A controller is configured to use an energy cost function to predict a total cost of energy purchased from an energy provider as a function of one or more setpoints provided by the controller. The energy cost function includes a demand charge term defining a cost per unit of power corresponding to a maximum power usage of the building system. The controller is configured to linearize the demand charge term by imposing demand charge constraints and to mask each of the demand charge constraints that applies to an inactive pricing period. The controller is configured to determine optimal values of the one or more setpoints by performing an optimization procedure that minimizes the total cost of energy subject to the demand charge constraints and to provide the optimal values of the one or more setpoints to equipment of the building system that operate to affect the maximum power usage.