QC松弛：最优潮流的理论和计算结果
The QC Relaxation: Theoretical and Computational Results on Optimal Power Flow
摘要：
近年来，潮流方程的凸松弛，特别是半定规划（SDP）和二阶锥（SOC）松弛，引起了人们极大的兴趣。二次凸（QC）松弛是一个偏离这些松弛的意义上，它施加约束，以保持更强的联系之间的电压变量通过凸包络的极坐标表示。本文系统地研究了带实际边约束的交流最优潮流的QC松弛问题。主要的理论结果表明，QC弛豫比SOC弛豫强，既不占主导地位，也不受SDP弛豫的支配。此外，全面的计算结果表明，QC松弛可以产生显着的改善，在SOC松弛在一个合理的计算成本的准确性，特别是对于网络的相位角差的严格限制。QC和SOC松弛也被证明是显着更快，更可靠的SDP松弛给定的当前状态的相应求解器相比。
英文摘要：
Convex relaxations of the power flow equations and, in particular, the Semi-Definite Programming (SDP) and Second-Order Cone (SOC) relaxations, have attracted significant interest in recent years. The Quadratic Convex (QC) relaxation is a departure from these relaxations in the sense that it imposes constraints to preserve stronger links between the voltage variables through convex envelopes of the polar representation. This paper is a systematic study of the QC relaxation for AC Optimal Power Flow with realistic side constraints. The main theoretical result shows that the QC relaxation is stronger than the SOC relaxation and neither dominates nor is dominated by the SDP relaxation. In addition, comprehensive computational results show that the QC relaxation may produce significant improvements in accuracy over the SOC relaxation at a reasonable computational cost, especially for networks with tight bounds on phase angle differences. The QC and SOC relaxations are also shown to be significantly faster and reliable compared to the SDP relaxation given the current state of the respective solvers.
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