支路潮流模型：松弛与凸化（第I、II部分）
Branch Flow Model: Relaxations and Convexification (Parts I, II)
AI总结：
提出支路潮流模型，通过两步松弛（角度松弛和锥松弛）高效求解最优潮流问题，证明辐射状网络松弛精确，网状网络通过移相器凸化可保证全局最优。
摘要：
我们提出了一种用于网状和辐射状网络分析与优化的支路潮流模型。该模型导致了一种解决最优潮流（OPF）的新方法，包括两个松弛步骤。第一步消除电压和电流角度，第二步将所得问题近似为一个可以高效求解的锥规划。对于辐射状网络，我们证明只要负载没有上界，两个松弛步骤总是精确的。对于网状网络，锥松弛总是精确的，但角度松弛可能不精确，我们提供了一种简单方法来判断松弛解是否为全局最优。我们提出使用移相器对网状网络进行凸化，使得凸化后的网络的最优潮流问题总能高效求解。我们证明凸化只需要在网络的一棵生成树之外放置移相器，且其位置仅取决于网络拓扑，而非潮流、发电、负载或运行约束。第I部分介绍了我们的支路潮流模型，解释了两个松弛步骤，并证明了精确松弛的条件。第II部分描述了网状网络的凸化，并给出了仿真结果。
英文摘要：
We propose a branch flow model for the anal- ysis and optimization of mesh as well as radial networks. The model leads to a new approach to solving optimal power flow (OPF) that consists of two relaxation steps. The first step eliminates the voltage and current angles and the second step approximates the resulting problem by a conic program that can be solved efficiently. For radial networks, we prove that both relaxation steps are always exact, provided there are no upper bounds on loads. For mesh networks, the conic relaxation is always exact but the angle relaxation may not be exact, and we provide a simple way to determine if a relaxed solution is globally optimal. We propose convexification of mesh networks using phase shifters so that OPF for the convexified network can always be solved efficiently for an optimal solution. We prove that convexification requires phase shifters only outside a spanning tree of the network and their placement depends only on network topology, not on power flows, generation, loads, or operating constraints. Part I introduces our branch flow model, explains the two relaxation steps, and proves the conditions for exact relaxation. Part II describes convexification of mesh networks, and presents simulation results.
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。
