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This paper presents a generalized transmission-line approach to determine the transfer function of a power-line network of a two-conductor system (two parallel conductors) with distributed branches. The channel frequency responses are derived considering different terminal loads and branches. The model's time-domain behavior is validated using commercial power system simulation software called Alternative Transients Program-Electromagnetic Transients Program (ATP-EMTP). The simulation results from the model for three different topologies considered have excellent agreement with corresponding ATP-EMTP results. Hence, the model can be considered as a tool to characterize any given power-line channel topology that involves the two-conductor system. In the companion paper (Part II), the proposed method is extended for a multiconductor power-line system.