The ZCell BMS is powered from a DC power source.
The original BMS model was powered with anything in the range of 9-28 volts DC.
The latest model is able to be powered from DC between 9-65 volts, which mean it can be directly powered from the same 48V DC bus that the batteries are connected to. This is typically the simplest approach (via a suitable small fuse or circuit breaker).
Alternatively the BMS can be powered indirectly from an AC power source (i.e. using a small AC->DC power supply). Note that in on-grid situations where AC power is the preferred source, the use of an Automatic Transfer Switch such as the Victron Energy Filax 2 is preferred, to ensure uninterrupted energy supply to the BMS (and to other related system control components) across various combinations of AC source interruption.
Note: Do *not* plug a USB power cable into the Micro-USB socket on the side of the BMS unit. That Micro-USB socket should not be used in the ZCell BMS deployments. Doing so will disable the operation of ZCell's built in 'hardware watchdog' function - and its simply un-necessary.