Motor current signature analysis (MCSA) used in the diagnosis of centrifugal pumps has become a hot topic due to its non-intrusive and cost-effective nature. Yet, traditional current-based diagnosis methods show limitations as massive computation and power frequency interference. Moreover, most of them focus on the fault detection, fewer discuss the applications in operation evaluation. Therefore in this article, the hydro-mechanical-electric coupling effect that exists in the induction motor-centrifugal pump system is analyzed systematically. On this foundation, novel indicators that can reflect the harmonic distortion and noise proportion of stator current signals, and further indicate the hydraulic stability and operation status are proposed. Theoretical and experimental analysis support this paper, and results have demonstrated that our proposed indicators can indicate the operation change, identify the optimal operation region, and reflect the development of cavitation for centrifugal pumps. These indicators have the advantages of easy calculation and identification, therefore can be conveniently compared with accepted standards and enable immediate remedial actions to be implemented to ensure the stable operation.