Decentralized, Centralized, and Hierarchical Coordination of Residential DERs in Three-Phase Unbalanced Distribution Networks: A Comparative Analysis

The increasing use of residential distributed energy resources (DERs), including photovoltaic generation, electric vehicles, stationary batteries, and flexible electric water heaters, is changing the operation of low-voltage distribution networks. These resources can reduce household electricity costs and provide demand-side flexibility; however, uncoordinated operation can result in voltage deviations, network congestion, line overloading, and stress on distribution transformers. This paper presents a code-grounded comparison of three DER coordination architectures: decentralized household-level optimization, centralized feeder-level optimal power flow (OPF), and hierarchical aggregator-based coordination. The benchmark is conducted on a three-phase low-voltage distribution network with 157 residential households over a 24-hour horizon. The decentralized architecture optimizes each household individually, and the resulting network behavior is validated in OpenDSS. In the centralized architecture, detailed household DER models are integrated into a nonlinear AC-OPF formulation. The hierarchical architecture coordinates prosumer flexibility using local flexibility estimation, network-level activation, allocation, household-level tracking, and final OpenDSS validation. For the studied feeder, the results indicate that the hierarchical architecture provides the most favorable physically validated trade-off between customer economics and network performance among the three architectures considered. Compared with decentralized control, it decreases the mean daily household electricity cost from 6.74 to 6.14 GBP/home/day (an 8.9% reduction), reduces network peak demand by 20.4%, reduces the worst line-loading ratio by 15.3%, and reduces transformer loading by 19.0%. In this case study, all 157 households obtain lower daily electricity bills than under the decentralized baseline, indicating that the incentive-based coordination mechanism can align network-level objectives with individual customer benefits under the modeled conditions. The centralized OPF achieves the strongest nominal network performance but relies on restrictive assumptions regarding full DER observability and controllability and does not provide the same customer-level autonomy, compensation, or implementation pathway as the hierarchical framework; it is therefore treated as an idealized network benchmark rather than a directly deployable controller. It should be noted that the hierarchical architecture reduces, but does not fully eliminate, network constraint violations and that these findings are obtained for a single feeder under deterministic daily input profiles. Overall, the results suggest that DER coordination strategies should be assessed using a holistic framework that considers customer cost, network security, flexibility realization, fairness, computational effort, and physical validation, and that, under this broader evaluation, hierarchical coordination offers a practical compromise between decentralized autonomy and centralized optimality for the studied network.