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
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
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
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
This paper presents some important properties emanating from the pair of conjugate trees. The properties are obtained by resorting to the fundamental loops and cutsets in the circuit topology. The existence of such a ...This paper presents some important properties emanating from the pair of conjugate trees. The properties are obtained by resorting to the fundamental loops and cutsets in the circuit topology. The existence of such a pair is one of the conditions for a nonlinear resistive circuit to have one and only one DC solution.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
Controlled islanding of power system is an emer-gency control to stop the propagation of disturbances and to avoid blackouts. This paper presents a three-stage method for intentional controlled islanding of power syst...Controlled islanding of power system is an emer-gency control to stop the propagation of disturbances and to avoid blackouts. This paper presents a three-stage method for intentional controlled islanding of power systems. It enables to search out reasonable islanding cutsets, which have the minimum load-generation imbalance or the minimal power flow disruption, without low-voltage problems. In the first stage, a self-adaptive graph simplification algorithm is proposed to obtain a two-terminal graph as a suitable islanding cutset search area from the original power network graph model. In the second stage, an islanding cutset search algorithm is designed to find all of islanding cutsets, including the minimum load-generation imbalance cutset, in the two-terminal graph. In the third stage, an islanding scheme checking algorithm is developed to examine the outputs of stage two. It uses the depth first search algorithm to determine reasonable islanding cutsets without low-voltage problems. The IEEE30-bus system and the IEEE 118-bus system are utilized to demonstrate the proposed method. The simulation results show its validity and accuracy in large-scale power systems.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This paper presents some important properties emanating from the pair of conjugate trees. The properties are obtained by resorting to the fundamental loops and cutsets in the circuit topology. The existence of such a pair is one of the conditions for a nonlinear resistive circuit to have one and only one DC solution.
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.
基金supported by National Key Research and Development Program of China (No. 2017YFB0903601)National Natural Science Foundation of China (No. 51777088)
文摘Controlled islanding of power system is an emer-gency control to stop the propagation of disturbances and to avoid blackouts. This paper presents a three-stage method for intentional controlled islanding of power systems. It enables to search out reasonable islanding cutsets, which have the minimum load-generation imbalance or the minimal power flow disruption, without low-voltage problems. In the first stage, a self-adaptive graph simplification algorithm is proposed to obtain a two-terminal graph as a suitable islanding cutset search area from the original power network graph model. In the second stage, an islanding cutset search algorithm is designed to find all of islanding cutsets, including the minimum load-generation imbalance cutset, in the two-terminal graph. In the third stage, an islanding scheme checking algorithm is developed to examine the outputs of stage two. It uses the depth first search algorithm to determine reasonable islanding cutsets without low-voltage problems. The IEEE30-bus system and the IEEE 118-bus system are utilized to demonstrate the proposed method. The simulation results show its validity and accuracy in large-scale power systems.
