We consider belief propagation (BP) as an efficient and scalable tool for state estimation and optimization problems in supply networks such as power grids. BP algorithms make use of factor graph representations, whose assignment to the problem of interest is not unique. It depends on the state variables and their mutual interdependencies. Many short loops in factor graphs may impede the accuracy of BP. We propose a systematic way to cluster loops of naively assigned factor graphs such that the resulting transformed factor graphs have no additional loops as compared to the original network. They guarantee an accurate performance of BP with only slightly increased computational effort, as we demonstrate by a concrete and realistic implementation for power grids. The method outperforms existing alternatives to handle the loops. We point to other applications to supply networks such as gas-pipeline or other flow networks that share the structure of constraints in the form of analogues to Kirchhoff's laws. Whenever small and abundant loops in factor graphs are systematically generated by constraints between variables in the original network, our factor-graph assignment in BP complements other approaches. It provides a fast and reliable algorithm to perform marginalization in tasks like state determination, estimation, or optimization issues in supply networks.
翻译:我们认为,信仰传播(BP)是电网等供应网络中国家估计和优化问题的有效和可扩缩的工具。BP算法使用要素图形表示法,该表示法不是独特的,它取决于国家变量及其相互依存性。要素图中的许多短环可能妨碍BP的准确性。我们提出一个系统的方法,将天真分配要素图的循环分组,这样,与原网络相比,由此产生的变换要素图没有额外的循环。它们保证BP的准确性,只略微增加计算努力,我们通过具体和现实地执行电网来证明。这种方法优于现有处理循环的替代方法。我们指出,其他应用到供应网络,如气管或其他流动网络,这些网络与Kirchhoff法律相似,以类比形式分享制约结构。每当原网络变量之间的制约系统地生成要素图中的小和丰富的循环时,我们在BP的系数图分配则补充了其他方法。该方法优于现有处理循环的替代方法。我们指出,该方法超越了处理循环的替代方法。我们指出,例如气管线或其他流流流流网络的快速和可靠的算法,以便进行边际分析。