CN108767844A - The adaptive state estimation method of Data Injection Attacks lower network multi-region power system - Google Patents
The adaptive state estimation method of Data Injection Attacks lower network multi-region power system Download PDFInfo
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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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- 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
- H02J3/04—Circuit arrangements for ac mains or ac distribution networks for connecting networks of the same frequency but supplied from different sources
- H02J3/06—Controlling transfer of power between connected networks; Controlling sharing of load between connected networks
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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
- H02J2203/00—Indexing scheme relating to details of circuit arrangements for AC mains or AC distribution networks
- H02J2203/20—Simulating, e g planning, reliability check, modelling or computer assisted design [CAD]
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Abstract
The invention discloses a kind of adaptive state estimation methods of multizone networked power system under Data Injection Attacks.Consider to provide a new measurement equation to each region in the case of system mode and signal to attack at the same time first, state estimation is converted to constrained Optimization Solution problem；Then some dummy node fillet systems are constructed, realize the communication constraint between adjacent area, and the Lagrangian with constraint information is given using variational inequality principle；The method for estimating state for becoming punishment parameter is finally proposed, realizes the state estimation under Data Injection Attacks, wherein the punishment parameter can will be adaptively sized according to evaluated error and boundary error progress, and then improve the accuracy and speed of estimation.The present invention is to be applied to extensive multi-region power system state estimation under Data Injection Attacks, can ensure accuracy and speed well, to meet the growth requirement of the following intelligent grid.
Description
Technical field
The present invention relates to a kind of method for estimating state of electric system, specifically a kind of Data Injection Attacks lower network is more
The adaptive state estimation method of regional power system.
Background technology
Power system state estimation (PSSE) is the core component of energy management system (EMS).In present electric power
In system, the electricity needs of user is higher and higher so that and the scale of electric system becomes larger, the complication of structure more, by
Gradually develop in the direction of multi-region power system.It is logical in subsystem and between each region to multi-area Interconnected Power System
There are two types of letter connection type is usual：One is point-to-point leased-line communication method, another kind is open power telecom network.Phase
For traditional point-to-point special line communication connection type, had by the way of open powerline network convenient for wiring, easily
In installation maintenance, it is easy to operate, of low cost, flexibility is big the advantages that.However, opening due to networking multi-region power system
Put formula communication so that by the network attack of malice, extremely strong destructiveness is easily caused to multi-region power system for it.Common
Attack form has：Wrong data injection attacks (FDI), Denial of Service attack, Replay Attack etc..The Iranian Bushire since 2010
Nuclear power station data are acquired with monitoring system by StuxNet (" shake net " virus) attack, cause serious consequence, common people is enabled to shake
Frightened, exposing traditional EMS, there are serious problems to the real-time monitoring of system and processing aspect, and state estimation is the core of EMS
The state estimation strategy that the heart carries important task, therefore is badly in need of under research attack.Control system safety problem is increasingly becoming
Countries in the world focus of attention.The research of International Academic bound pair safety problem gives great attention, such as IEEE Systems
Journal(2012)、IEEE Control System Magazine(2015)、IEEE Transaction on Control
And Network Systems (2015) etc. have published the research monograph in terms of network security.
Currently, the state estimation of multi-region power system can substantially be divided into two classes：1) by different level based on composition decomposition
Distributed state estimation method, but subregion side, coordination side separately iteratively solve, and generally only acquire suboptimal solution；2) it is not necessarily to coordinate
The distributed method of side is not necessarily to Central co-ordination side, but constringency performance is weak.Therefore there is certain deficiency in above two method,
And only only account for obeying the noise of specific distribution, it cannot be adapted to that there are in the electric system of random signal to attack, it is difficult to full
The growth requirement of foot modern times large-scale electrical power system.
In multi-region power system, being in communication with each other between subsystem is certainly existed, there are the identical shapes of certain nodes sharings
The case where state information, thus must take into consideration in state estimation the communication constraint problem between adjacent subsystems.Due to networking electricity
There are the signal to attack of malice in Force system, and it is destructive greatly, therefore are being disliked to networking multi-region power system
The research of the lower state estimation algorithm of meaning attack is very urgent.Rational state estimation algorithm how is designed, is not being changed as far as possible
The state of system is estimated in the case of becoming electric system control structure and a great problem that numerous researchers must solve.
Invention content
It is an object of the invention to overcome the deficiencies in the prior art to design a kind of data with the thought of variational inequality
The adaptive state estimation method of injection attacks lower network multi-region power system.
In order to achieve the above objectives, design of the invention is as follows：
First, consider to provide a new amount to each subsystem in the case of system mode and signal to attack at the same time
Equation is surveyed, state estimation problem is converted to constrained Optimization Solution problem using the measurement equation.Then one is constructed
A little effective dummy nodes carry out fillet system, to realize the communication of power system between different sub-systems.Then base is proposed
In the distributed state estimation method of punishment parameter, to realize that state of the electric system under FDI attacks is restored, the wherein punishment
Parameter can carry out adaptive adjustment according to dynamic internal error and boundary error, with existing Power system state estimation
Method is compared, which is improved in accuracy and real-time, while can also estimate the attack letter of malice together
Number.Finally, simulation example illustrates the validity of adaptive state estimation method.
In order to realize above-mentioned target, the technical scheme is that：
A kind of adaptive state estimation method of Data Injection Attacks lower network multi-region power system, including have as follows
Body step：
Step 1：The networked power system of big scale is divided into multiple control zones, each control zone be exactly one or
Several busbares and generator connected to it, i.e. a subsystem；If given electric system is divided into p subsystem,
Wherein p is positive integer.
Step 2：The metric data of different zones is read, the measurement of system includes voltage magnitude and phase angle measurements, busbar
It is active with idle injecting power measurement, branch active reactive trend measurement, measurement equation is as follows：
Pik=Vi 2(gik+gsik)-ViVk(gikcos(θi-θk)+biksin(θi-θk))
Qik=-Vi 2(bik+bsik)-ViVk(giksin(θi-θm)-bikcos(θi-θk))
θi=arctan (fi/ei)
Wherein, i is to belong to subsystem SaA wiring；Vi、Pik、Qik、Pi、QiBe respectively voltage magnitude at wiring l and m,
The measuring value of active and reactive power flow, active and idle injection trend；Vi、VkIt is the voltage magnitude of wiring l and m respectively；θi、θk
It is the angle values of wiring l and m respectively；gi+jbikIt is branch i-k series admittance values；gsik+jbsikIt is branch i-k shunt admittance values；
gi+jbiIt is attached to the shunt admittance value of line i；A (i) is to be connected on i and belong to region SaWired set；b(i)
To be connected on i and belonging to region SaWired set (i ≠ k)；eiIndicate the active component of branch i；fiIndicate branch
The reactive component of i；
Step 3：Assuming that the measurement of subsystems and quantity of state are linear, and provide the lower measurement equation of FDI attacks,
It is simultaneously comprising attack information and status information：
In formula：ziFor the measurement of subsystem i, HiFor the Jacobian matrix of subsystem i, I is unit battle array, xiFor subsystem i
State variable, aiFor the FDI signal to attack of subsystem i.
Since measuring instrument is numerous in electric system, the finite energy of attacker, therefore only a small number of measuring values are disliked
The attack of meaning namely signal to attack have sparsity.Compared with measuring noise, measures noise general satisfaction and be specifically distributed, and
FDI has very strong randomness.
In electric system there are two types of the modes of estimated state：One is in the way of Load flow calculation, another kind is to utilize
The mode of state estimation.In Load flow calculation, the dimension for measuring vector is identical with unknown state vector dimension, however estimates in state
In meter method, the dimension for measuring vector is more than the dimension of unknown state vector, that is to say, that in state estimation, HiIt is m × n ranks
Measurement matrix, so if selecting suitable measurement equation, it is ensured that ΦiIt is sequency spectrum matrix.Load flow calculation can be regarded as
A kind of special state estimation as m=n.
Step 4：Boundary condition amount is consistent between subsystem in order to ensure multizone networked power system and introducing is following
Equality constraint：
In formula：xs[t]、xt[s] is respectively the boundary condition variable of subsystem s, t.NsFor the subsystem adjacent with subsystem s
System set.
In networking multi-region power system, more accurate state estimation Optimized model should include that boundary constraint is believed
Breath, the state estimation object function with boundary information constraints, which is given below, is：
Step 5：In order to preferably indicate constraint information, dummy node b is built, the communication connection between adjacent subsystems can be with
Regard the connection between part of nodes and dummy node b in subsystem as.Therefore, constraints is converted into following form：
In formula：ybIndicate the state of dummy node, setIncluding all bridge nodes, A indicates all node compositions
Set.Set NbIndicate the neighbor node being connected with bridge node b.∑|B||Nb| indicate the communication of all nodes and bridge node b about
Beam.
It is differed by the principle of variational inequality it is found that solving above-mentioned state estimation problem and can be converted to the following variation of solution
Formula problem：
(x-x*)TF'(x*)≥0,Belong to nonempty closed set conjunction
Wherein x*For the minimum value of function F, and belong to during nonempty closed set closes.
Step 6：It is being examined for solving state estimation problem according to variational inequality thought and the dummy node b of structure
In the case of considering boundary information constraint, establish with change punishment parameter βi,bLagrangian：
Wherein λi,bFor adjustment parameter, βi,bTo become punishment parameter.
Further, state estimation problem, which is transformed into, solves following variational inequality, purpose namely the following change of searching
Divide the optimal solution r of inequalityi k+1,Variational inequality is as follows：
Wherein k is iterations, F'(ri k+1)、F (r are indicated respectivelyi,yb,λi,b) function pair ri k+1With's
Derived function, γ ∈ (0,2), usually, best performance when taking γ=1.618.
In existing research, punishment parameter β is a fixed value or a monotonic sequence, in state estimation mistake
Cheng Zhong, computational efficiency is not high, therefore the present invention proposes a kind of change punishment parameterIt can dynamically be adjusted according to evaluated error
Its whole size, and then the speed of state estimation can be improved.
Step 7：Rule change it is as follows：
WhereinIndicate the iteration that system mode and signal to attack are walked in kth
Error, μ ∈ (0,1), λi,b∈Nb, nonnegative sequenceMeetAnd
IfSo during next iteration,It should increase, on the contrary, ifWhen, during next iterationIt should reduce, here it is the basic thoughts of the strategy.In iteration
In the process, parameterIts size can be dynamically adjusted according to evaluated error, and then improves the estimating speed of algorithm, realize shape
The adaptive characteristic of state estimation.
Optimal value is iteratively solved according to above equation, until error precision meets requirement of the system to estimated value.
Data Injection Attacks lower network multi-region power system adaptive state estimation method proposed by the present invention, it is excellent
Putting is：
1) scalability：After subregion, the subproblem scale in each region of this method is very small, therefore can cope with big rule
The networked power system of mould；
2) maintainable：Generally speaking, what this method only needed each subsystem and adjacent subsystems cooperates with iteration, does not need
Control centre just coordinates, handles, and need not safeguard huge several models；
3) speed：By establishing dummy node, proposes the adaptive state estimation method for becoming punishment parameter, can improve
The speed of state estimation disclosure satisfy that requirement of real-time of the electric system to state.
Description of the drawings
Fig. 1 is the flow chart of the method for the present invention.
Fig. 2 is 4 regional power system distribution maps under FDI attacks.
Fig. 3 is dummy node structure schematic diagram.
Fig. 4 is the three Regional Networked electric system attacked by FDI.
Fig. 5 is frequency state estimation curve and actual frequency curve of the region 1 under FDI attacks.
Fig. 6 is frequency state estimation curve and actual frequency curve of the region 2 under FDI attacks.
Fig. 7 is frequency state estimation curve and actual frequency curve of the region 3 under FDI attacks.
Fig. 8 is the estimation curve for the FDI signal to attack that region 1 is subjected to and true signal to attack curve.
Fig. 9 is the evaluated error of three regional power systems.
Figure 10 is 1 punishment parameter β of region1,bChange procedure.
Specific implementation mode
The present invention proposes the networking multi-region power system adaptive state estimation side under a kind of Data Injection Attacks
Method, in the following with reference to the drawings and specific embodiments, the present invention is further elaborated, it should be understood that these embodiments are merely to illustrate
The present invention effect rather than limit the scope of the invention, after having read the present invention, those skilled in the art are to this hair
The modification of bright various equivalent forms falls within the application range as defined in the appended claims.
As shown in Figure 1, a kind of networking multi-region power system adaptive state estimation method under Data Injection Attacks,
Include the following steps：
1) the networked power system of big scale is divided into multiple control zones, a control zone is exactly one or several
Busbar and generator connected to it namely a subsystem.Assuming that given electric system is divided into p subsystem, p is
Positive integer gives 4 Regional Networked electric system, p=4 as shown in Figure 2.Between part of nodes in region 1 and region 2,3
Mutually there are communications, is adjacent area, such as：1,2 nodes in region 1 are in communication with each other with 5,7 nodes in region 2；Area
2 nodes in domain 1 are communicated with 11 node mutuals in region 3 (description step in detail below by taking region 1 as an example, indicates arbitrary
Region, each region are same treatment).
2) new measurement model is established to each region of electric system after division, it is as follows it includes FDI signal to attack
Formula：
Wherein ziFor the measurement of region i, xiIndicate the state of region i, aiIndicate the signal to attack that region i is subjected to, HiFor
The measurement matrix of region i, element are determined by following measurement equation：
Pik=Vi 2(gik+gsik)-ViVk(gikcos(θi-θk)+biksin(θi-θk))
Qik=-Vi 2(bik+bsik)-ViVk(giksin(θi-θm)-bikcos(θi-θk))
θi=arctan (fi/ei)
Wherein, above-mentioned is the measurement in the i of region, Vi、Pik、Qik、Pi、QiIt is voltage amplitude at wiring l and m respectively
The measuring value of value, active and reactive power flow, active and idle injection trend；Vi、VkIt is the voltage magnitude of wiring l and m respectively；θi、
θkIt is the angle values of wiring l and m respectively；gi+jbikIt is branch i-k series admittance values；gsik+jbsikIt is branch i-k shunt admittances
Value；gi+jbiIt is attached to the shunt admittance value of line i；A (i) is to be connected on i and belong to region SaWired set；b
(i) it is to be connected on i and belong to region SaWired set (i ≠ k)；eiIndicate the active component of branch i；fiIt indicates
The reactive component of branch i.
3) object function and constraints of region i state estimations are established：
4) it in order to preferably indicate the communication constraint between region i and neighbours region, is indicated by building dummy node b
Constraint between communication, as shown in figure 3, the interconnection between boundary node is regarded as the connection with dummy node, dot-dashed line table
Show the communication connection between the subsystem of boundary, the connection is become to connect with the horizontal dotted line of dummy node b using dummy node, namely
Constraints can be converted to following form：
Wherein, ybIndicate the state of dummy node, setIncluding all bridge nodes, A indicates all node compositions
Set.Set NbIndicate the neighbor node being connected with bridge node b.The research object of the example is 3rd area attacked by FDI
Domain networked power system, as shown in Figure 4.
5) variational inequality principle is utilized, for state estimation, first according to above-mentioned state estimation Solve problems, is proposed
With change punishment parameter βi,bLagrangian：
6) and then solving state estimation problem is converted to according to above-mentioned Lagrangian and solves a variational inequality
Problem, namely solve the optimal solution r of following variational inequalityi k+1,Inequality is as follows：
Wherein k is iterations, F'(ri k+1)、F (r are indicated respectivelyi,yb,λi,b) function pair ri k+1With's
Derived function, γ ∈ (0,2), usually, best performance when taking γ=1.618.
7) the optimal solution r for meeting inequality under the i present cases of region first, is iteratively solved out for the first timei 1；Secondly, most
Excellent solution, which substitutes into, to be solvedInequality in, solve optimal solution at this time；Then the r of solutioni 1WithIt substitutes intoSolve etc.
The value of the λ in next step iteration is calculated in formula.The optimal solution for having solved region i at this time, most for other regions
Excellent solution is similar with the solution of region i.
Pay attention to：The punishment parameter β in iteration each timei,bIt is that dynamic adjusts, in this example, adjustment rule is as follows：
If relationship of the kth time between iteration error and boundary error isAnd iterations k≤
When 50, then the punishment parameter of+1 iteration of kth is 2 times of kth time iterative penalty parameter, i.e.,If kth time
Relationship between iteration error and boundary error isAnd when iterations k≤50, then kth+1 time
The punishment parameter of iteration is the half of kth time iterative penalty parameter, i.e.,Conversely, in the case of other, kth+
The punishment parameter of 1 iteration is equal with punishment parameter when kth time iteration, i.e.,
8) condition of convergence judges, is calculated according to above-mentioned steps progressive alternate, until acquired solution meets ‖ e (rk+1) ‖ < ε when
(ε be require evaluated error precision) stops iterative process, and optimal solution at this time, which can be regarded as approximately, exactly to be needed to solve
True solution.
The frequency state band in final each region attacked by FDI under estimated value and actual value change curve such as Fig. 5,6,
Shown in 7, as can be seen from the figure method proposed by the present invention can avoid the influence that FDI is attacked, and then accurately estimate and be
The state of system, while the signal to attack change curve that system is subjected to can also be estimated, as shown in Figure 8.With traditional distribution
Formula method of estimation compares, it can be seen that method estimating speed proposed by the present invention faster, estimated accuracy higher, as shown in Figure 9.
In this example, the change punishment parameter β in region 11,bChange procedure curve is as shown in Figure 10.It should be pointed out that the present invention is
Implementation process is described in detail in the electric system for using the interconnection of three Regional Networkeds, in the multizone electricity of bigger scale
In the case of Force system, the advantage of calculating speed of the invention and estimated accuracy can more protrude with significantly.
In conclusion the present invention can estimate shape of the multi-region power system after being attacked by FDI in real time in line
State, can be destructive caused by electric system to avoid malicious attack, and the precision of state estimation is high, estimating speed is fast, energy
Enough influences for timely rejecting FDI signal to attack, obtain accurate system status information；Meanwhile the present invention is virtual by building
Node realizes multi-region field communication, has coordinated the operating status in each region well, it is proposed that becomes punishment parameter and improves state
The speed of estimation meets requirement of real-time of the system to state.For complexity, big scale, multizone networked power
System, the state estimation under FDI attacks is one of the Chinese medicine module at following intelligent grid energy management center, to promoting intelligence
The further development of energy power grid is of great significance.
Claims (1)
1. a kind of adaptive state estimation method of Data Injection Attacks lower network multi-region power system, utilizes the amount of system
Measured data carries out state estimation, which is characterized in that the method includes the steps of：
Step 1：The networked power system of big scale is divided into multiple control zones, each control zone is exactly one or several
Busbar and generator connected to it, i.e. a subsystem；If given electric system is divided into p subsystem, wherein p
For positive integer；
Step 2：Read the metric data of different zones, the measurement of system, which includes voltage magnitude and phase angle measurements, busbar, to be had
Work(and idle injecting power measurement, branch active reactive trend measurement, measurement equation are as follows：
Pik=Vi 2(gik+gsik)-ViVk(gikcos(θi-θk)+biksin(θi-θk))
Qik=-Vi 2(bik+bsik)-ViVk(giksin(θi-θm)-bikcos(θi-θk))
θi=arctan (fi/ei)
Wherein, i is to belong to subsystem SaA wiring；Vi、Pik、Qik、Pi、QiIt is voltage magnitude at wiring l and m respectively, active
With reactive power flow, the measuring value of active and idle injection trend；Vi、VkIt is the voltage magnitude of wiring l and m respectively；θi、θkRespectively
It is the angle values of wiring l and m；gi+jbikIt is branch i-k series admittance values；gsik+jbsikIt is branch i-k shunt admittance values；gi+
jbiIt is attached to the shunt admittance value of line i；A (i) is to be connected on i and belong to region SaWired set；B (i) is
It is connected on i and belongs to region SaWired set (i ≠ k)；eiIndicate the active component of branch i；fiIndicate branch i
Reactive component；
Step 3：Assuming that the measurement of subsystems and quantity of state are linear, and provide the lower measurement equation of FDI attacks, it is same
When include attack information and status information：
In formula：ziFor the measurement of subsystem i, HiFor the Jacobian matrix of subsystem i, I is unit battle array, xiFor the shape of subsystem i
State variable, aiFor the FDI signal to attack of subsystem i；
Step 4：Provide the object function and boundary communication constraints of state estimation：
In formula：xs[t]、xt[s] is respectively the boundary condition variable of subsystem s, t, NsFor the subsystem collection adjacent with subsystem s
It closes；
Step 5：In order to preferably carry out the state estimation of multizone, the communication between different zones is realized, by building virtually
The form of node indicates the communication constraint between adjacent area：
In formula：ybIndicate the state of dummy node, setIncluding all bridge nodes, A indicates the collection of all node compositions
It closes, set NbIndicate the neighbor node being connected with bridge node b；
Step 6：Using variational inequality principle, above-mentioned state estimation problem is converted to solution Variational Inequalities Problem, is found out
The optimal solution for meeting inequality condition, provides Lagrangian first,
Wherein λi,bFor adjustment parameter, βi,bTo become punishment parameter；
Based on Lagrangian F (ri,yb,λi,b), provide and need the variational inequality that solves, below three formulas solve respectively
Go out optimal solution ri k+1,
Wherein k is iterations, F (r are indicated respectivelyi,yb,λi,b) function pairWithLead letter
Number, adjustment parameter γ ∈ (0,2)；
Step 7：It is required to judge the requirement whether current state estimation error precision reaches system before iteration each time,
Stop iteration if reaching, needs the relationship according to current evaluated error and boundary error dynamically to be adjusted if not reaching
Integral function F (ri,yb,λi,b) change punishment parameterIt adjusts rule：
WhereinIndicate the iteration error that system mode and signal to attack are walked in kth,
μ ∈ (0,1), λi,b∈Nb, nonnegative sequenceMeetAndAccording to above equation iteration
Optimal value is solved, until error precision meets requirement of the system to estimated value.
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| CN110865616A (en) * | 2019-11-07 | 2020-03-06 | 河南农业大学 | Design method of event trigger zone memory DOF controller under random FDI attack |
| CN112398117A (en) * | 2020-09-24 | 2021-02-23 | 北京航空航天大学 | False data injection attack construction and defense method causing line load overload |
| CN112421611A (en) * | 2019-11-06 | 2021-02-26 | 国网江苏省电力有限公司南通供电分公司 | Power distribution network data security detection method based on interval state estimation |
| CN115065549A (en) * | 2022-07-13 | 2022-09-16 | 南京邮电大学 | Distributed event trigger consistency control method for networked multi-Euler-Lagrange system under DoS attack |
| CN117039890A (en) * | 2023-10-08 | 2023-11-10 | 南京邮电大学 | Network attack detection-oriented power distribution network prediction auxiliary interval state estimation method |
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