Conceptually, since the airship is tethered to the ground during that compression, the power could be sourced from a ground tether as well. The problem would be

Conceptually, since the airship is tethered to the ground during that compression, the power could be sourced from a ground tether as well. The problem would be the pressure vessel, which is why something like a 200,000 m3 1 atm helium going to 150,000 m3 1.33 atm would be more reasonable.