Hierarchical stability-constrained co-optimization and adaptive protection of microgrids with hybrid storage and power-to-hydrogen assets via proximal bundle decomposition and holomorphic embedding

• Tested on modified distribution systems from 33 to 132 buses. • Integrates economic dispatch, stability, and adaptive protection. • Coordinates multi-energy resources and hybrid storage. • Maintains protection selectivity under dynamic operation. • Enables scalable near-real-time microgrid optimization. The increasing penetration of inverter-based renewable resources and emerging energy assets introduces significant operational and stability challenges in modern microgrids. This paper proposes a tri-level hierarchical optimization framework for coordinated economic dispatch, dynamic stability enhancement, and adaptive protection coordination in inverter-dominated microgrids. The framework integrates multiple energy resources, including hybrid energy storage systems, electric vehicles with vehicle-to-grid capability, and power-to-hydrogen conversion technologies, within a unified operational structure. To efficiently handle the non-convex stability and protection constraints, a solution strategy combining Proximal Bundle Decomposition with the Holomorphic Embedding Method (HEM) is developed, enabling accurate stability assessment without relying on computationally expensive time-domain simulations. The proposed approach is validated on modified IEEE distribution test systems representing practical microgrid configurations. Simulation results demonstrate that the proposed framework improves the overall operational performance of the microgrid by reducing operational cost while simultaneously enhancing voltage and frequency stability margins and maintaining reliable protection coordination under varying operating conditions. A statistical analysis over multiple operating scenarios (with varying load and renewable profiles) confirms that these improvements are robust and statistically significant. The results also show improved system resilience against disturbances and better utilization of distributed energy resources compared with conventional optimization approaches. These findings confirm that the proposed hierarchical framework provides an effective and computationally efficient solution for the coordinated management of future inverter-dominated microgrids.