The inclusion-exclusion formula (IEF) is a fundamental tool for evaluating network reliability with known minimal paths or minimal cuts. However, the formula contains many pairs of terms which cancel. Using the notion...The inclusion-exclusion formula (IEF) is a fundamental tool for evaluating network reliability with known minimal paths or minimal cuts. However, the formula contains many pairs of terms which cancel. Using the notion of comparable node partitions some properties of canceling terms in IEF are given. With these properties and the thought of “dynamic programming” method, a simple and efficient inclusion-exclusion algorithm for evaluating the source-to-terminal reliability of a network starting with cutsets is presented. The algorithm generates all the non-canceling terms in the unreliability expression. The computational complexity of the algorithm is O(n+m3+M), where n and m are the numbers of nodes and minimal cuts of the given network respectively, M is the number of terms in the final symbolic unreliability expression that generated using the presented algorithm. Examples are shown to illustrate the effectiveness of the algorithm.展开更多
New concepts of reducible independent cutset and reducible independent loop are developedthrough an analysis of the ladder network.A new analytic method,named structural analysis method,is pres-entod.It evaluates the ...New concepts of reducible independent cutset and reducible independent loop are developedthrough an analysis of the ladder network.A new analytic method,named structural analysis method,is pres-entod.It evaluates the controllability and observability of a network based on its structure rather than onits state equation.Some problems in the conventional network analysis can be solved using this method.Re-sults obtained by this method are in good agreement with those obtained by that of state space analysis,butthis method is much simpler in use.A practical example is given.展开更多
Several conclusions on minimal cutset are proposed, from which a new algorithm is deduced to evaluate the unreliability of flow networks. Beginning with one unreliability product of the network, disjointed unreliabili...Several conclusions on minimal cutset are proposed, from which a new algorithm is deduced to evaluate the unreliability of flow networks. Beginning with one unreliability product of the network, disjointed unreliability products are branched out one by one, every of which is selected from the network minimal cutsets. Finally the unreliability of the network is obtained by adding all these unreliability products up.展开更多
There are many methods to enumerate cutsets of a graph, but all of these are involved with ad-vanced mathematics. This paper gives a method with which combinations of nodes to enumerate allminimal cutsets of all termi...There are many methods to enumerate cutsets of a graph, but all of these are involved with ad-vanced mathematics. This paper gives a method with which combinations of nodes to enumerate allminimal cutsets of all terminals in a graph are used.展开更多
Given a hypergraph, this paper provides three algorithms for finding all its minimal cutsets, minimal link cutsets and the least cutsets. The result not only set up a new studying field on cutsets of hypergraph, but a...Given a hypergraph, this paper provides three algorithms for finding all its minimal cutsets, minimal link cutsets and the least cutsets. The result not only set up a new studying field on cutsets of hypergraph, but also lay a foundation of analyzing the performance of multibus systems. The algorithm for determining all the least cutsets in a hypergraph is polynomial complex and more efficient than that in [2].展开更多
有效的电力系统在线暂态稳定分析和临界割集识别算法对保证互联电力系统的安全稳定运行有着重要的意义。本文针对支路势能边界面方法(BPEBS)的不足,在支路势能函数和势能脊(RIDGE)方法的基础上,推导出了具有高可靠性的电力系统暂态稳定...有效的电力系统在线暂态稳定分析和临界割集识别算法对保证互联电力系统的安全稳定运行有着重要的意义。本文针对支路势能边界面方法(BPEBS)的不足,在支路势能函数和势能脊(RIDGE)方法的基础上,推导出了具有高可靠性的电力系统暂态稳定及临界割集识别判据——支路势能脊(BPR)判据。同时,定义了计算简单的支路和系统稳定度指标,并给出基于支路势能脊和支路稳定度指标的电力系统暂态稳定和临界割集识别算法。该算法建立在电力系统网络信息的动态响应轨迹的基础上,在已知电网结构参数的情况下,只需要实时获得电网母线电压幅值和相角即可进行电力系统暂态稳定状态和临界割集的实时分析和识别,由于无需进行两群失稳模式的假设,因此该算法对于多摆失稳和多群失稳模式依然适用。New England 10机系统的仿真算例验证了该算法的有效性。展开更多
文摘The inclusion-exclusion formula (IEF) is a fundamental tool for evaluating network reliability with known minimal paths or minimal cuts. However, the formula contains many pairs of terms which cancel. Using the notion of comparable node partitions some properties of canceling terms in IEF are given. With these properties and the thought of “dynamic programming” method, a simple and efficient inclusion-exclusion algorithm for evaluating the source-to-terminal reliability of a network starting with cutsets is presented. The algorithm generates all the non-canceling terms in the unreliability expression. The computational complexity of the algorithm is O(n+m3+M), where n and m are the numbers of nodes and minimal cuts of the given network respectively, M is the number of terms in the final symbolic unreliability expression that generated using the presented algorithm. Examples are shown to illustrate the effectiveness of the algorithm.
文摘New concepts of reducible independent cutset and reducible independent loop are developedthrough an analysis of the ladder network.A new analytic method,named structural analysis method,is pres-entod.It evaluates the controllability and observability of a network based on its structure rather than onits state equation.Some problems in the conventional network analysis can be solved using this method.Re-sults obtained by this method are in good agreement with those obtained by that of state space analysis,butthis method is much simpler in use.A practical example is given.
文摘Several conclusions on minimal cutset are proposed, from which a new algorithm is deduced to evaluate the unreliability of flow networks. Beginning with one unreliability product of the network, disjointed unreliability products are branched out one by one, every of which is selected from the network minimal cutsets. Finally the unreliability of the network is obtained by adding all these unreliability products up.
文摘There are many methods to enumerate cutsets of a graph, but all of these are involved with ad-vanced mathematics. This paper gives a method with which combinations of nodes to enumerate allminimal cutsets of all terminals in a graph are used.
文摘Given a hypergraph, this paper provides three algorithms for finding all its minimal cutsets, minimal link cutsets and the least cutsets. The result not only set up a new studying field on cutsets of hypergraph, but also lay a foundation of analyzing the performance of multibus systems. The algorithm for determining all the least cutsets in a hypergraph is polynomial complex and more efficient than that in [2].
文摘有效的电力系统在线暂态稳定分析和临界割集识别算法对保证互联电力系统的安全稳定运行有着重要的意义。本文针对支路势能边界面方法(BPEBS)的不足,在支路势能函数和势能脊(RIDGE)方法的基础上,推导出了具有高可靠性的电力系统暂态稳定及临界割集识别判据——支路势能脊(BPR)判据。同时,定义了计算简单的支路和系统稳定度指标,并给出基于支路势能脊和支路稳定度指标的电力系统暂态稳定和临界割集识别算法。该算法建立在电力系统网络信息的动态响应轨迹的基础上,在已知电网结构参数的情况下,只需要实时获得电网母线电压幅值和相角即可进行电力系统暂态稳定状态和临界割集的实时分析和识别,由于无需进行两群失稳模式的假设,因此该算法对于多摆失稳和多群失稳模式依然适用。New England 10机系统的仿真算例验证了该算法的有效性。
文摘为了克服人为选定割集以及没有考虑故障后系统轨迹的缺点,提出了一种基于支路势能的电力系统暂态稳定最脆弱支路及临界割集的候选集辨识方法,并结合改进的综合指标来辨识临界割集.该方法把故障后电力系统在势能最大值处的拥有最大支路势能的支路作为最脆弱线路,以此线路作为基本线路形成候选集,再根据改进的综合指标来确定临界割集.该方法无需等时域仿真结束后就能确定最脆弱线路及临界割集.仿真研究表明,这种方法因部分计及了故障后系统的轨迹而提高了辨识准确度,辨识速度也由原来的5 s缩短为现在的0.35 s.
