The connected battery acts as a damper, of sorts, to soften the output of the converter. Without it, the converter will jump up and down in output voltage depending on the need sensed. When you turn on a lamp, a TV, or the fan motor kicks in, the converter jumps to respond instantly. These "jumps" are seen as surges, and can age bulbs, and damage electronics. Sort of like tapping a water cooler tank, or directly from the city pressure.
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