Methods of determining natural frequencies in coils and windings

A knowledge of the natural frequencies of transformer, reactor, and generator windings is essential for the determination of the transient response of such coils to lightning waves and switching surges, as well as for the calculation of the recovery characteristics of circuit breakers and expulsion gaps. Different testing methods have been employed to determine these natural frequencies, and it has usually been taken for granted that each of these different testing procedures gives results in substantial agreement. Recently, however, in a study of transformer transients it was found that several different methods of test failed to agree, and an investigation as to the cause of the discrepancies disclosed that all of these usual methods are not equally valid or reliable. It is, therefore, the object of this paper to discuss various testing procedures, and to point out their theoretical limitations toward yielding the supposed information. The voltage distribution along the winding of a grounded neutral transformer is discussed analytically and the basic equations are developed. Results of voltage distribution tests made by several methods are reported and compared. The various methods of testing are discussed and compared with the conclusion that the method of free oscillation is, in general, preferable.