Mathematical modeling describing the performance of open loop multivariable vapor compression chiller model: implications for sustainable HVAC in social housing development

Introduction: This study introduces a simplified multi-variable state-space model of a vapour compression chiller system, focusing on key components such as the condenser and evaporator. Methods: The model is based on a previously validated state-space framework and has been further developed to generate a transfer function matrix with two inputs (refrigerant and cold carrier flow rates) and two outputs (cooling capacity and outlet temperature). The simplified model offers an accurate yet computationally efficient representation of the system’s dynamics. Simulations of the open-loop system were carried out using SIMULINK/MATLAB software. The results were plotted to validate the model's ability to predict system responses accurately. These simulations encompassed various conditions, including operational changes, fouling on the evaporator, and thermal load fluctuations. Results: Open-loop simulation results show that the system reaches steady-state values with a response time of approximately 40 seconds for the cold carrier temperature and 70 seconds for cooling capacity. Meanwhile, the system exhibits strong coupling between inputs and outputs, with disturbances such as inlet temperature variations causing oscillations in the cooling capacity. Discussion: The novelty of this work lies in reducing a complex validated chiller model into a practical two-input, two-output framework, which enables simplified analysis and serves as a robust foundation for advanced multivariable control design. This contribution addresses the critical need for efficient HVAC control strategies in sustainable building applications. This research presents a foundational mathematical model for developing advanced feedback control strategies that can enhance system stability, improve energy efficiency, and support sustainable HVAC operations while maintaining thermal comfort. These advancements are especially relevant for social housing, where energy-efficient HVAC systems are essential for achieving sustainable and resilient building practices in extreme climate conditions.