Joint Energy–Resilience Optimization of Grid-Forming Storage in Islanded Microgrids via Wasserstein Distributionally Robust Framework

The increasing deployment of islanded microgrids in disaster-prone and infrastructure-constrained regions has elevated the importance of resilient energy storage systems capable of supporting autonomous operation. Grid-forming energy storage (GFES) units—designed to provide frequency reference, voltage regulation, and black-start capabilities—are emerging as critical assets for maintaining both energy adequacy and dynamic stability in isolated environments. However, conventional storage planning models fail to capture the interplay between uncertain renewable generation, time-coupled operational constraints, and control-oriented performance metrics such as virtual inertia and voltage ride-through. To address this gap, this paper proposes a novel distributionally robust optimization (DRO) framework that jointly optimizes the siting and sizing of GFES under renewable and load uncertainty. The model is grounded in Wasserstein-metric DRO, allowing worst-case expectation minimization over an ambiguity set constructed from empirical historical data. A multi-period convex formulation is developed that incorporates energy balance, degradation cost, state-of-charge dynamics, black-start reserve margins, and stability-aware constraints. Frequency sensitivity and voltage compliance metrics are explicitly embedded into the optimization, enabling control-aware dispatch and resilience-informed placement of storage assets. A tractable reformulation is achieved using strong duality and solved via a nested column-and-constraint generation algorithm. The framework is validated on a modified IEEE 33-bus distribution network with high PV penetration and heterogeneous demand profiles. Case study results demonstrate that the proposed model reduces worst-case blackout duration by 17.4%, improves voltage recovery speed by 12.9%, and achieves 22.3% higher SoC utilization efficiency compared to deterministic and stochastic baselines. Furthermore, sensitivity analyses reveal that GFES deployment naturally concentrates at nodes with high dynamic control leverage, confirming the effectiveness of the control-informed robust design. This work provides a scalable, data-driven planning tool for resilient microgrid development in the face of deep temporal and structural uncertainty.