Bridging Market Efficiency and System Resilience: Unified Multi-Service Operation of Long-Duration Energy Storage in Decarbonized Power Systems

The rapid growth of variable renewable generation and the increasing frequency of extreme events demand power systems that are both economical and resilient. Long-duration energy storage (LDES) stands out as a unique solution, capable of shifting energy across multiple days while providing critical support during large-scale outages. However, our review of existing approaches highlights critical gaps: market operations and system restoration are typically optimized in isolation, and the technology-specific characteristics of LDES make their coordinated use especially challenging. We first investigate these challenges, including efficiency-capacity trade-offs, duration mismatches, and restoration-sequence dependencies, and underscore the need for an integrated framework. To address this gap, this paper introduces a unified multi-service optimization model that co-optimizes LDES for both economic and resilience objectives within a single mixed-integer linear program. The formulation combines energy arbitrage, capacity adequacy, and renewable integration with resilience metrics based on avoided unserved energy and a priority-based restoration mechanism capturing spatiotemporal re-energization and progressive load pickup. Multi-objective Pareto analysis reveals cost-resilience trade-offs, providing actionable insights for system planners. To demonstrate technology-agnostic applicability, the model is applied to two contrasting LDES technologies, hydrogen (H$_{2}$) and flow battery (FB), on a benchmark test system with seasonal PV and load profiles under diverse blackout scenarios. Simulation results show that the proposed framework reduces operating costs in normal conditions while accelerating critical-load recovery and system-wide restoration after disruptions, advancing the state-of-the-art in storage-integrated power system operation.