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We propose a novel algorithm to solve optimal power flow (OPF) that aims atdispatching controllable distributed energy resources (DERs) for voltageregulation at minimum cost. The proposed algorithm features unprecedentedscalability to large distribution networks by utilizing an informationstructure based on networked autonomous grids (AGs). Specifically, each AG is asubtree of a large distribution network that has a tree topology. The topologyand line parameters of each AG are known only to a regional coordinator (RC)that is responsible for communicating with and dispatching the DERs within thisAG. The reduced network, where each AG is treated as a node, is managed by acentral coordinator (CC), which knows the topology and line parameters of thereduced network only and communicates with all the RCs. We jointly explore thisinformation structure and the structure of the linearized distribution powerflow (LinDistFlow) model to derive a hierarchical, distributed implementationof the primal-dual gradient algorithm that solves the OPF. The proposedimplementation significantly reduces the computation burden compared to thecentrally coordinated implementation of the primal-dual algorithm. Numericalresults on a 4,521-node test feeder show that the proposed hierarchicaldistributed algorithm can achieve an improvement of more than tenfold in thespeed of convergence compared to the centrally coordinated primal-dualalgorithm.

Hierarchical Distributed Voltage Regulation in Networked Autonomous Grids