A recent frequency-domain, subspace-based algorithm as well as the well-known nonlinear least-squares algorithm are used in the identification of a power transformer whose frequency response has a dynamic range of $1$MHz. When the model complexity is not restricted, both the algorithms produce highly accurate models. Low complexity models are extracted from the high order identified ones via the method of balanced truncation. It is observed that this two-step procedure yields more accurate results than an approach of direct identification of a low order model. The utility of identified models for the purpose of transformer fault detection is also briefly discussed.