In recent years, there has been significant interest in the development of machine learning-based optimization proxies for AC Optimal Power Flow (AC-OPF). Although significant progress has been achieved in predicting high-quality primal solutions, no existing learning-based approach can provide valid dual bounds for AC-OPF. This paper addresses this gap by training optimization proxies for a convex relaxation of AC-OPF. Namely, the paper considers a second-order cone (SOC) relaxation of ACOPF, and proposes a novel dual architecture that embeds a fast, differentiable (dual) feasibility recovery, thus providing valid dual bounds. The paper combines this new architecture with a self-supervised learning scheme, which alleviates the need for costly training data generation. Extensive numerical experiments on medium- and large-scale power grids demonstrate the efficiency and scalability of the proposed methodology.

翻译：近年来，基于机器学习的交流最优潮流（AC-OPF）优化代理研究引起了广泛关注。尽管在预测高质量原始解方面取得了显著进展，但现有基于学习的方法均无法为AC-OPF提供有效的对偶界。本文通过训练针对AC-OPF凸松弛的优化代理来填补这一空白。具体而言，本文考虑二阶锥（SOC）松弛的AC-OPF，并提出一种新颖的对偶架构，该架构嵌入了快速且可微的（对偶）可行性恢复过程，从而提供有效的对偶界。本文将这一新架构与自监督学习框架相结合，无需生成昂贵的训练数据。在中等规模及大规模电力系统上的广泛数值实验验证了所提方法的效率与可扩展性。