  In the context of managing distributed energy resources (DERs) within
distribution networks (DNs), this work focuses on the task of developing local
controllers. We propose an unsupervised learning framework to train functions
that can closely approximate optimal power flow (OPF) solutions. The primary
aim is to establish specific conditions under which these learned functions can
collectively guide the network towards desired configurations asymptotically,
leveraging an incremental control approach. The flexibility of the proposed
methodology allows to integrate fairness-driven components into the cost
function associated with the OPF problem. This addition seeks to mitigate power
curtailment disparities among DERs, thereby promoting equitable power
injections across the network. To demonstrate the effectiveness of the proposed
approach, power flow simulations are conducted using the IEEE 37-bus feeder.
The findings not only showcase the guaranteed system stability but also
underscore its improved overall performance.
