B737 Classic alternate battery charger source

[Banana Joe]

With the Transfer Switch Off the electrical system is effectively split in left and right, however, the AC Standby Bus and DC Standby Bus would automatically transfer to their alternate source (Battery Bus) if the Engine Driven Generator 1 was to be switched off. Would the automatic transfer happen also for the battery charger from Ground Service Bus to Main Bus 2 or is the transfer inhibited in for the battery charger? If not, the battery would be discharging in this case.