Security-Constrained Optimal Power Flow (SCOPF) plays a crucial role in power
grid stability but becomes increasingly complex as systems grow. This paper
introduces PDL-SCOPF, a self-supervised end-to-end primal-dual learning
framework for producing near-optimal solutions to large-scale SCOPF problems in
milliseconds. Indeed, PDL-SCOPF remedies the limitations of supervised
counterparts that rely on training instances with their optimal solutions,
which becomes impractical for large-scale SCOPF problems. PDL-SCOPF mimics an
Augmented Lagrangian Method (ALM) for training primal and dual networks that
learn the primal solutions and the Lagrangian multipliers, respectively, to the
unconstrained optimizations. In addition, PDL-SCOPF incorporates a repair layer
to ensure the feasibility of the power balance in the nominal case, and a
binary search layer to compute, using the Automatic Primary Response (APR), the
generator dispatches in the contingencies. The resulting differentiable program
can then be trained end-to-end using the objective function of the SCOPF and
the power balance constraints of the contingencies. Experimental results
demonstrate that the PDL-SCOPF delivers accurate feasible solutions with
minimal optimality gaps. The framework underlying PDL-SCOPF aims at bridging
the gap between traditional optimization methods and machine learning,
highlighting the potential of self-supervised end-to-end primal-dual learning
for large-scale optimization tasks.

PDL-SCOPF 是一种自我监督的端到端原始 - 对偶学习框架，用于以毫秒级生成大规模 SCOPF 问题的接近最优解。该框架旨在通过结合传统优化方法和机器学习，缩小大规模优化任务之间的差距。

大规模预防性安全约束的自监督学习直流最优潮流

Self-Supervised Learning for Large-Scale Preventive Security Constrained  DC Optimal Power Flow

This paper studies how to train machine-learning models that directly
approximate the optimal solutions of constrained optimization problems. This is
an empirical risk minimization under constraints, which is challenging as
training must balance optimality and feasibility conditions. Supervised
learning methods often approach this challenge by training the model on a large
collection of pre-solved instances. This paper takes a different route and
proposes the idea of Primal-Dual Learning (PDL), a self-supervised training
method that does not require a set of pre-solved instances or an optimization
solver for training and inference. Instead, PDL mimics the trajectory of an
Augmented Lagrangian Method (ALM) and jointly trains primal and dual neural
networks. Being a primal-dual method, PDL uses instance-specific penalties of
the constraint terms in the loss function used to train the primal network.
Experiments show that, on a set of nonlinear optimization benchmarks, PDL
typically exhibits negligible constraint violations and minor optimality gaps,
and is remarkably close to the ALM optimization. PDL also demonstrated improved
or similar performance in terms of the optimality gaps, constraint violations,
and training times compared to existing approaches.

本文研究了如何训练机器学习模型直接逼近受约束优化问题的最优解，提出了一种新的自监督训练方法 Primal-Dual Learning（PDL），该方法不需要预先解决实例集合或优化程序来进行训练和推理，而是同时训练原始神经网络和对偶神经网络来模仿增广 Lagrangian 方法的轨迹，实验证明 PDL 在非线性优化基准测试中表现出极小的约束违规和微小的最优性差距，与 ALM 优化非常接近，并且在最优性差距、约束违规和训练时间方面表现出更好或相似的性能。