CN102945315B - Consider the totally digitilized reliability of relay protection appraisal procedure of software failure and human failure - Google Patents
Consider the totally digitilized reliability of relay protection appraisal procedure of software failure and human failure Download PDFInfo
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Abstract
Consider totally digitilized reliability of relay protection system and the appraisal procedure of software failure and human failure, belong to relay protection of power system reliability field.System comprises hardware reliability system, software reliability system and artificial reliability system, wherein loses efficacy in arbitrary system, and reliability of relay protection system all can be caused to occur losing efficacy.Set up totally digitilized relay protection hardware reliability system, software reliability and artificial reliability system; Set up the Markov state space of described system; According to Markov system-computed system availability.The plateau probability sum of system normal condition is system availability.Contemplated by the invention the software and human failure that affect reliability of relay protection; establish the reliability of relay protection system and appraisal procedure that effectively can simulate digital relay protection system state transfer case; solve existing system only considers protection hardware failure from protective device angle, do not consider other factors of protection reliability.
Description
Technical field
The present invention relates to a kind of method of reliability of relay protection system and assessment, especially one relates to totally digitilized relay protection
Belief system and appraisal procedure, belong to relay protection of power system reliability field.
Background technology
Protective relaying device, as the first line of defence of electric system, has decisive role in guarantee electric power netting safe running.Guarantee that the reliability of protective relaying device is one of important content ensureing power network safety operation.Along with the digital improvement of transformer station is upgraded, 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, and thus Markov state-space method is usually used in the Reliability modeling of relay protection system.
At present, the relay protection Markov system of foundation, just for conventional relay protection system.In system, relay protection system is seen as an element, just by considering that maintenance, self-inspection, primary equipment state, relaying configuration scheme etc. carry out continuous refinement state space, thus simulates the actual transfer process of relay protection system state better.
In fact, totally digitilized relay protection contains more electronic installation, can be divided into different operating unit according to function, and being regarded as an element can not simulating actual conditions very well to carry out modeling.Meanwhile, existing model only considered hardware failure, cannot simulation softward and human factor on the impact of system reliability.And in fact, in 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 Logarithmicexponential system of John D.Musa is a kind of software reliability system of widespread use, the function that lost efficacy in system occurs and exponential taper with inefficacy.The thought of exponential taper is: the reduction effect of inefficacy to inefficacy function of the failure ratio discovery in late period of early detection is large.
2) the basic object of personnel encourages is the impact that the misdeed of quantitative evaluation people causes system.Personnel encourages develops into nearly 20 kinds of analytical approachs at present, as the THERP method of Swain A.D, the HEART method of Humphreys P, the HCR method etc. of Spurgin A.J, wherein, most widely used is human error rate forecasting techniques (THERP) and personnel's Cognitive Reliability (HCR) systems technology.(e.g., Zhang Jingjing, Ding Ming, " 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: HCR system is when analyzing human reriability, based on cognitive psychology, the dynamic cognitive process of research people under emergent sight emphatically, comprise detect, break, the intentional behavior such as decision-making, probe into the error mechanism of people and set up system.Personnel's crash rate that in system, human error causes obeys Weibull distribution, obtains Weibull distribution parameters just can obtain personnel's crash rate by matching.(e.g., Wang Hongde, " studying based on the human error in operation of Cognitive Reliability (HCR) system of people " [J], " China Safety Science journal ", 2006,16 (7).）
Summary of the invention
The research object that the present invention is directed to the assessment of existing reliability of relay protection is GPF (General Protection False; the hardware failure of protection is only considered from the angle of protective device; and do not consider other factors of protection reliability, thus cannot simulate digital relay protection system practical operation situation.Digital relay protection system is divided into different operating unit according to function from system-level angle by the present invention; consider the software and human failure that affect reliability of relay protection, establish the reliability of relay protection system and appraisal procedure that effectively can simulate digital relay protection system state transfer case.
Main contents of the present invention comprise:
1) totally digitilized relay protection system hardware reliability system is set up;
2) totally digitilized relay protection system software reliability and artificial reliability system is set up;
3) the Markov state space of all-digital protection system is set up;
4) according to Markov system-computed system availability.
Consider a totally digitilized reliability of relay protection system for 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 reflecting hardware failure rule that totally digitilized relay protection hardware configuration is set up;
Total digitalization relay protection software reliability system, this system is for totally digitilized relay protection system software failure, a kind of belief system set up in conjunction with Software failure modes;
Total digitalization relay protection artificial reliability system, this system is that the totally digitilized relay protection caused for human factor was lost efficacy, in conjunction with a kind of belief system of human failure Model Establishment;
There are hardware failure, software failure and human failure three kinds of failure modes in total digitalization relay protection, forms by hardware reliability system, software reliability system and artificial reliability system the totally digitilized relay protection system belief system considering software and human failure based on Markov state space theory;
Hardware reliability system, software reliability system and artificial reliability system three are separate; wherein lost efficacy in arbitrary system; capital causes reliability of relay protection system to occur losing efficacy, and hardware reliability system, software reliability system and artificial reliability system form reliability of relay protection system jointly.
Described a kind of totally digitilized relay protection system belief system and reliability estimation method considering software and human failure; it is characterized in that the Markov system considering software and human failure; specifically relay protection system was lost efficacy and be divided into hardware, software and human failure; set up hardware, software and human failure system respectively, thus 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; namely mutual inductor unit, mutual inductor are to the secondary circuit of protective device, protective device unit and protective device to secondary circuit four parts of isolating switch, and its crash rate estimated respectively by handbook to adopt reliability of electronic equipment to estimate.
Described totally digitilized relay protection software reliability and artificial reliability system, adopt Logarithmic exponential system to study the reliability of protection software particularly, software failure rate is λ (u)=λ
0e
-θ u; Adopting the Cognitive Reliability systems technology of HCR(people) 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 write thrashing state; determine the state transfer relationship of each state, set up the Markov state space of system based on Markov process.By system state space, row write state-transition matrix, and set up state transition equation, solving state equation of transfer obtains plateau probability, and the plateau probability sum of system normal condition is system availability.
Contemplated by the invention the software and human failure that affect reliability of relay protection, establish the reliability of relay protection system and appraisal procedure that effectively can simulate digital relay protection system state transfer case.Solve existing system only considers protection hardware failure from the angle of protective device, and do not consider other factors of protection reliability.
Accompanying drawing explanation
Fig. 1 is the inventive method process flow diagram.
Fig. 2 is relay protection system hardware reliability system unit module schematic diagram.
Fig. 3 is the state space graph of all-digital protection system.
Embodiment
Below in conjunction with accompanying drawing, preferred embodiment is elaborated.It is emphasized that following explanation is only exemplary, instead of in order to limit the scope of the invention and apply.
Consider a totally digitilized reliability of relay protection system for 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 reflecting hardware failure rule that totally digitilized relay protection hardware configuration is set up;
Total digitalization relay protection software reliability system, this system is for totally digitilized relay protection system software failure, a kind of belief system set up in conjunction with Software failure modes;
Total digitalization relay protection artificial reliability system, this system is that the totally digitilized relay protection caused for human factor was lost efficacy, in conjunction with a kind of belief system of human failure Model Establishment;
There are hardware failure, software failure and human failure three kinds of failure modes in total digitalization relay protection, forms by hardware reliability system, software reliability system and artificial reliability system the totally digitilized relay protection system belief system considering software and human failure based on Markov state space theory;
Hardware reliability system, software reliability system and artificial reliability system three are separate; wherein lost efficacy in arbitrary system; capital causes reliability of relay protection system to occur losing efficacy, and hardware reliability system, software reliability system and artificial reliability system form reliability of relay protection system jointly.
Fig. 1 is a kind of all-digital protection reliability estimation method process flow diagram considering software failure and human failure.In Fig. 1, by setting up hardware reliability system, software reliability and artificial reliability system respectively, obtain the Markov system of all-digital protection, the process realizing 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 schematic 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, namely mutual inductor unit, mutual inductor are to the secondary circuit of protective device, protective device unit and protective device to secondary circuit four parts of isolating switch.
1) mutual inductor unit: general employing electromagnetic type current-voltage transformer in conventional substation, general employing electronic mutual inductor or optical transformer in digital transformer substation.
2) secondary circuit 1: in conventional substation, adopts cable point to point connect between mutual inductor and protective device, transmission current voltage sample value.In digital transformer substation, there are two kinds of different modes, some employing fiber optic point connect point mode, some employing group of switches net modes, 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 is substantially identical at software section relay protective scheme computing module.
4) secondary circuit 2: in conventional substation, adopts cable point to point connect between protective device and isolating switch go, transmission trip signal.The employing fiber optic point had in digital transformer substation is to point mode, and some employing group of switches net modes, transmit trip signal.
If only consider the crash rate of electronic devices and components random failure type.According to the feature of electronic devices and components each in mechanical and electrical protection system, handbook carries out reliability estimation to adopt reliability of electronic equipment to estimate, crash rate formula is:
λ
i=(C
1π
Tπ
V+C
2π
E)π
Lπ
Q
λ=∑λ
i
In formula, λ i is the crash rate of components and parts; λ is the crash rate of all components and parts in electronic equipment; C1 is circuit complexity coefficient; π T is temperature acceleration factor; π V is that voltage stress subtracts and answers coefficient; C2 is the complexity factor based on encapsulation situation; π E is facility environment coefficient; π L is components and parts mature coefficient; π Q is component quality equivalent coefficient.
Step 2: set up totally digitilized relay protection software reliability and artificial reliability system.
The factor affecting protective relaying device software reliability mainly contains the following aspects:
1) software structure design imperfection: do not consider comprehensive etc. to situation;
2) input problem: mistake input is accepted, correct input is rejected;
3) problem is exported: export not exclusively, omit, grammar issue etc.;
4) test lack of standardization.
According to the feature of Microcomputer Protection software, Logarithmic exponential system is adopted to study the reliability of protection software.The crash rate that can be obtained software by this system is:
λ(u)=λ
0e
-θu
In formula,
λ 0 is primary fault probability; θ is fault slip coefficient; U is the accumulative mistake found in system cloud gray model.
Compared with GPF (General Protection False device, totally digitilized protective relaying device software does not have too large change substantially at relay protective scheme calculating section.
The basic object of personal reliability is the impact that the misdeed of quantitative evaluation people causes system.Personal reliability develops into nearly 20 kinds of analytical approachs at present.Choose the Cognitive Reliability systems technology of HCR(people herein) Weibull Distribution method carries out personnel's crash rate and quantitatively calculates, then and personnel's crash rate is:
λ
p=exp{-[(t/T
1/2)/η]
β}
In formula, t is the response time; T1/2 is the Median Time that personnel complete that this time operation is used; 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
From above formula, personnel's crash rate be obtained, only need determine η and β.We think that the lost efficacy protection system tripping that causes of personnel is identical with the probability of malfunction.
Step 3: the Markov state space setting up all-digital protection system.
Software failure rate is λ 1, and repair rate is μ 1.Human factor crash rate is λ 2, and the failure rate of repair rate loop 1, protective device, each cell failure of secondary circuit 2 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 by the repair rate that self-inspection is measured.Hardware failure can be respectively out c1, c2, c3, c4 by self-monitoring probability and represent.
The state that protection system work is possible thus has:
State 0: whole four unit are all normal;
State 1: software failure;
State 2: human factor;
State 3: mutual inductor occurs can not by the fault of self-inspection, and remaining element is normal;
State 4: mutual inductor occurs can by the fault of self-inspection, and remaining element is normal;
State 5: secondary circuit 1 occurs can not by the fault of self-inspection, and remaining element is normal;
State 6: secondary circuit 1 occurs can by the fault of self-inspection, and remaining element is normal;
State 7: protective device occurs can not by the hardware fault of self-inspection, and remaining element is normal;
State 8: protective device occurs can by the hardware fault of self-inspection, and remaining element is normal;
State 9: secondary circuit 2 occurs can not by the fault of self-inspection, and remaining element is normal;
State 10: secondary circuit 2 occurs can by the fault of self-inspection, and remaining element is normal;
The state space graph of all-digital protection system is obtained, as shown in Figure 3 by above state classification.Fig. 3 is the state space graph of all-digital protection system.
Step 4: according to Markov system-computed system availability.
By state space graph can the transition matrix of this system be:
In transition matrix:
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
Solve:
P
0be protection system availability.
System unreliable degree P
P=1-P
0
Contemplated by the invention the software and human failure that affect reliability of relay protection, establish the reliability of relay protection system and appraisal procedure that effectively can simulate digital relay protection system state transfer case.Solve existing system only considers protection hardware failure from the angle of protective device, and do not consider other factors of protection reliability.
The above; be only the present invention's preferably embodiment, but protection scope of the present invention is not limited thereto, is anyly familiar with those skilled in the art in the technical scope that the present invention discloses; the change 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 (2)
1. consider a totally digitilized reliability of relay protection system for software failure and human failure, it 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 reflecting hardware failure rule that totally digitilized relay protection hardware configuration is set up;
Total digitalization relay protection software reliability system, this system is for totally digitilized relay protection system software failure, a kind of belief system set up in conjunction with Software failure modes;
Total digitalization relay protection artificial reliability system, this system is that the totally digitilized relay protection caused for human factor was lost efficacy, in conjunction with a kind of belief system of human failure Model Establishment;
There are hardware failure, software failure and human failure three kinds of failure modes in total digitalization relay protection, forms by hardware reliability system, software reliability system and artificial reliability system the totally digitilized relay protection system belief system considering software and human failure based on Markov state space theory;
Hardware reliability system, software reliability system and artificial reliability system three are separate, wherein lost efficacy in arbitrary system, capital causes reliability of relay protection system to occur losing efficacy, and hardware reliability system, software reliability system and artificial reliability system form reliability of relay protection system jointly;
Described totally digitilized relay protection hardware reliability system comprises: mutual inductor unit, mutual inductor are to the secondary circuit of protective device, protective device unit and protective device to secondary circuit four parts of isolating switch:
1) mutual inductor unit: general employing electromagnetic type current-voltage transformer in conventional substation, general employing electronic mutual inductor or optical transformer in digital transformer substation;
2) secondary circuit 1: in conventional substation, adopts cable point to point connect between mutual inductor and protective device, transmission current voltage sample value; In digital transformer substation, there are two kinds of different modes, fiber optic point connects or group of switches net mode point mode, transmission current voltage sample value;
3) protective device unit: protective device unit is the body of relay protection;
4) secondary circuit 2: in conventional substation, adopts cable point to point connect between protective device and isolating switch go, transmission trip signal; In digital transformer substation, adopt fiber optic point to point mode or group of switches net mode, transmission trip signal;
If only consider the crash rate of electronic devices and components random failure type, according to the feature of electronic devices and components each in mechanical and electrical protection system, handbook carries out reliability estimation to adopt reliability of electronic equipment to estimate, crash rate formula is:
λ
i＝(C
1π
Tπ
V+C
2π
E)π
Lπ
Q
λ＝∑λ
i
In formula, λ i is the crash rate of components and parts; λ is the crash rate of all components and parts in electronic equipment; C1 is circuit complexity coefficient; π T is temperature acceleration factor; π V is that voltage stress subtracts and answers coefficient; C2 is the complexity factor based on encapsulation situation; π E is facility environment coefficient; π L is components and parts mature coefficient; π Q is component quality equivalent coefficient;
Described totally digitilized relay protection software reliability system adopts Logarithmic exponential system to study the reliability of protection software, and the crash rate that can be obtained software by this system is:
λ(u)＝λ
0e
-θu，
In formula, λ 0 is primary fault probability; θ is fault slip coefficient; U is the accumulative mistake found in system cloud gray model;
The basic object of personal reliability is the impact that the misdeed of quantitative evaluation people causes system;
Choose personnel's Cognitive Reliability system (HCR) Weibull Distribution method to 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 formula, t is the response time; T1/2 is the Median Time that personnel complete that this time operation is used; η, β are yardstick and the form parameter of cognitive behavior system;
Pass between variable is:
η＝1/(ln 2)
1/β
T
1/2＝η(ln 2)
1/β
From above formula, personnel's crash rate be obtained, only need determine η and β;
The person's of making us protection system tripping caused of losing efficacy is identical with the probability of malfunction;
In total digitalization relay protection system belief system, software failure rate is λ 1, software failure repair rate is μ 1, human factor crash rate is λ 2, human factor repair rate is μ 2, mutual inductor, secondary circuit 1, protective device, the failure rate of each cell failure of secondary circuit 2 is respectively λ 3, λ 4, λ 5, λ 6, described each unit occurs to be respectively μ 3 by the fault restoration rate of self-inspection, μ 5, μ 7, μ 9, described each unit occurs to be respectively μ 4 by the fault restoration rate of self-inspection, μ 6, μ 8, μ 10, the hardware failure of described each unit can be used c1 respectively by the probability of self-inspection, c2, c3, c4 represents,
The 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 by the fault of self-inspection, and remaining element is normal;
State 4: mutual inductor occurs can by the fault of self-inspection, and remaining element is normal;
State 5: secondary circuit 1 occurs can not by the fault of self-inspection, and remaining element is normal;
State 6: secondary circuit 1 occurs can by the fault of self-inspection, and remaining element is normal;
State 7: protective device occurs can not by the hardware fault of self-inspection, and remaining element is normal;
State 8: protective device occurs can by the hardware fault of self-inspection, and remaining element is normal;
State 9: secondary circuit 2 occurs can not by the fault of self-inspection, and remaining element is normal;
State 10: secondary circuit 2 occurs can by the fault of self-inspection, and remaining element is normal;
The state space graph of all-digital protection system is obtained by above state classification.
2. consider an appraisal procedure for 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, namely mutual inductor unit, mutual inductor are to the secondary circuit of protective device, protective device unit and protective device to secondary circuit four parts of isolating switch:
1) mutual inductor unit: general employing electromagnetic type current-voltage transformer in conventional substation, general employing electronic mutual inductor or optical transformer in digital transformer substation;
2) secondary circuit 1: in conventional substation, adopts cable point to point connect between mutual inductor and protective device, transmission current voltage sample value; In digital transformer substation, there are two kinds of different modes, fiber optic point connects or group of switches net mode point mode, transmission current voltage sample value;
3) protective device unit: protective device unit is the body of relay protection;
4) secondary circuit 2: in conventional substation, adopts cable point to point connect between protective device and isolating switch go, transmission trip signal; In digital transformer substation, adopt fiber optic point to point mode or group of switches net mode, transmission trip signal;
If only consider the crash rate of electronic devices and components random failure type, according to the feature of electronic devices and components each in mechanical and electrical protection system, handbook carries out reliability estimation to adopt reliability of electronic equipment to estimate, crash rate formula is:
λ
i＝(C
1π
Tπ
V+C
2π
E)π
Lπ
Q
λ＝∑λ
i
In formula, λ i is the crash rate of components and parts; λ is the crash rate of all components and parts in electronic equipment; C1 is circuit complexity coefficient; π T is temperature acceleration factor; π V is that voltage stress subtracts and answers coefficient; C2 is the complexity factor based on encapsulation situation; π E is facility environment coefficient; π L is components and parts mature coefficient; π Q is 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 reliability of protection software, the crash rate that can be obtained software by this system is:
λ(u)＝λ
0e
-θu，
In formula, λ 0 is primary fault probability; θ is fault slip coefficient; U is the accumulative mistake found in system cloud gray model;
The basic object of personal reliability is the impact that the misdeed of quantitative evaluation people causes system;
Choose personnel's Cognitive Reliability system (HCR) Weibull Distribution method to 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 formula, t is the response time; T1/2 is the Median Time that personnel complete that this time operation is used; η, β are yardstick and the form parameter of cognitive behavior system;
Pass between variable is:
η＝1/(ln 2)
1/β
T
1/2＝η(ln 2)
1/β
From above formula, personnel's crash rate be obtained, only need determine η and β;
The person's of making us protection system tripping caused of losing efficacy is identical with the probability of malfunction;
Step 3: 10 the state Markov state spaces setting up all-digital protection system
Software failure rate is λ 1; software failure repair rate is μ 1; human factor crash rate is λ 2; human factor repair rate is μ 2; the failure rate of mutual inductor, secondary circuit 1, protective device, each cell failure of secondary circuit 2 is respectively λ 3, λ 4, λ 5, λ 6; described each unit occurs to be respectively μ 3, μ 5, μ 7, μ 9 by the fault restoration rate of self-inspection; described each unit occurs to be respectively μ 4, μ 6, μ 8, μ 10 by the fault restoration rate of self-inspection; the hardware failure of described each unit can be represented with c1, c2, c3, c4 respectively by the probability of self-inspection
Protection system work 10 states have thus:
State 0: whole four unit are all normal;
State 1: software failure;
State 2: human factor;
State 3: mutual inductor occurs can not by the fault of self-inspection, and remaining element is normal;
State 4: mutual inductor occurs can by the fault of self-inspection, and remaining element is normal;
State 5: secondary circuit 1 occurs can not by the fault of self-inspection, and remaining element is normal;
State 6: secondary circuit 1 occurs can by the fault of self-inspection, and remaining element is normal;
State 7: protective device occurs can not by the hardware fault of self-inspection, and remaining element is normal;
State 8: protective device occurs can by the hardware fault of self-inspection, and remaining element is normal;
State 9: secondary circuit 2 occurs can not by the fault of self-inspection, and remaining element is normal;
State 10: secondary circuit 2 occurs can by the fault of self-inspection, and remaining element is normal;
The state space graph of all-digital protection system is obtained by above state classification;
Step 4: according to Markov system-computed system availability
By 10 state space graphs can the transition matrix of this system be:
In transition matrix:
System is at the plateau probability of 10 states:
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
Solve:
P
0be protection system availability,
System unreliable degree P:
P＝1-P
0。
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|---|---|---|---|---|
| CN103197172A (en) * | 2013-03-05 | 2013-07-10 | 华北电力大学 | Direct current protection system reliability assessment method in 'two from three' mode |
| CN103198219A (en) * | 2013-04-03 | 2013-07-10 | 中国南方电网有限责任公司超高压输电公司广州局 | Time varying failure rate estimation method of relay protection device and based on failure mode distinction and norm distribution |
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| CN103809119B (en) | 2013-11-26 | 2016-05-18 | 中国矿业大学 | The quantitative evaluating method of Markov model switched reluctance motor system reliability |
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| CN104915558B (en) * | 2015-06-05 | 2018-05-04 | 工业和信息化部电子第五研究所 | MEMS reliability estimation methods |
| CN107730070B (en) * | 2017-08-28 | 2021-06-08 | 国家电网公司 | Intelligent substation relay protection system maintenance method based on state monitoring |
| CN108122007B (en) * | 2017-12-20 | 2022-04-01 | 西安航空学院 | Establishment and discrimination method of forced shutdown model based on human factors |
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