阅读说明：本技术 一种考虑mmc模块间相关性的子模块冗余优化配置方法及系统 (Submodule redundancy optimization configuration method and system considering correlation between MMC modules ) 是由 郑文迪 许启东 邵振国 王向杰 李怡馨 曾祥勇 周腾龙 于 2019-09-17 设计创作，主要内容包括：本发明涉及一种考虑MMC模块间相关性的子模块冗余优化配置方法及系统,计及模块间相关性,引入Copula理论,利用极大似然估计理论得到模块间的相关系数,进而建立未配置冗余子模块和配置冗余子模块下的MMC可靠性分析模型；采用拐点法计算MMC的冗余和可靠性指标,以此确定最佳的MMC冗余子模块配置方案。本发明避免了传统MMC可靠性分析方法未考虑所有模块具有相关性的不利影响。(The invention relates to a submodule redundancy optimization configuration method and a submodule redundancy optimization configuration system considering correlation among MMC modules, wherein the correlation among the modules is considered, a Copula theory is introduced, a correlation coefficient among the modules is obtained by utilizing a maximum likelihood estimation theory, and an MMC reliability analysis model under an unconfigured redundancy submodule and a configured redundancy submodule is further established; and calculating redundancy and reliability indexes of the MMC by adopting an inflection point method so as to determine an optimal MMC redundancy submodule configuration scheme. The invention avoids the adverse effect that the traditional MMC reliability analysis method does not consider all modules to have correlation.)

1. A submodule redundancy optimization configuration method considering correlation among MMC modules is characterized in that correlation among the modules is considered, a Copula theory is introduced, a correlation coefficient among the modules is obtained by utilizing a maximum likelihood estimation theory, and an MMC reliability analysis model under an unconfigured redundant submodule and a configured redundant submodule is further established; and calculating redundancy and reliability indexes of the MMC by adopting an inflection point method so as to determine an optimal MMC redundancy submodule configuration scheme.

2. The sub-module redundancy optimization configuration method considering the correlation between MMC modules according to claim 1, characterized by comprising the following steps:

step S1: modeling MMC sub-modules, wherein the MMC sub-modules are of a half-bridge topological structure, and each MMC sub-module comprises two IGBT modules T1 and T2, an energy storage capacitor C, a bypass switch K1 and a crimping type packaging thyristor K2;

step S2: reliability R of sub-module_SM(t) is calculated using the formula:

in the formula, R_I、R_cap、R_K1、R_K2The reliability functions of the IGBT module, the capacitor, the bypass switch K1 and the compression joint type packaging thyristor K2 are respectively; the failure rate of the sub-module is:

λ_SM＝2λ_I+λ_cap+λ_K1+λ_K2；

in the formula, λ_I、λ_cap、λ_K1、λ_K2The failure rates of the IGBT module, the capacitor, the bypass switch K1 and the compression joint type packaging thyristor K2 are respectively;

step S3: reliability R of bridge arm control system_cp(t) is calculated using the formula:

in the formula, λ_cpFor the failure rate of the bridge arm control system, R_cpA reliability function for the bridge arm control system;

step S4: suppose there are N sub-modules per bridge arm, the lifetime of the ith sub-module is X_iLife time ofDistribution function of F_i(t)＝P{X_iT, i is equal to 1,2, …, N; service life of bridge arm control module is X_cpWith a life distribution function of F_cp(t)＝P{X_cpT is less than or equal to t }; introducing a Gumbel-Copula function into MMC reliability analysis to obtain an N-dimensional Gumbel-Copula function:

in the formula, F_i(t) denotes the lifetime distribution of the i-th submodule, F_cp(t) represents a life distribution of the control system, and θ represents F₁(t),F₂(t),…,F_i(t),F_cp(t) correlation coefficient between;

step S5: obtaining a maximum likelihood function by adopting a maximum likelihood estimation theory, obtaining zero correlation coefficient by enabling the maximum likelihood function to calculate partial derivatives of the correlation coefficient, and further determining the range of the correlation coefficient;

step S6: performing reliability analysis without redundant configuration, performing reliability analysis of redundant configuration, and obtaining a bridge arm reliability model considering correlation;

step S7: changing the quantity value of the redundant sub-modules, bringing a bridge arm reliability model taking correlation into consideration to obtain a series of discrete points, and fitting the series of discrete points to obtain a fitting function;

step S8: and determining the configuration number interval of the redundant sub-modules by using an inflection point method.

3. The method according to claim 2, wherein the step S5 is specifically as follows: obtaining a maximum likelihood function by adopting a maximum likelihood estimation theory:

wherein T is the number of years of operation,is a probability density function of the sub-module,is a probability density function of the bridge arm control system,is the cumulative distribution function of the sub-modules,is a cumulative distribution function of the bridge arm control system, where F^-1(t) is the inverse of F (t); x_Nt、X_cpRespectively is the service life data of the sub-module and the bridge arm control system, reliability statistical data based on the traditional VSC is substituted into the formula to estimate the correlation coefficient, and an equation can be solvedAnd obtaining the correlation coefficient theta among the modules, and further determining the range theta.

4. The method according to claim 2, wherein in step S6, the reliability analysis without redundancy configuration specifically comprises: when the redundancy configuration is not carried out, at the time t, the bridge arm reliability function with N sub-modules is as follows:

in the formula (I), the compound is shown in the specification,

5. the method of claim 2 for sub-module redundancy optimization configuration considering correlation between MMC modules, which comprisesCharacterized in that, in step S6, reliability analysis of the redundant configuration is performed, and the bridge arm reliability model taking the correlation into account is specifically: when performing redundancy configuration, at time t, configure N₀The reliability model of the bridge arm when each redundant submodule is as follows:

in the formula (I), the compound is shown in the specification, representing the reliability of the k sub-modules put into operation.

6. The method according to claim 2, wherein the step S7 is specifically as follows: number N of redundant sub-modules to be configured₀The value is changed by using configuration N₀The bridge arm reliability model of each redundant submodule obtains a series of discrete points (N)₀,R₂) The series of discrete points was fitted using a MATLAB fitting toolbox to give a fitting function of f (x).

7. The method according to claim 2, wherein the step S8 is specifically to calculate the second derivative of the fitting function f (x) to 0, and solve to obtain two special inflection points x₁、x₂Respectively rounding up and rounding down to obtain N₀[x₁]、N₀[x₂]In (N)₀[x₁],N₀[x₂]) And selecting the number of the configured redundant sub-modules in the interval.

8. A sub-module redundancy optimization configuration system taking into account dependencies between MMC modules, comprising a computer program in a memory, a processor and being executable on said processor, characterized in that the processor, when executing said computer program, implements the steps of the method according to any of claims 1 to 7.

9. A computer-readable storage medium, in which a computer program is stored which, when being executed by a processor, carries out the steps of the method according to any one of claims 1 to 7.

Technical Field

The invention relates to the technical field of modularization and multilevel, in particular to a submodule redundancy optimization configuration method and a submodule redundancy optimization configuration system considering correlation among MMC modules.

Background

In recent years, the modularized multi-level technology has wide application in the field of high-voltage direct-current transmission by virtue of the great advantages of the modularized multi-level technology in the multi-level field. With the rise of the voltage level, the number of the sub-modules is greatly increased, the sub-modules are inevitably failed under the condition of long-term operation, and in order to avoid the influence of the sub-modules on the normal operation of the system, redundant sub-modules are usually required to be configured.

The current method for researching the redundancy configuration of the sub-modules mainly comprises the following steps:

1. and analyzing the reliability of the submodule and the MMC, and providing 2 engineering redundancy reference values of the submodule. When the redundancy configuration quantity of the sub-modules of the MMC is between the 2 redundancy reference values, the reliability of the MMC can be increased by adding the redundancy sub-modules, redundancy and reliability indexes are defined on the basis, and the reliability efficiency of the redundancy sub-modules of different MMCs can be measured.

2. Starting from 3 targets of improving system reliability and effective utilization rate of redundant sub-modules and reducing the number of the redundant sub-modules, a multi-target optimization function is established, and then the number of the optimal redundant sub-modules is obtained through solving.

3. And analyzing a half-full-bridge mixed MMC, and using an equal micro-increment rate submodule to carry out redundant submodule configuration. Firstly, a semi-bridge submodule, a full-bridge submodule and a hybrid MMC reliability model based on a classical general model are given. Secondly, on the basis of reliability calculation of the semi-full hybrid MMC, the configuration schemes of the redundant sub-modules under two constraint conditions of sub-module cost and reliability are discussed respectively.

The method obtains a configuration scheme with better quantity of redundant sub-modules on the premise of meeting the reliability requirement of the MMC, but the influence of the correlation between the modules on the reliability is not considered, and the research proves that the influence of the correlation on the MMC is not negligible.

Disclosure of Invention

In view of this, the present invention provides a sub-module redundancy optimization configuration method and system considering correlation between MMC modules, so as to avoid adverse effects of correlation of all modules that is not considered in the conventional MMC reliability analysis method.

The invention is realized by adopting the following scheme: a submodule redundancy optimization configuration method considering correlation among MMC modules takes account of correlation among the modules, introduces Copula theory, obtains correlation coefficient among the modules by utilizing maximum likelihood estimation theory, and further establishes an MMC reliability analysis model under a condition that a redundancy submodule is not configured and a redundancy submodule is configured; and calculating redundancy and reliability indexes of the MMC by adopting an inflection point method so as to determine an optimal MMC redundancy submodule configuration scheme.

Further, the invention specifically comprises the following steps:

step S1: modeling MMC sub-modules, wherein the MMC sub-modules are of a half-bridge topological structure, and each MMC sub-module comprises two IGBT modules T1 and T2, an energy storage capacitor C, a bypass switch K1 and a crimping type packaging thyristor K2;

step S2: reliability R of sub-module_SM(t) is calculated using the formula:

in the formula, R_I、R_cap、R_K1、R_K2The reliability functions of the IGBT module, the capacitor, the bypass switch K1 and the compression joint type packaging thyristor K2 are respectively; the failure rate of the sub-module is:

λ_SM＝2λ_I+λ_cap+λ_K1+λ_K2；

in the formula, λ_I、λ_cap、λ_K1、λ_K2The failure rates of the IGBT module, the capacitor, the bypass switch K1 and the compression joint type packaging thyristor K2 are respectively;

step S3: reliability R of bridge arm control system_cp(t) is calculated using the formula:

in the formula, λ_cpFor the failure rate of the bridge arm control system, R_cpA reliability function for the bridge arm control system;

step S4: assuming that each bridge arm has N submodules, the service life random function of the ith submodule is X_iWith a life distribution function of F_i(t)＝P{X_iT, i is equal to or less than 1,2, …, N, and the service life of the bridge arm control module is X_cpWith a life distribution function of F_cp(t)＝P{X_cpT is less than or equal to t }; introducing a Gumbel-Copula function into MMC reliability analysis to obtain an N-dimensional Gumbel-Copula function:

in the formula, F_i(t) denotes the lifetime distribution of the i-th submodule, F_cp(t) represents a life distribution of the control system, and θ represents F₁(t),F₂(t),…,F_i(t),F_cp(t) correlation coefficient between;

step S5: obtaining a maximum likelihood function by adopting a maximum likelihood estimation theory, obtaining zero correlation coefficient by enabling the maximum likelihood function to calculate partial derivatives of the correlation coefficient, and further determining the range of the correlation coefficient;

step S6: performing reliability analysis without redundant configuration, performing reliability analysis of redundant configuration, and obtaining a bridge arm reliability model considering correlation;

step S7: changing the quantity value of the redundant sub-modules, bringing a bridge arm reliability model taking correlation into consideration to obtain a series of discrete points, and fitting the series of discrete points to obtain a fitting function;

step S8: and determining the configuration number interval of the redundant sub-modules by using an inflection point method.

Further, step S5 is specifically: obtaining a maximum likelihood function by adopting a maximum likelihood estimation theory:

wherein T is the number of years of operation,is a probability density function of the sub-module,is a probability density function of the bridge arm control system,is the cumulative distribution function of the sub-modules,is a cumulative distribution function of the bridge arm control system, where F^-1(t) is the inverse of F (t); x_Nt、X_cpRespectively is the service life data of the sub-module and the bridge arm control system, reliability statistical data based on the traditional VSC is substituted into the formula to estimate the correlation coefficient, and an equation can be solvedAnd obtaining the correlation coefficient theta among the modules, and further determining the range theta.

Further, in step S6, the reliability analysis without redundancy configuration specifically includes: when the redundancy configuration is not carried out, at the time t, the bridge arm reliability function with N sub-modules is as follows:

in the formula (I), the compound is shown in the specification,

further onIn step S6, reliability analysis of the redundant configuration is performed, and the bridge arm reliability model considering the correlation is specifically obtained as follows: when performing redundancy configuration, at time t, configure N₀The reliability model of the bridge arm when each redundant submodule is as follows:

in the formula (I), the compound is shown in the specification,indicating the reliability of the k normally functioning sub-modules.

Further, step S7 is specifically: number N of redundant sub-modules to be configured₀The value is changed by using configuration N₀The bridge arm reliability model of each redundant submodule obtains a series of discrete points (N)₀,R₂) The series of discrete points was fitted using a MATLAB fitting toolbox to give a fitting function of f (x).

Further, step S8 is to calculate the second derivative of the fitting function f (x) to be 0, and obtain two special inflection points x₁、x₂Respectively rounding up and rounding down to obtain N₀[x1]、N₀[x2]In (N)₀[x1],N₀[x2]) And selecting the number of the configured redundant sub-modules in the interval.

The invention also provides a sub-module redundancy optimization configuration system considering the correlation between MMC modules, which comprises a computer program which is arranged in a memory and a processor and can run on the processor, wherein the processor realizes the steps of the method when executing the computer program.

The invention also provides a computer-readable storage medium, in which a computer program is stored which, when being executed by a processor, carries out the steps of the method as described above.

On the basis of analyzing the topological structure of the MMC, the invention considers the correlation between each sub-module and a control module, introduces a Gumbel-Copula function, estimates the correlation coefficient between the modules by utilizing the maximum likelihood theory, then respectively establishes an MMC reliability analysis model under the condition that the redundancy sub-modules are not configured and the redundancy sub-modules are configured, discusses the influence of redundancy, the correlation coefficient and the operation years on the reliability of the MMC on the basis of the established MMC reliability model, and further discusses the redundancy optimization configuration of the sub-modules after the reliability index is reached.

Compared with the prior art, the invention has the following beneficial effects: the invention relates to correlation among modules, avoids the adverse effect that all modules have correlation in the traditional MMC reliability analysis method, introduces a Copula theory, obtains correlation coefficients among all modules by utilizing a maximum likelihood estimation theory, further establishes an MMC reliability analysis model under a redundancy submodule which is not configured and a redundancy submodule which is configured, and calculates redundancy and reliability indexes of an MMC by adopting an Inflection Point Method (IPM) when analyzing and configuring the reliability model under the redundancy submodule so as to determine the optimal MMC submodule configuration scheme. The redundancy configuration method not only aims at HBSM, but also can be applied to FBSM, CDSM and SCDSM, and has strong applicability.

Drawings

FIG. 1 is an MMC topology according to an embodiment of the present invention.

Fig. 2 is a schematic diagram of a half-bridge sub-module structure according to an embodiment of the present invention.

Fig. 3 is a diagram of sub-module combination relation according to the embodiment of the present invention.

Fig. 4 is a diagram of a bridge arm module combination relationship according to an embodiment of the present invention.

Fig. 5 is a schematic diagram of the principle of the method according to the embodiment of the present invention.

Detailed Description

The invention is further explained below with reference to the drawings and the embodiments.

It should be noted that the following detailed description is exemplary and is intended to provide further explanation of the disclosure. Unless defined otherwise, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this application belongs.

It is noted that the terminology used herein is for the purpose of describing particular embodiments only and is not intended to be limiting of example embodiments according to the present application. As used herein, the singular forms "a", "an" and "the" are intended to include the plural forms as well, and it should be understood that when the terms "comprises" and/or "comprising" are used in this specification, they specify the presence of stated features, steps, operations, devices, components, and/or combinations thereof, unless the context clearly indicates otherwise.

As shown in fig. 1, the present embodiment provides a sub-module redundancy optimization configuration method considering correlation between MMC modules, which takes into account correlation between the modules, introduces Copula theory, obtains correlation coefficient between the modules by using maximum likelihood estimation theory, and further establishes an MMC reliability analysis model without configuring a redundancy sub-module and under configuring the redundancy sub-module; and calculating redundancy and reliability indexes of the MMC by adopting an inflection point method so as to determine an optimal MMC redundancy submodule configuration scheme.

The embodiment specifically comprises the following steps:

step S1: modeling MMC sub-modules, wherein the MMC sub-modules are of a half-bridge topological structure, and each MMC sub-module comprises two IGBT modules T1 and T2, an energy storage capacitor C, a bypass switch K1 and a crimping type packaging thyristor K2; as shown in fig. 1, the modular multilevel converter is composed of A, B, C three-phase bridge arms, each of which is divided into an upper bridge arm and a lower bridge arm, and each of which is composed of n sub-modules in cascade connection. U shape_dcAnd I_dcThe voltage and the current of the direct current side are respectively, and O is a zero potential reference point of the direct current side. The MMC submodule structure can adopt half-bridge, full-bridge, mixed topological structures and the like. However, the MMC adopting the sub-modules in the hybrid or full-bridge structure has the capabilities of self-clearing of direct-current faults, uninterrupted operation and the like, and when the number of the sub-modules is large, the loss and the cost are correspondingly large. Therefore, the half-bridge structure of the embodiment performs reliability analysis; the submodule is the most basic constituent unit of the MMC, each half-bridge submodule is composed of 2 IGBT modules T1, T2, an energy storage capacitor C and a protection switch (a bypass switch K1 and a crimping type encapsulation thyristor K2), wherein the submodule control system comprises a driving board, a submodule controller and an optical fiber communication module, and is specifically shown in fig. 2. The control system is used for sending a trigger signal to control the conduction of the IGBT moduleAnd when the valve module is in fault, triggering the bypass thyristor and the bypass switch to enable the fault submodule to exit from operation.

Firstly, mathematical modeling is performed on the components of the submodule, the service life of the components can be described by using a non-negative random variable X, and then the corresponding distribution function of the random variable X is as follows:

F(t)＝P{X≤t},(t＞0)；(1)

where f (t) is referred to as the cumulative distribution function, which has the physical meaning that the lifetime of the element is less than the distribution function of t, then the remaining lifetime of the device at time t is:

R(t)＝P{X＞t}＝1-F(t)；(2)

where R (t) is referred to as the reliability function, which represents the probability that the component will not fail during the time [0, t ]. For convenience of calculation, in this embodiment, assuming that each element in the MMC system is in a stable operation period in a life curve, and its life follows an exponential distribution, the reliability of element i at t is:

in the formula, λ_iIs the failure rate of element i.

Step S2: according to the structure and operation principle of the sub-module, the established half-bridge sub-module element combination relation diagram is shown in fig. 3, the reliability of the sub-module is determined by 2 IGBT modules, a capacitor, a bypass switch and a crimping type packaging thyristor, and the reliability R of the sub-module is determined_SM(t) is calculated using the formula:

in the formula, R_I、R_cap、R_K1、R_K2The reliability functions of the IGBT module, the capacitor, the bypass switch K1 and the compression joint type packaging thyristor K2 are respectively; because the service lives of all elements of the sub-modules are subjected to exponential distribution, the failure rate of the sub-modules is as follows:

λ_SM＝2λ_I+λ_cap+λ_K1+λ_K2；(5)

in the formula, λ_I、λ_cap、λ_K1、λ_K2The failure rates of the IGBT module, the capacitor, the bypass switch K1 and the compression joint type packaging thyristor K2 are respectively;

step S3: in addition to the basic elements of the sub-modules, the reliability of the MMC is also closely related to the control protection system. For the same reason, in order to facilitate the calculation of the reliability of the MMC, in this embodiment, it is assumed that the service life of the bridge arm control system follows the exponential distribution, and the reliability R of the bridge arm control system is represented by_cp(t) is calculated using the formula:

in the formula, λ_cpFor the failure rate of the bridge arm control system, R_cpA reliability function for the bridge arm control system; if the sub-modules adopt other topological structures (full-bridge structures, mixed structures and the like), the element combination relation is analyzed firstly, and then the corresponding sub-module reliability function and the corresponding bridge arm control system reliability function are calculated.

In the MMC, for example, interphase circulating current flows through all sub-modules of the same bridge arm due to the influence of some factors, and the switching frequency of the whole bridge arm sub-module is influenced by the switching of some sub-modules. When the MMC sub-module breaks down, the sub-module capacitor voltage of the bridge arm where the fault sub-module is located is affected by different degrees, and the ripple amplitude of the sub-module capacitor changes.

When the sub-modules adopt the hot standby control strategy under different operating conditions, the algorithm time complexity and the algorithm space complexity in the hot standby control strategy are different, so that the degrees of reducing the interphase circulating current and the fluctuation amplitude of the sub-module capacitance and voltage are different. Meanwhile, the calculation amount of the algorithm of different fault-tolerant control strategies is different, so that the investment time of corresponding sub-modules is different, and other voltage ripples are changed to different degrees during the sub-module fault period. Thus, different control strategies may result in different degrees of variation in ripple voltage for each sub-module.

From the above analysis, it can be known that the submodules also have mutual influence between the submodules and the bridge arm control system, and have strong correlation with each other, so that the MMC modules have a certain degree of correlation.

The joint distribution function of the random variables can reflect the correlation characteristics among the variables. Therefore, the most effective method for analyzing the correlation between multidimensional variables is to solve the joint distribution function of the multidimensional variables. However, if the random variables are subject to the non-normal distribution, the explicit expression of the joint distribution function is not easy to obtain, and the Copula function is a function which connects the joint distribution function of the variables and the respective edge distribution functions thereof, and provides a flexible method for solving the joint distribution function.

In the field of reliability analysis, related researches have been introduced into Gumbel-Copula and Clayton-Copula functions in archimedean Copula functions for reliability analysis, in this embodiment, the Gumbel-Copula functions are selected from the characteristics of the archimedean Copula functions for MMC reliability analysis, taking two elements as an example, and the generation element isThe binary Copula function is defined as:

wherein u and v are random variables; and theta epsilon (0,1) is a correlation coefficient between the random variables u and v.

If the description object is a multi-element joint distribution function, the N-dimensional Gumbel-Copula function is:

step S4: assuming that each bridge arm has N submodules, the service life random function of the ith submodule is X_iWith a life distribution function of F_i(t)＝P{X_iT, i is equal to or less than 1,2, …, N, and the service life of the bridge arm control module is X_cpWith a life distribution function of F_cp(t)＝P{X_cp≤t}The bridge arm module combination relation diagram is shown in FIG. 4; introducing a Gumbel-Copula function into MMC reliability analysis to obtain an N-dimensional Gumbel-Copula function:

in the formula, F_i(t) denotes the lifetime distribution of the i-th submodule, F_cp(t) represents a life distribution of the control system, and θ represents F₁(t),F₂(t),…,F_i(t),F_cp(t) correlation coefficient between;

in this embodiment, it is assumed that there is correlation between modules, and a Maximum Likelihood Estimation (MLE) is generally used for obtaining a correlation coefficient, since the first MMC-HVDC project in the world, Trans Bay Cable flexible dc transmission project, is put into operation from 2010, if it is desired to obtain a correlation coefficient from original reliability data, it is temporarily impossible to obtain a correlation coefficient, and with the wide development of flexible dc transmission technology, a large amount of data can be used to obtain a correlation coefficient between modules in the future. Therefore, in order to obtain reliability simulation data between modules, first, the inter-module cumulative distribution function is obtained by equations (1) to (6):

F(t)＝1-e^λt；

the probability density function is then: f (t) ═ λ e^-λt；

Step S5: obtaining a maximum likelihood function by adopting a maximum likelihood estimation theory, obtaining zero correlation coefficient by enabling the maximum likelihood function to calculate partial derivatives of the correlation coefficient, and further determining the range of the correlation coefficient; the method specifically comprises the following steps:

obtaining a maximum likelihood function by adopting a maximum likelihood estimation theory:

wherein T is the number of years of operation,is a probability density function of the sub-module,is a probability density function of the bridge arm control system,is the cumulative distribution function of the sub-modules,is a cumulative distribution function of the bridge arm control system, where F^-1(t) is the inverse of F (t); x_Nt、X_cpThe service life data of the sub-module and the service life data of the bridge arm control system are respectively, the service life data cannot be obtained temporarily in the MMC-HVDC engineering, and the VSC-HVDC engineering has a longer operation life, so that the reliability statistical data based on the traditional VSC can be substituted into the above formula to estimate the correlation coefficient, and the equation can be solvedAnd obtaining the correlation coefficient theta among the modules, and further determining the range theta.

According to the MMC, three phases are completely symmetrical, the upper bridge arm and the lower bridge arm are also completely identical, a valve level control system closely related to the sub-module can also be divided into the upper bridge arm part and the lower bridge arm part, and the structures of controllers are also identical. Therefore, the reliability of the MMC in this embodiment is characterized by its bridge arm reliability. And further analyzing and calculating a relevant bridge arm reliability model by using a Gumbel-Copula function and a Sklar theory Copula function on the premise of not configuring a redundant sub-module and configuring the redundant sub-module.

Step S6: performing reliability analysis without redundant configuration, performing reliability analysis of redundant configuration, and obtaining a bridge arm reliability model considering correlation;

the reliability analysis without redundancy configuration specifically includes: in this embodiment, the reliability of a non-configured redundant sub-module is analyzed, and when the initial time t is 0, all elements of the system are in an ideal state and start to operate simultaneously, the service life of the system depends on the minimum value of the service lives of the elements, that is, when one of the sub-modules of the bridge arm fails, the bridge arm is unreliable. The life of the series system is then:

X＝min(X₁,X₂,....,X_N)；

at the moment t, the reliability of the bridge arm is equal to the service time X of the submodule with the shortest service life being more than t, namely the service lives X of all the submodules₁,X₂,...,X_NIf the values are all larger than t, the unconfigured redundant sub-modules can be obtained by an addition formula, and the reliability function of the bridge arm with N sub-modules is as follows:

in the above formula, the first and second carbon atoms are,can be calculated from the following formula:

because the life of each submodule is distributed identically and each joint density function in the above formula can represent that the edge distribution is compounded with the Copula function, the above formula can be simplified as follows:

in the formula, since F_i1, (∞), thus, F_iF (t) or 1, m is the number of F (F) (t).

According to the Sklar correlation theorem, the method can be used forCan be seen as two distribution functions, P (X)_cpT) andconstituent Copula functions. Therefore, the kth term in the bridge arm reliability function can be simplified as:

in summary, when the redundancy configuration is not performed, at time t, the bridge arm reliability function with N sub-modules is:

in the formula (I), the compound is shown in the specification,

the reliability analysis of the redundant configuration is performed, and the obtained bridge arm reliability model considering the correlation is specifically as follows: as can be seen from the above, when configuring redundant sub-modules, the redundancy sub-modules are defined by N + N₀In the system formed by the submodules, if N or more submodules meet the requirements, the bridge arm normally works at the moment. In other words, the number of the bridge arm failure submodules is greater than or equal to N₀When the inverter fails, the inverter fails.

When the correlation between the same bridge arm module is considered, the first secondary N + N is set₀Selecting k sub-modules in normal work from the sub-modules, enabling the control system to work normally at the moment, and then reordering to obtain a group of new random variables: and the group of random variables formed by the other sub-modules is as follows:then the reliability of the bridge arm with k submodules working normally selected for the first time is as follows:

since l may occur 1, 2.Thus, redundancy N is configured₀The bridge arm reliability for a submodule is:

similarly, according to the Sklar correlation theorem: can be combined withViewed as aAnda Copula function consisting of two distribution functions, wherein,the method comprises the steps of taking a k-D dimension Copula function as an (N + N0-k) -D dimension Copula function, and then respectively calculating two distribution functions by using a reliability function of the formula without redundant configuration to obtain that when the redundant configuration is carried out, N is configured at the time t₀The reliability model of the bridge arm when each redundant submodule is as follows:

in the formula (I), the compound is shown in the specification,representing the reliability of the k sub-modules put into operation. The equation is the bridge arm reliability when all sub-module dependencies are considered. Nowadays, flexible direct current transmission projects in the world are gradually increased, and parameter estimation of the correlation degree theta can be carried out through a large number of obtained data samples in the future.

Step S7: as can be seen from the above, configuration N₀Each redundancy submodule can be configured by N₀The reliability of the bridge arm is obtained by the reliability model of the bridge arm when the redundant sub-modules are arranged, so that the reliability of the bridge arm can be obtained when the redundant sub-modules are arranged₀When different values are taken, the corresponding reliability degrees are all obtained, in a certain range, the more redundant sub-modules are, the higher the reliability is, and after the number of the configured redundant sub-modules reaches a certain number, the reliability degree isThe improvement is not obvious, and the loss and cost investment caused by the larger number of configured redundant sub-modules are increased, so that the redundancy configuration scheme needs to be optimized.

For analyzing the redundant configuration, N is fixed (actual engineering is necessarily known), and the quantity value N of the redundant sub-modules is changed₀Carrying in a bridge arm reliability model taking correlation into account to obtain a series of discrete points, and fitting the series of discrete points to obtain a fitting function; in particular the number N of redundant sub-modules to be configured₀The value is changed by using configuration N₀The bridge arm reliability model of each redundant submodule obtains a series of discrete points (N)₀,R₂) The series of discrete points was fitted using a MATLAB fitting toolbox to give a fitting function of f (x).

Step S8: and determining the configuration number interval of the redundant sub-modules by using an inflection point method. Specifically, the second derivative of the fitting function f (x) is calculated and set to 0, and two special inflection points x are obtained by solving₁、x₂Respectively rounding up and rounding down to obtain N₀[x₁]、N₀[x₂]In (N)₀[x₁],N₀[x₂]) And selecting the number of the configured redundant sub-modules in the interval.

Preferably, an index S of how fast the reliability increases can be defined_RIt is defined as:

obviously, in (x)₁,x₂) Within the interval, R₂With N₀Increases with increasing, approximately linear variation; and is in (x)₁,x₂) Outside the interval, R₂With N₀Is slow, it is obviously not reasonable to configure the sub-modules in this interval. N is a radical of₀[x₁]、N₀[x₂]Two engineering reference values are provided for redundancy configuration, at (N)₀[x₁],N₀[x₂]) In addition, reliability is increased with the addition of redundant sub-modules, as can be seen hereThe number of the redundancy sub-modules configured in the interval is selected, and the redundancy configuration method not only aims at HBSM, but also can be applied to FBSM, CDSM and SCDSM, and has strong applicability.

The present embodiment also provides a sub-module redundancy optimization configuration system considering the correlation between MMC modules, including a computer program running in a memory and a processor, where the processor executes the computer program to implement the steps of the method described above.

The present embodiment also provides a computer-readable storage medium, which stores a computer program that, when executed by a processor, implements the steps of the method as described above.

In the embodiment, on the basis of analyzing the MMC topological structure, the relativity between each submodule and a control module is considered, a Gumbel-Copula function is introduced, the correlation coefficient between the submodules is estimated by utilizing a maximum likelihood theory, then an MMC reliability analysis model is respectively established when the redundancy submodule and the redundancy submodule are not configured, the influence of the redundancy, the correlation coefficient and the operation year on the reliability of the MMC is discussed on the basis of the established MMC reliability model, and the redundancy optimization configuration of the submodules is further discussed after the reliability index is reached. A detailed method schematic is shown in fig. 5.

As will be appreciated by one skilled in the art, embodiments of the present application may be provided as a method, system, or computer program product. Accordingly, the present application may take the form of an entirely hardware embodiment, an entirely software embodiment or an embodiment combining software and hardware aspects. Furthermore, the present application may take the form of a computer program product embodied on one or more computer-usable storage media (including, but not limited to, disk storage, CD-ROM, optical storage, and the like) having computer-usable program code embodied therein.

The present application is described with reference to flowchart illustrations and/or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of the application. It will be understood that each flow and/or block of the flow diagrams and/or block diagrams, and combinations of flows and/or blocks in the flow diagrams and/or block diagrams, can be implemented by computer program instructions. These computer program instructions may be provided to a processor of a general purpose computer, special purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, create means for implementing the functions specified in the flowchart flow or flows and/or block diagram block or blocks.

These computer program instructions may also be stored in a computer-readable memory that can direct a computer or other programmable data processing apparatus to function in a particular manner, such that the instructions stored in the computer-readable memory produce an article of manufacture including instruction means which implement the function specified in the flowchart flow or flows and/or block diagram block or blocks.

These computer program instructions may also be loaded onto a computer or other programmable data processing apparatus to cause a series of operational steps to be performed on the computer or other programmable apparatus to produce a computer implemented process such that the instructions which execute on the computer or other programmable apparatus provide steps for implementing the functions specified in the flowchart flow or flows and/or block diagram block or blocks.

The foregoing is directed to preferred embodiments of the present invention, other and further embodiments of the invention may be devised without departing from the basic scope thereof, and the scope thereof is determined by the claims that follow. However, any simple modification, equivalent change and modification of the above embodiments according to the technical essence of the present invention are within the protection scope of the technical solution of the present invention.