the ith region;
the system state equation of the N (N is more than or equal to 2) area can be obtained by the following formula:
Figure BDA0003493910000000031
where u (t) is the control input, a (t) is the unknown FDI attack signal,
x(t)＝[x1 T(t),x2 T(t),…,xN T(t)]T，u(t)＝[u1 T(t),u2 T(t),…,uN T(t)]T，
Figure BDA0003493910000000032
Figure BDA0003493910000000033
yi(t)＝[ACET(t),∫ACEi T(t)]T
Figure BDA0003493910000000034
Figure BDA0003493910000000035
Figure BDA0003493910000000036
Figure BDA0003493910000000037
further, in S2, the specific steps of establishing the mathematical models of the DoS attack and the FDI attack are as follows:
firstly, considering the influence of DoS attack, establishing a non-periodic DoS attack mathematical model; specifically, the DoS attack signal is a group of time-limited attack signals, which occupy limited network channels to block normal communication of the system, and is expressed by a formula
Figure RE-GDA0003571284150000041
To represent; wherein,
Figure RE-GDA0003571284150000042
Tndenotes the start of the sleep interval, T, of the (n + 1) th DoS attackoff,nIndicates the length of the nth sleep interval, Tn+Toff,nRepresents the attack interval beginning of the (n + 1) th DoS attackAttack time sequence satisfying gn+1>gn+Toff,n(ii) a Collection
Figure RE-GDA0003571284150000043
The DoS attack-free interval is shown, and the signal can be normally transmitted at the moment; collection
Figure RE-GDA0003571284150000044
The DoS attack interval is shown, at the moment, the communication network is occupied, and system signals cannot be transmitted;
secondly, considering the influence of the FDI attack, establishing a mathematical model of the FDI attack; specifically, unknown FDI attack signal passes through a formula
Figure BDA0003493910000000045
To represent; wherein D and E are both known constant matrixes, eta (t) is unknown FDI attack quantity, and a (t) is unknown FDI attack signal.
Further, the specific step of S3 is:
designing a state observer to estimate the state vector x (t), the state observer and the observed state signal of the system, by a formula
Figure BDA0003493910000000046
Represents; wherein,
Figure BDA0003493910000000047
Υ1,nis DoS dormancy zone, gamma2,nIn order to be the DoS attack interval,
Figure BDA0003493910000000048
is a state vector estimator, u (t) is a control input, a (t) is an unknown FDI attack signal, y (t) is a system output, A, B, C is a known constant matrix, and G is a state observer gain matrix to be solved; error of state observer
Figure BDA0003493910000000049
By the formula
Figure BDA00034939100000000410
Represents; wherein,
Figure BDA00034939100000000411
Υ1,nis DoS dormancy zone, gamma2,nFor DoS attack interval, x (t) is the state vector,
Figure BDA00034939100000000412
is a state vector estimator, u (t) is a control input, ω (t) is a system disturbance, A, C, F are all known constant matrices, and G is an observer gain matrix to be solved;
designing an attack observer to estimate or reconstruct an unknown FDI attack signal; attack observer and unknown FDI attack signal observed by attack observer through formula
Figure BDA0003493910000000051
Represents; wherein,
Figure BDA0003493910000000052
Υ1,nis DoS dormancy zone, gamma2,nIn order to be the DoS attack interval,
Figure BDA0003493910000000053
in order to be an intermediate estimator,
Figure BDA0003493910000000054
an estimate is made of the unknown FDI attack,
Figure BDA0003493910000000055
the state vector estimator is used, u (t) is used as control input, A, B, D, E are all known constant matrixes, G is a state observer gain matrix to be solved, and L is an attack observer gain matrix to be solved; unknown FDI attack observation error
Figure BDA0003493910000000056
By the formula
Figure BDA0003493910000000057
Represents; wherein,
Figure BDA0003493910000000058
Υ1,nis DoS dormancy zone, gamma2,nEta (t) is the unknown FDI attack quantity,
Figure BDA0003493910000000059
for unknown estimates of FDI attacks, B, D, E are all known constant matrices, L is the observer gain matrix to be solved,
Figure BDA00034939100000000510
m (t) is an intermediate quantity, η (t) is an unknown FDI attack quantity;
considering the common effects of DoS attacks and FDI attacks, the system control inputs with attack compensation are:
Figure RE-GDA00035712841500000511
wherein,
Figure RE-GDA00035712841500000512
the signal is estimated for an unknown FDI attack,
Figure RE-GDA00035712841500000513
Υ1,nis DoS dormancy zone, gamma2,nIn order to be the DoS attack interval,
Figure RE-GDA00035712841500000514
an estimate is made of the unknown FDI attack,
Figure RE-GDA00035712841500000515
for the state vector estimator C, E are known constant matrices and K is the controller gain matrix that is evaluated.
Further, the modeling of the mathematical model for controlling the load frequency of the multi-region power system under the hybrid attack is as follows:
Figure BDA00034939100000000516
wherein,
Figure BDA00034939100000000517
Υ1,nis DoS dormancy zone, gamma2,nIn order to be the DoS attack interval,
Figure BDA0003493910000000061
Figure BDA0003493910000000062
A. b, C, D, E and F are both known constant matrices, x (t) is a state vector, ex(t) is a state observation error, eη(t) is an attack observation error, ω (t) is system interference, y (t) is system output, G is a state observer gain matrix to be solved, L is an attack observer gain matrix to be solved, and K is a controller gain matrix to be solved.
Further, the solving process of the controller gain matrix K, the state observer gain matrix G and the attack observer gain matrix L is as follows: for a given disturbance suppression level gamma > 0, a parameter delta of the DoS attack is preset11，δ12，δ21，δ22Parameters D, E of the FDI attack, and a tunable parameter λ1，λ2，θ1，θ2，ε1，ε2If there is a matrix Q0＞0，Qij＞0，Xi＞0，i,j＝1,2，Q01，Q02，R，
Figure BDA0003493910000000063
Y1，Y2And k ═ 1,2 satisfies the following matrix inequality:
Figure BDA0003493910000000064
Figure BDA0003493910000000065
Q11≤λ1Q22,Q21≤λ2Q12，X2≤λ1X1,X1≤λ2X2
Figure BDA0003493910000000066
Figure BDA0003493910000000067
wherein:
Figure BDA0003493910000000068
Figure BDA0003493910000000071
Figure BDA0003493910000000072
Figure BDA0003493910000000073
Figure BDA0003493910000000074
Φ1jk＝-BY1C,Φ2jk＝0
Figure BDA0003493910000000075
Figure BDA0003493910000000076
Figure BDA0003493910000000077
Figure BDA0003493910000000078
the system is stable; wherein, is the transpose term corresponding to the matrix, and C is U [ C ═ C0 0]VT，
Figure RE-GDA0003571284150000079
CQ0RC; finally, a substitute matrix Q is calculated according to the matrix inequalityij,Q0,XiAnd calculating the gain of the controller
Figure RE-GDA00035712841500000710
Gain of state observer
Figure RE-GDA00035712841500000711
And attack observer gain
Figure RE-GDA00035712841500000712
The invention has the beneficial effects that: the control method of the invention can switch when DoS attacks exist through the switching system method, thereby coping with different conditions; when the FDI attack is encountered, the attack observer estimates an attack signal to reconstruct the attack, so that the influence of the FDI attack is eliminated through the designed attack compensator; therefore, the stable, safe and reliable operation of the frequency of the multi-region power system under the DoS and FDI mixed attack is ensured.
Drawings
In order that the present invention may be more readily and clearly understood, a more particular description of the invention briefly described above will be rendered by reference to specific embodiments that are illustrated in the appended drawings.
FIG. 1 is a schematic flow diagram of the process of the present invention;
fig. 2 is a schematic structural diagram of a multi-region load frequency system for hybrid attack according to the present invention.
Fig. 3 is a frequency deviation diagram of a two-region power system under a hybrid attack according to the present invention.
Detailed Description
In order to make the technical solution of the present invention better understood by researchers in the technical field, the following will be clearly and completely described in combination with the technical solution in the embodiments of the present invention. It is to be understood that the described embodiments are merely illustrative of some, but not all, of the embodiments of the invention, and that the preferred embodiments of the invention are shown in the drawings. This invention may be embodied in many different forms and should not be construed as limited to the embodiments set forth herein, but rather should be construed as broadly as the present disclosure is set forth in order to provide a more thorough understanding thereof. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.
Fig. 1 shows an attack reconfiguration and elastic control method for a multi-region load frequency system under hybrid attack, which includes the steps of:
s1, establishing a load frequency control mathematical model of the multi-region power system under the condition of no network attack;
s2, establishing mathematical models of DoS attack and FDI attack;
s3, constructing mathematical models of a state observer and an attack observer, jointly estimating the system state and the FDI attack, considering the influence of the system state and the FDI attack, and constructing a controller with attack compensation;
s4, considering the influence of DoS attack and FDI attack, and establishing a mathematical model for controlling the load frequency of the multi-region power system under the mixed attack;
s5, design satisfies H∞And determining a controller gain matrix K, a state observer gain matrix G and an attack observer gain matrix L of the load frequency control model under the hybrid attack according to the controller criterion of the multi-region power system load frequency control system with the performance index.
Wherein, the attack model of the DoS attack and the FDI attack is used for simulating a special situation of the real malicious attack; in addition, a multi-region power system mathematical model is established based on the attack model and the switching system method.
Specifically, since the load fluctuation of the power system is small in normal operation, the dynamic model thereof is linearized in the vicinity of the operation point. Fig. 2 shows a load frequency structure of a multi-zone power system zone i, a zone error control signal is transmitted to a controller through a communication network, the controller transmits an adjustment signal to a speed regulator through the communication network for adjustment, and then an ith sub-zone linearization model of the multi-zone power system with N (N ≧ 2) sub-zones is:
Figure BDA0003493910000000091
in which s is a complex number,. DELTA.fiIs a frequency deviation of the i-th area,
Figure BDA0003493910000000092
is the link power of the i-th zone,
Figure BDA0003493910000000093
the mechanical output deviation of the generator in the i-th zone,
Figure BDA0003493910000000094
deviation of valve position in i-th area, ACEiIs a control error of the i-th area,
Figure BDA0003493910000000095
is the load disturbance deviation of the i-th area, MiIs the generator moment of inertia of the i-th region, DiIs the generator damping coefficient of the i-th zone,
Figure BDA0003493910000000096
is the turbine time constant of the i-th region, TijThe link synchronization coefficients of the ith area and the jth area,
Figure BDA0003493910000000097
governor time constant of i-th zone，RiFor the i-th zone of reduced rotational speed, betaiIs a frequency deviation factor of the i-th region, aiAnd (3) unknown FDI attack signals for the ith region.
The system state equation of the N (N is more than or equal to 2) area can be obtained by the following formula:
Figure BDA0003493910000000098
where u (t) is the control input, a (t) is the unknown FDI attack signal,
x(t)＝[x1 T(t),x2 T(t),…,xN T(t)]T，u(t)＝[u1 T(t),u2 T(t),…,uN T(t)]T，
Figure BDA0003493910000000099
Figure BDA00034939100000000910
yi(t)＝[ACET(t),∫ACEi T(t)]T
Figure BDA0003493910000000101
Figure BDA0003493910000000102
Figure BDA0003493910000000103
Figure BDA0003493910000000104
for S2, mathematical models of DoS attacks and FDI attacks are established:
firstly, considering the influence of DoS attack, establishing a non-periodic DoS attack mathematical model, specifically, a DoS attack signal is a group of attack signals with limited time, and can occupy limited network channels to block normal communication of a system, and the DoS attack signal is obtained by a formula
Figure BDA0003493910000000105
To represent; wherein,
Figure BDA0003493910000000106
Tndenotes the start of the sleep interval, T, of the (n + 1) th DoS attackoff,nIndicates the length of the nth sleep interval, Tn+Toff,nRepresenting the attack interval starting time of the (n + 1) th DoS attack, the attack time sequence satisfies gn+1＞gn+Toff,n(ii) a Collection
Figure BDA0003493910000000107
The DoS attack-free interval is shown, and the signal can be normally transmitted at the moment; collection
Figure BDA0003493910000000108
The DoS attack interval is shown, at this time, the communication network is occupied, and the system signal cannot be transmitted.
Secondly, considering the influence of the FDI attack, establishing a mathematical model of the FDI attack, and specifically, passing an unknown FDI attack signal through a formula
Figure BDA0003493910000000111
To represent; wherein D and E are both known constant matrixes, eta (t) is unknown FDI attack quantity, and a (t) is unknown FDI attack signal.
In S3, mathematical models of a state observer and an attack observer are constructed, a system state and an FDI attack are jointly estimated, and a controller with attack compensation is constructed in consideration of influences of the system state and the FDI attack:
first, a state observer is designed to estimateCalculating a state vector x (t) of the system; state observer and observed state signal pass formula
Figure BDA0003493910000000112
Represents; wherein,
Figure BDA0003493910000000113
Υ1,nis DoS dormancy zone, gamma2,nIn order to be the DoS attack interval,
Figure BDA0003493910000000114
is a state vector estimator, u (t) is a control input, a (t) is an unknown FDI attack signal, y (t) is a system output, A, B, C is a known constant matrix, and G is a state observer gain matrix to be solved; error of state observer
Figure BDA0003493910000000115
By the formula
Figure BDA0003493910000000116
Represents; wherein,
Figure BDA0003493910000000117
Υ1,nis DoS dormancy zone, gamma2,nFor DoS attack interval, x (t) is the state vector,
Figure BDA0003493910000000118
for the state vector estimator, u (t) is the control input, ω (t) is the system disturbance, A, C, F is a known constant matrix, and G is the observer gain matrix to be solved for.
Second, an attack observer is designed to estimate or reconstruct the unknown FDI attack signal. Attack observer and unknown FDI attack signal observed by attack observer through formula
Figure BDA0003493910000000119
Represents; wherein,
Figure BDA00034939100000001110
Υ1,nis DoS dormancy zone, gamma2,nIn order to be the DoS attack interval,
Figure BDA00034939100000001111
in order to be an intermediate estimator,
Figure BDA00034939100000001112
an estimate is made of the unknown FDI attack,
Figure BDA00034939100000001113
the state vector estimator is used, u (t) is used as control input, A, B, D, E are all known constant matrixes, G is a state observer gain matrix to be solved, and L is an attack observer gain matrix to be solved; unknown FDI attack observation error
Figure BDA0003493910000000121
By the formula
Figure BDA0003493910000000122
Represents; wherein,
Figure BDA0003493910000000123
Υ1,nis DoS dormancy zone, gamma2,nEta (t) is the unknown FDI attack quantity,
Figure BDA0003493910000000124
for unknown estimates of FDI attacks, B, D, E are all known constant matrices, L is the observer gain matrix to be solved,
Figure BDA0003493910000000125
m (t) is an intermediate quantity, η (t) is an unknown FDI attack quantity;
finally, considering the common impact of DoS attacks and FDI attacks, the system control inputs with attack compensation are:
Figure RE-GDA00035712841500001211
wherein,
Figure RE-GDA00035712841500001212
the signal is estimated for an unknown FDI attack,
Figure RE-GDA00035712841500001213
Υ1,nis DoS dormancy zone, gamma2,nIn order to be the DoS attack interval,
Figure RE-GDA00035712841500001214
an estimate is made of the unknown FDI attack,
Figure RE-GDA00035712841500001215
for the state vector estimator C, E are known constant matrices and K is the controller gain matrix that is evaluated.
In S4, considering the influence of the aperiodic DoS attack and the FDI attack, the mathematical model for load frequency control of the multi-region power system under the hybrid attack is established as follows:
Figure BDA00034939100000001211
wherein,
Figure BDA00034939100000001212
Υ1,nis DoS dormancy zone, gamma2,nIn order to be the DoS attack interval,
Figure BDA00034939100000001213
Figure BDA00034939100000001214
A. b, C, D, E and F are both known constant matrices, x (t) is a state vector, ex(t) is a state observation error, eη(t) is an attack observation error, ω (t) is system interference, y (t) is system output, G is a state observer gain matrix to be solved, L is an attack observer gain matrix to be solved, and K is a controller gain matrix to be solved.
In S5, the solving process of the controller gain matrix K, the state observer gain matrix G, and the attack observer gain matrix L is as follows: for a given disturbance suppression level gamma > 0, a parameter delta of the DoS attack is preset11，δ12，δ21，δ22Parameters D, E of the FDI attack, and a tunable parameter λ1，λ2，θ1，θ2，ε1，ε2If there is a matrix Q0＞0，Qij＞0，Xi＞0，i,j＝1,2，Q01，Q02，R，
Figure BDA0003493910000000131
Y1，Y2And k ═ 1,2 satisfies the following matrix inequality:
Figure BDA0003493910000000132
Figure BDA0003493910000000133
Q11≤λ1Q22,Q21≤λ2Q12，X2≤λ1X1,X1≤λ2X2
Figure BDA0003493910000000134
Figure BDA0003493910000000135
wherein:
Figure BDA0003493910000000136
Figure BDA0003493910000000137
Figure BDA0003493910000000138
Figure BDA0003493910000000139
Figure BDA00034939100000001310
Φ1jk＝-BY1C,Φ2jk＝0
Figure BDA0003493910000000141
Figure BDA0003493910000000142
Figure BDA0003493910000000143
Figure BDA0003493910000000144
the system is stable; wherein, is the transpose term corresponding to the matrix, and C is U [ C ═ C0 0]VT,
Figure BDA0003493910000000145
CQ0RC; finally, a matrix Q to be solved is calculated according to the matrix inequalityij,Q0,XiAnd calculating the gain of the controller
Figure BDA0003493910000000146
Gain of state observer
Figure BDA0003493910000000147
And attack observer gain
Figure BDA0003493910000000148
Based on the documents Z.Cheng, D.Yue, S.Hu, X.Xie, and C.Huang, detective based weighted H∞LFC for multi-area power systems under DoS attacks,”IET Control Theory&Applications, vol.13, No.12, pp.1909-1919,2019 the system parameters can be taken as:
Figure BDA0003493910000000149
Figure BDA00034939100000001410
other parameters were taken as: gamma 50, lambda1＝1.05,λ2＝1.05,θ1＝1.03，θ2＝1.03,ε1＝1.02, ε2＝1.02,δ11＝2，δ12＝3，δ21＝1，δ22＝2。
By MATLAB simulation experiment, gain matrixes of the attack compensation controller, the state observer and the attack observer are respectively as follows:
Figure BDA0003493910000000151
Figure BDA0003493910000000152
the frequency deviation graph of the two-zone power system under the hybrid attack is shown in fig. 3.
Although the present invention has been described in detail with reference to the foregoing embodiments, it will be apparent to those skilled in the art that modifications may be made to the embodiments described in the foregoing detailed description, or equivalent changes may be made in some of the features of the embodiments described above. All equivalent structures made by using the contents of the specification and the attached drawings of the invention can be directly or indirectly applied to other related technical fields, and are also within the protection scope of the patent of the invention.

Claims (6)

1. An attack reconstruction and elastic control method of a multi-region load frequency system is characterized by comprising the following steps:
s1: establishing a load frequency control mathematical model of a multi-region power system under the condition of no network attack;
s2: establishing mathematical models of DoS attack and FDI attack;
s3: constructing mathematical models of a state observer and an attack observer, jointly estimating the system state and the FDI attack, considering the influence of the system state and the FDI attack, and constructing a controller with attack compensation;
s4: considering the influence of DoS attack and FDI attack, and establishing a mathematical model for controlling the load frequency of the multi-region power system under hybrid attack;
s5: designed to satisfy H∞And obtaining a controller gain matrix K, a state observer gain matrix G and an attack observer gain matrix L with attack compensation according to the multi-region power system load frequency control criterion of the performance index.
2. The method of claim 1, wherein the step S1 of using a linear model to represent the system approaching the normal operating point comprises obtaining the following mathematical models:
Figure RE-FDA0003571284140000011
in which s is a complex number,. DELTA.fiIs a frequency deviation of the i-th area,
Figure RE-FDA0003571284140000012
is the link power of the i-th zone,
Figure RE-FDA0003571284140000013
the mechanical output deviation of the generator in the i-th zone,
Figure RE-FDA0003571284140000014
deviation of valve position in i-th area, ACEiIs a control error of the i-th area,
Figure RE-FDA0003571284140000015
is the load disturbance deviation of the i-th area, MiIs the generator moment of inertia of the i-th region, DiIs the generator damping coefficient of the i-th zone,
Figure RE-FDA0003571284140000016
is the turbine time constant of the i-th region, TijThe link synchronization coefficients of the ith area and the jth area,
Figure RE-FDA0003571284140000017
is the governor time constant of the i-th region, RiFor the i-th zone of reduced rotational speed, betaiIs a frequency deviation factor of the i-th region, aiUnknown attack FDI attack signals for the ith region;
the system state equation of the N (N is more than or equal to 2) area can be obtained by the following formula:
Figure RE-FDA0003571284140000021
where u (t) is the control input, a (t) is the unknown FDI attack signal,
x(t)＝[x1 T(t),x2 T(t),…,xN T(t)]T，u(t)＝[u1 T(t),u2 T(t),…,uN T(t)]T，
Figure RE-FDA0003571284140000022
Figure RE-FDA0003571284140000023
yi(t)＝[ACET(t),∫ACEi T(t)]T
Figure RE-FDA0003571284140000024
Figure RE-FDA0003571284140000025
Figure RE-FDA0003571284140000026
Figure RE-FDA0003571284140000031
3. the attack reconfiguration and resilient control method of a multi-region load frequency system according to claim 2, wherein in S2, the specific steps of establishing the mathematical models of DoS attack and FDI attack are as follows:
firstly, considering the influence of DoS attack, establishing a non-periodic DoS attack mathematical model; specifically, the DoS attack signal is a group of time-limited attack signals, which occupy limited network channels to block normal communication of the system, and is expressed by a formula
Figure RE-FDA0003571284140000032
To represent; wherein,
Figure RE-FDA0003571284140000033
Tndenotes the start of the sleep interval, T, of the (n + 1) th DoS attackoff,nIndicates the length of the nth sleep interval, Tn+Toff,nRepresenting the attack interval starting time of the (n + 1) th DoS attack, the attack time sequence satisfies gn+1>gn+Toff，n(ii) a Collection
Figure RE-FDA0003571284140000034
The DoS attack-free interval is shown, and the signal can be normally transmitted at the moment; collection
Figure RE-FDA0003571284140000035
The DoS attack interval is shown, at the moment, the communication network is occupied, and system signals cannot be transmitted;
secondly, considering the influence of the FDI attack, establishing a mathematical model of the FDI attack; specifically, unknown FDI attack signal passes through a formula
Figure RE-FDA0003571284140000036
To represent; wherein D and E are both known constant matrixes, eta (t) is unknown FDI attack quantity, and a (t) is unknown FDI attack signal.
4. The attack reconfiguration and resilient control method according to claim 2, wherein the specific steps of S3 are as follows:
designing a state observer to estimate the state vector x (t), the state observer and the observed state signal of the system, by a formula
Figure RE-FDA0003571284140000037
Represents; wherein,
Figure RE-FDA0003571284140000038
Υ1,nis DoS dormancy zone, gamma2,nIn order to be the DoS attack interval,
Figure RE-FDA0003571284140000039
is a state vector estimator, u (t) is a control input, a (t) is an unknown FDI attack signal, y (t) is a system output, A, B, C is a known constant matrix, and G is a state observer gain matrix to be solved; error of state observer
Figure RE-FDA0003571284140000041
By the formula
Figure RE-FDA0003571284140000042
Represents; wherein,
Figure RE-FDA0003571284140000043
Υ1,nis DoS dormancy zone, gamma2,nFor DoS attack interval, x (t) is the state vector,
Figure RE-FDA0003571284140000044
is a state vector estimator, u (t) is a control input, ω (t) is a system disturbance, A, C, F are all known constant matrices, and G is an observer gain matrix to be solved;
designing an attack observer to estimate or reconstruct an unknown FDI attack signal; attack observer and unknown FDI attack signal observed by attack observer through formula
Figure RE-FDA0003571284140000045
Represents; wherein,
Figure RE-FDA0003571284140000046
Υ1,nis DoS dormancy zone, gamma2,nIn order to be the DoS attack interval,
Figure RE-FDA0003571284140000047
in order to be an intermediate estimator,
Figure RE-FDA0003571284140000048
an estimate is made of the unknown FDI attack,
Figure RE-FDA0003571284140000049
the state vector estimator is used, u (t) is used as control input, A, B, D, E are all known constant matrixes, G is a state observer gain matrix to be solved, and L is an attack observer gain matrix to be solved; unknown FDI attack observation error
Figure RE-FDA00035712841400000410
By the formula
Figure RE-FDA00035712841400000411
Represents; wherein,
Figure RE-FDA00035712841400000412
Υ1,nis DoS dormancy zone, gamma2,nEta (t) is the unknown FDI attack quantity,
Figure RE-FDA00035712841400000413
for unknown estimates of FDI attacks, B, D, E are all known constant matrices, L is the observer gain matrix to be solved,
Figure RE-FDA00035712841400000414
m (t) is an intermediate quantity, η (t) is an unknown FDI attack quantity;
considering the common effects of DoS attacks and FDI attacks, the system control inputs with attack compensation are:
Figure RE-FDA00035712841400000415
wherein,
Figure RE-FDA00035712841400000416
is unknown FDI attackThe evaluation signal is hit and the estimated value is,
Figure RE-FDA00035712841400000417
Υ1,nis DoS dormancy zone, gamma2,nIn order to be the DoS attack interval,
Figure RE-FDA00035712841400000418
an estimate is made of the unknown FDI attack,
Figure RE-FDA00035712841400000419
for the state vector estimator C, E are known constant matrices and K is the controller gain matrix that is evaluated.
5. The method of claim 1, wherein in step S4, the mathematical model for controlling the load frequency of the multi-region power system under the hybrid attack is modeled as:
Figure RE-FDA0003571284140000051
wherein,
Figure RE-FDA0003571284140000052
Υ1,nis DoS dormancy zone, gamma2,nIn order to be the DoS attack interval,
Figure RE-FDA0003571284140000053
Figure RE-FDA0003571284140000054
Figure RE-FDA0003571284140000055
A. b, C, D, E and F are both known constant matrices, x (t) is a state vector, ex(t) is a state observation error, eη(t) is the attack observation error, ω (t) isAnd y (t) is system interference, G is a state observer gain matrix to be solved, L is an attack observer gain matrix to be solved, and K is a controller gain matrix to be solved.
6. The attack reconstruction and resilient control method of the multi-region load frequency system according to claim 5, wherein the solving process of the controller gain matrix K, the state observer gain matrix G and the attack observer gain matrix L is as follows:
for a given disturbance suppression level gamma>0, presetting a parameter delta of DoS attack11，δ12，δ21，δ22Parameters D, E of the FDI attack, and a tunable parameter λ1，λ2，θ1，θ2，ε1，ε2If there is a matrix Q0>0，Qij>0，Xi>0，i,j＝1,2，Q01，Q02，R，
Figure RE-FDA0003571284140000056
Y1，Y2And k ═ 1,2 satisfies the following matrix inequality:
Figure RE-FDA0003571284140000057
Figure RE-FDA0003571284140000058
Q11≤λ1Q22,Q21≤λ2Q12，X2≤λ1X1,X1≤λ2X2
Figure RE-FDA0003571284140000059
Figure RE-FDA0003571284140000061
wherein:
Figure RE-FDA0003571284140000062
Figure RE-FDA0003571284140000063
Figure RE-FDA0003571284140000064
Figure RE-FDA0003571284140000065
Figure RE-FDA0003571284140000066
Φ1jk＝-BY1C,Φ2jk＝0
Figure RE-FDA0003571284140000067
Figure RE-FDA0003571284140000068
Figure RE-FDA0003571284140000069
Figure RE-FDA00035712841400000610
the system is stable; wherein, is the transpose term corresponding to the matrix, and C is U [ C ═ C0 0]VT，
Figure RE-FDA00035712841400000611
CQ0RC; finally, a substitute matrix Q is calculated according to the matrix inequalityij,Q0,XiAnd calculating the gain of the controller
Figure RE-FDA00035712841400000612
Gain of state observer
Figure RE-FDA00035712841400000613
And attack observer gain
Figure RE-FDA00035712841400000614
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