The existence of multiple solutions to AC optimal power flow (ACOPF) problems has been noted for decades. Existing solvers are generally successful in finding local solutions, which are stationary points but may not be globally optimal. In this paper, we propose a simple iterative approach to find globally optimal solutions to ACOPF problems. First, we call an existing solver for the ACOPF problem. From the solution and the associated dual variables, we form a partial Lagrangian. Then we optimize this partial Lagrangian and use its solution as a warm start to call the solver again for the ACOPF problem. By repeating this process, we can iteratively improve the solution quality, moving from local solutions to global ones. We show the effectiveness our algorithm on standard IEEE networks. The simulation results show that our algorithm can escape from local solutions to achieve global optimums within a few iterations.

中文翻译：

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寻找交流最优潮流问题全局解的迭代方法

几十年来，人们已经注意到了针对交流最佳功率流（ACOPF）问题的多种解决方案。现有的求解器通常可以成功地找到局部解，这些局部解是固定点，但可能不是全局最优的。在本文中，我们提出了一种简单的迭代方法来找到ACOPF问题的全局最优解。首先，我们将现有的求解器称为ACOPF问题。根据解和相关的对偶变量，我们形成了局部拉格朗日方程。然后，我们优化此部分拉格朗日方法，并将其解用作热启动，再次针对ACOPF问题调用求解器。通过重复此过程，我们可以迭代地提高解决方案质量，从本地解决方案过渡到全局解决方案。我们展示了我们的算法在标准IEEE网络上的有效性。