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This contribution proposes an efficient methodology in time domain (TD) based on companion-circuit analysis (CCA) and a Newton method of extrapolation to the Limit Cycle (periodic steady state solution) based on a Numerical Differentiation (ND) process. Its formulation is amenable to the solution approach followed by standardized digital simulators widely accepted by the power industry, such as EMTP and/or EMTDC. The particular application reported in this research is oriented to the dynamic and fast periodic steady state solution of nonlinear single-phase electrical networks incorporating photovoltaic (PV) systems under harmonic distortion conditions. Fundamentally, the proposed methodology is based on the representation of linear and nonlinear elements (e.g., switching elements), using Norton equivalents. This solution method is based on the determination of discrete differential equations sets, obtained by nodal analysis. The solution process is iteratively obtained by using LU decomposition. In general terms, the application is based on the combination of the CCA and ND methods (CCA-ND), for the applying in different case studies associated with the assessment of harmonics distortion, in terms of individual and total harmonic distortion at the point of common coupling (PCC) between the PV system and the electrical system are reported. It is shown that the methodology is precise, reliable and efficient. The documented results have been successfully validated against those obtained PSCAD/EMTDC® simulator, widely accepted by the power industry.

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