大规模市场导向交流最优功率流的SDP、SOCP和QC凸松弛比较
Comparative Evaluation of SDP, SOCP, and QC Convex Relaxations for Large-Scale Market-Based AC Optimal Power Flow
AI总结：
本文比较了SDP、SOCP和QC松弛在大规模市场导向ACOPF中的性能，通过统一框架评估了不同松弛方法的求解质量、运行时间和内存消耗，为选择合适松弛方法提供了指导。
摘要：
交流最优功率流（ACOPF）问题在现代电力系统运行中至关重要，确定如何生成和传输电力以在尊重物理和运行约束的情况下最大化社会福利。然而，AC功率流方程的非线性和非凸性质使得在大规模网络中找到全局最优解在计算上是不可行的。凸松弛——包括半正定规划（SDP）、二次锥规划（SOCP）和二次凸（QC）公式——提供了可处理的替代方案，可以在适当条件下提供可证明最优或近似最优的解。本文对多个应用于市场导向福利最大化ACOPF的松弛进行了全面比较研究。我们使用MOSEK Fusion API在一个统一的求解器原生框架中实现了DCOPF、Shor的SDP松弛（复数和实数形式）、弦SDP、Jabr的SOCP松弛和QC松弛，消除了诸如CVXPY等高级框架中存在的建模开销。为了解决QC松弛所需的缺失或过于保守的角度差界限的实践挑战，我们采用准蒙特卡洛抽样与Sobol序列进行经验估计以获得更紧的界限。我们对来自ARPA-E数据集的大小不一的子网络进行了评估，系统比较了解决方案质量、运行时间和内存消耗。我们的结果展示了松弛紧密性和计算效率之间的权衡，为基于网络规模和解决方案需求选择适当公式提供了实用指导。
英文摘要：
The alternating current optimal power flow (ACOPF) problem is central to modern power system operations, determining how electricity is generated and transmitted to maximize social welfare while respecting physical and operational constraints. However, the nonlinear and non-convex nature of AC power flow equations makes finding globally optimal solutions computationally intractable for large networks. Convex relaxations - including semidefinite programming (SDP), second-order cone programming (SOCP), and quadratic convex (QC) formulations - provide tractable alternatives that can yield provably optimal or near-optimal solutions under appropriate conditions. This paper presents a comprehensive comparative study of multiple ACOPF relaxations applied to market-based welfare maximization. We implement DCOPF, Shor's SDP relaxation (complex and real-valued forms), chordal SDP, Jabr's SOCP relaxation, and QC relaxations in a unified, solver-native framework using the MOSEK Fusion API, eliminating modeling overhead present in high-level frameworks such as CVXPY. To address the practical challenge of missing or overly conservative angle difference bounds required by QC relaxations, we employ quasi-Monte Carlo sampling with Sobol sequences to empirically estimate tighter bounds. We evaluate these relaxations on subnetworks of varying sizes derived from the ARPA-E dataset, systematically comparing solution quality, runtime, and memory consumption. Our results demonstrate the trade-offs between relaxation tightness and computational efficiency, providing practical guidance for selecting appropriate formulations based on network scale and solution requirements.
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。
