Optimization Models for Distributed Energy Systems Under CO₂ Constraints: Sizing, Operating, and Regulating Power Provision

The increasing penetration of variable renewable energy sources has intensified the need for ancillary services to maintain grid stability, and demand-side flexibility, particularly through distributed energy systems (DESs), is expected to play an important role. This study proposes a two-stage optimization framework for DESs under CO${}_2$ constraints that enables gas engines and battery energy storage systems (BESS) to provide regulating power equivalent to Load Frequency Control (LFC). The framework consists of an Equipment Sizing Optimization Model (ESM) and an Equipment Operation Optimization Model (EOM), both formulated as mixed-integer linear programming (MILP) models. The ESM determines equipment capacities using simplified operational representations, where partial-load efficiencies are approximated through linear programming (LP)-based constraints. The EOM incorporates detailed operational characteristics, including start-up/shutdown states and partial-load efficiencies, to perform daily scheduling. Information obtained from the ESM, such as the CO${}_2$ emissions, the equipment capacities, and the BESS state of charge, is passed to the EOM to maintain consistency. A case study shows that providing regulating power reduces total system cost and that CO${}_2$ reduction constraints alter the equipment mix. These findings demonstrate that the proposed framework offers a practical and computationally efficient approach for designing and operating DESs under CO${}_2$ constraints.