A fluid extraction system is presented. The fluid extraction system includes a direct current (DC) bus and a plurality of fluid extraction sub-systems configured to be electrically coupled to the DC-bus. At least one fluid extraction sub-system includes an electric machine configured to aid in the extraction of a fluid from a well. The electric machine includes a plurality of phase windings and a rotor. The at least one fluid extraction sub-system further includes a control sub-system to control a rotational speed of the rotor by selectively controlling a supply of a phase current to the plurality of phase windings such that the rotational speed of the rotor of the electric machine is different from rotational speed of a rotor of another electric machine in at least one of other fluid extraction sub-systems. Related method for controlling rotational speeds of electric machines is also presented.