A central plant includes storage devices configured to store resources purchased from a utility or generated by the central plant and to discharge the one or more resources. The central plant includes a controller configured to obtain a cost function comprising a peak load contribution (PLC) term representing a cost based on an amount of the one or more resources purchased during coincidental peak (CP) subperiods. The controller is configured to modify the cost function by applying a peak subperiods mask to the PLC term, wherein, for each subperiod, the peak subperiods mask modifies a portion of the PLC term corresponding to the subperiod based on a probability that the subperiod will be one of the CP subperiods. The controller is also configured to perform an optimization of the modified cost function.