Cut-set Theory Research Articles

A computer program for generating power-system load-point minimal paths

In reliability evaluation that uses minimal cut-set theory, the deduction of minimal cut-set orders is crucial and depends on all the identified minimal paths associated with the load point whose reliability indices are desired. An input-reduction programming technique that automates this deduction is presented. The technique can be applied to a network of any configuration and finds its greatest application in complex networks with multiple inputs. The power-system structure in the form of power-arms (termination busbars, branch and protective device) is the only initial input data needed. The results obtained, in terms of minimal paths and minimal cut-set orders for all the load points, using the program on a sample power system compare well with the existing results. The program is compact, modular, and easy to use and can be applied to any complex system to generate minimal cut-sets of the desired orders. >

A fixed minimal path array method of evaluating reliability indices of power systems

In this paper, an efficient method for deducing the minimal cut set and evaluating load point reliability indices of an electrical power network is presented. The method is an extension of the binary formulation of the minimal cut set (BFMCS) theory. It is accomplished in three steps: (1) reduction of the network to a non-series-parallel equivalent, (2) deduction of the minimal cut set from all possible minimal paths (MPs) via a system minimal path array (MPA) of fixed size, and (3) computation of load point reliability indices. All these steps are coded in a Fortran language. The conventional BFMCS method uses an MPA whose size depends on the complexity, number of components and location of the load point (LDP) of interest relative to the sources in the network. There is, therefore, a great variation in MPA size from one LDP to another within the same network. This usually results in abortion of the program execution as a result of the MPA overflow. When the MPA does not overflow, the execution time is usually prohibitive. With the method of this paper, an MPA size of fixed dimension is used. The size is independent of the LDP minimal paths since the same MPA size is used for each of the LDPs in the network being analysed. The reduction process is based on the normal circuit theory in which series and parallel components between connected adjacent busbars are combined appropriately to form a single equivalent component. The resulting network is non-series-parallel. The non-series-parallel network is operated on to deduce the minimal cut sets from the system MPA. The reduction process produces a network having fewer components, fewer LDP minimal paths, fewer sets of minimal cut set order of interest and, overall, a greatly reduced execution time. The method of the paper is applied to a sample network. Results obtained with this method are compared with those of the conventional binary formulation of the minimal cut set theory.

Reliability optimization with integer constraint coefficients : K. B. Misra and J. Sharma. Microelectron. & Reliab.12, 431 (1973)

In this paper, an efficient method for deducing the minimal cut set and evaluating load point reliability indices of an electrical power network is presented. The method is an extension of the binary formulation of the minimal cut set (BFMCS) theory. It is accomplished in three steps: (1) reduction of the network to a non-series-parallel equivalent, (2) deduction of the minimal cut set from all possible minimal paths (MPs) via a system minimal path array (MPA) of fixed size, and (3) computation of load point reliability indices. All these steps are coded in a Fortran language.The conventional BFMCS method uses an MPA whose size depends on the complexity, number of components and location of the load point (LDP) of interest relative to the sources in the network. There is, therefore, a great variation in MPA size from one LDP to another within the same network. This usually results in abortion of the program execution as a result of the MPA overflow. When the MPA does not overflow, the execution time is usually prohibitive. With the method of this paper, an MPA size of fixed dimension is used. The size is independent of the LDP minimal paths since the same MPA size is used for each of the LDPs in the network being analysed. The reduction process is based on the normal circuit theory in which series and parallel components between connected adjacent busbars are combined appropriately to form a single equivalent component. The resulting network is non-series-parallel. The non-series-parallel network is operated on to deduce the minimal cut sets from the system MPA. The reduction process produces a network having fewer components, fewer LDP minimal paths, fewer sets of minimal cut set order of interest and, overall, a greatly reduced execution time.The method of the paper is applied to a sample network. Results obtained with this method are compared with those of the conventional binary formulation of the minimal cut set theory.