Reference Frame Theory. Paul C. Krause

Preface

      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