# Switching Surges: A Study of Transient Phenomena in Electro-Magnetic Machinery, with Particular Reference to the Use of the Heaviside Operational Calculus

Coombs, Allen W. M (1936) Switching Surges: A Study of Transient Phenomena in Electro-Magnetic Machinery, with Particular Reference to the Use of the Heaviside Operational Calculus. PhD thesis, University of Glasgow.

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## Abstract

The Thesis is divided primarily into three parts. In the first of these three parts is considered the standard treatment of transient phenomena by the methods of the Newtonian Calculus. Various problems are worked out by these methods. Part I,C, refers to the original article "Ignition Coils", published by the author in the "Royal Technical College Journal", January, 1934, a copy of which article forms a part of the Thesis. Part I,D, contains a method of dealing with the transformer magnetising current surge by regarding the magnetisation curve as made up of two straight lines, a method which the author believes is original. Part I,E, contains a summary of two methods of direct mathematical attack on the problem of alternator short-circuit, due respectively to Shimidzu and Ito, and to Rudenberg. Part I also shows wherein the difficulties of normal mathematical methods usually lie, - viz., in the evaluation of the arbitrary constants. Part II is devoted mainly to the exposition of the principles of the Operational Calculus invented by Heaviside. One or two simple problems are worked out, and the solutions shown to be identical with those obtained by the standard methods of Part I. The last section of Part II is given over to a general survey of problems arising in connection with the Operational Calculus; more particularly, various formulae necessary for the work of Part III are established. Of these, those relating to the solution of simultaneous operational equations having a cyclically symmetrical matrixdeterminant, and applied forces symmetrically disposed in the complex plane, are original. Part III forms the main body of the Thesis. It is devoted exclusively to the application of operational methods to the case of transients in rotating machinery, in particular, to the case of alternator short-circuit. In general, two methods are used in this treatment, the "Method of Reflections", and the "Method of Equivalent Circuits" - both of which are derived from the Heaviside Calculus. So far as the author is aware, the Heaviside Calculus has not before been adapted in this particular manner, so that Part III is in the main an original treatment.

Item Type: Thesis (PhD) Doctoral Electromagnetics 1936 Enlighten Team glathesis:1936-80083 Copyright of this thesis is held by the author. 03 Mar 2020 09:32 03 Mar 2020 09:32 https://theses.gla.ac.uk/id/eprint/80083