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With regard to emerging utilization of the HF band for power-line communication applications, narrowband statistical characteristics of corresponding fading channels along single-phase electric networks are being investigated. By the reasonable two-conductor transmission line approach for cabling components, a model giving channel transfer functions on account of multi-path propagation is proposed Appropriate assumptions based on indoor electric networks' topology are adopted concerning scattering points' spatial allocation, by which path amplitudes are demonstrated to follow the lognormal distribution, whereas the normal distribution is extracted for arrival times. For this theoretical treatment, a suitable definition of the term "path" is introduced, inferred by reflection points discrete spatial distribution. Verification of statistical modelling is established, involving path inventory through simulation. During the simulating process, a well applicable cable transmission-line model is used, and the configuration of a bus having numerous transverse branches connected in parallel is considered, which forms the fundamental topological element for electric networks. Simulation results show remarkable compliance with the behaviour theoretically anticipated, and the model proposed herein seems to precisely describe the power delay profile of indoor single-phase power-line communication channels in the HF spectral area.