Modeling and identification of multi-stage thermal inertia for reliable MPC in high-inertia water-based HVAC systems

Water-based HVAC systems exhibit strong thermal inertia distributed across the heat source, hydronic network, and building envelope, which can significantly affect model predictive control (MPC) performance if not properly represented. This paper develops a unified, control-oriented model that explicitly captures multi-stage thermal inertia into a linear state–space framework. A plant-side identification workflow is proposed that estimates the source time constant and network delay–attenuation using only routinely available supply and return water temperatures from an air-source heat pump district heating system (ASHP–DHS). The identified parameters are then embedded into an MPC formulation that regulates indoor temperature while limiting electrical power use and actuation variability. Closed-loop simulations compare four MPC configurations with different levels of inertia awareness. Results show that network-side inertia is the dominant factor for warm-up and cooldown behavior: neglecting distribution delay and attenuation leads to longer recovery times and larger temperature-tracking errors. Source-side inertia mainly shapes short-term electrical power ramps, with strong sensitivity when the source time constant is comparable to the control interval. Parameter sweeps further quantify how performance degrades as inertia parameters are mis-specified, providing practical guidance on when explicit multi-stage inertia modeling is essential for reliable control.