  Machine learning assisted optimal power flow (OPF) aims to reduce the
computational complexity of these non-linear and non-convex constrained
optimization problems by consigning expensive (online) optimization to offline
training. The majority of work in this area typically employs fully connected
neural networks (FCNN). However, recently convolutional (CNN) and graph (GNN)
neural networks have also been investigated, in effort to exploit topological
information within the power grid. Although promising results have been
obtained, there lacks a systematic comparison between these architectures
throughout literature. Accordingly, we introduce a concise framework for
generalizing methods for machine learning assisted OPF and assess the
performance of a variety of FCNN, CNN and GNN models for two fundamental
approaches in this domain: regression (predicting optimal generator set-points)
and classification (predicting the active set of constraints). For several
synthetic power grids with interconnected utilities, we show that locality
properties between feature and target variables are scarce and subsequently
demonstrate marginal utility of applying CNN and GNN architectures compared to
FCNN for a fixed grid topology. However, with variable topology (for instance,
modeling transmission line contingency), GNN models are able to
straightforwardly take the change of topological information into account and
outperform both FCNN and CNN models.
