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High performance of HVAC connected Building Integrated Photovoltaic/Thermal (BIPV/T) systems relies on appropriate control. However, optimal control is often overlooked, resulting in systems that operate inefficiently. This paper investigates how model predictive control (MPC) can improve the operation of open loop air-based BIPV/T systems connected to multiple thermal applications. The BIPV/T system at the first institutional net-zero energy building in Canada, the Varennes library, is used as an archetype. The BIPV/T covers 16% of the south-facing roof and operates under a simple rule-based control strategy. The developed control and design strategies consider variations of this system, to achieve higher thermal utilization efficiency. A control-oriented BIPV/T model is developed and calibrated using monitored data. The BIPV/T airflow is regulated through MPC for simultaneous heat supply to an Energy Recovery Ventilator and air-to-water heat pump. The BIPV/T air flow is efficiently controlled, considering the connected thermal applications, environmental conditions, and PV temperature. Model-based control for BIPV/T systems can increase the amount of useful heat and reduce PV overheating. The MPC controller for the examined system reduced the building energy consumption compared to the business-as-usual operation by 40% and together with increased BIPV/T area can supply excess heat to adjacent buildings. [ABSTRACT FROM AUTHOR]