This paper proposes a novel analytical solution framework for power flow (PF) solutions in active distribution networks under uncertainty. We use the Gaussian process (GP) regression to learn node voltage as a function of effective bus load or negative net-injection vector. The proposed approximation is valid over a subspace of load and provides an understanding of system behavior under uncertainty via GP interpretability. We interpret the relative variation extent of different node voltages using the quality ratio (QR) defined based on the hyper-parameters of GP. Further, the application of the proposed framework in calculation of voltage limit violation probability and dominant voltage influencer ranking has also been presented. Through test simulations for 33-bus and 56-bus systems, the proposed method achieves low mean absolute error (MAE) of order E-05 (pu) in voltage magnitude and E-04 (rad) in angle. The discussions on salient features of the proposed method and comparative analysis with large-scale Monte-Carlo simulations, and state-of-art methods is also presented for the proposed applications.

中文翻译：

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使用高斯过程学习的分析潮流解决方案的框架


本文提出了一种新颖的分析解决方案框架，用于不确定性下主动配电网络中的功率流（PF）解决方案。我们使用高斯过程（GP）回归来学习节点电压作为有效总线负​​载或负净注入向量的函数。所提出的近似在负载子空间上有效，并通过 GP 可解释性提供对不确定性下系统行为的理解。我们使用基于 GP 超参数定义的品质比（QR）来解释不同节点电压的相对变化程度。此外，还介绍了所提出的框架在计算电压限制违规概率和主要电压影响因素排名中的应用。通过对 33 总线和 56 总线系统的测试模拟，所提出的方法实现了电压幅度 E-05 (pu) 级和角度 E-04 (rad) 级的低平均绝对误差 (MAE)。还对所提出的方法的显着特征进行了讨论，并与大规模蒙特卡罗模拟进行了比较分析，并且还针对所提出的应用提出了最先进的方法。