This paper introduces a novel online adaptive protection scheme to detect and diagnose broken bar faults (BBFs) in induction motors during steady-state conditions based on an analytical approach. The proposed scheme can detect precisely adjacent and non-adjacent BBFs in their incipient phases under different inertia, variable loading conditions, and noisy environments. The main idea of the proposed scheme is monitoring the variation in the phase angle of the main sideband frequency components by applying Fast Fourier Transform to only one phase of the stator current. The scheme does not need any predetermined settings but only one of the stator current signals during the commissioning phase. The threshold value is calculated adaptively to discriminate between healthy and faulty cases. Besides, an index is proposed to designate the fault severity. The performance of this scheme is verified using two simulated motors with different designs by applying the finite element method in addition to a real experimental dataset. The results show that the proposed scheme can effectively detect half, one, two, or three broken bars in adjacent/non-adjacent versions and also estimate their severity under different operating conditions and in a noisy environment, with accuracy reaching 100% independently from motor parameters.