Transient Oscillations in Distributed Circuits With Special Reference to Transformer Windings

Abstract
This paper is essentially a mathematical study of transient voltages in transformer and other distributed windings, and is primarily concerned with showing the effects of wave shape, circuit constants and neutral impedances on the voltage distributions, and how these distributions may be controlled or changed. In the appendix there is derived the general differential equation for a circuit consisting of distributed self and mutual inductance, series and shunt capacitance, series resistance, and conductance along the stack and to ground. This equation is solved for the following conditions: (1) initial and final conditions with generalized impedance in the neutral; (2) grounded neutral; (3) isolated neutral for zero losses; and (4) capacitance in the neutral when the losses and mutual inductance are neglected. Equations are given corresponding to a number of different applied waves, showing the effects of wavelength, wave front, damped and sustained oscillations, and typical lightning waves, and these effects are illustrated by curves and oscillograms. Equations are also given for the potential difference between any two points on the winding and for the voltage gradients. Tables are included showing the influence of the various circuit constants on the amplitude and frequency of oscillation, linear velocity and surge impedance of harmonic waves, and the type of propagation. These effects are illustrated by curves of the potential distribution at different instants of time. Methods of controlling the transient so as to prevent or alleviate abnormal voltage distributions are discussed at length.

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