When i switch off the mains the home UPS/INVERTER works well but when the electrcity is gone it doesnt works..?

A UPS means uninterrupted power supply, which will have a battery. This you probably know. So, what you are saying is impossible IF it is fitted correctly. You say there is no load problem and it works in one circumstance but not another. I don't really understand what you mean if the electricity is switched off because you say it works well then you say it doesn't, but give no indication of where the electricity is turning off different to that of the mains power. Anyway, if the same load is being used, the same battery for the UPS and nothing else has changed, then that is impossible that turning the power off at one place as opposed to another makes any difference as the UPS will sense the drop and provide the needed power for as long as the battery lasts.

If all the power to the house goes through the UPS then it shouldn't make a blind bit of difference whether it is being switched off deliberately by you, by the meter running out or by a power cut.

It's possible that your electricity supply is not failing completely; just enough for your appliances not to work, but not enough for the UPS to kick in. If so, then it needs its sensitivity adjusting. You will have to refer to the instruction manual to find out how to do this.