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The aim of this paper is to study the problem of load-time variation in power line communication (PLC) systems and to analyze asynchronous impulsive noise and related channel variations due to switch commutations. A numerical model of the time-varying communication channel is developed by using scattering parameters in the wavelet domain. The proposed method uses the N-port description of the elements that constitute a time-varying PLC system in terms of real matrices with constant elements. This represents a valid alternative to the time domain description usually adopted for analyzing time-varying networks. The comparison with results obtained from other numerical models and with experimental data has confirmed the accuracy and the efficiency of the proposed method.