Iterative harmonic load flow by using the point-estimate method and complex affine arithmetic for radial distribution systems with photovoltaic uncertainties

Load and generation variations and the random nature of harmonics in non-linear devices (NLDs) are the source of multiple uncertainties that can be handled in harmonic load flows (HLFs) by probabilistic or interval formulations. The paper presents a new combined analytical technique (CAT) for iterative HLFs in the presence of correlated input uncertainties from photovoltaic (PV) systems in radial distribution systems (RDSs). This technique merges the point-estimate method (PEM), a probabilistic formulation, and complex affine arithmetic (AA), an interval formulation. It then uses the information derived in Legendre series approximation (LGSA) to approximate harmonic voltage distributions. Unlike other methods, this CAT includes iterative harmonic penetration (IHP), which provides a way to deal with the interaction of background harmonic voltage on PV harmonic current. The CAT was examined in a real ENDE 100 RDS system. Thanks to PEM and AA, the CAT significantly reduced the computational burden, an evident improvement over the Monte-Carlo simulation (MCS). Furthermore, the simulation results showed that it accurately reconstructed the harmonic voltage distributions (magnitude and phase angle). The iterative approach also underlines the relevance of background harmonic interaction. The CAT outperformed the incomplete CAT (ICAT), which was based solely on a probabilistic HLF formulation.