Very small. It only needs power when going up and down and nothing after that. I believe the power supply requires 5 amps and runs at 48VDC.
However, you will need A/C power all the time to run the Power Inserter, the satellite receiver and the TV if not a DC TV. That's going to add to the power requirements. I found an inexpensive 750W which is over kill but I would stick with something in the 500W range if it was me. The small inverters tend to be noisy with their fan running so you might want to place it closer to the batteries and run A/C power line from there to where all the electronics will be.
What I post is my 2 cents and nothing more. Please don't read anything into my post that's not there. If you disagree, that's OK.
Can't we all just get along?