CN103985059B - Power grid transformer operational risk assessment method based on fuzzy fault rate - Google Patents

Abstract

The invention relates to a power grid transformer operational risk assessment method based on a fuzzy fault rate, and belongs to the field of operational risk assessment of an electric power system. According to the power grid transformer operational risk assessment method, various operational states of a transformer are divided, a transformer sudden failure rate and ageing fault rate represented in a triangular fuzzy number mode are given, a transformer Markov state transition differential equation set based on the fuzzy fault rate is established to describe the state transition behavior of the transformer, the transformer state transition differential equation set is solved through Laplace transformation, a transformer availability analysis formula based on the fuzzy failure rate is given out, the probability of a power grid in various operation modes is calculated based on the transformer availability analysis formula, and at last the transformer operational risk indicators of the power grid at all moments are calculated. The power grid transformer operational risk assessment method can be used for conducting power grid transformer operational risk assessment under the condition that historical statistical data are insufficient, by the aid of manual experience, an optimistic value, a pessimistic value and an intermediate value of the power grid transformer operational risk indicators are given, and therefore more sufficient decision support is provided for scheduling personnel.

Description

A kind of network transformer operation risk assessment method based on fuzzy failure rate

Technical field

The present invention relates to a kind of network transformer operation risk assessment method based on fuzzy failure rate, belong to power system Operation risk assessment field.

Background technology

Risk is the comprehensive measurement of event possibility occurrence and seriousness, and power networks risk assessment can consider electricity The order of severity being broken down in network operation and probability of happening, thus disclosing electrical network weak link, to dispatching of power netwoks, personnel determine Plan provides reference frame.

In the assessment of traditional power networks risk, the calculating of fault possibility occurrence depends primarily on electrical equipment fault rate Parameter, and equipment failure rate parameter is mainly derived from the reference value that long history statistical data or equipment production firm provide, this One method faces problems with present:

1st, because the probability of device fails is extremely low, failure-rate data measurement period is extremely very long, and this results in perhaps In many area power grids power equipment historical statistical data sample less it is difficult to accurate computing device fault rate；

2nd, in the more weak local distribution network of some infrastructure, fallen behind due to facility, lack of capital or manpower not The reasons such as foot, many equipment lack historical statistical datas it is impossible to computing device fault rate；

3rd, equipment failure rate would generally change with equipment operating condition and external environment, there is a waving interval, and Fault rate reference value that equipment production firm provides it is difficult to actual operating mode residing for reflection equipment and external environment condition etc. because Element, therefore accuracy are poor.

Content of the invention

The purpose of the present invention is to propose to a kind of network transformer operation risk assessment method based on fuzzy failure rate, be given Transformator catastrophic failure rate and degradation failure rate that Triangular Fuzzy Number form represents, and establish the change based on fuzzy failure rate Depressor Markovian state shifts differential equation group, obtains transformator by solution transformer state transfer differential equation group and can use Degree analytic expression, and the transformer station high-voltage side bus risk indicator in each moment of electrical network is calculated based on transformator availability analytic expression.

Network transformer operation risk assessment method based on fuzzy failure rate proposed by the present invention, comprises the following steps:

(1) by the state demarcation of transformator be working condition and malfunction, wherein working condition include normally, attention and Abnormal, it is designated as 0,1 and 2 respectively, malfunction is subdivided into catastrophic failure and degradation failure according to failure cause, be designated as 3 Hes respectively 4；

(2) use respectivelyWith withCatastrophic failure rate under normal, attention and abnormality for the indication transformer, WithThe degradation failure rate of indication transformer, represents catastrophic failure rate and aging event with Triangular Fuzzy Number form as follows Barrier rate:

${\widetilde{\mathrm{\λ}}}_{03}=({\underset{\&overbar;}{\mathrm{\λ}}}_{03},{\widehat{\mathrm{\λ}}}_{03},{\stackrel{\&overbar;}{\mathrm{\λ}}}_{03})$

${\widetilde{\mathrm{\λ}}}_{13}=({\underset{\&overbar;}{\mathrm{\λ}}}_{13},{\widehat{\mathrm{\λ}}}_{13},{\stackrel{\&overbar;}{\mathrm{\λ}}}_{13})$

${\widetilde{\mathrm{\λ}}}_{23}=({\underset{\&overbar;}{\mathrm{\λ}}}_{23},{\widehat{\mathrm{\λ}}}_{23},{\stackrel{\&overbar;}{\mathrm{\λ}}}_{23})$

${\widetilde{\mathrm{\λ}}}_{24}=({\underset{\&overbar;}{\mathrm{\λ}}}_{24},{\widehat{\mathrm{\λ}}}_{24},{\stackrel{\&overbar;}{\mathrm{\λ}}}_{24})$

Whereinλ ₀₃、λ ₁₃Withλ ₂₃The lower limit of catastrophic failure rate under normal, attention and abnormality for the indication transformer respectively Value,WithCatastrophic failure rate higher limit under normal, attention and abnormality for the indication transformer respectively, WithCatastrophic failure rate intermediate value under normal, attention and abnormality for the indication transformer respectively,λ ₂₄Indication transformer old Change fault rate lower limit,The degradation failure rate higher limit of indication transformer,In the middle of the degradation failure rate of indication transformer Value；The fault rate optimistic estimate value that lower limit is given based on experience for dispatcher, span is 0～0.005 times/day, on Limit value is the fault rate pessimism estimated value that dispatcher is given based on experience, and span is 0～0.1 times/day, and intermediate value is to adjust The actual estimated value that degree personnel are given based on experience and the current operating condition of transformator, span is 0～0.01 times/day.

(3) set up a transformator Markovian state transfer differential equation group as follows:

$\left\{\begin{array}{c}\frac{d{\tilde{p}}_0}{\mathrm{dt}}=-({\mathrm{\λ}}_{01}+{\widetilde{\mathrm{\λ}}}_{03}){\tilde{p}}_0+{\mathrm{\μ}}_b{\tilde{p}}_{3.0}+{\mathrm{\μ}}_c{\tilde{p}}_4\\ \frac{d{\tilde{p}}_1}{\mathrm{dt}}={\mathrm{\λ}}_{01}{\tilde{p}}_0-({\mathrm{\λ}}_{12}+{\widetilde{\mathrm{\λ}}}_{13}){\tilde{p}}_1+{\mathrm{\μ}}_b{\tilde{p}}_{3.2}\\ \frac{d{\tilde{p}}_2}{\mathrm{dt}}={\mathrm{\λ}}_{12}{\tilde{p}}_1-({\widetilde{\mathrm{\λ}}}_{23}+{\widetilde{\mathrm{\λ}}}_{24}){\tilde{p}}_2+{\mathrm{\μ}}_b{\tilde{p}}_{3.2}\\ \frac{d{\tilde{p}}_{3.2}}{\mathrm{dt}}={\widetilde{\mathrm{\λ}}}_{23}{\tilde{p}}_2-{\mathrm{\μ}}_b{\tilde{p}}_{3.2}\\ \frac{d{\tilde{p}}_{3.1}}{\mathrm{dt}}={\widetilde{\mathrm{\λ}}}_{13}{\tilde{p}}_1-{\mathrm{\μ}}_b{\tilde{p}}_{3.1}\\ \frac{d{\tilde{p}}_{3.0}}{\mathrm{dt}}={\widetilde{\mathrm{\λ}}}_{03}{\tilde{p}}_0-{\mathrm{\μ}}_b{\tilde{p}}_{3.0}\\ \frac{d{\tilde{p}}_4}{\mathrm{dt}}={\widetilde{\mathrm{\λ}}}_{24}{\tilde{p}}_2-{\mathrm{\μ}}_c{\tilde{p}}_4\end{array}\right.$

Wherein, λ₀₁Indication transformer is by the transfer rate of normal condition to attention state, λ₁₂Indication transformer is by noting shape State is to the transfer rate of abnormality, μ_cThe repair rate of indication transformer degradation failure, span is 0～1 times/day, μ_bRepresent The repair rate of transformator catastrophic failure, span is 0～10 times/day,WithRespectively indication transformer be in normally, Note the probability with abnormality,Indication transformer is in degradation failure shape probability of state,Indication transformer is in burst Malfunction and before breaking down transformator be in the probability of normal condition,Indication transformer be in catastrophic failure state and Before breaking down, transformator is in the probability of attention state,Before indication transformer is in catastrophic failure state and breaks down Transformator is in the probability of abnormality；

(4) differential equation group is shifted according to Markovian state, obtain the availability analytic expression of transformator, detailed process bag Include following steps:

(4-1) it is in normal condition when setting transformator initialization, using Laplace transformation, above-mentioned differential equation group is changed into Following Algebraic Equation set:

$\left\{\begin{array}{c}s{\tilde{p}}_0-1=-({\mathrm{\λ}}_{01}+{\widetilde{\mathrm{\λ}}}_{03}){\tilde{p}}_0+{\mathrm{\μ}}_b{\tilde{p}}_{3.0}+{\mathrm{\μ}}_c{\tilde{p}}_4\\ s{\tilde{p}}_1={\mathrm{\λ}}_{01}{\tilde{p}}_0-({\mathrm{\λ}}_{12}+{\widetilde{\mathrm{\λ}}}_{13}){\tilde{p}}_1+{\mathrm{\μ}}_b{\tilde{p}}_{3.1}\\ s{\tilde{p}}_2={\mathrm{\λ}}_{12}{\tilde{p}}_1-({\widetilde{\mathrm{\λ}}}_{23}+{\widetilde{\mathrm{\λ}}}_{24}){\tilde{p}}_2+{\mathrm{\μ}}_b{\tilde{p}}_{3.2}\\ s{\tilde{p}}_{3.2}={\widetilde{\mathrm{\λ}}}_{23}{\tilde{p}}_2-{\mathrm{\μ}}_b{\tilde{p}}_{3.2}\\ s{\tilde{p}}_{3.1}={\widetilde{\mathrm{\λ}}}_{13}{\tilde{p}}_1-{\mathrm{\μ}}_b{\tilde{p}}_{3.1}\\ s{\tilde{p}}_{3.0}={\widetilde{\mathrm{\λ}}}_{03}{\tilde{p}}_0-{\mathrm{\μ}}_b{\tilde{p}}_{3.0}\\ s{\tilde{p}}_4={\widetilde{\mathrm{\λ}}}_{24}{\tilde{p}}_2-{\mathrm{\μ}}_c{\tilde{p}}_4\end{array}\right.$

Wherein, s is the complex frequency in Laplace transformation, and Laplace transformation is answering in complex frequency domain by the functional transformation in time domain One integral transformation process of varying function；

(4-2) with Laplace transformation complex frequency s as independent variable, with transformator be in normally, note and abnormality probability WithFor dependent variable, incite somebody to actionWithExpressed with following canonical form with the relation of s:

${\tilde{p}}_0\left(s\right)=\underset{i=0}{\overset{6}{\mathrm{\σ}}}\frac{{\tilde{l}}_{0i}}{s-{\tilde{s}}_i}$

${\tilde{p}}_1\left(s\right)=\underset{i=1}{\overset{8}{\mathrm{\σ}}}\frac{{\tilde{l}}_{1i}}{s-{\tilde{s}}_i}$

${\tilde{p}}_2\left(s\right)=\underset{i=1}{\overset{10}{\mathrm{\σ}}}\frac{{\tilde{l}}_{2i}}{s-{\tilde{s}}_i}$

WhereinWithFor the middle coefficient in canonical form, usually plural number, the span of its mould is led to It is often 0～1；

(4-3) above-mentioned standard form is carried out Laplace inverse transformation, obtain transformator t be in normally, note and different Often the time domain analytical expression of shape probability of state is as follows:

${\tilde{p}}_0=\underset{i=0}{\overset{6}{\mathrm{\σ}}}{\tilde{l}}_{0i}{e}^{{\tilde{s}}_{i}t}$

${\tilde{p}}_1=\underset{i=1}{\overset{8}{\mathrm{\σ}}}{\tilde{l}}_{1i}{e}^{{\tilde{s}}_{i}t}$

${\tilde{p}}_2=\underset{i=1}{\overset{10}{\mathrm{\σ}}}{\tilde{l}}_{2i}{e}^{{\tilde{s}}_{i}t}$

(4-4) the time domain analytical expression according to step (4-3), obtains the availability in t for the transformatorParsing Formula is as follows:

$\tilde{a}\left(t\right)={\tilde{p}}_0+{\tilde{p}}_1+{\tilde{p}}_2=\underset{i=0}{\overset{6}{\mathrm{\σ}}}{\tilde{l}}_{0i}{e}^{{\tilde{s}}_{i}t}+\underset{i=1}{\overset{8}{\mathrm{\σ}}}{\tilde{l}}_{1i}{e}^{{\tilde{s}}_{i}t}+\underset{i=1}{\overset{10}{\mathrm{\σ}}}{\tilde{l}}_{2i}{e}^{{\tilde{s}}_{i}t};$

(5) by above-mentioned transformator t availabilityIt is expressed as Triangular Fuzzy Number form as follows:

$\tilde{a}\left(t\right)=(\underset{\&overbar;}{a}\left(t\right),\hat{a}\left(t\right),\stackrel{\&overbar;}{a}\left(t\right))$

Whereina(t) indication transformer in the availability lower limit of t,Indication transformer is in the availability of t Higher limit,, in the availability intermediate value of t, the solution procedure of lower limit, higher limit and intermediate value is such as indication transformer Under:

(5-1) use the higher limit of the transformator catastrophic failure rate of above-mentioned steps (2)WithReplace step (3) horse Er Kefu state shifts the catastrophic failure rate in differential equation groupWithTransformator degradation failure with step (2) The higher limit of rateStep (3) Markovian state is replaced to shift the degradation failure rate in differential equation groupExecution step (4-1)～step (4-4), obtains the availability lower limit in t for the transformatora(t)；

(5-2) use the lower limit of the transformator catastrophic failure rate of above-mentioned steps (2)λ ₀₃、λ ₁₃Withλ ₂₃Replace step (3) Ma Er Husband's state can shift the catastrophic failure rate in differential equation groupWithTransformator degradation failure rate with step (2) Lower limitStep (3) Markovian state is replaced to shift the degradation failure rate in differential equation groupExecution step (4- 1)～step (4-4), obtains the higher limit of the availability in t for the transformator

(5-3) use the intermediate value of the transformator catastrophic failure rate of above-mentioned steps (2)WithReplace step (3) horse Er Kefu state shifts the catastrophic failure rate in differential equation groupWithTransformator degradation failure with step (2) The intermediate value of rateStep (3) Markovian state is replaced to shift the degradation failure rate in differential equation groupExecution step (4-1)～step (4-4), obtains the intermediate value of the availability in t for the transformator

(6) set electrical network and be in a kind of probability of running status in tFor:

$\tilde{p}\left(t\right)=\underset{i\&element;s_{\mathrm{on}}}{\mathrm{\π}}{\tilde{a}}_i\left(t\right)\underset{i\&element;s_{\mathrm{off}}}{\mathrm{\π}}(1-{\tilde{a}}_i\left(t\right))$

Wherein, s_onRepresent the in running order transformator set under this running status of electrical network, s_offRepresent electrical network at this It is in the transformator set of malfunction, subscript i indication transformer is numbered under running status,Represent that i-th transformator exists The availability of t；

(7) set and network transformer is carried out with the time span of operation risk assessment as t, in electrical network, have n platform transformator, meter Calculate network transformer operation risk indexProcess as follows:

(7-1) when initializing, if moment t=0；

(7-2) make t=t+1, by electrical network t transformer station high-voltage side bus risk indicatorIt is expressed as Triangular Fuzzy Number form such as Under:

$\tilde{r}\left(t\right)=(\underset{\&overbar;}{r}\left(t\right),\hat{r}\left(t\right),\stackrel{\&overbar;}{r}\left(t\right))$

WhereinrT () represents the lower limit in t transformer station high-voltage side bus risk indicator for the electrical network,Represent electrical network in t The higher limit of transformer station high-voltage side bus risk indicator,Represent the intermediate value in t transformer station high-voltage side bus risk indicator for the electrical network, respectively Calculate electrical network as follows in the higher limit of t transformer station high-voltage side bus risk indicator, lower limit and intermediate value:

(7-2-1) enumerate all running statuses of t electrical network, according to operation of power networks state, determine every kind of operation respectively In running order transformator set s under state_onWith the transformator set s being in malfunction_off；

(7-2-2) utilize power grid load flow calculation method, calculate mistake loading s under each running status for the electrical network_j T (), subscript j is the numbering of this running status；

(7-2-3) the every kind of running status to electrical network, with each transformator availability higher limit of step (5)Replace Transformator availability in step (6)Formula using step (6) is calculated, and result of calculation is designated asProfit It is calculated the lower limit of t network transformer operation risk index with following formula:

$\underset{\&overbar;}{r}\left(t\right)=\underset{j=1}{\overset{2^n}{\mathrm{\σ}}}{\stackrel{\&overbar;}{p}}_j\left(t\right)\·s_j\left(t\right);$

(7-2-4) the every kind of running status to electrical network, is replaced with each transformator availability lower limit a (t) of step (5) Transformator availability in step (6)Formula using step (6) is calculated, and result of calculation is designated asp _j(t), profit It is calculated the higher limit of t network transformer operation risk index with following formula:

$\stackrel{\&overbar;}{r}\left(t\right)=\underset{j=1}{\overset{2^n}{\mathrm{\σ}}}{\underset{\&overbar;}{p}}_j\left(t\right)\·s_j\left(t\right);$

(7-2-5) the every kind of running status to electrical network, with each transformator availability intermediate value of step (5)Replace Transformator availability in step (6)Formula using step (6) is calculated, and result of calculation is designated asProfit It is calculated the intermediate value of t network transformer operation risk index with following formula:

$\hat{r}\left(t\right)=\underset{j=1}{\overset{2^n}{\mathrm{\σ}}}{\hat{p}}_j\left(t\right)\·s_j\left(t\right);$

(7-3) moment t is judged, if t is ＜ t, return to step (7-2), if t=t, with above-mentioned steps (7-2)As network transformer operation risk index.

A kind of network transformer operation risk assessment method based on fuzzy failure rate proposed by the present invention, its advantage is: The inventive method uses for reference artificial experience, with Triangular Fuzzy Number form indication transformer catastrophic failure rate and degradation failure rate, is given Transformator availability analytic expression based on fuzzy failure rate, by using for reference artificial experience, effectively compensate for historical statistical data Not enough defect, solves traditional method and is difficult to accurately calculate power networks risk index in the case of historical statistical data deficiency This problem, and, the method is by providing optimistic value, pessimistic value and the intermediate value of network transformer operation risk index, and can With weak link present in more accurately reaction operation of power networks, thus providing more fully decision-making to prop up to dispatching of power netwoks personnel Hold.

Specific embodiment

Network transformer operation risk assessment method based on fuzzy failure rate proposed by the present invention, comprises the following steps:

(1) by the state demarcation of transformator be working condition and malfunction, wherein working condition include normally, attention and Abnormal, it is designated as 0,1 and 2 respectively, malfunction is subdivided into catastrophic failure and degradation failure according to failure cause, be designated as 3 Hes respectively 4；

(2) use respectivelyWithCatastrophic failure rate under normal, attention and abnormality for the indication transformer, usesThe degradation failure rate of indication transformer, represents catastrophic failure rate and degradation failure with Triangular Fuzzy Number form as follows Rate:

${\widetilde{\mathrm{\λ}}}_{03}=({\underset{\&overbar;}{\mathrm{\λ}}}_{03},{\widehat{\mathrm{\λ}}}_{03},{\stackrel{\&overbar;}{\mathrm{\λ}}}_{03})$

${\widetilde{\mathrm{\λ}}}_{13}=({\underset{\&overbar;}{\mathrm{\λ}}}_{13},{\widehat{\mathrm{\λ}}}_{13},{\stackrel{\&overbar;}{\mathrm{\λ}}}_{13})$

${\widetilde{\mathrm{\λ}}}_{23}=({\underset{\&overbar;}{\mathrm{\λ}}}_{23},{\widehat{\mathrm{\λ}}}_{23},{\stackrel{\&overbar;}{\mathrm{\λ}}}_{23})$

${\widetilde{\mathrm{\λ}}}_{24}=({\underset{\&overbar;}{\mathrm{\λ}}}_{24},{\widehat{\mathrm{\λ}}}_{24},{\stackrel{\&overbar;}{\mathrm{\λ}}}_{24})$

Whereinλ ₀₃、λ ₁₃Withλ ₂₃The lower limit of catastrophic failure rate under normal, attention and abnormality for the indication transformer respectively Value,WithCatastrophic failure rate higher limit under normal, attention and abnormality for the indication transformer respectively,WithCatastrophic failure rate intermediate value under normal, attention and abnormality for the indication transformer respectively,λ ₂₄Represent and become The degradation failure rate lower limit of depressor,The degradation failure rate higher limit of indication transformer,The degradation failure of indication transformer Rate intermediate value；The fault rate optimistic estimate value that lower limit is given based on experience for dispatcher, span be 0～0.005 time/ My god, higher limit is the fault rate pessimism estimated value that dispatcher is given based on experience, and span is 0～0.1 times/day, middle Be worth the actual estimated value providing for dispatcher based on experience and the current operating condition of transformator, span be 0～0.01 time/ My god.

(3) set up a transformator Markovian state transfer differential equation group as follows:

$\left\{\begin{array}{c}\frac{d{\tilde{p}}_0}{\mathrm{dt}}=-({\mathrm{\λ}}_{01}+{\widetilde{\mathrm{\λ}}}_{03}){\tilde{p}}_0+{\mathrm{\μ}}_b{\tilde{p}}_{3.0}+{\mathrm{\μ}}_c{\tilde{p}}_4\\ \frac{d{\tilde{p}}_1}{\mathrm{dt}}={\mathrm{\λ}}_{01}{\tilde{p}}_0-({\mathrm{\λ}}_{12}+{\widetilde{\mathrm{\λ}}}_{13}){\tilde{p}}_1+{\mathrm{\μ}}_b{\tilde{p}}_{3.2}\\ \frac{d{\tilde{p}}_2}{\mathrm{dt}}={\mathrm{\λ}}_{12}{\tilde{p}}_1-({\widetilde{\mathrm{\λ}}}_{23}+{\widetilde{\mathrm{\λ}}}_{24}){\tilde{p}}_2+{\mathrm{\μ}}_b{\tilde{p}}_{3.2}\\ \frac{d{\tilde{p}}_{3.2}}{\mathrm{dt}}={\widetilde{\mathrm{\λ}}}_{23}{\tilde{p}}_2-{\mathrm{\μ}}_b{\tilde{p}}_{3.2}\\ \frac{d{\tilde{p}}_{3.1}}{\mathrm{dt}}={\widetilde{\mathrm{\λ}}}_{13}{\tilde{p}}_1-{\mathrm{\μ}}_b{\tilde{p}}_{3.1}\\ \frac{d{\tilde{p}}_{3.0}}{\mathrm{dt}}={\widetilde{\mathrm{\λ}}}_{03}{\tilde{p}}_0-{\mathrm{\μ}}_b{\tilde{p}}_{3.0}\\ \frac{d{\tilde{p}}_4}{\mathrm{dt}}={\widetilde{\mathrm{\λ}}}_{24}{\tilde{p}}_2-{\mathrm{\μ}}_c{\tilde{p}}_4\end{array}\right.$

Wherein, λ₀₁Indication transformer is by the transfer rate of normal condition to attention state, λ₁₂Indication transformer is by noting shape State is to the transfer rate of abnormality, μ_cThe repair rate of indication transformer degradation failure, span is 0～1 times/day, μ_bRepresent The repair rate of transformator catastrophic failure, span is 0～10 times/day,WithRespectively indication transformer be in normally, Note the probability with abnormality,Indication transformer is in degradation failure shape probability of state,Indication transformer is in prominent Before sending out malfunction and breaking down, transformator is in the probability of normal condition,Indication transformer is in catastrophic failure state And transformator is in the probability of attention state before breaking down,Indication transformer is in catastrophic failure state and breaks down Front transformator is in the probability of abnormality；

(4) differential equation group is shifted according to Markovian state, obtain the availability analytic expression of transformator, detailed process bag Include following steps:

(4-1) it is in normal condition when setting transformator initialization, using Laplace transformation, above-mentioned differential equation group is changed into Following Algebraic Equation set:

$\left\{\begin{array}{c}s{\tilde{p}}_0-1=-({\mathrm{\λ}}_{01}+{\widetilde{\mathrm{\λ}}}_{03}){\tilde{p}}_0+{\mathrm{\μ}}_b{\tilde{p}}_{3.0}+{\mathrm{\μ}}_c{\tilde{p}}_4\\ s{\tilde{p}}_1={\mathrm{\λ}}_{01}{\tilde{p}}_0-({\mathrm{\λ}}_{12}+{\widetilde{\mathrm{\λ}}}_{13}){\tilde{p}}_1+{\mathrm{\μ}}_b{\tilde{p}}_{3.1}\\ s{\tilde{p}}_2={\mathrm{\λ}}_{12}{\tilde{p}}_1-({\widetilde{\mathrm{\λ}}}_{23}+{\widetilde{\mathrm{\λ}}}_{24}){\tilde{p}}_2+{\mathrm{\μ}}_b{\tilde{p}}_{3.2}\\ s{\tilde{p}}_{3.2}={\widetilde{\mathrm{\λ}}}_{23}{\tilde{p}}_2-{\mathrm{\μ}}_b{\tilde{p}}_{3.2}\\ s{\tilde{p}}_{3.1}={\widetilde{\mathrm{\λ}}}_{13}{\tilde{p}}_1-{\mathrm{\μ}}_b{\tilde{p}}_{3.1}\\ s{\tilde{p}}_{3.0}={\widetilde{\mathrm{\λ}}}_{03}{\tilde{p}}_0-{\mathrm{\μ}}_b{\tilde{p}}_{3.0}\\ s{\tilde{p}}_4={\widetilde{\mathrm{\λ}}}_{24}{\tilde{p}}_2-{\mathrm{\μ}}_c{\tilde{p}}_4\end{array}\right.$

Wherein, s is the complex frequency in Laplace transformation, and Laplace transformation is answering in complex frequency domain by the functional transformation in time domain One integral transformation process of varying function；

(4-2) with Laplace transformation complex frequency s as independent variable, with transformator be in normally, note and abnormality probability WithFor dependent variable, incite somebody to actionWithExpressed with following canonical form with the relation of s:

${\tilde{p}}_0\left(s\right)=\underset{i=0}{\overset{6}{\mathrm{\σ}}}\frac{{\tilde{l}}_{0i}}{s-{\tilde{s}}_i}$

${\tilde{p}}_1\left(s\right)=\underset{i=1}{\overset{8}{\mathrm{\σ}}}\frac{{\tilde{l}}_{1i}}{s-{\tilde{s}}_i}$

${\tilde{p}}_2\left(s\right)=\underset{i=1}{\overset{10}{\mathrm{\σ}}}\frac{{\tilde{l}}_{2i}}{s-{\tilde{s}}_i}$

WhereinWithFor the middle coefficient in canonical form, usually plural number, the span of its mould is led to It is often 0～1；

(4-3) above-mentioned standard form is carried out Laplace inverse transformation, obtain transformator t be in normally, note and different Often the time domain analytical expression of shape probability of state is as follows:

${\tilde{p}}_0=\underset{i=0}{\overset{6}{\mathrm{\σ}}}{\tilde{l}}_{0i}{e}^{{\tilde{s}}_{i}t}$

${\tilde{p}}_1=\underset{i=1}{\overset{8}{\mathrm{\σ}}}{\tilde{l}}_{1i}{e}^{{\tilde{s}}_{i}t}$

${\tilde{p}}_2=\underset{i=1}{\overset{10}{\mathrm{\σ}}}{\tilde{l}}_{2i}{e}^{{\tilde{s}}_{i}t}$

(4-4) the time domain analytical expression according to step (4-3), obtains the availability in t for the transformatorParsing Formula is as follows:

$\tilde{a}\left(t\right)={\tilde{p}}_0+{\tilde{p}}_1+{\tilde{p}}_2=\underset{i=0}{\overset{6}{\mathrm{\σ}}}{\tilde{l}}_{0i}{e}^{{\tilde{s}}_{i}t}+\underset{i=1}{\overset{8}{\mathrm{\σ}}}{\tilde{l}}_{1i}{e}^{{\tilde{s}}_{i}t}+\underset{i=1}{\overset{10}{\mathrm{\σ}}}{\tilde{l}}_{2i}{e}^{{\tilde{s}}_{i}t};$

(5) by above-mentioned transformator t availabilityIt is expressed as Triangular Fuzzy Number form as follows:

$\tilde{a}\left(t\right)=(\underset{\&overbar;}{a}\left(t\right),\hat{a}\left(t\right),\stackrel{\&overbar;}{a}\left(t\right))$

Whereina(t) indication transformer in the availability lower limit of t,Indication transformer is in the availability of t Higher limit,, in the availability intermediate value of t, the solution procedure of lower limit, higher limit and intermediate value is such as indication transformer Under:

(5-1) use the higher limit of the transformator catastrophic failure rate of above-mentioned steps (2)WithReplace step (3) horse Er Kefu state shifts the catastrophic failure rate in differential equation groupWithTransformator degradation failure with step (2) The higher limit of rateStep (3) Markovian state is replaced to shift the degradation failure rate in differential equation groupExecution step (4-1)～step (4-4), obtains the availability lower limit in t for the transformatora(t)；

(5-2) use the lower limit of the transformator catastrophic failure rate of above-mentioned steps (2)λ ₀₃、λ ₁₃Withλ ₂₃Replace step (3) Ma Er Husband's state can shift the catastrophic failure rate in differential equation groupWithTransformator degradation failure rate with step (2) Lower limitλ ₂₄Step (3) Markovian state is replaced to shift the degradation failure rate in differential equation groupExecution step (4- 1)～step (4-4), obtains the higher limit of the availability in t for the transformator

(5-3) use the intermediate value of the transformator catastrophic failure rate of above-mentioned steps (2)WithReplace step (3) horse Er Kefu state shifts the catastrophic failure rate in differential equation groupWithTransformator degradation failure with step (2) The intermediate value of rateStep (3) Markovian state is replaced to shift the degradation failure rate in differential equation groupExecution step (4-1)～step (4-4), obtains the intermediate value of the availability in t for the transformator

(6) set electrical network and be in a kind of probability of running status in tFor:

$\tilde{p}\left(t\right)=\underset{i\&element;s_{\mathrm{on}}}{\mathrm{\π}}{\tilde{a}}_i\left(t\right)\underset{i\&element;s_{\mathrm{off}}}{\mathrm{\π}}(1-{\tilde{a}}_i\left(t\right))$

Wherein, s_onRepresent the in running order transformator set under this running status of electrical network, s_offRepresent electrical network at this It is in the transformator set of malfunction, subscript i indication transformer is numbered under running status,Represent that i-th transformator exists The availability of t；

(7) set and network transformer is carried out with the time span of operation risk assessment as t, in electrical network, have n platform transformator, meter Calculate network transformer operation risk indexProcess as follows:

(7-1) when initializing, if moment t=0；

(7-2) make t=t+1, by electrical network t transformer station high-voltage side bus risk indicatorIt is expressed as Triangular Fuzzy Number form such as Under:

$\tilde{r}\left(t\right)=(\underset{\&overbar;}{r}\left(t\right),\hat{r}\left(t\right),\stackrel{\&overbar;}{r}\left(t\right))$

WhereinrT () represents the lower limit in t transformer station high-voltage side bus risk indicator for the electrical network,Represent electrical network in t The higher limit of transformer station high-voltage side bus risk indicator,Represent the intermediate value in t transformer station high-voltage side bus risk indicator for the electrical network, point Not Ji Suan electrical network as follows in the higher limit of t transformer station high-voltage side bus risk indicator, lower limit and intermediate value:

(7-2-1) enumerate all running statuses of t electrical network, according to operation of power networks state, determine every kind of operation respectively In running order transformator set s under state_onWith the transformator set s being in malfunction_off；

(7-2-2) utilize power grid load flow calculation method, calculate mistake loading s under each running status for the electrical network_j T (), subscript j is the numbering of this running status；

(7-2-3) the every kind of running status to electrical network, with each transformator availability higher limit of step (5)Replace Transformator availability in step (6)Formula using step (6) is calculated, and result of calculation is designated asProfit It is calculated the lower limit of t network transformer operation risk index with following formula:

$\underset{\&overbar;}{r}\left(t\right)=\underset{j=1}{\overset{2^n}{\mathrm{\σ}}}{\stackrel{\&overbar;}{p}}_j\left(t\right)\·s_j\left(t\right);$

(7-2-4) the every kind of running status to electrical network, with each transformator availability lower limit of step (5)aT () replaces Transformator availability in step (6)Formula using step (6) is calculated, and result of calculation is designated asp _j(t), profit It is calculated the higher limit of t network transformer operation risk index with following formula:

$\stackrel{\&overbar;}{r}\left(t\right)=\underset{j=1}{\overset{2^n}{\mathrm{\σ}}}{\underset{\&overbar;}{p}}_j\left(t\right)\·s_j\left(t\right);$

(7-2-5) the every kind of running status to electrical network, with each transformator availability intermediate value of step (5)Replace Transformator availability in step (6)Formula using step (6) is calculated, and result of calculation is designated asProfit It is calculated the intermediate value of t network transformer operation risk index with following formula:

$\hat{r}\left(t\right)=\underset{j=1}{\overset{2^n}{\mathrm{\σ}}}{\hat{p}}_j\left(t\right)\·s_j\left(t\right);$

(7-3) moment t is judged, if t is ＜ t, return to step (7-2), if t=t, with above-mentioned steps (7-2)As network transformer operation risk index.

Claims (1)

1. a kind of network transformer operation risk assessment method based on fuzzy failure rate it is characterised in that the method include following Step:

(1) by the state demarcation of transformator be working condition and malfunction, wherein working condition include normally, attention and different Often, it is designated as 0,1 and 2 respectively, malfunction is subdivided into catastrophic failure and degradation failure according to failure cause, be designated as 3 and 4 respectively；

(2) use respectivelyWithCatastrophic failure rate under normal, attention and abnormality for the indication transformer, usesTable Show the degradation failure rate of transformator, represent catastrophic failure rate and degradation failure rate with Triangular Fuzzy Number form as follows:

${\widetilde{\mathrm{\λ}}}_{03}=({\underset{\&overbar;}{\mathrm{\λ}}}_{03},{\widehat{\mathrm{\λ}}}_{03},{\stackrel{\&overbar;}{\mathrm{\λ}}}_{03})$

${\widetilde{\mathrm{\λ}}}_{13}=({\underset{\&overbar;}{\mathrm{\λ}}}_{13},{\widetilde{\mathrm{\λ}}}_{13},{\stackrel{\&overbar;}{\mathrm{\λ}}}_{13})$

${\widetilde{\mathrm{\λ}}}_{23}=({\underset{\&overbar;}{\mathrm{\λ}}}_{23},{\widetilde{\mathrm{\λ}}}_{23},{\stackrel{\&overbar;}{\mathrm{\λ}}}_{23})$

${\widetilde{\mathrm{\λ}}}_{24}=({\underset{\&overbar;}{\mathrm{\λ}}}_{24},{\widetilde{\mathrm{\λ}}}_{24},{\stackrel{\&overbar;}{\mathrm{\λ}}}_{24})$

Whereinλ ₀₃、λ ₁₃Withλ ₂₃The lower limit of catastrophic failure rate under normal, attention and abnormality for the indication transformer respectively,WithCatastrophic failure rate higher limit under normal, attention and abnormality for the indication transformer respectively,WithCatastrophic failure rate intermediate value under normal, attention and abnormality for the indication transformer respectively,λ ₂₄Indication transformer aging Fault rate lower limit,The degradation failure rate higher limit of indication transformer,The degradation failure rate intermediate value of indication transformer； The fault rate optimistic estimate value that lower limit is given based on experience for dispatcher, span is 0～0.005 times/day, higher limit The fault rate pessimism estimated value being given based on experience for dispatcher, span is 0～0.1 times/day, and intermediate value is scheduling people The actual estimated value that member is given based on experience and the current operating condition of transformator, span is 0～0.01 times/day；

(3) set up a transformator Markovian state transfer differential equation group as follows:

$\left\{\begin{array}{c}\frac{d{\tilde{p}}_0}{dt}=-({\mathrm{\λ}}_{01}+{\widetilde{\mathrm{\λ}}}_{03}){\tilde{p}}_0+{\mathrm{\μ}}_0{\tilde{p}}_{3.0}+{\mathrm{\μ}}_c{\tilde{p}}_4\\ \frac{d{\tilde{p}}_1}{dt}={\mathrm{\λ}}_{01}{\tilde{p}}_0-({\mathrm{\λ}}_{12}+{\widetilde{\mathrm{\λ}}}_{13}){\tilde{p}}_1+{\mathrm{\μ}}_b{\tilde{p}}_{3.1}\\ \frac{d{\tilde{p}}_2}{dt}={\mathrm{\λ}}_{12}{\tilde{p}}_1-({\widetilde{\mathrm{\λ}}}_{23}+{\widetilde{\mathrm{\λ}}}_{24}){\tilde{p}}_2+{\mathrm{\μ}}_b{\tilde{p}}_{3.2}\\ \frac{d{\tilde{p}}_{3.2}}{dt}={\widetilde{\mathrm{\λ}}}_{23}{\tilde{p}}_2-{\mathrm{\μ}}_b{\tilde{p}}_{3.2}\\ \frac{d{\tilde{p}}_{3.1}}{dt}={\widetilde{\mathrm{\λ}}}_{13}{\tilde{p}}_1-{\mathrm{\μ}}_b{\tilde{p}}_{3.1}\\ \frac{d{\tilde{p}}_{3.0}}{dt}={\widetilde{\mathrm{\λ}}}_{03}{\tilde{p}}_0-{\mathrm{\μ}}_b{\tilde{p}}_{3.0}\\ \frac{d{\tilde{p}}_4}{dt}={\widetilde{\mathrm{\λ}}}_{24}{\tilde{p}}_2-{\mathrm{\μ}}_c{\tilde{p}}_4\end{array}\right.$

Wherein, λ₀₁Indication transformer is by the transfer rate of normal condition to attention state, λ₁₂Indication transformer by attention state to The transfer rate of abnormality, μ_cThe repair rate of indication transformer degradation failure, span is 0～1 times/day, μ_bRepresent transformation The repair rate of device catastrophic failure, span is 0～10 times/day,WithRespectively indication transformer be in normally, note With the probability of abnormality,Indication transformer is in degradation failure shape probability of state,Indication transformer is in catastrophic failure State and before breaking down transformator be in the probability of normal condition,Indication transformer is in catastrophic failure state and event occurs Before barrier, transformator is in the probability of attention state,Indication transformer be in catastrophic failure state and break down before transformator It is in the probability of abnormality；

(4) according to Markovian state shift differential equation group, obtain the availability analytic expression of transformator, detailed process include with Lower step:

(4-1) it is in normal condition when setting transformator initialization, using Laplace transformation, above-mentioned differential equation group is changed into as follows Algebraic Equation set:

$\left\{\begin{array}{c}s{\tilde{p}}_0-1=-({\mathrm{\λ}}_{01}+{\widetilde{\mathrm{\λ}}}_{03}){\tilde{p}}_0+{\mathrm{\μ}}_b{\tilde{p}}_{3.0}+{\mathrm{\μ}}_c{\tilde{p}}_4\\ s{\tilde{p}}_1={\mathrm{\λ}}_{01}{\tilde{p}}_0-({\mathrm{\λ}}_{12}+{\widetilde{\mathrm{\λ}}}_{13}){\tilde{p}}_1+{\mathrm{\μ}}_b{\tilde{p}}_{3.1}\\ s{\tilde{p}}_2={\mathrm{\λ}}_{12}{\tilde{p}}_1-({\mathrm{\λ}}_{23}+{\widetilde{\mathrm{\λ}}}_{24}){\tilde{p}}_2+{\mathrm{\μ}}_b{\tilde{p}}_{3.2}\\ s{\tilde{p}}_{3.2}={\widetilde{\mathrm{\λ}}}_{23}{\tilde{p}}_2-{\mathrm{\μ}}_b{\tilde{p}}_{3.2}\\ s{\tilde{p}}_{3.1}={\widetilde{\mathrm{\λ}}}_{13}{\tilde{p}}_1-{\mathrm{\μ}}_b{\tilde{p}}_{3.1}\\ s{\tilde{p}}_{3.0}={\widetilde{\mathrm{\λ}}}_{03}{\tilde{p}}_0-{\mathrm{\μ}}_b{\tilde{p}}_{3.0}\\ s{\tilde{p}}_4={\widetilde{\mathrm{\λ}}}_{24}{\tilde{p}}_2-{\mathrm{\μ}}_c{\tilde{p}}_4\end{array}\right.$

Wherein, s is the complex frequency in Laplace transformation, and Laplace transformation is the multiple change letter by the functional transformation in time domain in complex frequency domain One integral transformation process of number；

(4-2) with Laplace transformation complex frequency s as independent variable, with transformator be in normally, note and abnormality probability WithFor dependent variable, incite somebody to actionWithExpressed with following canonical form with the relation of s:

${\tilde{p}}_0\left(s\right)=\underset{i=0}{\overset{6}{\σ}}\frac{{\tilde{l}}_{0i}}{s-{\tilde{s}}_i}$

${\tilde{p}}_1\left(s\right)=\underset{i=0}{\overset{8}{\σ}}\frac{{\tilde{l}}_{1i}}{s-{\tilde{s}}_i}$

${\tilde{p}}_2\left(s\right)=\underset{i=0}{\overset{10}{\σ}}\frac{{\tilde{l}}_{2i}}{s-{\tilde{s}}_i}$

WhereinWithFor the middle coefficient in canonical form, usually plural number, the span of its mould is usually 0 ～1；

(4-3) above-mentioned standard form is carried out Laplace inverse transformation, obtain transformator t be in normally, note and abnormal shape The time domain analytical expression of probability of state is as follows:

${\tilde{p}}_0=\underset{i=0}{\overset{6}{\σ}}{\tilde{l}}_{0i}{e}^{{\tilde{s}}_{i}t}$

${\tilde{p}}_1=\underset{i=0}{\overset{8}{\σ}}{\tilde{l}}_{1i}{e}^{{\tilde{s}}_{i}t}$

${\tilde{p}}_2=\underset{i=0}{\overset{10}{\σ}}{\tilde{l}}_{2i}{e}^{{\tilde{s}}_{i}t}$

(4-4) the time domain analytical expression according to step (4-3), obtains the availability in t for the transformatorAnalytic expression is such as Under:

$\tilde{a}\left(t\right)={\tilde{p}}_0+{\tilde{p}}_1+{\tilde{p}}_2=\underset{i=0}{\overset{6}{\σ}}{\tilde{l}}_{0i}{e}^{{\tilde{s}}_{i}t}+\underset{i=0}{\overset{8}{\σ}}{\tilde{l}}_{1i}{e}^{{\tilde{s}}_{i}t}+\underset{i=0}{\overset{\mathrm{10}}{\σ}}{\tilde{l}}_{2i}{e}^{{\tilde{s}}_{i}t};$

(5) by above-mentioned transformator t availabilityIt is expressed as Triangular Fuzzy Number form as follows:

$\tilde{a}\left(t\right)=\left(\underset{\&overbar;}{a}\right(t),\hat{a}(t),\stackrel{\&overbar;}{a}(t\left)\right)$

Whereina(t) indication transformer in the availability lower limit of t,Indication transformer is in the availability upper limit of t Value,, in the availability intermediate value of t, the solution procedure of lower limit, higher limit and intermediate value is as follows for indication transformer:

(5-1) use the higher limit of the transformator catastrophic failure rate of above-mentioned steps (2)WithReplacement step (3) Ma Er can Husband's state shifts the catastrophic failure rate in differential equation groupWithUpper with the transformator degradation failure rate of step (2) Limit valueStep (3) Markovian state is replaced to shift the degradation failure rate in differential equation groupExecution step (4-1)～ Step (4-4), obtains the availability lower limit in t for the transformatora(t)；

(5-2) use the lower limit of the transformator catastrophic failure rate of above-mentioned steps (2)λ ₀₃、λ ₁₃Withλ ₂₃Replace step (3) markov State shifts the catastrophic failure rate in differential equation groupWithWith under the transformator degradation failure rate of step (2) Limit valueλ ₂₄Step (3) Markovian state is replaced to shift the degradation failure rate in differential equation groupExecution step (4-1)～ Step (4-4), obtains the higher limit of the availability in t for the transformator

(5-3) use the intermediate value of the transformator catastrophic failure rate of above-mentioned steps (2)WithReplacement step (3) Ma Er can Husband's state shifts the catastrophic failure rate in differential equation groupWithWith the transformator degradation failure rate of step (2) Intermediate valueStep (3) Markovian state is replaced to shift the degradation failure rate in differential equation groupExecution step (4-1) ～step (4-4), obtains the intermediate value of the availability in t for the transformator

(6) set electrical network and be in a kind of probability of running status in tFor:

$\tilde{p}\left(t\right)=\underset{i\&element;s_{on}}{\π}{\tilde{a}}_i\left(t\right)\underset{i\&element;s_{off}}{\π}(1-{\tilde{a}}_i(t\left)\right)$

Wherein, s_onRepresent the in running order transformator set under this running status of electrical network, s_offRepresent electrical network in this operation It is in the transformator set of malfunction, subscript i indication transformer is numbered under state,Represent i-th transformator in t Availability；

(7) set and network transformer is carried out with the time span of operation risk assessment as t, in electrical network, have n platform transformator, calculate electricity Net transformer station high-voltage side bus risk indicatorProcess as follows:

(7-1) when initializing, if moment t=0；

(7-2) make t=t+1, by electrical network t transformer station high-voltage side bus risk indicatorIt is expressed as Triangular Fuzzy Number form as follows:

$\stackrel{\&overbar;}{r}\left(t\right)=\left(\underset{\&overbar;}{r}\right(t),\hat{r}(t),\stackrel{\&overbar;}{r}(t\left)\right)$

WhereinrT () represents the lower limit in t transformer station high-voltage side bus risk indicator for the electrical network,Represent electrical network in t transformation The higher limit of device operation risk index,Represent that electrical network, in the intermediate value of t transformer station high-voltage side bus risk indicator, calculates respectively Electrical network is as follows in the higher limit of t transformer station high-voltage side bus risk indicator, lower limit and intermediate value:

(7-2-1) enumerate all running statuses of t electrical network, according to operation of power networks state, determine every kind of running status respectively Under in running order transformator set s_onWith the transformator set s being in malfunction_off；

(7-2-2) utilize power grid load flow calculation method, calculate mistake loading s under each running status for the electrical network_j(t), subscript J is the numbering of this running status；

(7-2-3) the every kind of running status to electrical network, with each transformator availability higher limit of step (5)Replace step (6) the transformator availability inFormula using step (6) is calculated, and result of calculation is designated asUsing following formula It is calculated the lower limit of t network transformer operation risk index:

$\underset{\&overbar;}{r}\left(t\right)=\underset{j=1}{\overset{2^n}{\σ}}{\stackrel{\&overbar;}{p}}_j\left(t\right)\·s_j\left(t\right);$

(7-2-4) the every kind of running status to electrical network, with each transformator availability lower limit of step (5)aT () replaces step (6) the transformator availability inFormula using step (6) is calculated, and result of calculation is designated asp _jT (), under utilizing Formula is calculated the higher limit of t network transformer operation risk index:

$\stackrel{\&overbar;}{r}\left(t\right)=\underset{j=1}{\overset{2^n}{\σ}}{\underset{\&overbar;}{p}}_j\left(t\right)\·s_j\left(t\right);$

(7-2-5) the every kind of running status to electrical network, with each transformator availability intermediate value of step (5)Replace step (6) the transformator availability inFormula using step (6) is calculated, and result of calculation is designated asUsing following formula It is calculated the intermediate value of t network transformer operation risk index:

$\hat{r}\left(t\right)=\underset{j=1}{\overset{2^n}{\σ}}{\hat{p}}_j\left(t\right)\·s_j\left(t\right);$

(7-3) moment t is judged, if t < t, return to step (7-2), if t=t, with above-mentioned steps (7-2) As network transformer operation risk index.