Robust sizing and IGDT-based energy management for multi-energy microgrids with integrated power-to-gas and gas-to-power systems

Optimal sizing is essential in microgrid design to ensure reliable operation and cost efficiency. This study introduces an integrated Multi-Energy System architecture that couples the microgrid, micro-heat, micro-gas, and the interface systems to collectively meet electricity, heat, and gas demands by harnessing a diversified portfolio of energy resources. The first objective is to determine the optimal sizing of the PV surface area, wind turbine radius, and battery capacity under power load uncertainty. This is achieved by managing the trade-off between two conflicting goals: maximizing the utilization of renewable energy and battery storage, and minimizing total system costs. The second objective focuses on the coordinated management of power, heat, and gas flows under uncertain power loads. To achieve this, two Information Gap Decision Theory (IGDT) strategies are employed to support energy management under both robustness- and opportunity-oriented conditions. These problems are formulated as Mixed-Integer Nonlinear Programming (MINLP) models and solved using the BARON solver in the GAMS environment. Results show that incorporating power load uncertainty into the component sizing process leads to a 61.6% increase in PV surface area and a 7% increase in wind turbine radius, with no change in battery capacity compared to the case without considering uncertainty. In the energy management stage, the robustness-focused IGDT strategy increases overall system cost by 32.7%, ensuring higher resilience under uncertainty, while the opportunity-focused strategy reduces total cost by 29.8%, emphasizing economic efficiency compared to the deterministic case.