CN108596361B - Selection method for practical measurement protection scheme of power system - Google Patents
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Abstract
The invention discloses a selection method of a practical measurement protection scheme of an electric power system, which comprises the following steps: step S1, establishing a protection return on investment rate evaluation model of the power system measuring device; step S2, determining a mathematical model optimization target of the optimal measurement protection scheme selection problem; step S3, determining the mathematical model constraint condition of the optimal measurement protection scheme selection problem; step S4, establishing a mathematical model of the optimal measurement protection scheme selection problem; step S5, converting the optimization problem into a minimum Steiner tree problem; and step S6, approximately solving the minimum Steiner tree problem by using the improved minimum spanning tree algorithm. The invention fully considers the individual difference of the measuring device of the power system and the cost performance of protecting the specific measuring device, improves the rationality and the practicability of the existing method, has good calculation performance, and can meet the requirement of selecting a measuring protection scheme when the power system defends false data injection attack by time complexity and solving effect of an algorithm.
Description
Technical Field
The invention relates to the technical field of power systems, in particular to a selection method of a practical measurement protection scheme of a power system.
Background
The advanced information communication technology is deeply integrated with the smart grid, so that the automation level of the electric power system is greatly improved, and meanwhile, hidden dangers are buried for the information safety risks in a network space to penetrate into the electric power system. The SCADA System collects values of electrical quantities of the smart grid during dynamic operation in real time to a power regulation and control department through a large number of measuring devices and a complex communication network, and the sensing of the real-time operation mode of the smart grid can be realized through the application of State Estimation (SE) in an Energy Management System (EMS). Because the existing SCADA system still has the measuring device with hidden vulnerability and the transmission protocol with low security, once some measuring devices or communication links are invaded by attackers, virtual and false data are injected into partial measured data, which may cause misjudgment on the current operation mode of the power grid under the condition that the attack cannot be found by state estimation, thereby seriously affecting the subsequent analysis and control of the power grid, and the method is the action principle of false data injection attack.
At present, an effective method for defending against false data injection attacks is to strengthen protection on part of key measurement devices in a smart grid so that the key measurement devices cannot be invaded by attackers. The selection of the measurement protection scheme can be generally modeled as an optimization problem, and the constraint condition of the optimization problem relates to the observability problem of the state variable and can be equivalent to a Steiner tree problem in graph theory; and the optimal measurement protection scheme is selected from different angles according to different optimization target settings. Due to the fact that the cost and expected return required for protecting different measuring devices are different, reasonable selection of the measuring protection scheme is not only related to the success rate of defending false data injection attacks, but also related to the economic benefits of power enterprise operation. The Return On Investment (ROI) is a type of economic model, which is currently used to evaluate the expected return on the security investment of the internal computer system of an enterprise, and can be introduced into the optimization target after modeling the measurement device in the smart grid, as an idea for evaluating the economic performance of the measurement protection scheme.
In addition, the Steiner tree problem is an N-P difficult problem. The actual power system is typically large in scale and the time complexity of directly searching for the smallest steiner tree in a larger topology is unacceptable. The minimum spanning tree algorithm is a common algorithm in graph theory, and under the same topological scale, the time overhead for searching the minimum spanning tree is far less than that for searching the minimum Steiner tree. Therefore, the approximate minimum Steiner tree can be found in a reasonable time overhead by improving the minimum spanning tree algorithm and is used for solving a group of approximate optimal measurement protection schemes.
Disclosure of Invention
The technical problem to be solved by the present invention is to provide a method for selecting a practical measurement protection scheme for an electric power system, which can effectively improve the economy of the selected measurement protection scheme when defending against the injection attack of false data estimated by the state of the electric power system, and ensure that the measurement protection scheme has better expandability after the electric power system is scaled up.
In order to solve the above technical problems, the present invention provides a method for selecting a practical measurement protection scheme for an electrical power system, comprising the following steps:
step S1, establishing a protection return on investment rate evaluation model of the power system measuring device;
step S2, determining a mathematical model optimization target of the optimal measurement protection scheme selection problem;
step S3, determining the mathematical model constraint condition of the optimal measurement protection scheme selection problem;
step S4, establishing a mathematical model of the optimal measurement protection scheme selection problem;
step S5, converting the optimization problem into a minimum Steiner tree problem;
and step S6, approximately solving the minimum Steiner tree problem by using the improved minimum spanning tree algorithm.
The step S1 is specifically to establish a protection return on investment evaluation model of the power system measurement apparatus according to the risk exposure RE caused by injecting the dummy data into a measurement apparatus, the risk elimination rate RM caused by taking appropriate protection measures, the annual total cost CP of the adopted protection measures, and the effect discount rate PD caused by the individual performance defect of the protected measurement apparatus.
Wherein the protection return on investment assessment model is represented as:
ROI＝(RE×RM％-CP)×PD％/CP.。
wherein the risk exposure RE is expressed as the sum of expected economic loss values ALE caused by various types of potential false data injection attacks in one year, namely
RE＝∑ALE＝∑SLE×ARO,
Wherein SLE is the economic loss possibly caused by one-time false data injection attack, and ARO is the annual incidence rate of the type of attack;
the risk elimination rate RM% is obtained by carrying out simulation analysis on an information security risk assessment framework;
the annual cost C of protecting a certain measurement device can be calculated by the following formula:
wherein CI is the total initial investment of hardware, software and service required by taking the protective measure, CM is the annual maintenance expense required by maintaining the protective measure, CE is used for evaluating the negative influence of taking the protective measure on the measuring device on the normal work of the data acquisition and monitoring system, Y represents the rated service life of the measuring device, and the annual total cost CP of the measuring protection scheme is the sum of the annual costs of the measuring device contained in the scheme;
the effect discount rate PD% is obtained by comprehensively evaluating the historical fault records of the measuring device, the measurement deviation, the service life and other indexes, and is used for representing the influence of the factors such as the operation reliability, the measurement precision and the like of the protected measuring device on the protection effect.
The possible economic loss SLE caused by one false data injection attack comprises two parts, namely direct economic loss and indirect economic loss, and is represented as follows:
the formula comprises M direct economic losses DL and N indirect economic losses, the indirect economic losses amplify the direct economic losses in a form of multiplying by a weight WAThe effect of the strength of the spurious data injection attack on the SLE is characterized.
In step S2, the optimization objective is to protect the selected metrology devices with the highest sum of return on investment.
In step S3, the constraint condition should satisfy the rank of the sub-matrix H { P } formed by the rows corresponding to all the protected measurement devices in the system measurement jacobian matrix H, which is equal to the sum of the rank of the sub-matrix H { P } formed by the rows corresponding to all the protected measurement devices P in H and the columns corresponding to the state variables { X \ D } other than D in H, and the number | D | of the state variables in D, that is, it is ensured that D can be observed by P.
Wherein, the step S5 should satisfy the following transformation principles at the same time:
if a line tidal volume measuring device exists on one transmission line, the transmission line corresponds to one measuring device;
if no line tidal current measuring device exists on one transmission line, injecting the transmission line into a power measuring device corresponding to a node arranged on a bus at the head end and the tail end of the transmission line;
the transmission lines and the measuring devices must correspond to each other one by one;
each transmission line has a weight w-ROImax-ROI, wherein ROI represents a return on investment for protecting the measurement device corresponding to the transmission line, ROImaxIndicating the maximum return on investment among all the measurement devices corresponding to the transmission line.
Wherein, the step S6 specifically includes:
step S61, obtaining the current node set VcAnd a current total weight WcSelecting and V from the measurement set PcAll measurement subsets P of the correlationc；
Step S62, performing Gaussian elimination on the measured Jacobian matrix H, and subtracting P from PcK of them satisfying VcMinimal set of measurands P of observabilityk；
Step S63, measure the set P of kkK minimum spanning trees T are obtained by utilizing maximum flow algorithmkEach branch of the spanning tree corresponds to P according to the transformation principlekOne measurement of;
step S64, a tree pruning mechanism is introduced to determine whether the nodes in the minimum spanning tree can be pruned one by one, if yes, the sub-trees formed by the node and all the descendant nodes are pruned, and the measurement set P is updatedkAnd minimum spanning tree Tk；
Step S65, from all k pruned minimum spanning trees TkSelects the one with the smallest total weight, and updates the current weight W with its total weightcUpdating the current set of nodes V with the nodes it containsc；
Iteratively executing the steps S61-S65 repeatedly until the current weight WcNo longer reduced, at which point the pruned minimum spanning tree TkThe one with the smallest total weight in (1) is the approximate smallest steiner tree.
The principle of judging whether the nodes in the minimum spanning tree can be pruned is as follows:
the node v and the descendant nodes D (v) thereof do not contain a node corresponding to any state variable in the state variable set D;
after cutting out { vu D (v)) }, all injection power measurement devices installed at nodes in { vu D (v)) } should be removed.
The embodiment of the invention has the beneficial effects that: the invention fully considers the individual difference of the measuring device of the power system and the cost performance of protecting the specific measuring device, improves the rationality and the practicability of the existing method, has good calculation performance, and can meet the requirement of selecting a measuring protection scheme when the power system defends false data injection attack by time complexity and solving effect of an algorithm.
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In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings used in the description of the embodiments or the prior art will be briefly described below, it is obvious that the drawings in the following description are only some embodiments of the present invention, and for those skilled in the art, other drawings can be obtained according to the drawings without creative efforts.
Fig. 1 is a schematic flow chart illustrating a method for selecting a practical measurement protection scheme for an electrical power system according to an embodiment of the present invention.
Fig. 2 is a schematic flow chart illustrating a method for selecting a practical measurement protection scheme for an electrical power system according to an embodiment of the present invention.
Fig. 3 is a topology diagram of an IEEE 14 node standard system including measurement information according to an embodiment of the present invention.
FIG. 4 is a flowchart of an embodiment of the present invention for approximating a minimum Steiner tree problem using an improved minimum spanning tree algorithm.
FIG. 5 is a maximum flow model for building a minimum spanning tree according to an embodiment of the present invention.
Detailed Description
The following description of the embodiments refers to the accompanying drawings, which are included to illustrate specific embodiments in which the invention may be practiced.
Referring to fig. 1, an embodiment of the present invention provides a method for selecting a practical measurement protection scheme for an electrical power system, including the following steps:
step S1, establishing a protection return on investment rate evaluation model of the power system measuring device;
step S2, determining a mathematical model optimization target of the optimal measurement protection scheme selection problem;
step S3, determining the mathematical model constraint condition of the optimal measurement protection scheme selection problem;
step S4, establishing a mathematical model of the optimal measurement protection scheme selection problem;
step S5, converting the optimization problem into a minimum Steiner tree problem;
and step S6, approximately solving the minimum Steiner tree problem by using the improved minimum spanning tree algorithm.
As further described below in conjunction with fig. 3-5.
Step S1, establishing a protection return on investment evaluation model of the power system measurement device
The development of an information attack technology enables an intelligent power grid SCADA system to inevitably comprise a part of measuring devices with potential safety hazards; a large number of non-proprietary protocols such as TCP/IP are adopted for communication, and the non-proprietary protocols are easy to threaten by information attack. Information attackers typically exploit vulnerabilities in the measurement devices or communication protocols to intrude into the field devices, to seize transmission channels, or to directly penetrate the computers of the regulatory authorities of the electrical power system to tamper with the measurement information and to hinder the normal operation of the SCADA system. Table 1 lists the types of information attacks and the corresponding defensive measures that are common for smart grid SCADA systems.
TABLE 1 common information attack types and corresponding defense measures of smart grid SCADA system
Different defense measures are adopted at different costs, the generated defense effects are different, and in addition, the reliability and the measurement precision of the measurement devices are not completely the same, so that factors such as risk exposure RE caused by injecting false data into a certain measurement device, risk elimination rate RM caused by adopting proper protection measures, annual total cost CP of adopted protection measures, effect discount rate PD% caused by individual performance flaws of the protected measurement device and the like need to be comprehensively considered, and an investment return rate evaluation model for protecting the power system measurement device is established.
The risk exposure RE can be expressed as the sum of the expected economic loss values ALE for each type of potential spurious data injection attack over the year, i.e.
RE＝∑ALE＝∑SLE×ARO,
Among them, SLE is the economic loss that may be caused by a false data injection attack, and ARO is the annual incidence of this type of attack. SLE shall comprise both direct and indirect economic losses, which can be expressed as
The M-type direct economic loss DL and the N-type indirect economic loss are jointly considered, and the indirect economic loss amplifies the direct economic loss in a form of multiplying by the weight W. WAThe impact of the strength of the characterizing spurious data injection attack on SLE is typically less than 1.
Multiple protective measures are often applied in conjunction to the protected measurement devices to improve their ability to defend against spurious data injection attacks. By taking various protective measures, partial risk exposure, expressed as risk elimination rate RM%, can be eliminated to some extent. The RM% can be obtained by simulation analysis of an information security risk assessment framework.
The annual cost C of protecting a certain measurement device can be calculated by the following formula:
wherein CI is the total initial investment of hardware, software and services required for taking the protective measures, CM is the annual maintenance overhead required for maintaining the protective measures, CE is used for evaluating the negative influence of taking the protective measures on the normal operation of a data acquisition and monitoring (SCADA) system, and Y represents the rated service life of the measuring device. The total annual cost CP of the metered protection scheme is the sum of the annual costs of the metering devices included in the scheme.
The effect discount rate PD% can be obtained by comprehensively evaluating the historical fault records of the measuring device, the measurement deviation, the service life and other indexes, and is used for representing the influence of the factors such as the operation reliability, the measurement precision and the like of the protected measuring device on the protection effect.
Combining the above factors, the evaluation model of the return on investment can be expressed as:
ROI＝(RE×RM％-CP)×PD％/CP.
step S2, determining the mathematical model optimization target of the optimal measurement protection scheme selection problem
In order to have optimal economics when taking protective measures for a given measurement in the measurement protection scheme while ensuring that a spurious data injection attack can always be detected, the mathematical model optimization objective of the optimal measurement protection scheme selection problem can be specified as:
namely, the total return on investment of the protection scheme is measured to be the maximum. Wherein P is the set of all measurement devices included in the measurement protection scheme, and ROIp is the return on investment of one measurement device P in protection P.
Step S3, determining the mathematical model constraint condition of the optimal measurement protection scheme selection problem
In order to ensure that a false data injection attack on a set of state variables D can be always detected by protecting a set of measurement devices P, the constraint condition should satisfy the rank of the submatrix H { P } formed by the rows corresponding to all the protected measurement devices in the system measurement jacobian H, which is equal to the sum of the rank of the submatrix H { P } formed by the rows corresponding to all the protected measurement devices P in H and the columns corresponding to the state variables { X \ D } other than D in H, and the number | D | of the state variables in D, namely:
rank(H{P},*)＝rank(H{P},{X\D})+|D|.
step S4, establishing a mathematical model of the optimal measurement protection scheme selection problem
According to the steps, the optimal measurement protection scheme selection problem data model for defending against the power system state estimation false data injection attack and considering the return on investment rate is as follows:
s.t.rank(H{P},*)＝rank(H{P},{X\D})+|D|.
step S5, converting the optimization problem into the minimum Steiner tree problem
According to the theory of relevance of the graph theory, finding a set of measurements P makes a set of state variables D observable, which is equivalent to finding a tree in the network topology that connects network nodes corresponding to all state variables in D, and at the same time, each branch of the tree must correspond to one measurement according to the following principle:
(1) if there is a line tide flow measurement on this branch, then this branch is assigned to one of the measurements. As shown in FIG. 3, branches 6-11 may correspond to line tidal flow measurements (7);
(2) if no line tide volume measurement exists on the branch, the branch is injected with a power measurement corresponding to a node installed on its head end or tail end node. As shown in FIG. 3, branches 6-12 may correspond to node injection power measurements (18);
(3) the branches and the measuring devices must be in one-to-one correspondence and can not be in repeated correspondence;
all measurements corresponding to all branches of a tree satisfying the above principles can form a set of feasible measurement sets P, and such a tree is called a steiner tree. Weighting each branch of Steiner tree with weight w ═ ROImax-ROI, wherein ROI represents the return on investment measured corresponding to the protection of the branch, ROImaxAnd representing the protection investment return rate with the maximum measurement in the P, and forming an optimal measurement protection scheme by the measurement set P corresponding to the Steiner tree with the minimum total weight.
Step S6, using improved minimum spanning tree algorithm to approximately solve the minimum Steiner tree problem
It is an N-P difficult problem to directly find the minimum steiner tree in the power grid topology shown in fig. 3, and the time complexity thereof is unacceptable along with the growth speed of the topology scale, so that it is necessary to reasonably approximate the minimum steiner tree in order to select a group of approximately optimal measurement protection schemes by using the minimum spanning tree algorithm introducing tree pruning.
A flow chart for approximating a minimum steiner tree problem using the modified minimum spanning tree algorithm is shown in fig. 4.
First, obtain the current node set Vc(initialisation to all nodes V in the topology) and the current total weight Wc(initialized to 0), selecting from the measurement set P the sum VcAll measurement subsets P of the correlationc. The measure p is related to the node v, and means that the measure p directly measures the node injection power on v or measures the power flow on a line connected with v.
Second, the measured Jacobian matrix H is eliminated from PcK of them satisfying VcMinimal set of measurands P of observabilityk. K is an adjustable approximate factor, and the value of k is adjusted, so that the problem solving time cost and the solved approximate optimal solution precision can be balanced.
Third, measure the set P of kkUsing maximumObtaining k minimum spanning trees T by Flow (Max Flow) algorithmkEach branch of the spanning tree corresponds to P as originally in step S5kOne of the measurements.
Taking the topology in FIG. 3 as an example, if the current node set Vc＝{v1,v2,v4,v5,v6V is specified1Is a reference node, then V is guaranteedcA set of observable measurands may be P k1,6,12,14, and the set of measurements PkRelated topological edge Ek＝{e1,e2,e5,e7,e10}. Building a maximum flow model, reference node v, as shown in FIG. 41Specifying as a resulting spanning tree TkRoot node of, temporarily first from EkIn which one and v are specified1Connected edge e1Is added to TkIn fig. 5, the maximum flow rate and the minimum flow rate of each side corresponding to e1 in the maximum flow model are both set to 1, the maximum flow rate of each of the remaining sides is set to 1, and the minimum capacity is set to 0. Solving the maximum flow problem by using the Ford-Fulkerson algorithm, such as at the guaranteed edge e1If the flow is 1, the corresponding relation between the measurement and the edge can be obtained according to the maximum flow model if the solution exists; if at the guaranteed edge e1If there is no solution when the flow rate is 1, e is required to be set1Move out of TkAnd selecting the other and v1Joined edge join TkAnd repeating the above operations. Because of V0Can be covered by PkObserving that a set of measurements and corresponding relationships between edges must be obtained, e.g.
These edges constitute a junction VcThe minimum spanning tree of (3).
Fourthly, introducing a tree pruning mechanism, and judging whether the nodes in the minimum spanning tree can be pruned one by one according to the judgment principle: (1) the node v and the descendant nodes D (v) thereof do not contain a node corresponding to any state variable in the state variable set D; (2) after cutting out { vu D (v)) }, all injection power measurement devices installed at nodes in { vu D (v)) } should be removed. If the node can be pruned, the subtree formed by the node and all the descendant nodes thereof is pruned, and the measurement set Pk and the minimum spanning tree Tk are updated.
The fifth step, from all the k pruned minimum spanning trees TkSelects the one with the smallest total weight, and updates the current weight W with its total weightcUpdating the current set of nodes V with the nodes it containsc. Repeatedly and iteratively executing the first step to the fifth step until the current weight WcNo longer decreases. The minimum spanning tree T trimmed at this timekThe measurement set P corresponding to the one with the smallest total weight in the least approximate Steiner treekThe method is a practical measurement protection scheme with approximate optimal return on investment.
The following example is used to verify the ability of the improved minimum spanning tree algorithm to solve for near optimal solutions. For example: when the ROI of the measurement apparatus in fig. 3 is set as the value in table 2 and k is set as 15, D includes any state variables m — 2,4,7,9, and 11, and the measurement protection scheme with the approximately maximum total return on investment is sequentially obtained. For each value of m, repeating the random construction of 20 groups D, and averaging the obtained total return on investment to obtain ROI when m takes different valuesm. And meanwhile, solving the global optimal total return on investment ROI by utilizing an exhaustion method when different m values are obtained. Dividing r into ROImthe/ROI is listed in table 3. As can be seen from table 3, when m is 2,4,7,9, and 11, the ratio of the approximately optimal solution to the globally optimal solution is close to 1, thereby verifying that the improved minimum spanning tree algorithm can obtain the approximately optimal measurement protection scheme.
TABLE 2 shows the return on investment ROI of each measurement device in the IEEE 14 node standard system
TABLE 3 ratio of near-optimal solution to global optimal solution at different values of m
The following embodiments are used to verify that the improved minimum spanning tree algorithm has better scalability for the network topology scale. Setting k to 15, and solving an approximately optimal measurement protection scheme by using a modified minimum spanning tree algorithm in an IEEE 14,30,57,118 node standard system respectively for defending false data injection attacks aiming at state variables with different proportions. The statistics of the above network topology are shown in table 4. The experiment was repeated 50 times in each case, and the time overhead was averaged and listed in table 5. It can be seen from table 5 that the time overhead of improving the minimum spanning tree algorithm increases twice with the topology scale, and the time overhead of directly solving the minimum steiner tree problem increases exponentially with the topology scale, so the method has better expandability.
TABLE 4 IEEE 14,30,57,118 node Standard System network Structure statistics
TABLE 5 time overhead (in ms) for solving the near-optimal metrology protection scheme at different network scales
The method combines the actual use scene of the electric power system measuring device to establish an investment return rate evaluation model for protecting the measuring device; meanwhile, the minimum total return on investment of the measurement protection scheme is taken as an optimization target, the selected measurement protection scheme can always ensure that the false data injection attack is successfully detected as a constraint condition, a mathematical model of an optimization problem is established, and the approximately optimal measurement protection scheme is solved in a reasonable time overhead range by introducing an improved minimum spanning tree algorithm of a tree pruning mechanism. The invention fully considers the individual difference of the measuring device of the power system and the cost performance of protecting the specific measuring device, improves the rationality and the practicability of the existing method, has good calculation performance, and can meet the requirement of selecting a measuring protection scheme when the power system defends false data injection attack by time complexity and solving effect of an algorithm.
The above disclosure is only for the purpose of illustrating the preferred embodiments of the present invention, and it is therefore to be understood that the invention is not limited by the scope of the appended claims.
Claims (8)
1. A method for selecting a practical measurement protection scheme of an electric power system comprises the following steps:
step S1, according to the risk exposure RE caused by injecting false data into a certain measuring device, the risk elimination rate RM% caused by adopting proper protective measures and the annual total cost C of the protective schemePAnd the effect discount rate PD% caused by individual performance flaws of the protected measuring device, and establishing a protection return on investment rate evaluation model of the electric power system measuring device;
step S2, determining a mathematical model optimization target of the optimal measurement protection scheme selection problem;
step S3, determining the mathematical model constraint condition of the optimal measurement protection scheme selection problem;
step S4, establishing a mathematical model of the optimal measurement protection scheme selection problem;
step S5, converting the optimization problem into a minimum Steiner tree problem;
step S6, approximately solving the problem of the minimum Steiner tree by using an improved minimum spanning tree algorithm;
the risk exposure RE is expressed as the sum of the expected economic loss values ALE caused by various types of potential spurious data injection attacks in one year, namely
RE＝∑ALE＝∑SLE×ARO,
Wherein, SLE is the economic loss possibly caused by the occurrence of one false data injection attack, and ARO is the annual incidence rate of the corresponding type of attack;
the risk elimination rate RM% is obtained by carrying out simulation analysis on an information security risk assessment framework;
the annual cost C of protecting a certain measurement device can be calculated by the following formula:
wherein, CIThe total initial investment of hardware, software and services required to take this protective measure, CMyThe annual maintenance costs required for maintaining the protective measures, CEThe method is used for evaluating the negative influence of protective measures taken on the measuring device on the normal work of the data acquisition and monitoring system, Y represents the rated service life of the measuring device, and the annual total cost C of the measured protective schemePThe sum of the annual costs C of protecting a certain measuring device contained in the scheme;
the effect discount rate PD% is obtained by comprehensively evaluating the historical fault record, the measurement deviation and the service life index of the measuring device and is used for representing the influence of the operation reliability and the measurement precision factors of the protected measuring device on the protection effect.
2. The selection method of claim 1, wherein the protection return on investment assessment model is represented as:
ROI＝(RE×RM％-CP)×PD％/CP.。
3. the selection method of claim 1, wherein the possible economic loss SLE caused by the occurrence of one dummy data injection attack comprises two parts, namely direct economic loss and indirect economic loss, and is represented as:
middle ladleIncluding M-class direct economic losses DL and N-class indirect economic losses, amplifying the direct economic losses in the form of multiplying by a weight WAThe effect of the strength of the spurious data injection attack on the SLE is characterized.
4. The method of selecting as claimed in claim 1, wherein in step S2, the optimization objective is to maximize the sum of the return on investment for protecting the selected metrology devices.
5. The method of claim 1, wherein in step S3, the constraint condition is satisfied that a rank of a submatrix H { P }, formed by rows corresponding to all protected metrology devices in the system metrology jacobian H, is equal to a sum of a submatrix H { P }, formed by rows corresponding to the metrology set P formed by all protected metrology devices in H and columns corresponding to other state variables { X \ D } except a set of state variables D in H, and a rank of { X \ D } and a number | D | of state variables in D, i.e. D is guaranteed to be observable by the metrology set P.
6. Selection method according to claim 5, characterized in that said step S5 simultaneously satisfies the following transformation principles:
(1) if a line tidal volume measuring device exists on one transmission line, the transmission line corresponds to one measuring device;
(2) if no line tidal current measuring device exists on one transmission line, injecting the transmission line into a power measuring device corresponding to a node arranged on a bus at the head end and the tail end of the transmission line;
(3) the transmission lines and the measuring devices must correspond to each other one by one;
(4) each transmission line has a weight w-ROImax-ROI, wherein ROI represents a return on investment for protecting the measurement device corresponding to the transmission line, ROImaxIndicating the maximum return on investment among all the measurement devices corresponding to the transmission line.
7. The selection method according to claim 6, wherein the step S6 specifically includes:
step S61, obtaining the current node set VcAnd a current total weight WcSelecting and V from a measurement set P formed by all protected measurement devicescAll measurement subsets P of the correlationc；
Step S62, performing Gaussian elimination on the measured Jacobian matrix H, and subtracting P from PcK of them satisfying VcMinimal set of measurands P of observabilityk；
Step S63, measure the set P of kkK minimum spanning trees T are obtained by utilizing maximum flow algorithmkEach branch of the spanning tree corresponds to P according to the transformation principlekOne measurement of;
step S64, a tree pruning mechanism is introduced to determine whether the nodes in the minimum spanning tree can be pruned one by one, if yes, the sub-trees formed by the node and all the descendant nodes are pruned, and the measurement set P is updatedkAnd minimum spanning tree Tk；
Step S65, from all k pruned minimum spanning trees TkSelects the one with the smallest total weight, and updates the current weight W with its total weightcUpdating the current set of nodes V with the nodes it containsc；
Iteratively executing the steps S61-S65 repeatedly until the current weight WcNo longer reduced, at which point the pruned minimum spanning tree TkThe one with the smallest total weight in (1) is the approximate smallest steiner tree.
8. The selection method of claim 7, wherein the principle of determining whether the node in the minimum spanning tree can be pruned is:
(1) the node v and the descendant nodes D (v) thereof do not contain a node corresponding to any state variable in the state variable set D;
(2) after cutting out { vu D (v)) }, all injection power measurement devices installed at nodes in { vu D (v)) } should be removed.
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