WO2019134258A1 - 一种大规模多状态串并联系统的可靠性近似计算方法 - Google Patents

一种大规模多状态串并联系统的可靠性近似计算方法 Download PDF

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WO2019134258A1
WO2019134258A1 PCT/CN2018/079377 CN2018079377W WO2019134258A1 WO 2019134258 A1 WO2019134258 A1 WO 2019134258A1 CN 2018079377 W CN2018079377 W CN 2018079377W WO 2019134258 A1 WO2019134258 A1 WO 2019134258A1
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parent node
state
parallel
probability distribution
series
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丁一
林雨
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Zhejiang University
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    • G—PHYSICS
    • G06—COMPUTING OR CALCULATING; COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F17/00—Digital computing or data processing equipment or methods, specially adapted for specific functions
    • G06F17/10—Complex mathematical operations
    • G06F17/18—Complex mathematical operations for evaluating statistical data, e.g. average values, frequency distributions, probability functions, regression analysis
    • G—PHYSICS
    • G06—COMPUTING OR CALCULATING; COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F30/00—Computer-aided design [CAD]
    • G06F30/20—Design optimisation, verification or simulation
    • G—PHYSICS
    • G06—COMPUTING OR CALCULATING; COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F17/00—Digital computing or data processing equipment or methods, specially adapted for specific functions
    • G06F17/10—Complex mathematical operations
    • G06F17/17—Function evaluation by approximation methods, e.g. inter- or extrapolation, smoothing, least mean square method
    • Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
    • Y02—TECHNOLOGIES OR APPLICATIONS FOR MITIGATION OR ADAPTATION AGAINST CLIMATE CHANGE
    • Y02E—REDUCTION OF GREENHOUSE GAS [GHG] EMISSIONS, RELATED TO ENERGY GENERATION, TRANSMISSION OR DISTRIBUTION
    • Y02E60/00—Enabling technologies; Technologies with a potential or indirect contribution to GHG emissions mitigation
    • Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
    • Y04—INFORMATION OR COMMUNICATION TECHNOLOGIES HAVING AN IMPACT ON OTHER TECHNOLOGY AREAS
    • Y04S—SYSTEMS INTEGRATING TECHNOLOGIES RELATED TO POWER NETWORK OPERATION, COMMUNICATION OR INFORMATION TECHNOLOGIES FOR IMPROVING THE ELECTRICAL POWER GENERATION, TRANSMISSION, DISTRIBUTION, MANAGEMENT OR USAGE, i.e. SMART GRIDS
    • Y04S40/00—Systems for electrical power generation, transmission, distribution or end-user application management characterised by the use of communication or information technologies, or communication or information technology specific aspects supporting them
    • Y04S40/20—Information technology specific aspects, e.g. CAD, simulation, modelling, system security

Definitions

  • the invention relates to reliability evaluation of a multi-state series-parallel system, in particular to a reliability approximation calculation method for a large-scale multi-state series-parallel system.
  • the multi-state system can describe the complex system in actual engineering in more detail.
  • the series-parallel structure is one of the most common system structures, and is widely used in power systems, transmission systems, etc.
  • the installation problems and standby design problems based on series-parallel systems are popular research directions. Therefore, the reliability evaluation of multi-state series-parallel systems plays an important role in practical engineering.
  • the object of the present invention is to overcome the shortcomings of the current large-scale system reliability evaluation method, and propose a reliability approximate calculation method for a large-scale multi-state series-parallel system, which adopts a continuous discrete approximation method to quickly and efficiently approximate a large-scale multi-state.
  • the reliability of the series-parallel system and provides a relatively accurate, error-acceptable approximation.
  • the large scale of the present invention refers to a series-parallel system in which the system components in the series-parallel system reach a component size of one hundred or more. When the component reaches or exceeds this magnitude, the traditional system reliability accurate evaluation method will be very computationally inefficient and computationally inefficient.
  • connection structure between any parent node and all its sub-nodes is divided into four categories.
  • the first type is that only a plurality of components are connected in parallel as child nodes.
  • a parallel subsystem formed by connecting to the same parent node, and a second type is a parallel subsystem formed by connecting a plurality of components and a plurality of subordinate connection modes as a child node in parallel to the same parent node, and the third type
  • a series subsystem formed by connecting a plurality of components in series to the same parent node, and the fourth class is formed by connecting a plurality of components and a plurality of subordinate connection methods in parallel as a child node to the same parent node.
  • the subordinate connection mode of the parent node may not be concatenated, because all subordinates of the subordinate node whose subordinate connection mode is connected in series may be equivalently regarded as subordinate connection manner.
  • the components of the parent node are connected in parallel.
  • the subordinate connection mode of the parent node is parallel, the subordinate connection mode of the subordinate subordinates of the parent node may not be parallel, because the subordinate connection mode is subordinate to the subordinate node. All components can be equivalently considered as subordinate connection elements that are subordinate to the parent node in parallel.
  • the subordinate connection modes are parallel nodes.
  • the state probability distribution is discretized and processed.
  • the state probability distributions of the component nodes are discrete and do not need to be discretized, so that all the child nodes of the parent node are discretized, and then the UGF method is used to calculate the parent.
  • the complete tree structure is progressively advanced from the end leaf nodes to the parent nodes of the respective levels by the above four classifications.
  • the state probability distribution is calculated in turn, and finally the state probability distribution of the root parent node of the entire multi-state series-parallel system can be obtained, thereby obtaining the reliability of the multi-state series-parallel system.
  • any multi-state series-parallel system is converted into a tree structure, and the series or parallel layer of the tree structure has the structure shown in FIG. 3 or FIG. 4, that is, any parent node having a parallel subordinate connection manner P has only the child node S having the serial subordinate connection mode and the child node E representing the element; conversely, any parent node S having the serial subordinate connection mode has only the child node S having the parallel subordinate connection mode and the child node E representing the element.
  • the system structure tree representation can clearly and clearly reflect the structural information of the series-parallel system, and divide the series-parallel system into different levels of series subsystems and parallel subsystems.
  • the multi-state series-parallel system has been converted into a tree structure, which is divided into series subsystems and parallel subsystems of different levels.
  • each leaf node at the end of the tree structure records state probability distribution information of one component, one leaf node corresponds to one component, and the end of the tree structure is a leaf node, and the parent node in the parent child node records the parent node. Subordinate connection with all child nodes of the subordinate.
  • the leaf node represented by the component and all other nodes have multiple states, each state having its own probability.
  • the state probability distribution of the component is known, and the state probability distributions of other nodes other than the leaf nodes of the component are unknown, and need to be calculated by the method of the present invention.
  • the types and quantities of states of different components or nodes may be different, resulting in different state probability distributions of the various nodes.
  • the components refer to working elements in a multi-state system, such as: a thermal power generator in a power generation system, a wind power generator, a photovoltaic solar panel, etc.; a transmission belt, a pipeline, a power transmission line, etc. in a transmission system; Various types of devices, etc.
  • the A) is a parallel subsystem formed by connecting a plurality of components as child nodes in parallel to the same parent node (that is, the parent node has a parallel subordinate connection mode), and is specifically processed in the following manner:
  • the A) is a parallel subsystem formed by connecting a node in which a plurality of components and a plurality of subordinate connection modes are connected in series as a child node to the same parent node (that is, the parent node has a parallel subordinate connection mode), specifically adopting Processing in the following ways:
  • the state probability distribution of the components is discrete; the state of the components is limited to a limited range, and the subsystems of all the independent components are connected in parallel.
  • the state probability distribution approaches the Gaussian distribution.
  • the Gaussian approximation method is used to calculate the state probability distribution of the parent node, which is specifically:
  • the expected value and the variance value of the parent node are obtained by the following formula, and the Gaussian distribution of the parent node is formed by the expected value and the variance value of the parent node, and is used as the state probability distribution of the parent node:
  • ⁇ represents the expected value of the parent node
  • ⁇ 2 represents the variance value of the parent node.
  • i represents the ordinal number of the child node subordinate to the parent node
  • n represents the total number of child nodes subordinate to the parent node.
  • State probability weighted average Is the value obtained by multiplying all states under the child node by their respective state probability values, and then adding the average value. It is the variance calculated from all states of the child nodes and their respective state probability values.
  • the state probability distribution of the nodes in which the subordinate connection modes are all connected is discretized and processed, specifically:
  • the state probability distribution of the child nodes is not discrete, the state probability distribution of the child nodes must be Gaussian, so the discretization is performed in the following way:
  • the state probability distribution of the child nodes located in the interval of [ ⁇ -3 ⁇ , ⁇ +3 ⁇ ] is equally divided into D subinterval segments, ⁇ represents the expected value in the state probability distribution of the child nodes, and ⁇ represents the state of the child nodes.
  • the standard deviation in the probability distribution takes the state between the endpoints of adjacent subinterval segments and the outer endpoints of the two subinterval segments as discrete states, obtains D+1 discrete states, and then uses the following formula to perform probability normalization. Get the final state probability distribution:
  • f( ⁇ ) is the probability distribution function of the Gaussian distribution of the child nodes
  • w k and p k are the probability of the k-th discrete state after the probability normalization and the discrete state, respectively.
  • the state probability distribution of each subordinate connection mode is a series connection node is obtained by the same process in C) or D) manner, specifically: the subordinate has only components and the subordinate connection mode is a serial connection node (as shown in the figure).
  • the state probability distribution shown in 1) is obtained by the method of C), and the state probability of the subordinate node and the plurality of subordinate connection modes are parallel sub-nodes and the subordinate connection mode is a series connection node (as shown in FIG. 3).
  • the distribution was obtained by the D) method.
  • the state probability distribution of each of the subordinate connection modes that are connected in parallel is obtained by the same process using A) or B), specifically: the subordinate has only components and the subordinate connection mode is a parallel node (as shown in the figure).
  • the state probability distribution shown in 2) is obtained by the method A), and the subordinate includes the state in which the component and the plurality of subordinate connection modes are connected in series and the subordinate connection mode is a parallel node (as shown in FIG. 3).
  • the probability distribution is obtained by the B) method.
  • the invention takes a large-scale multi-state series-parallel system as an analysis object, and proposes a continuous discrete approximation method to approximate the reliability of the calculation system.
  • the present invention adjusts the calculation process by a preset continuousization threshold and discretization value to achieve a balance between calculation accuracy and calculation efficiency. Moreover, the invention increases the computational complexity from the originally calculated exponential complexity to the quadratic term, which greatly improves the calculation speed.
  • the present invention has the characteristics of high calculation efficiency, small result error, flexible calculation, and wide application range.
  • the invention provides an effective technical approach for fast calculation of large-scale power system reliability analysis.
  • FIG. 1 is a schematic diagram of one of the typical structures of a multi-state series-parallel system according to the present invention.
  • FIG. 2 is a schematic diagram of a second typical structure of a multi-state series-parallel system according to the present invention.
  • FIG. 3 is a schematic diagram of a third structure of a multi-state series-parallel system according to the present invention.
  • FIG. 4 is a schematic diagram of a fourth structure of a multi-state series-parallel system according to the present invention.
  • FIG. 5 is a schematic diagram showing the structure of a multi-state series-parallel system according to an embodiment of the present invention.
  • connection structure between any parent node and all its sub-nodes is divided into four categories, and the first type is only The components are connected as parallel nodes connected to the same parent node as a child node, and the second type is a parallel connection formed by connecting a plurality of components and a plurality of subordinate connection modes as a child node in parallel to the same parent node.
  • the third type is a series subsystem formed by connecting multiple elements in series to the same parent node
  • the fourth type is a node connected in parallel by multiple elements and multiple subordinate connection methods as sub-nodes connected in series to a serial subsystem formed by the same parent node;
  • the subordinate connection mode of the parent node may not be concatenated, because all subordinates of the subordinate node whose subordinate connection mode is connected in series may be equivalently regarded as subordinate connection manner.
  • the components of the parent node are connected in parallel.
  • the subordinate connection mode of the parent node is parallel, the subordinate connection mode of the subordinate subordinates of the parent node may not be parallel, because the subordinate connection mode is subordinate to the subordinate node. All components can be equivalently considered as subordinate connection elements that are subordinate to the parent node in parallel.
  • any multi-state series-parallel system is converted into a tree structure, and the series or parallel layer of the tree structure has the structure shown in FIG. 3 or FIG. 4, that is, any parent node having a parallel subordinate connection manner P has only the child node S having the serial subordinate connection mode and the child node E representing the element; conversely, any parent node S having the serial subordinate connection mode has only the child node S having the parallel subordinate connection mode and the child node E representing the element.
  • the system structure tree representation can clearly and clearly reflect the structural information of the series-parallel system, and divide the series-parallel system into different levels of series subsystems and parallel subsystems.
  • the A) is a parallel subsystem formed by connecting a plurality of components as child nodes in parallel to the same parent node (that is, the parent node has a parallel subordinate connection mode), and is specifically processed in the following manner:
  • the A) is a parallel subsystem formed by connecting a node in which a plurality of components and a plurality of subordinate connection modes are connected in series as a child node to the same parent node (that is, the parent node has a parallel subordinate connection mode), specifically adopting Processing in the following ways:
  • the Gaussian approximation method is used to calculate the state probability distribution of the parent node, which is specifically:
  • the expected value and the variance value of the parent node are obtained by the following formula, and the Gaussian distribution of the parent node is formed by the expected value and the variance value of the parent node, and is used as the state probability distribution of the parent node:
  • ⁇ represents the expected value of the parent node
  • ⁇ 2 represents the variance value of the parent node.
  • i represents the ordinal number of the child node subordinate to the parent node
  • n represents the total number of child nodes subordinate to the parent node.
  • State probability weighted average Is the value obtained by multiplying all states under the child node by their respective state probability values, and then adding the average value. It is the variance calculated from all states of the child nodes and their respective state probability values.
  • the state probability distribution of each node whose connection mode is connected in series is obtained by the same processing in C) or D) manner, specifically: the state in which the subordinate has only components and the subordinate connection mode is a serial connection node (as shown in FIG. 1 ).
  • the probability distribution is obtained by the method of C).
  • the state probability distribution of the subordinates and the subordinates whose subordinates are connected in parallel and whose subordinate connection is connected in series (as shown in Fig. 3) is performed by D) Processing is obtained.
  • the subordinate connection modes are parallel nodes.
  • the state probability distribution is discretized and processed.
  • the state probability distributions of the component nodes are discrete and do not need to be discretized, so that all the child nodes of the parent node are discretized, and then the UGF method is used to calculate the parent.
  • the state probability distribution of the nodes whose subordinate connection methods are connected in parallel is discretized and processed, specifically:
  • the state probability distribution of the child nodes is not discrete, the state probability distribution of the child nodes must be Gaussian, so the discretization is performed in the following way:
  • the state probability distribution of the child nodes located in the interval of [ ⁇ -3 ⁇ , ⁇ +3 ⁇ ] is equally divided into D subinterval segments, ⁇ represents the expected value in the state probability distribution of the child nodes, and ⁇ represents the state of the child nodes.
  • the standard deviation in the probability distribution takes the state between the endpoints of adjacent subinterval segments and the outer endpoints of the two subinterval segments as discrete states, obtains D+1 discrete states, and then uses the following formula to perform probability normalization. Get the final state probability distribution:
  • f( ⁇ ) is the probability distribution function of the Gaussian distribution of the child nodes
  • w k and p k are the probability of the k-th discrete state after the probability normalization and the discrete state, respectively.
  • the state probability distribution of each subordinate connection mode that is connected in parallel is obtained by the same processing in A) or B) manner, specifically: the state in which the subordinate has only components and the subordinate connection mode is a parallel node (as shown in FIG. 2).
  • the probability distribution is obtained by the method of A).
  • the subordinate belongs to the sub-node with multiple subordinates connected in series and the subordinates are connected in parallel (as shown in Figure 3).
  • the state probability distribution is B) Processed to obtain.
  • the present invention is embodied as follows:
  • This embodiment takes a simplified power system as an example, and the system structure tree of the system is shown in FIG. 5.
  • the power system is divided into two parts: a power generation system and a power transmission system.
  • the power generation system consists of 7 units in parallel, which are 2 A-type units and 5 B-type units.
  • the state distribution of each unit is shown in Table 1.
  • the transmission line system consists of three identical transmission lines.
  • the transmission capacity of each transmission line during normal operation is 285 kW, and the probability of failure is 0.03.
  • the reliability of the power system is calculated using the continuous discrete approximation method proposed by the present invention.
  • the system can be divided into a transmission subsystem P 1 and a power generation subsystem P 2 .
  • the power generation subsystem uses Gaussian approximation to calculate its Gaussian function.
  • the probability state distribution obtained by discretizing the Gaussian function and the probability state distribution of the transmission subsystem are calculated by using the UGF method to calculate the reliability distribution of the power system.
  • This embodiment uses different discretization values D to have different effects. If the power system of this embodiment adopts accurate calculation, 2261 different states are needed to represent the final reliability distribution result of the system, and with the continuous discrete method of the present invention, the required number of states is greatly reduced.
  • the present invention can efficiently calculate the reliability of the power system, and the accuracy of the approximated result obtained is high.
  • the advantages of the present invention in terms of computational efficiency and computational accuracy will be more apparent when dealing with large scale systems.
  • the preset parameters Q 0 and D By adjusting the preset parameters Q 0 and D, the computational complexity and calculation accuracy can be adjusted; and the selection of parameters can be determined according to the actual situation of the system scale and available computing resources.

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Abstract

本发明公开了一种大规模多状态串并联系统的可靠性近似计算方法。针对多状态串并联系统，将任一父节点与其下属的所有子节点之间的连接结构分为四类，然后针对四类采用不同方式进行处理，通过上述四种分类对完整树结构从末端的叶节点开始向上递进对各个层次的父节点的状态概率分布依次进行计算，最终能获得整个多状态串并联系统的根端父节点的状态概率分布，从而获得多状态串并联系统的可靠性。本发明实现了大规模多状态串并联系统的可靠性近似计算，实现了计算精度和计算效率的平衡，将计算复杂度从原先精确计算的指数式复杂度提升到二次项式，大大提高了计算速度。

Description

一种大规模多状态串并联系统的可靠性近似计算方法 技术领域
本发明涉及多状态串并联系统的可靠性评估，特别是一种大规模多状态串并联系统的可靠性近似计算方法。
背景技术
多状态系统作为二元状态系统的推广，能够更加细致地描述实际工程中的复杂系统。而串并联结构是一种最常见的系统结构，广泛地应用于电力系统、传输系统等领域；同时，基于串并联系统的装机问题、备用设计问题等都是时下热门的研究方向。因此，多状态串并联系统的可靠性评估在实际工程中有着重要的作用。
而随着工业水平的发展，工程系统的规模逐步扩大。在大规模多状态串并联系统中，系统的元件与状态数量都非常庞大。比如，随着新能源的快速发展，越来越多的风力发电机连接到电网中，而一个风机的可靠性就需要数十个、上百个状态来精细地刻画。因此，大规模多状态串并联系统对可靠性的计算效率提出了极高的要求。
传统的多状态串并联系统的评估方法，比如UGF方法、迭代法(recursive method)、蒙特卡洛模拟法等，在计算大规模系统时都因为计算效率而受局限。由于精确计算系统可靠性往往需要指数式的计算复杂度，这种计算负担对大规模系统是无法承受的。所以寻找一种既计算高效、有结果准确的大规模多状态串并联系统可靠性评估的近似计算方法就成为了当务之急。
发明内容
本发明的目的是克服当前大规模系统可靠性评估方法的不足，提出了一种大规模多状态串并联系统的可靠性近似计算方法，采用连续离散近似方式来快速高效地近似计算大规模多状态串并联系统的可靠性，并且提供一个相对准确、误差可接受的近似结果。
本发明的大规模是指串并联系统中的系统元件达到百个及以上元件规模的串并联系统。当元件达到或者超过这个量级时，传统的系统可靠性精确评估法计算耗时将十分巨大、而且计算效率低下。
本发明的目的是通过以下步骤的技术方案实现的：
针对已转换为用树结构表示的多状态串并联系统，然后将任一父节点与其下属的所有子节点之间的连接结构分为四类，第一类为仅由多个元件作为子节 点并联连接到同一父节点而形成的并联子系统，第二类为由多个元件和多个下属连接方式均为串联的节点作为子节点并联连接到同一父节点而形成的并联子系统，第三类为仅由多个元件串联连接到同一父节点而形成的串联子系统，第四类为由多个元件和多个下属连接方式均为并联的节点作为子节点串联连接到同一父节点而形成的串联子系统；
若父节点的下属连接方式为串联，则父节点下属的子节点的下属连接方式不可能为串联，是由于下属连接方式为串联的子节点下属的元件全部都可等价地视为下属连接方式为串联的父节点下属的元件；同理，若父节点的下属连接方式为并联，则父节点下属的子节点的下属连接方式不可能为并联，是由于下属连接方式为并联的子节点下属的元件全部都可等价地视为下属连接方式为并联的父节点下属的元件。
针对四类采用不同方式进行处理：
A)针对如图2所示的仅由多个元件作为子节点并联连接到同一父节点而形成的并联子系统，先计算连续化值(continuation value)并比较，然后采用高斯近似法或者UGF方法进行计算获得父节点的状态概率分布；
B)针对如图4所示的由多个元件和多个下属连接方式均为串联的节点作为子节点并联连接到同一父节点而形成的并联子系统，先计算连续化值(continuation value)并比较，然后采用高斯近似法或者UGF方法进行计算获得父节点的状态概率分布；其中每个下属连接方式均为串联的节点的状态概率分布采用C)或者D)方式进行相同处理获得；
B)具体实施是将每个下属连接方式均为串联的节点均看做一个元件，再采用A)方式进行相同处理获得父节点的状态概率分布。
C)针对如图1所示的仅由多个元件串联连接到同一父节点而形成的串联子系统，采用UGF方法计算获得父节点的状态概率分布；
D)针对如图3所示的由多个元件和多个下属连接方式均为并联的节点作为子节点串联连接到同一父节点而形成的串联子系统，首先对下属连接方式均为并联的节点的状态概率分布进行离散化判断和处理，元件节点的状态概率分布都是离散的不需要进行离散化处理，使得父节点下属的所有子节点均为离散化状态，然后用UGF方法进行计算获得父节点的状态概率分布；其中每个下属连接方式均为并联的节点的状态概率分布采用A)或者B)方式进行相同处理获得；
D)具体实施是将每个下属连接方式均为并联的节点均看做一个元件，再采用C)方式进行相同处理获得父节点的状态概率分布。
由于用树结构表示的多状态串并联系统均可细分为上述四种分类情况的组 合，因此通过上述四种分类对完整树结构从末端的叶节点开始向上递进对各个层次的父节点的状态概率分布依次进行计算，最终能获得整个多状态串并联系统的根端父节点的状态概率分布，从而获得多状态串并联系统的可靠性。
本发明中，任意的多状态串并联系统转化为一棵树结构，而这棵树结构的串联或并联层具有图3或者图4所示的结构，即：任意具有并联下属连接方式的父节点P只有具有串联下属连接方式的子节点S和代表元件的子节点E；反之，任意具有串联下属连接方式的父节点S只有具有并联下属连接方式的子节点S和代表元件的子节点E。系统结构树表示法，可以简单明了地体现串并联系统的结构信息，并将串并联系统分割成不同层次的串联子系统和并联子系统。
本发明方法实施前已将将多状态串并联系统转换为用树结构表示，分为不同层次的串联子系统和并联子系统。
所述的树结构中，树结构末端的每个叶节点记录有一个元件的状态概率分布信息，一个叶节点对应一个元件，并且树结构末端均为叶节点，父子节点中的父节点记录父节点与下属的所有子节点之间的下属连接方式。
元件代表的叶节点和所有其他节点均具有多种状态，各个状态具有各自的概率。初始情况下，元件的状态概率分布是已知的，元件的叶节点以外的其他节点的状态概率分布均是未知，需要通过本发明方法进行计算获得。不同的元件或者节点的状态种类和数量可以不同，而导致了各个节点的状态概率分布的可以不同。
父节点与其下属的所有子节点之间的连接方式仅有一种，为串联或者并联。如图2中，若父节点为P，则表示父节点与其所有子节点以并联方式连接；如图1中，若父节点为S，则表示父节点与其所有子节点以串联的方式连接。
所述的元件是指多状态系统中的工作元件，例如：发电系统中的火力发电机、风力发电机、光伏太阳能板等；传输系统中的传输带、管道、输电线等；机械系统中的各类器件等。
所述A)针对仅由多个元件作为子节点并联连接到同一父节点(即该父节点具有并联下属连接方式)而形成的并联子系统，具体采用以下方式进行处理：
首先，采用以下公式计算获得并联子系统的父节点的连续化值：
Figure PCTCN2018079377-appb-000001
其中，Q表示连续化值，|E i|表示各个元件所具有的状态数量，i表示元件的序数，n表示元件的总数；
然后，将计算得到的连续化值Q与预先设定的连续化阈值Q 0比较：
若Q<Q 0，则认为当前计算复杂度较小，采用通用生成函数法(UGF，Universal  Generating Function)方法计算得到父节点的状态概率分布；
若Q≥Q 0则认为当前计算复杂度较高，采用高斯近似方法计算得到父节点的状态概率分布。
所述A)针对仅由多个元件和多个下属连接方式均为串联的节点作为子节点并联连接到同一父节点(即该父节点具有并联下属连接方式)而形成的并联子系统，具体采用以下方式进行处理：
首先，采用以下公式计算获得并联子系统的父节点的连续化值：
Figure PCTCN2018079377-appb-000002
其中，|E i|表示第i个元件节点所具有的状态数量，i表示元件的序数，n表示元件的总数；|S j|表示第j个下属连接方式均为串联的节点所具有的状态数量(若节点下还有其他子节点，将所有状态数量取并集，重叠出现相同的状态合并为一个状态来计算)，j表示下属连接方式均为串联的节点的序数，m表示下属连接方式均为串联的节点的总数；
然后，将计算得到的连续化值Q与预先设定的连续化阈值Q 0比较：
若Q<Q 0，则认为当前计算复杂度较小，采用通用生成函数法(UGF，Universal Generating Function)方法方法计算得到父节点的状态概率分布；
若Q≥Q 0则认为当前计算复杂度较高，采用高斯近似方法计算得到父节点的状态概率分布。
本发明中，认为所有元件均满足条件：各个元件之间是独立的；元件的状态概率分布是离散的；元件的状态限定在一个有限范围内，则所有各独立元件的并联后组成的子系统的状态概率分布趋近于高斯分布。
所述采用高斯近似方法计算得到父节点的状态概率分布，具体为：
采用以下公式计算获得父节点的期望值和方差值，并由父节点的期望值和方差值构成父节点的高斯分布，并作为父节点的状态概率分布：
Figure PCTCN2018079377-appb-000003
其中，μ表示父节点的期望值，
Figure PCTCN2018079377-appb-000004
表示父节点下属的第i个子节点的状态概率加权平均值，σ 2表示父节点的方差值，
Figure PCTCN2018079377-appb-000005
表示父节点下属的第i个子节点的方差值，i表示父节点下属的子节点的序数，n表示父节点下属的子节点的总数。
状态概率加权平均值
Figure PCTCN2018079377-appb-000006
是由子节点下所有状态与各自的状态概率值相乘后再相加取平均的值，方差值
Figure PCTCN2018079377-appb-000007
是由子节点所有状态与各自的状态概率值计算获得的方差。
所述D)中，对下属连接方式均为并联的节点的状态概率分布进行离散化 判断和处理，具体为：
首先，进行判断：
如果子节点的状态概率分布是离散的，则不进行离散化处理；
如果子节点的状态概率分布是不离散的，则子节点的状态概率分布一定为高斯分布，因此采用以下方式进行离散化处理：
然后，将位于[α-3·β,α+3·β]区间段内的子节点的状态概率分布等分成D个子区间段，α表示子节点状态概率分布中的期望值，β表示子节点状态概率分布中的标准差，取相邻子区间段之间的端点和两侧子区间段的外端点所在的状态为离散状态，获得D+1个离散状态，再采用以下公式进行概率归一化得到最终状态概率分布：
w k＝max(α-3·β,0)+k×6β/D
Figure PCTCN2018079377-appb-000008
其中，f(·)为子节点的高斯分布的概率分布函数，w k和p k分别为概率归一化后的第k个离散状态以及离散状态的概率。
所述B)中，每个下属连接方式均为串联的节点的状态概率分布采用C)或者D)方式进行相同处理获得，具体为：下属仅有元件且下属连接方式为串联的节点(如图1所示)的状态概率分布采用C)方法进行处理获得，下属有元件和多个下属连接方式均为并联的子节点且自身下属连接方式为串联的节点(如图3所示)的状态概率分布采用D)方法进行处理获得。
所述D)中，每个下属连接方式均为并联的节点的状态概率分布采用A)或者B)方式进行相同处理获得，具体为：下属仅有元件且下属连接方式为并联的节点(如图2所示)的状态概率分布采用A)方法进行处理获得，下属包含有元件和多个下属连接方式均为串联的子节点且自身下属连接方式为并联的节点(如图3所示)的状态概率分布采用B)方法进行处理获得。
本发明的有益效果：
本发明以大规模多状态串并联系统为分析对象，提出连续离散近似法来近似计算系统的可靠性。
本发明通过预先设定的连续化阈值和离散化值调整计算过程，以实现计算精度和计算效率的平衡。并且本发明将计算复杂度从原先精确计算的指数式复杂度提升到二次项式，大大提高了计算速度。
因此，本发明具有计算效率高、结果误差小、计算灵活强、适用范围广的 特点。本发明为大规模电力系统可靠性分析的快速计算提供了一条行之有效的技术途径。
附图说明
附图1为本发明多状态串并联系统典型结构之一的示意图。
附图2为本发明多状态串并联系统典型结构之二的示意图。
附图3为本发明多状态串并联系统典型结构之三的示意图。
附图4为本发明多状态串并联系统典型结构之四的示意图。
附图5为本发明实施例的多状态串并联系统结构的示意图。
附图6为实施例以D＝11的连续离散方法得到的可靠性分布函数与其精确分布的对比图。
附图7为实施例以D＝30时连续离散方法得到的可靠性分布函数图。
具体实施方式
本发明以下结合实施例及其附图作进一步说明如下。
本发明具体实施中，针对已转换为用树结构表示的多状态串并联系统，然后将任一父节点与其下属的所有子节点之间的连接结构分为四类，第一类为仅由多个元件作为子节点并联连接到同一父节点而形成的并联子系统，第二类为由多个元件和多个下属连接方式均为串联的节点作为子节点并联连接到同一父节点而形成的并联子系统，第三类为仅由多个元件串联连接到同一父节点而形成的串联子系统，第四类为由多个元件和多个下属连接方式均为并联的节点作为子节点串联连接到同一父节点而形成的串联子系统；
若父节点的下属连接方式为串联，则父节点下属的子节点的下属连接方式不可能为串联，是由于下属连接方式为串联的子节点下属的元件全部都可等价地视为下属连接方式为串联的父节点下属的元件；同理，若父节点的下属连接方式为并联，则父节点下属的子节点的下属连接方式不可能为并联，是由于下属连接方式为并联的子节点下属的元件全部都可等价地视为下属连接方式为并联的父节点下属的元件。
本发明中，任意的多状态串并联系统转化为一棵树结构，而这棵树结构的串联或并联层具有图3或者图4所示的结构，即：任意具有并联下属连接方式的父节点P只有具有串联下属连接方式的子节点S和代表元件的子节点E；反之，任意具有串联下属连接方式的父节点S只有具有并联下属连接方式的子节点S和代表元件的子节点E。系统结构树表示法，可以简单明了地体现串并联系统的结构信息，并将串并联系统分割成不同层次的串联子系统和并联子系统。
针对四类采用不同方式进行处理：
A)针对如图2所示的仅由多个元件作为子节点并联连接到同一父节点而形成的并联子系统，先计算连续化值(continuation value)并比较，然后采用高斯近似法或者UGF方法进行计算获得父节点的状态概率分布；
所述A)针对仅由多个元件作为子节点并联连接到同一父节点(即该父节点具有并联下属连接方式)而形成的并联子系统，具体采用以下方式进行处理：
首先，采用以下公式计算获得并联子系统的父节点的连续化值：
Figure PCTCN2018079377-appb-000009
其中，Q表示连续化值，|E i|表示各个元件所具有的状态数量，i表示元件的序数，n表示元件的总数；
然后，将计算得到的连续化值Q与预先设定的连续化阈值Q 0比较：
若Q<Q 0，则认为当前计算复杂度较小，采用通用生成函数法(UGF，Universal Generating Function)方法计算得到父节点的状态概率分布；
若Q≥Q 0则认为当前计算复杂度较高，采用高斯近似方法计算得到父节点的状态概率分布。
所述A)针对仅由多个元件和多个下属连接方式均为串联的节点作为子节点并联连接到同一父节点(即该父节点具有并联下属连接方式)而形成的并联子系统，具体采用以下方式进行处理：
首先，采用以下公式计算获得并联子系统的父节点的连续化值：
Figure PCTCN2018079377-appb-000010
其中，|E i|表示第i个元件节点所具有的状态数量，i表示元件的序数，n表示元件的总数；|S j|表示第j个下属连接方式均为串联的节点所具有的状态数量(若节点下还有其他子节点，将所有状态数量取并集，重叠出现相同的状态合并为一个状态来计算)，j表示下属连接方式均为串联的节点的序数，m表示下属连接方式均为串联的节点的总数；
然后，将计算得到的连续化值Q与预先设定的连续化阈值Q 0比较：
若Q<Q 0，则认为当前计算复杂度较小，采用通用生成函数法(UGF，Universal Generating Function)方法方法计算得到父节点的状态概率分布；
若Q≥Q 0则认为当前计算复杂度较高，采用高斯近似方法计算得到父节点的状态概率分布。
所述采用高斯近似方法计算得到父节点的状态概率分布，具体为：
采用以下公式计算获得父节点的期望值和方差值，并由父节点的期望值和方差值构成父节点的高斯分布，并作为父节点的状态概率分布：
Figure PCTCN2018079377-appb-000011
其中，μ表示父节点的期望值，
Figure PCTCN2018079377-appb-000012
表示父节点下属的第i个子节点的状态概率加权平均值，σ 2表示父节点的方差值，
Figure PCTCN2018079377-appb-000013
表示父节点下属的第i个子节点的方差值，i表示父节点下属的子节点的序数，n表示父节点下属的子节点的总数。
状态概率加权平均值
Figure PCTCN2018079377-appb-000014
是由子节点下所有状态与各自的状态概率值相乘后再相加取平均的值，方差值
Figure PCTCN2018079377-appb-000015
是由子节点所有状态与各自的状态概率值计算获得的方差。
B)针对如图4所示的由多个元件和多个下属连接方式均为串联的节点作为子节点并联连接到同一父节点而形成的并联子系统，先计算连续化值(continuation value)并比较，然后采用高斯近似法或者UGF方法进行计算获得父节点的状态概率分布；其中每个下属连接方式均为串联的节点的状态概率分布采用C)或者D)方式进行相同处理获得；
B)具体实施是将每个下属连接方式均为串联的节点均看做一个元件，再采用A)方式进行相同处理获得父节点的状态概率分布。
每个下属连接方式均为串联的节点的状态概率分布采用C)或者D)方式进行相同处理获得，具体为：下属仅有元件且下属连接方式为串联的节点(如图1所示)的状态概率分布采用C)方法进行处理获得，下属有元件和多个下属连接方式均为并联的子节点且自身下属连接方式为串联的节点(如图3所示)的状态概率分布采用D)方法进行处理获得。
C)针对如图1所示的仅由多个元件串联连接到同一父节点而形成的串联子系统，采用UGF方法计算获得父节点的状态概率分布；
D)针对如图3所示的由多个元件和多个下属连接方式均为并联的节点作为子节点串联连接到同一父节点而形成的串联子系统，首先对下属连接方式均为并联的节点的状态概率分布进行离散化判断和处理，元件节点的状态概率分布都是离散的不需要进行离散化处理，使得父节点下属的所有子节点均为离散化状态，然后用UGF方法进行计算获得父节点的状态概率分布；其中每个下属连接方式均为并联的节点的状态概率分布采用A)或者B)方式进行相同处理获得；
D)具体实施是将每个下属连接方式均为并联的节点均看做一个元件，再采用C)方式进行相同处理获得父节点的状态概率分布。
对下属连接方式均为并联的节点的状态概率分布进行离散化判断和处理，具体为：
首先，进行判断：
如果子节点的状态概率分布是离散的，则不进行离散化处理；
如果子节点的状态概率分布是不离散的，则子节点的状态概率分布一定为高斯分布，因此采用以下方式进行离散化处理：
然后，将位于[α-3·β,α+3·β]区间段内的子节点的状态概率分布等分成D个子区间段，α表示子节点状态概率分布中的期望值，β表示子节点状态概率分布中的标准差，取相邻子区间段之间的端点和两侧子区间段的外端点所在的状态为离散状态，获得D+1个离散状态，再采用以下公式进行概率归一化得到最终状态概率分布：
w k＝max(α-3·β,0)+k×6β/D
Figure PCTCN2018079377-appb-000016
其中，f(·)为子节点的高斯分布的概率分布函数，w k和p k分别为概率归一化后的第k个离散状态以及离散状态的概率。
每个下属连接方式均为并联的节点的状态概率分布采用A)或者B)方式进行相同处理获得，具体为：下属仅有元件且下属连接方式为并联的节点(如图2所示)的状态概率分布采用A)方法进行处理获得，下属包含有元件和多个下属连接方式均为串联的子节点且自身下属连接方式为并联的节点(如图3所示)的状态概率分布采用B)方法进行处理获得。
本发明实施例如下：
本实施例以一个简化的电力系统为例，该系统的系统结构树如图5所示。该电力系统分为发电系统和电力传输系统两个部分。发电系统由7个机组并联组成，分别是2个A型机组和5个B型机组，各机组的状态分布见表1。传输线系统由3根相同的传输线组成，每条传输线正常运行时的传输容量为285kW，其故障概率为0.03。本实施例采用连续离散近似法评估该电力系统的可靠性，并将近似结果和精确结果对比。在本实施例的计算过程中，取连续化阈值Q 0＝1000。
表1电力系统各机组的状态分布
Figure PCTCN2018079377-appb-000017
Figure PCTCN2018079377-appb-000018
采用本发明提出的连续离散近似法计算该电力系统可靠性。该系统可以分成传输子系统P 1和发电子系统P 2。传输子系统的连续化值小于连续化阈值Q＝2 3<Q 0，而发电子系统的连续化值大于连续化阈值Q＝6 7>Q 0，因此，传输子系统采用UGF方法计算其精确结果，而发电子系统采用高斯近似计算其高斯函数。然后，再将高斯函数离散化得到的概率状态分布与传输子系统的概率状态分布，采用UGF方法计算二者串联的结果，即可得到该电力系统的可靠性分布。
本实施例采用不同的离散化值D会有不同的效果。该实施例电力系统若采用精确计算，需要2261个不同的状态来表示系统最终的可靠性分布结果，而采用本发明的连续离散方法，所需要的状态数量会大大降低。图6给出当D＝11的连续离散方法得到的可靠性分布函数与其精确分布的对比图。当D＝11时，只需要13个状态来表示该系统，而在这13个状态处的可靠性绝对误差的平均值为0.0212。图7给出了当D＝30时连续离散方法得到的可靠性分布函数。此时，连续离散近似法采用32个状态来表示最终的结果，而在这32状态处的可靠性绝对误差的平均值为0.0111。对比图6和图7，可知提高参数D可以提升计算结果的准确程度。
由此可见，本发明可以高效地计算电力系统的可靠性，并且得到的近似结果的精度较高。当处理大规模系统时，本发明在计算效率和计算精确性方面的优势将更加明显。而通过调整预设定参数Q 0和D，可以调整计算复杂度和计算精确度；而参数的选定可根据所处理的系统规模和可利用的计算资源等实际情况而定。
最后应当说明的是，以上实例仅用于说明本发明的技术方案和效果，而非对其使用范围的限定。

Claims (8)

  1. 一种大规模多状态串并联系统的可靠性近似计算方法，其特征在于：
    针对已转换为用树结构表示的多状态串并联系统，将任一父节点与其下属的所有子节点之间的连接结构分为四类，第一类为仅由多个元件作为子节点并联连接到同一父节点而形成的并联子系统，第二类为由多个元件和多个下属连接方式均为串联的节点作为子节点并联连接到同一父节点而形成的并联子系统，第三类为仅由多个元件串联连接到同一父节点而形成的串联子系统，第四类为由多个元件和多个下属连接方式均为并联的节点作为子节点串联连接到同一父节点而形成的串联子系统；
    针对四类采用不同方式进行处理：
    A)针对仅由多个元件作为子节点并联连接到同一父节点而形成的并联子系统，先计算连续化值并比较，然后采用高斯近似法或者UGF方法进行计算获得父节点的状态概率分布；
    B)针对由多个元件和多个下属连接方式均为串联的节点作为子节点并联连接到同一父节点而形成的并联子系统，先计算连续化值并比较，然后采用高斯近似法或者UGF方法进行计算获得父节点的状态概率分布；其中每个下属连接方式均为串联的节点的状态概率分布采用C)或者D)方式进行相同处理获得；
    C)针对仅由多个元件串联连接到同一父节点而形成的串联子系统，采用UGF方法计算获得父节点的状态概率分布；
    D)针对由多个元件和多个下属连接方式均为并联的节点作为子节点串联连接到同一父节点而形成的串联子系统，首先对下属连接方式均为并联的节点的状态概率分布进行离散化判断和处理，使得父节点下属的所有子节点均为离散化状态，然后用UGF方法进行计算获得父节点的状态概率分布；其中每个下属连接方式均为并联的节点的状态概率分布采用A)或者B)方式进行相同处理获得；
    通过上述四种分类对完整树结构从末端的叶节点开始向上递进对各个层次的父节点的状态概率分布依次进行计算，最终能获得整个多状态串并联系统的根端父节点的状态概率分布，从而获得多状态串并联系统的可靠性。
  2. 根据权利要求1所述的一种大规模多状态串并联系统的可靠性近似计算方法，其特征在于：所述的树结构中，树结构末端的每个叶节点记录有一个元件的状态概率分布信息，父子节点中的父节点记录父节点与下属的所有子节点之间的下属连接方式。
  3. 根据权利要求1所述的一种大规模多状态串并联系统的可靠性近似计算方法，其特征在于：所述A)针对仅由多个元件作为子节点并联连接到同一父节点而形成的并联子系统，具体采用以下方式进行处理：
    首先，采用以下公式计算获得并联子系统的父节点的连续化值：
    Figure PCTCN2018079377-appb-100001
    其中，Q表示连续化值，|E i|表示各个元件所具有的状态数量，i表示元件的序数，n表示元件的总数；
    然后，将计算得到的连续化值Q与预先设定的连续化阈值Q 0比较：
    若Q<Q 0，则采用通用生成函数法方法计算得到父节点的状态概率分布；
    若Q≥Q 0，则采用高斯近似方法计算得到父节点的状态概率分布。
  4. 根据权利要求1所述的一种大规模多状态串并联系统的可靠性近似计算方法，其特征在于：
    所述A)针对仅由多个元件和多个下属连接方式均为串联的节点作为子节点并联连接到同一父节点而形成的并联子系统，具体采用以下方式进行处理：
    首先，采用以下公式计算获得并联子系统的父节点的连续化值：
    Figure PCTCN2018079377-appb-100002
    其中，|E i|表示第i个元件节点所具有的状态数量，i表示元件的序数，n表示元件的总数；|S j|表示第j个下属连接方式均为串联的节点所具有的状态数量，j表示下属连接方式均为串联的节点的序数，m表示下属连接方式均为串联的节点的总数；
    然后，将计算得到的连续化值Q与预先设定的连续化阈值Q 0比较：
    若Q<Q 0，则采用通用生成函数法方法计算得到父节点的状态概率分布；
    若Q≥Q 0，则采用高斯近似方法计算得到父节点的状态概率分布。
  5. 根据权利要求3或4所述的一种大规模多状态串并联系统的可靠性近似计算方法，其特征在于：所述采用高斯近似方法计算得到父节点的状态概率分布，具体为：采用以下公式计算获得父节点的期望值和方差值，并由父节点的期望值和方差值构成父节点的高斯分布，并作为父节点的状态概率分布：
    Figure PCTCN2018079377-appb-100003
    其中，μ表示父节点的期望值，
    Figure PCTCN2018079377-appb-100004
    i表示父节点下属的第i个子节点的状态概率加权平均值，σ 2表示父节点的方差值，
    Figure PCTCN2018079377-appb-100005
    表示父节点下属的第i个子节点的方差值，i表示父节点下属的子节点的序数，n表示父节点下属的子节点的总数。
  6. 根据权利要求1所述的一种大规模多状态串并联系统的可靠性近似计算 方法，其特征在于：所述D)中，对下属连接方式均为并联的节点的状态概率分布进行离散化判断和处理，具体为：
    首先，进行判断：
    如果子节点的状态概率分布是离散的，则不进行离散化处理；
    如果子节点的状态概率分布是不离散的，则采用以下方式进行离散化处理：
    然后，将位于[α-3·β,α+3·β]区间段内的子节点的状态概率分布等分成D个子区间段，α表示子节点状态概率分布中的期望值，β表示子节点状态概率分布中的标准差，取相邻子区间段之间的端点和两侧子区间段的外端点所在的状态为离散状态，获得D+1个离散状态，再采用以下公式进行概率归一化得到最终状态概率分布：
    w k＝max(α-3·β,0)+k×6β/D
    Figure PCTCN2018079377-appb-100006
    其中，f(·)为子节点的高斯分布的概率分布函数，w k和p k分别为概率归一化后的第k个离散状态以及离散状态的概率。
  7. 根据权利要求1所述的一种大规模多状态串并联系统的可靠性近似计算方法，其特征在于：所述B)中，每个下属连接方式均为串联的节点的状态概率分布采用C)或者D)方式进行相同处理获得，具体为：下属仅有元件且下属连接方式为串联的节点的状态概率分布采用C)方法进行处理获得，下属有元件和多个下属连接方式均为并联的子节点且自身下属连接方式为串联的节点的状态概率分布采用D)方法进行处理获得。
  8. 根据权利要求1所述的一种大规模多状态串并联系统的可靠性近似计算方法，其特征在于：所述D)中，每个下属连接方式均为并联的节点的状态概率分布采用A)或者B)方式进行相同处理获得，具体为：下属仅有元件且下属连接方式为并联的节点的状态概率分布采用A)方法进行处理获得，下属包含有元件和多个下属连接方式均为串联的子节点且自身下属连接方式为并联的节点的状态概率分布采用B)方法进行处理获得。
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