An air handling unit (AHU) or rooftop unit (RTU) in a building HVAC system includes one or more powered components, a battery, and a predictive controller. The powered components include a fan configured to generate a supply airstream provided to one or more building zones. The battery is configured to store electric energy and discharge the stored electric energy for use in powering the powered components. The predictive controller is configured to optimize a predictive cost function to determine an optimal amount of electric energy to purchase from an energy grid and an optimal amount of electric energy to store in the battery or discharge from the battery for use in powering the powered components at each time step of an optimization period.