Most switchgear suppliers can come up with the amps needed for a breaker close coil, trip coil, indicating lights, spring charging motors and other devices. Add any continuous loads such as indicating lights, protective relay and metering power supplies, PLC communications devices or control relays. This will give you a list of current draw per device.
The engineer, owner or designer has to decide how long the DC system is supposed to supply power when AC is down and what is supposed to happen at the beginning, during and at the end of the outage.
A typical scenario is: Trip all breakers at start of outage, maintain 300 watts of continuous load for 24 hours and still have enough battery power to close, trip and close "x" breakers to return power. (Make sure protection and tripping power is available when AC returns. The breaker(s) might have to trip right away if there is a problem.) Remember, when most breakers trip or close, their spring charging motors run to recharge the operating spring. Include those amps.
Combine the list of amps per device and the operating scenario to come up with a time profile for the battery. Consider all of the trips and breaker recharge last one minute even though it may only be 1-2 seconds. (IEEE battery sizing standard). The end of interval loads are also counted as one minute minimum.
Send the load profile to a battery supplier and they can size the battery.
Decide whether to use Ni-Cad, Lead Acid, or other battery types.
As to why DC power? Many utility and industrial switchgear systems use DC control to make sure that tripping power is available in a fault. The high voltage switchgear breakers do not have integral trip units like molded case CB?s. They need a signal from a protective relay to trip.