CN108182536A - A kind of power distribution network CPS safety defense methods based on bounded rationality - Google Patents
A kind of power distribution network CPS safety defense methods based on bounded rationality Download PDFInfo
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- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06Q—INFORMATION AND COMMUNICATION TECHNOLOGY [ICT] SPECIALLY ADAPTED FOR ADMINISTRATIVE, COMMERCIAL, FINANCIAL, MANAGERIAL OR SUPERVISORY PURPOSES; SYSTEMS OR METHODS SPECIALLY ADAPTED FOR ADMINISTRATIVE, COMMERCIAL, FINANCIAL, MANAGERIAL OR SUPERVISORY PURPOSES, NOT OTHERWISE PROVIDED FOR
- G06Q10/00—Administration; Management
- G06Q10/06—Resources, workflows, human or project management; Enterprise or organisation planning; Enterprise or organisation modelling
- G06Q10/063—Operations research, analysis or management
- G06Q10/0635—Risk analysis of enterprise or organisation activities
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- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06Q—INFORMATION AND COMMUNICATION TECHNOLOGY [ICT] SPECIALLY ADAPTED FOR ADMINISTRATIVE, COMMERCIAL, FINANCIAL, MANAGERIAL OR SUPERVISORY PURPOSES; SYSTEMS OR METHODS SPECIALLY ADAPTED FOR ADMINISTRATIVE, COMMERCIAL, FINANCIAL, MANAGERIAL OR SUPERVISORY PURPOSES, NOT OTHERWISE PROVIDED FOR
- G06Q50/00—Systems or methods specially adapted for specific business sectors, e.g. utilities or tourism
- G06Q50/06—Electricity, gas or water supply
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- H—ELECTRICITY
- H04—ELECTRIC COMMUNICATION TECHNIQUE
- H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
- H04L63/00—Network architectures or network communication protocols for network security
- H04L63/14—Network architectures or network communication protocols for network security for detecting or protecting against malicious traffic
- H04L63/1408—Network architectures or network communication protocols for network security for detecting or protecting against malicious traffic by monitoring network traffic
- H04L63/1416—Event detection, e.g. attack signature detection
Abstract
The invention discloses a kind of power distribution network CPS safety defense methods based on bounded rationality, fully with power grids multi-source datas such as Distribution Network Equipment data, power distribution network operation data, the residence time of history attacker, average reaction time, mean repair times, overall power distribution net CPS risk assessment indexs are established in terms of physical system and information system two so that each circuit risk evaluation result effectively helps the side of setting up defences to realize tactful selection of setting up defences by the learning method of playing chess based on bounded rationality.It is specific to obtain each benefit value of setting up defences for attacking strategy pair of setting up defences in terms of economic benefit and safety two respectively, final expected utility when the side of setting up defences takes Different Strategies and average benefit are obtained using logarithm synthetic method, represent that attacker and the side of setting up defences choose the dynamic change rate of certain strategy, and then the dynamic differential equation group for establishing learning model obtains power distribution network CPS Prevention-Securities satisfaction strategy with dynamic differential equation.
Description
Technical field
The present invention relates to transmission ＆ distribution electro-technical field more particularly to a kind of power distribution network CPS Prevention-Securities based on bounded rationality
Method.
Background technology
With the continuous development of intelligent grid construction, the extensive access of distributed generation resource, electric vehicle etc., power distribution network
It has been developing progressively to have the power distribution network CPS of various CPS characteristic features, it is higher and higher to the interdependency of information network.Due to
Distribution net work structure and the very big variation of operational management, if a kind of effectively reliable distribution of state-of-the-art technology research cannot be utilized
Net Prevention-Security strategy choosing method, power distribution network is difficult to successfully manage various bursts and cascading failure can to meet user security
By the demand of power supply.Therefore, there is an urgent need to carry out the research of power distribution network CPS Prevention-Security strategy choosing methods.
Risk assessment is the working condition of the various accidents and electrical equipment occurred according to power distribution network to predict distribution
The probability that net breaks down leads to the size of risk so as to predict to break down, is the important foundation of early warning and Prevention-Security,
It has been obtained for widely studying and applying；Traditional risk assessment index only considers electric system physical part, with electric power
Physics-information depth coupling, the integrity problem of information link also results in the operation risk of physical system, to ensure distribution
Net CPS it is safe and stable, it is continuous, effectively run, power distribution network CPS integrated risk evaluation indexes need to be built.
Existing power grid security defence control is mainly Passive Defence, and real time information availability is low.Learning method play chess in work
The rise of journey practical application provides new thinking to the selection of power distribution network Prevention-Security strategy.But the application of the strategy is built mostly
It stands on the basis of rational, and actual conditions deviation is larger, reduces the confidence level that strategy chooses result.
Currently based on the study of playing chess of bounded rationality as a kind of cross-cutting, across task method, in field of power
In cause the concern of more and more scholars.Study of playing chess is that the problem of different but related field is asked with existing knowledge
One kind side of setting up defences decision choosing method of solution.It is premised on bounded rationality：(1) due to the influence of a large amount of uncertain factors, appoint
One participant can not accurately all grasp feature, set of strategies and the Efficiency set of every other participant.(2) since attacker is every
Secondary adversely affected to system is not necessarily consequence most serious under current operating conditions, i.e., participant need to seek satisfied determine
Plan rather than optimizing decision.The situation that interdepends between color this strategy of jade under same power distribution network CPS is considered simultaneously, is obtained closer
The practical side's of setting up defences decision is chosen as a result, the analysis and prediction of power distribution network CPS Prevention-Securities can be realized effectively.
Invention content
According to problem of the existing technology, the invention discloses a kind of power distribution network CPS based on bounded rationality is anti-safely
Imperial method, by obtaining power grid multi-source data, risk evaluation model is established in terms of physical system and information system two,
The integrated risk of each circuit can effectively be assessed；Build the learning model of playing chess based on bounded rationality；Again respectively from economic benefit and
Two aspect of safety obtains each benefit value of setting up defences for attacking strategy pair of setting up defences, and obtains the side of setting up defences using logarithm synthetic method and adopts
Final expected utility and average benefit when taking Different Strategies；And then establish the dynamic differential equation group of learning model, it obtains
Obtain Prevention-Security satisfaction strategy.
Concrete scheme is：
Step 1：Power grid multi-source data is obtained, including meteorological data, Distribution Network Equipment data, power distribution network operation data, is gone through
Residence time, average reaction time, mean repair time of history attacker etc., in terms of physical system and information system two
Risk evaluation model is established, for describing the value-at-risk of each circuit；
Step 2：According to the risk evaluation result of each circuit, the learning model of playing chess based on bounded rationality is built, including structure
Build attacker's type space set, the side's of setting up defences type space set, attacker's set of strategies, the side's of setting up defences set of strategies, participant play chess
Efficiency set, participant are played chess probability set；
Step 3：For attacker choose strategy, according to participant play chess probability set choose reasonably set up defences strategy omit,
Each benefit value of setting up defences for attacking strategy pair of setting up defences is obtained in terms of economic benefit and safety two respectively, is synthesized using logarithm
Method obtains the side of setting up defences and takes the final expected utility of Different Strategies and average benefit；
Step 4：Strategy of specifically setting up defences for some omit, the circuit ratio for choosing the strategy is the function of time, with move
The state differential equation represents its dynamic change rate.Similarly, the arbitrarily optional attack strategies of attacker can be obtained dynamically micro- accordingly
Divide equation.Consequence most serious under current operating conditions is not necessarily since attacker adversely affects every time to system, i.e.,
Participant need to seek satisfactory decision-making rather than optimizing decision.It establishes the dynamic differential equation group of learning model, acquires differential side
Journey stable equilibrium solution obtains Prevention-Security satisfaction strategy.
Further, the step 1 includes：
Risk assessment is carried out from tripartites such as customer impact, electric network influencing, external factor in face of power distribution network physical system, is commented
Estimate index and include power failure number ratio, Custom interruption cost rate, it is rate of energy loss after heavily loaded overload prevention device number, failure, important
User's power failure risk, emergency set are equipped with ability, repair time influence factor and weather conditions etc..
Risk assessment, assessment are carried out from information security, communication security and physical security tripartite in face of distribution web information system
Index includes completeness check, identity discriminating, access control, end user privacy safety, communication protocol safety, information transmission
Safety, operating system security, virus prevention, equipment safety, network environment safety etc..
Further, the step 2 includes：
The power distribution network CPS attacks the learning model M that sets up defences against, and can be expressed as 4 tuples, i.e. M=(N, S, B, P), N
=(NA, NP) it is the participant space pair of learning model of playing chess, wherein, NAFor attacker's type space set, NPFor the side of setting up defences
Type space set；S=(SA, SP) it is participant's set of strategies pair, SA={ SA1, SA2, SAn, n ∈ N and n >=2 represent attacker
Set of strategies, SP={ SP1, SP2, SPnRepresent the side's of setting up defences set of strategies；B=(BA, BP) it is that participant plays chess Efficiency set, by all ginsengs
It is codetermined with the strategy of person；P=(p, q) is that participant plays chess probability set, piRepresent that attacker selects attack strategies SAiIt is general
Rate, qjThe expression side of setting up defences selects the tactful S that sets up defencesPiProbability.Due to the influence of a large amount of uncertain factors, any participant is not
Feature, set of strategies and the Efficiency set of every other participant can accurately be grasped.
Further, the step 3 includes：
Step 31：Played chess using Different Strategies, obtain corresponding economic benefit matrix and safety matrix：
Wherein, aij、bijRepresent that attacker and the side of setting up defences take S respectivelyAi、SPjWhen economic benefit, cij、dijTable respectively
Show that attacker and the side of setting up defences take SAi、SPjWhen safety, n, m represent in the side of setting up defences and attacker's set of strategies element respectively
Number.
Step 32：For the side of setting up defences, policymaker is with different probability qiS is omited to each strategy of setting up defencesPiIt is chosen, but
Condition is met for entire set of strategies：Equally, attacker policymaker is with different Probability psiTo each attack strategies
SAiIt is chosen, entire set of strategies is met：Calculate the economic benefit expectation that the side's of setting up defences difference is set up defences tactful
IncomeAnd its average yield
…
Calculate the side's of setting up defences difference set up defences strategy safety expected revenusAnd its average yield
…
Using logarithm synthetic method calculate the side's of setting up defences difference set up defences strategy synthesis expected revenusWith comprehensive average yield
…
Further, the step 4 includes：
Step 41：Since the side of setting up defences income junior can learn to imitate the strategy selected by high yield person, for the side of setting up defences
Optional strategy in set of strategies, choosing the circuit ratio of Different Strategies will change over time, use qi(t)
It represents, wherein, qi(t) it represents to select the strategy summary S that sets up defencesPiCircuit ratio, and meetAttacker chooses different
The circuit ratio dynamic change at any time of strategy, uses pi(t) it is indicated, wherein, pi(t) meet
Step 42：For some specific defence policies Spi, the circuit ratio for choosing the strategy is the function of time, is moved
State rate of change can be represented with dynamic differential equation：
Wherein λiRepresent the random variability using the tactful i that sets up defences, kαiFor strength factor.
For the arbitrary optional attack strategies S of attackerAiIt can obtain corresponding dynamic differential equation：
Wherein ρiRepresent the random variability using attack strategies i, kβiFor strength factor.
Step 43：It enablesStable equilibrium solution is acquired, obtains Prevention-Security satisfaction strategy, i.e.,
The side of setting up defences can defend successful most simple strategy.By drawing the phase diagram of dynamic differential equation, power distribution network Prevention-Security is realized
The analysis and prediction of strategy.
By adopting the above-described technical solution, a kind of power distribution network CPS based on bounded rationality provided by the invention is anti-safely
Imperial method, when fully using Distribution Network Equipment data, power distribution network operation data, the residence time of history attacker, average response
Between, the power grids multi-source data such as mean repair time, establish overall power distribution net CPS in terms of physical system and information system two
Risk assessment index so that each circuit risk evaluation result is effectively helped by the learning method of playing chess based on bounded rationality
It realizes the selection for strategy of setting up defences, in particular to works as since attacker adversely affects to be not necessarily every time to system in the side of setting up defences
Consequence most serious under preceding operation conditions, i.e. participant need to seek satisfactory decision-making rather than optimizing decision, respectively from economic benefit and
Two aspect of safety obtains each benefit value of setting up defences for attacking strategy pair of setting up defences, and obtains the side of setting up defences using logarithm synthetic method and adopts
Final expected utility and average benefit when taking Different Strategies represent that attacker and the side of setting up defences choose certain with dynamic differential equation
The dynamic change rate of strategy, and then the dynamic differential equation group for establishing learning model obtains power distribution network CPS Prevention-Securities
Satisfied strategy.The essence of this method is to build the integrated risk evaluation index of physics-information coupling, and limited by being based on
The method of playing chess of rationality makes the strategy of setting up defences of selection slightly more meet reality, realize power distribution network CPS Prevention-Security strategies analysis and
Prediction.
Description of the drawings
In order to illustrate the technical solutions in the embodiments of the present application or in the prior art more clearly, below will to embodiment or
Attached drawing needed to be used in the description of the prior art is briefly described, it should be apparent that, the accompanying drawings in the following description is only
Some embodiments described in the application, for those of ordinary skill in the art, in the premise not made the creative labor
Under, it can also be obtained according to these attached drawings other attached drawings.
Fig. 1 is the corresponding flow chart of steps of the method for the invention；
Fig. 2 is the corresponding core procedure figure of the method for the invention；
Fig. 3 is the corresponding power distribution network CPS integrated risk evaluation indexes of the method for the invention；
Fig. 4 is that the corresponding attacker of the method for the invention and the side's of setting up defences study play chess to set；
Fig. 5 (1) is the corresponding side's of the setting up defences dynamic differential equation phase diagram of the method for the invention；
Fig. 5 (2) is the corresponding side's of the setting up defences dynamic differential equation phase diagram of the method for the invention
Specific embodiment
To make technical scheme of the present invention and advantage clearer, with reference to the attached drawing in the embodiment of the present invention, to this
Technical solution in inventive embodiments is clearly completely described：
A kind of power distribution network CPS safety defense methods based on bounded rationality as Figure 1-Figure 5, the specific steps are：
Step 1：Power grid multi-source data is obtained, including meteorological data, Distribution Network Equipment data, power distribution network operation data, is gone through
Residence time, average reaction time, mean repair time of history attacker etc., in terms of physical system and information system two
Risk evaluation model is established, for describing the value-at-risk of each circuit；Wherein history attacker includes power distribution network in past several years
Physical attacks person and information attack person, phenomena such as physical attacks person includes harsh weather, equipment is impaired, information attack person packet
Virus is included, phenomena such as hacker.Wherein participant refers to the side of setting up defences and attacker
Further, the step 1 includes：
As Fig. 1 gives the present invention power distribution network CPS integrated risk evaluation indexes used.The index includes physical system
Risk assessment index and evaluating information system risk index.
Risk assessment is carried out from tripartites such as customer impact, electric network influencing, external factor in face of power distribution network physical system, is commented
Estimate index and include power failure number ratio, Custom interruption cost rate, it is rate of energy loss after heavily loaded overload prevention device number, failure, important
User's power failure risk, emergency set are equipped with ability, repair time influence factor and weather conditions etc..Table 1 provides power distribution network physics
System risk grade and quantized value.
1 physical system risk indicator value of table and corresponding risk class quantized value
Risk assessment, assessment are carried out from information security, communication security and physical security tripartite in face of distribution web information system
Index includes completeness check, identity discriminating, access control, end user privacy safety, communication protocol safety, information transmission
Safety, operating system security, virus prevention, equipment safety, network environment safety etc..According to evaluating information system risk index
System, safe class are divided into 7 grades, respectively very safe (95-100), safety (85-90), safer (80-85), general (70-
80), relatively hazardous (65-70), dangerous (60-65), danger close (<60).
Step 2：According to the risk evaluation result of each circuit, the learning model of playing chess based on bounded rationality is built, including structure
Build attacker's type space set, the side's of setting up defences type space set, attacker's set of strategies, the side's of setting up defences set of strategies, participant play chess
Efficiency set, participant are played chess probability set；Further, wherein
The step 2 includes：
The power distribution network CPS attacks the learning model M that sets up defences against, and can be expressed as 4 tuples, i.e. M=(N, S, B, P), N
=(NA, NP) it is the participant space pair of learning model of playing chess, wherein, NAFor attacker's type space set, NPFor the side of setting up defences
Type space set；S=(SA, SP) it is participant's set of strategies pair, it is assumed that { SA1,SA2And { SP1,SP2Be respectively attacker and
The set of strategies for the side of setting up defences,；P=(p, q) is that participant plays chess probability set, piRepresent that attacker selects attack strategies SAiProbability,
qjThe expression side of setting up defences selects the tactful S that sets up defencesPiProbability, both sides with different probability in respective set of strategies strategy carry out
It chooses.Due to the influence of a large amount of uncertain factors, any participant can not accurately all grasp the spy of every other participant
Sign, set of strategies and Efficiency set.Its both sides study plays chess to set such as Fig. 4.
Step 3：For attacker choose strategy, according to participant play chess probability set choose reasonably set up defences strategy omit,
Each benefit value of setting up defences for attacking strategy pair of setting up defences is obtained in terms of economic benefit and safety two respectively, is synthesized using logarithm
Method obtains the final expected utility and average benefit when the side of setting up defences takes Different Strategies；Further, the step 3 includes：
Step 31：Played chess using Different Strategies, obtain corresponding economic benefit matrix and safety matrix：
Step 32：For the side of setting up defences, policymaker is with different probability qiEach strategy of setting up defences is omitedIt is chosen, but
Condition is met for entire set of strategies：Equally, attacker policymaker is with different Probability psiTo each attack strategies
SAiIt is chosen, entire set of strategies is met：Calculate the economic benefit expectation that the side's of setting up defences difference is set up defences tactful
IncomeAnd its average yield
Calculate the side's of setting up defences difference set up defences strategy safety expected revenusAnd its average yield
Using logarithm synthetic method calculate the side's of setting up defences difference set up defences strategy synthesis expected revenusWith comprehensive average yield
It similarly, can be in the hope of calculating attacker's Different Strategies in terms of economic benefit and safety two for attacker
Expected revenus and average yield.
Calculate the safety expected revenus of attacker's difference attack strategiesAnd its average yield
Using logarithm synthetic method calculate attacker's difference set up defences strategy synthesis expected revenusWith comprehensive average yield
Step 4：Strategy of specifically setting up defences for some omit, the circuit ratio for choosing the strategy is the function of time, with move
The state differential equation represents its dynamic change rate.Similarly, the arbitrarily optional attack strategies of attacker can be obtained dynamically micro- accordingly
Divide equation.Consequence most serious under current operating conditions is not necessarily since attacker adversely affects every time to system, i.e.,
Participant need to seek satisfactory decision-making rather than optimizing decision.It establishes the dynamic differential equation group of learning model, acquires differential side
Journey stable equilibrium solution obtains Prevention-Security satisfaction strategy；Further, the step 4 includes：
For some specific defence policies SP1, the circuit ratio for choosing the strategy is the function of time, and dynamic change is fast
Rate can be represented with dynamic differential equation：
Enable SP(q)=0 solution q=0, q=1, then can be obtained,
For some specific defence policies SA1, the circuit ratio for choosing the strategy is the function of time, and dynamic change is fast
Rate can be represented with dynamic differential equation：
Enable SA(p)=0 solution p=0, p=1, then can be obtained,
It enablesThe equilibrium state that the study is played chess can be obtained.Finally it is solved to：Wherein F1Choose pure strategy S in the expression side of setting up defencesP2, attacker's selection pure strategy SA2；Wherein F2Expression is set
Anti- side chooses pure strategy SP2, attacker's selection pure strategy SA1；Wherein F3Choose pure strategy S in the expression side of setting up defencesP1, attack
Choose pure strategy S in the side of hittingA2；Wherein F1Choose pure strategy S in the expression side of setting up defencesP1, attacker's selection pure strategy SA1；Wherein F5The expression side of setting up defences is to mix probabilistic combination (M, 1-M) Selection Strategy { SP1,SP2, attacker is general to mix
Rate combination (N, 1-N) Selection Strategy { SA1,SA2}。
Play chess the dynamic differential equation that is individually present of both sides in model for study, by taking the side of setting up defences as an example, it is micro- to draw dynamic
Divide the phase diagram of equation, learn the stable equilibrium solution progress detailed analysis that model obtains of playing chess to it.
WhenAndWhen, then q is the Prevention-Security satisfaction strategy for the side of setting up defences.I.e. dynamic differential equation is bent
Line intersects with horizontal axis and tangent slope be negative point is exactly the side's of setting up defences Prevention-Security satisfaction strategy.
(1) work as p<During M, the side of setting up defences dynamic differential equation phase diagram such as Fig. 5 (1), q=0, q=1 are 2 stable states,
Based on above-mentioned analysis, q=0 is the Prevention-Security satisfaction strategy for the side of setting up defences；
(2) work as p>During M, the side of setting up defences dynamic differential equation phase diagram such as Fig. 5 (2), q=0, q=1 are 2 stable states,
Based on above-mentioned analysis, q=1 is the Prevention-Security satisfaction strategy for the side of setting up defences；
The stable equilibrium of dynamic differential equation can be obtained by the analysis for result of playing chess to study, and can be to strategy
The variation of selection mechanism is analyzed and predicted, and realizes the selection of power distribution network CPS Prevention-Securities satisfaction strategy.
The foregoing is only a preferred embodiment of the present invention, but protection scope of the present invention be not limited to
This, any one skilled in the art in the technical scope disclosed by the present invention, according to the technique and scheme of the present invention
And its inventive concept is subject to equivalent substitution or change, should be covered by the protection scope of the present invention.
Claims (4)
1. a kind of power distribution network CPS safety defense methods based on bounded rationality, it is characterised in that include the following steps：
S1：Power grid multi-source data information is obtained, is used for describing the value-at-risk of each circuit from physical system and information system foundation
Power grid risk assessment model, wherein power grid multi-source data include meteorological data, Distribution Network Equipment data, power distribution network operation data,
Residence time, average reaction time and the mean repair time of history attacker；
S2：Power distribution network CPS is built according to the risk evaluation result of circuit each in power grid and attacks the learning model M that sets up defences against；Wherein
The model is built to include building attacker's type space set, the side's of setting up defences type space set, attacker's set of strategies, the side of setting up defences
Set of strategies, participant play chess Efficiency set and participant plays chess probability set；
S3：For attacker choose strategy according to participant play chess probability set selection set up defences strategy omit, respectively from economic benefit
Each benefit value of setting up defences for attacking strategy pair of setting up defences is obtained with safety, the side of setting up defences is obtained using logarithm synthetic method and takes difference
Final expected utility and average benefit when tactful；
S4：The circuit ratio that strategy of specifically setting up defences for some slightly chooses the strategy is the function of time, with dynamic differential side
Journey represents its dynamic change rate, establishes the dynamic differential equation group of learning model, acquires differential equation stable equilibrium solution
Obtain Prevention-Security satisfaction strategy.
2. a kind of power distribution network CPS safety defense methods based on bounded rationality according to claim 1, feature also exist
In：Power distribution network CPS described in S2 attacks the learning model M that sets up defences against, and can be expressed as four-tuple, i.e. M=(N, S, B, P), N=
(NA, NP) it is the participant space pair of learning model of playing chess, wherein, NAFor attacker's type space set, NPFor the side's of setting up defences type
Spatial aggregation；S=(SA, SP) it is participant's set of strategies pair, SA={ SA1, SA2, SAn, n ∈ N and n >=2 represent attackers' strategy
Collection, SP={ SP1, SP2, SPnRepresent the side's of setting up defences set of strategies；B=(BA, BP) it is that participant plays chess Efficiency set, by all participants'
Strategy codetermines；P=(p, q) is that participant plays chess probability set, piRepresent that attacker selects attack strategies SAiProbability, qjTable
Show that the side of setting up defences selects the tactful S that sets up defencesPiProbability.
3. a kind of power distribution network CPS safety defense methods based on bounded rationality according to claim 1, feature also exist
In：In S3 specifically in the following way：
S31：Played chess using Different Strategies, obtain corresponding economic benefit matrix and safety matrix：
Wherein, aij、bijRepresent that attacker and the side of setting up defences take S respectivelyAi、SPjWhen economic benefit, cij、dijAttack is represented respectively
Side and the side of setting up defences take SAi、SPjWhen safety, n, m represent element number in the side of setting up defences and attacker's set of strategies respectively；
S32：For the side of setting up defences, policymaker is with different probability qiS is omited to each strategy of setting up defencesPiIt is chosen, for entire plan
Slightly collection meets condition：Equally, attacker policymaker is with different Probability psiTo each attack strategies SAiIt is chosen,
Entire set of strategies is met：Calculate the side's of setting up defences difference set up defences strategy economic benefit expected revenusIt is and its flat
Equal income
Calculate the side's of setting up defences difference set up defences strategy safety expected revenusAnd its average yield
Using logarithm synthetic method calculate the side's of setting up defences difference set up defences strategy synthesis expected revenusWith comprehensive average yield
4. a kind of power distribution network CPS safety defense methods based on bounded rationality according to claim 1, feature also exist
In：S4 specifically uses following scheme：
S41：For the optional strategy that strategy of setting up defences slightly is concentrated, choose Different Strategies circuit ratio will over time and
It changes, uses qi(t) it represents, wherein, qi(t) it represents to select the strategy summary S that sets up defencesPiCircuit ratio, and meet
Attacker chooses the circuit ratio dynamic change at any time of Different Strategies, uses pi(t) it is indicated, wherein, pi(t) meet
S42：For some specific defence policies SPi, the circuit ratio for choosing the strategy is the function of time, and dynamic change is fast
Rate is represented with dynamic differential equation：
Wherein λiRepresent the random variability using the tactful i that sets up defences, kαiFor strength factor；
For the arbitrary optional attack strategies S of attackerAiObtain corresponding dynamic differential equation：
Wherein ρiRepresent the random variability using attack strategies i, kβiFor strength factor；
S42：It enablesStable equilibrium solution is acquired, obtains Prevention-Security satisfaction strategy, that is, setting up defences can
Enough successful most simple strategies of defence；By drawing the phase diagram of dynamic differential equation, point of power distribution network Prevention-Security strategy is realized
Analysis and prediction.
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| CN109299160A (en) * | 2018-10-30 | 2019-02-01 | 东北大学 | A kind of electric power CPS Safety Analysis Method excavated based on monitoring big data |
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| CN111563330A (en) * | 2020-05-07 | 2020-08-21 | 东北大学 | Information physical system security optimization analysis method based on zero sum game strategy |
| CN111563330B (en) * | 2020-05-07 | 2023-08-04 | 东北大学 | Information physical system security optimization analysis method based on zero and game countermeasures |
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| CN112688315A (en) * | 2020-12-16 | 2021-04-20 | 国网辽宁省电力有限公司经济技术研究院 | Attack and defense system and method based on electric vehicle power distribution network information physical system |
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