A Study on the Strong Duality of Second-Order Conic Relaxation of AC Optimal Power Flow in Radial Networks
A Study on the Strong Duality of Second-Order Conic Relaxation of AC Optimal Power Flow in Radial Networks
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DOI：
10.1109/tpwrs.2021.3087639
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发表时间：
2022-01-01
影响因子：
6.6
通讯作者：
Zeng, Bo
中科院分区：
文献类型：
--
作者：
Cao, Xiaoyu;Wang, Jianxue;Zeng, Bo
对于径向网络中流行的交流最优潮流（OPF）的二阶二次曲线规划（SOCP）公式，本文首先表明它不具有一般的强对偶性。然后，通过一系列限制性的重新表述，我们推导出一组网络参数的封闭式充分条件，以确保其强对偶性。对 IEEE 33 总线、69 总线测试网络和两个现实世界配电系统的数值研究证实，该 SOCP 公式中确实存在不可忽略的对偶间隙，并且还证明了所提出的消除对偶间隙的充分条件的有效性。我们的结果提供了一个分析工具，以确保 SOCP 潮流公式的强大对偶性并支持其复杂扩展的算法开发。
For the popular second-order conic program (SOCP) formulation of AC optimal power flow (OPF) in a radial network, this paper first shows that it does not have the strong duality property in general. Then, through a series of restrictive reformulations, we derive a set of closed-form sufficient conditions on network parameters that ensure its strong duality. Numerical studies on IEEE 33-bus, 69-bus test networks and two real-world distribution systems confirm that non-negligible duality gaps do exist in this SOCP formulation, and also demonstrate the validity of the proposed sufficient conditions on closing the duality gap. Our results provide an analytical tool to ensure the strong duality of the SOCP power flow formulation and to support algorithm developments for its complex extensions.