No-load conditions of single-phase induction motors and phase converters

This paper shows methods and derives formulas for the determination of the fields, the stator and rotor magnetizing currents, and the tertiary voltages for phase converters and single-phase induction motors at no-load. Previous publications on this subject, including text books, are usually rather vague and incomplete, especially with regard to the secondary magnetizing currents and the field forms. Furthermore, numerous conflicting statements are found in previous literature, thus leaving the subject, as a whole, in a rather confusing condition. This paper treats a large number of different cases along similar lines, thereby coordinating and explaining many phenomena previously observed, and it should, therefore, form a desirable basis for further investigations and discussion of this subject matter. The treatment of all cases is rather uniformly based on the following fundamental considerations. The sum of all e.m.fs. must be zero in both the primary and secondary circuits. With the impressed primary e.m.f. known, this leads to definite conditions governing the primary counter e.m.fs. The same law applied to the secondary circuits gives the condition that the induced voltages must be equal and opposite to the ohmic drops. Having thus certain laws governing the voltages to be induced in the windings, we have at once certain laws governing the fluxes for inducing these voltages. In most cases, it is then found, that only a single definite local distribution of the resultant field satisfies both the conditions for the primary and secondary windings simultaneously; having thus established the required resultant field distribution, we have at once laws for the required resultant distribution of ampere turns around the circumference to bring about such field distributions. Whenever certain portions of the circumference have conductors of either the primary winding or secondary winding alone, the resultant ampere turns found represent at once the ampere turns for the single winding located at this portion. With this fact known, a number of facts regarding the currents can be determined. Whenever both primary and secondary turns coincide at the same portion of the circumference, certain problems arise in determining the distribution of the resultant ampere turns between the two windings. A number of different considerations are used for the various cases to assist in the solution of these problems; all these considerations are, however, based on simple facts. In order to demonstrate the method by means of the simplest mathematics, two cases of small practical application are given first merely in order to separate the fundamentals from a rather large amount of mathematics which, while necessary, in connection with the more practical cases, are of little value in connection with the understanding of the fundamental principles. Starting out from these simple cases, the influence of various factors are taken up in the following cases, one at a time, because a simultaneous consideration of all of them make a clear understanding practically impossible. The paper is arranged so that it can be read to good advantage without going through those mathematical parts marked by vertical rules. By reading the conclusions at the end of the paper, a fair idea of the principal points brought out in the paper can be obtained.