Two-Stage Distributionally Robust Optimization for the Integrated Energy System Considering the Correlations of Renewables and Loads

The integrated energy system (IES) plays a crucial role in optimizing energy use. However, how to deal with the uncertainty of the IES effectively is a problem worthy of further discussion. Therefore, we introduce a two-stage distributionally robust optimization (DRO) framework for the IES considering demand response (DR) and the uncertainties and correlations of wind, photovoltaic (PV), loads. First, we present a scenario generation and reduction methodology that takes uncertainty and correlation into account. Second, we propose an IES optimization model that considers uncertainties, correlations, and DR. Third, we construct a data-driven two-stage DRO framework for the IES. In Stage I of the framework, we consider the start-up cost of the unit. In Stage II, 1-norm and ∞-norm limit the uncertainty probability distribution confidence set at the same time to obtain the optimal solution of the model given the worst-case probability distribution. Finally, we employ a column-and-constraint generation method (C&CG) algorithm to tackle the proposed two-stage DRO model. Finally, we verify the effectiveness and robustness of the proposed model and algorithm through conducting numerical simulations.