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This paper presents experimental validation of a distributed optimization-based voltage control system. The dual-decomposition method is used in this paper to solve the voltage optimization problem in a fully distributed way. Device-to-device communication is implemented to enable peer-to-peer data exchange between agents of the proposed voltage control system. The paper presents the design, development and hardware setup of a laboratory-based testbed used to validate the performance of the proposed dual-decomposition-based peer-to-peer voltage control. The architecture of the setup consists of four layers: microgrid, control, communication, and monitoring. The key question motivating this research was whether distributed voltage control systems are a technically effective alternative to centralized ones. The results discussed in this paper show that distributed voltage control systems can indeed provide satisfactory regulation of the voltage profiles.

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This report serves as a technology description of a Julia-based re-implementation of the fixed-point current injection algorithm, available in PowerModelsDistribution.jl [1]. This report does not describe a novel method for solving unbalanced power flow problems. It merely provides a description of the fixed point iteration variant of the current injection method, inspired by the existing open-source implementation in OpenDSS 1 [2]. The current injection method is commonly conceived as a system of nonlinear equalities solved by Newton's method [3,4]. However, as Roger Dugan points out in the OpenDSS documentation, the fixed point iteration variant commonly outperforms most methods, while supporting meshed topologies from the ground up.We note that the unbalanced power flow algorithm in turn relies on matrix solvers for sparse systems of equations. In the context of circuits and factorizing nodal admittance matrices, the sparsity-exploiting 'KLU' solver [5] has proven to be both reliable and scalable. OpenDSS uses KLU.This report documents work-in-progress, and the authors aim to update it when learnings are obtained or more features are added to the implementation in PowerModelsDistribution.jl. The authors invite collaborators to contribute through pull requests on the repository 2 .

Due to the rising renewable penetration rate, modern low voltage distribution network (LVDN) calls for active control with tractable computation and limited communication. To tackle this, the paper proposes a novel stochastic distributed optimization approach. The computation of optimum is completely decentralized, with a global broadcast signal is used as public reference in order to guarantee the consistency among individual shapeable energy resources. The proposed approach employs Bernoulli trials to imitate the searching process in classical gradient descent approach, and player compatible relationship is employed to play the role of gradients to indicate the direction of the search. Working in a model-free manner without relying on iterations, the proposed approach offers an approximate optimization to minimize the accumulated compensation of reshaping/deferring the shapeable energy resources in a given LVDN while respecting the system constraints. A 103 nodes test network based on a realistic Belgian semi-urban distribution network is used for validation. With two different profiles and a special case of communication failure, the proposed approach is validated and benchmarked with a classical AC optimal power flow algorithm. The results prove that the proposed approach is able to deliver a good approximation to the theoretical optimum with reasonable gap.

This paper develops a novel nonconvex formulation of the unbalanced power flow equations. This formulation extends the lifted nonconvex 'DistFlow' a.k.a. balanced branch flow model formulation to the unbalanced case. The feasible set is characterized by linear and nonconvex quadratic equations in matrix variables. It is shown that this formulation is equivalent to previously published rank-constrained semidefinite programming formulations. The formulation is implemented and compared numerically with rectangular and polar versions of the nonlinear AC unbalanced optimal power flow problem.

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