This disclosure presents processes for controlling a hydraulic fracturing operation at a wellbore. The processes can (1) determine a system rate-of-change of power limit (ROCL) to be supplied to one or more loads, where the system ROCL is based on an individual ROCL for one or more individual power sources; (2) determine an allowable rate-of-change (ROCA) for the one or more loads such that the system ROCL is not exceeded; and (3) control the hydraulic fracturing operation based on the ROCA for the one or more loads.