CN112234629B - Sliding mode load frequency control method of multi-region power system based on deception attack - Google Patents

Sliding mode load frequency control method of multi-region power system based on deception attack Download PDF

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CN112234629B
CN112234629B CN202011184161.2A CN202011184161A CN112234629B CN 112234629 B CN112234629 B CN 112234629B CN 202011184161 A CN202011184161 A CN 202011184161A CN 112234629 B CN112234629 B CN 112234629B
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CN112234629A (en
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刘兴华
白丹丹
关建伟
同向前
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Xian University of Technology
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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
    • Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
    • Y04—INFORMATION OR COMMUNICATION TECHNOLOGIES HAVING AN IMPACT ON OTHER TECHNOLOGY AREAS
    • Y04S—SYSTEMS INTEGRATING TECHNOLOGIES RELATED TO POWER NETWORK OPERATION, COMMUNICATION OR INFORMATION TECHNOLOGIES FOR IMPROVING THE ELECTRICAL POWER GENERATION, TRANSMISSION, DISTRIBUTION, MANAGEMENT OR USAGE, i.e. SMART GRIDS
    • Y04S40/00—Systems for electrical power generation, transmission, distribution or end-user application management characterised by the use of communication or information technologies, or communication or information technology specific aspects supporting them
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Abstract

A sliding mode load frequency control method of a multi-region power system based on cheating attack comprises the following steps: step 1, establishing a multi-region power system load frequency control model based on deception attack; step 2, designing an observer and a sliding mode surface; step 3, providing asymptotic stability in the safety sense, and carrying out accessibility analysis on the generated sliding mode dynamics; the method has the advantages of strong robustness, high response speed and good control effect.

Description

Sliding mode load frequency control method of multi-region power system based on deception attack
Technical Field
The invention belongs to the technical field of power system automation, and particularly relates to a sliding mode load frequency control method of a multi-region power system based on deception attack.
Background
During the operation of a multi-area networking power system, the stability of the system can be seriously influenced by random changes of power loads and various external interferences. Such instability can cause fluctuations in the system voltage and frequency, adversely affecting the quality of the power system, and even causing a voltage or frequency collapse. Load Frequency Control (LFC) is an important means to ensure active power balance and to maintain grid frequency stability, with the purpose of adjusting the system frequency to a nominal value (e.g. 50Hz) and maintaining the exchange power of regional junctors as planned. In recent years, with the popularization of multi-region interconnected power systems, it is of great significance to control and regulate a power grid through wireless communication. However, in a real network communication environment, an open channel always encounters a serious security problem. Various network attacks, such as denial of service attacks, replay attacks, spoofing attacks, etc., have become a significant threat to the power grid. Therefore, the safety issues of multi-area networked power systems should be highly appreciated. Sliding Mode Control (SMC) is a special variable structure control with good insensitivity to model errors, parameter variations and external disturbances. The motion of the system on the sliding mode surface is called the sliding mode, and the controlled system on the sliding mode has strong robustness. The characteristics and parameters of the sliding mode variable structure control only depend on the designed switch hyperplane and are irrelevant to external interference, so the sliding mode variable structure control has strong robustness. In recent years, a sliding mode variable structure method is more and more emphasized, and various systems are widely applied. The design purpose is as follows:
a sliding mode exists; secondly, the motion trail which is not on the sliding mode surface s (t) can reach the sliding mode surface s (t) in a certain time; and the controlled system can ensure good performance index.
The following are advantages and disadvantages of SMC.
1) The SMC has the advantages that: the method can overcome the uncertainty of the system, has strong robustness to interference and unmodeled dynamics, and particularly has good control effect on the control of a nonlinear system. The variable structure control system has simple algorithm and high response speed, has robustness to external noise interference and parameter perturbation, and is widely applied to the control field.
2) Some of the disadvantages of SMC: when the state trajectory reaches the sliding mode surface, the state trajectory is difficult to strictly slide along the sliding mode surface to the equilibrium point, but approaches the equilibrium point in a back-and-forth traversing manner on two sides of the state trajectory, so that buffeting is generated, and the buffeting is also a main obstacle in the practical application of sliding mode control.
Disclosure of Invention
In order to overcome the defects of the prior art, the invention aims to provide a sliding mode load frequency control method of a multi-region power system based on deception attack, which solves the problem that the multi-region power system cannot stably operate under the condition of network attack; the method has the advantages of strong robustness, high response speed and good control effect.
In order to achieve the purpose, the invention adopts the technical scheme that: a sliding mode load frequency control method of a multi-region power system based on cheating attack comprises the following steps:
step 1, establishing a multi-region power system load frequency control model based on deception attack;
step 2, designing an observer and a sliding mode surface;
and 3, giving the asymptotic stability in the safety sense, and carrying out accessibility analysis on the generated sliding mode dynamics.
In step 1, a linear model is used to represent a system close to a normal operating point, and firstly, the following mathematical model can be obtained:
Figure BDA0002750996960000031
in the formula,. DELTA.fiIs the i-th zone system deviation value, Δ PmiAs a deviation value of the mechanical power, Δ PviTo adjust the valve position quantity, Δ PdiIn order to load the ith area,
Figure BDA0002750996960000032
as a coefficient of speed reduction, MiIs the moment of inertia of the generator, DiAs damping coefficient of the generator, TchiAnd TgiRespectively, steam capacity time constant and governor time constant, betaiConversion factor for system power and frequency, ACEi(t) is a zone control error signal for the ith zone, Δ Ptie-iFor net exchange of i-th control area tie line power, TijThe synchronization coefficient of a connecting line between the ith control area and the jth control area, and u (t) is the input quantity of the system;
from equation (1), the system state equation can be obtained as follows:
Figure BDA0002750996960000033
wherein x (t) is the state vector of the ith sub-region of the system,
Figure BDA0002750996960000034
y (t) is the output vector of the ith sub-region of the system,
Figure BDA0002750996960000035
ω (t) is the load, ωi(t)＝ΔPdi(t); A. b, F and C are coefficient matrices;
the ACE signals are transmitted to the sliding mode controllers in corresponding areas through the power system shared network, network time delay and packet loss are inevitably caused, wireless transmission is easy to attack due to openness of network communication, and deception attack is consideredThe impact will destroy the integrity of the transmitted signal and can derive a damage measurement
Figure BDA0002750996960000041
Comprises the following steps:
Figure BDA0002750996960000042
where υ (t) ═ u (t) + ζ (t) is a spoof attack signal initiated by an enemy, and ζ (t) belongs to L 20, + ∞), α (t) is a random variable that obeys a bernoulli distribution, which is desirably E { α (t) } ═ α (t) } α0，
On the basis of the traditional LFC model, the influence of network attack is considered, random deception attack is added, and after the deception attack is added, the state equation of the system can be rewritten as follows:
Figure BDA0002750996960000043
where τ (t) is a time-varying delay and
Figure BDA0002750996960000044
in the step 2, the sliding mode control method is adopted for carrying out the specific steps of:
step 2.1, designing a Luenberger observer;
Figure BDA0002750996960000045
in the formula (I), the compound is shown in the specification,
Figure BDA0002750996960000046
is the state of the observer, L is the observer gain to be designed,
Figure BDA0002750996960000047
is the output of the observer;
defining systematic errorsIs composed of
Figure BDA0002750996960000048
The derivative thereof can be found to be:
Figure BDA0002750996960000049
wherein the content of the first and second substances,
Figure BDA00027509969600000410
step 2.2, design of slip form surface
For the LFC problem, the following integral sliding mode surface is used:
Figure BDA0002750996960000051
where K and X are coefficient matrices, K is selected to satisfy A + BK as a Helvelz matrix, and X is designed as BTXB is non-singular, a coefficient matrix K is chosen that satisfies a + BK as helvets, i.e. all eigenvalues of a + BK have a negative real part, eigenvalue permutations can always be performed to find the matrix K,
the derivative of the sliding mode surface s (t) with respect to t is as follows:
Figure BDA0002750996960000052
order to
Figure BDA0002750996960000053
The equivalent control law is then given as follows:
Figure BDA0002750996960000054
substituting the equivalent control law equation (9) into the Luenberger observer equation (5), the state equation of the observer can be written as:
Figure BDA0002750996960000055
the step 3 specifically comprises:
step 3.1, stability analysis
Taking a closed-loop system formula (10) as a main research object, giving a sufficient condition for ensuring the asymptotic stability of the system, and judging the stability of the system by mainly utilizing a Lyapunov second method, namely analyzing and judging the stability by defining a scalar function of a Lyapunov function; equation (10) of the closed-loop system is asymptotically stable if the following condition is satisfied, and H∞The level of disturbance rejection is gamma and,
1) the system (10) is asymptotically stable when ω (t) is 0 and ζ (t) is 0, i.e., there are successive first order partial derivatives of v (t) and v (t) with respect to x in the vicinity of the equilibrium state if v (t) is positive and constant
Figure BDA0002750996960000056
Negative, then the system is progressively stable at equilibrium;
2) under the zero initial condition, for any nonzero omega (t) epsilon L2[0,∞]And ζ (t) is epsilon L2[0,∞]For a given γ, if E { | | y (t) | luminance2}＜γE{||ω(t)||2+||ζ(t)||2If it is true, the closed-loop system formula (10) satisfies H∞Performance;
first, the lyapunov function is constructed as:
Figure BDA0002750996960000061
then, by deriving and expecting equation (11), through Schur's complement and a series of mathematical transformations, it is deduced that the sliding mode satisfies the optimized performance index (weight H)∞Performance), under zero initial conditions, one can finally obtain:
E{||y(t)||2}＜γE{||ω(t)||2+||ζ(t)||2} (12)
wherein γ > 0 is the inhibition level,
when ω (t) ≠ 0 and ζ (t) ≠ 0, there is one scalar ε > 0, so that the following equation holds:
Figure BDA0002750996960000062
therefore, when ω (t) ≠ 0 and ζ (t) ≠ 0, equation (13) demonstrates that closed-loop system equation (10) generated under zero initial conditions has H∞Inhibition performance; for ω (t) ═ 0 and ζ (t) ═ 0, it is further derived from formula (12) that the resulting closed-loop system formula (10) is asymptotically stable in a safe sense;
step 3.2 reachability analysis
For the generated closed-loop system formula (10), a sliding surface of the formula (7) is designed, under the action of the following controller, the system track can reach the sliding surface in a limited time,
Figure BDA0002750996960000063
where η > 0 is a real constant, sgn (. cndot.) is a common sign function, and δ (t) is as follows:
δ(t)＝||(BTXB)-1||[||BTXLζ(t)||+2||BTXLCe(t-τ(t))||] (15)
it can therefore be concluded that the trajectory of the formula (10) can reach the sliding surface in a limited time under the action of the proposed sliding-mode control (14).
The invention has the beneficial effects that:
through SMC, make multizone power system even can guarantee stable operation when suffering spoofing the attack immediately. In particular, when the system is attacked by the network, various problems such as delay, packet loss, etc. are likely to be caused, thereby affecting the performance of the system. Therefore, by introducing SMC into LFC, the system state observed by the Luenberger observer will be driven by the designed sliding mode controller over time to the appropriate sliding mode surface, i.e. the accessibility of SMC, and then asymptotically stabilize along this sliding mode surface to the equilibrium point. The design of the sliding mode controller can change along with the state of the controlled system in different control areas, so that the controlled system still keeps strong robustness when the internal parameters of the controlled system slightly change or interference occurs.
Drawings
FIG. 1 is a diagram of a system control input trajectory.
Fig. 2 is a system state trace diagram.
FIG. 3 is an observer state trace diagram.
Fig. 4 is a system error trajectory diagram.
Detailed Description
The present invention will be described in detail below with reference to the accompanying drawings and specific embodiments.
A first part:
the invention relates to a sliding mode load frequency control method of a multi-region power system based on deception attack, which comprises the following steps:
step 1, establishing a multi-region power system load frequency control model based on deception attack;
step 2, designing an observer and a sliding mode surface;
and 3, giving the asymptotic stability in the safety sense, and carrying out accessibility analysis on the generated sliding mode dynamics.
Wherein the step 1 specifically comprises the following steps:
the actual power system is a complex nonlinear dynamic system, and because the load of the power system is small when the power system operates at a nominal point, a linear model can be used for representing the system close to a normal operating point, and firstly, the following mathematical model can be obtained:
Figure BDA0002750996960000081
in the formula,. DELTA.fiIs the i-th zone system deviation value, Δ PmiAs a deviation value of the mechanical power, Δ PviTo adjust the valve position quantity, Δ PdiIn order to load the ith area,
Figure BDA0002750996960000082
as a coefficient of speed reduction, MiIs the moment of inertia of the generator, DiAs damping coefficient of the generator, TchiAnd TgiRespectively, steam capacity time constant and governor time constant, betaiConversion factor for system power and frequency, ACEi(t) is a zone control error signal for the ith zone, Δ Ptie-iFor net exchange of i-th control area tie line power, TijThe synchronization coefficient of a connecting line between the ith control area and the jth control area, and u (t) is the input quantity of the system;
from equation (1), the system state equation can be obtained as follows:
Figure BDA0002750996960000083
wherein x (t) is the state vector of the ith sub-region of the system,
Figure BDA0002750996960000091
y (t) is the output vector of the ith sub-region of the system,
Figure BDA0002750996960000092
ω (t) is the load, ωi(t)＝ΔPdi(t); A. b, F and C are coefficient matrices;
the ACE signal is transmitted to the sliding mode controller in the corresponding area through the power system shared network, network time delay, packet loss and other phenomena are inevitably caused, wireless transmission is easy to attack due to openness of network communication, integrity of the transmission signal is damaged by considering deception attack, and a damage measured value can be deduced
Figure BDA0002750996960000093
Comprises the following steps:
Figure BDA0002750996960000094
wherein upsilon (t) ═ u (t) + ζ (t) is an enemyA spoofing attack signal is initiated, ζ (t) being L 20, + ∞), α (t) is a random variable that obeys a bernoulli distribution, which is desirably E { α (t) } ═ α (t) } α0，
On the basis of the traditional LFC model, the influence of network attack is considered, random deception attack is added, and after the deception attack is added, the state equation of the system can be rewritten as follows:
Figure BDA0002750996960000095
where τ (t) is a time-varying time delay and
Figure BDA0002750996960000096
in the step 2, the sliding mode control method is adopted for carrying out the specific steps of:
step 2.1, designing a Luenberger observer;
Figure BDA0002750996960000097
in the formula (I), the compound is shown in the specification,
Figure BDA0002750996960000098
is the state of the observer, L is the observer gain to be designed,
Figure BDA0002750996960000099
is the output of the observer;
defining a system error as
Figure BDA0002750996960000101
The derivative thereof can be found to be:
Figure BDA0002750996960000102
wherein, the first and the second end of the pipe are connected with each other,
Figure BDA0002750996960000103
step 2.2, design of slip form surface
For the LFC problem, the following integral sliding mode surface is designed:
Figure BDA0002750996960000104
where K and X are coefficient matrices, K is selected to satisfy A + BK as a Helvelz matrix, and X is designed as BTXB is non-singular, a coefficient matrix K is chosen that satisfies a + BK as helvets, i.e. all eigenvalues of a + BK have a negative real part, eigenvalue permutations can always be performed to find the matrix K,
the derivative of sliding mode surface s (t) with respect to t is as follows:
Figure BDA0002750996960000105
order to
Figure BDA0002750996960000106
The equivalent control law is then given as follows:
Figure BDA0002750996960000107
substituting the equivalent control law equation (9) into the Luenberger observer equation (5), the state equation of the observer can be written as:
Figure BDA0002750996960000108
the step 3 comprises the following steps:
step 3.1, stability analysis;
next, taking the closed-loop system (10) as a main research object, giving sufficient conditions for ensuring the asymptotic stability of the system, and judging the stability of the system mainly by utilizing the Lyapunov second method, namely by defining aThe discriminant stability is analyzed as a scalar function of individual lyapunov functions. Equation (10) of the closed-loop system is asymptotically stable if the following condition is satisfied, and H∞The level of disturbance rejection is gamma and,
1) the system (10) is asymptotically stable when ω (t) is 0 and ζ (t) is 0, i.e., there are successive first order partial derivatives of v (t) and v (t) with respect to x in the vicinity of the equilibrium state if v (t) is positive and constant
Figure BDA0002750996960000111
Negative, then the system is progressively stable at equilibrium;
2) under the zero initial condition, for any nonzero omega (t) epsilon L2[0,∞]And ζ (t) is epsilon L2[0,∞]For a given γ, if E { | | y (t) | luminance2}＜γE{||ω(t)||2+||ζ(t)||2Is true, the closed loop system (10) satisfies H∞Performance;
first, the lyapunov function is constructed as:
Figure BDA0002750996960000112
then, by deriving and expecting equation (11), through Schur's complement and a series of mathematical transformations, it is deduced that the sliding mode satisfies the optimized performance index (weight H)∞Performance), under zero initial conditions, one can finally obtain:
E{||y(t)||2}＜γE{||ω(t)||2+||ζ(t)||2} (12)
wherein γ > 0 is the inhibition level.
When ω (t) ≠ 0 and ζ (t) ≠ 0, there is one scalar ε > 0, such that the following equation holds:
Figure BDA0002750996960000113
therefore, when ω (t) ≠ 0 and ζ (t) ≠ 0, equation (13) demonstrates generation under zero initial conditionsHas a closed loop system (10) of H∞The inhibition performance, for ω (t) ═ 0 and ζ (t) ═ 0, further yields from formula (12) that the resultant closed-loop system formula (10) is asymptotically stable in the safety sense;
step 3.2 reachability analysis
For the generated closed-loop system formula (10), a sliding surface of the form (7) is designed, under the action of the following controller, the system track can reach the sliding surface in a limited time,
Figure BDA0002750996960000121
where η > 0 is a real constant, sgn (. cndot.) is a common sign function, and δ (t) is as follows:
δ(t)＝||(BTXB)-1||[||BTXLζ(t)||+2||BTXLCe(t-τ(t))||] (15)
it can therefore be concluded that the trajectory of the formula (10) can reach the sliding surface in a limited time under the action of the proposed sliding-mode control (14).
A second part:
in this section, the effectiveness of the proposed control scheme is verified by numerical calculations and simulations. A three-area interconnected networked power system is contemplated. In our simulation, the sampling period T is set to 0.01, then the simulation time is calculated as T0.01 × step size, the spoofing attack model (4) is considered, and α0＝0.2，τ(t)＝0.1。
The control inputs are shown in fig. 1. The state track and the observer state track of the closed-loop three-area networked power system are respectively shown in fig. 2 and fig. 3, and it can be seen from fig. 4 that the error of the closed-loop system tends to zero after 7 seconds.

Claims (1)

1. A sliding mode load frequency control method of a multi-region power system based on spoofing attack is characterized by comprising the following steps:
step 1, establishing a multi-region power system load frequency control model based on deception attack;
in step 1, a linear model is used to represent a system close to a normal operating point, and first, the following mathematical model can be obtained:
Figure FDA0003612274870000011
in the formula,. DELTA.fiIs the i-th zone system deviation value, Δ PmiAs a deviation value of the mechanical power, Δ PviTo adjust the valve position quantity, Δ PdiIn order to load the ith area,
Figure FDA0003612274870000012
as a coefficient of speed reduction, MiIs the moment of inertia of the generator, DiAs damping coefficient of the generator, TchiAnd TgiRespectively, steam capacity time constant and governor time constant, betaiConversion factor for system power and frequency, ACEi(t) is a zone control error signal for the ith zone, Δ Ptie-iFor net exchange of i-th control area tie line power, TijThe synchronization coefficient of a connecting line between the ith control area and the jth control area, and u (t) is the input quantity of the system;
from equation (1), the system state equation can be obtained as follows:
Figure FDA0003612274870000013
wherein x (t) is the state vector of the ith sub-region of the system,
Figure FDA0003612274870000021
y (t) is the output vector of the ith sub-region of the system,
Figure FDA0003612274870000022
ω (t) is the load, ωi(t)＝ΔPdi(t); A. b, F and C are coefficient matrices;
the ACE signal is transmitted to the sliding mode controller of the corresponding area through the power system shared network, network time delay and packet loss are inevitably caused, wireless transmission is easily attacked due to openness of network communication, the integrity of the transmission signal is damaged by considering deception attack, and a damage measured value can be deduced
Figure FDA0003612274870000023
Is composed of
Figure FDA0003612274870000024
Where υ (t) ═ u (t) + ζ (t) is a spoof attack signal initiated by an enemy, and ζ (t) belongs to L20, + ∞), α (t) is a random variable that obeys a bernoulli distribution, which is desirably E { α (t) } ═ α (t) } α0，
On the basis of the traditional LFC model, the influence of network attack is considered, random deception attack is added, and after the deception attack is added, the state equation of the system can be rewritten as follows:
Figure FDA0003612274870000025
where τ (t) is a time-varying delay and
Figure FDA0003612274870000029
step 2, designing an observer and a sliding mode surface;
in the step 2, the sliding mode control method is adopted to perform the specific steps of:
step 2.1, designing a Luenberger observer;
Figure FDA0003612274870000026
in the formula (I), the compound is shown in the specification,
Figure FDA0003612274870000027
is the state of the observer, L is the observer gain to be designed,
Figure FDA0003612274870000028
is the output of the observer and is,
defining a system error as
Figure FDA0003612274870000031
The derivative thereof can be found to be:
Figure FDA0003612274870000032
wherein the content of the first and second substances,
Figure FDA0003612274870000033
step 2.2, design of slip form surface
For the LFC problem, the following integral sliding mode surface is used:
Figure FDA0003612274870000034
where K and X are coefficient matrices, K is selected to satisfy A + BK as a Helvelz matrix, and X is designed as BTXB is non-singular, a matrix K of coefficients satisfying a + BK as helvets is chosen, i.e. all eigenvalues of a + BK have a negative real part, eigenvalue permutations can always be made to find the matrix K,
Figure FDA0003612274870000035
is the state of the observer under integration,
the derivative of the sliding mode surface s (t) with respect to t is as follows:
Figure FDA0003612274870000036
order to
Figure FDA0003612274870000037
The equivalent control law is then given as follows:
Figure FDA0003612274870000038
substituting the equivalent control law equation (9) into the Luenberger observer equation (5), the state equation of the observer can be written as:
Figure FDA0003612274870000039
step 3, providing asymptotic stability in the safety sense, and carrying out accessibility analysis on the generated sliding mode dynamics;
the step 3 specifically comprises:
step 3.1, stability analysis
Taking a closed-loop system formula (10) as a main research object, giving sufficient conditions for ensuring the asymptotic stability of the system, judging the stability of the system by mainly utilizing a Lyapunov second method, namely analyzing and judging the stability by defining a scalar function of the Lyapunov function, wherein the closed-loop system formula (10) is asymptotically stable if the following conditions are met, and H is H∞The level of disturbance rejection is gamma and,
when ω (t) is 0 and ζ (t) is 0, the closed-loop system (10) is asymptotically stable, i.e. in the vicinity of the equilibrium state, there is v (t) and successive first partial derivatives of v (t) with respect to x, if v (t) is positive and
Figure FDA0003612274870000041
negative, then the system is progressively stable at equilibrium;
under the zero initial condition, for any nonzero omega (t) epsilonL2[0,∞]And ζ (t) is epsilon L2[0,∞]For a given γ, if E { | | y (t) | luminance2}＜γE{||ω(t)||2+||ζ(t)||2If it is true, the closed-loop system formula (10) satisfies H∞The performance of the composite material is as follows,
first, the lyapunov function is constructed as:
Figure FDA0003612274870000042
then, by deriving and expecting equation (11), through Schur's complement and a series of mathematical transformations, it is deduced that the sliding mode satisfies the optimized performance index (weight H)∞Performance) under zero initial conditions, the following can be obtained:
E{||y(t)||2}＜γE{||ω(t)||2+||ζ(t)||2} (12)
wherein γ > 0 is the inhibition level,
when ω (t) ≠ 0 and ζ (t) ≠ 0, there is one scalar ε > 0, such that the following equation holds:
Figure FDA0003612274870000043
therefore, when ω (t) ≠ 0 and ζ (t) ≠ 0, equation (13) demonstrates that closed-loop system equation (10) generated under zero initial conditions has H∞Inhibition performance; for ω (t) ═ 0 and ζ (t) ═ 0, it is further derived from formula (12) that the resulting closed-loop system formula (10) is asymptotically stable in a safe sense;
step 3.2 reachability analysis
For the generated closed-loop system formula (10), a sliding surface of the formula (7) is designed, under the action of the following controller, the system track can reach the sliding surface in a limited time,
Figure FDA0003612274870000051
where η > 0 is a real constant, sgn (. cndot.) is a common sign function, and δ (t) is as follows:
δ(t)＝||(BTXB)-1||[||BTXLζ(t)||+2||BTXLCe(t-τ(t))||] (15)
it can therefore be concluded that the trajectory of the formula (10) can reach the sliding surface in a limited time under the action of the proposed sliding-mode control (14).
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Citations (3)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN106374461A (en) * 2016-09-29 2017-02-01 重庆大学 Event trigger load frequency control-based method of multi-zone interconnected power system
CN109659959A (en) * 2019-01-14 2019-04-19 南京师范大学 Electric system loads control method for frequency based on the H ∞ of caching type event trigger method under spoofing attack
CN110518573A (en) * 2019-07-29 2019-11-29 浙江工业大学 A kind of multi-region electric network design method based on adaptive event triggering sliding formwork control

Patent Citations (3)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN106374461A (en) * 2016-09-29 2017-02-01 重庆大学 Event trigger load frequency control-based method of multi-zone interconnected power system
CN109659959A (en) * 2019-01-14 2019-04-19 南京师范大学 Electric system loads control method for frequency based on the H ∞ of caching type event trigger method under spoofing attack
CN110518573A (en) * 2019-07-29 2019-11-29 浙江工业大学 A kind of multi-region electric network design method based on adaptive event triggering sliding formwork control

Non-Patent Citations (1)

* Cited by examiner, † Cited by third party
Title
Stability Analysis for Networked Power Systems with LFC and Event-Triggered Communication;Xinghua Liu等;《2020 39th Chinese Control Conference (CCC)》;20200909;第4424-4429页 *

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