How to calculate battery capacity required for home applications?
Your 75W fan required 220 Volts, it will not operate at typical battery voltages such as 12V. 

A 75W fan operating (indirectly) from a 12V supply would draw 6.25 A not 0.34 A. 

Even with a theoretical 100% efficient invertor, the current on the 12V side is greater than the current on the 220V side to deliver the same power across the system from battery to Fan. 

Note that the reason that power is delivered through the grid at high voltage is to keep currents low. losses and cable sizes are proportional to (a function of) current. High V are used to keep currents low. 

You convert 12V DC into 220 V AC using your inverter. Depending on capacity and utilisation the efficiency of an inverter might be the 80% you estimate or it may be worse - 50% Ref So your 6.25A may become 13A drawn from the 12V battery.

Therefore your 300 Ah battery-set might power a 75W fan for less than 24 hours.



Update: for 2 x nominal 12V SLA battery, the following diagram may clarify what is happening.







simulate this circuit &ndash; Schematic created using CircuitLab