Ensuring Solution Uniqueness in Fixed-Point-Based Harmonic Power Flow Analysis with Converter-Interfaced Resources: Ex-post Conditions

Antonio Di Pasquale,Johanna Kristin Maria Becker,Andreas Martin Kettner,Mario Paolone

IEEE Trans Smart Grid（2025）

University of Naples Federico II Department of Electrical Engineering and Information Technology | PSI NEPLAN AG

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Abstract

Recently, the authors of this paper proposed a method for the HarmonicPower-Flow (HPF) calculus in polyphase grids with widespread deployment ofConverter-Interfaced Distributed Energy Resources (CIDERs). The HPF problem wasformulated by integrating the hybrid nodal equations of the grid with adetailed representation of the CIDERs hardware, sensing, and controls as LinearTime-Periodic (LTP) systems, and solving the resulting mismatch equations usingthe Newton-Raphson (NR) method. This work introduces a novel problemformulation based on the fixed-point algorithm that, combined with thecontraction property of the HPF problem, provides insights into the uniquenessof its solution. Notably, the effectiveness of the fixed-point formulation andthe uniqueness of the solution are evaluated through numerical analysesconducted on a modified version of the CIGRE low-voltage benchmark microgrid.

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Key words

converter-interfaced resources,distributed energy resources,harmonic power-flow study,fixed point method,solution uniqueness

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