A tri-level hierarchical optimization framework for smart homes, microgrids, and distribution networks with hydrogen integration using a distributed ADMM approach

This paper proposes a tri-level hierarchical optimization framework to coordinate decision-making in modern power distribution systems with high penetrations of distributed energy resources (DERs). In the bottom tier (Level 1), individual smart homes optimize local photovoltaic generation, battery storage, and electric vehicle charging to reduce costs or enhance self-consumption. Microgrids (Level 2) aggregate household decisions, share resources such as wind turbines and fuel cells, and allow peer-to-peer energy trading. At the top tier (Level 3), the distribution system operator (DSO) dispatches centralized generation, enforces line limits, and defines price signals or incentives to maintain overall reliability. Because direct solution of this large-scale Mixed-Integer Linear Program is computationally challenging, the tri-level problem is decomposed via a Hierarchical Distributed ADMM (Hier-ADMM) algorithm. Numerical results on the IEEE 33-bus and 69-bus feeders show that the proposed tri-level approach consistently outperforms both fully decentralized and simpler two-level methods. In the 33-bus system, total daily operating costs fall by about 12 % relative to a fully decentralized baseline, while network losses drop from 4.1 to 3.3 % and peak line loading improves from 90 to 80 %. The extended 69-bus test confirms the method's scalability: even with over 400 smart homes and eight microgrids, the algorithm converges in under two hours and lowers daily operating costs by around 10 % compared to uncoordinated operation. These coordinated scheduling decisions leverage localized storage, demand response, and peer-to-peer trades to reduce peak imports and system congestion. The results demonstrate that tri-level hierarchical coordination provides a flexible, computationally tractable solution for integrating distributed resources effectively in large-scale distribution networks.