This plant comprises N (N>1) air distillation units (1) in parallel, each one of which comprises a main air compressor (3) driven by a steam turbine (4); an air distillation apparatus (8) producing liquid oxygen and/or liquid nitrogen; at least one pump (9) for pumping liquid oxygen and/or liquid nitrogen to a high production pressure; and a cycle compressor (10) adapted to compress part of a cycle fluid. Each cycle compressor (10) is driven by an electric motor (11), and an (N+1)th steam turbine (12) drives an alternator (13) supplying the electric motors (11) with electric current. Application to supplying units (2) for producing synthetic hydrocarbons with high-pressure oxygen.