The invention relates to an on-line estimation method and system for a permanent magnet chain of a compressor, and a storage medium. The method comprises the steps of S10, after the compressor is started, obtaining extended permanent magnet chains defined in the description; S20, according to the extended permanent magnet chains defined in the description, obtaining a permanent magnet chain modulus value defined in the description; and S30, according to the permanent magnet chain modulus value defined in the description, obtaining a permanent magnet chain estimated value, defined in the description, corresponding to a minimum moment of a phase current modulus value I in the running process of the compressor. Compared with the prior art, the influence of other parameters of the compressor can be avoided, and on-line estimation of the permanent magnet chain of the compressor in non-electrolytic control is completed through a small amount of overheads.