CN102945315A - Fully-digital relay protection reliability system based on software failure and human failure, and evaluation method of system - Google Patents

Fully-digital relay protection reliability system based on software failure and human failure, and evaluation method of system Download PDF

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CN102945315A
CN102945315A CN2012104120018A CN201210412001A CN102945315A CN 102945315 A CN102945315 A CN 102945315A CN 2012104120018 A CN2012104120018 A CN 2012104120018A CN 201210412001 A CN201210412001 A CN 201210412001A CN 102945315 A CN102945315 A CN 102945315A
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reliability
relay protection
failure
software
state
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CN102945315B (en
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薛安成
王宝
罗麟
王睿琛
毕天姝
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North China Electric Power University
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North China Electric Power University
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Abstract

The invention relates to a fully-digital relay protection reliability system based on software failure and human failure, and an evaluation method of the system, and belongs to the field of relay protection reliability of power systems. The fully-digital relay protection reliability system comprises a hardware reliability system, a software reliability system and a human reliability system, and when a failure occurs in any one of the hardware reliability system, the software reliability system and the human reliability system, the fully-digital relay protection reliability system fails to work. The evaluation method comprises the following steps: establishing the hardware reliability system, the software reliability system and the human reliability system for the fully-digital relay protection reliability system; establishing a Markov state space of the fully-digital relay protection reliability system; and calculating the availability of the fully-digital relay protection reliability system according to a Markov system. The sum of the probabilities of steady state of the fully-digital relay protection reliability system in the normal state is the system availability. By considering the software and human failures which influence the relay protection reliability, the relay protection reliability system capable of effectively simulating the condition of state transition of the fully-digital relay protection system, and the evaluation method are established, and the problem that the conventional system considers the hardware failure in protection only from a perspective of the protective device without considering other factors of protection reliability is solved.

Description

Consider the totally digitilized reliability of relay protection appraisal procedure of software failure and human failure
Technical field
The present invention relates to the method for a kind of reliability of relay protection system and assessment, especially a kind ofly relate to totally digitilized relay protection
Belief system and appraisal procedure belong to relay protection of power system reliability field.
Background technology
Protective relaying device has decisive role as the first line of defence of electric system aspect the guarantee electric power netting safe running.The reliability of guaranteeing protective relaying device is one of important content that ensures power network safety operation.Along with the digital improvement upgrading of transformer station, totally digitilized relay protection just progressively replaces GPF (General Protection False and is widely used.
The method of research reliability of relay protection has the methods such as Monte Carlo (Monte Carlo) simulation, network technique, Fault Tree and Markov state-space method.Relay protection is recoverable system, and such system can describe with Markov process, thereby the Markov state-space method is usually used in the Reliability modeling of relay protection system.
At present, the relay protection Markov system of foundation is just for conventional relay protection system.In the system, relay protection system is regarded as an element, just comes continuous refinement state spaces by consideration maintenance, self check, primary equipment state, protection allocation plan etc., thereby simulates better the actual transfer process of relay protection system state.
In fact, totally digitilized relay protection has comprised more electronic installation, can be divided into the different operating unit according to function, with its regard as an element carry out modeling can not fine simulating actual conditions.Simultaneously, existing model has only been considered hardware failure, can't simulation softward and human factor on the impact of system reliability.And in fact, in the relay protection device operational process, except the hardware failure that electronic installation brings, software and human factor also may cause the stoppage in transit of relay protection device.
1) Logarithmic exponential system: the Logarithmic exponential system of John D.Musa is a kind of software reliability system of widespread use, and the inefficacy function occured and exponential taper with losing efficacy in the system.The thought of exponential taper is: the inefficacy of finding failure ratio late period of early detection to the inefficacy function to reduce effect large.
2) human reliability to analyze basic purpose be the impact that the behavior of quantitative evaluation human error causes system.The human reliability analyzes to develop into nearly 20 kinds of analytical approachs at present, THERP method such as Swain A.D, the HEART method of Humphreys P, the HCR method of Spurgin A.J etc., wherein, most widely used is human error rate forecasting techniques (THERP) and personnel's Cognitive Reliability (HCR) systems technology.(as, Zhang Jingjing, fourth is bright, " human error is on the impact of protection system reliability ", [J], " Automation of Electric Systems ", 2012,36 (8))
3) personnel's Cognitive Reliability system (HCR) technology Weibull Distribution method: the HCR system is when analyst's reliability, take cognitive psychology as the basis, study emphatically the dynamic cognitive process of people under emergent sight, comprise detect, break, the intentional behavior such as decision-making, probe into people's error mechanism and set up system.Personnel's crash rate that human error causes in the system is obeyed Weibull distribution, obtains Weibull distribution parameters by match and just can obtain personnel's crash rate.(such as, Wang Hongde, " based on the human error in operation research of people's Cognitive Reliability (HCR) system " [J], " China Safety Science journal ", 2006,16 (7).)
Summary of the invention
The research object that the present invention is directed to existing reliability of relay protection assessment is GPF (General Protection False; only considered the hardware failure of protection from the angle of protective device; and do not consider other factors of protection reliability, thereby can't simulate digital relay protection system practical operation situation.The present invention is divided into different operating unit with digital relay protection system according to function from system-level angle; consider to affect software and the human failure of reliability of relay protection, set up reliability of relay protection system and the appraisal procedure that effectively to simulate digital relay protection system state transitions situation.
Main contents of the present invention comprise:
1) sets up totally digitilized relay protection system hardware reliability system;
2) set up totally digitilized relay protection system software reliability and artificial reliability system;
3) set up the Markov state space of all-digital protection system;
4) according to Markov system-computed system availability.
A kind of totally digitilized reliability of relay protection system that considers software failure and human failure, described reliability of relay protection system comprises:
Total digitalization relay protection hardware reliability system, this system is for totally digitilized relay protection hardware failure, based on a kind of belief system that reflects the hardware failure rule of totally digitilized relay protection hardware configuration foundation;
Total digitalization relay protection software reliability system, this system is for totally digitilized relay protection system software failure, a kind of belief system of setting up in conjunction with Software failure modes;
Total digitalization relay protection artificial reliability system, this system lost efficacy for the totally digitilized relay protection that human factor causes, in conjunction with a kind of belief system of human failure Model Establishment;
The total digitalization relay protection exists hardware failure, software failure and three kinds of failure modes of human failure, consists of the totally digitilized relay protection system belief system of considering software and human failure based on the Markov state space theory by hardware reliability system, software reliability system and artificial reliability system;
Hardware reliability system, software reliability system and the three of artificial reliability system are separate; wherein lost efficacy in arbitrary system; the capital causes the reliability of relay protection system to occur losing efficacy, and hardware reliability system, software reliability system and artificial reliability system consist of the reliability of relay protection system jointly.
Described a kind of totally digitilized relay protection system belief system and reliability estimation method of considering software and human failure; it is characterized in that considering the Markov system of software and human failure; specifically relay protection system was lost efficacy and be divided into hardware, software and human failure; set up respectively hardware, software and human failure system, thereby obtain totally digitilized relay protection system belief system.
Described totally digitilized relay protection hardware reliability system; specifically totally digitilized relay protection is divided into four working cells by function; four parts of secondary circuit that are mutual inductor unit, mutual inductor to secondary circuit, protective device unit and the protective device of protective device to isolating switch adopt reliability of electronic equipment to estimate that handbook estimates respectively its crash rate.
Described totally digitilized relay protection software reliability and artificial reliability system adopt Logarithmic exponential system to study the protection reliability of software particularly, and the software failure rate is λ (u)=λ 0e -θ uAdopting HCR(people's Cognitive Reliability systems technology) the Weibull Distribution method carries out personnel's crash rate and quantitatively calculates, and personnel's crash rate is λ p=exp{-[(t/T 1/2)/η] β.
Described totally digitilized relay protection system Calculation of Availability method is combined with hardware belief system, software reliability system and artificial reliability system; row are write the thrashing state; determine the state transitions relation of each state, set up the Markov state space of system based on Markov process.By system state space, row are write state-transition matrix, set up state transition equation, and the solving state equation of transfer obtains the plateau probability, and the plateau probability sum of system's normal condition is system availability.
The present invention has considered to affect software and the human failure of reliability of relay protection, has set up reliability of relay protection system and the appraisal procedure that can effectively simulate digital relay protection system state transitions situation.Solve existing system and only considered the hardware failure of protection from the angle of protective device, and do not considered other factors of protection reliability.
Description of drawings
Fig. 1 is the inventive method process flow diagram.
Fig. 2 is relay protection system hardware reliability system unit module diagram.
Fig. 3 is the state space graph of all-digital protection system.
Embodiment
Below in conjunction with accompanying drawing, preferred embodiment is elaborated.Should be emphasized that following explanation only is exemplary, rather than in order to limit the scope of the invention and to use.
A kind of totally digitilized reliability of relay protection system that considers software failure and human failure, this reliability of relay protection system comprises:
Total digitalization relay protection hardware reliability system, this system is for totally digitilized relay protection hardware failure, based on a kind of belief system that reflects the hardware failure rule of totally digitilized relay protection hardware configuration foundation;
Total digitalization relay protection software reliability system, this system is for totally digitilized relay protection system software failure, a kind of belief system of setting up in conjunction with Software failure modes;
Total digitalization relay protection artificial reliability system, this system lost efficacy for the totally digitilized relay protection that human factor causes, in conjunction with a kind of belief system of human failure Model Establishment;
The total digitalization relay protection exists hardware failure, software failure and three kinds of failure modes of human failure, consists of the totally digitilized relay protection system belief system of considering software and human failure based on the Markov state space theory by hardware reliability system, software reliability system and artificial reliability system;
Hardware reliability system, software reliability system and the three of artificial reliability system are separate; wherein lost efficacy in arbitrary system; the capital causes the reliability of relay protection system to occur losing efficacy, and hardware reliability system, software reliability system and artificial reliability system consist of the reliability of relay protection system jointly.
Fig. 1 is a kind of all-digital protection reliability estimation method process flow diagram of considering software failure and human failure.Among Fig. 1, by setting up respectively hardware reliability system, software reliability and artificial reliability system, obtain the Markov system of all-digital protection, realize that the process of the reliability assessment of relay protection system comprises:
Step 1: set up totally digitilized relay protection hardware reliability system.
Fig. 2 is relay protection system hardware reliability system unit module diagram.As shown in Figure 2; for conventional relay protection and totally digitilized relay protection; all can be divided into following four working cells by function, i.e. mutual inductor unit, mutual inductor four parts of secondary circuit to secondary circuit, protective device unit and the protective device of protective device to isolating switch.
1) mutual inductor unit: the general electromagnetic type current-voltage transformer that adopts in conventional substation, general electronic mutual inductor or the optical transformer of adopting in digital transformer substation.
2) secondary circuit 1: in conventional substation, adopt cable point to point connect, transmission current voltage sample value between mutual inductor and the protective device.Have two kinds of different modes in digital transformer substation, the employing fiber optic point that has connects point mode, the employing group of switches net mode that has, transmission current voltage sample value.
3) protective device: the hardware configuration of all-digital protection device is simpler than the hardware configuration of GPF (General Protection False, and is basic identical in software section protection logical calculated module.
4) secondary circuit 2: in conventional substation, adopt the cable point to point connect between protective device and isolating switch go, the transmission trip signal.The employing fiber optic point that has in digital transformer substation is to point mode, and the employing group of switches net mode that has transmits trip signal.
If only consider the crash rate of electronic devices and components random failure type.According to the characteristics of each electronic devices and components in the mechanical and electrical protection system, adopt reliability of electronic equipment to estimate that handbook carries out reliability and estimates that the crash rate formula is:
λ i=(C 1π Tπ V+C 2π ELπ Q
λ=∑λ i
In the formula, λ i is the crash rate of components and parts; λ is the crash rate of all components and parts in the electronic equipment; C1 is the circuit complexity coefficient; π T is the temperature accelerator coefficient; π V is that voltage stress subtracts and answers coefficient; C2 is the complexity factor based on the encapsulation situation; π E is the facility environment coefficient; π L is the components and parts mature coefficient; π Q is the component quality equivalent coefficient.
Step 2: set up totally digitilized relay protection software reliability and artificial reliability system.
The factor that affects the protective relaying device software reliability mainly contains the following aspects:
1) software structure design imperfection: situation is not considered comprehensive etc.;
2) input problem: mistake input is accepted, and correct input is rejected etc.;
3) output problem: output is not exclusively omitted grammer problem etc.;
4) test is lack of standardization.
According to the characteristics of Microcomputer Protection software, adopt Logarithmic exponential system to study the protection reliability of software.The crash rate that can be got software by this system is:
λ(u)=λ 0e -θu
In the formula,
λ 0 is the primary fault probability; θ is fault slip coefficient; U is the mistake that system's accumulative total in service is found.
Compare with the GPF (General Protection False device, totally digitilized protective relaying device software is in the basic not too large variation of protection logical calculated part.
The basic purpose of people's fail-safe analysis is the impact that the behavior of quantitative evaluation human error causes system.People's fail-safe analysis develops into nearly 20 kinds of analytical approachs at present.This paper chooses HCR(people's Cognitive Reliability systems technology) the Weibull Distribution method carries out personnel's crash rate and quantitatively calculates, and then personnel's crash rate is:
λ p=exp{-[(t/T 1/2)/η] β}
In the formula, t is the response time; T1/2 this time operates used Median Time for personnel finish; η, β are yardstick and the form parameter of cognitive behavior system.
Pass between variable is:
η=1/(ln2) 1/β
T 1/2=η(ln2) 1/β
By following formula as can be known, personnel's crash rate be obtain, η and β only needed to determine.We think that the lost efficacy probability of the protection system tripping that causes and malfunction of personnel is identical.
Step 3: the Markov state space of setting up all-digital protection system.
The software failure rate is λ 1, and repair rate is μ 1.The human factor crash rate is λ 2, and the failure rate of repair rate loop 1, protective device, secondary circuit 2 each cell failure is respectively μ 2.Mutual inductor, secondary are λ 3, λ 4, λ 5, λ 6, can not be respectively μ 3, μ 4, μ 5, μ 6, μ 7, μ 8, μ 9, μ 10 from detected repair rate.Hardware failure can be respectively out c1, c2 by self-monitoring probability, c3, c4 represent.
The possible state of protection system work has thus:
State 0: whole four unit are all normal;
State 1: software failure;
State 2: human factor;
State 3: mutual inductor occurs can not be by the fault of self check, and remaining element is normal;
State 4: mutual inductor occurs can be by the fault of self check, and remaining element is normal;
State 5: secondary circuit 1 occurs can not be by the fault of self check, and remaining element is normal;
State 6: secondary circuit 1 occurs can be by the fault of self check, and remaining element is normal;
State 7: protective device occurs can not be by the hardware fault of self check, and remaining element is normal;
State 8: protective device occurs can be by the hardware fault of self check, and remaining element is normal;
State 9: secondary circuit 2 occurs can not be by the fault of self check, and remaining element is normal;
State 10: secondary circuit 2 occurs can be by the fault of self check, and remaining element is normal;
Get the state space graph of all-digital protection system by above state classification, as shown in Figure 3.Fig. 3 is the state space graph of all-digital protection system.
Step 4: according to Markov system-computed system availability.
Transition matrix that can this system by state space graph is:
Figure BDA0000230331891
In the transition matrix: Z = 2 * Σ i = 3 6 λ i - Σ i = 1 4 c i λ i + 2 + λ 1 + λ 2 .
System is at the plateau probability of each state:
P(n)=[P 0,P 1,P 2,P 3,P 4,P 5,P 6,P 7,P 8,P 9,P 10]
The plateau transfering density matrix A of system
Figure BDA0000230331893
By system of equations:
P(n)·A=0
Σ 0 10 P i = 1
Solve:
P 0 = 1 1 + λ 1 μ 1 + λ 2 μ 2 + ( 1 - c 1 ) λ 3 μ 3 + λ 3 μ 4 + ( 1 - c 2 ) λ 4 μ 5 + λ 4 μ 6 + ( 1 - c 3 ) λ 5 μ 7 + λ 5 μ 8 + ( 1 - c 4 ) λ 6 μ 9 + λ 6 μ 10
P 0Be the protection system availability.
The unreliable degree P of system
P=1-P 0
The present invention has considered to affect software and the human failure of reliability of relay protection, has set up reliability of relay protection system and the appraisal procedure that can effectively simulate digital relay protection system state transitions situation.Solve existing system and only considered the hardware failure of protection from the angle of protective device, and do not considered other factors of protection reliability.
The above; only for the better embodiment of the present invention, but protection scope of the present invention is not limited to this, anyly is familiar with those skilled in the art in the technical scope that the present invention discloses; the variation that can expect easily or replacement all should be encompassed within protection scope of the present invention.Therefore, protection scope of the present invention should be as the criterion with the protection domain of claim.

Claims (6)

1. a totally digitilized reliability of relay protection system that considers software failure and human failure is characterized in that, described reliability of relay protection system comprises:
Total digitalization relay protection hardware reliability system, this system is for totally digitilized relay protection hardware failure, based on a kind of belief system that reflects the hardware failure rule of totally digitilized relay protection hardware configuration foundation;
Total digitalization relay protection software reliability system, this system is for totally digitilized relay protection system software failure, a kind of belief system of setting up in conjunction with Software failure modes;
Total digitalization relay protection artificial reliability system, this system lost efficacy for the totally digitilized relay protection that human factor causes, in conjunction with a kind of belief system of human failure Model Establishment;
The total digitalization relay protection exists hardware failure, software failure and three kinds of failure modes of human failure, consists of the totally digitilized relay protection system belief system of considering software and human failure based on the Markov state space theory by hardware reliability system, software reliability system and artificial reliability system;
Hardware reliability system, software reliability system and the three of artificial reliability system are separate; wherein lost efficacy in arbitrary system; the capital causes the reliability of relay protection system to occur losing efficacy, and hardware reliability system, software reliability system and artificial reliability system consist of the reliability of relay protection system jointly.
2. an appraisal procedure of considering the totally digitilized reliability of relay protection system of software failure and human failure is characterized in that described method comprises the following steps:
Step 1: set up totally digitilized relay protection hardware reliability system;
Based on system hardware structure, totally digitilized relay protection system is divided into four working cells by function, carry out respectively fail-safe analysis;
Step 2: set up totally digitilized relay protection system software reliability system and artificial reliability system;
In conjunction with relay protection software failure and human failure feature, set up system software belief system and artificial reliability system and come simulation softward to lose efficacy and human failure; Adopt Logarithmic exponential system to obtain the crash rate of software, set up the software reliability system, adopt personnel Cognitive Reliability systems (HCR) Weibull Distribution method to carry out personnel's crash rate and quantitatively calculate, set up the artificial reliability system;
Step 3: the Markov state space of setting up all-digital protection;
Combined with hardware belief system, software reliability system and artificial reliability system list the thrashing state, determine the state transitions relation of each state, set up the Markov state space of system based on Markov process;
Step 4: according to Markov system-computed system availability;
By system state space, row are write state-transition matrix, set up state transition equation, and the solving state equation of transfer obtains the plateau probability, and the plateau probability sum of system's normal condition is system availability.
3. a kind of appraisal procedure of considering the totally digitilized reliability of relay protection system of software failure and human failure according to claim 2; it is characterized in that; described hardware reliability system is: totally digitilized relay protection is divided into four working cells by function; four parts of secondary circuit that are mutual inductor unit, mutual inductor to secondary circuit, protective device unit and the protective device of protective device to isolating switch; adopt reliability of electronic equipment expectation handbook to estimate respectively its crash rate, obtain the hardware reliability system.
4. a kind of appraisal procedure of considering the totally digitilized reliability of relay protection system of software failure and human failure according to claim 2; it is characterized in that; described software reliability system is: adopt Logarithmic exponential system to study the protection reliability of software, the software failure rate is λ (u)=λ 0e -θ u, wherein, λ 0Be the primary fault probability; θ is fault slip coefficient; U is the mistake that system's accumulative total in service is found.
5. a kind of totally digitilized relay protection system reliability estimation method of considering software and human failure according to claim 2; it is characterized in that; described artificial reliability system is: adopt personnel Cognitive Reliability systems (HCR) Weibull Distribution method to carry out personnel's crash rate and quantitatively calculate, personnel's crash rate is λ p=exp{-[(t/T 1/2)/η] β, wherein, t is the response time; T1/2 this time operates used Median Time for personnel finish; η, β are yardstick and the form parameter of cognitive behavior system.
6. appraisal procedure of considering the totally digitilized reliability of relay protection system of software and human failure, the method comprises the steps:
Step 1: set up totally digitilized relay protection hardware reliability system
For conventional relay protection system and totally digitilized relay protection system; be divided into following four working cells by function, i.e. mutual inductor unit, mutual inductor four parts of secondary circuit to secondary circuit, protective device unit and the protective device of protective device to isolating switch:
1) mutual inductor unit: the general electromagnetic type current-voltage transformer that adopts in conventional substation, general electronic mutual inductor or the optical transformer of adopting in digital transformer substation;
2) secondary circuit 1: in conventional substation, adopt cable point to point connect, transmission current voltage sample value between mutual inductor and the protective device; Have two kinds of different modes in digital transformer substation, fiber optic point connects or the group of switches net mode point mode, transmission current voltage sample value;
3) protective device unit: the protective device unit is the body of relay protection;
4) secondary circuit 2: in conventional substation, adopt the cable point to point connect between protective device and isolating switch go, the transmission trip signal; In digital transformer substation, adopt fiber optic point to point mode or group of switches net mode, the transmission trip signal;
If only consider the crash rate of electronic devices and components random failure type, according to the characteristics of each electronic devices and components in the mechanical and electrical protection system, adopt reliability of electronic equipment to estimate that handbook carries out reliability and estimates that the crash rate formula is:
λ i=(C 1π Tπ V+C 2π ELπ Q
λ=∑λ i
In the formula, λ i is the crash rate of components and parts; λ is the crash rate of all components and parts in the electronic equipment; C1 is the circuit complexity coefficient; π T is the temperature accelerator coefficient; π V is that voltage stress subtracts and answers coefficient; C2 is the complexity factor based on the encapsulation situation; π E is the facility environment coefficient; π L is the components and parts mature coefficient; π Q is the component quality equivalent coefficient;
Step 2: set up totally digitilized relay protection system software reliability system and artificial reliability system
Adopt Logarithmic exponential system to study the protection reliability of software, the crash rate that can be got software by this system is:
λ(u)=λ 0e -θu,
In the formula, λ 0 is the primary fault probability; θ is fault slip coefficient; U is the mistake that system's accumulative total in service is found;
The basic purpose of people's fail-safe analysis is the impact that the behavior of quantitative evaluation human error causes system;
Choose personnel's Cognitive Reliability system (HCR) Weibull Distribution method and carry out personnel's crash rate and quantitatively calculate, then personnel's crash rate is:
λ p=exp{-[(t/T 1/2)/η] β},
In the formula, t is the response time; T1/2 this time operates used Median Time for personnel finish; η, β are yardstick and the form parameter of cognitive behavior system;
Pass between variable is:
η=1/(ln2) 1/β
T 1/2=η(ln2) 1/β
By following formula as can be known, personnel's crash rate be obtain, η and β only needed to determine;
The protection system tripping that the person of making us inefficacy causes is identical with the probability of malfunction;
Step 3: the Markov state space of setting up all-digital protection system
The software failure rate is λ 1; repair rate is μ 1; the human factor crash rate is λ 2; the failure rate of repair rate loop 1, protective device, secondary circuit 2 each cell failure is respectively μ 2; mutual inductor, secondary are λ 3, λ 4, λ 5, λ 6, can not be respectively μ 3, μ 4, μ 5, μ 6, μ 7, μ 8, μ 9, μ 10 from detected repair rate.Hardware failure can be respectively out c1, c2 by self-monitoring probability, c3, c4 represent,
The possible state of protection system work has thus:
State 0: whole four unit are all normal;
State 1: software failure;
State 2: human factor;
State 3: mutual inductor occurs can not be by the fault of self check, and remaining element is normal;
State 4: mutual inductor occurs can be by the fault of self check, and remaining element is normal;
State 5: secondary circuit 1 occurs can not be by the fault of self check, and remaining element is normal;
State 6: secondary circuit 1 occurs can be by the fault of self check, and remaining element is normal;
State 7: protective device occurs can not be by the hardware fault of self check, and remaining element is normal;
State 8: protective device occurs can be by the hardware fault of self check, and remaining element is normal;
State 9: secondary circuit 2 occurs can not be by the fault of self check, and remaining element is normal;
State 10: secondary circuit 2 occurs can be by the fault of self check, and remaining element is normal;
Got the state space graph of all-digital protection system by above state classification;
Step 4: according to Markov system-computed system availability
Transition matrix that can this system by state space graph is:
Figure FDA0000230331881
In the transition matrix: Z = 2 * Σ i = 3 6 λ i - Σ i = 1 4 c i λ i + 2 + λ 1 + λ 2 .
System is at the plateau probability of each state:
P(n)=[P 0,P 1,P 2,P 3,P 4,P 5,P 6,P 7,P 8,P 9,P 10]
The plateau transfering density matrix A of system
By system of equations:
P(n)·A=0
Σ 0 10 P i = 1
Solve:
P 0 = 1 1 + λ 1 μ 1 + λ 2 μ 2 + ( 1 - c 1 ) λ 3 μ 3 + λ 3 μ 4 + ( 1 - c 2 ) λ 4 μ 5 + λ 4 μ 6 + ( 1 - c 3 ) λ 5 μ 7 + λ 5 μ 8 + ( 1 - c 4 ) λ 6 μ 9 + λ 6 μ 10
P 0Be the protection system availability,
The unreliable degree P of system:
P=1-P 0
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CN113011765A (en) * 2021-03-30 2021-06-22 广东电网有限责任公司电力调度控制中心 Reliability assessment method for remotely modifying relay protection setting value
CN113076657A (en) * 2021-04-21 2021-07-06 华北电力大学 Relay protection device retirement time determination method suitable for localization of core components
CN113242570A (en) * 2021-04-26 2021-08-10 深圳供电局有限公司 Reliability evaluation method and device for uplink communication module and computer equipment
CN113255100A (en) * 2021-04-21 2021-08-13 华北电力大学 Dual relay protection reliability assessment method suitable for localization of core components

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