Embodiments of a system, a method, and a computer-program product (e.g., software) for aggregating an energy service from a group of loads with time-varying operating cycles are described. This aggregation may be performed by an aggregator, which provides the energy service to a power-system operator. In particular, for a desired demand response, a demand-response mechanism may modify a demand response of a given load by mapping an initial operating cycle of the load before a demand-response event to a final operating cycle. In addition, the demand-response mechanism may transition the given load to a new operating cycle associated with the demand-response event using a temporal set-point trajectory. This aggregation technique may ensure that a distribution of phases of the group of loads is, on average, uncorrelated with each other, either by preserving or modifying the distribution of phases prior to the demand-response event.