Two-Stage Robust Optimization of Integrated Energy Systems Considering Uncertainty in Carbon Source Load

Integrated Energy Systems (IESs) interconnect various energy networks to achieve coordinated planning and optimized operation among heterogeneous energy subsystems, making them a hot topic in current energy research. However, with the high integration of renewable energy sources, their fluctuation characteristics introduce uncertainties to the entire system, including the corresponding indirect carbon emissions from electricity. To address these issues, this paper constructs a two-stage, three-layer robust optimization operation model for IESs from day-ahead to intra-day. The model analyzes the uncertainties in carbon emission intensity at grid-connected nodes, as well as the uncertainty characteristics of photovoltaic, wind turbine, and cooling, heating, and electricity loads, expressed using polyhedral uncertainty sets. It standardizes the modeling of internal equipment in the IES, introduces carbon emission trading mechanisms, and constructs a low-carbon economic model, transforming the objective function and constraints into a compact form. The column-and-constraint generation algorithm is applied to transform the three-layer model into a single-layer main problem and a two-layer subproblem for iterative solution. The Karush–Kuhn–Tucker (KKT) condition is used to convert the two-layer subproblem into a linear programming model. A case study conducted on a park shows that while the introduction of uncertainty optimization increases system costs and carbon emissions compared to deterministic optimization, the scheduling strategy is more stable, significantly reducing the impact of uncertainties on the system. Moreover, the proposed strategy reduces total costs by 5.03% and carbon emissions by 1.25% compared to scenarios considering only source load uncertainty, fully verifying that the proposed method improves the economic and low-carbon performance of the system.