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Graphical models for optimal power flow
Constraints ( IF 1.6 ) Pub Date : 2016-09-13 , DOI: 10.1007/s10601-016-9253-y
Krishnamurthy Dvijotham , Michael Chertkov , Pascal Van Hentenryck , Marc Vuffray , Sidhant Misra

Optimal power flow (OPF) is the central optimization problem in electric power grids. Although solved routinely in the course of power grid operations, it is known to be strongly NP-hard in general, and weakly NP-hard over tree networks. In this paper, we formulate the optimal power flow problem over tree networks as an inference problem over a tree-structured graphical model where the nodal variables are low-dimensional vectors. We adapt the standard dynamic programming algorithm for inference over a tree-structured graphical model to the OPF problem. Combining this with an interval discretization of the nodal variables, we develop an approximation algorithm for the OPF problem. Further, we use techniques from constraint programming (CP) to perform interval computations and adaptive bound propagation to obtain practically efficient algorithms. Compared to previous algorithms that solve OPF with optimality guarantees using convex relaxations, our approach is able to work for arbitrary tree-structured distribution networks and handle mixed-integer optimization problems. Further, it can be implemented in a distributed message-passing fashion that is scalable and is suitable for “smart grid” applications like control of distributed energy resources. Numerical evaluations on several benchmark networks show that practical OPF problems can be solved effectively using this approach.

中文翻译:

图形模型可实现最佳功率流

最优潮流(OPF)是电网中的核心优化问题。尽管在电网运行过程中可以常规解决,但通常已知它在树状网络上通常是强NP难的,而在NP网络上是弱NP的。在本文中,我们将树型网络上的最佳潮流问题公式化为节点变量为低维向量的树状结构图形模型上的推理问题。我们采用标准的动态规划算法,通过树结构的图形模型来推断OPF问题。结合节点变量的间隔离散化,我们为OPF问题开发了一种近似算法。此外,我们使用约束编程(CP)中的技术来执行间隔计算和自适应边界传播,以获得实用的算法。与以前的使用凸松弛来求解具有最优性保证的OPF的算法相比,我们的方法能够用于任意树形结构的配电网络并处理混合整数优化问题。此外,它可以以可伸缩的分布式消息传递方式实现,并且适合于“智能电网”应用程序,例如分布式能源的控制。对几个基准网络的数值评估表明,使用这种方法可以有效解决实际的OPF问题。它可以以可伸缩的分布式消息传递方式实现,并且适合于“智能电网”应用程序,例如分布式能源的控制。对几个基准网络的数值评估表明,使用这种方法可以有效解决实际的OPF问题。它可以以可伸缩的分布式消息传递方式实现,并且适合于“智能电网”应用程序,例如分布式能源的控制。对几个基准网络的数值评估表明,使用这种方法可以有效解决实际的OPF问题。
更新日期:2016-09-13
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