CN113972671B - Elastic load frequency control method for multi-region electric power system under denial of service attack - Google Patents
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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
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- H—ELECTRICITY
- H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
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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
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Abstract
A method for controlling the frequency of an elastic load of a multi-zone power system under denial of service attack, the method comprising: establishing a multi-region power system model based on a dynamic event triggering mechanism under a DoS attack; acquiring conditions for enabling the multi-region power system model to stably run; solving a trigger matrix and a gain matrix, and determining the gain of the controller; and constructing a controller and performing elastic control on the multi-region power system according to the controller. Compared with the traditional static event triggering mechanism, the method and the device can reduce the transmission quantity of redundant signals to a greater extent, lighten the network transmission pressure and save the resources required by communication while ensuring the safe and stable operation of the system under the condition that the DoS attack possibly occurs.
Description
Technical Field
The invention belongs to the technical field of power system controller design, and particularly relates to an elastic load frequency control method of a multi-region power system under denial of service attack.
Background
Load Frequency Control (LFC) is important in the design and operation of power systems. In interconnected power systems, the primary goal of LFCs is to provide adequate and reliable power with quality assurance by maintaining the frequency and power exchange with the neighborhood at a predetermined value. Generally, there are two communication methods to connect adjacent areas in a multi-area power system, namely a dedicated communication channel and an open communication infrastructure. Open communication infrastructure has been widely used in LFCs of multi-zone power systems due to its low cost and flexibility advantages compared to dedicated communication channels. However, network attacks can cause significant damage to the power system due to the openness of the communication network. Thus, the opening of communication channels in multi-zone power systems results in new security challenges.
In general, network attacks can be classified into denial of service (DoS) attacks and spoofing attacks. DoS attacks prevent the interconnection of communication nodes, resulting in data that cannot be transmitted in time, and even in system instability. For network control systems, real-time, accurate data is of paramount importance for state estimation and dynamic control of the system. Meanwhile, in a multi-region power system with limited bandwidth resources, how to save bandwidth, avoid congestion, and increase the timeliness of control is also important. Therefore, how to ensure the safety and reliability of the multi-region power system under the external malicious DoS attack is a popular research topic. Meanwhile, under the conditions of ensuring the stability of the system and the expected performance of people, the data transmission times are reduced, and the valuable bandwidth resource is saved, so that the problem of urgent need to be solved under the eyes is also solved.
Disclosure of Invention
In order to solve the technical problems, the present invention provides a method for controlling the elastic load frequency of a multi-region power system under denial of service attack
The elastic load frequency control method of the multi-region power system under the denial of service attack comprises the following steps:
step 1, establishing a multi-region power system model based on a dynamic event trigger mechanism under a denial of service (DoS) attack;
step 2, obtaining the condition for enabling the multi-region power system model to stably operate;
step 3, solving an event trigger matrix and a gain matrix, and determining the gain of the controller; and
and 4, constructing a controller, and performing elastic control on the multi-region power system according to the controller.
Further, the establishing the multi-region power system model based on the dynamic event triggering mechanism under the DoS attack comprises the following steps:
step 101, establishing a multi-region power system model under discrete time with uncertain parameters;
step 102, introducing a DoS attack model into the power system model;
step 103, introducing a dynamic event triggering mechanism into the power system model with DoS attack.
Further, the DoS attack model is an aperiodic DoS attack model, including:
wherein s is n Indicating that the (n-1) th attack interval is finished, the signal transmission is normal, h n Represents the length of the attack-free interval s n +h n Is the nth attack starting time, and the attack time sequence satisfies s n+1 ＞s n +h n The method comprises the steps of carrying out a first treatment on the surface of the At the same time, the average residence time ADT model is employed to constrain the frequency and duration of DoS attacks.
Further, the introducing a dynamic event trigger mechanism includes:
the trigger condition of the dynamic event trigger mechanism is configured to be related to the current sampling signal and the previous trigger signal only, and when the preset trigger condition is met, the current sampling signal is sent to the controller end, and the controller updates the control signal once.
Further, obtaining conditions that stabilize the multi-zone power system model includes:
and determining condition parameters when switching is performed at a switching point, so that the multi-region power system model can stably run, wherein the switching point refers to a switching point of a DoS attack section and a non-attack section.
Further, the multi-region power system model based on the dynamic event triggering mechanism under DoS attack comprises:
wherein I is 1,n ＝[s n ,s n +h n ) As non-attack interval, I 2,n ＝[s n +h n ,s n+1 ) To attack interval, ψ m,n Gamma for event trigger interval m,j For the sampling interval, the trigger error e (k) satisfies the following relationshipx (k) represents a state signal of the system, ΔP d (k) Representing interference signals of the system, τ (k) e 0, τ M ]Representing system delay, λ (K) representing dynamic variables, κ being a given positive scalar, A, B, C and F being constant matrices, K being the control gain matrix to be solved, Ω being the trigger matrix to be solved, Δa (K) being the reaction system modelAn unknown real matrix of medium parameter uncertainty having the form: Δa (k) =gh (k) E 1 Wherein H (k) is H T (k) An uncertainty matrix of H (k). Ltoreq.I, wherein H T (k) Is the transpose of H (k), G and E 1 Is a known constant matrix for reflecting the uncertain parameter structure information.
Further, the conditions for stabilizing the multi-zone power system model include:
wherein the method comprises the steps of
Γ 1 ＝[A+ΔA BKC 0 BKC F]，
Γ 2 ＝[A+ΔA-I BKC 0 BKC F]，
Γ 3 ＝[X 1 Y 1 -X 1 -Y 1 0 0]，
Ξ 1 ＝[A+ΔA 0 0 F]，
Ξ 2 ＝[A+ΔA-I 0 0 F]，
Ξ 3 ＝[X 0 Y 0 -X 0 -Y 0 0]，
Positive definite matrix P i ,Q i ,R i ,M i (i=0, 1) is the matrix to be solved, X i ,Y i (i=0, 1) matrix to be solved of appropriate dimension, 0 < μ 1 ＜1，μ 0 ＞1，α i ＞1(i＝0,1)，γ,τ M ,τ D ,T α Any constant that satisfies a condition.
Further, the solving the trigger matrix and the gain matrix includes:
for DoS attack parameter tau meeting condition D ,T α Adjustable parameter epsilon, tau M ,μ 1 ,μ 0 ,α 1 ,α 0 Setting positive symmetry matrix in gamma, epsilon, sigma and deltaAnd matrix of appropriate dimension->Constructing a linear matrix inequality for enabling a multi-region power system model to normally operate;
according to the inequality of the linear matrix and the condition for stabilizing the multi-region power system model, calculating a trigger parameter (sigma, omega) and a matrix to be solvedAnd
Calculating a controller gain matrix
Further, the controller is expressed as:
compared with the prior art, the invention has the following beneficial effects: introducing an aperiodic DoS attack model in view of security control issues; the dynamic event triggering mechanism is introduced in consideration of the current situation that bandwidth resources are limited, and a mathematical model established by the dynamic event triggering mechanism and the dynamic event triggering mechanism is combined. When the power system does not encounter an attack, the system operates normally; when an attack is encountered, the switching point performs switching to ensure the normal operation of the system; the event triggering mechanism is only related to the current sampling signal and the last triggering signal, when the sampling signal meets the triggering condition, the sampling signal is sent to the controller end, otherwise, the current sampling signal is not sent. Compared with a static event triggering mechanism, the method ensures that the system can safely and stably run under the condition that DoS attack is possible, reduces the transmission quantity of redundant signals, reduces the transmission pressure of a network and saves the energy source required by communication.
Drawings
Fig. 1 is a flow chart of a portion of an elastic LFC method in a multi-zone power system in an embodiment of the present invention.
Fig. 2 is a block diagram of a multi-zone power system in an embodiment of the invention.
FIG. 3 is a schematic diagram of the operation of a dynamic event trigger in an embodiment of the present invention.
Detailed Description
The technical scheme of the invention is further described in detail below with reference to the attached drawings.
The invention provides an elastic LFC method under a multi-region power system. Firstly, considering system safety and saving communication resources, a dynamic event triggering communication scheme under aperiodic DoS interference is designed, and a time lag modeling and switching system modeling method is utilized to build a segmentation augmentation system model with time lag. Secondly, based on the model, adopting a segmented Lyapunov functional method and a linear matrix inequality technology, designing an elastic controller to ensure the control performance of the system, wherein the method mainly comprises the following steps of:
step S1, establishing a multi-region power system model based on a dynamic event triggering mechanism under DoS attack can be expressed as:
wherein I is 1,n ＝[s n ,s n +h n ) As non-attack interval, I 2,n ＝[s n +h n ,s n+1 ) To attack interval, ψ m,n Gamma for event trigger interval m,j For the sampling interval, the trigger error e (k) satisfies the following relationshipx (k) represents a state signal of the system, ΔP d (k) Representing interference signals of the system, τ (k) e 0, τ M ]Representing system delay, λ (K) representing dynamic variables, κ being a given positive scalar, A, B, C and F being constant matrices, K being a control gain matrix to be solved, Ω being a trigger matrix to be solved, Δa (K) being an unknown real matrix reflecting parameter uncertainty in the system model, having the form: Δa (k) =gh (k) E 1 Wherein H (k) is H T (k) An uncertainty matrix of H (k). Ltoreq.I, wherein H T (k) Is the transpose of H (k), G and E 1 Is a known constant matrix for reflecting the uncertain parameter structure information.
The construction process of the model mainly comprises three steps of:
and step S101, establishing a multi-region power system model under discrete time with uncertain parameters.
An ith control zone schematic diagram in a multi-zone power system is shown in fig. 2, in which dual communication channels are used to connect distributed control zones to ensure reliability of communication. The discretized multi-region power system model consisting of the ith control region in fig. 2 is:
state variable x in i (k)＝[Δf i ΔP tie ΔP mi ΔP υi ∫ACE i ] T Output variable y i (k)＝[ACE i ∫ACE i ] T ，ΔP υi 、ΔP mi 、ΔP di And Δf i The threshold deviation, generator output, load and frequency of the ith area in the LFC power system are shown, respectively. Discretized system matrix Wherein h is the discrete sampling frequency, where
Alpha in the formula i ,β i As a known constant term, R i 、M i 、D i 、T chi And T gi Respectively representing the speed drop, the generator moment of inertia, the generator damping coefficient, the turbine time constant and the speed regulator time constant of the ith area in the LFC power system, T ij Is the link synchronization coefficient between the ith and jth control regions, ΔP tie Is the i-th control area tie net switching power. ACE (Area Control Error) for each zone represents a linear combination of link switching power and frequency deviation between zones, which can be written as:
ACE i ＝β i Δf i +ΔP tie
the following PI controller is selected as LFC scheme:
u i (k)＝-K Pi ACE i -K Ii ∫ACE i
ACE in i Region control error indicative of the ith region in a multi-region power system, +.ACE i Is ACE i Integral of K Pi And K Ii Proportional gain and integral gain, respectively. On the basis of the single-region power system model (1), a multi-region power system model with uncertain parameters under linear discrete time is established:
in the middle of ΔA＝diag{ΔA 1 ,ΔA 2 ,K,ΔA n }，B＝diag{B 1 ,B 2 ,K,B n },F＝diag{F 1 ,F 2 ,K,F n },C＝diag{C 1 ,C 2 ,K,C n },K＝diag{K 1 ,K 2 ,K,K n }, itMiddle K i ＝[K Pi ,K Ii ]。
Step S102, introducing a DoS attack model into the power system model.
As shown in fig. 2, a DoS attack model is introduced in a multi-zone power system. In step S102, a DoS attack model is constructed, where DoS signals are a set of attack signals with limited energy, and occupy limited channels to block communication, and the expression is as follows:
where n is the number of attacks, s n Indicating that the (n-1) th attack interval is finished, the signal transmission is normal, h n Represents the length of the attack-free interval s n +h n Is the nth attack start time. Attack timing satisfies s n+1 ＞s n +h n Therefore, no section is covered. Meanwhile, an average residence time (ADT) model is employed to constrain the frequency and duration of DoS attacks:
wherein N (k, k) 0 ) Represented at [ k ] 0 ,k]Frequency of DoS attacks during time period y (k, k) 0 ) Represented at [ k ] 0 ,k]The duration of the DoS attack within the time period,for a given positive real number, τ D ≥2，T α And > 1 is any constant that satisfies the condition. For convenience and brevity of the following description, define event trigger interval +.>Sampling interval y m,0 ＝[k m,n ,k m,n +τ M +1)，Υ m,j ＝[k m,n +j+τ M ,k m,n +j+τ M +1),j＝1,2,K,d-1，Υ m,d ＝[k m,n +d+τ M ,k m+1,n ) τ in M Represents the upper bound of delay, { k m,n The sequence of control signals represents the successful update time, i.e. the control signal generated by the event trigger mechanism, and k 0,n ＝s n 。
Step S103, introducing a dynamic event triggering mechanism into the power system model with the DoS attack.
The following dynamic event trigger mechanism is designed aiming at the DoS attack, and the network communication pressure is reduced while the gradual stability of the system under the action of the controller is ensured. The dynamic event triggering conditions are as follows:
wherein k is m Is a positive integer which is used for the preparation of the high-voltage power supply,is a positive weighting matrix with appropriate dimensions, σ, κ is a bounded positive real number, y (k) m ) Is the trigger signal at the current time, y (k m +j) is the latest sampling signal, λ (k) represents a dynamic variable, whose expression is:
where ρ is a bounded positive real number, an initial value of λ (0) =λ 0 Is a given positive scalar. If the trigger condition is met, the sampled value of the current time of the phasor measurement unit (Phasor Measurement Unit, PMU) is recorded and transmitted to the controller. If not, the sampling value at the current moment is not recorded. However, this trigger condition cannot be used directly when an attack signal is present. The invention defines that the event trigger time when the attack signal appears should satisfy k m+1 ＝{k m +min{j|L(y,λ)＜0}}U{s n },k∈[s n ,s n +h n )。
For convenience ofCalculation and recordingTwo segmentation equations are defined:
based on the definition of τ (k) and e (k), and taking into account the uncertainty of the parameters, the final system model is:
the dynamic event trigger mechanism can be expressed as:
the dynamic event trigger conditional expression indicates: the trigger condition is only related to the current sampling signal and the previous trigger signal, and when the preset trigger condition is met, the current sampling signal is sent to the controller end, and the controller updates the control signal once.
The purpose of steps S102 and S103 is to introduce an aperiodic DoS attack and a dynamic event triggering mechanism to build the final model. Compared with the traditional network control system design, the model constructed in the step S102 considers the security control problem, introduces a specific network attack, and completes the establishment of an attack model.
Step S103 builds a dynamic trigger mechanism, as shown in FIG. 3, in a normal controller, a trigger model is added, and when to update a control signal is determined through the numerical calculation of a trigger function.
And S2, acquiring conditions for enabling the multi-region power system model to stably operate.
The conditions required for guaranteeing the stability of the power system under the DoS attack are as follows:
wherein:
Γ 1 ＝[A+ΔA BKC 0 BKC F]，
Γ 2 ＝[A+ΔA-I BKC 0 BKC F]，
Γ 3 ＝[X 1 Y 1 -X 1 -Y 1 0 0]，
Ξ 1 ＝[A+ΔA 0 0 F]，
Ξ 2 ＝[A+ΔA-I 0 0 F]，
Ξ 3 ＝[X 0 Y 0 -X 0 -Y 0 0].
positive definite matrix P i ,Q i ,R i ,M i (i=0, 1) is the matrix to be solved, X i ,Y i (i=0, 1) matrix to be solved of appropriate dimension, 0 < μ 1 ＜1，μ 0 ＞1，α i ＞1(i＝0,1)，γ,τ M Any constant that satisfies a condition.
The invention adopts the switching system, the above conditions are required to be met when the switching point is switched, and the solved elastic event trigger controller can ensure the stable operation of the power system and is not damaged by attack signals when the aperiodic denial of service attack occurs.
The switching condition in the step S2 is introduced into the multi-region power system, and the switching condition is a condition which must be met when the attack region and the non-attack region are switched, and the power system can stably run only when the condition is met.
Step S3, solving a trigger matrix and a gain matrix, and determining the gain of the controller, wherein the step comprises the following steps:
step S301, parameter τ for given DoS attack D ,T α Adjustable parameter epsilon, tau M ,μ 1 ,μ 0 ,α 1 ,α 0 Setting positive symmetry matrix in gamma, epsilon, sigma and deltaAnd matrix of appropriate dimension->Constructing a linear matrix inequality for enabling a multi-region power system model to normally operate;
step S302, according to the linear matrix inequality and the multi-region power systemCalculating trigger parameters (sigma, omega) and a matrix to be solved under the condition of stable operation of the modelStep S303, calculating a controller gain matrix +.>
In step S301, the linear matrix inequality constructed to enable the multi-region power system model to operate normally includes:
wherein:
all are matrices to be solved, I is an identity matrix with proper dimension, and I is a transpose item corresponding to the identity matrix in the matrix.
Then in step S302 and step S303, the trigger parameters (sigma, omega) and the matrix to be solved are calculated according to the matrix inequalityThen calculate the controller gain matrix +.>
And S4, constructing a controller, and performing elastic control on the multi-region power system according to the controller.
The spring controller constructed in this step can be expressed as:
the method introduces a non-periodic DoS attack model in consideration of the security control problem; the dynamic event triggering mechanism is introduced in consideration of the current situation that bandwidth resources are limited, and a mathematical model established by the dynamic event triggering mechanism and the dynamic event triggering mechanism is combined. When the power system does not encounter an attack, the system operates normally; when an attack is encountered, the switching point performs switching to ensure the normal operation of the system; the event triggering mechanism is only related to the current sampling signal and the last triggering signal, when the sampling signal meets the triggering condition, the sampling signal is sent to the controller end, otherwise, the current sampling signal is not sent. Compared with the traditional static event triggering mechanism, under the condition that DoS attack is possible to occur, the dynamic event triggering mechanism can reduce the transmission quantity of redundant signals to a greater extent while ensuring the safe and stable operation of the system, lighten the transmission pressure of the network and save the resources required by communication.
The above description is merely of preferred embodiments of the present invention, and the scope of the present invention is not limited to the above embodiments, but all equivalent modifications or variations according to the present disclosure will be within the scope of the claims.
Claims (7)
1. The elastic load frequency control method of the multi-region power system under the denial of service attack is characterized by comprising the following steps of: the method comprises the following steps:
step 1, establishing a multi-region power system model based on a dynamic event trigger mechanism under a denial of service (DoS) attack;
step 2, obtaining the condition for enabling the multi-region power system model to stably operate;
step 3, solving an event trigger matrix and a gain matrix, and determining the gain of the controller;
solving the trigger matrix and the gain matrix includes:
for DoS attack parameter tau meeting condition D ,T α Adjustable parameter epsilon, tau M ,μ 1 ,μ 0 ,α 1 ,α 0 Setting positive symmetry matrix in gamma, epsilon, sigma and deltaAnd matrix of appropriate dimension->Constructing a linear matrix inequality for enabling a multi-region power system model to normally operate;
according to the inequality of the linear matrix and the condition for stabilizing the multi-region power system model, calculating a trigger parameter (sigma, omega) and a matrix to be solvedN; calculating a controller gain matrix +.>
Step 4, constructing a controller, and performing elastic control on the multi-region power system according to the controller;
the constructed elastic controller is expressed as:
2. the method for controlling the frequency of the elastic load of a multi-zone power system under denial of service attack according to claim 1, wherein: the multi-region power system model based on the dynamic event triggering mechanism under the DoS attack comprises the following steps:
step 101, establishing a multi-region power system model under discrete time with uncertain parameters;
step 102, introducing a DoS attack model into the power system model;
step 103, introducing a dynamic event triggering mechanism into the power system model with DoS attack.
3. The method for controlling the frequency of the elastic load of a multi-zone power system under denial of service attack according to claim 2, wherein: the DoS attack model is an aperiodic DoS attack model, comprising:
wherein s is n Indicating that the (n-1) th attack interval is finished, the signal transmission is normal, h n Represents the length of the attack-free interval s n +h n Is the nth attack starting time, and the attack time sequence satisfies s n+1 ＞s n +h n The method comprises the steps of carrying out a first treatment on the surface of the At the same time, the average residence time ADT model is employed to constrain the frequency and duration of DoS attacks.
4. The method for controlling the frequency of the elastic load of a multi-zone power system under denial of service attack according to claim 2, wherein: the introducing a dynamic event trigger mechanism comprises:
the trigger condition of the dynamic event trigger mechanism is configured to be related to the current sampling signal and the previous trigger signal only, and when the preset trigger condition is met, the current sampling signal is sent to the controller end, and the controller updates the control signal once.
5. The method for controlling the frequency of the elastic load of a multi-zone power system under denial of service attack according to claim 1, wherein: acquiring conditions for stabilizing the multi-zone power system model includes:
and determining condition parameters when switching is performed at a switching point, so that the multi-region power system model can stably run, wherein the switching point refers to a switching point of a DoS attack section and a non-attack section.
6. The method for controlling the frequency of the elastic load of a multi-zone power system under denial of service attack according to claim 1, wherein: the multi-region power system model based on the dynamic event triggering mechanism under the DoS attack comprises:
wherein I is 1,n ＝[s n ,s n +h n ) As non-attack interval, I 2,n ＝[s n +h n ,s n+1 ) To attack interval, ψ m,n Gamma for event trigger interval m,j For the sampling interval, the trigger error e (k) satisfies the following relationshipSigma epsilon [0, 1), x (k) represents the state signal of the system, ΔP d (k) Representing interference signals of the system, τ (k) e 0, τ M ]Representing system delay, λ (K) representing dynamic variables, κ being a given positive scalar, A, B, C and F being constant matrices, K being a control gain matrix to be solved, Ω being a trigger matrix to be solved, Δa (K) being an unknown real matrix reflecting parameter uncertainty in the system model, having the form: Δa (k) =gh (k) E 1 Wherein H (k) is H T (k) An uncertainty matrix of H (k). Ltoreq.I, wherein H T (k) Is the transpose of H (k), G and E 1 Is a known constant matrix for reflecting the uncertain parameter structure information.
7. The method for controlling the frequency of elastic loading of a multi-zone power system under denial of service attack according to claim 6, wherein: the conditions for stabilizing the multi-zone power system model include:
wherein the method comprises the steps of
Γ 1 ＝[A+ΔA BKC 0 BKC F]，
Γ 2 ＝[A+ΔA-I BKC 0 BKC F]，
Γ 3 ＝[X 1 Y 1 -X 1 -Y 1 0 0]，
Ξ 1 ＝[A+ΔA 0 0 F]，
Ξ 2 ＝[A+ΔA-I 0 0 F]，
Ξ 3 ＝[X 0 Y 0 -X 0 -Y 0 0]，
Positive definite matrix P i ,Q i ,R i ,M i (i=0, 1) is the matrix to be solved, X i ,Y i (i=0, 1) matrix to be solved of appropriate dimension, 0 < μ 1 ＜1，μ 0 ＞1，α i ＞1(i＝0,1)，γ,τ M ,τ D ,T α Any constant that satisfies a condition.
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