Microgrids equipped with distributed renewable energy resources, energy storage systems, controllable loads, and vehicle-to-grid (V2G) technologies have emerged as critical enablers for sustainable energy transitions. However, their effective integration into day-ahead electricity markets requires advanced decentralized coordination mechanisms that ensure both robust scheduling under uncertainty and the preservation of agent privacy. Hence, this paper introduces a two-layer optimization framework to coordinate residential and industrial microgrids with the distribution network operator (DNO), addressing economic, technical, and environmental objectives. The proposed model employs an enhanced alternating direction method of multipliers (ADMM) algorithm, which dynamically adjusts power exchange prices based on carbon tax rates. This approach incentivizes low-carbon operations while preserving the confidentiality of internal microgrid schedules. Residential and industrial microgrids perform day-ahead scheduling in the first layer by leveraging the flexible capacities of their diverse technologies. Subsequently, they submit their desired exchange plans for participation in the day-ahead electricity market to the DNO in the second layer, where the feasibility of their implementation is evaluated. The model was validated on a 123-bus electricity distribution network comprising 32 residential microgrids and 17 industrial microgrids. The results demonstrated its effectiveness, achieving a 12.19 % reduction in carbon emissions and a 11.24 % decrease in operational costs. Furthermore, the proposed enhanced ADMM reduced convergence time by 43.16 % compared to the standard ADMM, significantly expediting coordination among decentralized agents in day-ahead markets.

The increasing frequency of environmental events driven by global warming poses a significant threat to smart network operations, highlighting the need for advanced self-healing techniques to enhance grid stability and accelerate recovery during emergencies. This study proposes a two-stage distributed optimization mechanism for self-healing in coupled electricity and gas networks. The mechanism leverages the capabilities of smart prosumers, such as industrial parks, charging stations, and power-to-hydrogen (P2H) units, to minimize load shedding and bolster resilience under emergency conditions. In the first stage, the distribution system operator optimally reconfigures electricity and gas networks, plans distribution feeder operations, and deploys fuel cell-equipped trucks to allocate the required power and gas capacities to smart prosumers via signal pulses. The second stage focuses on modeling the smart prosumers, enabling them to offer their available capacities to the network operator in response to these signals. To ensure secure convergence with minimal information exchange between the two stages, an augmented Alternating Direction Method of Multipliers (ADMM) algorithm is utilized. The proposed mechanism was validated on two different test systems, solved using the GUROBI solver within GAMS. Simulation results demonstrate that the mechanism effectively harnesses maximum capacities from smart prosumers, reducing load shedding by 64.08 % and improving the resilience index by 80.34 %. Furthermore, the augmented ADMM enhanced computational efficiency, achieving a 45.3 % faster solution compared to the standard version while ensuring global optimality.