Theory of the transient oscillations of electrical networks and transmission systems

The purpose of this research was to make a broad theoretical study of transient phenomena with a view to developing methods of calculation directly applicable to engineering problems. The investigation starts with the problem of formulating the current in an electrical network or transmission system in response to a suddenly applied e.m.f. of arbitrary form. A simple formula is derived which expresses this current in terms of two independent functions: one, the applied e.m.f. expressed as a time function, and the other a characteristic function of the constants and connections of the system, this latter being termed the “indicial admittance” of the system. A knowledge of the indicial admittance, therefore, completely determines the behavior of the system to all types of applied voltages including both transient and steady states. A systematic investigation of methods for solving and computing the indicial admittance follows, in the course of which original solutions for transmission and artificial lines are derived and a new method involving integral equations is developed. This latter is particularly well adapted to handle the difficult problem of taking into account the effects of terminal impedances in transmission systems.