Multidimensional Uncertainty Integration based on Spatiotemporal Hybrid Copula: A Resilience-Oriented Modeling Paradigm for IES and Virtual Power Plant

Integrated Energy Systems (IES) and Virtual Power Plants (VPPs) are pivotal for achieving the "dual-carbon" goals, yet they face significant challenges from multidimensional spatiotemporal uncertainties. Traditional uncertainty modeling methods, relying on static correlation assumptions, are inadequate for dynamically capturing the complex fluctuations in source-load-market parameters, especially the aggregation uncertainties inherent in VPPs. This paper proposes a novel resilience-oriented modeling paradigm centered on a spatiotemporal hybrid Copula (ST-HC) framework. The primary innovation lies in its dynamic correlation capture mechanism, which integrates time-decay and spatial-distance factors to accurately characterize nonlinear, time-varying dependencies among cross-regional uncertainties. Furthermore,a comprehensive five-dimensional evaluation system is established, incorporating metrics for storage flexibility, degradation, market volatility, risk preference, and system efficiency—including a novel data security risk entropy indicator. Validated through case studies, the proposed approach demonstrates superior performance over conventional static models, enhancingplanning accuracy and reducing total costs by approximately 9.98%, while effectively quantifying the economic-low-carbon trade-offs under different risk strategies for IES-VPP synergy.