Paul C. Krause - Reference Frame Theory

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Library of Congress Cataloging‐in‐Publication Data

Names: Krause, Paul C., author.

Title: Reference frame theory : development and applications / Paul C.

Krause, PC Krause and Associates.

Description: First edition. | Hoboken, New Jersey : Wiley‐IEEE Press,

[2020] | Includes bibliographical reference and index.

Identifiers: LCCN 2020029315 (print) | LCCN 2020029316 (ebook) | ISBN

9781119721635 (cloth) | ISBN 9781119721635 (paperback) | ISBN

9781119721628 (adobe pdf) | ISBN 9781119721659 (epub)

Subjects: LCSH: Relativity (Physics)

Classification: LCC QC173.5 .K73 2020 (print) | LCC QC173.5 (ebook) | DDC

530.11–dc23

LC record available at https://lccn.loc.gov/2020029315

LC ebook record available at https://lccn.loc.gov/2020029316

Paul C. Krausereceived a BSEE in 1956, a BSME in 1957, and a MSEE in 1958 from the University of Nebraska. He received a PhD in EE in 1961 from Kansas University. He taught at several colleges for 52 years retiring in 2009, after 39 years as a full professor, with Purdue University. He is the 2010 recipient of the IEEE Nikola Tesla Award. He has published over 100 technical papers and four text books in Electric Machines and Drives with two in their third edition.

The change of variables was introduced to me at the beginning of the PhD program. At that time, it was a mystery as to where the transformation originated, and it remained a mystery for nearly 60 years. Although there has been considerable work in the area since Park wrote his 1929 paper, no one to my knowledge has set forth the basis of the transformation. With the advent of the computer and power electronics, reference frame theory has become necessary in the teaching of machines and drives. However, the concept of reference frame theory was difficult to teach since the transformation seemed to appear from out of the blue. One had to more or less accept that it worked.

In 2016, during the writing of “Introduction to Power and Drive Systems,” the connection between Tesla's rotating magnetic field and reference frame theory was uncovered, and it then became clear that the change of variables made the substitute variables portray the correct view of Tesla's rotating magnetic field from a given reference frame. This gave meaning to the transformation, and it is now easier to understand. This information was later published in the third edition of “Electromechanical Motion Devices” and an IEEE Paper.

This book covers some of the aspects of reference frame theory that the author has been involved with during the past 60 years, from the arbitrary reference frame to the basis of reference frame theory and field orientation. Other work including neglecting stator transients, multiple reference frames, and the relation of the transformation to symmetrical components are also discussed.

It is interesting that reference frame theory is contained in Tesla's rotating magnetic field, which is the basis of all known real transformations. Moreover, since the arbitrary reference frame can be used to derive symmetrical components, Tesla's rotating magnetic field, although not as direct, can also be considered the basis for complex transformations such as the symmetrical component transformation. Thus, it appears that all transformations, real and complex, used in the power and drives areas can be traced back to Tesla's rotating magnetic field.

This book is written for the engineers working in the power and drives areas as a reference and for the graduate students who want to know more about the history and basis of reference frame theory. It can be used as a textbook, and some instructors may want their class to become more informed regarding reference frame theory and require it as a reference text.

Paul Krause

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