Aircraft air conditioning system with an electrically driven ambient air compressor and method for operating such an aircraft air conditioning system

A method for operating an aircraft air conditioning system with the steps:

• conducting ambient air through an ambient air supply line, which comprises a first end connected to an ambient air inlet and a second end connected to a mixing chamber of the aircraft air conditioning system,
• compressing the ambient air flowing through the ambient air supply line in a first ambient air compressor arranged in the ambient air supply line,
• driving the first ambient air compressor by an electrically driven air cycle machine,
• conducting ambient air through a first ambient air branch line, which branches off from the ambient air supply line upstream of the first ambient air compressor and rejoins the ambient air supply line downstream of the first ambient air compressor,
• compressing the ambient air flowing through the first ambient air branch line in a second ambient air compressor arranged in the first ambient air branch line,
• conducting outgoing cabin exhaust air through a cabin exhaust air line, which has a first end connectable to an aircraft area to be air conditioned,
• driving a cabin exhaust air turbine arranged in the cabin exhaust air line and coupled to the second ambient air compressor by the cabin exhaust air flowing through the cabin exhaust air line,
• driving the second ambient air compressor by the cabin exhaust air turbine,
• transferring heat from the compressed ambient air flowing through a second ambient air branch line to the cabin exhaust air flow flowing through the cabin exhaust air line by a cabin exhaust air reheater arranged in the cabin exhaust air line upstream of the cabin exhaust air turbine, wherein the cabin exhaust air reheater is thermally coupled to the second ambient air branch line, which branches off from the ambient air supply line downstream of the first ambient air compressor and the second ambient air compressor and rejoins the ambient air supply line downstream of the cabin exhaust air reheater.