Distributed energy system design including unbalanced AC power flow for large LV networks with ADMM

With the addition of large numbers of distributed energy resources (DERs) to distribution networks comes the increasing risk that their operation may violate the safety constraints of these networks. The problem considered in this paper is that of combined siting, sizing and dispatch of these DERs, also known as distributed energy system (DES) design, to help meet electrical and heat loads within the network. Here, the operation of these DERs is modelled, along with the unbalanced three-phase alternating current (AC) power flow in the network. When this network power flow is considered, it admits a non-convex mixed-integer nonlinear program (MINLP) model formulation which scales poorly with network size in terms of solve time. To address this, the problem is decomposed into a series of algorithmic steps, between the binary decision variables and the nonlinear power flow constraints. Where solve times still remain unacceptably high for large problem sizes however, a further hybrid spatial/temporal decomposition strategy is presented, and solved with an alternating direction method of multipliers (ADMM)-based distributed optimisation method. The novelty of this approach therefore lies in enabling the applicability of this method to large-scale problem instances in a scalable manner. Results are presented for networks with up to 55 loads and 120 timepoints, with the ADMM approach showing speed-ups of up to 13 x when considering parallel computation of the subproblems, for a maximum observed optimality gap of 0.61 % .