Electricity markets rely on the rapid solution of the optimal power flow (OPF) problem to determine generator power levels and set nodal prices. Traditionally, the OPF problem has been formulated using linearized, approximate models, ignoring nonlinear alternating current (AC) physics. These approaches do not guarantee global optimality or even feasibility in the real ACOPF problem.

We introduce an outer-approximation approach to solve the ACOPF problem to global optimality based on alternating solution of upper- and lower-bounding problems. The lower-bounding problem is a piecewise relaxation based on strong second-order cone relaxations of the ACOPF, and these piecewise relaxations are selectively refined at each major iteration through increased variable domain partitioning. Our approach is able to efficiently solve all but one of the test cases considered to an optimality gap below 0.1%. Furthermore, this approach opens the door for global solution of MINLP problems with AC power flow equations.

电力市场依靠最佳潮流（OPF）问题的快速解决方案来确定发电机的功率水平并设定节点价格。传统上，OPF问题是使用线性化的近似模型来表述的，而忽略了非线性交流（AC）物理原理。这些方法不能保证在实际的ACOPF问题中具有全局最优性，甚至不能保证其可行性。

我们引入一种外部近似方法，基于上下界问题的交替解决方案，将ACOPF问题求解为全局最优。下界问题是基于ACOPF的强二阶圆锥松弛的分段松弛，这些分段松弛通过增加可变域划分在每次主要迭代中被选择性地完善。我们的方法能够有效地解决所有测试案例，但其中一个被认为具有小于0.1％的最佳差距。此外，这种方法为使用交流潮流方程式的MINLP问题的整体解决方案打开了大门。