Coalition-Stabilized Distributionally Robust Optimization of Inter-Provincial Power Networks Under Stochastic Loads, Renewable Variability, and Emergency Mobilization Constraints

This paper proposes a coalition-based framework for the coordinated operation of multi-regional power systems subject to extreme uncertainty in demand surges, renewable variability, and resource mobilization delays. Methodologically, we integrate Bayesian learning with distributionally robust optimization (DRO), embedding dynamically updated scenario posteriors into a Wasserstein ambiguity set. This construction captures both stochastic variability from renewable and load realizations and epistemic uncertainty from incomplete knowledge of probability distributions. To align individual incentives with system-level efficiency, we design a risk-adjusted utility mechanism that combines VCG transfers, Shapley allocations, and nucleolus refinements. These mechanisms explicitly consider agent heterogeneity, risk aversion, and coalition stability, ensuring that cooperation remains both efficient and sustainable. The optimization model maximizes expected social welfare while incorporating constraints on transmission corridor capacities, mobilization logistics, demand–response rebound effects, and mobile energy storage operations. A hierarchical decomposition algorithm integrates the Bayesian-DRO dispatch layer with cooperative game-theoretic allocations to maintain tractability and robustness at large scale. A case study on a six-province interconnected system with 14–26 GW peak demand, 10.2 GW solar, 8.6 GW wind, 14 GW peaking units, and 6.8 GW mobile storage demonstrates the effectiveness of the approach. Results indicate that the proposed framework raises expected welfare by nearly 10% relative to a non-cooperative baseline, reduces the probability of unserved energy exceeding 1.5% from almost 2% to negligible levels, and narrows payment disparities across provinces to strengthen coalition stability. Demand response peaks at 250–300 MW with rebound averaging 25%, while mobile BESS units cycle frequently to enhance local reliability. Overall, the findings highlight a robust and incentive-compatible pathway for resilient inter-provincial operation, providing both methodological advances and policy-relevant insights for multi-regional energy governance.