A rotating electrical machine includes a stator, a rotor and at least one active magnetic bearing including a bearing winding, which is an air-gap winding, and includes at least a first phase winding and a second phase winding. A measurement arrangement measures the radial displacement of the rotor by injecting a displacement measurement injected signal into at least one section of at least one of the bearing windings of one of the magnetic bearings, and capturing at least one displacement measurement signal wherein this displacement measurement signal depends on the rotor displacement in a radial direction relative to the stator, this dependency being due to eddy currents in the rotor induced by the displacement measurement injected signal.