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For flyback converter applications, an accurate model of the transformer is necessary for simulation studies, as well as a basis for model-based controller design. In general, transformer modeling has either focused on the winding model, using frequency-domain methods, or on the nonlinear core model, using time-domain methods. Nonlinear modeling is confined to the time domain and certain difficulties have precluded the use of time-domain methods for winding model estimation, resulting in the lack of integrated modeling approaches. This paper focuses on identifying a complete nonlinear dynamic model of a 3-winding transformer using time-domain system identification approaches. Our study demonstrates a possible way to handle the difficulties of working in the time domain and provides a model at least as accurate as that obtained with the frequency response data. In addition to the parameters of the Jiles-Atherton model, which is used to describe the nonlinear core behavior, the air-gap length is also computed from the experimental data to enhance the core model accuracy. The obtained transformer winding model, core model, and full model are experimentally verified. [ABSTRACT FROM AUTHOR]