Semidefinite relaxation techniques have shown great promise for nonconvex optimal power flow problems. However, a number of independent numerical experiments have led to concerns about scalability and robustness of existing SDP solvers. To address these concerns, we investigate some numerical aspects of the problem and compare different state-of-the-art solvers. Our results demonstrate that semidefinite relaxations of large problem instances with on the order of 10,000 buses can be solved reliably and to reasonable accuracy within minutes. Furthermore, the semidefinite relaxation of a test case with 25,000 buses can be solved reliably within half an hour; the largest test case with 82,000 buses is solved within 8 h. We also compare the lower bound obtained via semidefinite relaxation to locally optimal solutions obtained with nonlinear optimization methods and calculate the optimality gap.

中文翻译：

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关于最优潮流问题的半定松弛的鲁棒性和可扩展性

半定松弛技术已显示出非凸最优潮流问题的广阔前景。但是，许多独立的数值实验引起了对现有SDP求解器的可伸缩性和鲁棒性的担忧。为了解决这些问题，我们研究了问题的一些数值方面，并比较了不同的最新解决方案。我们的结果表明，可以在数分钟内可靠且以合理的精度解决大型问题实例（具有10,000辆公交车）的半确定松弛。此外，可以在半小时内可靠地解决具有25,000辆公交车的测试用例的半确定松弛问题。在8小时内解决了拥有82,000辆公交车的最大测试案例。