Abstract 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.

中文翻译：

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基于点估计法和复仿射算法的具有光伏不确定性的径向配电系统的迭代谐波潮流

摘要 非线性设备 (NLD) 中的负荷和发电变化以及谐波的随机性是多种不确定性的来源，可以通过概率或区间公式在谐波潮流 (HLF) 中处理这些不确定性。本文提出了一种新的组合分析技术 (CAT)，用于在存在来自径向分布系统 (RDS) 中的光伏 (PV) 系统的相关输入不确定性的情况下进行迭代 HLF。该技术融合了概率公式点估计法 (PEM) 和区间公式复数仿射算术 (AA)。然后使用勒让德级数近似 (LGSA) 中得出的信息来近似谐波电压分布。与其他方法不同，该 CAT 包括迭代谐波穿透 (IHP)，它提供了一种处理背景谐波电压对光伏谐波电流的相互作用的方法。CAT 在真实的ENDE 100 RDS 系统中进行了检查。多亏了 PEM 和 AA，CAT 显着减少了计算负担，明显优于蒙特卡洛模拟 (MCS)。此外，仿真结果表明，它准确地重建了谐波电压分布（幅度和相角）。迭代方法还强调了背景谐波相互作用的相关性。CAT 优于仅基于概率 HLF 公式的不完全 CAT (ICAT)。此外，仿真结果表明，它准确地重建了谐波电压分布（幅度和相角）。迭代方法还强调了背景谐波相互作用的相关性。CAT 优于仅基于概率 HLF 公式的不完全 CAT (ICAT)。此外，仿真结果表明，它准确地重建了谐波电压分布（幅度和相角）。迭代方法还强调了背景谐波相互作用的相关性。CAT 优于仅基于概率 HLF 公式的不完全 CAT (ICAT)。