基于贝叶斯网络时序模拟的配电系统可靠性评估
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摘要
配电系统的运行和规划都离不开可靠性评估，现有的配电系统可靠性指标求解方法各有不足，有些方法只适合简单配电系统，有些方法不能求解出配电系统的全部可靠性指标，也不能有效识别系统的薄弱环节，有些模拟方法缺乏收敛判据或收敛判据不尽合理。近年来，随着全球对环境保护和节能问题的日益关注，含分布式电源的配电系统逐年增多，因此，研究含分布式电源的配电系统可靠性评估也是必要的。针对上述种种问题，本文作了深入研究，主要研究成果如下：
（1）采用从负荷点出发，先前向遍历再后向遍历的搜索策略遍历元件关系表，以故障模式影响分析法和条件概率算法为依据，能够自动生成描述贝叶斯网络结构的“或”关系表，“联合”关系表、“因果”关系表和各子结点的条件概率。实例结果表明该方法的可行性。
（2）分别建立了时不变负荷和时变负荷的基于贝叶斯网络时序模拟的配电系统可靠性指标计算模型，并提出了相应的贝叶斯网络时序模拟推理算法。该算法不但能够求解配电系统的全部可靠性指标，还能够求解出系统故障条件下各个元件故障的条件概率。既能得出对整个系统的总体评价，又能识别系统的薄弱环节。
（3）依据中心极限定理和大数定理，推导出模拟算法中样本容量与绝对误差的平方成反比这一结论。为了兼顾模拟时间和计算精度，本章研究了独立事件的选取，拓展了独立事件概念，构造了独立广义事件，即各独立广义事件产生的条件是：初始种子是随机的、循环次数是相同的。（4）针对可靠性评估指标有多个，并且既有有名值指标又有标幺值指标的问题，提出了选取标幺值指标作为收敛判据的依据指标。由于标幺值具有一定的稳定性，所以，选取标幺值指标作为收敛判据的依据指标具有广泛的适用性，它既适用于简单系统也适用于复杂系统。（5）鉴于模拟方法的不确定性，分析了标幺值指标在给定置信概率下总体均值的置信区间，得出置信区间的长度与样本均值的最大绝对误差相关的结论，即置信区间长度的一半等于样本均值的最大绝对误差，进而提出了用绝对误差描述的收敛判据，并将最大绝对误差小于给定计算精度作为主要的实用收敛判据。实例结果验证了该实用收敛判据的正确性与可行性。（6）将系统中的分布式电源作为叶子结点，建立了含分布式电源的配电系统的树状结构。依据孤岛划分原则，描述了约束条件和目标函数数学模型，采用有根树深度优先的搜索策略对含分布式电源的配电系统进行了孤岛划分。实例结果表明该孤岛划分方法的可行性。
（7）分析了含分布式电源的配电系统在元件故障后的开关操作过程，提出了含分布式电源配电系统可靠性评估的贝叶斯网络生成方法。分别采用模拟推理算法和精确推理算法对含分布式电源的配电系统进行了评估，结果进一步验证本文提出的基于贝叶斯网络时序模拟推理算法的正确性与优越性。
Operation and planning of distribution systems are inseparable from thereliability assessment, the existing distribution system reliability assessmentmethods have deficiencies, some are only suitable for the simple distributionsystem, some can not solve all of the distribution system reliability indices,also cannot effectively identify the weak links of the system, and somesimulation methods have not convergence criterion or have not rationalconvergence criterion. In recent years, with the global environmentalprotection and energy saving problem attention increasingly, more and moredistribution systems with distributed generations(DGs) are coming, therefore,it is also necessary to study reliability assessment of distribution systemswith DGs. In view of the above problems, the reliability assessment basedon Bayesian network timing sequence simulation(BNTSS) for distributionsystems are researched. the main research results are as follows:
(1) A search strategy that starting from load points, first forwardTraversal then backward Traversal components relationship table ofdistribution system is proposed, according to failure mode and effectanalysis(FMEA) and conditional probability algorithm, A“or”relations table,A“union” relations table and A“causal” relations table that describe BNstructure are established, and the conditional probabilities of childnodes of theBN are calculated.The example results indicate the feasibility of the proposedmethod.
(2) Distribution system reliability indices computing model based onBNTSS for unchanged loads and time-varying loads are separated established,Corresponding inference algorithm is proposed, that sove not only allreliability indices but also conditional probabilities of every component onsystem failure, thus,both overall assessment for distribution systems andIdentifing weaknesses in the distribution systems.
(3) According as central limit theorem and laws of large numbers, inferout a conclusion that sample capacity is inversely proportional to square ofabsolute error. In order to give consideration to both simulation time andcalculation accuracy, how to selecting independent event is studied,independent event concept is expanded, independent generalized events are structured,which are random seeds,the same cycle number of times.
(4) In view of distribution system having multiple reliability assessmentindices,and some indices are well-known value, some indices are per-unitvalue, the per-unit value indices as the basis indices of convergence criterionis put forwarded. As per-unit values have stability character, the per-unit valueindices as the basis indices of convergence criterion has wider applicability. Itis suitable for simple system and complex system.
(5) Since uncertainty of simulation methods, confidence interval ofpopulation mean of per-unit value indices on a given confidence probability isanalyzed and expressed. It is concluded that length of confidence interval andsample mean maximum absolute error is related, that half the length ofconfidence interval is equal to the sample mean maximum absolute error, andthen main practical convergence criterion with absolute error is proposed thatthe sample mean maximum absolute error is less than the given calculationaccuracy. The sample results verify the validity and feasibility of the proposedmethod.
(6) DGs are treated as end nodes, A tree structure described distributionsystems with DGs is established. On the basis of isolated island dividingprinciples, constraint conditions and target function mathematical model are expressed, isolated island dividing for distribution systems with DGs iscompleted by depth-first search strategy on rooted tree. The example resultsindicate the feasibility of the method.
(7) The switch operating process are analyzed when components ofdistribution systems with DGs is failure,A method establishing BN fordistribution systems with DGs is proposed. reliability assessment exampleseparated by simulation inference algorithm and precise inference algorithmfor distribution systems with DGs are gived, the example results indicatefurther the validity and superiority of the method based on BNTSS.
（1）采用从负荷点出发，先前向遍历再后向遍历的搜索策略遍历元件关系表，以故障模式影响分析法和条件概率算法为依据，能够自动生成描述贝叶斯网络结构的“或”关系表，“联合”关系表、“因果”关系表和各子结点的条件概率。实例结果表明该方法的可行性。
（2）分别建立了时不变负荷和时变负荷的基于贝叶斯网络时序模拟的配电系统可靠性指标计算模型，并提出了相应的贝叶斯网络时序模拟推理算法。该算法不但能够求解配电系统的全部可靠性指标，还能够求解出系统故障条件下各个元件故障的条件概率。既能得出对整个系统的总体评价，又能识别系统的薄弱环节。
（3）依据中心极限定理和大数定理，推导出模拟算法中样本容量与绝对误差的平方成反比这一结论。为了兼顾模拟时间和计算精度，本章研究了独立事件的选取，拓展了独立事件概念，构造了独立广义事件，即各独立广义事件产生的条件是：初始种子是随机的、循环次数是相同的。（4）针对可靠性评估指标有多个，并且既有有名值指标又有标幺值指标的问题，提出了选取标幺值指标作为收敛判据的依据指标。由于标幺值具有一定的稳定性，所以，选取标幺值指标作为收敛判据的依据指标具有广泛的适用性，它既适用于简单系统也适用于复杂系统。（5）鉴于模拟方法的不确定性，分析了标幺值指标在给定置信概率下总体均值的置信区间，得出置信区间的长度与样本均值的最大绝对误差相关的结论，即置信区间长度的一半等于样本均值的最大绝对误差，进而提出了用绝对误差描述的收敛判据，并将最大绝对误差小于给定计算精度作为主要的实用收敛判据。实例结果验证了该实用收敛判据的正确性与可行性。（6）将系统中的分布式电源作为叶子结点，建立了含分布式电源的配电系统的树状结构。依据孤岛划分原则，描述了约束条件和目标函数数学模型，采用有根树深度优先的搜索策略对含分布式电源的配电系统进行了孤岛划分。实例结果表明该孤岛划分方法的可行性。
（7）分析了含分布式电源的配电系统在元件故障后的开关操作过程，提出了含分布式电源配电系统可靠性评估的贝叶斯网络生成方法。分别采用模拟推理算法和精确推理算法对含分布式电源的配电系统进行了评估，结果进一步验证本文提出的基于贝叶斯网络时序模拟推理算法的正确性与优越性。
Operation and planning of distribution systems are inseparable from thereliability assessment, the existing distribution system reliability assessmentmethods have deficiencies, some are only suitable for the simple distributionsystem, some can not solve all of the distribution system reliability indices,also cannot effectively identify the weak links of the system, and somesimulation methods have not convergence criterion or have not rationalconvergence criterion. In recent years, with the global environmentalprotection and energy saving problem attention increasingly, more and moredistribution systems with distributed generations(DGs) are coming, therefore,it is also necessary to study reliability assessment of distribution systemswith DGs. In view of the above problems, the reliability assessment basedon Bayesian network timing sequence simulation(BNTSS) for distributionsystems are researched. the main research results are as follows:
(1) A search strategy that starting from load points, first forwardTraversal then backward Traversal components relationship table ofdistribution system is proposed, according to failure mode and effectanalysis(FMEA) and conditional probability algorithm, A“or”relations table,A“union” relations table and A“causal” relations table that describe BNstructure are established, and the conditional probabilities of childnodes of theBN are calculated.The example results indicate the feasibility of the proposedmethod.
(2) Distribution system reliability indices computing model based onBNTSS for unchanged loads and time-varying loads are separated established,Corresponding inference algorithm is proposed, that sove not only allreliability indices but also conditional probabilities of every component onsystem failure, thus,both overall assessment for distribution systems andIdentifing weaknesses in the distribution systems.
(3) According as central limit theorem and laws of large numbers, inferout a conclusion that sample capacity is inversely proportional to square ofabsolute error. In order to give consideration to both simulation time andcalculation accuracy, how to selecting independent event is studied,independent event concept is expanded, independent generalized events are structured,which are random seeds,the same cycle number of times.
(4) In view of distribution system having multiple reliability assessmentindices,and some indices are well-known value, some indices are per-unitvalue, the per-unit value indices as the basis indices of convergence criterionis put forwarded. As per-unit values have stability character, the per-unit valueindices as the basis indices of convergence criterion has wider applicability. Itis suitable for simple system and complex system.
(5) Since uncertainty of simulation methods, confidence interval ofpopulation mean of per-unit value indices on a given confidence probability isanalyzed and expressed. It is concluded that length of confidence interval andsample mean maximum absolute error is related, that half the length ofconfidence interval is equal to the sample mean maximum absolute error, andthen main practical convergence criterion with absolute error is proposed thatthe sample mean maximum absolute error is less than the given calculationaccuracy. The sample results verify the validity and feasibility of the proposedmethod.
(6) DGs are treated as end nodes, A tree structure described distributionsystems with DGs is established. On the basis of isolated island dividingprinciples, constraint conditions and target function mathematical model are expressed, isolated island dividing for distribution systems with DGs iscompleted by depth-first search strategy on rooted tree. The example resultsindicate the feasibility of the method.
(7) The switch operating process are analyzed when components ofdistribution systems with DGs is failure,A method establishing BN fordistribution systems with DGs is proposed. reliability assessment exampleseparated by simulation inference algorithm and precise inference algorithmfor distribution systems with DGs are gived, the example results indicatefurther the validity and superiority of the method based on BNTSS.
引文
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