Tracing harmonic distortion and voltage unbalance in secondary radial distribution networks with photovoltaic uncertainties by an iterative multiphase harmonic load flow

Abstract

Secondary radial distribution networks (SRDNs) have been increasingly affected by the uncertainties of harmonic sources associated with photovoltaic (PV) systems. The quantitative assessment of uncertainty propagation causing harmonic distortion and voltage unbalance can be successively handled by probabilistic or affine formulations of harmonic load flows (HLFs). This study developed a general analytical technique (GAT) for solving iterative multiphase HLFs in SRDNs with PV uncertainties. This technique merges the point-estimate method (PEM) and complex affine arithmetic (AA), combined with Legendre series approximation (LGSA). It also models the input correlation. One advantage of this GAT is that the iterative harmonic penetration (IHP) method, modeled for HLF, accounts for the interaction of background harmonic voltage with the PV harmonic current. The first prerequisite was evidently an uncertainty model for PV harmonic current. This paper presents the results for a real unbalanced three-phase SRDN and compares them with those obtained with the Monte-Carlo simulation (MCS). These confirmed the accuracy of GAT as well as its lower computational cost. The numerical results obtained showed that the GAT outperformed the incomplete GAT (IGAT), which is solely based on PEM and Cornish-Fisher expansion, thanks to the ability of AA to bound the outputs used in the LGSA.