Modern power grids have become increasingly complex, with greater uncertainty

due to the widespread integration of renewable energy resources potentially

leading to higher operating costs. The optimal operation of these networks can

be accomplished using optimal power flow (OPF), a fundamental optimisation

tool for power networks with objectives including generation cost minimisation.

Whilst the OPF problem itself is not new, quickly solving problems of a practical

scale remains an active research area. Two approaches here are distributed

optimisation and, more recently, machine learning (ML). Distributed optimisation

improves scalability, avoids single points of failure, and enhances user

privacy, whilst ML has the potential to provide solutions significantly faster

than traditional optimisation methods.

The goal of this review is to present approaches which overlap both areas, identifying

complementary aspects as well as areas for further exploration. For example,

one drawback of the alternating direction method of multipliers (ADMM),

a distributed optimisation algorithm, is that it has slow convergence. Several reviewed

papers have mitigated this, using ML to accelerate convergence through

the prediction of consensus variable values, demonstrating improvements in

terms of convergence time. Challenges remain, including the generalisation of

results across different network topologies, something with the potential to be

addressed with additional ML models such as graph neural networks (GNNs).

Further areas to explore at the intersection of these two areas are identified, including

augmented Lagrangian alternating direction inexact Newton (ALADIN)

and overlapping Schwarz decomposition optimisation methods and ML models

such as GNNs and physics-informed neural networks (PINNs).