CN112398117A - False data injection attack construction and defense method causing line load overload - Google Patents

False data injection attack construction and defense method causing 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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overload
line
attack
power
power generation
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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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  • Power Engineering (AREA)
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Abstract

The invention discloses a false data injection attack construction and defense method causing line load overload in the field of power grid information security. Firstly, constructing a false data injection attack model based on alternating current state estimation, adding line active power overrun constraint to realize line load overload, converting an objective function of the attack model into an L1 norm, and solving the optimization model by adopting a Gradient Projection Method (GPM); in order to prevent the power system from running due to line overload, a rapid and accurate re-power generation method is provided for defense, the calculation of a sensitivity matrix and a Lagrange function is avoided, and the calculation time overhead is shortened on the premise of ensuring sufficient power generation. The invention improves the feasibility of constructing the novel power grid false data injection attack, improves the effectiveness and the speed of resisting the attack, and verifies the capability of the power system to cope with the false data injection attack.

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. A false data injection attack construction and defense method for causing line load overload is characterized by comprising the following steps:
step 1: acquiring power system quantity measurement (node injection power and line power flow) and state quantity (voltage amplitude and voltage phase angle), and calculating the conductance and susceptance of the line between nodes according to the nonlinear relation between the quantity measurement and the state quantity;
step 2: establishing an objective function of an attack model by considering the limited attack capability of an attacker;
and step 3: based on a set attack objective function, adding a constraint condition to construct an attack model, wherein the constraint condition can bypass a Bad Data Detection (BDD) link in state estimation and can cause overload of a certain line when the constraint condition meets the attack; solving an attack model by using a Gradient Projection Method (GPM) to generate an attack vector a, and generating a false quantity measurement in the injection quantity measurement;
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;
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；
And step 9: setting the convergence criterion of the method, judging whether the method is converged, and if so, stopping the method; otherwise, updating the iteration number and returning to the step 5.
2. A method for constructing and defending against false data injection attacks according to claim 1, characterized in that in step 1, the following formula is usedFormula calculates conductance G between nodes i and jijAnd susceptance Bij：
Figure FDA0002698384800000021
Wherein P isiAnd QiFor active and reactive injected power, p, at node iijAnd q isijFor injecting power, V, both active and reactive on the lineiIs the magnitude of the voltage at node i, qijIs the phase angle difference between node i and node j.
3. The method for constructing and defending against injection attack of false data causing line load overload according to claim 1, wherein in step 2, considering the limited attack capability of the attacker, the following attack objective function is established by setting the injected attack vector as a:
Figure FDA0002698384800000022
wherein P isa,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 hair0Representing the L0 norm.
4. The method for constructing and defending against false data injection attacks that cause line load overload according to claim 1, wherein in step 3, the specific steps for solving the attack model are as follows:
step 301: adding constraint conditions to the objective function of the attack model to construct the following attack model, wherein the constraint conditions are required to ensure that the attack can pass bad data detection and cause overload of a certain line:
Figure FDA0002698384800000023
s.t. za＝z+a，amin<a<amax (4)
Figure FDA0002698384800000024
Figure FDA0002698384800000025
Figure FDA0002698384800000026
Figure FDA0002698384800000027
Figure FDA0002698384800000028
defining an attack vector
Figure FDA0002698384800000031
The line connected with the nodes is L, and the line set is L; wherein
Figure FDA0002698384800000032
And
Figure FDA0002698384800000033
for measuring active and reactive power flows, P, of a line in a measurementi *And
Figure FDA0002698384800000034
the active and reactive injected power of the node in the measurement are measured,
Figure FDA0002698384800000035
for the phase angle q of the voltage after attackiAnd q isjThe difference between the difference of the two phases,
Figure FDA0002698384800000036
maximum active power allowed for the line;
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:
Figure FDA0002698384800000037
s.t. (4),(5),(6),(7),(8),(9) (11)
step 303: and injecting the solved attack vector into the measurement to generate false quantity measurement.
5. The method for constructing and defending against injection attacks of false data causing overload on line load as claimed in claim 1, wherein in step 4, the generating load and the line load are specified, the voltage phase angle and amplitude, and the generating power transfer distribution factor are calculated according to the following formula:
Figure FDA0002698384800000038
Figure FDA0002698384800000039
wherein P isGi，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 FDA00026983848000000310
causing a power change value, S, of the line L for node kLkThe distribution factor is transferred for the generated power.
6. The method for constructing and defending against injection attack of false data causing line overload according to claim 1, wherein in step 5, the number of initialization iterations k is 1, and whether there is a line with overload is determined, and if there is no overload line, step 9 is executed; otherwise, step 6 is executed.
7. The method for constructing and defending against the injection attack of the false data causing the overload of the line according to claim 1, wherein in step 6, the steps of calculating the overload load matrix on the overload line, reducing the required power generation cost of the overload and transferring the distribution factor matrix are 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 FDA0002698384800000041
Wherein h isLFor 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 FDA0002698384800000042
wherein p isijAnd
Figure FDA0002698384800000043
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 (16)
wherein H is a lineLoad overload on way L hLConstituent overload matrix, Δ PGAnd the delta U is the power generation planned variation of the generator for reducing the overload of the line.
8. The method for constructing and defending against the injection attack of the false data causing the overload of the line according to claim 1, wherein in step 7, the power generation plan variation Δ U is calculated according to the overload matrix H and the transfer factor matrix a to find out a new overload line, and the specific steps are 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 (17)
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 (18)。
9. the method for constructing and defending against the injection of false data causing line load overload according to claim 1, wherein in step 8, the amount of state change, the amount of state and the amount of power generation plan are calculated 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) (19)
Step 802: updating the state quantity xk+1＝xk+ Δ x, and planned amount of power generation Uk+1＝Uk+ΔUk。
10. The method for constructing and defending against false data injection attacks according to claim 1, wherein in step 9, whether the proposed method converges or not is determined according to the following steps, and if the condition is satisfied, the convergence is stopped; otherwise, setting k to k +1 and returning to the step 5:
|C(xk+1,Uk+1)|≤ε (20)
where C (x, U) is a cost function for shedding 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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