The implementation of optimal power flow (OPF) methods to perform voltage and power flow regulation in electric networks is generally believed to require communication. We consider distribution systems with multiple controllable Distributed Energy Resources (DERs) and present a data-driven approach to learn control policies for each DER to reconstruct and mimic the solution to a centralized OPF problem from solely locally available information. Collectively, all local controllers closely match the centralized OPF solution, providing near-optimal performance and satisfaction of system constraints. A rate distortion framework facilitates the analysis of how well the resulting fully decentralized control policies are able to reconstruct the OPF solution. Our methodology provides a natural extension to decide what buses a DER should communicate with to improve the reconstruction of its individual policy. The method is applied on both single- and three-phase test feeder networks using data from real loads and distributed generators. It provides a framework for Distribution System Operators to efficiently plan and operate the contributions of DERs to active distribution networks.
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