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Considering the proliferation of power electronics applications and distributed energy resources, modern power grids are facing a significant increase in harmonic currents circulation and supply voltage deterioration, occasionally associated with small frequency variations. In such a context, the understanding of power phenomena in circuits with linear and non-linear loads under non-sinusoidal voltage conditions is nontrivial and still does not allow for an easy interpretation of harmonic sources, harmonic power flow or the identification of the parameters of a proper equivalent circuit. The main challenge is to develop modern theoretical approaches for load characterization, modeling, and parameter estimation so that new techniques can be formulated to provide adequate guiding for the analysis, compensation, revenue metering, accountability and other applications of power systems. Thus, based on the Conservative Power Theory (CPT) and further decomposition of its apparent power and power factor definitions, this paper proposes a novel methodology for estimating equivalent parameters and for proposing proper equivalent circuits capable of representing/modeling the main characteristics of single-phase generic loads (black boxes) and the related power phenomena in terms of passive dipoles (linear loads) or of harmonic voltage/current sources and their intrinsic transimpedances/transadmittances (non-linear loads). Simulation and experimental results were depicted to support and validate the proposed approach, showing that it might be a powerful modeling technique to represent generic loads in a modern power grid scenario, while …