Decoupling Simulation of Thermal Processes with Two-Time Scale for Heated Buildings in Cold Regions

To accommodate the development of Internet of Things (IoT) technology and the increasing demand for automatic control in district heating systems, efficient modeling of building thermal processes is imperative. This study aims to establish a low-dimensional and physically interpretable thermal process model for residential buildings in severe cold regions, facilitating the design of simplified control systems. Based on the lumped parameter method and heat balance principles, an 8th-order state-space model is developed to characterize the building thermal dynamics. The two-time scale decoupling of this model is achieved using the regular perturbation method, decomposing it into a fast subsystem representing the indoor air thermal response and a slow subsystem representing the building envelope thermal response. Both the original and decoupled models are validated against measured data, with the error of 3.24%. During the decoupling process, the time-scale separation criterion is revised, and a new criterion: f₁ < 10⁻¹ and f₂ < 10⁻⁶ is proposed specifically for buildings with heavyweight masonry external envelopes. Future work will further investigate time-scale separation criteria for other building types and lay the theoretical foundation for designing control systems based on the decoupled two-time-scale model.