Unified harmonic modeling framework and comparative assessment of harmonic power flow formulations for distribution systems with LCCs

Harmonic power flow analysis (HPFA) is essential for planning, operation, and power quality assessment in distribution systems with line commutated converters (LCCs). Conventional methods assume independent harmonic behaviour and neglect voltage-current coupling effects, which can lead to inaccurate distortion predictions. This paper presents and compares three HPFA formulations for distribution systems containing 6-pulse LCCs loads. The coupled HPFA method accounts for harmonic coupling by using a harmonically coupled admittance representation that captures inter-harmonic and conjugate interactions in a physically consistent and computationally efficient manner. In contrast, the decoupled HPFA formulation simplifies the analysis by neglecting coupling terms and solving each harmonic order independently, while the harmonic current source model represents converters as fixed harmonic current injections without voltage dependency. Case studies considering variations in background harmonics, DC-link inductance, firing angle, and the penetration level demonstrate that harmonic coupling results in larger changes in harmonic voltage distortion, while simplified models tend to underestimate the corresponding THD. The results provide practical guidance for selecting appropriate HPFA methods in converter-rich distribution systems.