Problem For Large Networks Research Articles

Analytical and computational improvements in performance-index ranking algorithms for networks

Performance-index ranking algorithms, relatively recent innovations in network analysis, are distinguished by the fact that they can rank a large set of network parameter and injection change cases very rapidly. To date, their major application has been for automatic contingency selection in power systems. Here, various enhancements to the approach are given and it is shown how general ranking formulas, valid for multiple branch contingencies, can be derived easily. A ranking formula for generator contingencies, hitherto unavailable, is presented. A sparse matrix technique that permits the rapid exact evaluation of the ranking formulas is given. The speed of the performance-index ranking algorithm is estimated for several large network problems, and found to be orders of magnitude higher than that of its direct though more versatile alternative, explicit linearized contingency evaluation.

A fixed routing problem in large and high connectivity networks

A fixed routing problem in large and high connectivity networks

Testing of a large-scale network optimization program

This paper describes the experimental results of testing a “large-scale” program for solving minimum-cost network flow problems. With this program, general structure transshipment problems with over ten thousand nodes and thirty thousand arcs have been easily solved without resorting to auxiliary storage. The algorithm is a variant of the primal revised simplex method; the computer code is called LPNET illustrating the close connection between linear programming and network graphs. This approach substantially improves computer processing timeand core storage, especially for relatively large network problems. The results of these experiments are provided. It is emphasized that an organized experimental design and a detailed series of empirical tests are crucial for an efficient implementation.

Bus Admittance Tearing and the Partial Inverse

Tearing permits larger problems to be solved on a given computer. It also permits solutions to parts of large network problems when the entire solution is unnecessary. This is very important to power organizations who find it increasingly impractical to solve an entire interconnected power pool when only local answers are desired. The partial inverse provides an excellent means for simplifying tearing while yielding useful intermediate results that have physical and electrical meanings. The tearing aspects presented in this paper have not been previously described.

Convergence of iterative load-flow studies

A THEORY has been developed for explaining the convergence of iteration methods used in the solution of power flow problems in large electric networks. This theory will predict the improvement to be expected when using certain acceleration techniques, thus giving a means for determining the fastest convergence for a given problem. The new understanding that this theory gives of the mechanism of convergence of problems of this type should lead to new and better methods of solving power system problems on a digital computer.

Convergence of Iterative Load-Flow Studies

A THEORY has been developed for explaining the convergence of iteration methods used in the solution of power flow problems in large electric networks. This theory will predict the improvement to be expected when using certain acceleration techniques, thus giving a means for determining the fastest convergence for a given problem. The new understanding that this theory gives of the mechanism of convergence of problems of this type should lead to new and better methods of solving power system problems on a digital computer.