CN106099920A - A kind of modern power transmission network false data attack method based on parameter estimation - Google Patents

Abstract

The invention discloses a kind of based on parameter estimation the modern power transmission network false data attack method in power system information security study field.The present invention is primarily based on the Optimized model of traditional Power system state estimation the Theory Construction false data vector of attack, and use alternating direction multiplier method (Alternating Direction Method of Multipliers, ADMM) to solve this Optimized model.There is error, even completely and there is the problem of bad data in metric data, then by method of Lagrange multipliers and the augmented state estimation technique in the electric parameter facing grasp for assailant, it is achieved the estimation to unknown branch road susceptance.Optimized model finally by false data vector of attack builds false data vector of attack.The present invention improves motility and the effectiveness that false data is attacked, and can be used for testing the effect of false data attack defense method, the ability that checking modern power transmission network reply false data is attacked simultaneously.

Description

A kind of modern power transmission network false data attack method based on parameter estimation

Technical field

The present invention relates to power system information security fields, be specifically related to modern power transmission network false data attack method neck Territory, particularly to a kind of modern power transmission network false data attack method based on parameter estimation.

Background technology

EMS (Energy Management System, EMS) be important power information communication system it One, mainly include the basic functions such as data acquisition, energy management and analysis of network, the safe and stable operation of power system is played Important function.State estimation is one of Core Feature of EMS, is that EMS performs load prediction, optimal load flow calculates and transient stability The correlation analysiss such as analysis control the basis of function.False data attacks (False Data Injection Attacks, FDI) A kind of network attack utilizing Legacy Status to estimate detection leak initiation.False data is attacked based on DC flow model, Point out when vector of attack be power system observation Jacobian matrix H column vector linear combination time, assailant can successfully around Cross the raw data detection device in state estimation, reach to revise measuring value and state variable, the control power system of power system Running status or obtain the illegal purpose such as economic interests.False data is attacked and is equally attacked with AC power flow mould simultaneously State estimator based on type.FDI attacks and takes full advantage of the leak that Legacy Status is estimated, this kind is attacked the most hidden, right Power system safety and stability runs very harmful, in some instances it may even be possible to cause large-scale blackout.

Due to the restriction of intrusion scene protection relevant with power system regulation, assailant is difficult to obtain completely power system Electric parameter and topological parameter, and electric parameter along with environmental condition different it may happen that change, such as line admittance and environment Temperature is correlated with, and its actual value and design load have certain deviation.But, by bribing the data of interior employee or public publication Etc. means, it is possible to obtain the part relevant parameter of power system, therefore, for assailant, the most real situation is to grasp Some electrical power systematic parameter, but assailant can only start local assault, and other node cannot be attacked.Assailant can pass through Start false data to attack metric data analysis, but do not utilize the parameters of electric power system of grasp, also there is no treating capacity Survey the bad data in data.Generally speaking, assailant faces the electric parameter of grasp and there is error, even complete and measure The problem that there is bad data in data.

Summary of the invention

The present invention is directed to the deficiencies in the prior art, it is provided that a kind of modern power transmission network false data based on parameter estimation is attacked Hit method.The present invention uses method for parameter estimation to build modern power transmission network false data vector of attack, improves false data and attacks The motility hit and effectiveness, can be used for testing the effect of false data attack defense method, the transmission of electricity of checking modern times simultaneously The ability that net reply false data is attacked.

The concrete technical scheme of the present invention is:

Step 1: calculate the susceptance of unknown parameter branch road according to method of Lagrange multipliers and the augmented state estimation technique；

Step 2: calculate Jacobian matrix H according to following formula_x；

In formula, h (x, p_e) represent and state variable x and branch parameters error p_eRelevant nonlinear function, P_ijRepresent and prop up Road trend, P_iRepresent the injecting power of bus, θ_iRepresent the phase place of bus i, b_ijRepresent the susceptance of branch road ij, B_iiRepresent bus i Self-admittance.

Step 3: using the Optimized model of ADMM Algorithm for Solving false data vector of attack, this model is as follows, obtains VariableIn relevant position completion 0 and 1, obtain suboptimum vector of attack a_x；

$\begin{array}{cc}\underset{c}{\min }& \left|\right|a_{\stackrel{\‾}{P}k}|{|}_1\end{array}$

$\begin{array}{cc}s.t.& B_{\stackrel{\‾}{P}k}{a}_{\stackrel{\‾}{P}k}=-b_k\end{array}$

In formula,Represent from matrixIn remove b_kRear submatrix,Representing matrix B removes with to gather P corresponding Submatrix after column vector, b_kKth row column vector in representing matrix B, wherein B=H (H^TH)^-1H^T-I, H represent observation Jacobi Matrix,Represent from vectorIn remove the vector after element a (k),With set in expression vector of attack aCorresponding The vector that element is constituted, a (k) represents the kth element in vector a.

Step 4: inject metric data z after false data_x=z+a_x, z represents original measurement number during unimplanted false data According to.

The detailed process of described step 1 is as follows；

The true value assuming branch parameters is p_t, error vector is p_e, then the measured value of branch parameters is shown below:

P=p_t+p_e

During Legacy Status is estimated, it is assumed that the error vector of branch parameters is 0, it is i.e. to have described in following formula to retrain；

p_e=0

This constraint is injected the constraints of weighted least-squares state estimation model under equality constraint as zero, obtain as Under described Optimized model:

$\begin{array}{cc}\min & J\left(x\right)=\frac{1}{2}{r}^{T}Wr\end{array}$

s.t.c(x,p_e)=0

p_e=0

In formula, W is for measuring weight diagonal matrix, r=z-h (x, p_e) represent measuring value residual error, h (x, p_e) represent and shape State variable x and branch parameters error p_eRelevant nonlinear function, c (x, p_e) represent not only there is no load but also there is no the mother of electromotor The injecting power of line；

To above-mentioned Optimized model application method of Lagrange multipliers, obtain Lagrangian as follows, adopt further The susceptance of unknown parameter branch road is calculated by method of Lagrange multipliers and the augmented state estimation technique:

$L=\frac{1}{2}{r}^{T}Wr-{\mathrm{\μ}}^{T}c(x,p_e)-{\mathrm{\λ}}^T{p}_e.$

In formula, μ and λ is Lagrange multiplier.

The detailed process of described step 3 is as follows；

In a power system with N bar bus, including voltage magnitude and phase angle, remove outside reference mode, altogether Having 2N-1 state variable, state variable is collectively expressed as x=[x₁,x₂,…,x_n]^T, n=2N-1；

Making the following assumptions, the voltage magnitude of all buses is equal and is 1, ignores line resistance, then in measuring value not There is reactive power, state variable only has voltage phase angle；Now, meet linear relationship between measuring value and state variable, obtain The DC power flow equation being shown below:

Z=Hx+e e～N (0, Σ_e)

Now, observation Jacobian matrix H=H_xFor constant matrices.If with a=[a₁,a₂,…,a_m]^TRepresent that disabled user exists The false data vector injected in measuring value, then actual measurement data is z_bad=z+a, c=[c₁,c₂,…,c_n]^TRepresent by In the error vector being infused in state variable introducing of false data, e=[e₁,e₂,…,e_m]^TRepresent measurement error, and Obeying average is 0, and variance is diagonal matrixNormal distribution, the state variable of estimation isFrom the angle of assailant, when building vector of attack a, it is desirable to reach with minimum intrusion scene and cost Purpose, therefore there is an optimal value in vector of attack a；The measuring point that in vector of attack a, nonzero element correspondence is attacked, nonzero element Number l₀Norm represents, the Optimized model of vector of attack is shown below:

$\begin{array}{cc}\underset{c}{\min }& \left|\right|a|{|}_0\end{array}$

S.t.a=Hc

In formula, | | a | |₀Represent the l of vector a₀Norm, l₀Norm is the least, and the degree of rarefication of vector of attack a is the highest；

Use convex relaxing techniques, above-mentioned Optimized model can be further converted to following formula:

$\begin{array}{cc}\underset{c}{\min }& \left|\right|a_{\stackrel{\‾}{P}k}|{|}_1\end{array}$

$\begin{array}{cc}s.t.& B_{\stackrel{\‾}{P}k}{a}_{\stackrel{\‾}{P}k}=-b_k\end{array}$

In formula, defining shielded measuring point numbering collection and be combined into P, unprotected measuring point collection is combined into||(·)||₁Table Show l1-norm,Represent from matrixIn remove b_kRear submatrix,Represent from vectorIn remove element a (k) after Vector；Use this model of ADMM Algorithm for Solving, obtain variableIn relevant position completion 0 and 1, obtain suboptimum vector of attack ax。

The susceptance of described unknown parameter branch road uses method of Lagrange multipliers and the augmented state estimation technique to calculate.

Described false data vector of attack Optimized model is used for the false data vector of attack that amount of calculation measuring point is corresponding.Should Model is l0-norm optimization problem, belongs to NP-hard problem, in order to improve computational efficiency, uses convex relaxing techniques, by this mould Type is converted into the l1-norm optimization problem of standard.

Preferably, alternating direction multiplier method (Alternating Direction Method of is used Multipliers, ADMM) solve false data vector of attack Optimized model.ADMM algorithm has separability and Fast Convergent Advantage, be suitable for process big data, drastically increase the solution efficiency of false data vector of attack.

Compared with prior art, the present invention has the following advantages and beneficial effect:

Solve assailant face the electric parameter of grasp exist error, even complete and metric data exist bad The problem of data so that false data is attacked more flexibly and effective.

Accompanying drawing explanation

Fig. 1 false data based on parameter estimation attack method flow chart.

Detailed description of the invention

Below with reference to specific embodiments and the drawings, the present invention is described further.

Fig. 1 is the false data attack method flow chart of parameter estimation, implements step as follows:

Step 1: calculate the susceptance of unknown parameter branch road according to method of Lagrange multipliers and the augmented state estimation technique；

The true value assuming branch parameters is p_t, error vector is p_e, then the measured value of branch parameters is shown below.

P=p_t+p_e

During Legacy Status is estimated, it is assumed that the error vector of branch parameters is 0, it is i.e. to have described in following formula to retrain.

p_e=0

This constraint is injected the constraints of weighted least-squares state estimation model under equality constraint as zero, obtain as Under described Optimized model.

$\begin{array}{cc}\min & J\left(x\right)=\frac{1}{2}{r}^{T}Wr\end{array}$

s.t.c(x,p_e)=0

p_e=0

In formula, r=z-h (x, p_e) represent measuring value residual error, h (x, p_e) represent and state variable x and branch parameters error p_eRelevant nonlinear function, c (x, p_e) represent the injecting power of the bus not only not had load but also do not have electromotor.

To above-mentioned Optimized model application method of Lagrange multipliers, obtain Lagrangian as follows, adopt further The susceptance of unknown parameter branch road is calculated by method of Lagrange multipliers and the augmented state estimation technique.

$L=\frac{1}{2}{r}^{T}Wr-{\mathrm{\μ}}^{T}c(x,p_e)-{\mathrm{\λ}}^T{p}_e$

Step 2: calculate Jacobian matrix H according to following formula_x；

In formula, h (x, p_e) represent and state variable x and branch parameters error p_eRelevant nonlinear function, P_ijRepresent and prop up Road trend, P_iRepresent the injecting power of bus, θ_iRepresent the phase place of bus i, b_ijRepresent the susceptance of branch road ij, B_iiRepresent bus i Self-admittance.

Step 3: using the Optimized model of ADMM Algorithm for Solving false data vector of attack, this model is as follows, obtains VariableIn relevant position completion 0 and 1, obtain suboptimum vector of attack a_x；

In a power system with N bar bus, state variable is typically taken as the complex voltage of each bus, including electricity Pressure amplitude value and phase angle, remove outside reference mode, and a total of 2N-1 state variable, state variable is collectively expressed as x=[x₁, x₂,…,x_n]^T, n=2N-1.For a properly functioning power system, its busbar voltage is near rated voltage, and props up Two ends, road phase angle difference is the least, and for supertension network, branch resistance is more much smaller than reactance.Therefore, make the following assumptions, all mothers The voltage magnitude of line is equal and is 1, ignores line resistance, then there is not reactive power in measuring value, and state variable is only Voltage phase angle.Now, between measuring value and state variable, meet linear relationship, obtain the DC power flow equation being shown below.

Z=Hx+e e～N (0, Σ_e)

If with a=[a₁,a₂,…,a_m]^TRepresent disabled user injects in measuring value false data vector, then reality Measurement data is z_bad=z+a, c=[c₁,c₂,…,c_n]^TRepresent the mistake being infused in state variable introducing due to false data Difference vector, the state variable of estimation isFrom the angle of assailant, when building vector of attack a, it is desirable to use Minimum intrusion scene and cost achieve the goal, and therefore vector of attack a exists an optimal value.Nonzero element in vector of attack a The corresponding measuring point attacked, nonzero element number l₀Norm represents, the Optimized model of vector of attack is shown below.

$\begin{array}{cc}\underset{c}{\min }& \left|\right|a|{|}_0\end{array}$

S.t.a=Hc

In formula, | | a | |₀Represent the l of vector a₀Norm, l₀Norm is the least, and the degree of rarefication of vector of attack a is the highest.

Use convex relaxing techniques, above-mentioned Optimized model can be further converted to following formula.

$\begin{array}{cc}\underset{c}{\min }& \left|\right|a_{\stackrel{\‾}{P}k}|{|}_1\end{array}$

$\begin{array}{cc}s.t.& B_{\stackrel{\‾}{P}k}{a}_{\stackrel{\‾}{P}k}=-b_k\end{array}$

In formula, defining shielded measuring point numbering collection and be combined into P, unprotected measuring point collection is combined into||(·)||₁Table Show l1-norm,Represent from matrixIn remove b_kRear submatrix,Represent from vectorIn remove element a (k) after Vector.Use this model of ADMM Algorithm for Solving, obtain variableIn relevant position completion 0 and 1, obtain suboptimum vector of attack a_x。

Step 4: inject metric data z after false data_x=z+a_x。

Specific embodiment described herein is only to present invention spirit explanation for example.Technology neck belonging to the present invention Described specific embodiment can be made various amendment or supplements or use similar mode to replace by the technical staff in territory Generation, but without departing from the spirit of the present invention or surmount scope defined in appended claims.

Claims (3)

1. a modern power transmission network false data attack method based on parameter estimation, it is characterised in that comprise the following steps:

Step 1, calculate the susceptance of unknown parameter branch road according to method of Lagrange multipliers and the augmented state estimation technique；

Step 2, according to following formula calculate Jacobian matrix H_x；

In formula, h (x, p_e) represent and state variable x and branch parameters error p_eRelevant nonlinear function, P_ijRepresent branch road tide Stream, P_iRepresent the injecting power of bus, θ_iRepresent the phase place of bus i, b_ijRepresent the susceptance of branch road ij, B_iiRepresent bus i from Admittance；

Step 3, the Optimized model of employing ADMM Algorithm for Solving false data vector of attack, this model is as follows, obtains variableIn relevant position completion 0 and 1, obtain suboptimum vector of attack a_x；

$\begin{array}{cc}\underset{c}{\min }& \left|\right|a_{\stackrel{\‾}{P}k}|{|}_1\end{array}$

$\begin{array}{cc}s.t.& B_{\stackrel{\‾}{P}k}{a}_{\stackrel{\‾}{P}k}=-b_k\end{array}$

In formula, defining shielded measuring point numbering collection and be combined into P, unprotected measuring point collection is combined into(·)||₁Represent 11-model Number,Represent from matrixIn remove b_kRear submatrix,After representing matrix B removes the column vector corresponding with gathering P Submatrix, b_kKth row column vector in representing matrix B, wherein B=H (H^TH)^-1H^T-I, H represent observation Jacobian matrix,Table Show from vectorIn remove the vector after element a (k),With set in expression vector of attack aCorresponding element is constituted Vector, a (k) represents the kth element in vector a；

Metric data z after step 4, injection false data_x=z+a_x, z_x=z+a_x, z represents original vol during unimplanted false data Survey data.

A kind of modern power transmission network false data attack method based on parameter estimation the most according to claim 1, its feature It is: the detailed process of described step 1 is as follows；

The true value assuming branch parameters is p_t, error vector is p_e, then the measured value of branch parameters is shown below:

P=p_t+p_e

During Legacy Status is estimated, it is assumed that the error vector of branch parameters is 0, it is i.e. to have described in following formula to retrain；

p_e=0

This constraint is injected the constraints of weighted least-squares state estimation model under equality constraint as zero, obtains following institute State Optimized model:

$\begin{array}{cc}\min & J\left(x\right)=\frac{1}{2}{r}^{T}Wr\end{array}$

s.t.c(x,p_e)=0

p_e=0

In formula, W is for measuring weight diagonal matrix, r=z-h (x, p_e) represent measuring value residual error, h (x, p_e) represent and state change Amount x and branch parameters error p_eRelevant nonlinear function, c (x, p_e) represent the bus that not only do not had load but also do not have electromotor Injecting power；

To above-mentioned Optimized model application method of Lagrange multipliers, obtain Lagrangian as follows, use further and draw Ge Lang multiplier method and the augmented state estimation technique calculate the susceptance of unknown parameter branch road:

$L=\frac{1}{2}{r}^{T}Wr-{\mathrm{\μ}}^{T}c(x,p_e)-{\mathrm{\λ}}^T{p}_e.$

A kind of modern power transmission network false data attack method based on parameter estimation the most according to claim 2, its feature It is: the detailed process of described step 3 is as follows；

In a power system with N bar bus, including voltage magnitude and phase angle, remove outside reference mode, a total of 2N- 1 state variable, state variable is collectively expressed as x=[x₁,x₂,…,x_n]^T, n=2N-1；

Making the following assumptions, the voltage magnitude of all buses is equal and is 1, ignores line resistance, then do not exist in measuring value Reactive power, state variable only has voltage phase angle；Now, between measuring value and state variable, meet linear relationship, obtain as follows DC power flow equation shown in formula:

Z=Hx+e e～N (0, Σ_e)

If with a=[a₁,a₂,…,a_m]^TRepresent the false data vector that disabled user injects in measuring value, then actual measurement Data are z_bad=z+a, c=[c₁,c₂,…,c_n]^TRepresent due to false data be infused in state variable introduce error to Amount, the state variable of estimation isFrom the angle of assailant, when building vector of attack a, it is desirable to minimum Intrusion scene and cost achieve the goal, therefore vector of attack a exist an optimal value；In vector of attack a, nonzero element is corresponding The measuring point attacked, nonzero element number l₀Norm represents, the Optimized model of vector of attack is shown below:

$\begin{array}{cc}\underset{c}{\min }& \left|\right|a|{|}_0\end{array}$

S.t.a=Hc

In formula, | | a | |₀Represent the l of vector a₀Norm, l₀Norm is the least, and the degree of rarefication of vector of attack a is the highest；

Use convex relaxing techniques, above-mentioned Optimized model can be further converted to following formula:

$\begin{array}{cc}\underset{c}{\min }& \left|\right|a_{\stackrel{\‾}{P}k}|{|}_1\end{array}$

$\begin{array}{cc}s.t.& B_{\stackrel{\‾}{P}k}{a}_{\stackrel{\‾}{P}k}=-b_k\end{array}$

In formula, defining shielded measuring point numbering collection and be combined into P, unprotected measuring point collection is combined into(·)||₁Represent 11-model Number,Represent from matrixIn remove b_kRear submatrix,After representing matrix B removes the column vector corresponding with gathering P Submatrix, b_kKth row column vector in representing matrix B, wherein B=H (H^TH)^-1H^T-I, H represent observation Jacobian matrix,Table Show from vectorIn remove the vector after element a (k),With set in expression vector of attack aCorresponding element is constituted Vector, a (k) represents the kth element in vector a；Use this model of ADMM Algorithm for Solving, obtain variableIn relevant position Completion 0 and 1, obtains suboptimum vector of attack a_x。