CN101251835A - Method for evaluating reliability of +/- 800kV current exchanging station main wire connection - Google Patents

Abstract

The invention provides a method for a reliability evaluation of a main wiring of a +-800kV convertor station, which is characterized in: establishing improved models of four states of elements; reliability models of relay protection and a secondary device in a process of evaluating the reliability of the main wiring; simplifying the prior complicated main wiring of the +-800kV convertor station by using partition of the elements; applying the improved models of the four states of the elements in each simplified partition; redefining abnormal states and maintenance states of the elements; combining and classifying a state maintenance state and a planned maintenance state of the elements into the maintenance state of the elements; determining conversion relationships between the states and acquiring parameters; simplifying a minimal path matrix searching method by a matrix multiplication to perform a minimal path searching to a directed network; enumerating states of various failures of the directed network by using an analysis method; and calculating reliable data of the network.

Description

A kind of ± 800kV converter substation scheme reliability estimation method

Technical field:

The present invention relates to the Model in Reliability Evaluation of Power Systems technical field, especially a kind of ± 800kV converter substation scheme reliability estimation method.

Background technology:

Because greatly developing of domestic Condition-Based Maintenance Technology, the repair based on condition of component state of element has become an indispensable state in the element state conversion, and in classical element four condition model, do not take into account the repair based on condition of component state of element, think that therefore classical element four condition model has not met the actual conditions of element state conversion.

List of references:

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[8] Lu Zongxiang, Guo Yongji. power station electrical main connecting wire reliability assessment. Automation of Electric Systems, 2001,25 (18): 16-19

[9] Guo Yongji. Power System Reliability Analysis. publishing house of Tsing-Hua University.

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[12] Hu Xiao, Huang Xiaoming. ± 800kV extra-high voltage current conversion station reliability assessment. Sichuan power technology, 2007,30 (3): 1-5

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[17] Zhou Niancheng, Xie Kaigui, Zhou Jiaqi, Zhao Yuan, Liu Yang. get complicated evaluating reliability of distribution network block algorithm based on shortest path. Automation of Electric Systems, 2005,29 (22): 39-44

[18] Zhang Peng, Wang Shouxiang. the improvement interval method of distribution Power System Reliability assessment. Automation of Electric Systems, 2003,27 (17): 50-55

Summary of the invention

The objective of the invention is to propose a kind of ± 800kV converter substation scheme reliability estimation method, this method has proposed the improvement four condition model of element and has been applied to ± 800kV converter substation scheme reliability assessment.Because the importance and the reliability requirement of ± 800kV current conversion station are all very high, therefore in assessment main electrical scheme reliability process, having added the reliability model of continue guarantor and secondary device, purpose is the reliability that can more detailed and accurately react current conversion station.The merging subregion that this method is utilized element originally more complicated ± 800kV converter substation scheme simplifies, and the element four condition model of application enhancements each subregion after simplifying.This model redefines the abnormality and the inspecting state of element, and the repair based on condition of component state of element and scheduled overhaul state are merged the inspecting state that is included into element, and determines asking for of transformational relation between each state and parameter.Proposition utilizes the merging partition method of element to simplify main electrical scheme, forms a simple directed networks, and improved element four condition model is applied to determining of subregion dependability parameter.Use the method for matrix multiplication simplification minimal path matrix search directed networks is carried out the minimal path search, utilize analytical method to enumerate the various malfunctions of directed networks, and calculate the reliability data of this network.

Concrete steps of the present invention are as follows:

(1) sets up improvement element four condition model.Redefine the abnormality of equipment, inspecting state and malfunction, and correlationship, and set up transformational relation, on classical element four condition model basis, increase element abnormality A.As shown in Figure 1.

Element abnormality (A): some function of element breaks down or element residing state of this element when breaking down sign;

Element inspecting state (M):, comprise scheduled overhaul state and repair based on condition of component state for element is in the state of maintenance;

Element fault state (R): residing state when element can't guarantee its due function of tonic chord, for switchgears such as isolating switchs, the malfunction into element is concluded in its malfunction and tripping.

(2) in the main electrical scheme reliability assessment, increased to continue and protected and the reliability model of secondary device, so that converter substation scheme's reliability is more near true horizon.

(3) element merges subregion.Main electrical scheme four condition model is carried out subregion, major component and its subsidiary component merge the formation subregion, if the merging of adjacent series and parallel major component does not influence the mode of connection then can merge into a subregion, influence the mode of connection if merge the back, then separately as subregion, as Fig. 4 and Fig. 5.

(4) the subregion dependability parameter determines.Because each subregion all is made of element, then will improves element four condition model and be used for determining of each subregion dependability parameter.For with improved element four condition model better application in each subregion, define the state of each subregion: the inspecting state (M) of the abnormality of subregion (A), subregion, the malfunction (R) of subregion.Conversion between each subregion state is with reference to the element four condition model of figure 1.Improved element four condition model is applied to the dependability parameter of each subregion in the hope of each subregion.

(5) utilize the minimal path search procedure that the network that subregion forms is searched for.

Description of drawings:

Fig. 1 is improved element four condition model.

Wherein: N is the element normal condition; A is the element abnormality; R is the element fault state; M is the element inspecting state; λ _ABecome the probability of abnormality from normal condition for element; λ _MBe the maintenance rate of equipment, λ ' _MFor element transfers the repair based on condition of component rate of inspecting state, ' ' λ to from abnormality _MScheduled overhaul rate for element; λ _RBe element failure rate; λ ' _ABecome the probability of malfunction from abnormality for element; μ _RBe the element repair rate; μ _MBe the element repair rate.

Fig. 2 is the existing equipment condition curve.

Fig. 3 is the main wiring diagram of certain current conversion station.

Fig. 4 is the main wiring diagram of an one pole merging subregion among Fig. 3.

Fig. 5 is a main electrical scheme subregion reduced graph.

Wherein: zone11 to zone43 is each divisional symble

Fig. 6 is the calculation process block scheme according to the reliability index of the present invention's proposition.

Embodiment

Describe in detail below in conjunction with embodiment and accompanying drawing thereof.

(1) sets up improvement element four condition model

In the repair based on condition of component, when a certain equipment is when overhauling according to the repair based on condition of component mode, the state of equipment is the foundation of repair based on condition of component mode.As Fig. 2, in the equipment state overhauling mode, equipment failure sign point is from the A point, when occurring unusually promptly detecting failure symptom B, the state of equipment points out now, the staff can this failure symptom point B take place to fault constantly D during this period of time in monitor equipment status closely, when equipment state arrival state threshold points C, will have two kinds of processing modes: 1, to the equipment maintenance of stopping transport; 2, when being reduced to state point D, equipment state repairs or replaces.By these two modes we as can be seen, when this equipment when the mode 1 transfers the forced outage state to from abnormality, this equipment transfers malfunction to from abnormality when for mode 2.

In classical element four condition model the inside, only forced outage mode and the scheduled overhaul mode to equipment defines, and do not consider the repair based on condition of component mode of equipment.To the analysis of repair based on condition of component process, it is considered herein that the repair based on condition of component of equipment also should be included element four condition model in according to Fig. 2 equipment state curve and the preceding paragraph.The present invention redefines the abnormality of equipment, inspecting state and malfunction, and correlationship, and set up and improve element four condition model such as Fig. 1.

According to improving element four condition model, element is from corresponding inspecting state M of normal condition N and abnormality A, the abnormality A of element is converted to malfunction R and inspecting state M, promptly show: element is from normal operation, may enter inspecting state because of scheduled overhaul, also may be because little defect or the abnormality that enters element unusually, and after element is in abnormality, may be because find its abnormal conditions early, so element is carried out repair based on condition of component, also possible because repair again after finding its situation early or deliberately waiting until its fault, and make element enter malfunction.Element is meant repair process after the fault of equipment to normal condition by malfunction.

By contrasting improved element four condition model and classical element four condition model as can be known, improve the conversion of element four condition model between more can the clear performance element state, and the extraction of the record of M state and R state is easier.Because the M state is the record that element is in inspecting state, the R state is the record that element is in malfunction.Required increase be the record of element A condition, and because improvement four condition model of the present invention is to be based upon on the Condition Monitoring Technology basis of equipment, the record of element abnormality A also obtains easily.

(2) secondary and the guarantor's reliability model that continues in the main electrical scheme reliability assessment, have been increased.The reliability of relay protection relates to two parts of software and hardware.Hardware reliability is:

λ＝γ _Q(C ₁γ _Tγ _V+C ₂γ _E)γ _L(1)

${\mathrm{\λ}}_M=\underset{i=1}{\overset{N}{\mathrm{\Σ}}}{\mathrm{\λ}}_i---\left(2\right)$

λ _H＝λ _T+λ _J(3)

In the formula: γ _QBe the device quality factor; C ₁Be the circuit complexity factor; γ _TBe the temperature accelerated factor; γ _VBe voltage stress factor C ₂Be the encapsulation complexity factor; γ _EBe the applied environment factor; γ _LFor being the ripe factor of device; N is total number of components and parts among the module M.λ _HBe the hardware fault rate; λ _TBe the communication module failure rate; λ _JBe relay protection module failure rate.

Software reliability model adopts John Musa model ^[11]Handle, the software failure rate of this model is:

${\mathrm{\λ}}_s=e^{-\frac{{\mathrm{\τ}}^{\′}}{\mathrm{\τ}}{M}_0{T}_0}={\mathrm{\λ}}_0{e}^{-\frac{{\mathrm{\τ}}^{\′}}{\mathrm{\τ}}}---\left(4\right)$

In the formula: τ is the accumulation execution time, and promptly program is from bringing into operation the time that this assessment reliability experienced; τ ' is a program runtime, promptly from this assessment, but the time of program failure-free operation; λ ₀Be the primary fault rate, with initial failure free time T ₀And the defective sum M of software ₀Relevant.

Reliability of relay protection is made up of software reliability and hardware reliability two parts, and both also have the feature of polyphone incident, then reliability of relay protection as shown in the formula:

λ _JB＝λ _S+λ _H(5)

In the formula: λ _JBBe the relay protection fault rate; λ _SBe software failure rate; λ _HBe the hardware fault rate.

(3) element merges subregion.With certain ± 800kV converter substation scheme is an example, as Fig. 3.Because number of elements is numerous in the current conversion station,, utilizes element to merge partitioned method main electrical scheme is carried out subregion for making things convenient for the main electrical scheme reliability assessment.Cardinal rule is: major component and its subsidiary component merge the formation subregion, if the merging of adjacent series and parallel major component does not influence the mode of connection then can merge into a subregion, influence the mode of connection if merge the back, then separately as subregion.According to above principle, should ± 800kV converter substation scheme can form following subregion:

A. AC circuit breaker, converter power transformer and protective relaying device thereof form a subregion in the current conversion station.

B. converter valve and its affiliated lightning arrester are as a subregion.

C. smoothing reactor and wave filter are as a subregion.

D. the DC side isolating switch forms a subregion.

Then main electrical scheme utmost point 1-1 group is simplified as Fig. 4, among the figure frame of broken lines represent divide subregion.

By above partition method as can be known, the current conversion station overall simplification as shown in Figure 5, wherein zone11～zone43 is subregion name.

(4) application enhancements element four condition model is asked for each subregion dependability parameter.

For with improved element four condition model better application in each subregion, the definition:

The abnormality of subregion (A): major component is under the situation of abnormality or the normal operation of major component, the residing state of this subregion during its monitoring equipment fault.

Definition is because if when the protection of major component, monitoring equipment fault like this; though to the connective nothing influence of main electrical scheme; but cause the possibility of stealthy fault or multiple failure to increase; security and the reliability for current conversion station all will have considerable influence this moment, and then this moment, this element was in abnormality.For example; suppose the converter valve operate as normal; and its converter valve lightning arrester fault; can't play the protective effect of shoving; and the lightning arrester monitoring equipment also lost efficacy or operations staff when not noting its fault-signal, and in the thunderbolt incident, the possibility of converter valve fault will increase greatly; but whole current conversion station still can continue operation, claims that then this moment, converter valve was in abnormality.

The inspecting state of subregion (M): no matter be subsidiary component or main element,, then be called inspecting state in the subregion as long as be in any in scheduled overhaul state or the repair based on condition of component state.

The malfunction of subregion (R): the residing state of this subregion during the major component fault or during its protection equipment failure in the subregion.Normally move as, transformer fault or when transformer, but when protecting equipment tripping or malfunction, can think that this subregion is a malfunction.

Conversion between each subregion state is with reference to figure 1.Improved element four condition model is applied to the dependability parameter of each subregion in the hope of each subregion.For the subregion that isolating switch-converter power transformer forms, its failure rate parameter as shown in the formula:

Since each subregion all be by elements combination and, the state correspondence of visible element each subregion state, and element four condition model is applied to each subregion, to obtain the subregion dependability parameter, for the subregion that isolating switch-converter power transformer forms, its failure rate parameter as shown in the formula:

λ _R＝λ _R(d-b)+λ _(JB)

λ _A＝λ _A(d-b)+λ _x

λ′ _M＝λ _x

λ′ _A＝λ _JB

${\mathrm{\μ}}_M=\frac{{\mathrm{\λ}}_{d-M}+{\mathrm{\λ}}_{b-M}+{\mathrm{\λ}}_x+{\mathrm{\λ}}_{\mathrm{JB}}}{\frac{{\mathrm{\λ}}_{d-M}}{{\mathrm{\μ}}_{d-M}}+\frac{{\mathrm{\λ}}_{b-M}}{{\mathrm{\μ}}_{b-M}}+\frac{{\mathrm{\λ}}_x}{{\mathrm{\μ}}_x}+\frac{{\mathrm{\λ}}_{\mathrm{JB}}}{{\mathrm{\μ}}_{\mathrm{JB}}}}---\left(6\right)$

${\mathrm{\μ}}_R=\frac{{\mathrm{\λ}}_{d-R}+{\mathrm{\λ}}_{b-R}}{\frac{{\mathrm{\λ}}_{d-R}}{{\mathrm{\μ}}_{d-R}}+\frac{{\mathrm{\λ}}_{b-R}}{{\mathrm{\μ}}_{b-R}}}$

Wherein: λ _RBe subregion failure rate, λ _ABe the unusual probability of subregion, λ ' _MBe subregion state maintenance probability, λ ' _ABe subregion state maintenance probability, μ _MBe subregion maintenance repair rate, μ _RBe subregion fault restoration rate; λ _{R (d-b)}Be isolating switch and transformer fault rate sum; λ _{A (d-b)}Be isolating switch and transformer abnormality rate sum, λ _D-MBe isolating switch maintenance rate, λ _B-MBe Repair of Transformer rate, λ _D-RBe circuit breaker failure rate, λ _B-RBe transformer fault rate, μ _D-MBe isolating switch maintenance repair rate, μ _B-MBe Repair of Transformer repair rate, μ _D-RBe circuit breaker failure repair rate, μ _B-RBe the transformer fault repair rate;

For the subregion that converter valve, lightning arrester form, its failure rate parameter as shown in the formula:

λ _R＝λ _h-R+λ _bl

λ _A＝λ _bl＝λ′ _A

λ′ _M＝0(7)

${\mathrm{\μ}}_M=\frac{{\mathrm{\λ}}_{h-M}+{\mathrm{\λ}}_{\mathrm{bl}}}{\frac{{\mathrm{\λ}}_{h-M}}{{\mathrm{\μ}}_{h-M}}+\frac{{\mathrm{\λ}}_{\mathrm{bl}}}{{\mathrm{\μ}}_{\mathrm{bl}}}}$

${\mathrm{\μ}}_R=\frac{{\mathrm{\λ}}_{h-R}+{\mathrm{\λ}}_{\mathrm{bl}}}{\frac{{\mathrm{\λ}}_{h-R}}{{\mathrm{\μ}}_{h-R}}+\frac{{\mathrm{\λ}}_{\mathrm{bl}}}{{\mathrm{\μ}}_{\mathrm{bl}}}}$

Wherein: λ _H-RBe converter fault rate, λ _H-ABe the unusual rate of transverter, λ _H-MBe transverter maintenance rate, λ _BlBe lightning arrester failure rate, μ _H-MBe transverter maintenance repair rate, μ _H-RBe the converter fault repair rate;

For the subregion that smoothing reactor, wave filter form, its failure rate parameter as shown in the formula:

λ _R＝λ _c-R+λ _k-R

λ _A＝0＝λ′ _M＝λ′ _A

${\mathrm{\μ}}_M=\frac{{\mathrm{\λ}}_{c-M}+{\mathrm{\λ}}_{k-M}}{\frac{{\mathrm{\λ}}_{c-M}}{{\mathrm{\μ}}_{c-M}}+\frac{{\mathrm{\λ}}_{k-M}}{{\mathrm{\μ}}_{k-M}}}---\left(8\right)$

${\mathrm{\μ}}_R=\frac{{\mathrm{\λ}}_{c-R}+{\mathrm{\λ}}_{k-R}}{\frac{{\mathrm{\λ}}_{c-R}}{{\mathrm{\μ}}_{c-R}}+\frac{{\mathrm{\λ}}_{k-R}}{{\mathrm{\μ}}_{k-R}}}$

Wherein: λ _C-RBe wave filter failure rate, λ _C-MBe wave filter maintenance repair rate, λ _K-RBe smoothing reactor failure rate, λ _K-MBe smoothing reactor maintenance repair rate, μ _C-MBe wave filter maintenance repair rate, μ _C-RBe wave filter fault restoration rate; μ _K-MBe smoothing reactor maintenance repair rate, μ _K-RBe smoothing reactor fault restoration rate;

For the subregion that the DC side isolating switch forms, its failure rate parameter as shown in the formula:

λ _R＝λ _p-R+λ _JB

λ _A＝λ _x＝λ′ _M

λ′ _A＝λ _JB (9)

${\mathrm{\μ}}_M=\frac{{\mathrm{\λ}}_{p-M}+{\mathrm{\λ}}_x+{\mathrm{\λ}}_{\mathrm{JB}}}{\frac{{\mathrm{\λ}}_{p-M}}{{\mathrm{\μ}}_{p-M}}+\frac{{\mathrm{\λ}}_x}{{\mathrm{\μ}}_x}+\frac{{\mathrm{\λ}}_{\mathrm{JB}}}{{\mathrm{\μ}}_{\mathrm{JB}}}}$

${\mathrm{\μ}}_R=\frac{{\mathrm{\λ}}_{p-R}+{\mathrm{\λ}}_{\mathrm{JB}}}{\frac{{\mathrm{\λ}}_{p-R}}{{\mathrm{\μ}}_{p-R}}+\frac{{\mathrm{\λ}}_{\mathrm{JB}}}{{\mathrm{\μ}}_{\mathrm{JB}}}}$

Wherein: λ _P-RBe DC side circuit breaker failure rate, λ _P-MBe DC side isolating switch maintenance rate, μ _P-RBe DC side circuit breaker failure repair rate, μ _P-MBe DC side isolating switch maintenance repair rate, μ _xBe isolating switch communication module maintenance repair rate, μ _JBFor continuing, isolating switch protects the module repair rate,

(5) minimal path of section post formation network is searched for

According to Fig. 5 as can be known, each subregion forms a directed networks.Utilize matrix multiplication that minimal path is searched for, method is as follows:

A. defining each subregion is a node, sets up the adjacency matrix A of network ₁=[a ¹ _Ij].

Wherein: as node v _iAnd v _jBetween when connection is arranged, a ¹ _Ij=1 or a ¹ _Ij=-1; Work as v _jAnd v _jBetween do not have to connect or during j=i a ¹ _Ij=a ¹ _Ji=0.

B. set up network in abutting connection with terminal point matrix R=[r _Jk].

Wherein: as node v _jWith terminal point v _kBetween when connection is arranged, r ¹ _Jk=1; Work as v _jAnd v _kBetween do not have to connect or during j=k r ¹ _Jk=0;

C. with matrix A ₁R multiplies each other with adjacency terminal point matrix, obtains new matrix A ₂=[a ² _Ik].

$a_{\mathrm{ik}}^2=\left\{a_{\mathrm{ij}}^1{r}_{\mathrm{jk}}\right|j=\mathrm{1,2},\·\·\·n\}---\left(10\right)$

Wherein: work as i, j, when three nodes of k have nothing in common with each other, a ² _Ik=a ¹ _Ijr _JkWork as a ¹ _Ij=0 or r _Jk=0 or v _kAt least with v _iAnd v _jIn one when identical, a ² _Ik=0.

D. change terminal point v _k, repeat above step, obtain matrix A ₃, A ₄... A _N-1,

E. with A ₁, A ₂... A _N-1(i, nonzero element j) combines middle correspondence position, just obtains from node i to all minimal paths the node j.

F. because the selected node of the application has comprised the element of all needs assessments in the main electrical scheme, do not have the single node element to be omitted, then this minimal path collection matrix is final road collection matrix.Utilize road collection matrix to carry out the cut set analysis to node arbitrarily.

Reliability index statistics flow process as shown in Figure 6.Idiographic flow is as follows: read in topology network, form network information matrix, form minimal path collection matrix, enumerate network state, calculate minimal cut set, add up each state lower network reliability index.

Claims (1)

1. one kind ± 800kV converter substation scheme reliability estimation method, it is characterized in that: set up improved element four condition model, the reliability model that in assessment main electrical scheme reliability process, having added continue guarantor and secondary device, the merging subregion that utilizes element originally more complicated ± 800kV converter substation scheme simplifies, and the element four condition model of application enhancements each subregion after simplifying, redefine the abnormality and the inspecting state of element, the repair based on condition of component state and the scheduled overhaul state of element are merged the inspecting state that is included into element, and determine asking for of transformational relation between each state and parameter, simplify the method for minimal path matrix search with matrix multiplication directed networks is carried out the minimal path search, utilize analytical method to enumerate the various malfunctions of directed networks, and calculate the reliability data of this network, concrete steps are as follows:

(1) sets up improvement element four condition model

In improving element four condition model, redefine the abnormality of equipment, inspecting state and malfunction, and correlationship:

Element abnormality (A): the residing state of this element during sign that the element secondary function breaks down or element breaks down;

Element inspecting state (M):, comprise scheduled overhaul state and repair based on condition of component state for element is in the state of maintenance;

Element fault state (R): residing state when element can't guarantee its due major function, for switchgear, the malfunction into element is concluded in its malfunction and tripping;

According to improving element four condition model, element is from corresponding inspecting state M of normal condition N and abnormality A, and the abnormality A of element is converted to malfunction R and inspecting state M;

(2) increased to continue in the main electrical scheme reliability assessment and protect and the reliability model of secondary device, continued and protect reliability and comprise two parts of software and hardware, hardware reliability is:

λ＝γ _Q(C ₁γ _Tγ _V+C ₂γ _E)γ _L

${\mathrm{\λ}}_M=\underset{i=1}{\overset{N}{\mathrm{\Σ}}}{\mathrm{\λ}}_i$

λ _H＝λ _T+λ _J

In the formula: γ _QBe the device quality factor; C ₁Be the circuit complexity factor; γ _TBe the temperature accelerated factor; γ _VBe the voltage stress factor; C ₂Be the encapsulation complexity factor; γ _EBe the applied environment factor; γ _LFor being the ripe factor of device; N is total number of components and parts among the module M; λ _HBe the hardware fault rate; λ _TBe the communication module failure rate; λ _JBe relay protection module failure rate;

Software reliability model adopts John Musa models treated, and the software failure rate of this model is:

${\mathrm{\λ}}_s=e^{-\frac{{\mathrm{\τ}}^{\′}}{\mathrm{\τ}}{M}_0{T}_0}={\mathrm{\λ}}_0{e}^{-\frac{{\mathrm{\τ}}^{\′}}{\mathrm{\τ}}}$

In the formula: τ is the accumulation execution time, and promptly program is from bringing into operation the time that this assessment reliability experienced; τ ' is a program runtime, promptly from this assessment, but the time of program failure-free operation; λ ₀Be the primary fault rate, with initial failure free time T ₀And the defective sum M of software ₀Relevant;

Then reliability of relay protection as shown in the formula:

λ _JB＝λ _S+λ _H

In the formula: λ _JBBe the relay protection fault rate; λ _SBe software failure rate; λ _HBe the hardware fault rate;

(3) element merges subregion

Main electrical scheme four condition model is carried out subregion, and major component and its subsidiary component merge the formation subregion, if the merging of adjacent series and parallel major component does not influence the mode of connection then can merge into a subregion, influence the mode of connection if merge the back, then separately as subregion;

(4) the subregion dependability parameter determines

Since each subregion all be by elements combination and, the state correspondence of visible element each subregion state, and element four condition model is applied to each subregion, to obtain the subregion dependability parameter, for the subregion that isolating switch-converter power transformer forms, its failure rate parameter as shown in the formula:

λ _R＝λ _R(d-b)+λ _(Jb)

λ _A＝λ _A(d-b)+λ _x

λ′ _M＝λ _x

λ′ _A＝λ _JB

${\mathrm{\μ}}_M=\frac{{\mathrm{\λ}}_{d-M}+{\mathrm{\λ}}_{b-M}+{\mathrm{\λ}}_x+{\mathrm{\λ}}_{\mathrm{JB}}}{\frac{{\mathrm{\λ}}_{d-M}}{{\mathrm{\μ}}_{d-M}}+\frac{{\mathrm{\λ}}_{b-M}}{{\mathrm{\μ}}_{b-M}}+\frac{{\mathrm{\λ}}_x}{{\mathrm{\μ}}_x}+\frac{{\mathrm{\λ}}_{\mathrm{JB}}}{{\mathrm{\μ}}_{\text{JB}}}}$

${\mathrm{\μ}}_R=\frac{{\mathrm{\λ}}_{d-R}+{\mathrm{\λ}}_{b-R}}{\frac{{\mathrm{\λ}}_{d-R}}{{\mathrm{\μ}}_{d-R}}+\frac{{\mathrm{\λ}}_{b-R}}{{\mathrm{\μ}}_{b-R}}}$

Wherein: λ _RBe subregion failure rate, λ _ABe the unusual probability of subregion, λ ' _MBe subregion state maintenance probability, λ ' _ABe subregion state maintenance probability, μ _MBe subregion maintenance repair rate, μ _RBe subregion fault restoration rate; λ _{R (d-b)}Be isolating switch and transformer fault rate sum; λ _{A (d-b)}Be isolating switch and transformer abnormality rate sum, λ _D-MBe isolating switch maintenance rate, λ _B-MBe Repair of Transformer rate, λ _D-RBe circuit breaker failure rate, λ _B-RBe transformer fault rate, μ _D-MBe isolating switch maintenance repair rate, μ _B-MBe Repair of Transformer repair rate, μ _D-RBe circuit breaker failure repair rate, μ _B-RBe the transformer fault repair rate;

For the subregion that converter valve, lightning arrester form, its failure rate parameter as shown in the formula:

λ _R＝λ _h-R+λ _bl

λ _A＝λ _bl＝λ′ _A

λ′ _M＝0

${\mathrm{\μ}}_M=\frac{{\mathrm{\λ}}_{h-M}+{\mathrm{\λ}}_{\mathrm{bl}}}{\frac{{\mathrm{\λ}}_{h-M}}{{\mathrm{\μ}}_{h-M}}+\frac{{\mathrm{\λ}}_{\mathrm{bl}}}{{\mathrm{\μ}}_{\mathrm{bl}}}}$

${\mathrm{\μ}}_R=\frac{{\mathrm{\λ}}_{h-R}+{\mathrm{\λ}}_{\mathrm{bl}}}{\frac{{\mathrm{\λ}}_{h-R}}{{\mathrm{\μ}}_{h-R}}+\frac{{\mathrm{\λ}}_{\mathrm{bl}}}{{\mathrm{\μ}}_{\mathrm{bl}}}}$

Wherein: λ _H-RBe converter fault rate, λ _H-ABe the unusual rate of transverter, λ _H-MBe transverter maintenance rate, λ _BlBe lightning arrester failure rate, μ _H-MBe transverter maintenance repair rate, μ _H-RBe the converter fault repair rate;

For the subregion that smoothing reactor, wave filter form, its failure rate parameter as shown in the formula:

λ _R＝λ _c-R+λ _k-R

λ _A＝0＝λ′ _M＝λ′ _A

${\mathrm{\μ}}_M=\frac{{\mathrm{\λ}}_{c-M}+{\mathrm{\λ}}_{k-M}}{\frac{{\mathrm{\λ}}_{c-M}}{{\mathrm{\μ}}_{c-M}}+\frac{{\mathrm{\λ}}_{k-M}}{{\mathrm{\μ}}_{k-M}}}$

${\mathrm{\μ}}_R=\frac{{\mathrm{\λ}}_{c-R}+{\mathrm{\λ}}_{k-R}}{\frac{{\mathrm{\λ}}_{c-R}}{{\mathrm{\μ}}_{c-R}}+\frac{{\mathrm{\λ}}_{k-R}}{{\mathrm{\μ}}_{k-R}}}$

Wherein: λ _C-RBe wave filter failure rate, λ _C-MBe wave filter maintenance repair rate, λ _K-RBe smoothing reactor failure rate, λ _K-MBe smoothing reactor maintenance repair rate, μ _C-MBe wave filter maintenance repair rate, μ _C-RBe wave filter fault restoration rate; μ _K-MBe smoothing reactor maintenance repair rate, μ _K-RBe smoothing reactor fault restoration rate;

For the subregion that the DC side isolating switch forms, its failure rate parameter as shown in the formula:

λ _R＝λ _p-R+λ _JB

λ _A＝λ _x＝λ′ _M

λ′ _A＝λ _JB

${\mathrm{\μ}}_M=\frac{{\mathrm{\λ}}_{p-M}+{\mathrm{\λ}}_x+{\mathrm{\λ}}_{\mathrm{JB}}}{\frac{{\mathrm{\λ}}_{p-M}}{{\mathrm{\μ}}_{p-M}}+\frac{{\mathrm{\λ}}_x}{{\mathrm{\μ}}_x}+\frac{{\mathrm{\λ}}_{\mathrm{JB}}}{{\mathrm{\μ}}_{\mathrm{JB}}}}$

${\mathrm{\μ}}_R=\frac{{\mathrm{\λ}}_{p-R}+{\mathrm{\λ}}_{\mathrm{JB}}}{\frac{{\mathrm{\λ}}_{p-R}}{{\mathrm{\μ}}_{p-R}}+\frac{{\mathrm{\λ}}_{\mathrm{JB}}}{{\mathrm{\μ}}_{\mathrm{JB}}}}$

Wherein: λ _P-RBe DC side circuit breaker failure rate, λ _P-MBe DC side isolating switch maintenance rate, μ _P-RBe DC side circuit breaker failure repair rate, μ _P-MBe DC side isolating switch maintenance repair rate, μ _xBe isolating switch communication module maintenance repair rate, μ _JBFor continuing, isolating switch protects the module repair rate;

(5) utilize the minimal path search procedure that the network that subregion forms is searched for, concrete steps are as follows:

A. defining each subregion is a node, sets up the adjacency matrix A of network ₁=[a ¹ _Ij];

Wherein: as node v _iAnd v _jBetween when connection is arranged, a ¹ _Ij=1 or a ¹ _Ij=-1; Work as v _jAnd v _jBetween do not have to connect or during j=i a ¹ _Ij=a ¹ _Ji=0;

B. set up network in abutting connection with terminal point matrix R=[r _Jk];

Wherein: as node v _jWith terminal point v _kBetween when connection is arranged, r ¹ _Jk=1; Work as v _jAnd v _kBetween do not have to connect or during j=k r ¹ _Jk=0;

C. with matrix A ₁R multiplies each other with adjacency terminal point matrix, obtains new matrix A ₂=[a ² _Ik];

$a_{\mathrm{ik}}^2=\left\{a_{\mathrm{ij}}^1{r}_{\mathrm{jk}}\right|j=\mathrm{1,2},\·\·\·n\}$

Wherein: work as i, j, when three nodes of k have nothing in common with each other, a ² _Ik=a ¹ _Ijr _JkWork as a ¹ _Ij=0 or r _Jk=0 or v _kAt least with v _iAnd v _jIn one when identical, a ² _Ik=0;

D. change terminal point v _k, repeat above step, obtain matrix A ₃, A ₄... A _N-1

E. with A ₁, A ₂... A _N-1Middle correspondence position (i, nonzero element j) combines, and just obtains from node i to all minimal paths the node j;

F. because selected node has comprised the element of all needs assessments in the main electrical scheme, do not have the single node element to be omitted, then this minimal path collection matrix is final road collection matrix, utilizes road collection matrix to carry out the cut set analysis to node arbitrarily.

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