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In this paper, a model developed for a transformer monitoring system to estimate transformer tank vibration is presented. The model calculates vibration on the transformer tank starting from some input variables that can be easily measured on the transformer. Tank vibration is also measured, showing a good concordance between estimated and measured values if the transformer is healthy. In case of a winding deformation winding vibration and, consequently, that of the tank, changes and a big difference between estimated and measured vibration appear. To estimate tank vibration, the model takes into account the main physical phenomena generating vibrations in the different transformer elements and how these vibrations are superposed and transmitted to the tank. The model has been tested experimentally on a test transformer fitted with internal and external accelerometers. A deformation has been provoked in the test transformer winding with the aim of testing the model's ability to detect it. The model has been also tested on several in-service grid transformers. The results of the experimental validation are shown in Part II of the paper.