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This work presents a channel model for the broadband characterization of power lines in presence of time variation of the loads. The model is characterized by taking into account both measured and geometrical channel characteristics and can easily be used to take into account also the presence of noise. The channel is described by a two-port equivalent described by a scattering matrix determined from a wavelet-based expansion of the input and output quantities. Upper and lower bounds for the response of the channel in presence of time-varying loads are determined in a fast and efficient way avoiding time consuming Monte Carlo simulations. The bounds determination allows the estimate of noteworthy quantities for the tuning of currently used modulation schemes for power lines communications such as orthogonal frequency-division multiplexing.