High voltage (HV) power lines have been used as a communications medium since the 1920s. Those point to point links were typically based on single-sideband amplitude modulation. Nowadays, the state of the art in HV power line carrier (PLC) communications comprises the combination of analog systems, mainly for teleprotection tasks, and digital systems, used for voice and data transmission. Beside traditional core services (monitoring, operation management, and limitation and removal of failures), electrical utilities would like to satisfy the increasing need of new internal applications. In that way, quadrature amplitude modulation and, most recently, multicarrier modulation (MCM) based modems are beginning to play an important role in HV PLC systems. Although the typical 4 kHz bandwidth has been recently increased up to 32 kHz, this paper proposes a low-power 256 kHz bandwidth orthogonal frequency division multiplexing (OFDM) based physical layer. Based on channel measurements, the OFDM symbol has been designed and tested in order to increase the user bit rate while keeping both the power spectral density and bit error rate low.