reviews: 
Comments: This paper presents a graph neural network architecture for solving AC Optimal Power Flow models.
The paper describes a physics-informed loss for training the model in a self-supervised manner, and conducts numerical experiments on systems with up to 118 buses.
Strengths: The proposed methodologies has two positive aspects
* it uses a graph-based architecture, which supports changes in grid topology (however this capability was not demonstrated)
* it uses a self-supervised training scheme that does not require the (expensive) use of an optimization solver to generate data

However, neither of these are new, and the paper suffers from multiple limitations (see below).
Weaknesses: Limitations of the methodologies / experiments:

* The paper incorrectly states that previous works do not handle multiple generators per bus.
  * _Confidence-Aware Graph Neural Networks for Learning Reliability Assessment Commitments_ (https://doi.org/10.1109/TPWRS.2023.3298735) consider graph neural network architectures for unit-commitment problems, and present an encoder-based mechanism for handling multiple generators per bus
  * _CANOS: A Fast and Scalable Neural AC-OPF Solver Robust To N-1 Perturbations_ (https://arxiv.org/abs/2403.17660) does support such features:
    _We also use artificial edges to connect the subnodes to their respective bus (these do not model any physical equipment)._
  * It should be noted that handling multiple generators at a single bus is not a hard task, as they can easily be aggregated into a single generator; an aggregated solution can then be disaggregated in closed-form.

* I believe the augmented Lagrangian in Eq. (5) is incorrect, specifically the term $\mu_{k} g_{j}(w_{u}^{k})^2$.
  Assuming inequality constraints are of the form $g(w) \leq 0$, this quadratic term effectively drives all inequality constraints towards being binding (i.e. $g(w) = 0$), which is not theoretically sound.

* The paper argues that the use of a graph neural network supports changes in the grid topology, but does not present experiments that corroborate this claim

* The paper claims that the proposed model can achieve "zero violation of inequality constraints." This is not a substantial achievement, given that said inequality constraints are either simple variable bounds (which can be enforced via a bounded activation function) or simple l2 norm constraint (which can also be enforced by a simple scheme). The complexity of AC-OPF is in satisfying _both_ equality and inequality constraints. It is straightforward to enforced either set of constraints separately (i.e. only equality or only inequality constraints).

* Numerical experiments consider AC-OPF instances on systems with up to 118 buses. This is 100x smaller than real-life instances, which comprise (at least) in the order of 10,000 buses. 

  It should be noted that several works have trained ML models to predict AC-OPF with systems of that scale:
  * _Spatial Network Decomposition for Fast and Scalable AC-OPF Learning_ (https://doi.org/10.1109/TPWRS.2021.3124726)
  * _Compact optimization learning for AC Optimal Power Flow_ (https://arxiv.org/abs/2301.08840): up to 30,000 buses
  * _CANOS: A Fast and Scalable Neural AC-OPF Solver Robust To N-1 Perturbations_ (https://arxiv.org/abs/2403.17660): up to 10,000 buses, and also uses graph neural network architectures

* Training times appear to be very large (10 to 24 hours as reported in Section 5). Given that the paper only considers very small artificial systems, it is not clear that the proposed scheme would scale to real-life systems. A reasonable target would be at most 6-8hrs of training time on a systems with about 10,000 buses.

* Numerical experiments do not compare against any existing ML methodology for AC-OPF problems.

Issues about the paper:
* Not all notations are properly defined. For instance, the formalism of equality and inequality constraints is not defined before the Augmented Lagrangian presented in Eq. (5). Similarly, this equation uses a parameter $w^{k}_{u}$ that is not defined.
* the paper does not present the data distribution used to train the model. It should be noted that generating data by perturbing individual loads independently is not realistic, as it leads to a very narrow variability in total demand.

  Note that there are open-source datasets and data generators for AC-OPF problems, e.g.:
  * OPFData (https://arxiv.org/html/2406.07234v1) is an open-source dataset of AC-OPF instances and their solutions
  * OPFGenerator (https://github.com/AI4OPT/OPFGenerator) is an open-source instance generator for various OPF formulations

* In addition to the comments, above, the paper sometimes makes misleading claims. For instance, at lines 88-89, it is stated that "INCO allows for solving the AC-OPF **without violations**." This claim is not substantiated by the results reported in Section 4 (Tables 1 and 2).
Recommendation: 1
Reviewer confidence: 5
Soundness/correctness: 2
Clarity: 1