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Switching operations within a power system can generate transients that are comprised of a broad spectrum of frequency components. If the frequency content of these transients happens to align with a resonant frequency mode within a power transformer, the resulting internal voltage amplification can eventually lead to the transformer's dielectric failure. This paper presents a hybrid modelling methodology for analysing scenarios such as this. The approach uses a Black Box model of the transformer within an EMTP system study in order to take advantage of its mathematical flexibility and modelling accuracy. Terminal transient scenarios determined by EMTP are then injected into a Grey Box transformer model, which facilitates the analysis of the internal response of the transformer. The proposed modelling methodology does not require a priori knowledge of the transformer's internal geometry, but instead relies upon external measurement techniques and knowledge of common transformer design practices. This is a distinct advantage over more traditional modelling approaches since in most cases such information is unavailable due to manufacturer intellectual property restrictions and internal access limitations. The paper applies the methodology to a substation within the Itaipu hydroelectric system in Brazil. [ABSTRACT FROM PUBLISHER]