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Studies of rotor asymmetries in squirrel-cage induction motors have traditionally focused on analyses of the effects of the breakage of adjacent bars on the magnetic field and current spectrum. However, major motor manufacturers have reported cases where damaged bars are randomly distributed around the rotor perimeter of large HV machines. In some of these cases, the motors were being monitored under maintenance programs based on motor current signature analysis (MCSA), and the degree of degradation found in the rotor was much greater than that predicted by analysis of their current spectra. For this reason, a complete study was carried out, comprising a theoretical analysis, as well as simulation and tests, to investigate the influence that the number and location of faulty bars has on the traditional MCSA diagnosis procedure. From the theoretical analysis, based on the application of the fault-current approach and space-vector theory, a very simple method is deduced, which enables the left sideband amplitude to be calculated for any double bar breakage, per unit of the sideband amplitude corresponding to a single breakage. The proposed methodology is generalized for the estimation of the sideband amplitude in the case of multiple bar breakages and validated by simulation using a finite-element-based model, as well as by laboratory tests.