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The aim of this paper is to characterize oil-filled power transformers in the narrow-band power-line communication (PLC) frequency range of 50-150 kHz. A new model is proposed for such type of a transformer, in the aforementioned frequency range of interest, in order to study its influence on the signal transmission and to investigate the possibility that the PLC signal can cross the power transformer itself. The new model is simpler than those previously proposed in literature, and it can be used in the whole frequency range available for NB PLC according to the CENELEC EN 50065-1 A-band. In order to validate the model, simulation and measurement results are compared for four oil-filled power transformers with different rated power values. A complete PLC system in the case of a medium-voltage (MV) power network is also simulated, in order to perform a preliminary evaluation of the influence of power transformers on the communication system. The MV overhead power line, the oil-filled power transformers, the MV signal coupling network, and two ST7540 frequency shift keying (FSK) power-line transceivers are included in the simulated system. The performances of the complete PLC communication system are evaluated in the case of both MV to low voltage (LV) and LV to MV transmissions. The analysis is carried out by evaluating the signal attenuation, which is computed as the ratio between the received and transmitted voltage signals, in the case of different line lengths and carrier frequency values.