When the mains switch is turned off the amps are running off the batteries. When the mains switch is turned on, the power supplies power all amps and also charge the batteries at the same time.
Even though the pre and power amps will use battery power, I still feel it neccessary to provide as clean a power supply as reasonably possible for the times when the sound is being powered by the mains supply.
There will only be one power supply for the pre amps and one for the power amps. It would be better to have a separate supply for left and right channels but that would increase the size of the amps (the transformer alone is 55mm by 110mm) and cost significantly. Since the amps are designed to use batteries a lowering of quality for ‘back-up power’ is a reasonable compromise I feel.
In the image is shown the filtering that will be used at the mains input. The red component on the right is a varistor (voltage dependant resistor) to protect against over voltage. The two large blue lumps are common-mode inductors and the other bits and pieces are class X and Y capacitors which together with the inductors filter out most of the rubbish superimposed on the mains signal by fridges, lightning, vehicle ignitions etc.
This side of the filter are two bridge rectifiers, one for the pre amp supply and one for the power amp supply. They have a peak average forward current of 6 amps which is plenty for the power amps and complete overkill for the pre amps. But buying in bulk keeps the cost down so the same device is used for both.