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Determining whether power transformers are suffering from internal arcing or dangerous levels of partial discharge (PD) is important because failure without warning can result in damage to neighboring equipment, customer dissatisfaction, disruption to economic activity, and the imposition of regulatory fines. This paper provides an overview of the excitation of UHF signals by PD inside transformers. The use of externally mounted sensors has been outlined, and the structure of a dielectric window that can be constructed on an inspection hatch has been outlined. Attenuation of UHF signals propagating inside a transformer tank has been shown to be relatively low. A new approach to locating PD sources in three dimensions has been presented, based on using a numerical model of the transformer materials, which defines electromagnetic propagation velocities on a mesh of 5-cm sub-cells. The concepts of the propagation-velocity matrix (PVM) and the propagation-time matrix (PTM) were thereby introduced. Once the PD source has been located to a specific region of the transformer, the PVM might be used to index a database of physical descriptions of the transformer that could provide additional information to assist with diagnosis.