DIAGNOSIS You are overloading the inverter. Microwaves have a very high startup surge and running wattage. The smell is the inverter's transformer or MOSFETs overheating. The insulation is getting hot. This will cause permanent damage.
FIX Stop immediately. Unplug the microwave. Let the unit cool completely. Do not use microwaves, even small ones, with this power station. Check your microwave's rated output wattage—the input wattage is often 50-100% higher, easily exceeding 1000W.
IF THAT DIDN'T WORK If the smell persists after cooling and using a small, proper load, internal damage has occurred. Components have been thermally stressed. The unit may fail soon or have reduced capacity.
HEADS UP The burning smell is a serious warning. Continuing will melt solder joints or destroy the inverter. The unit's protection may not engage fast enough to prevent thermal damage. This is misuse, not a defect.