\begin{document}


\title{Data-Driven Decentralized Optimal Power Flow For Distributed Energy Services in Distribution Grids}


\author{Roel~Dobbe,~Oscar~Sondermeijer,~David~Fridovich-Keil,~Daniel~Arnold, Duncan~Callaway~and~Claire~Tomlin

\thanks{R. Dobbe, D Fridovich-Keil and C. Tomlin are with the Department
of Electrical Engineering \& Computer Sciences, UC Berkeley, Berkeley, CA 94702 USA e-mail: dobbe@berkeley.edu. D. Arnold is with the Grid Integration Group at Lawrence Berkeley National Laboratory. D. Callaway is with the Energy \& Resources Group at UC Berkeley.}
\thanks{Manuscript received June 2018.}}


\maketitle


\begin{abstract}


The implementation of optimal power flow (OPF) methods to perform voltage and power flow regulation in electric networks is generally believed to require extensive 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 enables the analysis of how well the resulting fully decentralized control policies are able to reconstruct the OPF solution.
The methodology provides a natural extension to decide what nodes 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, focusing on DERs that do not exhibit intertemporal dependencies.
It provides a framework for Distribution System Operators to efficiently plan and operate the contributions of DERs to active distribution networks.


\end{abstract}


\IEEEpeerreviewmaketitle


\input{introduction}


\input{opf}

\input{ratedistortion}

\input{regression}

\input{results}

\input{discussion}

\input{conclusions}


\section*{Acknowledgments}
We thank Michael Sankur for contributions to the code base for this work. This work is supported by the National Science Foundation’s CPS FORCES Grant (award number CNS-1239166) and the UC-Philippine-California Advanced Research Institute (award number IIID-2015-10).


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