Since a three-phase squirrel-cage induction motor （IM） is widely used，it is very important to accurately estimate the performance for the IM under unbalanced voltage. This is because unbalanced voltage can lead to the following undesirable effects in the IM; torque reduction，efficiency reduction，vibrating torque，abnormal temperature rise，etc. In this paper，a simple and practical calculation method is proposed and verified for the IM under an unbalanced three-phase voltage condition. The proposed method is based on the tensor analysis，and an equivalent circuit comprising positive and negative sequence circuits is used. Circuit constants are determined by the“type-T equivalent direct method” to account for the effect of slip frequency on the equivalent secondary resistance. By comparing calculation results with detai1ed experimental results，it is clarified that the performance of the IM under unbalanced voltage can be accurately calculated at not only varying amplitudes of the one-phase voltage but also varying phase angles of the one-phase voltage in the three-phase line voltage. The vibrating torque of the IM can also be precisely ca1culated by using the proposed method. Furthermore，based on simulation results for large IMs，it is established that the unbalanced current is seriously affected by the primary and secondary leakage reactances.

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