The efficiency can range from something just over 50% when a trickle of power is in use, little more than 90% when the output is approaching the inverter rated output. An inverter will use some power from the batteries even when you are drawing an alternating current from it. The result is the low efficiency at low power levels.
A 3kW inverter can usually draw around 20 watts to the batteries when AC power is not used. It would be that if you use 20 watts of alternating current, the inverter will be drawing 40 watts from the batteries and the efficiency is only 50%.A small 200W inverter on the other hand can only draw 25 watts from the battery to give a 20-watt AC outpur, resulting in efficiency of 80%.
Larger inverters typically have a structure that could be called a "Sleep Mode" to increase overall efficiency. This is a sensor inside the drive sensing AC power, if needed. Otherwise, the drive will actually go off, continuing to sense when the power is required. This can usually be adjusted to ensure that the simple power of light is small enough to "turn the inverter.
This of course means that the equipment can not be left in "standby", and found that some devices with timers (eg, washing) reach a point in their cycle when not draw enough power to keep the drive " on ", unless something else, such as a light, is at the same time.
Another important factor concerns the waveform and inductive loads (ie, a device which is provided an electrical resistance, which includes anything with a motor.) Any waveform that is not a true sine wave (that is a square, square wave or modified) will be less efficient when food inductive loads - it may use the power of 20% more than if you use a pure sine wave.