# Steinmetz 1909

**Zusammenfassung:**(OCR text)

PREFACE

The following work owes its origin to a course of instruction given during the last few years to the senior class in electrical engineering at Union University and represents the work of a number of years. It comprises the investigation of phenomena which heretofore have rarely been dealt with in text-books but have now become of such importance that a knowledge of them is essential for every electrical engineer, as they include some of the most important problems which electrical engineering will have to solve in the near future to maintain its thus far unbroken progress.

A few of these transient phenomena were observed and experimentally investigated in the early days of electrical engineering, for instance, the building up of the voltage of direct-current generators from the remanent magnetism. Others, such as the investigation of the rapidity of the response of a compound generator or a booster to a change of load, have become of importance with the stricter requirements now made on electric systems. Transient phenomena which were of such short duration and small magnitude as to be negligible with the small apparatus of former days have become of serious importance in the huge generators and high power systems of to-day, as the discharge of generator fields, the starting currents of transformers, the short-circuit currents of alternators, etc. Especially is this the case with two classes of phenomena closely related to each other: the phenomena of distributed capacity and those of high frequency currents. Formerly high frequency currents were only a subject for brilliant lecture experiments; now, however, in the wireless telegraphy they have found an important industrial use. Telephony has advanced from the art of designing elaborate switchboards to an engineering science, due to the work of M. L Pupin and others, dealing with the fairly high frequency of sound waves. Especially lightning and all the kindred high voltage and high frequency phenomena in electric systems have become of great and still rapidly increasing importance, due to the great increase in extent and in power of the modem electric systems, to the interdependence of all the electric power users in a large territory, and to the destructive capabilities resulting from such disturbances. Where hundreds of miles of high and medium potential circuits, overhead lines and underground cables, are interconnected, the phenomena of distributed capacity, the effects of charging currents of lines and cables, have become such as to require careful study. Thus phenomena which once were of scientific interest only, as the unequal current distribution in conductors carrying alternating currents, the finite velocity of propagation of the electric field, etc., now require careful study by the electrical engineer, who meets them in the rail return of the single-phase railway, in the effective impedance interposed to the lightning discharge on which the safety of the entire system depends, etc.

The characteristic of all these phenomena is that they are transient functions of the independent variable, time or distance, that is, decrease with increasing value of the independent variable, gradually or in an oscillatory manner, to zero at infinity, while the functions representing the steady flow of electric energy are constants or periodic functions.

While thus the phenomena of alternating currents are represented by the periodic function, the sine wave and its higher harmonics or overtones, most of the transient phenomena lead to a function which is the product of exponential and trigonometric terms, and may be called an oscillating function, and its overtones or higher harmonics.

A second variable, distance, also enters into many of these phenomena; and while the theory of alternating-current apparatus and phenomena usually has to deal only with functions of one independent variable, time, which variable is eliminated by the introduction, of the complex quantity, in this volume we have frequently to deal with functions of time and of distance.

We thus have to consider alternating functions and transient functions of time and of distance.

The theory of alternating functions of time is given in "Theory and Calculation of Alternating Current Phenomena." Transient functions of time are studied in the first section of the present work, and in the second section are given periodic transient phenomena, which have become of industrial importance, for instance, in rectifiers, for circuit control, etc. The third section gives the theory of phenomena which are alternating in time and transient in distance, and the fourth and last section gives phenomena transient in time and in distance.

To some extent this volume can thus be considered as a continuation of "Theory and Calculation of Alternating Current Phenomena."

In editing this work, I have been greatly assisted by Prof. O. Ferguson, of Union University, who has carefully revised the manuscript, the equations and the numerical examples and checked the proofs, so that it is hoped that the errors in the work are reduced to a minimum.

Great credit is due to the publishers and their technical staff for their valuable assistance in editing the manuscript and for the representative form of the publication they have produced.

CHARLES P. STEINMETZ.

Schenectady, December, 1908.

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