Capacity-Operation Co-Optimization of Building Thermal Inertia and Thermal Energy Storage for Integrated Energy Systems

Under the energy transition, renewable intermittency poses a challenge to supply–demand matching. Buildings possess thermal inertia that can serve as virtual storage. This study proposed a capacity-operation co-optimization model for a heating-season-integrated energy system, integrating building thermal inertia with thermal energy storage (TES). The building envelope was modeled as a first-order resistor–capacitor (RC) thermal network, and TES capacity was treated as a decision variable within a mixed-integer quadratic programming (MIQP) framework. The objective minimized total costs, including operating, TES investment, curtailment penalties, and demand response compensation, subject to power balance, thermal comfort, and renewable accommodation constraints. Four scenarios were compared to quantify the substitution effect. The results showed that building thermal inertia increased the net benefit by 23.87% by shifting heat supply to low-price periods. Capacity optimization reduced TES capacity from 600 kWh to 137.82 kWh, a 77.03% decrease. Building thermal inertia substituted 57.5% of the optimized TES capacity, corresponding to a 90.24% total capacity reduction relative to the fixed 600 kWh configuration, and this substitution effect may become more evident with larger thermal capacitance, smaller peak–valley price gaps, and wider temperature ranges, although these trends were not quantitatively analyzed in this study. The synergy of both measures lowered total cost by 22.73% and reduced TES cycling intensity and state-of-charge (SOC) fluctuations, which may help extend equipment life. These findings provided a quantitative basis for sizing TES in heating-season-integrated energy systems.