A local power control arbiter is provided to interface with a global power control unit of a processing platform having a plurality of processing entities. The local power control arbiter controls a local processing unit of the processing platform. The local power arbiter has an interface to receive from the global power control unit, a local performance limit allocated to the local processing unit depending on a global power control evaluation and processing circuitry to determine any change to one or more processing conditions prevailing in the local processing unit on a timescale shorter than a duration for which the local performance limit is applied to the local processing unit by the global power control unit and to select a performance level for the local processing unit depending on both the local performance limit and the determined change, if any, to the prevailing processing conditions on the local processing unit.