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This paper presents a computational efficient distributed circuit model for broadband power-line communications (PLC) in the frequency range of 1 to 30 MHz. The model is derived based on the full wave approach and it takes into account the mutual coupling between the power lines, the effect of the ground plane and the discontinuity along the lines (e.g., PLC line bent with an arbitrary angle and the terminations). To derive the distributed circuit model, the PLC lines were divided into many small elements with each element treated as a dipole antenna. The electromagnetic fields along the power lines were considered as the summation of the field of these elements solved by the boundary conditions at the air-conductor and the air-ground interfaces from which the explicit expressions of the per-unit-length circuit parameters were obtained. To check the accuracy of our proposed model, the current distributions along PLC lines excited by an external source were determined using the chain matrix approach. Common-mode current is calculated with the transmission line equations. The agreement between our theoretical calculations with the experimental data as well as with full wave approach shows the validity and applicability of our proposed model for such PLC applications.