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.

中文翻译：

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基于分层分布算法的多相配电网加速调压

我们提出了一种分层分布式算法来解决最优潮流 (OPF) 问题，该算法旨在以最低成本调度可控分布式能源 (DER) 进行电压调节。所提出的算法通过联合探索大型径向配电网络的树/子树结构和线性化配电潮流 (LinDistFlow) 模型的结构，以推导出原始的分层分布式实现，从而对大型多相配电网络具有前所未有的可扩展性。 -解决OPF的双梯度算法。与相同原始对偶算法的中央协调实现相比，所提出的实现显着减少了计算负载，而不会影响最优性。4 上的数值结果，