Let me explain my point of view.
1. When Electricity is on: In this state, battery will charge at around 200w (14.4v*15A). Plus, whatever load is connected to inverter will be fed directly from mains power (inverter connects mains to load directly).
2. When electricity is gone: inverter will turn on (with relay) and feed power from battery. Here, there is conversion loss.
Lead acid Battery charging has three stages: bulk, absorption and float. At float, battery charges at around 20w. So, if your battery is bad, then this stage will never reach and battery will always charge at 100-200w. If one cell is dead, then battery will boil and get warm.
So, there is loss in charging and discharging from transformer. Copper based transformer has lower loss compared to aluminium. But for your case this won't consume many units.
With the above knowledge, check how many units it consume to charge without connecting the load and see if the power settles down to float.