Optimizing virtual power plant coordination through locational marginal flexibility under network constraints

The transition toward deeply decarbonized energy systems requires optimization frameworks that can simultaneously capture long-term dynamics, operational reliability, and contractual stability while managing multiple forms of uncertainty. This paper introduces a comprehensive modeling and solution framework for long-term welfare optimization of virtual power plants, where seasonal, annual, and rolling horizons are jointly considered under constraints of network feasibility, renewable integration, reliability assurance, and carbon accountability. A unified welfare objective is formulated to internalize operating cost, curtailment penalties, reliability risk, and carbon charges, with constraints codifying the technical physics of dispatch, reserve adequacy, and contract coverage. The methodology employs a distributionally robust optimization layer combined with scenario reduction, stability metrics, and fairness tracking to ensure computational tractability and resilience to stochastic variations in renewable output and demand. A case study on a 33-bus system with heterogeneous virtual power plants demonstrates the effectiveness of the approach. Results show that the proposed optimization reduces total seasonal welfare costs by 8-13%, cuts curtailment by up to 45%, and lowers overload probabilities on critical lines by 20-30%. Attribution analysis reveals that 55% of carbon abatement arises from curtailment relief, 25% from redispatch optimization, 12% from loss reduction, and 8% from contract rebalancing, underscoring the multi-mechanistic nature of emission savings. The contributions of this paper are fourfold: the design of a multi-layered welfare optimization model for long-term horizons, the integration of distributionally robust techniques with fairness and stability considerations, the demonstration of quantitative improvements in both welfare and reliability, and the attribution of carbon reduction across complementary drivers. Together, these elements provide a rigorous and adaptable blueprint for optimizing future low-carbon virtual power plant systems under uncertainty.