Heating, ventilation, and air conditioning (HVAC) systems present significant opportunities for energy optimization and integration with renewable energy sources. Advanced control strategies are essential to manage energy consumption while enhancing system efficiency and overall performance. A key requirement for such control strategies is the availability of a dynamic model. This paper proposes a novel model-based methodology for real-time compressor control in HVAC systems, utilizing a switching event-triggered model predictive control (MPC) framework. The proposed approach enables dynamic mode switching between different operational states while having configurable constraints, facilitating a multivariable control scheme. The controller models for each operating mode are developed using data-driven system identification techniques and validated with experimental data acquired from air-to-water heat pumps in the test field. The effectiveness and performance of the proposed control strategy are evaluated through Model-in-the-Loop (MIL) simulations on various scenarios systematically testing the control within a single operational mode and upon mode switches. The event-triggered model predictive control method is compared with other control strategies, including event-triggered LQR and event-triggered PID, to highlight its superior performance.