# Accelerated Voltage Regulation in Multi-Phase Distribution Networks Based on Hierarchical Distributed Algorithm

## TL;DR

This paper introduces a hierarchical distributed algorithm for voltage regulation in large multi-phase distribution networks, significantly improving computational efficiency and scalability while maintaining optimality.

## Contribution

It presents a novel hierarchical distributed primal-dual gradient algorithm leveraging network structure and linearized power flow models for scalable OPF solutions.

## Key findings

- Achieves over 10-fold acceleration in convergence speed.
- Reduces computational loads compared to centralized methods.
- Demonstrates effectiveness on a 4,521-node test feeder.

## Abstract

We propose a hierarchical distributed algorithm to solve optimal power flow (OPF) problems that aim at dispatching controllable distributed energy resources (DERs) for voltage regulation at minimum cost. The proposed algorithm features unprecedented scalability to large multi-phase distribution networks by jointly exploring the tree/subtrees structure of a large radial distribution network and the structure of the linearized distribution power flow (LinDistFlow) model to derive a hierarchical, distributed implementation of the primal-dual gradient algorithm that solves OPF. The proposed implementation significantly reduces the computation loads compared to the centrally coordinated implementation of the same primal-dual algorithm without compromising optimality. Numerical results on a 4,521-node test feeder show that the designed algorithm achieves more than 10-fold acceleration in the speed of convergence compared to the centrally coordinated primal-dual algorithm through reducing and distributing computational loads.