CN106026089A - Transmission network false data attack defense method based on protection measurement point - Google Patents

Abstract

The invention discloses a modern transmission network false data attack defense method based on a protection measurement point in the field of information security research of a power system. The method provided by the invention comprises the steps that a false data attack vector optimization model is constructed based on a traditional power system state estimation theory; according to the optimization model, a false data attack defense measure based on indexes Vk and Rk is provided; the basic idea is to reduce the number of vulnerable nodes vulnerable to attacks in the power system and to enhance the overall ability to deal with false data attacks; and according to an importance index Ik, the defense measure is realized, namely the target of the optimization indexes Vk and Rk is realized by protecting a high measurement point of the importance index Ik. According to the invention, the important measurement point is protected to effectively improve the attack cost and the attack difficulty of an attacker.

Description

A kind of power transmission network false data attack defense method based on protective number measuring point

Technical field

The present invention relates to power system information security fields, be specifically related to a kind of power transmission network based on protective number measuring point false Data attack defence method.

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.

In order to defend false data to attack, currently mainly from designing more excellent inspection policies and arranging protective number measuring point two Aspect launches research.By designing more excellent inspection policies, such as self adaptation CUSUM check algorithm, nuclear norm minimize method (Nuclear Norm Minimization) and low-rank matrix decomposition method (Low Rank Matrix Factorization), False data can be directly detected, it is not necessary to extra hardware puts into, and however it is necessary that and again develops software from metric data, Development risk is higher, the cycle is longer, and is likely to occur the attack pattern for new inspection policies.And by arranging protective number Measuring point, such as protection protect basic measuring point (Basic Measurements) and protection key stato variable, can be effectively Improve intrusion scene, increase and attack difficulty, it might even be possible to defence false data completely is attacked, although facing asking of hardware cost Topic, but there is the advantage that the construction cycle is shorter and development risk is little.Therefore, the most more efficiently defensive measure is to arrange Protective number measuring point.

Summary of the invention

The present invention is directed to the deficiencies in the prior art, it is provided that a kind of power transmission network false data based on protective number measuring point is attacked Defence method.The present invention proposes index V_kWith index R_k, resist from the local of power system and overall measurement power system respectively The ability that false data is attacked, by optimizing index V_kWith index R_kRealize the protection of significant quantity measuring point, reach to defend false data The purpose attacked.This invention can effectively strengthen the ability that power system defence false data is attacked.

The concrete technical scheme of the present invention is:

Step 1: attack all of measuring point in power system successively, obtain according to false data vector of attack Optimized model The vector of attack that all measuring points are corresponding, calculates index V of power system_kIf attacking index V under difficulty β meaning_k=0, Perform step 3, otherwise perform step 2；Wherein, index V_kFragile number of nodes is characterized from the angle of power system local；

Step 2: calculate and attack the importance degree index being subject to the fragile node that false data is attacked under difficulty β meaning I_k, then protection importance degree index I_kMaximum measuring point；If importance degree index I of maximum_kCorresponding multiple measuring points, the most at random A measuring point is selected to implement protection；Perform step 1；

Step 3: attack all of measuring point in power system successively, obtain the vector of attack that all measuring points are corresponding, meter Calculate index R of power system_kIf, indexThen algorithm terminates, and otherwise performs step 4；Wherein, index R_kFrom entirety Angle weigh power system defence false data attack ability,Represent index R_kThreshold value；

Step 4: calculate importance degree index I of all measuring points_k, then protection importance degree index I_kMaximum measuring point；If Maximum importance degree index I_kCorresponding multiple measuring points, then randomly choose a measuring point and implement protection；Perform step 3.

Described false data vector of attack Optimized model, index V_k, index R_kWith index I_kAs follows；

$\underset{c}{min}\left|\right|a_{\stackrel{\‾}{P}k}|{|}_1$

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

$V_k=\underset{k=1,2,...,m}{\&Sigma;}I\left(\right|\left|a_k^{*}\right|{|}_0<\mathrm{\&beta;})$

$R_k=\frac{\underset{k=1,2,...,m}{\&Sigma;}\left|\right|a_k^{*}|{|}_0}{m-t}$

$I_k=\underset{i=1,2,...,m}{\&Sigma;}I(k\&Element;A_i^{*})$

In formula, defining shielded measuring point numbering collection and be combined into P, unprotected measuring point collection is combined into||(·)||₀With | |(·)||₁Representing l0-norm and l1-norm respectively, k represents that measuring point is numbered,Represent from vectorIn remove element a Vector after (k), a (k) represents the kth element in vector of attack a,Represent from matrixIn remove b_kAfter sub-square Battle array, b_kKth row column vector in representing matrix B,Represent when attacking kth measuring value corresponding optimum false data attack to Amount, β represents attack difficulty, and m represents measuring point quantity, and t represents the measuring point quantity that there is not suboptimum vector of attack,Represent secondary In excellent vector of attackThe set that the numbering that middle nonzero element is corresponding is constituted, I () represents indicator function, it is assumed that S represents variable x Meet set, I () is shown below:

$I\left(x\right)=\left\{\begin{array}{cc}1& ifx\&Element;S\\ 0& ifx\&NotElement;S\end{array}\right..$

Described step 1 and 2 Main Function be to eliminate in power system to be subject to the fragile node that false data is attacked, The Main Function of step 3 and step 4 is an up power system entirety and resists the ability that false data is attacked.

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.

Described index V_kFragile number of nodes is characterized from the angle of power system local.If index V_k≠ 0, show electricity Existing in Force system to attack and be subject to the node that false data is attacked under difficulty β meaning, assailant can be fragile by these Node success offensive attack.Index V_kThe biggest, the node being subject to false data attack in power system is the most, is i.e. crisp Weak bus is the most, otherwise, if index V_kThe least, the node being subject to false data attack in power system is the fewest, is i.e. Fragile node is the fewest.

Described index R_kThe ability that power system defence false data is attacked, index R has been weighed from overall angle_kMore Greatly, the whole capability that now defence false data is attacked is the strongest.

Described importance degree index I_kFor weighing the significance level of measuring point in power system, importance degree index I_kIt is the biggest, Showing that the number of times that measuring point k occurs in the suboptimum vector of attack that power system is corresponding is the most, this measuring point is the most important.

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

1. propose index V_kWith index R_k, resist falseness from the local of power system and overall measurement power system respectively The ability of Data attack, can assess the ability that power system reply false data is attacked more reasonably and comprehensively.

2. propose by importance degree index I_kOptimizing index V_kWith index R_kFind protective number test points set, be greatly enhanced Computational efficiency.

3. propose a kind of power transmission network false data attack defense method based on protective number measuring point, by optimizing index V_k With index R_kRealize the protection of significant quantity measuring point, reach the purpose defending false data to attack, can be effectively increased assailant's Intrusion scene and attack difficulty.

Accompanying drawing explanation

Fig. 1 present invention is based on index V_kWith index R_kFalse data attack defense 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 based on index V_kWith index R_kFalse data attack defense method flow chart, implement step as follows:

Step 1: attack all of measuring point in power system successively, obtain according to false data vector of attack Optimized model The vector of attack that all measuring points are corresponding, calculates index V of power system_kIf attacking index V under difficulty β meaning_k=0, Perform step 3, otherwise perform step 2.

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, ∑_e)

In formula, H represents observation Jacobian matrix, e=[e₁,e₂,…,e_m]^TRepresent measurement error, and obey average and be 0, variance is diagonal matrixNormal distribution.

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.

$\underset{c}{min}\left|\right|a|{|}_0$

S.t.a=Hc

In formula, defining shielded measuring point numbering collection and be combined into P, unprotected measuring point collection is combined into||(·)||₀With | |(·)||₁Represent l0-norm and l1-norm, | | a | | respectively₀Represent the l of vector a₀Norm, l₀Norm is the least, vector of attack a Degree of rarefication the highest.

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

$\underset{c}{min}\left|\right|a_{\stackrel{\&OverBar;}{P}k}|{|}_1$

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

In formula,Represent from matrixIn remove b_kRear submatrix,Representing matrix B removes with to gather P corresponding Submatrix after column vector, wherein B=H (H^TH)-¹H^T-I, H represent observation Jacobian matrix,Represent from vectorIn remove Vector after element a (k),With set in expression vector of attack aThe vector that corresponding element is constituted.Use ADMM algorithm Solve this model, obtain false data vector of attack.

Attack m measuring point in power system, the suboptimum vector of attack l obtained successively₀There is a minima in norm, This value can represent the minimum cost attacked required for power system, is defined as follows index α shown in formula_k, this index expression kth The vector of attack l that individual measuring point is corresponding₀Norm minimum.

${\mathrm{\&alpha;}}_k=\underset{k=1,2,...,m}{min}\left|\right|a_k^{*}|{|}_0$

Assuming that difficulty is attacked in the power system that manager is arranged is β, is i.e. α_k>=β, now to successfully start false number According to attack, the l of suboptimum vector of attack₀Norm is more than β.

Index V_kShown in being defined as follows.

$V_k=\underset{k=1,2,...,m}{\&Sigma;}I\left(\right|\left|a_k^{*}\right|{|}_0<\mathrm{\&beta;})$

In formula,Representing optimum false data vector of attack corresponding when attacking kth measuring value, β represents attack difficulty, M represents measuring point quantity, and k represents that measuring point is numbered.

Step 2: calculate and attack the importance degree index being subject to the fragile node that false data is attacked under difficulty β meaning I_k, then protection importance degree index I_kMaximum measuring point.If importance degree index I of maximum_kCorresponding multiple measuring points, the most at random A measuring point is selected to implement protection.Perform step 1.

Importance degree index I_kShown in being defined as follows.

$I_k=\underset{i=1,2,...,m}{\&Sigma;}I(k\&Element;A_i^{*})$

In formula, k represents that measuring point is numbered, and m represents measuring point quantity,Represent in suboptimum vector of attackMiddle nonzero element The set that corresponding numbering is constituted, I () represents indicator function, it is assumed that S represents the set met of variable x, I () such as following formula Shown in.

$I\left(x\right)=\left\{\begin{array}{cc}1& ifx\&Element;s\\ 0& ifx\&NotElement;S\end{array}\right.$

Step 3: attack all of measuring point in power system successively, obtain the vector of attack that all measuring points are corresponding, meter Calculate index R of power system_kIf, indexThen algorithm terminates, and otherwise performs step 4.

Index R_kShown in being defined as follows.

$R_k=\frac{\underset{k=1,2,...,m}{\&Sigma;}\left|\right|a_k^{*}|{|}_0}{m-t}$

In formula,Representing optimum false data vector of attack corresponding when attacking kth measuring value, k represents that measuring point is compiled Number, m represents measuring point quantity, and t represents the measuring point quantity that there is not suboptimum vector of attack.

Step 4: calculate importance degree index I of all measuring points_k, then protection importance degree index I_kMaximum measuring point.If Maximum importance degree index I_kCorresponding multiple measuring points, then randomly choose a measuring point and implement protection.Perform step 3.

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 (2)

1. a power transmission network false data attack defense method based on protective number measuring point, it is characterised in that comprise the following steps:

Step 1: attack all of measuring point in power system successively, according to false data vector of attack Optimized model, uses and hands over Obtain, for direction multiplier method, the vector of attack that all measuring points are corresponding, calculate index V of power system_kIf attacking difficulty β meaning Index V under Yi_k=0, perform step 3, otherwise perform step 2；Wherein, index V_kCharacterize crisp from the angle of power system local Weak bus quantity；

Step 2: calculate and attack importance degree index I being subject to the fragile node that false data is attacked under difficulty β meaning_k, then Protection importance degree index I_kMaximum measuring point；If importance degree index I of maximum_kCorresponding multiple measuring points, then randomly choose one Measuring point implements protection；Perform step 1；

Step 3: attack all of measuring point in power system successively, obtain the vector of attack that all measuring points are corresponding, calculate electricity Index R of Force system_kIf, indexThen algorithm terminates, and otherwise performs step 4；Wherein, index R_kFrom overall angle Degree has weighed the ability that power system defence false data is attacked,Represent index R_kThreshold value；

Step 4: calculate importance degree index I of all measuring points_k, then protection importance degree index I_kMaximum measuring point；If it is maximum Importance degree index I_kCorresponding multiple measuring points, then randomly choose a measuring point and implement protection, perform step 3.

A kind of power transmission network false data attack defense method based on protective number measuring point the most according to claim 1, it is special Levy and be: described false data vector of attack Optimized model, index V_k, index R_kWith index I_kAs follows；

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

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

$V_k=\underset{k=1,2,...,m}{\&Sigma;}I\left(\right|\left|a_k^{*}\right|{|}_0<\mathrm{\&beta;})$

$R_k=\frac{\underset{k=1,2,...,m}{\&Sigma;}\left|\right|a_k^{*}|{|}_0}{m-t}$

$I_k=\underset{i=1,2,...,m}{\&Sigma;}I(k\&Element;A_i^{*})$

In formula, defining shielded measuring point numbering collection and be combined into P, unprotected measuring point collection is combined into||(·)||₀With | | (·)||₁Representing l0-norm and l1-norm respectively, k represents that measuring point is numbered,Represent from vectorIn remove element a (k) Vector afterwards, a (k) represents the kth element in vector of attack a,Represent from matrixIn remove b_kRear submatrix, b_k Kth row column vector in representing matrix B, wherein B=H (H^TH)-¹H^T-I, H represent observation Jacobian matrix,Represent and attack kth Optimum false data vector of attack corresponding during individual measuring value, β represents attack difficulty, and m represents measuring point quantity, and t represents and do not deposits In the measuring point quantity of suboptimum vector of attack,Represent in suboptimum vector of attackThe collection that the numbering that middle nonzero element is corresponding is constituted Closing, I () represents indicator function, it is assumed that S represents the set met of variable x, and I () is shown below:

$I\left(x\right)=\left\{\begin{array}{ccc}1& if& x\&Element;S\\ 0& if& x\&NotElement;S\end{array}\right..$