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UBC Theses and Dissertations

Methods of investigating phenomena arising from non-linearities in power systems Julien, Kenneth Stephen


Mathematical methods for investigating power-system phenomena arising from non-linearities are developed in this thesis. Most information available about power-system phenomena arising from non-linear effects is obtained from two main sources of research: field tests and miniature representation experiments. The use of equivalent circuits describing the physical system and the application of circuit analysis techniques is another approach to this problem. This thesis is concerned with the establishment of procedures for methods based on this approach. The incremental method is simple in theory but its application was difficult in the past because of the necessity of numerous calculations. The facilities of the digital computer overcome this difficulty and this method is fully explored. Certain aspects of the phenomena are investigated and some programming details of the method discussed. In contrast, the other methods require less calculations as the solutions are in the form of simple algebraic expressions. An insight into the system behaviour rather than accurate numerical results are obtained. Under the broad heading of analytical methods, the Method of Isoclines, the Principle of Harmonic Balance and the Method of Integral curves are investigated and used. The establishment of the equivalent circuits representing the physical system is studied and the adequacy of these representations is discussed. An interesting method of approaching the transient solution of the long-line equations is also developed. Comparison between the representations of the power transmission line by a finite number of T-sections and the use of distributed parameters is made. Underlying the whole study is the growing importance of non-linear effects and transient phenomena in power-system planning, design and operation.

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