A controller includes an interface and a processor. The interface is configured to communicate with one or more memory devices that include multiple memory blocks. The processor is configured to hold information regarding power consumption of the memory blocks, to group at least some of the memory blocks into one or more storage groups, based on the information, such that the memory blocks in each storage group jointly consume less than a predefined power limit when the memory blocks in the storage group are applied a storage operation in parallel, and to apply the storage operation, in parallel, to the memory blocks in a selected storage group.