In this paper, we propose a data-driven algorithm for probabilistic optimal power flow (POPF). In particular, we develop a nonparametric Bayesian framework based on the Dirichlet process mixture model (DPMM) and variational Bayesian inference (VBI) to establish a probabilistic model for capturing the uncertainties involved with wind generation and load power in power systems. In the proposed setup, the number of components in the mixture model can be automatically and analytically obtained from the consistently updated data. Moreover, we develop an efficient quasi-Monte Carlo sampling method to draw samples from the obtained DPMM, then propose the dynamic data-driven POPF algorithm. Performance of uncertainty modeling framework on publicly available datasets is examined by extensive numerical simulations. Furthermore, the proposed POPF algorithm is verified on multiple IEEE benchmark power systems. Numerical results show the feasibility and superiority of the proposed DPMM-based POPF algorithm for better informed decision-making in power systems with high level of uncertainties.

中文翻译：

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非参数贝叶斯建模与推断的数据驱动概率最优潮流

在本文中，我们提出了一种用于概率最优潮流（POPF）的数据驱动算法。特别是，我们基于Dirichlet过程混合模型（DPMM）和变分贝叶斯推断（VBI）开发了非参数贝叶斯框架，以建立概率模型来捕获电力系统中与风力发电和负荷功率有关的不确定性。在建议的设置中，可以从一致更新的数据中自动分析地获得混合物模型中的组分数量。此外，我们开发了一种有效的准蒙特卡洛采样方法来从获得的DPMM中抽取样本，然后提出动态数据驱动的POPF算法。广泛的数值模拟检查了不确定性建模框架在公开数据集上的性能。此外，提出的POPF算法已在多个IEEE基准电源系统上得到验证。数值结果表明，提出的基于DPMM的POPF算法在具有较高不确定性的电力系统中更好地进行明智决策的可行性和优越性。