Application of graph theoretic concepts in short circuit analysis of power systems.

Sen, Sri Moloy Kumar (1972) Application of graph theoretic concepts in short circuit analysis of power systems. Masters thesis, Memorial University of Newfoundland.

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Abstract

The ever increasing size of electrical power systems necessitates systematic and comprehensive methods for their analysis. This report is concerned with the application of graph theoretic concepts in power system analysis, with particular reference to short circuits. It is demonstrated that the application of graph concepts provides a very elegant method for the formulation and analysis of power systems problems. -- The formulation is based on a decomposition of the power systems into a number of subsystems. The subsystems are then combined according to their physical interconnection pattern - so that an appropriate mathematically equivalent system representation is available for the system as a whole. Such a method is considered to be particularly suitable for the analysis of large power systems. -- The formulation of the ZBUS and YBUS models for a typical transmission system is given. Also, as an example, the multi-terminal representation for a typical system containing an auto-transformer is derived. The method of combining different subsystems, such as the transmission systems and the generator systems, is demonstrated. Building algorithms, using the concepts of multi-terminal representations, are developed such that the impedance matrix (ZBUS) of a network can be formulated in stages - by adding one element at a time. Separate cases for (i) addition of a branch, not mutually coupled (ii) addition of a link, not mutually coupled (iii) addition of a mutually coupled group, are illustrated. The symbolic formulations of these cases are discussed. Numerical examples to illustrate the use of these algorithms are worked out. Finally, an attempt is made to obtain the short circuit currents and voltages of a typical power system, by application of graph theoretic principles. Separate cases for three phase faults, as well as for two simultaneous faults, are considered. In each of these cases, numerical examples which illustrate the formulation procedure and analysis are worked out.

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