Degree Type


Date of Award


Degree Name

Doctor of Philosophy


Electrical and Computer Engineering


This study investigates the nature of ferroresonance and the conditions under which it occurs. Analysis of this phenomenon is difficult because it requires the solution of a set of nonlinear differential equations;Two different methods for studying the ferroresonance phenomenon are studied in detail. The Two-slope Incremental Describing Function avoids the process of trial and error required by C. W. Gear's Digital Program. The polynomial equation model of the digital program can be of any order needed to accurately match the transformer's core characteristic. Therefore, the solution obtained through the Two-slope Method can be enhanced by the utilization of Gear's Digital Program without requiring significant additional effort;For this investigation, two basic approaches have been used to solve for the existence of ferroresonance in a circuit--the Incremental Describing Function of G. W. Swift, and the Piecewise Linearization Technique developed by Mukherjee and Ray. The limitations of both of these methods are discussed in detail;The major advantage of the Incremental Describing Function technique over the Piecewise Linearization Method is that the resulting differential equations are transformed into algebraic equations involving complex variables (i.e., phasors);The Two-slope Incremental Describing Function approach is an alternative to G. W. Swift's method because all power transformers are not represented by the same polynomial containing a linear term and a fifth order term. Unfortunately, if a higher order polynomial model is required for accurate results, it becomes extremely difficult to obtain the analytical solutions using Swift's method. To alleviate this problem, a Two-slope Model is used where only the coefficients for different transformer characteristics change in the describing function, instead of having to determine a new describing function for each type of transformer core material;Results obtained in this study, as verified in the laboratory, show that a transformer core characteristic model of the two-slope type yields reasonable ferroresonant data for both series and pi circuit configurations.



Digital Repository @ Iowa State University,

Copyright Owner

B. Peter Daay



Proquest ID


File Format


File Size

373 pages