X.2 References on Sparsity, Graph Theory and Triangularization

16. W. Tinney,N. Sato, "Techniques for Exploiting the Sparsity of the Network
    Admittance Matrix", IEEE PAS vol 82, Dec. 1963, pp 944-950
17. W. Tinney, J. Walker, "Direct Solutions of Sparse Network Equations by Optimally
     Ordered Triagular Factorization", Proc. IEEE Vol-55, pp 1801-1809, Nov 1967
18. A. Toalston, G. Duin, "Solution of Mixed Impedance and Admittance Networks by
     Ordered Elimination", IEEE PAS vol-88, May 1969, pp 610-616.
19. R. Berry, "An Optimal Ordering of Electronic Circuit Equations For a Sparse Matrix
     Solution", IEEE Trans on Circuit Theory", Vol CT-18, pp 40-49, January 1971.
20. Shimon Evens, "Graph Algorithms", Computer Science Press, 1979 (A Book).
21. R. Bronson, "Operations Research", Schaum's Outline Series,
    McGraw-Hill Co., 1982 (A Book)
22. Joseph Liu, "Solution of Large Positive Definite Matrix",

Glossary of Terms

The terms defined here applies only as it is used in the context of short circuit calculation and may have a different meaning when used in other fields of Electrical Engineering.

Automatically - Without user intervention. It is used to imply that the program and not the User is responsible for performing a task.

Branch - a connection between two nodes. Also known as element, segment. It can bea transmission line, a transformer impedance, a generator impedance or its equivalent circuits. In the Zbus Building Algorithm, branch has a special meaning. It is a segment wherein one of its end node is already included in the partial network.

Bus - Any junction in the electrical system. The point of contact between two or more distinct elements. It can also be an end of a hanging line. Also known as node.

Bus Incidence Matrix - matrix showing the incidence of a branch to a bus.

Card Image - A type of file which contains data in the same format as that displayed in input forms. If listed, a card image file looks identical to a listing of the corresponding input cards. It is stored in ASCII form and can be viewed on a screen in 80 columns.

Free Format - Data whose delimiters are commas (,).

Interactive - A type of computer environment where the User can view the inputs, outputs and interact with the computer processing by selecting a command from a "menu".

Linked List - (LIFO for Last-in First-out), a means of data access where a connection to a bus is determined without searching.

NBACK - the depth of neighborhood, or number of nodes away from a faulted bus.

Normally Closed Line - A switchable line normally in the closed condition.

Normally Open Line - A switchable line normally in the open condition.

Partial Network - branches and nodes comprising a subgraph of an input data file.

Partial Refactorization - factoring takes place on rows affected by the line outage/addition. The entire matrix is not factored.

Primitive Impedance Matrix - a matrix whose diagonal elements are the self-impedance, and the off-diagonal for the mutual coupling.

Renumbering - the compression of non-contiguous bus numbers into a sequence of contiguous numbers.

Reordering - the sequencing of a renumbered nodes into a favorable order so that a minimum fill-in will be encountered during the process of factorization.

SBL, System Bus List - list of busses included in the Partial Network.

Shipley Inversion - a procedure of matrix inversion where the input and output uses the same matrix.

Singular Transformation - transformation of primitive admittance matrix to bus admittance matrix using the bus incidence matrix.

Sparsity, Sparse - a matrix containing more zeroes than non-zero off-diagonals.

Step-by-step - a procedure of building Zbus/Ybus where each branch is added into the partial network until all branches are included.

Triangularization or LU Factorization - a procedure for solving a large simultaneous linear equations while retaining sparsity.

Valence - the number of off-diagonal elements for a row.

Ybus/Zbus - bus admittance, bus impedance matrix, a model of an electrical system.