Robust and Efficient AC Optimal Power Flow Algorithm Based on Augmented Quotient Gradient Systems

王志远; 李腾木; 吕宪龙; 刘志彬; 王琦; 江晓东

doi:10.13334/j.0258-8013.pcsee.241621

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Robust and Efficient AC Optimal Power Flow Algorithm Based on Augmented Quotient Gradient Systems

更新时间：2026-02-06

- Robust and Efficient AC Optimal Power Flow Algorithm Based on Augmented Quotient Gradient Systems
- Vol. 46, Issue 2, Pages: 532-544(2026)
- 作者机构：
  
  1. 南京师范大学电气与自动化工程学院,江苏省,南京市,210023
  2. 天津大学电气自动化与信息工程学院，天津市南开区,300072
  3. 济南大学自动化与电气工程学院,山东省,济南市,250001
  4. 美国康奈尔大学，美国伊萨卡,14850
- 作者简介：
- 基金信息：
- DOI：10.13334/j.0258-8013.pcsee.241621
  CLC：
- Published：2026
- 稿件说明：
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王志远, 李腾木, 吕宪龙, et al. Robust and Efficient AC Optimal Power Flow Algorithm Based on Augmented Quotient Gradient Systems[J]. 2026, 46(2): 532-544.
DOI：

王志远, 李腾木, 吕宪龙, et al. Robust and Efficient AC Optimal Power Flow Algorithm Based on Augmented Quotient Gradient Systems[J]. 2026, 46(2): 532-544. DOI： 10.13334/j.0258-8013.pcsee.241621.

摘要

由于交流最优潮流(optimal power flow，OPF)问题的非凸性，如何鲁棒快速地获得最优解仍然是最优潮流方法面临的一个挑战，而且往往存在收敛性问题。该文提出一种计算交流最优潮流最优解的增广商梯度系统方法(augmented quotient gradient system，AQGS)。通过提出的非线性动力系统QGS，可以将最优解的求解转换为对增广商梯度系统的常规稳定平衡点的搜索，进一步应用动力学系统的丰富理论和优良性质。理论结果表明，增广商梯度系统是完全稳定的，因此从根本上解决了交流最优潮流求解算法数值收敛性问题。从计算的角度来看，该方法的收敛性和计算速度在大量算例尤其是大规模算例中，例如1 888，4 661和13 659节点系统，均优于IPOPT求解器，在2~13 659节点规模的算例中均实现了完全收敛。

Abstract

Due to the non-convex of the AC optimal power flow (OPF) problem

obtaining the optimal solution robustly and efficiently remains a challenge for AC OPF methods

and often encountering convergence issues. This paper proposes an augmented quotient gradient system (AQGS) method for computing optimal solutions of AC OPF. By introducing the nonlinear dynamic AQGS system

the solution of the OPF is transformed into the search for its regular stable equilibrium points. The theoretical results indicate the AQGS is globally asymptotically stable

which fundamentally addresses numerical convergence issues in the algorithm. From a computational perspective

the method exhibits superior convergence and computational efficiency in numerous cases

particularly in large-scale instances such as 1 888

4 661

and 13 659-bus systems

outperforming the IPOPT solver. The method achieves complete solution success across instances ranging from 2 to 13 659 buses.

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