Robust Optimization for Multi-Energy Microgrid Sizing and Energy Management under Load Uncertainty with Demand Response

The growing interdependence among electricity, heat, and gas networks creates significant challenges for achieving reliable and cost-efficient design and operation in Multi-Energy Microgrids (MEMGs). Conventional optimization approaches often treat these subsystems separately, focus on either design or operational scheduling in isolation, and ignore load uncertainty. As a result, it leads to inefficient resource utilization and higher overall costs. To address these issues, this study proposes a two-stage robust optimization framework for the design and energy management of a MEMG under power-load uncertainties. In the first stage, the framework uses a biobjective model to determine the optimal sizes of key components—including the PV panel area, wind turbine radius, battery capacity, and gas allocation for the CHP unit—while accounting for uncertainty in power loads. The two objectives are: (i) maximizing the use of renewable and CHP resources, and (ii) minimizing the total system cost, which includes electricity, gas, emissions, operational, and demand-response costs. In the second stage, the optimized components are subsequently applied to an IEEE 14-bus MEMG test system, where a robust energy-management strategy coordinates power, heat, and gas flows under uncertain conditions using the Mixed-Integer Nonlinear Programming (MINLP) model. The results show that the robust strategy ensures all energy demands are met even under worst-case load variations. However, achieving this higher level of resilience increases electricity expenses by 21 %, emissions-related costs by 15 %, line losses by 0.8 %, and overall system cost by 6 %, while electricity exported to the main grid decreases by 17 %.