CN103323707A - Transformer failure rate predicating method based on half Markoff process - Google Patents

Abstract

The invention relates to a transformer failure rate predicating method based on the half Markoff process and belongs to the technical field of electrical equipment. According to the transformer failure rate predicating method based on the half Markoff process, the working state of a transformer is divided into an operation state and a failure rate, a thermal ageing process is set to be a progressive progress, the working state can be converted into the failure state directly from the operation state due to the influence of random factors, the converting progress of the failure rate of the transformer is irreversible, an adjacent matrix of a working state transition diagram of the transformer is obtained, the matrix of state transition probability of an embedded Markoff chain in the half Markoff process and the matrix of time condition probability distribution in the i state are obtained from historical operation data of a plurality of transformers, the matrix of transition probability in the half Markoff progress is solved with a numerical method, and the failure rate of the transformer is obtained through calculation. The transformer failure rate predicating method based on the half Markoff process has the advantages that the aging failure and the random failure are comprehensively considered, and the calculating structure is more practical.

Description

Transformer fault rate Forecasting Methodology based on half Markov process

Technical field

The present invention relates to a kind of transformer fault rate Forecasting Methodology based on half Markov process, belong to the electrical equipment technical field.

Background technology

Carrying out the failure rate prediction based on accurately comprehensive transformer fault model is one of Main Means of transformer fault prevention and life-span management.The fault of transformer can be divided into degradation failure and random fault, and degradation failure is because of the performance deteriorated fault that causes gradually, such as heat ageing; Random fault refers to the fault that causes because of enchancement factor, such as human factor, thunderbolt etc.In addition, existing statistics shows in the transformer fault that causes because of short-circuit impact, and approximately 70% transformer is namely to break down behind twice short-circuit impact suffering, so short-circuit impact also can be considered random fault.

Existing transformer fault model lays particular emphasis on the research of degradation failure.The principal element that transformer is aging is heat, and regardless of the residing external environment condition of transformer, Heat Ageing runs through transformer life all the time, and is considered to affect the principal element in life-span.Therefore, heat ageing is the major consideration of existing transformer fault rate forecast model.Yet in actual motion, random fault also can not be ignored, for example short-circuit impact is the first cause of China's transformer fault, can account for 50% of total number of accident, this shows, the failure process of transformer to be described comprehensively, the factor of degradation failure and random fault two aspects need to be considered.

Markov process is powerful commonly used during equipment dependability is analyzed, existing scholar has set up the failure rate forecast model of transformer based on Markov process (can be referring to document: Ning Liaoyi, Wu Wenchuan, Zhang Baiming. become outage model () during transformer in the operation risk assessment based on the failure rate method of estimation of the inner latency fault of transformer of operating condition, Automation of Electric Systems, 2010 (15): 9-13).The document is divided into one of four states based on the volume fraction of oil dissolved gas with transformer, has set up Markov model, has obtained the variation tendency of transformer fault rate.But this model is not considered random fault, and the state of dividing based on oil dissolved gas can corresponding various faults pattern, and not pointed, practical application is difficulty relatively.In addition, necessary obeys index distribution of the residence time of Markov process claimed condition, but the physical fault process of transformer does not satisfy this requirement.

Summary of the invention

The objective of the invention is to propose a kind of transformer fault rate Forecasting Methodology based on half Markov process, set up the fault model that comprises degradation failure and random fault based on half Markov process, determine the value of Model Parameter according to statistics, to overcome the deficiency of existing Markov process model, result of calculation is conformed to the transformer fault rate curve variation tendency of actual count.

The transformer fault rate Forecasting Methodology based on half Markov process that the present invention proposes may further comprise the steps:

(1) duty with transformer is divided into running status and malfunction, running status wherein, be divided into the first state according to the degree of polymerization DP of insulating paper in the transformer: the DP value is 1100-950, the second state: the DP value is 950-450, the third state: the DP value is 450-200; Malfunction wherein is divided into according to failure mode: the 4th state: the heat ageing malfunction, and the DP value is less than 200, the 5th state: the random fault that is caused by lightning impulse, the 6th state is impacted the random fault that causes by external short circuit, above-mentioned six kinds of states form a state set S={1,2,3,4,5,6}, the duty of transformer is counted m=6;

(2) impose a condition: Heat Ageing is progressive process, and the first state, the second state and the third state are because the impact of enchancement factor can be malfunction from running state conversion directly, and the transfer process of the malfunction of transformer is irreversible,

Impose a condition according to above-mentioned, the duty conversion adjacency matrix R that obtains transformer is:

$R=\left[\begin{array}{cccccc}0& 1& 0& 0& 1& 1\\ 0& 0& 1& 0& 1& 1\\ 0& 0& 0& 1& 1& 1\\ 0& 0& 0& 0& 0& 0\\ 0& 0& 0& 0& 0& 0\\ 0& 0& 0& 0& 0& 0\end{array}\right]$

Wherein, R _Ij=1(i=1,2...6; J=1,2...6) represent to have transfer relationship, R between i state and the j state _IjThere is not transfer relationship between=0 expression i state and the j state;

(3) obtain embedded markovian state transition probability matrix P and the time conditions probability distribution matrix G (t) that rests under the i state in half Markov process from the history data of many transformers, its process may further comprise the steps:

(3-1) from the history data of many transformers, obtain respectively the moment that many transformers respectively are in running status and malfunction;

(3-2) in the moment of above-mentioned running status and malfunction, obtain the transformer number of units n of first state that is in ₁, follow the tracks of this n ₁Platform transformer, and definite n ₁Have transfer relationship between i state and the j state among the duty conversion adjacency matrix R of platform transformer, namely the transformer platform number scale from the first state transitions to the second state is n ₁₂, be n from the transformer platform number scale of the first state transitions to the five states ₁₅, be n from the transformer platform number scale of the first state transitions to the six states ₁₆, according to above-mentioned transfer relationship, calculate the element among the embedded markovian state transition probability matrix P in half Markov process:

The transition probability of the first state to the second state

The transition probability of the first state to the five states

The transition probability of the first state to the six states

In the moment of above-mentioned running status and malfunction, obtain the transformer number of units n of second state that is in ₂, follow the tracks of this n ₂Platform transformer, and definite n ₂Have transfer relationship between i state and the j state among the duty conversion adjacency matrix R of platform transformer, namely the transformer platform number scale from the second state transitions to the third state is n ₂₃, be n from the transformer platform number scale of the second state transitions to the five states ₂₅, be n from the transformer platform number scale of the second state transitions to the six states ₂₆, according to above-mentioned transfer relationship, calculate the element among the embedded markovian state transition probability matrix P in half Markov process:

The second state is to the transition probability of the third state

The transition probability of the second state to the five states

The transition probability of the second state to the six states

In the moment of above-mentioned running status and malfunction, obtain being in the transformer number of units n of the third state ₃, follow the tracks of this n ₃Platform transformer, and definite n ₃Have transfer relationship between i state and the j state among the duty of the platform transformer conversion adjacency matrix R, the transformer platform number scale that namely is transferred to the 4th state from the third state is n ₃₄, the transformer platform number scale that is transferred to the 5th state from the third state is n ₃₅, the transformer platform number scale that is transferred to the 6th state from the third state is n ₃₆, according to above-mentioned transfer relationship, calculate the element among the embedded markovian state transition probability matrix P in half Markov process:

The transition probability of the third state to the four states

The transition probability of the third state to the five states

The transition probability of the third state to the six states

Then embedded markovian state transition probability matrix P is in half Markov process:

$P=\left[\begin{array}{cccccc}0& p_{12}& 0& 0& p_{15}& p_{16}\\ 0& 0& p_{23}& 0& p_{25}& p_{26}\\ 0& 0& 0& p_{34}& p_{35}& p_{36}\\ 0& 0& 0& 1& 0& 0\\ 0& 0& 0& 0& 1& 0\\ 0& 0& 0& 0& 0& 1\end{array}\right]$

(3-3) in the moment of above-mentioned running status and malfunction, obtain the transformer number of units n of first state that is in ₁, follow the tracks of this n ₁Platform transformer, and definite n ₁Have transfer relationship between i state and the j state among the duty conversion adjacency matrix R of platform transformer, namely the transformer platform number scale from the first state transitions to the second state is n ₁₂, be n from the transformer platform number scale of the first state transitions to the five states ₁₅, be n from the transformer platform number scale of the first state transitions to the six states ₁₆, according to above-mentioned transfer relationship, calculate the element among the time conditions probability distribution matrix G (t) under the first state in half Markov process:

$G_{12}\left(t_x\right)=\frac{n_{12}(t\≤t_x)}{n_{12}}$

Wherein, n ₁₂(t≤t _x) expression transfer relationship n ₁₂Be less than or equal to time t middle transfer time _xIn be in the transformer number of units of the first state, t _x=1,2...T+1, T are the transformer fault rate prediction moment;

$G_{15}\left(t_x\right)=\frac{n_{15}(t\≤t_x)}{n_{15}}$

Wherein, n ₁₅(t≤t _x) expression transfer relationship n ₁₅Be less than or equal to time t middle transfer time _xIn be in the transformer number of units of the first state;

$G_{16}\left(t_x\right)=\frac{n_{16}(t\≤t_x)}{n_{16}}$

Wherein, n ₁₆(t≤t _x) expression transfer relationship n ₁₆Be less than or equal to time t middle transfer time _xIn be in the transformer number of units of the first state;

In the moment of above-mentioned running status and malfunction, obtain the transformer number of units n of second state that is in ₂, follow the tracks of this n ₂Platform transformer, and definite n ₂Have transfer relationship between i state and the j state among the duty conversion adjacency matrix R of platform transformer, namely the transformer platform number scale from the second state transitions to the third state is n ₂₃, be n from the transformer platform number scale of the second state transitions to the five states ₂₅, be n from the transformer platform number scale of the second state transitions to the six states ₂₆, according to above-mentioned transfer relationship, calculate the element among the time conditions probability distribution matrix G (t) under the second state in half Markov process:

$G_{23}\left(t_x\right)=\frac{n_{23}(t\≤t_x)}{n_{23}}$

Wherein, n ₂₃(t≤t _x) expression transfer relationship n ₂₃Be less than or equal to time t middle transfer time _xIn be in the transformer number of units of the second state;

$G_{25}\left(t_x\right)=\frac{n_{25}(t\≤t_x)}{n_{25}}$

Wherein, n ₂₅(t≤t _x) expression transfer relationship n ₂₅Be less than or equal to time t middle transfer time _xIn be in the transformer number of units of the second state;

$G_{26}\left(t_x\right)=\frac{n_{26}(t\≤t_x)}{n_{26}}$

Wherein, n ₂₆(t≤t _x) expression transfer relationship n ₂₆Be less than or equal to time t middle transfer time _xIn be in the transformer number of units of the second state;

In the moment of above-mentioned running status and malfunction, obtain being in the transformer number of units n of the third state ₃, follow the tracks of this n ₃Platform transformer, and have transfer relationship between i state and the j state among the duty of the definite n3 platform transformer conversion adjacency matrix R is n from the transformer platform number scale that the third state is transferred to the 4th state namely ₃₄, the transformer platform number scale that is transferred to the 5th state from the third state is n ₃₅, the transformer platform number scale that is transferred to the 6th state from the third state is n ₃₆, according to above-mentioned transfer relationship, calculate the element among the time conditions probability distribution matrix G (t) under the third state in half Markov process:

$G_{34}\left(t_x\right)=\frac{n_{34}(t\≤t_x)}{n_{34}}$

Wherein, n ₃₄(t≤t _x) expression transfer relationship n ₃₄Be less than or equal to time t middle transfer time _xIn be in the transformer number of units of the third state;

$G_{35}\left(t_x\right)=\frac{n_{35}(t\≤t_x)}{n_{35}}$

Wherein, n ₃₅(t≤t _x) expression transfer relationship n ₃₅Be less than or equal to time t middle transfer time _xIn be in the transformer number of units of the third state;

$G_{36}\left(t_x\right)=\frac{n_{36}(t\≤t_x)}{n_{36}}$

Wherein, n ₃₆(t≤t _x) expression transfer relationship n ₃₆Be less than or equal to time t middle transfer time _xIn be in the transformer number of units of the third state;

Then the time conditions probability distribution matrix G (t) under the i state is in half Markov process:

$G\left(t\right)=\left[\begin{array}{cccccc}0& G_{12}\left(t\right)& 0& 0& G_{15}\left(t\right)& G_{16}\left(t\right)\\ 0& 0& G_{23}\left(t\right)& 0& G_{25}\left(t\right)& G_{26}\left(t\right)\\ 0& 0& 0& G_{34}\left(t\right)& G_{35}\left(t\right)& G_{36}\left(t\right)\\ 0& 0& 0& 1& 0& 0\\ 0& 0& 0& 0& 1& 0\\ 0& 0& 0& 0& 0& 1\end{array}\right]$

(4) according to the time conditions probability distribution matrix G (t) under the i state in embedded markovian state transition probability matrix P and half Markov process in the above-mentioned Markov process, adopt numerical solution to find the solution the transition probability matrix Φ (t) of half Markov process, matrix element is expressed as Φ _Uv(t), u=1,2...m; V=1,2...m; T=1,2 ... T+1, m are transformer duty number, and t is transformer fault rate prediction current time;

Detailed process may further comprise the steps:

(4-1) during initialization, establish transformer fault rate prediction current time t=0, Q (0)=0, U (0)=E, S (0)=0, D (0)=E,

Wherein, Q (t) is half markoff kernels, and matrix element is Q _Uv(t), U (t) is the first parameter matrix, and matrix element is U _Uv(t), S (t) is the second parameter matrix, and matrix element is S _Uv(t), D (t) is the 3rd parameter matrix, and matrix element is D _Uv(t), 0 expression null matrix, E representation unit matrix;

(4-2) set t=1,

(4-3) according to the time conditions probability distribution matrix G (t) under the i state in embedded markovian state transition probability matrix P and half Markov process in above-mentioned half Markov process, obtain half markoff kernels Q (t)=PG (t), wherein the element of " " representing matrix is point-to-point multiplies each other;

(4-4) set cycle index k=1;

(4-5) according to half markoff kernels Q (t), obtain the element among the second parameter matrix S (t)

(4-6) k is judged, if k less than m, then makes k=k+1, repeating step (4-5)-(4-6); If k more than or equal to m, then carries out step (4-7);

(4-7) according to half markoff kernels Q (t) and the second parameter matrix S (t), obtain the first parameter matrix U (t)=Q (t)-Q (t-1), and the 3rd parameter matrix D (t)=D (0)-S (t);

(4-8) t is judged, if t less than T+1, then makes t=t+1, repeating step (4-3)-(4-8) is if t more than or equal to T+1, then carries out step (4-9);

When (4-9) setting t=0, Φ (0)=D (0);

(4-10) set t=1;

(4-11) according to the 3rd parameter matrix D (t), obtain transition probability matrix Φ (t)=D (t);

(4-12) set cycle index s=1;

(4-13) according to transition probability matrix and the first parameter matrix, obtain transition probability matrix Φ (t)=Φ (t)+U (s) * Φ (t-s);

(4-14) cycle index s is judged, if s less than t, s=s+1 then, repeating step (4-13)-(4-14) is if s more than or equal to t, then carries out step (4-15);

(4-15) transformer fault rate prediction current time t is judged, if t less than T+1, then makes t=t+1, repeating step (4-11)-(4-15), if t is more than or equal to T+1, then prediction finishes, and obtains the transition probability matrix Φ (t) of half Markov process;

(5) according to above-mentioned result of calculation, when obtaining transformer at failure rate prediction current time t=0 and being in the i running status, failure rate λ (t) is:

$\mathrm{\λ}\left(t\right)=\frac{[{\mathrm{\Φ}}_{i4}(t+1)+{\mathrm{\Φ}}_{i5}(t+1)+{\mathrm{\Φ}}_{i6}(t+1)]-[{\mathrm{\Φ}}_{i4}\left(t\right)+{\mathrm{\Φ}}_{i5}\left(t\right)+{\mathrm{\Φ}}_{i6}\left(t\right)]}{1-[{\mathrm{\Φ}}_{i4}\left(t\right)+{\mathrm{\Φ}}_{i5}\left(t\right)+{\mathrm{\Φ}}_{i6}\left(t\right)]}.$

The transformer fault rate Forecasting Methodology based on half Markov process that the present invention proposes, its advantage is, only consider the deficiency of degradation failure for existing transformer fault rate model, the present invention has considered degradation failure and random fault comprehensively, computation process has adopted half Markov process, this is a kind of extended model of Markov process, the residence time that half Markov process has been cancelled running state of transformer is the restriction of exponential distribution, the residence time can be any distribution, thereby more possibilities are provided, the physical fault process that can conform to the transformer fault rate curve variation tendency of actual count is coincide better, and applicability is higher.

Embodiment

The transformer fault rate Forecasting Methodology based on half Markov process that the present invention proposes may further comprise the steps:

(1) duty with transformer is divided into running status and malfunction, running status wherein, be divided into the first state according to the degree of polymerization DP of insulating paper in the transformer: the DP value is 1100-950, the second state: the DP value is 950-450, the third state: the DP value is 450-200; Malfunction wherein is divided into according to failure mode: the 4th state: the heat ageing malfunction, and the DP value is less than 200, the 5th state: the random fault that is caused by lightning impulse, the 6th state is impacted the random fault that causes by external short circuit, above-mentioned six kinds of states form a state set S={1,2,3,4,5,6}, the duty of transformer is counted m=6;

(2) impose a condition: Heat Ageing is progressive process, and the first state, the second state and the third state are because the impact of enchancement factor can be malfunction from running state conversion directly, and the transfer process of the malfunction of transformer is irreversible,

Pass between above-mentioned six states ties up to based on analyzing under following 3 hypothesis: a) Heat Ageing is progressive process, does not consider such as the directly variation of the great-jump-forward from the first state to the third state; B) state of each normal operation: the first state, the second state and the third state, all may be because the impact of enchancement factor directly becomes malfunction from running status; C) do not consider failover process, the failure process of transformer is irreversible.

Impose a condition according to above-mentioned, the duty conversion adjacency matrix R that obtains transformer is:

$R=\left[\begin{array}{cccccc}0& 1& 0& 0& 1& 1\\ 0& 0& 1& 0& 1& 1\\ 0& 0& 0& 1& 1& 1\\ 0& 0& 0& 0& 0& 0\\ 0& 0& 0& 0& 0& 0\\ 0& 0& 0& 0& 0& 0\end{array}\right]$

Wherein, R _Ij=1(i=1,2 ... 6; J=1,2 ... 6) there is transfer relationship, R between expression i state and the j state _IjThere is not transfer relationship between=0 expression i state and the j state;

(3) obtain embedded markovian state transition probability matrix P and the time conditions probability distribution matrix G (t) that rests under the i state in half Markov process from the history data of many transformers, its process may further comprise the steps:

(3-1) from the history data of many transformers, obtain respectively the moment that many transformers respectively are in running status and malfunction;

(3-2) in the moment of above-mentioned running status and malfunction, obtain the transformer number of units n of first state that is in ₁, follow the tracks of this n ₁Platform transformer, and definite n ₁Have transfer relationship between i state and the j state among the duty conversion adjacency matrix R of platform transformer, namely the transformer platform number scale from the first state transitions to the second state is n ₁₂, be n from the transformer platform number scale of the first state transitions to the five states ₁₅, be n from the transformer platform number scale of the first state transitions to the six states ₁₆, according to above-mentioned transfer relationship, calculate the element among the embedded markovian state transition probability matrix P in half Markov process:

The transition probability of the first state to the second state

The transition probability of the first state to the five states

The transition probability of the first state to the six states

In the moment of above-mentioned running status and malfunction, obtain the transformer number of units n of second state that is in ₂, follow the tracks of this n ₂Platform transformer, and definite n ₂Have transfer relationship between i state and the j state among the duty conversion adjacency matrix R of platform transformer, namely the transformer platform number scale from the second state transitions to the third state is n ₂₃, be n from the transformer platform number scale of the second state transitions to the five states ₂₅, be n from the transformer platform number scale of the second state transitions to the six states ₂₆, according to above-mentioned transfer relationship, calculate the element among the embedded markovian state transition probability matrix P in half Markov process:

The second state is to the transition probability of the third state

The transition probability of the second state to the five states

The transition probability of the second state to the six states

In the moment of above-mentioned running status and malfunction, obtain being in the transformer number of units n of the third state ₃, follow the tracks of this n ₃Platform transformer, and definite n ₃Have transfer relationship between i state and the j state among the duty of the platform transformer conversion adjacency matrix R, the transformer platform number scale that namely is transferred to the 4th state from the third state is n ₃₄, the transformer platform number scale that is transferred to the 5th state from the third state is n ₃₅, the transformer platform number scale that is transferred to the 6th state from the third state is n ₃₆, according to above-mentioned transfer relationship, calculate the element among the embedded markovian state transition probability matrix P in half Markov process:

The transition probability of the third state to the four states

The transition probability of the third state to the five states

The transition probability of the third state to the six states

Then embedded markovian state transition probability matrix P is in half Markov process:

$P=\left[\begin{array}{cccccc}0& p_{12}& 0& 0& p_{15}& p_{16}\\ 0& 0& p_{23}& 0& p_{25}& p_{26}\\ 0& 0& 0& p_{34}& p_{35}& p_{36}\\ 0& 0& 0& 1& 0& 0\\ 0& 0& 0& 0& 1& 0\\ 0& 0& 0& 0& 0& 1\end{array}\right]$

(3-3) in the moment of above-mentioned running status and malfunction, obtain the transformer number of units n of first state that is in ₁, follow the tracks of this n ₁Platform transformer, and definite n ₁Have transfer relationship between i state and the j state among the duty conversion adjacency matrix R of platform transformer, namely the transformer platform number scale from the first state transitions to the second state is n ₁₂, be n from the transformer platform number scale of the first state transitions to the five states ₁₅, be n from the transformer platform number scale of the first state transitions to the six states ₁₆, according to above-mentioned transfer relationship, calculate the element among the time conditions probability distribution matrix G (t) under the first state in half Markov process:

$G_{12}\left(t_x\right)=\frac{n_{12}(t\≤t_x)}{n_{12}}$

Wherein, n ₁₂(t≤t _x) expression transfer relationship n ₁₂Be less than or equal to time t middle transfer time _xIn be in the transformer number of units of the first state, t _x=1,2...T+1, T are the transformer fault rate prediction moment;

$G_{15}\left(t_x\right)=\frac{n_{15}(t\≤t_x)}{n_{15}}$

Wherein, n ₁₅(t≤t _x) expression transfer relationship n ₁₅Be less than or equal to time t middle transfer time _xIn be in the transformer number of units of the first state;

$G_{16}\left(t_x\right)=\frac{n_{16}(t\≤t_x)}{n_{16}}$

Wherein, n ₁₆(t≤t _x) expression transfer relationship n ₁₆Be less than or equal to time t middle transfer time _xIn be in the transformer number of units of the first state;

In the moment of above-mentioned running status and malfunction, obtain the transformer number of units n of second state that is in ₂, follow the tracks of this n ₂Platform transformer, and definite n ₂Have transfer relationship between i state and the j state among the duty conversion adjacency matrix R of platform transformer, namely the transformer platform number scale from the second state transitions to the third state is n ₂₃, be n from the transformer platform number scale of the second state transitions to the five states ₂₅, be n from the transformer platform number scale of the second state transitions to the six states ₂₆, according to above-mentioned transfer relationship, calculate the element among the time conditions probability distribution matrix G (t) under the second state in half Markov process:

$G_{23}\left(t_x\right)=\frac{n_{23}(t\≤t_x)}{n_{23}}$

Wherein, n ₂₃(t≤t _x) expression transfer relationship n ₂₃Be less than or equal to time t middle transfer time _xIn be in the transformer number of units of the second state;

$G_{25}\left(t_x\right)=\frac{n_{25}(t\≤t_x)}{n_{25}}$

Wherein, n ₂₅(t≤t _x) expression transfer relationship n ₂₅Be less than or equal to time t middle transfer time _xIn be in the transformer number of units of the second state;

$G_{26}\left(t_x\right)=\frac{n_{26}(t\≤t_x)}{n_{26}}$

Wherein, n ₂₆(t≤t _x) expression transfer relationship n ₂₆Be less than or equal to time t middle transfer time _xIn be in the transformer number of units of the second state;

In the moment of above-mentioned running status and malfunction, obtain being in the transformer number of units n of the third state ₃, follow the tracks of this n ₃Platform transformer, and definite n ₃Have transfer relationship between i state and the j state among the duty of the platform transformer conversion adjacency matrix R, the transformer platform number scale that namely is transferred to the 4th state from the third state is n ₃₄, the transformer platform number scale that is transferred to the 5th state from the third state is n ₃₅, the transformer platform number scale that is transferred to the 6th state from the third state is n ₃₆, according to above-mentioned transfer relationship, calculate the element among the time conditions probability distribution matrix G (t) under the third state in half Markov process:

$G_{34}\left(t_x\right)=\frac{n_{34}(t\≤t_x)}{n_{34}}$

Wherein, n ₃₄(t≤t _x) expression transfer relationship n ₃₄Be less than or equal to time t middle transfer time _xIn be in the transformer number of units of the third state;

$G_{35}\left(t_x\right)=\frac{n_{35}(t\≤t_x)}{n_{35}}$

Wherein, n ₃₅(t≤t _x) expression transfer relationship n ₃₅Be less than or equal to time t middle transfer time _xIn be in the transformer number of units of the third state;

$G_{36}\left(t_x\right)=\frac{n_{36}(t\≤t_x)}{n_{36}}$

Wherein, n ₃₆(t≤t _x) expression transfer relationship n ₃₆Be less than or equal to time t middle transfer time _xIn be in the transformer number of units of the third state;

Then the time conditions probability distribution matrix G (t) under the i state is in half Markov process:

$G\left(t\right)=\left[\begin{array}{cccccc}0& G_{12}\left(t\right)& 0& 0& G_{15}\left(t\right)& G_{16}\left(t\right)\\ 0& 0& G_{23}\left(t\right)& 0& G_{25}\left(t\right)& G_{26}\left(t\right)\\ 0& 0& 0& G_{34}\left(t\right)& G_{35}\left(t\right)& G_{36}\left(t\right)\\ 0& 0& 0& 1& 0& 0\\ 0& 0& 0& 0& 1& 0\\ 0& 0& 0& 0& 0& 1\end{array}\right]$

(4) according to the time conditions probability distribution matrix G (t) under the i state in embedded markovian state transition probability matrix P and half Markov process in the above-mentioned Markov process, adopt numerical solution to find the solution the transition probability matrix Φ (t) of half Markov process, matrix element is expressed as Φ _Uv(t), u=1,2...m; V=1,2...m; T=1,2 ... T+1, m are transformer duty number, and t is transformer fault rate prediction current time;

Detailed process may further comprise the steps:

(4-1) during initialization, establish transformer fault rate prediction current time t=0, Q (0)=0, U (0)=E, S (0)=0, D (0)=E,

Wherein, Q (t) is half markoff kernels, and matrix element is Q _Uv(t), U (t) is the first parameter matrix, and matrix element is U _Uv(t), S (t) is the second parameter matrix, and matrix element is S _Uv(t), D (t) is the 3rd parameter matrix, and matrix element is D _Uv(t), 0 expression null matrix, E representation unit matrix;

(4-2) set t=1,

(4-3) according to the time conditions probability distribution matrix G (t) under the i state in embedded markovian state transition probability matrix P and half Markov process in above-mentioned half Markov process, obtain half markoff kernels Q (t)=PG (t), wherein the element of " " representing matrix is point-to-point multiplies each other;

(4-4) set cycle index k=1;

(4-5) according to half markoff kernels Q (t), obtain the element among the second parameter matrix S (t)

(4-6) k is judged, if k less than m, then makes k=k+1, repeating step (4-5)-(4-6); If k more than or equal to m, then carries out step (4-7);

(4-7) according to half markoff kernels Q (t) and the second parameter matrix S (t), obtain the first parameter matrix U (t)=Q (t)-Q (t-1), and the 3rd parameter matrix D (t)=D (0)-S (t);

(4-8) t is judged, if t less than T+1, then makes t=t+1, repeating step (4-3)-(4-8) is if t more than or equal to T+1, then carries out step (4-9);

When (4-9) setting t=0, Φ (0)=D (0);

(4-10) set t=1;

(4-11) according to the 3rd parameter matrix D (t), obtain transition probability matrix Φ (t)=D (t);

(4-12) set cycle index s=1;

(4-13) according to transition probability matrix and the first parameter matrix, obtain transition probability matrix Φ (t)=Φ (t)+U (s) * Φ (t-s);

(4-14) cycle index s is judged, if s less than t, s=s+1 then, repeating step (4-13)-(4-14) is if s more than or equal to t, then carries out step (4-15);

(4-15) transformer fault rate prediction current time t is judged, if t less than T+1, then makes t=t+1, repeating step (4-11)-(4-15), if t is more than or equal to T+1, then prediction finishes, and obtains the transition probability matrix Φ (t) of half Markov process;

(5) according to above-mentioned result of calculation, when obtaining transformer at failure rate prediction current time t=0 and being in the i running status, failure rate λ (t) is:

$\mathrm{\λ}\left(t\right)=\frac{[{\mathrm{\Φ}}_{i4}(t+1)+{\mathrm{\Φ}}_{i5}(t+1)+{\mathrm{\Φ}}_{i6}(t+1)]-[{\mathrm{\Φ}}_{i4}\left(t\right)+{\mathrm{\Φ}}_{i5}\left(t\right)+{\mathrm{\Φ}}_{i6}\left(t\right)]}{1-[{\mathrm{\Φ}}_{i4}\left(t\right)+{\mathrm{\Φ}}_{i5}\left(t\right)+{\mathrm{\Φ}}_{i6}\left(t\right)]}.$

Claims (1)

1. transformer fault rate Forecasting Methodology based on half Markov process is characterized in that this Forecasting Methodology may further comprise the steps:

(1) duty with transformer is divided into running status and malfunction, running status wherein, be divided into the first state according to the degree of polymerization DP of insulating paper in the transformer: the DP value is 1100-950, the second state: the DP value is 950-450, the third state: the DP value is 450-200; Malfunction wherein is divided into according to failure mode: the 4th state: the heat ageing malfunction, and the DP value is less than 200, the 5th state: the random fault that is caused by lightning impulse, the 6th state is impacted the random fault that causes by external short circuit, above-mentioned six kinds of states form a state set S={1,2,3,4,5,6}, the duty of transformer is counted m=6;

(2) impose a condition: Heat Ageing is progressive process, and the first state, the second state and the third state are because the impact of enchancement factor can be malfunction from running state conversion directly, and the transfer process of the malfunction of transformer is irreversible,

Impose a condition according to above-mentioned, the duty conversion adjacency matrix R that obtains transformer is:

$R=\left[\begin{array}{cccccc}0& 1& 0& 0& 1& 1\\ 0& 0& 1& 0& 1& 1\\ 0& 0& 0& 1& 1& 1\\ 0& 0& 0& 0& 0& 0\\ 0& 0& 0& 0& 0& 0\\ 0& 0& 0& 0& 0& 0\end{array}\right]$

Wherein, R _Ij=1(i=1,2...6; J=1,2...6) represent to have transfer relationship, R between i state and the j state _IjThere is not transfer relationship between=0 expression i state and the j state;

(3) obtain embedded markovian state transition probability matrix P and the time conditions probability distribution matrix G (t) that rests under the i state in half Markov process from the history data of many transformers, its process may further comprise the steps:

(3-1) from the history data of many transformers, obtain respectively the moment that many transformers respectively are in running status and malfunction;

(3-2) in the moment of above-mentioned running status and malfunction, obtain the transformer number of units n of first state that is in ₁, follow the tracks of this n ₁Platform transformer, and definite n ₁Have transfer relationship between i state and the j state among the duty conversion adjacency matrix R of platform transformer, namely the transformer platform number scale from the first state transitions to the second state is n ₁₂, be n from the transformer platform number scale of the first state transitions to the five states ₁₅, be n from the transformer platform number scale of the first state transitions to the six states ₁₆, according to above-mentioned transfer relationship, calculate the element among the embedded markovian state transition probability matrix P in half Markov process:

The transition probability of the first state to the second state

The transition probability of the first state to the five states

The transition probability of the first state to the six states

In the moment of above-mentioned running status and malfunction, obtain the transformer number of units n of second state that is in ₂, follow the tracks of this n ₂Platform transformer, and definite n ₂Have transfer relationship between i state and the j state among the duty conversion adjacency matrix R of platform transformer, namely the transformer platform number scale from the second state transitions to the third state is n ₂₃, be n from the transformer platform number scale of the second state transitions to the five states ₂₅, be n from the transformer platform number scale of the second state transitions to the six states ₂₆, according to above-mentioned transfer relationship, calculate the element among the embedded markovian state transition probability matrix P in half Markov process:

The second state is to the transition probability of the third state

The transition probability of the second state to the five states

The transition probability of the second state to the six states

In the moment of above-mentioned running status and malfunction, obtain being in the transformer number of units n of the third state ₃, follow the tracks of this n ₃Platform transformer, and definite n ₃Have transfer relationship between i state and the j state among the duty of the platform transformer conversion adjacency matrix R, the transformer platform number scale that namely is transferred to the 4th state from the third state is n ₃₄, the transformer platform number scale that is transferred to the 5th state from the third state is n ₃₅, the transformer platform number scale that is transferred to the 6th state from the third state is n ₃₆, according to above-mentioned transfer relationship, calculate the element among the embedded markovian state transition probability matrix P in half Markov process:

The transition probability of the third state to the four states

The transition probability of the third state to the five states

The transition probability of the third state to the six states

Then embedded markovian state transition probability matrix P is in half Markov process:

$P=\left[\begin{array}{cccccc}0& p_{12}& 0& 0& p_{15}& p_{16}\\ 0& 0& p_{23}& 0& p_{25}& p_{26}\\ 0& 0& 0& p_{34}& p_{35}& p_{36}\\ 0& 0& 0& 1& 0& 0\\ 0& 0& 0& 0& 1& 0\\ 0& 0& 0& 0& 0& 1\end{array}\right]$

(3-3) in the moment of above-mentioned running status and malfunction, obtain the transformer number of units n of first state that is in ₁, follow the tracks of this n ₁Platform transformer, and definite n ₁Have transfer relationship between i state and the j state among the duty conversion adjacency matrix R of platform transformer, namely the transformer platform number scale from the first state transitions to the second state is n ₁₂, be n from the transformer platform number scale of the first state transitions to the five states ₁₅, be n from the transformer platform number scale of the first state transitions to the six states ₁₆, according to above-mentioned transfer relationship, calculate the element among the time conditions probability distribution matrix G (t) under the first state in half Markov process:

$G_{12}\left(t_x\right)=\frac{n_{12}(t\≤t_x)}{n_{12}}$

Wherein, n ₁₂(t≤t _x) expression transfer relationship n ₁₂Be less than or equal to time t middle transfer time _xIn be in the transformer number of units of the first state, t _x=1,2...T+1, T are the transformer fault rate prediction moment;

$G_{15}\left(t_x\right)=\frac{n_{15}(t\≤t_x)}{n_{15}}$

Wherein, n ₁₅(t≤t _x) expression transfer relationship n ₁₅Be less than or equal to time t middle transfer time _xIn be in the transformer number of units of the first state;

$G_{16}\left(t_x\right)=\frac{n_{16}(t\≤t_x)}{n_{16}}$

Wherein, n ₁₆(t≤t _x) expression transfer relationship n ₁₆Be less than or equal to time t middle transfer time _xIn be in the transformer number of units of the first state;

In the moment of above-mentioned running status and malfunction, obtain the transformer number of units n of second state that is in ₂, follow the tracks of this n ₂Platform transformer, and definite n ₂Have transfer relationship between i state and the j state among the duty conversion adjacency matrix R of platform transformer, namely the transformer platform number scale from the second state transitions to the third state is n ₂₃, be n from the transformer platform number scale of the second state transitions to the five states ₂₅, be n from the transformer platform number scale of the second state transitions to the six states ₂₆, according to above-mentioned transfer relationship, calculate the element among the time conditions probability distribution matrix G (t) under the second state in half Markov process:

$G_{23}\left(t_x\right)=\frac{n_{23}(t\≤t_x)}{n_{23}}$

Wherein, n ₂₃(t≤t _x) expression transfer relationship n ₂₃Be less than or equal to time t middle transfer time _xIn be in the transformer number of units of the second state;

$G_{25}\left(t_x\right)=\frac{n_{25}(t\≤t_x)}{n_{25}}$

Wherein, n ₂₅(t≤t _x) expression transfer relationship n ₂₅Be less than or equal to time t middle transfer time _xIn be in the transformer number of units of the second state;

$G_{26}\left(t_x\right)=\frac{n_{26}(t\≤t_x)}{n_{26}}$

Wherein, n ₂₆(t≤t _x) expression transfer relationship n ₂₆Be less than or equal to time t middle transfer time _xIn be in the transformer number of units of the second state;

In the moment of above-mentioned running status and malfunction, obtain being in the transformer number of units n of the third state ₃, follow the tracks of this n ₃Platform transformer, and definite n ₃Have transfer relationship between i state and the j state among the duty of the platform transformer conversion adjacency matrix R, the transformer platform number scale that namely is transferred to the 4th state from the third state is n ₃₄, the transformer platform number scale that is transferred to the 5th state from the third state is n ₃₅, the transformer platform number scale that is transferred to the 6th state from the third state is n ₃₆, according to above-mentioned transfer relationship, calculate the element among the time conditions probability distribution matrix G (t) under the third state in half Markov process:

$G_{34}\left(t_x\right)=\frac{n_{34}(t\≤t_x)}{n_{34}}$

Wherein, n ₃₄(t≤t _x) expression transfer relationship n ₃₄Be less than or equal to time t middle transfer time _xIn be in the transformer number of units of the third state;

$G_{35}\left(t_x\right)=\frac{n_{35}(t\≤t_x)}{n_{35}}$

Wherein, n ₃₅(t≤t _x) expression transfer relationship n ₃₅Be less than or equal to time t middle transfer time _xIn be in the transformer number of units of the third state;

$G_{36}\left(t_x\right)=\frac{n_{36}(t\≤t_x)}{n_{36}}$

Wherein, n ₃₆(t≤t _x) expression transfer relationship n ₃₆Be less than or equal to time t middle transfer time _xIn be in the transformer number of units of the third state;

Then the time conditions probability distribution matrix G (t) under the i state is in half Markov process:

$G\left(t\right)=\left[\begin{array}{cccccc}0& G_{12}\left(t\right)& 0& 0& G_{15}\left(t\right)& G_{16}\left(t\right)\\ 0& 0& G_{23}\left(t\right)& 0& G_{25}\left(t\right)& G_{26}\left(t\right)\\ 0& 0& 0& G_{34}\left(t\right)& G_{35}\left(t\right)& G_{36}\left(t\right)\\ 0& 0& 0& 1& 0& 0\\ 0& 0& 0& 0& 1& 0\\ 0& 0& 0& 0& 0& 1\end{array}\right]$

(4) according to the time conditions probability distribution matrix G (t) under the i state in embedded markovian state transition probability matrix P and half Markov process in the above-mentioned Markov process, adopt numerical solution to find the solution the transition probability matrix Φ (t) of half Markov process, matrix element is expressed as Φ _Uv(t), u=1,2...m; V=1,2...m; T=1,2 ... T+1, m are transformer duty number, and t is transformer fault rate prediction current time;

Detailed process may further comprise the steps:

(4-1) during initialization, establish transformer fault rate prediction current time t=0, Q (0)=0, U (0)=E, S (0)=0, D (0)=E,

Wherein, Q (t) is half markoff kernels, and matrix element is Q _Uv(t), U (t) is the first parameter matrix, and matrix element is U _Uv(t), S (t) is the second parameter matrix, and matrix element is S _Uv(t), D (t) is the 3rd parameter matrix, and matrix element is D _Uv(t), 0 expression null matrix, E representation unit matrix;

(4-2) set t=1,

(4-3) according to the time conditions probability distribution matrix G (t) under the i state in embedded markovian state transition probability matrix P and half Markov process in above-mentioned half Markov process, obtain half markoff kernels Q (t)=PG (t), wherein the element of " " representing matrix is point-to-point multiplies each other;

(4-4) set cycle index k=1;

(4-5) according to half markoff kernels Q (t), obtain the element among the second parameter matrix S (t)

(4-6) k is judged, if k less than m, then makes k=k+1, repeating step (4-5)-(4-6); If k more than or equal to m, then carries out step (4-7);

(4-7) according to half markoff kernels Q (t) and the second parameter matrix S (t), obtain the first parameter matrix U (t)=Q (t)-Q (t-1), and the 3rd parameter matrix D (t)=D (0)-S (t);

(4-8) t is judged, if t less than T+1, then makes t=t+1, repeating step (4-3)-(4-8) is if t more than or equal to T+1, then carries out step (4-9);

When (4-9) setting t=0, Φ (0)=D (0);

(4-10) set t=1;

(4-11) according to the 3rd parameter matrix D (t), obtain transition probability matrix Φ (t)=D (t);

(4-12) set cycle index s=1;

(4-13) according to transition probability matrix and the first parameter matrix, obtain transition probability matrix Φ (t)=Φ (t)+U (s) * Φ (t-s);

(4-14) cycle index s is judged, if s less than t, s=s+1 then, repeating step (4-13)-(4-14) is if s more than or equal to t, then carries out step (4-15);

(4-15) transformer fault rate prediction current time t is judged, if t less than T+1, then makes t=t+1, repeating step (4-11)-(4-15), if t is more than or equal to T+1, then prediction finishes, and obtains the transition probability matrix Φ (t) of half Markov process;

(5) according to above-mentioned result of calculation, when obtaining transformer at failure rate prediction current time t=0 and being in the i running status, failure rate λ (t) is:

$\mathrm{\λ}\left(t\right)=\frac{[{\mathrm{\Φ}}_{i4}(t+1)+{\mathrm{\Φ}}_{i5}(t+1)+{\mathrm{\Φ}}_{i6}(t+1)]-[{\mathrm{\Φ}}_{i4}\left(t\right)+{\mathrm{\Φ}}_{i5}\left(t\right)+{\mathrm{\Φ}}_{i6}\left(t\right)]}{1-[{\mathrm{\Φ}}_{i4}\left(t\right)+{\mathrm{\Φ}}_{i5}\left(t\right)+{\mathrm{\Φ}}_{i6}\left(t\right)]}.$