The behaviour of a power transformer is complex and difficult to predict during transient conditions or during operation at frequencies below or above its nominal frequency, a phenomenon common in renewable energy plants due to harmonic distortion. Furthermore, the accuracy of a power system simulation depends on the models of critical subsystems such as the power transformers. This paper presents the use of a unique excitation waveform comprising of pseudo-random current impulses to accurately identify the wideband characteristics of a power transformer. By injecting the excitation waveform to the relevant transformer terminals, frequency responses are determined by cross-correlation of the perturbation signal, and the measured response. Compared to the traditional transformer identification methods, the pseudo-random current impulses offer a wideband excitation with a higher degree of controllability such that its spectral energy can be focused in the frequency band of interest. The proposed method was investigated on a 16 kVA, 22 kV/240 V single-phase transformer. The obtained wideband frequency responses provide useful information in harmonic penetration and over-voltage studies and are also used to estimate, with a high degree of accuracy, the lumped parameters of the equivalent transformer broadband circuit model.