交流辐射状网络可行集的凸限制
Convex Restriction of Feasible Sets for AC Radial Networks
AI总结：
针对交流辐射状网络潮流可行集非凸导致OPF难解的问题，提出显式且最大的凸限制构造方法及迭代改进算法，可在IEEE 123节点系统中快速获得可行解。
摘要：
电力系统中的许多问题都涉及在满足潮流方程和工程约束的条件下优化某个目标函数。求解这些问题的一个长期挑战是其可行集的非凸性。本文提出一种解析方法，用于构造辐射状网络中交流潮流可行集的凸限制。该构造依赖简单的几何思想，并且是显式的，即不涉及求解其他复杂优化问题。我们还表明，所构造的限制在某种意义上是最大的，也就是可能达到的最佳限制。受限于这些集合的优化问题不仅更易于求解，而且为原始OPF问题的解提供可行性保证。此外，我们提出一种迭代算法，通过依次构造一系列凸限制集合并在其上求解优化来提升解的质量。在IEEE 123节点配电网上的数值实验表明，我们的方法仅需少数几次迭代即可找到良好的可行解，并且能够很好地适配各种目标函数，即使在传统方法无法返回解的情形下也是如此。
英文摘要：
Many problems in power systems involve optimizing a certain objective function subject to power flow equations and engineering constraints. A long-standing challenge in solving them is the nonconvexity of their feasible sets. In this paper, we propose an analytical method to construct the convex restriction of the feasible set for AC power flows in radial networks. The construction relies on simple geometrical ideas and is explicit, in the sense that it does not involve solving other complicated optimization problems. We also show that the construct restrictions are in some sense maximal, that is, the best possible ones. Optimization problems constrained to these sets are not only simpler to solve but also offer feasibility guarantee for the solutions to the original OPF problem. Furthermore, we present an iterative algorithm to improve on the solution quality by successively constructing a sequence of convex restricted sets and solving the optimization on them. The numerical experiments on the IEEE 123-bus distribution network show that our method finds good feasible solutions within just a few iterations and works well with various objective functions, even in situations where traditional methods fail to return a solution.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
