CN101251835A - A Reliability Evaluation Method for Main Wiring of ±800kV Converter Station - Google Patents

Abstract

Translated fromChinese

一种±800kV换流站主接线可靠性评估方法，其特征在于：建立了改进的元件四状态模型，在评估主接线可靠性过程中加入了继保和二次设备的可靠性模型，利用元件的合并分区将原本比较复杂的±800kV换流站主接线进行简化，并应用改进的元件四状态模型于简化后的各分区，重新定义元件的异常状态和检修状态，将元件的状态检修状态与计划检修状态合并归入元件的检修状态，并确定各状态之间的转换关系以及参数的求取，用矩阵乘法简化最小路矩阵搜索的方法对有向网络进行最小路搜索，利用解析法枚举有向网络的各种故障状态，并计算出该网络的可靠性数据。

A method for evaluating the reliability of the main wiring of a ±800kV converter station, characterized in that: an improved four-state model of components is established, and reliability models of relay protection and secondary equipment are added to the process of evaluating the reliability of the main wiring. The merging partition of the original complex ±800kV converter station main wiring is simplified, and the improved four-state model of components is applied to each simplified partition, and the abnormal state and maintenance state of the components are redefined. The planned maintenance state is merged into the maintenance state of the component, and the conversion relationship between each state and the calculation of parameters are determined. The minimum path search method is used to simplify the minimum path matrix search for the directed network by matrix multiplication, and the analytical method is used to enumerate There are various fault states of the directed network, and the reliability data of the network is calculated.

Description

Translated fromChinese

一种±800kV换流站主接线可靠性评估方法A Reliability Evaluation Method for Main Wiring of ±800kV Converter Station

技术领域：Technical field:

本发明涉及电力系统可靠性评估技术领域，尤其是一种±800kV换流站主接线可靠性评估方法。The invention relates to the technical field of power system reliability evaluation, in particular to a method for evaluating the reliability of a main wiring of a ±800kV converter station.

背景技术：Background technique:

由于国内状态检修技术的大力发展，元件的状态检修状态已经成为元件状态转换中不可或缺的一个状态，而在经典元件四状态模型中，并没有计及元件的状态检修状态，因此认为经典元件四状态模型已经不符合元件状态转换的实际情况。Due to the vigorous development of domestic condition-based maintenance technology, the condition-based maintenance state of components has become an indispensable state in component state transitions. However, in the classic component four-state model, the condition-based maintenance state of components is not considered, so it is considered that the classic component The four-state model is no longer in line with the actual situation of component state transitions.

参考文献：references:

[1]Endrenyi J.Three State Models in Power System Reliability Evaluation.IEEE Trans.on PAS，1971，90：1909-1916.[1] Endrenyi J. Three State Models in Power System Reliability Evaluation. IEEE Trans. on PAS, 1971, 90: 1909-1916.

[2]Ringlee RJ，Goode SD.On procedures for reliability evaluation of transmission systems.IEEETrans.on Power Apparatus Syst.1970，80(4)：527-536.[2] Ringlee RJ, Goode SD. On procedures for reliability evaluation of transmission systems. IEEE Trans. on Power Apparatus Syst. 1970, 80(4): 527-536.

[3]Endrenyi J.Reliability evaluation of transmission systems with switching afterfaults-approximations and a computer program.IEEE Trans.on PAS.，1973，92：1863-1875.[3] Endrenyi J. Reliability evaluation of transmission systems with switching afterfaults-approximations and a computer program. IEEE Trans. on PAS., 1973, 92: 1863-1875.

[4]Sight c.Models and Concepts for power system reliability evaluation includingprotection-system failures.Electric Power and Energy System，1981.[4]Sight c. Models and Concepts for power system reliability evaluation including protection-system failures. Electric Power and Energy System, 1981.

[5]Allan RN，Ochoa JR.Modelling and assessment of station originated outage for compositesystem reliability evaluation.IEEE Trans.on PAS，1988，3(1)：158-165.[5] Allan RN, Ochoa JR. Modeling and assessment of station originated outage for compositesystem reliability evaluation. IEEE Trans. on PAS, 1988, 3(1): 158-165.

[6]Billiton R，Lian G.Station reliability evaluation using a Monte-Carlo approach.IEEE Trans.onPower Delivery，1993，8(3)：1239-1245.[6] Billiton R, Lian G. Station reliability evaluation using a Monte-Carlo approach. IEEE Trans. on Power Delivery, 1993, 8(3): 1239-1245.

[7]Billinton R，Chen H，Zhou J Q.Generalized n+2 state system markov model forstation-oriented reliability evaluation.IEEE Transactions on Power System，1997，12(4)：1511-1517.[7] Billinton R, Chen H, Zhou J Q. Generalized n+2 state system markov model forstation-oriented reliability evaluation. IEEE Transactions on Power System, 1997, 12(4): 1511-1517.

[8]鲁宗相，郭永基.水电站电气主接线可靠性评估.电力系统自动化，2001，25(18)：16-19[8] Lu Zongxiang, Guo Yongji. Reliability Assessment of Electrical Main Wiring of Hydropower Station. Automation of Electric Power Systems, 2001, 25(18): 16-19

[9]郭永基.电力系统可靠性分析.清华大学出版社.[9] Guo Yongji. Power System Reliability Analysis. Tsinghua University Press.

[10]陈少华，马碧燕，雷宇，桂存兵.综合定量计算继电保护系统的可靠性.电力系统自动化，2007，31(15)：111-115[10] Chen Shaohua, Ma Biyan, Lei Yu, Gui Cunbing. Comprehensive Quantitative Calculation of Reliability of Relay Protection System. Electric Power System Automation, 2007, 31(15): 111-115

[11]MUSA JD.The measurement and management of software reliability.Proceeding of theIEEE，1980，68(9)：1131-1143[11] MUSA JD. The measurement and management of software reliability. Proceeding of the IEEE, 1980, 68(9): 1131-1143

[12]胡晓，黄晓明.±800kV特高压换流站可靠性评估.四川电力技术，2007，30(3)：1-5[12] Hu Xiao, Huang Xiaoming. Reliability Evaluation of ±800kV UHV Converter Station. Sichuan Electric Power Technology, 2007, 30(3): 1-5

[13]宿志一，范建斌.葛洲坝和南桥换流站一次设备运行情况和健康水平评估.电力设备，2003，4(3)：1-9[13] Su Zhiyi, Fan Jianbin. Evaluation of primary equipment operation and health level of Gezhouba and Nanqiao converter stations. Electric Equipment, 2003, 4(3): 1-9

[14]任震，武娟，陈丽芳.高压直流输电可靠性评估得等效模型[J].电力系统自动化，1999，23(9)：38-42[14] Ren Zhen, Wu Juan, Chen Lifang. Equivalent Model for Reliability Assessment of HVDC Transmission [J]. Electric Power System Automation, 1999, 23(9): 38-42

[15]马为民，李亚男，周静.特高压直流输电系统可靠性和可用率指标研究.电力设备，2007，8(3)：85-88[15] Ma Weimin, Li Yanan, Zhou Jing. Research on Reliability and Availability Index of UHVDC Transmission System. Electric Power Equipment, 2007, 8(3): 85-88

[16]王遂，任震，蒋金良.混合法在高压直流输电系统可靠性评估中得应用.电网技术，2007，31(12)：42-46[16] Wang Sui, Ren Zhen, Jiang Jinliang. Application of Hybrid Method in Reliability Assessment of HVDC Transmission System. Power Grid Technology, 2007, 31(12): 42-46

[17]周念成，谢开贵，周家启，赵渊，刘洋.基于最短路得复杂配电网可靠性评估分块算法.电力系统自动化，2005，29(22)：39-44[17] Zhou Niancheng, Xie Kaigui, Zhou Jiaqi, Zhao Yuan, Liu Yang. Block Algorithm for Reliability Evaluation of Complex Distribution Network Based on Shortest Path. Automation of Power Systems, 2005, 29(22): 39-44

[18]张鹏，王守相.配电系统可靠性评估的改进区间方法.电力系统自动化，2003，27(17)：50-55[18] Zhang Peng, Wang Shouxiang. Improved Interval Method for Distribution System Reliability Assessment. Electric Power System Automation, 2003, 27(17): 50-55

发明内容Contents of the invention

本发明的目的是提出一种±800kV换流站主接线可靠性评估方法，该项方法提出了元件的改进四状态模型并应用于±800kV换流站主接线可靠性评估。由于±800kV换流站的重要性及可靠性要求都非常高，因此在评估主接线可靠性过程中加入了继保和二次设备的可靠性模型，目的是能更详细和精确地反应换流站的可靠性。本方法利用元件的合并分区将原本比较复杂的±800kV换流站主接线进行简化，并应用改进的元件四状态模型于简化后的各分区。该模型重新定义元件的异常状态和检修状态，将元件的状态检修状态与计划检修状态合并归入元件的检修状态，并确定各状态之间的转换关系以及参数的求取。提出利用元件的合并分区方法简化主接线，形成一个简单的有向网络，并将改进的元件四状态模型应用于分区可靠性参数的确定。借用矩阵乘法简化最小路矩阵搜索的方法对有向网络进行最小路搜索，利用解析法枚举有向网络的各种故障状态，并计算出该网络的可靠性数据。The purpose of the present invention is to propose a method for evaluating the reliability of the main wiring of a ±800kV converter station. The method proposes an improved four-state model of components and applies it to the reliability evaluation of the main wiring of a ±800kV converter station. Due to the high importance and reliability requirements of the ±800kV converter station, reliability models of relay protection and secondary equipment are included in the process of evaluating the reliability of the main wiring, in order to reflect the converter in more detail and accurately station reliability. This method simplifies the originally complex main wiring of ±800kV converter station by merging and subdividing components, and applies the improved four-state model of components to the simplified subregions. The model redefines the abnormal state and maintenance state of the component, combines the component's condition-based maintenance state and planned maintenance state into the component's maintenance state, and determines the conversion relationship between each state and the calculation of parameters. The method of merging and partitioning components is proposed to simplify the main wiring to form a simple directed network, and the improved four-state model of components is applied to the determination of partition reliability parameters. Borrowing the method of matrix multiplication to simplify the minimum path matrix search for the directed network, using the analytical method to enumerate various fault states of the directed network, and calculate the reliability data of the network.

本发明的具体步骤如下：Concrete steps of the present invention are as follows:

(1)建立改进元件四状态模型。重新定义设备的异常状态，检修状态和故障状态，及其相关关系，并建立了转换关系，在经典元件四状态模型基础上，增加元件异常状态A。如图1所示。(1) Establish the four-state model of the improved component. Redefine the abnormal state, maintenance state and fault state of the equipment, and their correlations, and establish the conversion relationship. On the basis of the classic four-state model of components, add the component abnormal state A. As shown in Figure 1.

元件异常状态(A)：元件某些功能出现故障或者元件出现故障征兆时该元件所处的状态；Component abnormal state (A): the state of the component when some functions of the component fail or the component has a symptom of failure;

元件检修状态(M)：为元件处于检修的状态，包含计划检修状态与状态检修状态；Component maintenance status (M): the component is in the maintenance status, including the planned maintenance status and status maintenance status;

元件故障状态(R)：当元件无法保证其应有的主功能时所处的状态，对于断路器等开关设备，其误动和拒动归纳入元件的故障状态。Component fault state (R): The state that the component is in when it cannot guarantee its proper main function. For switchgear such as circuit breakers, its malfunction and refusal to operate are included in the fault state of the component.

(2)在主接线可靠性评估中增加了继保及二次设备的可靠性模型，以使换流站主接线可靠性更接近真实水平。(2) The reliability model of relay protection and secondary equipment is added in the reliability evaluation of the main wiring to make the reliability of the main wiring of the converter station closer to the real level.

(3)元件合并分区。对主接线四状态模型进行分区，主元件与其附属元件合并形成分区，相邻串、并联主元件如果合并不影响接线方式则可以合并为一个分区，如果合并后影响接线方式，则单独作为分区，如图4及图5。(3) Component merge partition. Partition the main wiring four-state model. The main component and its subsidiary components are merged to form a partition. If the combination of adjacent series and parallel main components does not affect the wiring method, they can be merged into one partition. If the combination affects the wiring method, they can be used as a separate partition. As shown in Figure 4 and Figure 5.

(4)分区可靠性参数的确定。由于各分区皆由元件构成，则将改进元件四状态模型用于各分区可靠性参数的确定。为将改进的元件四状态模型更好的应用于各分区，定义各分区的状态：分区的异常状态(A)、分区的检修状态(M)、分区的故障状态(R)。各分区状态之间的转换参考图1的元件四状态模型。将改进的元件四状态模型应用于各分区以求得各分区的可靠性参数。(4) Determination of partition reliability parameters. Since each partition is composed of components, the improved four-state model of components is used to determine the reliability parameters of each partition. In order to better apply the improved four-state model of components to each partition, the state of each partition is defined: the abnormal state of the partition (A), the maintenance state of the partition (M), and the fault state of the partition (R). The transition between states of each partition refers to the element four-state model in FIG. 1 . The improved four-state model of components is applied to each partition to obtain the reliability parameters of each partition.

(5)利用最小路搜索法对分区形成的网络进行搜索。(5) Use the minimum path search method to search the network formed by partitions.

附图说明：Description of drawings:

图1是改进的元件四状态模型。Figure 1 is an improved four-state model of the element.

其中：N为元件正常状态；A为元件异常状态；R为元件故障状态；M为元件检修状态；λ_A为元件从正常状态变为异常状态的概率；λ_M为设备的检修率，λ‘_M为元件从异常状态转为检修状态的状态检修率，‘’λ_M为元件的计划检修率；λ_R为元件故障率；λ’_A为元件从异常状态变为故障状态的概率；μ_R为元件修复率；μ_M为元件修复率。Among them: N is the normal state of the component; A is the abnormal state of the component_{; R is the fault state of the component; M is the maintenance state of the component; λ Ais} the probability of the component changing from a normal state to an abnormal state;_M is the condition-based maintenance rate of components changing from abnormal state to maintenance state, ''λ_M is the planned maintenance rate of components; λ_R is the failure rate of components; λ'_A is the probability of components changing from abnormal state to fault state; μ_R is the component repair rate; μ_M is the component repair rate.

图2是现有设备状态曲线。Figure 2 is the state curve of the existing equipment.

图3是某个换流站的主接线图。Figure 3 is the main wiring diagram of a certain converter station.

图4是图3中一个单极合并分区的主接线图。Fig. 4 is a main wiring diagram of a single-pole merged partition in Fig. 3 .

图5是主接线分区简化图。Figure 5 is a simplified diagram of the main wiring partition.

其中：zone11至zone43为各分区代号Among them: zone11 to zone43 are the code names of each zone

图6是依据本发明提出的可靠性指标的计算流程方框图。Fig. 6 is a block diagram of the calculation flow of the reliability index proposed according to the present invention.

具体实施方式Detailed ways

下面结合实施例及其附图详细说明。The following describes in detail in conjunction with the embodiments and accompanying drawings.

(1)建立改进元件四状态模型(1) Establish a four-state model for improved components

状态检修中，当某一设备是按照状态检修方式进行检修时，设备的状态是状态检修方式的依据。如图2，在设备状态检修方式中，设备故障征兆点从A点开始，当设备的状态出现异常即检测到故障征兆B点出现时，工作人员会在此故障征兆点B到故障发生时刻D这段时间内密切监测设备状态，当设备状态到达状态阀值点C时将会有两种处理方式：1、对设备进行停运检修；2、直到设备状态降低到状态点D时进行维修或更换。通过这两个方式我们可以看出，当为方式1时该设备从异常状态转为强迫停运状态，当为方式2时该设备从异常状态转为故障状态。In condition-based maintenance, when a certain equipment is overhauled according to the condition-based maintenance method, the state of the equipment is the basis of the condition-based maintenance method. As shown in Figure 2, in the equipment condition-based maintenance mode, the equipment failure symptom point starts from point A. When the equipment status is abnormal, that is, when the fault symptom point B is detected, the staff will go from this fault symptom point B to the fault occurrence time D During this period of time, the equipment status is closely monitored. When the equipment status reaches the status threshold point C, there will be two processing methods: 1. Shut down the equipment for maintenance; 2. Perform maintenance or replace. Through these two methods, we can see that when the mode 1 is used, the equipment changes from the abnormal state to the forced outage state, and when the mode 2 is used, the equipment changes from the abnormal state to the failure state.

在经典元件四状态模型里面，只对设备的强迫停运方式以及计划检修方式进行了定义，没有考虑设备的状态检修方式。根据图2设备状态曲线以及上一段对状态检修过程的分析，本发明认为设备的状态检修也应该纳入元件四状态模型之中。本发明重新定义设备的异常状态，检修状态和故障状态，及其相关关系，并建立改进元件四状态模型如图1。In the classical component four-state model, only the forced outage mode and the planned maintenance mode of the equipment are defined, and the condition-based maintenance mode of the equipment is not considered. According to the equipment state curve in Figure 2 and the analysis of the condition-based maintenance process in the previous paragraph, the present invention considers that the condition-based maintenance of equipment should also be included in the four-state model of components. The present invention redefines the abnormal state, maintenance state and fault state of the equipment, and their correlations, and establishes a four-state model for improved components as shown in Figure 1.

根据改进元件四状态模型，元件从正常状态N出发对应检修状态M和异常状态A，元件的异常状态A转换为故障状态R和检修状态M，即表明：元件从正常运行开始，可能会因为计划检修进入检修状态，也可能因为小的毛病或者异常进入元件的异常状态，而元件处于异常状态后，可能因为及早发现其异常情况，所以对元件进行状态检修，也可能因为没有及早发现其情况或者故意等到其故障后再修理，而使元件进入故障状态。元件由故障状态到正常状态是指设备的故障后修复过程。According to the improved element four-state model, starting from the normal state N, the element corresponds to the maintenance state M and the abnormal state A, and the abnormal state A of the element is transformed into the fault state R and the maintenance state M, which means that: the element starts from normal operation, and may be due to the planned When the overhaul enters the overhaul state, it may also enter the abnormal state of the component due to a small fault or abnormality. After the component is in an abnormal state, it may be because of early detection of the abnormal situation, so the condition maintenance of the component may be carried out, or it may be because the condition was not detected early or Deliberately waiting until it fails before repairing it, causing the component to go into a failed state. The component from the fault state to the normal state refers to the repair process of the equipment after the fault.

通过对比改进的元件四状态模型与经典元件四状态模型可知，改进元件四状态模型更能清晰表现元件状态之间的转换，且M状态与R状态的记录提取更简便。因为M状态即为元件处于检修状态的纪录，R状态即为元件处于故障状态的纪录。所需要增加的是元件A状态的纪录，而由于本发明的改进四状态模型是建立在设备的状态监测技术基础上的，元件异常状态A的纪录也容易取得。By comparing the improved component four-state model with the classic component four-state model, it can be seen that the improved component four-state model can more clearly represent the transition between component states, and the record extraction of M state and R state is easier. Because the M state is the record that the component is in the maintenance state, and the R state is the record that the component is in the fault state. What needs to be added is the record of the state of the component A, and since the improved four-state model of the present invention is based on the state monitoring technology of the equipment, the record of the abnormal state A of the component is also easy to obtain.

(2)在主接线可靠性评估中增加了二次及继保可靠性模型。继电保护的可靠性涉及软件和硬件两个部分。硬件可靠性为：(2) In the main wiring reliability evaluation, the secondary and relay reliability models are added. The reliability of relay protection involves two parts, software and hardware. The hardware reliability is:

λ＝γ_Q(C₁γ_Tγ_V+C₂γ_E)γ_L(1)λ＝γ_Q (C₁ γ_T γ_V +C₂ γ_E )γ_L (1)

${\mathrm{<span><span>\&lambda;</span>\&lambda;</span>}}_{\mathrm{<span><span>M</span>m</span>}}<span><span>=</span>=</span>\underset{\mathrm{<span><span>i</span>i</span>}<span><span>=</span>=</span>\mathrm{<span><span>1</span>1</span>}}{\overset{\mathrm{<span><span>N</span>N</span>}}{\mathrm{<span><span>\&Sigma;</span>\&Sigma;</span>}}}{\mathrm{<span><span>\&lambda;</span>\&lambda;</span>}}_{\mathrm{<span><span>i</span>i</span>}}<span><span>-</span>-</span><span><span>-</span>-</span><span><span>-</span>-</span><span><span>(</span>(</span>\mathrm{<span><span>2</span>2</span>}<span><span>)</span>)</span>$

λ_H＝λ_T+λ_J(3)λ_H =λ_T +λ_J (3)

式中：γ_Q为器件质量因数；C₁为电路复杂因数；γ_T为温度加速因数；γ_V为电压应力因数C₂为封装复杂因数；γ_E为应用环境因数；γ_L为为器件成熟因数；N为模块M中元器件的总个数。λ_H为硬件故障率；λ_T为通讯模块故障率；λ_J为继电保护模块故障率。In the formula: γ_Q is the device quality factor; C₁ is the circuit complexity factor; γ_T is the temperature acceleration factor; γ_V is the voltage_stress factor C₂ is the package complexity factor; γ_E is the application environment factor; Factor; N is the total number of components in module M. λ_H is the hardware failure rate; λ_T is the communication module failure rate; λ_J is the relay protection module failure rate.

软件可靠性模型采用John Musa模型^[11]来处理，该模型的软件失效率为：The software reliability model is handled by the John Musa model^[11] , and the software failure rate of this model is:

${\mathrm{<span><span>\&lambda;</span>\&lambda;</span>}}_{\mathrm{<span><span>s</span>the\; s</span>}}<span><span>=</span>=</span>{\mathrm{<span><span>e</span>e</span>}}^{<span><span>-</span>-</span>\frac{{\mathrm{<span><span>\&tau;</span>\&tau;</span>}}^{<span><span>\&prime;</span>\&prime;</span>}}{\mathrm{<span><span>\&tau;</span>\&tau;</span>}}{\mathrm{<span><span>M</span>m</span>}}_{\mathrm{<span><span>0</span>0</span>}}{\mathrm{<span><span>T</span>T</span>}}_{\mathrm{<span><span>0</span>0</span>}}}<span><span>=</span>=</span>{\mathrm{<span><span>\&lambda;</span>\&lambda;</span>}}_{\mathrm{<span><span>0</span>0</span>}}{\mathrm{<span><span>e</span>e</span>}}^{<span><span>-</span>-</span>\frac{{\mathrm{<span><span>\&tau;</span>\&tau;</span>}}^{<span><span>\&prime;</span>\&prime;</span>}}{\mathrm{<span><span>\&tau;</span>\&tau;</span>}}}<span><span>-</span>-</span><span><span>-</span>-</span><span><span>-</span>-</span><span><span>(</span>(</span>\mathrm{<span><span>4</span>4</span>}<span><span>)</span>)</span>$

式中：τ为累积执行时间，即程序从开始运行到本次评估可靠性所经历的时间；τ’为程序运行时间，即从本次评估开始，程序可无故障运行的时间；λ₀为初始故障率，与最初的无故障时间T₀及软件的缺陷总数M₀有关。In the formula: τ is the cumulative execution time, that is, the time from the start of the program to the evaluation of reliability; τ' is the running time of the program, that is, the time for the program to run without failure from the beginning of this evaluation;_λ0 is The initial failure rate is related to the initial failure-free time T₀ and the total number of software defects M₀ .

继电保护可靠性由软件可靠性和硬件可靠性两部分组成，且两者也具有串连事件的特征，则继电保护可靠性如下式：The reliability of relay protection consists of two parts: software reliability and hardware reliability, and both of them also have the characteristics of series events, so the reliability of relay protection is as follows:

λ_JB＝λ_S+λ_H(5)λ_JB =λ_S +λ_H (5)

式中：λ_JB为继电保护故障率；λ_S为软件故障率；λ_H为硬件故障率。Where: λ_JB is the failure rate of relay protection; λ_S is the software failure rate; λ_H is the hardware failure rate.

(3)元件合并分区。以某个±800kV换流站主接线为例，如图3。由于换流站内元件数量众多，为方便主接线可靠性评估，利用元件合并分区的方法对主接线进行分区。基本原则为：主元件与其附属元件合并形成分区，相邻串、并联主元件如果合并不影响接线方式则可以合并为一个分区，如果合并后影响接线方式，则单独作为分区。根据以上原则，该±800kV换流站主接线可以形成以下分区：(3) Component merge partition. Take the main wiring of a ±800kV converter station as an example, as shown in Figure 3. Due to the large number of components in the converter station, in order to facilitate the reliability evaluation of the main wiring, the method of merging and partitioning the components is used to partition the main wiring. The basic principle is: the main component and its subsidiary components are combined to form a partition. If the combination of adjacent series and parallel main components does not affect the wiring method, they can be merged into one partition. If the combination affects the wiring method, they can be used as a separate partition. According to the above principles, the main wiring of the ±800kV converter station can form the following partitions:

a.换流站内交流断路器、换流变压器及其继电保护装置形成一个分区。a. The AC circuit breaker, converter transformer and its relay protection device in the converter station form a partition.

b.换流阀与其所属避雷器作为一个分区。b. The converter valve and its lightning arrester are regarded as a partition.

c.平波电抗器与滤波器作为一个分区。c. Smoothing reactor and filter as a partition.

d.直流侧断路器形成一个分区。d. DC side circuit breakers form a partition.

则主接线极1-1组简化如图4，图中虚线框表示所分分区。Then the main terminal pole 1-1 group is simplified as shown in Figure 4, and the dotted line box in the figure indicates the partition.

由以上分区方法可知，换流站整体简化如图5所示，其中zone11～zone43为分区命名。From the above zoning method, it can be known that the overall simplification of the converter station is shown in Figure 5, where zone11~zone43 are the names of the zones.

(4)应用改进元件四状态模型求取各分区可靠性参数。(4) Apply the improved component four-state model to obtain the reliability parameters of each partition.

为将改进的元件四状态模型更好的应用于各分区，定义：In order to better apply the improved element four-state model to each partition, define:

分区的异常状态(A)：主元件处于异常状态或主元件正常运行的情况下，其监测设备故障时该分区所处的状态。Abnormal state of the partition (A): When the main element is in an abnormal state or the main element is operating normally, the state of the partition when the monitoring equipment fails.

这样定义是因为如果主元件的保护、监测设备故障时，虽对主接线连通性无影响，但导致隐形故障或多重故障的可能性将会增大，此时对于换流站的安全性和可靠性都将有较大影响，则此时该元件处于异常状态。例如，假设换流阀正常工作，而其换流阀避雷器故障，无法起到涌流保护作用，且避雷器监测设备也失效或运行人员没注意其故障信号时，在雷击事件中，换流阀故障的可能性将大大增加，但是整个换流站仍然能继续运行，则称此时换流阀处于异常状态。This definition is because if the protection and monitoring equipment of the main components fail, although the connectivity of the main wiring will not be affected, the possibility of invisible faults or multiple faults will increase, which is very important for the safety and reliability of the converter station. will have a greater impact on the performance, then the component is in an abnormal state at this time. For example, assuming that the converter valve works normally, but the arrester of the converter valve is faulty, which cannot protect the inrush current, and the monitoring equipment of the arrester also fails or the operator does not pay attention to the fault signal, in the event of a lightning strike, the fault of the converter valve The possibility will be greatly increased, but the entire converter station can still continue to operate, it is said that the converter valve is in an abnormal state at this time.

分区的检修状态(M)：分区内不管是附属元件还是主要元件，只要处于计划检修状态或状态检修状态中的任何一种，则称为检修状态。The maintenance state of the partition (M): Whether it is an auxiliary component or a main component in the partition, as long as it is in any one of the planned maintenance state or the state maintenance state, it is called the maintenance state.

分区的故障状态(R)：分区内主元件故障时或者其保护设备故障时该分区所处的状态。如，变压器故障或者当变压器正常运行，但是保护设备拒动或误动时，可认为该分区为故障状态。Fault state of the partition (R): The state of the partition when the main component in the partition fails or its protection equipment fails. For example, when the transformer fails or when the transformer operates normally, but the protective equipment refuses to operate or malfunctions, the partition can be considered as a fault state.

各分区状态之间的转换参考图1。将改进的元件四状态模型应用于各分区以求得各分区的可靠性参数。对于断路器-换流变压器形成的分区，其故障率参数如下式：Refer to Figure 1 for the transition between partition states. The improved four-state model of components is applied to each partition to obtain the reliability parameters of each partition. For the partition formed by circuit breaker-converter transformer, the failure rate parameter is as follows:

由于各个分区都是由元件组合而且，可见元件的状态对应着各分区状态，将元件四状态模型应用于各分区，以取得分区可靠性参数，对于断路器-换流变压器形成的分区，其故障率参数如下式：Since each partition is composed of components and it can be seen that the state of the component corresponds to the state of each partition, the four-state model of the component is applied to each partition to obtain the reliability parameters of the partition. For the partition formed by the circuit breaker-converter transformer, its failure The rate parameter is as follows:

λ_R＝λ_R(d-b)+λ_(JB)λ_R = λ_{R (db)} + λ_(JB)

λ_A＝λ_A(d-b)+λ_xλ_A = λ_A(db) + λ_x

λ′_M＝λ_xλ′_M = λ_x

λ′_A＝λ_JBλ′_A =λ_JB

${\mathrm{<span><span>\&mu;</span>\&mu;</span>}}_{\mathrm{<span><span>M</span>m</span>}}<span><span>=</span>=</span>\frac{{\mathrm{<span><span>\&lambda;</span>\&lambda;</span>}}_{\mathrm{<span><span>d</span>d</span>}<span><span>-</span>-</span>\mathrm{<span><span>M</span>m</span>}}<span><span>+</span>+</span>{\mathrm{<span><span>\&lambda;</span>\&lambda;</span>}}_{\mathrm{<span><span>b</span>b</span>}<span><span>-</span>-</span>\mathrm{<span><span>M</span>m</span>}}<span><span>+</span>+</span>{\mathrm{<span><span>\&lambda;</span>\&lambda;</span>}}_{\mathrm{<span><span>x</span>x</span>}}<span><span>+</span>+</span>{\mathrm{<span><span>\&lambda;</span>\&lambda;</span>}}_{\mathrm{<span><span>JB</span>JB</span>}}}{\frac{{\mathrm{<span><span>\&lambda;</span>\&lambda;</span>}}_{\mathrm{<span><span>d</span>d</span>}<span><span>-</span>-</span>\mathrm{<span><span>M</span>m</span>}}}{{\mathrm{<span><span>\&mu;</span>\&mu;</span>}}_{\mathrm{<span><span>d</span>d</span>}<span><span>-</span>-</span>\mathrm{<span><span>M</span>m</span>}}}<span><span>+</span>+</span>\frac{{\mathrm{<span><span>\&lambda;</span>\&lambda;</span>}}_{\mathrm{<span><span>b</span>b</span>}<span><span>-</span>-</span>\mathrm{<span><span>M</span>m</span>}}}{{\mathrm{<span><span>\&mu;</span>\&mu;</span>}}_{\mathrm{<span><span>b</span>b</span>}<span><span>-</span>-</span>\mathrm{<span><span>M</span>m</span>}}}<span><span>+</span>+</span>\frac{{\mathrm{<span><span>\&lambda;</span>\&lambda;</span>}}_{\mathrm{<span><span>x</span>x</span>}}}{{\mathrm{<span><span>\&mu;</span>\&mu;</span>}}_{\mathrm{<span><span>x</span>x</span>}}}<span><span>+</span>+</span>\frac{{\mathrm{<span><span>\&lambda;</span>\&lambda;</span>}}_{\mathrm{<span><span>JB</span>JB</span>}}}{{\mathrm{<span><span>\&mu;</span>\&mu;</span>}}_{\mathrm{<span><span>JB</span>JB</span>}}}}<span><span>-</span>-</span><span><span>-</span>-</span><span><span>-</span>-</span><span><span>(</span>(</span>\mathrm{<span><span>6</span>6</span>}<span><span>)</span>)</span>$

${\mathrm{<span><span>\&mu;</span>\&mu;</span>}}_{\mathrm{<span><span>R</span>R</span>}}<span><span>=</span>=</span>\frac{{\mathrm{<span><span>\&lambda;</span>\&lambda;</span>}}_{\mathrm{<span><span>d</span>d</span>}<span><span>-</span>-</span>\mathrm{<span><span>R</span>R</span>}}<span><span>+</span>+</span>{\mathrm{<span><span>\&lambda;</span>\&lambda;</span>}}_{\mathrm{<span><span>b</span>b</span>}<span><span>-</span>-</span>\mathrm{<span><span>R</span>R</span>}}}{\frac{{\mathrm{<span><span>\&lambda;</span>\&lambda;</span>}}_{\mathrm{<span><span>d</span>d</span>}<span><span>-</span>-</span>\mathrm{<span><span>R</span>R</span>}}}{{\mathrm{<span><span>\&mu;</span>\&mu;</span>}}_{\mathrm{<span><span>d</span>d</span>}<span><span>-</span>-</span>\mathrm{<span><span>R</span>R</span>}}}<span><span>+</span>+</span>\frac{{\mathrm{<span><span>\&lambda;</span>\&lambda;</span>}}_{\mathrm{<span><span>b</span>b</span>}<span><span>-</span>-</span>\mathrm{<span><span>R</span>R</span>}}}{{\mathrm{<span><span>\&mu;</span>\&mu;</span>}}_{\mathrm{<span><span>b</span>b</span>}<span><span>-</span>-</span>\mathrm{<span><span>R</span>R</span>}}}}$

其中：λ_R为分区故障率，λ_A为分区异常概率，λ’_M为分区状态检修概率，λ’_A为分区状态检修概率，μ_M为分区检修修复率，μ_R为分区故障修复率；λ_R(d-b)为断路器和变压器故障率之和；λ_A(d-b)为断路器和变压器异常状态率之和，λ_d-M为断路器检修率，λ_b-M为变压器检修率，λ_d-R为断路器故障率，λ_b-R为变压器故障率，μ_d-M为断路器检修修复率，μ_b-M为变压器检修修复率，μ_d-R为断路器故障修复率，μ_b-R为变压器故障修复率；Among them: λ_R is the partition failure rate, λ_A is the abnormal probability of the partition, λ'_M is the partition state maintenance probability, λ'_A is the partition state maintenance probability, μ_M is the partition repair repair rate, and μ_R is the partition fault repair rate; λ_R(db) is the sum of failure rate of circuit breaker and transformer; λ_A(db) is the sum of abnormal state rate of circuit breaker and transformer, λ_dM is maintenance rate of circuit breaker, λ_bM is maintenance rate of transformer, λ_dR is open circuit λ_bR is the failure rate of the transformer, μ_dM is the maintenance and repair rate of the circuit breaker, μ_bM is the maintenance and repair rate of the transformer, μ_dR is the failure recovery rate of the circuit breaker, and μ_bR is the failure recovery rate of the transformer;

对于换流阀、避雷器形成的分区，其故障率参数如下式：For the partition formed by the converter valve and the arrester, the failure rate parameter is as follows:

λ_R＝λ_h-R+λ_blλ_R ＝ λ_hR + λ_bl

λ_A＝λ_bl＝λ′_Aλ_A =λ_bl =λ′_A

λ′_M＝0(7)λ′_M = 0(7)

${\mathrm{<span><span>\&mu;</span>\&mu;</span>}}_{\mathrm{<span><span>M</span>m</span>}}<span><span>=</span>=</span>\frac{{\mathrm{<span><span>\&lambda;</span>\&lambda;</span>}}_{\mathrm{<span><span>h</span>h</span>}<span><span>-</span>-</span>\mathrm{<span><span>M</span>m</span>}}<span><span>+</span>+</span>{\mathrm{<span><span>\&lambda;</span>\&lambda;</span>}}_{\mathrm{<span><span>bl</span>bl</span>}}}{\frac{{\mathrm{<span><span>\&lambda;</span>\&lambda;</span>}}_{\mathrm{<span><span>h</span>h</span>}<span><span>-</span>-</span>\mathrm{<span><span>M</span>m</span>}}}{{\mathrm{<span><span>\&mu;</span>\&mu;</span>}}_{\mathrm{<span><span>h</span>h</span>}<span><span>-</span>-</span>\mathrm{<span><span>M</span>m</span>}}}<span><span>+</span>+</span>\frac{{\mathrm{<span><span>\&lambda;</span>\&lambda;</span>}}_{\mathrm{<span><span>bl</span>bl</span>}}}{{\mathrm{<span><span>\&mu;</span>\&mu;</span>}}_{\mathrm{<span><span>bl</span>bl</span>}}}}$

${\mathrm{<span><span>\&mu;</span>\&mu;</span>}}_{\mathrm{<span><span>R</span>R</span>}}<span><span>=</span>=</span>\frac{{\mathrm{<span><span>\&lambda;</span>\&lambda;</span>}}_{\mathrm{<span><span>h</span>h</span>}<span><span>-</span>-</span>\mathrm{<span><span>R</span>R</span>}}<span><span>+</span>+</span>{\mathrm{<span><span>\&lambda;</span>\&lambda;</span>}}_{\mathrm{<span><span>bl</span>bl</span>}}}{\frac{{\mathrm{<span><span>\&lambda;</span>\&lambda;</span>}}_{\mathrm{<span><span>h</span>h</span>}<span><span>-</span>-</span>\mathrm{<span><span>R</span>R</span>}}}{{\mathrm{<span><span>\&mu;</span>\&mu;</span>}}_{\mathrm{<span><span>h</span>h</span>}<span><span>-</span>-</span>\mathrm{<span><span>R</span>R</span>}}}<span><span>+</span>+</span>\frac{{\mathrm{<span><span>\&lambda;</span>\&lambda;</span>}}_{\mathrm{<span><span>bl</span>bl</span>}}}{{\mathrm{<span><span>\&mu;</span>\&mu;</span>}}_{\mathrm{<span><span>bl</span>bl</span>}}}}$

其中：λ_h-R为换流器故障率，λ_h-A为换流器异常率，λ_h-M为换流器检修率，λ_bl为避雷器故障率，μ_h-M为换流器检修修复率，μ_h-R为换流器故障修复率；Among them: λ_hR is the failure rate of the converter, λ_hA is the abnormal rate of the converter, λ_hM is the repair rate of the converter, λ_bl is the failure rate of the arrester, μ_hM is the repair rate of the converter, and μ_hR is the converter repair rate. Flow device failure repair rate;

对于平波电抗器、滤波器形成的分区，其故障率参数如下式：For the partitions formed by smoothing reactors and filters, the failure rate parameters are as follows:

λ_R＝λ_c-R+λ_k-Rλ_R ＝ λ_{c R} + λ_{k R}

λ_A＝0＝λ′_M＝λ′_Aλ_A = 0 = λ'_M = λ'_A

${\mathrm{<span><span>\&mu;</span>\&mu;</span>}}_{\mathrm{<span><span>M</span>m</span>}}<span><span>=</span>=</span>\frac{{\mathrm{<span><span>\&lambda;</span>\&lambda;</span>}}_{\mathrm{<span><span>c</span>c</span>}<span><span>-</span>-</span>\mathrm{<span><span>M</span>m</span>}}<span><span>+</span>+</span>{\mathrm{<span><span>\&lambda;</span>\&lambda;</span>}}_{\mathrm{<span><span>k</span>k</span>}<span><span>-</span>-</span>\mathrm{<span><span>M</span>m</span>}}}{\frac{{\mathrm{<span><span>\&lambda;</span>\&lambda;</span>}}_{\mathrm{<span><span>c</span>c</span>}<span><span>-</span>-</span>\mathrm{<span><span>M</span>m</span>}}}{{\mathrm{<span><span>\&mu;</span>\&mu;</span>}}_{\mathrm{<span><span>c</span>c</span>}<span><span>-</span>-</span>\mathrm{<span><span>M</span>m</span>}}}<span><span>+</span>+</span>\frac{{\mathrm{<span><span>\&lambda;</span>\&lambda;</span>}}_{\mathrm{<span><span>k</span>k</span>}<span><span>-</span>-</span>\mathrm{<span><span>M</span>m</span>}}}{{\mathrm{<span><span>\&mu;</span>\&mu;</span>}}_{\mathrm{<span><span>k</span>k</span>}<span><span>-</span>-</span>\mathrm{<span><span>M</span>m</span>}}}}<span><span>-</span>-</span><span><span>-</span>-</span><span><span>-</span>-</span><span><span>(</span>(</span>\mathrm{<span><span>8</span>8</span>}<span><span>)</span>)</span>$

${\mathrm{<span><span>\&mu;</span>\&mu;</span>}}_{\mathrm{<span><span>R</span>R</span>}}<span><span>=</span>=</span>\frac{{\mathrm{<span><span>\&lambda;</span>\&lambda;</span>}}_{\mathrm{<span><span>c</span>c</span>}<span><span>-</span>-</span>\mathrm{<span><span>R</span>R</span>}}<span><span>+</span>+</span>{\mathrm{<span><span>\&lambda;</span>\&lambda;</span>}}_{\mathrm{<span><span>k</span>k</span>}<span><span>-</span>-</span>\mathrm{<span><span>R</span>R</span>}}}{\frac{{\mathrm{<span><span>\&lambda;</span>\&lambda;</span>}}_{\mathrm{<span><span>c</span>c</span>}<span><span>-</span>-</span>\mathrm{<span><span>R</span>R</span>}}}{{\mathrm{<span><span>\&mu;</span>\&mu;</span>}}_{\mathrm{<span><span>c</span>c</span>}<span><span>-</span>-</span>\mathrm{<span><span>R</span>R</span>}}}<span><span>+</span>+</span>\frac{{\mathrm{<span><span>\&lambda;</span>\&lambda;</span>}}_{\mathrm{<span><span>k</span>k</span>}<span><span>-</span>-</span>\mathrm{<span><span>R</span>R</span>}}}{{\mathrm{<span><span>\&mu;</span>\&mu;</span>}}_{\mathrm{<span><span>k</span>k</span>}<span><span>-</span>-</span>\mathrm{<span><span>R</span>R</span>}}}}$

其中：λ_c-R为滤波器故障率，λ_c-M为滤波器检修修复率，λ_k-R为平波电抗器故障率，λ_k-M为平波电抗器检修修复率，μ_c-M为滤波器检修修复率，μ_c-R为滤波器故障修复率；μ_k-M为平波电抗器检修修复率，μ_k-R为平波电抗器故障修复率；Among them: λ_cR is the failure rate of the filter, λ_cM is the maintenance and repair rate of the filter, λ_kR is the failure rate of the smoothing reactor, λ_kM is the maintenance and repair rate of the smoothing reactor, μ_cM is the maintenance and repair rate of the filter, μ_cR is the fault repair rate of the filter; μ_kM is the maintenance repair rate of the smoothing reactor, and μ_kR is the fault repair rate of the smoothing reactor;

对于直流侧断路器形成的分区，其故障率参数如下式：For the partition formed by the DC side circuit breaker, the failure rate parameter is as follows:

λ_R＝λ_p-R+λ_JBλ_R ＝ λ_pR + λ_JB

λ_A＝λ_x＝λ′_Mλ_A ＝ λ_x ＝ λ′_M

λ′_A＝λ_JB    (9)λ′_A =λ_JB (9)

${\mathrm{<span><span>\&mu;</span>\&mu;</span>}}_{\mathrm{<span><span>M</span>m</span>}}<span><span>=</span>=</span>\frac{{\mathrm{<span><span>\&lambda;</span>\&lambda;</span>}}_{\mathrm{<span><span>p</span>p</span>}<span><span>-</span>-</span>\mathrm{<span><span>M</span>m</span>}}<span><span>+</span>+</span>{\mathrm{<span><span>\&lambda;</span>\&lambda;</span>}}_{\mathrm{<span><span>x</span>x</span>}}<span><span>+</span>+</span>{\mathrm{<span><span>\&lambda;</span>\&lambda;</span>}}_{\mathrm{<span><span>JB</span>JB</span>}}}{\frac{{\mathrm{<span><span>\&lambda;</span>\&lambda;</span>}}_{\mathrm{<span><span>p</span>p</span>}<span><span>-</span>-</span>\mathrm{<span><span>M</span>m</span>}}}{{\mathrm{<span><span>\&mu;</span>\&mu;</span>}}_{\mathrm{<span><span>p</span>p</span>}<span><span>-</span>-</span>\mathrm{<span><span>M</span>m</span>}}}<span><span>+</span>+</span>\frac{{\mathrm{<span><span>\&lambda;</span>\&lambda;</span>}}_{\mathrm{<span><span>x</span>x</span>}}}{{\mathrm{<span><span>\&mu;</span>\&mu;</span>}}_{\mathrm{<span><span>x</span>x</span>}}}<span><span>+</span>+</span>\frac{{\mathrm{<span><span>\&lambda;</span>\&lambda;</span>}}_{\mathrm{<span><span>JB</span>JB</span>}}}{{\mathrm{<span><span>\&mu;</span>\&mu;</span>}}_{\mathrm{<span><span>JB</span>JB</span>}}}}$

${\mathrm{<span><span>\&mu;</span>\&mu;</span>}}_{\mathrm{<span><span>R</span>R</span>}}<span><span>=</span>=</span>\frac{{\mathrm{<span><span>\&lambda;</span>\&lambda;</span>}}_{\mathrm{<span><span>p</span>p</span>}<span><span>-</span>-</span>\mathrm{<span><span>R</span>R</span>}}<span><span>+</span>+</span>{\mathrm{<span><span>\&lambda;</span>\&lambda;</span>}}_{\mathrm{<span><span>JB</span>JB</span>}}}{\frac{{\mathrm{<span><span>\&lambda;</span>\&lambda;</span>}}_{\mathrm{<span><span>p</span>p</span>}<span><span>-</span>-</span>\mathrm{<span><span>R</span>R</span>}}}{{\mathrm{<span><span>\&mu;</span>\&mu;</span>}}_{\mathrm{<span><span>p</span>p</span>}<span><span>-</span>-</span>\mathrm{<span><span>R</span>R</span>}}}<span><span>+</span>+</span>\frac{{\mathrm{<span><span>\&lambda;</span>\&lambda;</span>}}_{\mathrm{<span><span>JB</span>JB</span>}}}{{\mathrm{<span><span>\&mu;</span>\&mu;</span>}}_{\mathrm{<span><span>JB</span>JB</span>}}}}$

其中：λ_p-R为直流侧断路器故障率，λ_p-M为直流侧断路器检修率，μ_p-R为直流侧断路器故障修复率，μ_p-M为直流侧断路器检修修复率，μ_x为断路器通讯模块检修修复率，μ_JB为断路器继保模块修复率，Among them: λ_pR is the failure rate of the DC side circuit breaker, λ_pM is the maintenance rate of the DC side circuit breaker, μ_pR is the failure recovery rate of the DC side circuit breaker, μ_pM is the maintenance and repair rate of the DC side circuit breaker, and μ_x is the communication of the circuit breaker Module maintenance and repair rate, μ_JB is the repair rate of circuit breaker relay protection module,

(5)对分区所形成网络的最小路搜索(5) Minimum path search for the network formed by the partition

根据图5可知，各分区形成一个有向网络。利用矩阵乘法对最小路进行搜索，方法如下：It can be known from Figure 5 that each partition forms a directed network. Use matrix multiplication to search for the minimum path, as follows:

a.定义各分区为一个节点，建立网络的邻接矩阵A₁＝[a¹_ij]。a. Define each partition as a node, and establish the adjacency matrix A₁ =[a¹_ij ] of the network.

其中：当节点v_i和v_j之间有连接时，a¹_ij＝1或a¹_ij＝-1；当v_j和v_j之间无连接或j＝i时，a¹_ij＝a¹_ji＝0。Where: when there is a connection between nodes v_i and v_j , a¹_ij =1 or a¹_ij =-1; when there is no connection between v_j and v_j or j=i, a¹_ij =a¹_ji =0.

b.建立网络的邻接终点矩阵R＝[r_jk]。b. Establish the adjacency terminal matrix R=[r_jk ] of the network.

其中：当节点v_j和终点v_k之间有连接时，r¹_jk＝1；当v_j和v_k之间无连接或j＝k时，r¹_jk＝0；Where: when there is a connection between node v_j and terminal v_k , r¹_jk =1; when there is no connection between v_j and v_k or j=k, r¹_jk =0;

c.将矩阵A₁与邻接终点矩阵R相乘，得到新矩阵A₂＝[a²_ik]。c. Multiply the matrix A₁ with the matrix R of the adjacent destination to obtain a new matrix A₂ =[a²_ik ].

${\mathrm{<span><span>a</span>a</span>}}_{\mathrm{<span><span>ik</span>ik</span>}}^{\mathrm{<span><span>2</span>2</span>}}<span><span>=</span>=</span><span><span>\{</span>\{</span>{\mathrm{<span><span>a</span>a</span>}}_{\mathrm{<span><span>ij</span>ij</span>}}^{\mathrm{<span><span>1</span>1</span>}}{\mathrm{<span><span>r</span>r</span>}}_{\mathrm{<span><span>jk</span>jk</span>}}<span><span>|</span>|</span>\mathrm{<span><span>j</span>j</span>}<span><span>=</span>=</span>\mathrm{<span><span>1,2</span>1,2</span>}<span><span>,</span>,</span><span><span>\&CenterDot;</span>\&CenterDot;</span><span><span>\&CenterDot;</span>\&Center\; Dot;</span><span><span>\&CenterDot;</span>\&Center\; Dot;</span>\mathrm{<span><span>n</span>no</span>}<span><span>\}</span>\}</span><span><span>-</span>-</span><span><span>-</span>-</span><span><span>-</span>-</span><span><span>(</span>(</span>\mathrm{<span><span>10</span>10</span>}<span><span>)</span>)</span>$

其中：当i，j,k三个节点各不相同时，a²_ik＝a¹_ijr_jk；当a¹_ij＝0或r_jk＝0或v_k至少与v_i和v_j中的一个相同时，a²_ik＝0。Where: when the three nodes i, j, and k are different, a²_ik = a¹_ij r_jk ; when a¹_ij = 0 or r_jk = 0 or v_k is at least one of v_i and v_j At the same time, a²_ik =0.

d.改变终点v_k，重复以上步骤，得到矩阵A₃，A₄，...A_n-1，d. Change the end point v_k and repeat the above steps to obtain the matrix A₃ , A₄ ,...A_n-1 ,

e.将A₁，A₂，...A_n-1中对应位置(i，j)的非零元素组合起来，就得到从节点i到节点j之间的所有最小路。e. Combining the non-zero elements corresponding to positions (i, j) in A₁ , A₂ , . . . A_n-1 , all the minimum paths from node i to node j are obtained.

f.由于本申请所选择的节点已经包含了主接线内所有需要评估的元件，没有单节点元件被遗漏，则该最小路集矩阵即为最终的路集矩阵。利用路集矩阵可以对任意的节点进行割集分析。f. Since the nodes selected in this application already contain all the elements that need to be evaluated in the main wiring, and no single node element is omitted, the minimum road set matrix is the final road set matrix. The road set matrix can be used to perform cut set analysis on any node.

可靠性指标统计流程如图6所示。具体流程如下：读入网络拓朴、形成网络信息矩阵、形成最小路集矩阵、枚举网络状态、计算最小割集、统计各状态下网络可靠性指标。The reliability index statistical process is shown in Figure 6. The specific process is as follows: read in the network topology, form the network information matrix, form the minimum road set matrix, enumerate the network status, calculate the minimum cut set, and count the network reliability indicators in each state.

Claims (1)

Translated fromChinese

1. 一种±800kV换流站主接线可靠性评估方法，其特征在于：建立了改进的元件四状态模型，在评估主接线可靠性过程中加入了继保和二次设备的可靠性模型，利用元件的合并分区将原本比较复杂的±800kV换流站主接线进行简化，并应用改进的元件四状态模型于简化后的各分区，重新定义元件的异常状态和检修状态，将元件的状态检修状态与计划检修状态合并归入元件的检修状态，并确定各状态之间的转换关系以及参数的求取，用矩阵乘法简化最小路矩阵搜索的方法对有向网络进行最小路搜索，利用解析法枚举有向网络的各种故障状态，并计算出该网络的可靠性数据，具体步骤如下：1. A reliability evaluation method for the main wiring of a ±800kV converter station, which is characterized in that: an improved four-state model of components is established, and the reliability model of relay protection and secondary equipment is added in the process of evaluating the reliability of the main wiring. The main wiring of the originally complicated ±800kV converter station is simplified by merging and partitioning components, and the improved four-state model of components is applied to the simplified partitions to redefine the abnormal state and maintenance state of components, and the state maintenance of components The state and planned maintenance state are merged into the maintenance state of the component, and the conversion relationship between each state and the calculation of parameters are determined. The minimum path search method is used to simplify the minimum path matrix search for the directed network by matrix multiplication, and the analytical method is used. Enumerate the various fault states of the directed network, and calculate the reliability data of the network, the specific steps are as follows:(1)建立改进元件四状态模型(1) Establish a four-state model for improved components在改进元件四状态模型中，重新定义设备的异常状态，检修状态和故障状态，及其相关关系：In the improved element four-state model, redefine the abnormal state, maintenance state and fault state of the equipment, and their correlations:元件异常状态(A)：元件次要功能出现故障或者元件出现故障征兆时该元件所处的状态；Component abnormal state (A): the state of the component when the secondary function of the component fails or the component has a symptom of failure;元件检修状态(M)：为元件处于检修的状态，包含计划检修状态与状态检修状态；Component maintenance status (M): the component is in the maintenance status, including the planned maintenance status and status maintenance status;元件故障状态(R)：当元件无法保证其应有的主要功能时所处的状态，对于开关设备，其误动和拒动归纳入元件的故障状态；Component failure state (R): the state that the component is in when it cannot guarantee its main function. For switchgear, its malfunction and refusal are included in the component's fault state;根据改进元件四状态模型，元件从正常状态N出发对应检修状态M和异常状态A，元件的异常状态A转换为故障状态R和检修状态M；According to the improved four-state model of the component, the component starts from the normal state N and corresponds to the maintenance state M and the abnormal state A, and the abnormal state A of the component is transformed into the fault state R and the maintenance state M;(2)在主接线可靠性评估中增加了继保及二次设备的可靠性模型，继保可靠性包括软件和硬件两个部分，硬件可靠性为：(2) The reliability model of relay protection and secondary equipment is added to the reliability evaluation of the main wiring. The reliability of relay protection includes two parts: software and hardware. The hardware reliability is:λ＝γ_Q(C₁γ_Tγ_V+C₂γ_E)γ_Lλ＝γ_Q (C₁ γ_T γ_V +C₂ γ_E )γ_L${\mathrm{<span><span>\&lambda;</span>\&lambda;</span>}}_{\mathrm{<span><span>M</span>m</span>}}<span><span>=</span>=</span>\underset{\mathrm{<span><span>i</span>i</span>}<span><span>=</span>=</span>\mathrm{<span><span>1</span>1</span>}}{\overset{\mathrm{<span><span>N</span>N</span>}}{\mathrm{<span><span>\&Sigma;</span>\&Sigma;</span>}}}{\mathrm{<span><span>\&lambda;</span>\&lambda;</span>}}_{\mathrm{<span><span>i</span>i</span>}}$    λ_H＝λ_T+λ_Jλ_H = λ_T + λ_J式中：γ_Q为器件质量因数；C₁为电路复杂因数；γ_T为温度加速因数；γ_V为电压应力因数；C₂为封装复杂因数；γ_E为应用环境因数；γ_L为为器件成熟因数；N为模块M中元器件的总个数；λ_H为硬件故障率；λ_T为通讯模块故障率；λ_J为继电保护模块故障率；In the formula: γ_Q is the device quality factor; C₁ is the circuit complexity factor; γ_T is the temperature acceleration factor; γ_V is the voltage stress factor; C₂ is the package complexity factor; γ_E is the application environment factor; γ_L is the device Maturity factor; N is the total number of components in module M; λ_H is the hardware failure rate; λ_T is the communication module failure rate; λ_J is the relay protection module failure rate;软件可靠性模型采用John Musa模型处理，该模型的软件失效率为：The software reliability model is processed by the John Musa model, and the software failure rate of this model is:${\mathrm{<span><span>\&lambda;</span>\&lambda;</span>}}_{\mathrm{<span><span>s</span>the\; s</span>}}<span><span>=</span>=</span>{\mathrm{<span><span>e</span>e</span>}}^{<span><span>-</span>-</span>\frac{{\mathrm{<span><span>\&tau;</span>\&tau;</span>}}^{<span><span>\&prime;</span>\&prime;</span>}}{\mathrm{<span><span>\&tau;</span>\&tau;</span>}}{\mathrm{<span><span>M</span>m</span>}}_{\mathrm{<span><span>0</span>0</span>}}{\mathrm{<span><span>T</span>T</span>}}_{\mathrm{<span><span>0</span>0</span>}}}<span><span>=</span>=</span>{\mathrm{<span><span>\&lambda;</span>\&lambda;</span>}}_{\mathrm{<span><span>0</span>0</span>}}{\mathrm{<span><span>e</span>e</span>}}^{<span><span>-</span>-</span>\frac{{\mathrm{<span><span>\&tau;</span>\&tau;</span>}}^{<span><span>\&prime;</span>\&prime;</span>}}{\mathrm{<span><span>\&tau;</span>\&tau;</span>}}}$式中：τ为累积执行时间，即程序从开始运行到本次评估可靠性所经历的时间；τ’为程序运行时间，即从本次评估开始，程序可无故障运行的时间；λ₀为初始故障率，与最初的无故障时间T₀及软件的缺陷总数M₀有关；In the formula: τ is the cumulative execution time, that is, the time from the start of the program to the evaluation of reliability; τ' is the running time of the program, that is, the time for the program to run without failure from the beginning of this evaluation;_λ0 is The initial failure rate is related to the initial failure-free time T₀ and the total number of software defects M₀ ;则继电保护可靠性如下式：The reliability of relay protection is as follows:λ_JB＝λ_S+λ_Hλ_JB =λ_S +λ_H式中：λ_JB为继电保护故障率；λ_S为软件故障率；λ_H为硬件故障率；In the formula: λ_JB is the relay protection failure rate; λ_S is the software failure rate; λ_H is the hardware failure rate;(3)元件合并分区(3) Component merge partition对主接线四状态模型进行分区，主元件与其附属元件合并形成分区，相邻串、并联主元件如果合并不影响接线方式则可以合并为一个分区，如果合并后影响接线方式，则单独作为分区；Partition the main wiring four-state model. The main component and its subsidiary components are merged to form a partition. If the combination of adjacent series and parallel main components does not affect the wiring method, they can be merged into one partition. If the combination affects the wiring method, they can be used as a separate partition;(4)分区可靠性参数的确定(4) Determination of partition reliability parameters由于各个分区都是由元件组合而且，可见元件的状态对应着各分区状态，将元件四状态模型应用于各分区，以取得分区可靠性参数，对于断路器-换流变压器形成的分区，其故障率参数如下式：Since each partition is composed of components and it can be seen that the state of the component corresponds to the state of each partition, the four-state model of the component is applied to each partition to obtain the reliability parameters of the partition. For the partition formed by the circuit breaker-converter transformer, its failure The rate parameter is as follows:λ_R＝λ_R(d-b)+λ_(Jb)λ_R = λ_{R (db)} + λ_(Jb)λ_A＝λ_A(d-b)+λ_xλ_A = λ_A(db) + λ_xλ′_M＝λ_xλ′_M = λ_xλ′_A＝λ_JBλ′_A =λ_JB${\mathrm{<span><span>\&mu;</span>\&mu;</span>}}_{\mathrm{<span><span>M</span>m</span>}}<span><span>=</span>=</span>\frac{{\mathrm{<span><span>\&lambda;</span>\&lambda;</span>}}_{\mathrm{<span><span>d</span>d</span>}<span><span>-</span>-</span>\mathrm{<span><span>M</span>m</span>}}<span><span>+</span>+</span>{\mathrm{<span><span>\&lambda;</span>\&lambda;</span>}}_{\mathrm{<span><span>b</span>b</span>}<span><span>-</span>-</span>\mathrm{<span><span>M</span>m</span>}}<span><span>+</span>+</span>{\mathrm{<span><span>\&lambda;</span>\&lambda;</span>}}_{\mathrm{<span><span>x</span>x</span>}}<span><span>+</span>+</span>{\mathrm{<span><span>\&lambda;</span>\&lambda;</span>}}_{\mathrm{<span><span>JB</span>JB</span>}}}{\frac{{\mathrm{<span><span>\&lambda;</span>\&lambda;</span>}}_{\mathrm{<span><span>d</span>d</span>}<span><span>-</span>-</span>\mathrm{<span><span>M</span>m</span>}}}{{\mathrm{<span><span>\&mu;</span>\&mu;</span>}}_{\mathrm{<span><span>d</span>d</span>}<span><span>-</span>-</span>\mathrm{<span><span>M</span>m</span>}}}<span><span>+</span>+</span>\frac{{\mathrm{<span><span>\&lambda;</span>\&lambda;</span>}}_{\mathrm{<span><span>b</span>b</span>}<span><span>-</span>-</span>\mathrm{<span><span>M</span>m</span>}}}{{\mathrm{<span><span>\&mu;</span>\&mu;</span>}}_{\mathrm{<span><span>b</span>b</span>}<span><span>-</span>-</span>\mathrm{<span><span>M</span>m</span>}}}<span><span>+</span>+</span>\frac{{\mathrm{<span><span>\&lambda;</span>\&lambda;</span>}}_{\mathrm{<span><span>x</span>x</span>}}}{{\mathrm{<span><span>\&mu;</span>\&mu;</span>}}_{\mathrm{<span><span>x</span>x</span>}}}<span><span>+</span>+</span>\frac{{\mathrm{<span><span>\&lambda;</span>\&lambda;</span>}}_{\mathrm{<span><span>JB</span>JB</span>}}}{{\mathrm{<span><span>\&mu;</span>\&mu;</span>}}_{\text{<span><span>JB</span>JB</span>}}}}$${\mathrm{<span><span>\&mu;</span>\&mu;</span>}}_{\mathrm{<span><span>R</span>R</span>}}<span><span>=</span>=</span>\frac{{\mathrm{<span><span>\&lambda;</span>\&lambda;</span>}}_{\mathrm{<span><span>d</span>d</span>}<span><span>-</span>-</span>\mathrm{<span><span>R</span>R</span>}}<span><span>+</span>+</span>{\mathrm{<span><span>\&lambda;</span>\&lambda;</span>}}_{\mathrm{<span><span>b</span>b</span>}<span><span>-</span>-</span>\mathrm{<span><span>R</span>R</span>}}}{\frac{{\mathrm{<span><span>\&lambda;</span>\&lambda;</span>}}_{\mathrm{<span><span>d</span>d</span>}<span><span>-</span>-</span>\mathrm{<span><span>R</span>R</span>}}}{{\mathrm{<span><span>\&mu;</span>\&mu;</span>}}_{\mathrm{<span><span>d</span>d</span>}<span><span>-</span>-</span>\mathrm{<span><span>R</span>R</span>}}}<span><span>+</span>+</span>\frac{{\mathrm{<span><span>\&lambda;</span>\&lambda;</span>}}_{\mathrm{<span><span>b</span>b</span>}<span><span>-</span>-</span>\mathrm{<span><span>R</span>R</span>}}}{{\mathrm{<span><span>\&mu;</span>\&mu;</span>}}_{\mathrm{<span><span>b</span>b</span>}<span><span>-</span>-</span>\mathrm{<span><span>R</span>R</span>}}}}$其中：λ_R为分区故障率，λ_A为分区异常概率，λ’_M为分区状态检修概率，λ’_A为分区状态检修概率，μ_M为分区检修修复率，μ_R为分区故障修复率；λ_R(d-b)为断路器和变压器故障率之和；λ_A(d-b)为断路器和变压器异常状态率之和，λ_d-M为断路器检修率，λ_b-M为变压器检修率，λ_d-R为断路器故障率，λ_b-R为变压器故障率，μ_d-M为断路器检修修复率，μ_b-M为变压器检修修复率，μ_d-R为断路器故障修复率，μ_b-R为变压器故障修复率；Among them: λ_R is the partition failure rate, λ_A is the abnormal probability of the partition, λ'_M is the partition state maintenance probability, λ'_A is the partition state maintenance probability, μ_M is the partition repair repair rate, and μ_R is the partition fault repair rate; λ_R(db) is the sum of failure rate of circuit breaker and transformer; λ_A(db) is the sum of abnormal state rate of circuit breaker and transformer, λ_dM is maintenance rate of circuit breaker, λ_bM is maintenance rate of transformer, λ_dR is open circuit λ_bR is the failure rate of the transformer, μ_dM is the maintenance and repair rate of the circuit breaker, μ_bM is the maintenance and repair rate of the transformer, μ_dR is the failure recovery rate of the circuit breaker, and μ_bR is the failure recovery rate of the transformer;对于换流阀、避雷器形成的分区，其故障率参数如下式：For the partition formed by the converter valve and the arrester, the failure rate parameter is as follows:λ_R＝λ_h-R+λ_blλ_R ＝ λ_hR + λ_blλ_A＝λ_bl＝λ′_Aλ_A =λ_bl =λ′_Aλ′_M＝0λ′_M =0${\mathrm{<span><span>\&mu;</span>\&mu;</span>}}_{\mathrm{<span><span>M</span>m</span>}}<span><span>=</span>=</span>\frac{{\mathrm{<span><span>\&lambda;</span>\&lambda;</span>}}_{\mathrm{<span><span>h</span>h</span>}<span><span>-</span>-</span>\mathrm{<span><span>M</span>m</span>}}<span><span>+</span>+</span>{\mathrm{<span><span>\&lambda;</span>\&lambda;</span>}}_{\mathrm{<span><span>bl</span>bl</span>}}}{\frac{{\mathrm{<span><span>\&lambda;</span>\&lambda;</span>}}_{\mathrm{<span><span>h</span>h</span>}<span><span>-</span>-</span>\mathrm{<span><span>M</span>m</span>}}}{{\mathrm{<span><span>\&mu;</span>\&mu;</span>}}_{\mathrm{<span><span>h</span>h</span>}<span><span>-</span>-</span>\mathrm{<span><span>M</span>m</span>}}}<span><span>+</span>+</span>\frac{{\mathrm{<span><span>\&lambda;</span>\&lambda;</span>}}_{\mathrm{<span><span>bl</span>bl</span>}}}{{\mathrm{<span><span>\&mu;</span>\&mu;</span>}}_{\mathrm{<span><span>bl</span>bl</span>}}}}$${\mathrm{<span><span>\&mu;</span>\&mu;</span>}}_{\mathrm{<span><span>R</span>R</span>}}<span><span>=</span>=</span>\frac{{\mathrm{<span><span>\&lambda;</span>\&lambda;</span>}}_{\mathrm{<span><span>h</span>h</span>}<span><span>-</span>-</span>\mathrm{<span><span>R</span>R</span>}}<span><span>+</span>+</span>{\mathrm{<span><span>\&lambda;</span>\&lambda;</span>}}_{\mathrm{<span><span>bl</span>bl</span>}}}{\frac{{\mathrm{<span><span>\&lambda;</span>\&lambda;</span>}}_{\mathrm{<span><span>h</span>h</span>}<span><span>-</span>-</span>\mathrm{<span><span>R</span>R</span>}}}{{\mathrm{<span><span>\&mu;</span>\&mu;</span>}}_{\mathrm{<span><span>h</span>h</span>}<span><span>-</span>-</span>\mathrm{<span><span>R</span>R</span>}}}<span><span>+</span>+</span>\frac{{\mathrm{<span><span>\&lambda;</span>\&lambda;</span>}}_{\mathrm{<span><span>bl</span>bl</span>}}}{{\mathrm{<span><span>\&mu;</span>\&mu;</span>}}_{\mathrm{<span><span>bl</span>bl</span>}}}}$其中：λ_h-R为换流器故障率，λ_h-A为换流器异常率，λ_h-M为换流器检修率，λ_bl为避雷器故障率，μ_h-M为换流器检修修复率，μ_h-R为换流器故障修复率；Among them: λ_hR is the failure rate of the converter, λ_hA is the abnormal rate of the converter, λ_hM is the repair rate of the converter, λ_bl is the failure rate of the arrester, μ_hM is the repair rate of the converter, and μ_hR is the converter repair rate. Flow device failure repair rate;对于平波电抗器、滤波器形成的分区，其故障率参数如下式：For the partitions formed by smoothing reactors and filters, the failure rate parameters are as follows:λ_R＝λ_c-R+λ_k-Rλ_R ＝ λ_{c R} + λ_{k R}λ_A＝0＝λ′_M＝λ′_Aλ_A = 0 = λ'_M = λ'_A${\mathrm{<span><span>\&mu;</span>\&mu;</span>}}_{\mathrm{<span><span>M</span>m</span>}}<span><span>=</span>=</span>\frac{{\mathrm{<span><span>\&lambda;</span>\&lambda;</span>}}_{\mathrm{<span><span>c</span>c</span>}<span><span>-</span>-</span>\mathrm{<span><span>M</span>m</span>}}<span><span>+</span>+</span>{\mathrm{<span><span>\&lambda;</span>\&lambda;</span>}}_{\mathrm{<span><span>k</span>k</span>}<span><span>-</span>-</span>\mathrm{<span><span>M</span>m</span>}}}{\frac{{\mathrm{<span><span>\&lambda;</span>\&lambda;</span>}}_{\mathrm{<span><span>c</span>c</span>}<span><span>-</span>-</span>\mathrm{<span><span>M</span>m</span>}}}{{\mathrm{<span><span>\&mu;</span>\&mu;</span>}}_{\mathrm{<span><span>c</span>c</span>}<span><span>-</span>-</span>\mathrm{<span><span>M</span>m</span>}}}<span><span>+</span>+</span>\frac{{\mathrm{<span><span>\&lambda;</span>\&lambda;</span>}}_{\mathrm{<span><span>k</span>k</span>}<span><span>-</span>-</span>\mathrm{<span><span>M</span>m</span>}}}{{\mathrm{<span><span>\&mu;</span>\&mu;</span>}}_{\mathrm{<span><span>k</span>k</span>}<span><span>-</span>-</span>\mathrm{<span><span>M</span>m</span>}}}}$${\mathrm{<span><span>\&mu;</span>\&mu;</span>}}_{\mathrm{<span><span>R</span>R</span>}}<span><span>=</span>=</span>\frac{{\mathrm{<span><span>\&lambda;</span>\&lambda;</span>}}_{\mathrm{<span><span>c</span>c</span>}<span><span>-</span>-</span>\mathrm{<span><span>R</span>R</span>}}<span><span>+</span>+</span>{\mathrm{<span><span>\&lambda;</span>\&lambda;</span>}}_{\mathrm{<span><span>k</span>k</span>}<span><span>-</span>-</span>\mathrm{<span><span>R</span>R</span>}}}{\frac{{\mathrm{<span><span>\&lambda;</span>\&lambda;</span>}}_{\mathrm{<span><span>c</span>c</span>}<span><span>-</span>-</span>\mathrm{<span><span>R</span>R</span>}}}{{\mathrm{<span><span>\&mu;</span>\&mu;</span>}}_{\mathrm{<span><span>c</span>c</span>}<span><span>-</span>-</span>\mathrm{<span><span>R</span>R</span>}}}<span><span>+</span>+</span>\frac{{\mathrm{<span><span>\&lambda;</span>\&lambda;</span>}}_{\mathrm{<span><span>k</span>k</span>}<span><span>-</span>-</span>\mathrm{<span><span>R</span>R</span>}}}{{\mathrm{<span><span>\&mu;</span>\&mu;</span>}}_{\mathrm{<span><span>k</span>k</span>}<span><span>-</span>-</span>\mathrm{<span><span>R</span>R</span>}}}}$其中：λ_c-R为滤波器故障率，λ_c-M为滤波器检修修复率，λ_k-R为平波电抗器故障率，λ_k-M为平波电抗器检修修复率，μ_c-M为滤波器检修修复率，μ_c-R为滤波器故障修复率；μ_k-M为平波电抗器检修修复率，μ_k-R为平波电抗器故障修复率；Among them: λ_cR is the failure rate of the filter, λ_cM is the maintenance and repair rate of the filter, λ_kR is the failure rate of the smoothing reactor, λ_kM is the maintenance and repair rate of the smoothing reactor, μ_cM is the maintenance and repair rate of the filter, μ_cR is the fault repair rate of the filter; μ_kM is the maintenance repair rate of the smoothing reactor, and μ_kR is the fault repair rate of the smoothing reactor;对于直流侧断路器形成的分区，其故障率参数如下式：For the partition formed by the DC side circuit breaker, the failure rate parameter is as follows:λ_R＝λ_p-R+λ_JBλ_R ＝ λ_pR + λ_JBλ_A＝λ_x＝λ′_Mλ_A ＝ λ_x ＝ λ′_Mλ′_A＝λ_JBλ′_A =λ_JB${\mathrm{<span><span>\&mu;</span>\&mu;</span>}}_{\mathrm{<span><span>M</span>m</span>}}<span><span>=</span>=</span>\frac{{\mathrm{<span><span>\&lambda;</span>\&lambda;</span>}}_{\mathrm{<span><span>p</span>p</span>}<span><span>-</span>-</span>\mathrm{<span><span>M</span>m</span>}}<span><span>+</span>+</span>{\mathrm{<span><span>\&lambda;</span>\&lambda;</span>}}_{\mathrm{<span><span>x</span>x</span>}}<span><span>+</span>+</span>{\mathrm{<span><span>\&lambda;</span>\&lambda;</span>}}_{\mathrm{<span><span>JB</span>JB</span>}}}{\frac{{\mathrm{<span><span>\&lambda;</span>\&lambda;</span>}}_{\mathrm{<span><span>p</span>p</span>}<span><span>-</span>-</span>\mathrm{<span><span>M</span>m</span>}}}{{\mathrm{<span><span>\&mu;</span>\&mu;</span>}}_{\mathrm{<span><span>p</span>p</span>}<span><span>-</span>-</span>\mathrm{<span><span>M</span>m</span>}}}<span><span>+</span>+</span>\frac{{\mathrm{<span><span>\&lambda;</span>\&lambda;</span>}}_{\mathrm{<span><span>x</span>x</span>}}}{{\mathrm{<span><span>\&mu;</span>\&mu;</span>}}_{\mathrm{<span><span>x</span>x</span>}}}<span><span>+</span>+</span>\frac{{\mathrm{<span><span>\&lambda;</span>\&lambda;</span>}}_{\mathrm{<span><span>JB</span>JB</span>}}}{{\mathrm{<span><span>\&mu;</span>\&mu;</span>}}_{\mathrm{<span><span>JB</span>JB</span>}}}}$${\mathrm{<span><span>\&mu;</span>\&mu;</span>}}_{\mathrm{<span><span>R</span>R</span>}}<span><span>=</span>=</span>\frac{{\mathrm{<span><span>\&lambda;</span>\&lambda;</span>}}_{\mathrm{<span><span>p</span>p</span>}<span><span>-</span>-</span>\mathrm{<span><span>R</span>R</span>}}<span><span>+</span>+</span>{\mathrm{<span><span>\&lambda;</span>\&lambda;</span>}}_{\mathrm{<span><span>JB</span>JB</span>}}}{\frac{{\mathrm{<span><span>\&lambda;</span>\&lambda;</span>}}_{\mathrm{<span><span>p</span>p</span>}<span><span>-</span>-</span>\mathrm{<span><span>R</span>R</span>}}}{{\mathrm{<span><span>\&mu;</span>\&mu;</span>}}_{\mathrm{<span><span>p</span>p</span>}<span><span>-</span>-</span>\mathrm{<span><span>R</span>R</span>}}}<span><span>+</span>+</span>\frac{{\mathrm{<span><span>\&lambda;</span>\&lambda;</span>}}_{\mathrm{<span><span>JB</span>JB</span>}}}{{\mathrm{<span><span>\&mu;</span>\&mu;</span>}}_{\mathrm{<span><span>JB</span>JB</span>}}}}$其中：λ_p-R为直流侧断路器故障率，λ_p-M为直流侧断路器检修率，μ_p-R为直流侧断路器故障修复率，μ_p-M为直流侧断路器检修修复率，μ_x为断路器通讯模块检修修复率，μ_JB为断路器继保模块修复率；Among them: λ_pR is the failure rate of the DC side circuit breaker, λ_pM is the maintenance rate of the DC side circuit breaker, μ_pR is the failure recovery rate of the DC side circuit breaker, μ_pM is the maintenance and repair rate of the DC side circuit breaker, and μ_x is the communication of the circuit breaker Module maintenance and repair rate, μ_JB is the repair rate of circuit breaker relay protection module;(5)利用最小路搜索法对分区形成的网络进行搜索，具体步骤如下：(5) Use the minimum path search method to search the network formed by the partition, the specific steps are as follows:a.定义各分区为一个节点，建立网络的邻接矩阵A₁＝[a¹_ij]；a. Define each partition as a node, and establish the adjacency matrix A₁ =[a¹_ij ] of the network;其中：当节点v_i和v_j之间有连接时，a¹_ij＝1或a¹_ij＝-1；当v_j和v_j之间无连接或j＝i时，a¹_ij＝a¹_ji＝0；Where: when there is a connection between nodes v_i and v_j , a¹_ij =1 or a¹_ij =-1; when there is no connection between v_j and v_j or j=i, a¹_ij =a¹_ji = 0;b.建立网络的邻接终点矩阵R＝[r_jk]；b. Establish the adjacent terminal matrix R=[r_jk ] of the network;其中：当节点v_j和终点v_k之间有连接时，r¹_jk＝1；当v_j和v_k之间无连接或j＝k时，r¹_jk＝0；Where: when there is a connection between node v_j and terminal v_k , r¹_jk =1; when there is no connection between v_j and v_k or j=k, r¹_jk =0;c.将矩阵A₁与邻接终点矩阵R相乘，得到新矩阵A₂＝[a²_ik]；c. Multiply the matrix A₁ with the adjacent end point matrix R to obtain a new matrix A₂ =[a²_ik ];${\mathrm{<span><span>a</span>a</span>}}_{\mathrm{<span><span>ik</span>ik</span>}}^{\mathrm{<span><span>2</span>2</span>}}<span><span>=</span>=</span><span><span>\{</span>\{</span>{\mathrm{<span><span>a</span>a</span>}}_{\mathrm{<span><span>ij</span>ij</span>}}^{\mathrm{<span><span>1</span>1</span>}}{\mathrm{<span><span>r</span>r</span>}}_{\mathrm{<span><span>jk</span>jk</span>}}<span><span>|</span>|</span>\mathrm{<span><span>j</span>j</span>}<span><span>=</span>=</span>\mathrm{<span><span>1,2</span>1,2</span>}<span><span>,</span>,</span><span><span>\&CenterDot;</span>\&CenterDot;</span><span><span>\&CenterDot;</span>\&CenterDot;</span><span><span>\&CenterDot;</span>\&Center\; Dot;</span>\mathrm{<span><span>n</span>no</span>}<span><span>\}</span>\}</span>$其中：当i，j，k三个节点各不相同时，a²_ik＝a¹_ijr_jk；当a¹_ij＝0或r_jk＝0或v_k至少与v_i和v_j中的一个相同时，a²_ik＝0；Where: when the three nodes i, j, k are different, a²_ik = a¹_ij r_jk ; when a¹_ij = 0 or r_jk = 0 or v_k is at least one of v_i and v_j At the same time, a²_ik =0;d.改变终点v_k，重复以上步骤，得到矩阵A₃，A₄，...A_n-1；d. Change the end point v_k and repeat the above steps to obtain matrices A₃ , A₄ ,...A_n-1 ;e.将A₁，A₂，...A_n-1中对应位置(i，j)的非零元素组合起来，就得到从节点i到节点j之间的所有最小路；e. Combine the non-zero elements corresponding to the position (i, j) in A₁ , A₂ ,...A_n-1 to get all the minimum paths from node i to node j;f.由于所选择的节点已经包含了主接线内所有需要评估的元件，没有单节点元件被遗漏，则该最小路集矩阵即为最终的路集矩阵，利用路集矩阵可以对任意的节点进行割集分析。f. Since the selected node already contains all the elements that need to be evaluated in the main connection, and no single node element is omitted, the minimum road set matrix is the final road set matrix, and any node can be evaluated by using the road set matrix Cut set analysis.

Images