This paper develops a physical model for three phase power transformers with the goal of advancing techniques for the physical interpretation of Frequency Response Analysis (FRA) data. The model is structured such that it facilitates end to end FRA tests. A parameter estimation algorithm is then simultaneously applied to the three end to end test permutations. The proposed model utilises parameters such as the core yoke and limb lengths, the core's cross sectional area, and the number of turns on each winding to determine the inductive relationships between each of the transformer's windings. Parameters such as the conductor cross sectional area and number of disc layers are used to account for skin and proximity effects within the windings. Furthermore, the various tank, core and interwinding capacitive couplings are also incorporated into the model. To demonstrate the veracity of the model, FRA tests were conducted on a Dyn1 1.3MVA 11kV/430V distribution transformer. Using the FRA data, the key parameter estimates for the proposed model were obtained and compared against their physically measured counterparts. The relative accuracy of the results demonstrates the applicability of the proposed transformer modelling approach.