CN112398117A - A False Data Injection Attack Structure and Defense Method Causes Line Load Overload - Google Patents

A False Data Injection Attack Structure and Defense Method Causes Line Load Overload Download PDF

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CN112398117A
CN112398117A CN202011019560.3A CN202011019560A CN112398117A CN 112398117 A CN112398117 A CN 112398117A CN 202011019560 A CN202011019560 A CN 202011019560A CN 112398117 A CN112398117 A CN 112398117A
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line
overload
load
attack
power
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CN112398117B (en
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李舟军
杨立群
刘连忠
翟优
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Beihang University
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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
    • 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
    • H02J3/008—Circuit arrangements for AC mains or AC distribution networks involving trading of energy or energy transmission rights
    • 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
    • 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
    • H02J3/38—Arrangements for parallely feeding a single network by two or more generators, converters or transformers
    • H02J3/46—Controlling of the sharing of output between the generators, converters, or transformers
    • H02J3/466—Scheduling the operation of the generators, e.g. connecting or disconnecting generators to meet a given demand
    • 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
    • H02J2203/10—Power transmission or distribution systems management focussing at grid-level, e.g. load flow analysis, node profile computation, meshed network optimisation, active network management or spinning reserve management
    • 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]
    • Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
    • Y04—INFORMATION OR COMMUNICATION TECHNOLOGIES HAVING AN IMPACT ON OTHER TECHNOLOGY AREAS
    • Y04S—SYSTEMS INTEGRATING TECHNOLOGIES RELATED TO POWER NETWORK OPERATION, COMMUNICATION OR INFORMATION TECHNOLOGIES FOR IMPROVING THE ELECTRICAL POWER GENERATION, TRANSMISSION, DISTRIBUTION, MANAGEMENT OR USAGE, i.e. SMART GRIDS
    • Y04S40/00—Systems for electrical power generation, transmission, distribution or end-user application management characterised by the use of communication or information technologies, or communication or information technology specific aspects supporting them
    • Y04S40/20—Information technology specific aspects, e.g. CAD, simulation, modelling, system security

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Abstract

本发明公开了电网信息安全领域中一种引起线路负荷过载的虚假数据注入攻击构造及防御方法。本发明首先基于交流状态估计构建虚假数据注入攻击模型，加入线路有功超限约束实现线路负荷过载，将攻击模型的目标函数转化为L1范数并采用梯度投影法(Gradient Projection Method，GPM)求解该优化模型；为防止线路过载导致电力系统奔溃，提出一种快速准确的重新发电方法加以防御，该方法中避免了对敏感度矩阵和拉格朗日函数的计算，在保证充足发电量的前提下缩短了计算时间开销。本发明提高了构建新型电网虚假数据注入攻击的可行性，同时提高了抵抗攻击的有效性和速度，验证了电力系统应对虚假数据注入攻击的能力。

Figure 202011019560

The invention discloses a false data injection attack structure and a defense method which cause overload of line load in the field of power grid information security. The present invention firstly constructs a fake data injection attack model based on the estimation of the AC state, adds the line active power over-limit constraint to realize the line load overload, converts the target function of the attack model into the L1 norm, and uses the Gradient Projection Method (GPM) to solve the problem. optimization model; in order to prevent the power system from crashing due to line overload, a fast and accurate regenerating method is proposed for defense, which avoids the calculation of the sensitivity matrix and Lagrangian function, and ensures sufficient power generation This reduces the computational time overhead. The invention improves the feasibility of constructing a new type of power grid false data injection attack, simultaneously improves the effectiveness and speed of resisting the attack, and verifies the ability of the power system to deal with the false data injection attack.

Figure 202011019560

Description

False data injection attack construction and defense method causing line load overload
Technical Field
The invention relates to the technical field of smart grid security, in particular to the field of false data injection attack construction and defense methods of a power grid, and provides a false data injection attack construction method capable of causing line load overload and a method for defending the attack.
Background
In order to improve the operating efficiency and reliability of the power system, the modern power grid is highly integrated with information technology and is converted into a smart power grid, which brings huge network security challenges to the power system. As an important application in the power system, the state estimation depends on Data interaction between a Supervisory Control and Data Acquisition (SCADA) system and a smart meter, so that the state estimation becomes a target of network attack. The false data injection attack interferes the state estimation result through manipulating the measured data, further causes the control center to issue wrong operation, influences the safe operation of the whole power system from the physical and economic aspects, achieves the purposes of changing the operation state of the power system, interfering the pricing of the power market, stealing the electric quantity of a terminal user and finally influences the scheduling of the power system. Unlike other attacks, the purpose of hiding the attack can be achieved by avoiding Bad Data Detection (BDD), and in addition, the attack of injecting the false Data can also destroy the power system for different purposes, and if an attacker intentionally causes overload on a line load through the attack of injecting the false Data, regional power failure is likely to be caused. Therefore, the method for providing the false data injection attack capable of causing the overload of the line load and the defense method for the attack have important significance for guaranteeing the safe and stable operation of the power system.
Considering the attack cost and the protection limit of the power system, an attacker hardly invades all meters to cause the sparsity of the attack vector. However, an attacker can invade the control center of the power system to steal the measurement data collected by the SCADA, and based on the measurement data, the attacker can add constraints such as bypass bad data detection, power flow balance and line load overload to realize false data injection attack under the condition of ensuring the goal of the least invasive instrument. For system protectors, replacing vulnerable meters such as PMU protection measurement data may be effective against the attack, but deploying a large number of hardware devices results in a significant cost increase. Therefore, from the essence of system operation, it is more realistic and effective to defend against such false data injection attacks by updating the system state quantity and modifying the system power generation strategy.
Disclosure of Invention
The invention provides a construction and defense method for false data injection attack capable of causing line load overload, aiming at overcoming the singleness of the existing false data injection attack model and embodying the purpose of novel false data injection attack. The invention adopts norm expression to establish the target function of the attack model, and establishes the attack model by adding constraint. Aiming at the attack, the invention provides a line load overload reduction method to defend the attack by updating the power generation strategy and the system state quantity of the power system.
The specific technical scheme of the invention is as follows:
step 1: acquiring the measurement and the state quantity of a power system, and calculating the conductance and the susceptance of a line between nodes according to the nonlinear relation between the measurement and the state quantity;
step 2: considering the limited attack capability of an attacker, the attack vector has sparsity, and a target function of an attack model is established by adopting norm operation;
and step 3: adding constraints to an attack objective function to generate an attack model, wherein the constraints can be satisfied by that the constructed attack can bypass Bad Data Detection (BDD) Detection and a power flow balance equation in state estimation and can cause line overload, solving the attack model by using a Gradient Projection Method (GPM) to generate an attack vector a, and measuring the injection quantity of the attack vector to generate a false quantity;
and 4, step 4: and calculating the power flow of the power system by using the false quantity measurement, and solving initial values of the voltage amplitude and the voltage phase angle. Calculating a power generation transfer distribution factor and storing the value of the power generation transfer distribution factor; (ii) a
And 5: initializing iteration times, judging whether a line with overload exists or not, and executing a subsequent method according to a judgment condition;
step 6: calculating an overload load matrix H on an overload line, and calculating a power generation cost C for reducing the overload load; appointing a power generation node and a variable and calculating a transfer distribution factor matrix A;
and 7: calculating a power generation plan variation delta U according to the overload load matrix H and the transfer factor matrix A, finding out a new overload circuit based on the variation, and executing the step 8 if no new overload circuit exists; otherwise, reducing the delta U according to the coefficient gamma and repeating the steps until no new overload circuit is generated;
and 8: power generation plan variation delta U for updating generator to reduce line overloadkCalculating the state variable variation amount Deltaxk(ii) a Updating planned power generation amount Uk+1And the state quantity xk+1；
Setting the convergence criterion of the method, judging whether the method is converged, and if so, stopping the method; otherwise, updating the iteration times and returning to the step 5;
the specific process of the step 1 is as follows:
the conductance G between nodes i and j is calculated from the following nonlinear relationship between the quantity measurements (node injected power and line power flow) and the state quantities (voltage magnitude and phase angle)ijAnd susceptance Bij：
Figure BDA0002698384810000031
Figure BDA0002698384810000032
pij＝-Vi 2Gij+ViVj(Gijcos(qij)+Bijsin(qij))
qij＝Vi 2Bij+ViVj(Gijsin(qij)-Bijcos(qij))
In the formula PiAnd QiFor active and reactive injected power, p, at node iijAnd q isijFor active and reactive power flows on the line, ViIs the magnitude of the voltage at node i, qijIs the phase angle difference between node i and node j;
the specific process of the step 2 is as follows:
considering the limited attack capability of an attacker, setting an injected attack vector as a, and setting an objective function of the following attack model by adopting norm calculation:
Figure BDA0002698384810000033
in the formula Pa,Qa,pa,qaThe active power and the reactive power of the nodes and the active power and the reactive power flow of the branch circuits are injected in the vector measurement; | | non-woven hair0Is the norm of L0;
the specific process of the step 3 is as follows:
step 301: adding constraint conditions to the attack objective function to construct an attack model, wherein the constraint conditions are required to ensure that the attack can be detected through bad data, a power flow balance equation and overload of a certain line:
Objective
Figure BDA0002698384810000034
s.t.za＝z+a，amin<a<amax
Figure BDA0002698384810000035
Figure BDA0002698384810000036
Figure BDA0002698384810000041
Figure BDA0002698384810000042
Figure BDA0002698384810000043
in the formula
Figure BDA0002698384810000044
And
Figure BDA0002698384810000045
for measuring active and reactive power, P, of the line in the processi *And
Figure BDA0002698384810000046
the active and reactive injected power of the node in the measurement are measured,
Figure BDA0002698384810000047
for the phase angle q of the voltage after attackiAnd q isjThe difference between the difference of the two phases,
Figure BDA0002698384810000048
the maximum load power allowed for the line. Defining an attack vector
Figure BDA0002698384810000049
The node connecting line is L, and the line set is L;
step 302: and (3) converting the objective function into an L1 norm by adopting a convex relaxation technology, and solving the following new attack model by using a gradient projection method:
Objective
Figure BDA00026983848100000410
s.t.za＝z+a，amin<a<amax
Figure BDA00026983848100000411
Figure BDA00026983848100000412
Figure BDA00026983848100000413
Figure BDA00026983848100000414
Figure BDA00026983848100000415
step 303: measuring the injection quantity of the attack vector generated after solving the attack model to generate a false quantity measurement;
the specific process of the step 4 is as follows:
specifying a power generation load and a line load, and calculating a voltage phase angle and an amplitude value and a power generation power transfer distribution factor according to the following formula:
Figure BDA00026983848100000416
Figure BDA00026983848100000417
pij＝-Vi 2Gij+ViVj(Gijcos(qi-qj)+Bijsin(qi-qj))
qij＝Vi 2Bij+ViVj(Gijsin(qi-qj)-Bijcos(qi-qj))
Figure BDA0002698384810000051
in the formula PGi，PDi，QGi，QDiRespectively outputting active power and reactive power q for the generator at node iiIs the phase angle of the voltage at node i,
Figure BDA0002698384810000052
causing a power change value, S, of the line L for node kLkTransferring distribution factors for the generated power;
the specific process of the step 5 is as follows:
initializing the iteration number k to 1, judging whether a line with overload load exists, and if no line with overload load exists, executing the step 9; otherwise, executing step 6;
the specific process of the step 6 is as follows:
step 601: defining an overloaded line set OL, and calculating the overload capacity h on the line L by using the following formulaL：
Figure BDA0002698384810000053
In the formula hLFor the load overload on line L, NG is the set of power generation nodes, Δ PGkGenerating a variable quantity for the kth generator to reduce overload on the line L;
step 602: the required power generation cost C to reduce the overload load is calculated using the following formula:
Figure BDA0002698384810000054
in the formula pijAnd
Figure BDA0002698384810000055
the actual load and the bearable maximum load of the line between the nodes i and j are obtained;
step 603: the transfer distribution factor matrix a is calculated using the following formula:
H＝AΔPG＝AΔU
where H is the load overload H on line LLConstituent overload matrix, Δ PGThe power generation plan variation of the generator for reducing the line overload is determined as delta U;
the specific process of the step 7 is as follows:
step 701: calculating the planned power generation variation delta U of the generator for reducing line overload by using the following pseudo-inverse technology:
ΔU＝(ATA)-1ATH＝DH，D＝(ATA)-1AT
step 702: substituting the delta U into the step 603 to recalculate the transfer distribution factor matrix and check the overload load component h in the matrixLJudging whether a newly added overload circuit exists or not, if not, executing the step 8, otherwise, updating the delta U according to the following formula and repeating the step until no new overload circuit is generated:
ΔU＝γΔU
the specific process of the step 8 is as follows:
step 801: updating delta Uk←γΔUkDefinition of Y ═ B-1Wherein S is Y.DELTA.U, wherein B isij＝ViVjBij，βk＝ViVj，BkFor susceptance of line k, t ═ β is definedkBk/(1-βkBk yk)，yk＝yii+yjj-2yij；
Assume that all node voltages are 1p.u. The state variable change amount Δ x is calculated using the following formulak：
Δxq＝Δqq＝tqk(yqi-yqj)+Sq+t(Si-Sj)(yqi-yqj)
Step 802: updating the state quantity xk+1＝xk+ Δ x, and planned amount of power generation Uk+1＝Uk+ΔUk；
The specific process of the step 9 is as follows:
judging whether the method is converged according to the following formula, if so, converging and stopping; otherwise, setting k to k +1 and returning to the step 5:
|C(xk+1,Uk+1)|≤ε
where C (x, U) is a cost function for reducing branch overload and ε is a sufficiently small positive number, usually set to 10-3。xk+1And Uk+1The state quantity and the planned power generation quantity after the (k + 1) th iteration are obtained.
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In order to clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the following description of the embodiments or the prior art will be briefly introduced by using the accompanying drawings, which are only used for illustration and are not to be construed as limiting the patent;
FIG. 1 is a schematic flow chart of the method of the present invention, which comprises the following steps:
step 1: the conductance G between nodes i and j is calculated from the following nonlinear relationship between the measured quantities (node injected active and reactive power P, Q, and line active and reactive power flows p, q) and the state quantities (voltage magnitude V and phase angle q)ijAnd susceptance Bij：
Figure BDA0002698384810000061
Figure BDA0002698384810000071
pij＝-Vi 2Gij+ViVj(Gijcos(qij)+Bijsin(qij))
qij＝Vi 2Bij+ViVj(Gijsin(qij)-Bijcos(qij))
In the formula PiAnd QiFor active and reactive injected power, p, at node iijAnd q isijFor active and reactive power flows on the line, ViIs the magnitude of the voltage at node i, qijIs the phase angle difference between node i and node j;
step 2: because the attack capability of an attacker is limited, an injected attack vector is set as a, and an L0 norm of the vector is used for representing the attack sparsity to set an objective function of an attack model:
Figure BDA0002698384810000072
in the formula Pa,Qa,pa,qaThe active power and the reactive power of the nodes and the active power and the reactive power flow of the branch circuits are injected in the vector measurement;
and step 3: for the purpose of realizing hidden attack, the proposed attack should satisfy a power flow balance equation and cause overload of a certain line through bad data detection, so that an attack model after adding a constraint condition can be expressed as follows:
Objective
Figure BDA0002698384810000073
s.t.za＝z+a，amin<a<amax
Figure BDA0002698384810000074
Figure BDA0002698384810000075
Figure BDA0002698384810000076
Figure BDA0002698384810000077
Figure BDA0002698384810000078
in the formula
Figure BDA0002698384810000079
And
Figure BDA00026983848100000710
for measuring the active and reactive power flow, P, of a line in a measurementi *And
Figure BDA00026983848100000711
the active and reactive injected power of the node in the measurement are measured,
Figure BDA00026983848100000712
for the phase angle q of the voltage after attackiAnd q isjThe difference between the difference of the two phases,
Figure BDA00026983848100000713
the maximum active power allowed for the line. Defining an attack vector
Figure BDA00026983848100000714
The node connecting line is L, and the line set is L;
and (3) converting the objective function into an L1 norm by adopting a convex relaxation technology, and solving the following new attack model by using a gradient projection method:
Objective
Figure BDA0002698384810000081
s.t.za＝z+a，amin<a<amax
Figure BDA0002698384810000082
Figure BDA0002698384810000083
Figure BDA0002698384810000084
Figure BDA0002698384810000085
Figure BDA0002698384810000086
solving the attack model, and generating a false quantity measurement in the injection quantity measurement of the attack vector obtained by the solution;
and 4, step 4: specifying a power generation load and a line load, and calculating a voltage phase angle and an amplitude value and a power generation power transfer distribution factor according to the following formula:
Figure BDA0002698384810000087
Figure BDA0002698384810000088
pij＝-Vi 2Gij+ViVj(Gijcos(qi-qj)+Bijsin(qi-qj))
qij＝Vi 2Bij+ViVj(Gijsin(qi-qj)-Bijcos(qi-qj))
Figure BDA0002698384810000089
in the formula PGi，PDi，QGi，QDiRespectively outputting active power and reactive power q for the generator at node iiIs the phase angle of the voltage at node i,
Figure BDA00026983848100000810
causing a power change value, S, of the line L for node kLkTransferring distribution factors for the generated power;
and 5: initializing the iteration number k to 1, judging whether a line with overload load exists, and if no line with overload load exists, executing the step 9; otherwise, executing step 6;
step 6: defining an overloaded line set OL, and calculating the overload capacity h on the line L by using the following formulaL：
Figure BDA0002698384810000091
In the formula hLFor the load overload on line L, NG is the set of power generation nodes, Δ PGkGenerating a variable quantity for the kth generator to reduce overload on the line L;
the required power generation cost C to reduce the overload load is calculated using the following formula:
Figure BDA0002698384810000092
in the formula pijAnd
Figure BDA0002698384810000093
the actual load and the bearable maximum load of the line between the nodes i and j are obtained;
the transfer distribution factor matrix a is calculated using the following formula:
H＝AΔPG＝AΔU
where H is the load overload H on line LLConstituent overload matrix, Δ PGThe power generation plan variation of the generator for reducing the line overload is determined as delta U;
and 7: calculating the planned power generation variation delta U of the generator for reducing line overload by using the following pseudo-inverse technology:
ΔU＝(ATA)-1ATH＝DH，D＝(ATA)-1AT
substituting the delta U into the step 6 to recalculate the transfer distribution factor matrix and check the overload load component h in the matrixLJudging whether there is new overload circuit, if there is no new overload circuit, executing step 8, otherwise updating delta U according to following formula and repeating said step until there is no new overload circuitRaw:
ΔU＝γΔU
and 8: updating delta Uk←γΔUkDefinition of Y ═ B-1Wherein S is Y.DELTA.U, wherein B isij＝ViVjBij，βk＝ViVj，BkFor susceptance of line k, t ═ β is definedkBk/(1-βkBk yk)，yk＝yii+yjj-2yij；
Assuming that all the node voltages have amplitudes of 1p.u., the state variable variation Δ x is calculated using the following formulak：
Δxq＝Δqq＝tqk(yqi-yqj)+Sq+t(Si-Sj)(yqi-yqj)
Wherein the subscript q denotes the qth element of the qth column or vector of the first matrix;
the state quantity and the planned power generation quantity are updated by adopting the following formula:
xk+1＝xk+Δx
Uk+1＝Uk+ΔUk
and step 9: judging whether the method is converged according to the following formula, if so, converging and stopping; otherwise, setting k to k +1 and returning to the step 5:
|C(xk+1,Uk+1)|≤ε
where C (x, U) is a cost function for reducing branch overload and ε is a sufficiently small positive number, usually set to 10-3。xk+1And Uk+1The state quantity and the planned power generation quantity after the (k + 1) th iteration are obtained.

Claims (10)

1.一种引起线路负荷过载的虚假数据注入攻击构造及防御方法，其特征在于，包括如下步骤：1. a false data injection attack structure and a defense method that cause line load overload, is characterized in that, comprises the steps: 步骤1：获取电力系统量测量(节点注入功率、线路功率潮流)和状态量(电压幅值、电压相角)，根据量测量和状态量间的非线性关系计算出节点间线路的电导和电纳；Step 1: Obtain the power system quantity measurement (node injection power, line power flow) and state quantity (voltage amplitude, voltage phase angle), and calculate the conductance and electricity of the line between nodes according to the nonlinear relationship between the quantity measurement and the state quantity. accept; 步骤2：考虑攻击者有限的攻击能力建立攻击模型的目标函数；Step 2: Consider the limited attack capability of the attacker to establish the objective function of the attack model; 步骤3：基于设定好的攻击目标函数，添加约束条件构建攻击模型，约束条件应满足攻击可以绕过状态估计中的坏数据检测(Bad Data Detection，BDD)环节，以及可导致某条线路过载；使用梯度投影法(GPM)求解攻击模型生成攻击向量a，将其注入量测量中生成虚假量测量；Step 3: Based on the set attack target function, add constraints to build an attack model. The constraints should satisfy that the attack can bypass the Bad Data Detection (BDD) link in the state estimation, and can cause a certain line to be overloaded. ;Use the gradient projection method (GPM) to solve the attack model to generate the attack vector a, and inject it into the volume measurement to generate a false volume measurement; 步骤4：使用虚假量测量计算电力系统潮流，求解电压幅值和电压相角的初始值。计算发电转移分布因子并存储其值；Step 4: Calculate the power flow using the spurious quantity measurement, and solve for the initial values of the voltage amplitude and voltage phase angle. Calculate the generation transfer distribution factor and store its value; 步骤5：初始化迭代次数，判断是否存在负荷过载的线路，并根据判断条件执行后续方法；Step 5: Initialize the number of iterations, determine whether there is an overloaded line, and execute subsequent methods according to the judgment conditions; 步骤6：计算过载线路上的过载负荷矩阵H，并计算消减过载负荷的发电成本C；指定发电节点及变量并计算转移分布因子矩阵A；Step 6: Calculate the overload load matrix H on the overloaded line, and calculate the power generation cost C for reducing the overload load; specify the power generation nodes and variables and calculate the transfer distribution factor matrix A; 步骤7：根据过载负荷矩阵H和转移因子矩阵A计算发电计划变化量ΔU，基于此变化量可找出新的过载线路，若无新的过载线路，执行步骤8；否则，按系数γ减小ΔU并重复此步骤至无新的过载线路产生；Step 7: Calculate the change amount ΔU of the power generation plan according to the overload load matrix H and the transfer factor matrix A. Based on this change amount, a new overload line can be found. If there is no new overload line, go to step 8; otherwise, decrease by the coefficient γ ΔU and repeat this step until no new overloaded lines are generated; 步骤8：更新发电机为消减线路过载的发电计划变化量ΔUk，计算状态变量变化量Δxk；更新发电计划量Uk+1和状态量xk+1；Step 8: Update the generator to reduce the line overload power generation plan change ΔU k , calculate the state variable change Δx k ; update the power generation plan amount U k+1 and the state variable x k+1 ; 步骤9：设置所提方法收敛准则，判断是否收敛，若收敛，所提方法停止；反之，更新迭代次数并返回步骤5。Step 9: Set the convergence criterion of the proposed method, and judge whether it converges. If it converges, the proposed method stops; otherwise, update the number of iterations and return to step 5. 2.根据权利要求1中所述的一种引起线路负荷过载的虚假数据注入攻击构造及防御方法，其特征在于，在步骤1中，使用如下公式计算节点i和j间的电导Gij和电纳Bij：2. according to a kind of false data injection attack structure and defense method that cause line load overload described in claim 1, it is characterized in that, in step 1, use following formula to calculate conductance G ij and electrical conductance between node i and j accept B ij :
Figure FDA0002698384800000021
Figure FDA0002698384800000021
 其中Pi和Qi为节点i上的有功和无功注入功率，pij和qij为线路上的有功和无功注入功率，Vi为节点i上的电压幅值，qij为节点i和节点j的相角差。where Pi and Qi are the active and reactive injected power at node i, p ij and q ij are the active and reactive injected power on the line, V i is the voltage amplitude at node i, and q ij is node i and the phase angle difference of node j. 3.根据权利要求1中所述的一种引起线路负荷过载的虚假数据注入攻击构造及防御方法，其特征在于，在步骤2中，考虑到攻击者有限的攻击能力，设注入的攻击向量为a，建立如下攻击目标函数：3. according to a kind of false data injection attack structure and defense method that cause line load overload described in claim 1, it is characterized in that, in step 2, in consideration of the limited attack capability of attacker, let the attack vector of injection be a, establish the following attack target function:
Figure FDA0002698384800000022
Figure FDA0002698384800000022
 其中Pa,Qa,pa,qa为向量测量中注入的节点有功、无功功率和支路的有功、无功潮流；||||0表示L0范数。Among them, P a , Q a , p a , q a are the node active and reactive power injected in the vector measurement and the active and reactive power flow of the branch; |||| 0 represents the L0 norm. 4.根据权利要求1中所述的一种引起线路负荷过载的虚假数据注入攻击构造及防御方法，其特征在于，在步骤3中，求解攻击模型的具体步骤如下：4. according to a kind of false data injection attack structure that causes line load overload described in claim 1 and defense method, it is characterized in that, in step 3, the concrete steps of solving attack model are as follows: 步骤301：为攻击模型的目标函数添加约束条件构建如下攻击模型，约束条件应保证攻击能通过坏数据检测及导致某条线路过载：Step 301: Add constraints to the objective function of the attack model to construct the following attack model. The constraints should ensure that the attack can pass bad data detection and cause a certain line to be overloaded:
Figure FDA0002698384800000023
Figure FDA0002698384800000023
 s.t. za＝z+a，amin<a<amax (4)st z a =z+a, a min <a<a max (4)
Figure FDA0002698384800000024
Figure FDA0002698384800000024
Figure FDA0002698384800000025
Figure FDA0002698384800000025
Figure FDA0002698384800000026
Figure FDA0002698384800000026
Figure FDA0002698384800000027
Figure FDA0002698384800000027
Figure FDA0002698384800000028
Figure FDA0002698384800000028
 定义攻击向量
Figure FDA0002698384800000031
节点相连的线路为l，线路集合为L；其中
Figure FDA0002698384800000032
和
Figure FDA0002698384800000033
为量测量中的线路有功和无功潮流，Pi *和
Figure FDA0002698384800000034
为量测量中的节点有功和无功注入功率，
Figure FDA0002698384800000035
为受攻击后电压相角qi和qj之差，
Figure FDA0002698384800000036
为线路允许的最大有功功率；Define attack vector
Figure FDA0002698384800000031
The line connected to the node is l, and the line set is L; where
Figure FDA0002698384800000032
and
Figure FDA0002698384800000033
For the line active and reactive power flows in the measurement, P i * and
Figure FDA0002698384800000034
Inject power for the active and reactive power of the nodes in the measurement,
Figure FDA0002698384800000035
is the difference between the voltage phase angles q i and q j after being attacked,
Figure FDA0002698384800000036
is the maximum active power allowed by the line; 步骤302：采用凸松弛技术将目标函数转化为L1范数，使用梯度投影法求解如下新的攻击模型：Step 302: Convert the objective function to L1 norm by using the convex relaxation technique, and use the gradient projection method to solve the following new attack model:
Figure FDA0002698384800000037
Figure FDA0002698384800000037
 s.t. (4),(5),(6),(7),(8),(9) (11)s.t. (4),(5),(6),(7),(8),(9) (11) 步骤303：将求解的攻击向量注入到量测量中，生成虚假量测量。Step 303: Inject the solved attack vector into the quantity measurement to generate a false quantity measurement. 5.根据权利要求1中所述的一种引起线路负荷过载的虚假数据注入攻击构造及防御方法，其特征在于，在步骤4中，指定发电负荷和线路负荷，根据下式计算电压相角及幅值，及发电功率转移分布因子：5. A kind of false data injection attack structure and defense method that cause overload of line load according to claim 1, it is characterized in that, in step 4, specify power generation load and line load, calculate voltage phase angle and Amplitude, and power generation power transfer distribution factor:
Figure FDA0002698384800000038
Figure FDA0002698384800000038
Figure FDA0002698384800000039
Figure FDA0002698384800000039
 其中PGi，PDi，QGi，QDi分别为节点i上的发电机输出有功、无功功率，qi为节点i上的电压相角，
Figure FDA00026983848000000310
为节点k引起线路L的功率变化值，SLk为发电功率转移分布因子。where P Gi , P Di , Q Gi , and Q Di are the active and reactive power output by the generator on node i , respectively, qi is the voltage phase angle on node i,
Figure FDA00026983848000000310
is the power variation value of line L caused by node k, and S Lk is the distribution factor of power generation power transfer. 6.根据权利要求1中所述的一种引起线路负荷过载的虚假数据注入攻击构造及防御方法，其特征在于，在步骤5中，初始化迭代次数k＝1，判断是否存在负荷过载的线路，若无过载线路，执行步骤9；反之，执行步骤6。6. A kind of false data injection attack structure and defense method that causes line load overload according to claim 1, it is characterized in that, in step 5, initialize iteration number k=1, judge whether there is a load overload line, If there is no overloaded line, go to step 9; otherwise, go to step 6. 7.根据权利要求1中所述的一种引起线路负荷过载的虚假数据注入攻击构造及防御方法，其特征在于，在步骤6中，计算过载线路上的过载负荷矩阵，消减过载负荷的所需发电成本及转移分布因子矩阵的具体步骤如下：7. A kind of false data injection attack structure and defense method that cause line load overload according to claim 1, is characterized in that, in step 6, calculates the overload load matrix on overloaded line, reduces the need of overload load The specific steps of generating cost and transfer distribution factor matrix are as follows: 步骤601：定义过载线路集合OL，使用如下公式计算线路L上的负荷过载量hL：Step 601: Define the overload line set OL, and use the following formula to calculate the load overload amount h L on the line L :
Figure FDA0002698384800000041
Figure FDA0002698384800000041
 其中hL为线路L上的负荷过载量，NG为发电节点集合，ΔPGk为第k个发电机发电变化量以消减线路L上的过载负荷；where h L is the load overload on line L, NG is the set of power generation nodes, and ΔP Gk is the change in power generation of the k-th generator to reduce the overload load on line L; 步骤602：使用如下公式计算消减过载负荷的所需发电成本C：Step 602: Use the following formula to calculate the required power generation cost C for reducing the overload load:
Figure FDA0002698384800000042
Figure FDA0002698384800000042
 其中pij和
Figure FDA0002698384800000043
为节点i，j间线路的实际负荷和可承受的最大负荷；where p ij and
Figure FDA0002698384800000043
is the actual load and the maximum bearable load of the line between nodes i and j; 步骤603：使用如下公式计算转移分布因子矩阵A：Step 603: Calculate the transfer distribution factor matrix A using the following formula: H＝AΔPG＝AΔU (16)H=AΔP G =AΔU (16) 其中H为线路L上的负荷过载量hL组成的过载负荷矩阵，ΔPG＝ΔU为发电机为消减线路过载的发电计划变化量。Among them, H is the overload load matrix composed of the load overload amount h L on the line L, and ΔP G =ΔU is the change amount of the power generation plan for the generator to reduce the overload of the line. 8.根据权利要求1中所述的一种引起线路负荷过载的虚假数据注入攻击构造及防御方法，其特征在于，在步骤7中，根据过载负荷矩阵H和转移因子矩阵A计算发电计划变化量ΔU找出新的过载线路，具体步骤如下：8. A false data injection attack structure and defense method for causing overload of line load according to claim 1, characterized in that, in step 7, according to the overload load matrix H and the transfer factor matrix A, the amount of change in the power generation plan is calculated ΔU finds out the new overloaded line, the specific steps are as follows: 步骤701：使用如下伪逆技术计算发电机为消减线路过载的发电计划变化量ΔU：Step 701: Use the following pseudo-inverse technique to calculate the power generation plan change ΔU of the generator to reduce line overload: ΔU＝(ATA)-1ATH＝DH，D＝(ATA)-1AT (17)ΔU=(A T A) -1 A T H=DH, D=(A T A) -1 A T (17) 步骤702：将ΔU代入步骤603重新计算转移分布因子矩阵，查看矩阵中负荷过载分量hL判断是否有新增的过载线路，若无新的过载线路执行步骤8，否则按如下公式更新ΔU并重复此步骤至无新的过载线路产生：Step 702: Substitute ΔU into step 603 to recalculate the transfer distribution factor matrix, check the load overload component h L in the matrix to determine whether there is a new overloaded line, if there is no new overloaded line, perform step 8, otherwise update ΔU according to the following formula and repeat This step until no new overloaded line is generated: ΔU＝γΔU (18)。ΔU=γΔU (18). 9.根据权利要求1中所述的一种引起线路负荷过载的虚假数据注入攻击构造及防御方法，其特征在于，在步骤8中，按如下步骤计算状态变化量，状态量并更新发电计划量：9. A kind of false data injection attack structure and defense method that cause overload of line load according to claim 1, it is characterized in that, in step 8, calculate state change amount according to the following steps, state amount and update power generation plan amount : 步骤801：更新ΔUk←γΔUk，定义Y＝B-1，S＝YΔU，其中Bij＝ViVjBij，βk＝ViVj，Bk为线路k的电纳，定义t＝βkBk/(1-βkBk yk)，yk＝yii+yjj-2yij。假设所有节点电压幅值为1p.u.。使用以下公式计算状态变量变化量Δxk；Step 801: Update ΔU k ←γΔU k , define Y=B −1 , S=YΔU, where B ij =V i V j B ij , β k =V i V j , and B k is the susceptance of line k, defined t=β k B k /(1−β k B k y k ), y k =y ii +y jj −2y ij . Assume that all node voltage amplitudes are 1p.u. Calculate the state variable change Δx k using the following formula; Δxq＝Δqq＝tqk(yqi-yqj)+Sq+t(Si-Sj)(yqi-yqj) (19)Δx q =Δq q =tq k (y qi -y qj )+S q +t(S i -S j )(y qi -y qj ) (19) 步骤802：更新状态量xk+1＝xk+Δx，及发电计划量Uk+1＝Uk+ΔUk。Step 802: Update the state quantity x k+1 =x k +Δx, and the power generation plan quantity U k+1 =U k +ΔU k . 10.根据权利要求1中所述的一种引起线路负荷过载的虚假数据注入攻击构造及防御方法，其特征在于，在步骤9中，按如下步骤判断所提方法是否收敛，若满足条件则收敛，停止；反之，设置k＝k+1并返回步骤5：10. A kind of false data injection attack structure and defense method that cause overload of line load according to claim 1, it is characterized in that, in step 9, according to the following steps to judge whether the proposed method converges, if the condition is satisfied then convergence , stop; otherwise, set k=k+1 and return to step 5: |C(xk+1,Uk+1)|≤ε (20)|C(x k+1 ,U k+1 )|≤ε (20) 其中C(x,U)为消减支路负荷过载的成本函数，ε为一足够小正数，通常设置为10-3。xk+1和Uk+1为迭代第k+1次后的状态量和发电计划量。where C(x, U) is the cost function of reducing the overload of the branch load, and ε is a small enough positive number, usually set to 10 -3 . x k+1 and U k+1 are the state quantity and power generation plan quantity after the k+1th iteration.
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