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The paper deals with a direct torque control (DTC) scheme for Induction Motor (IM) drives where flux and torque of the motor are estimated by the IM current model instead of by the voltage model. The scheme is intended to enable operation of the DTC IM drives at zero speed. As a return, its implementation requires the knowledge of speed, rotor time constant and inductive parameters of the motor. In the paper the performance of the proposed scheme is studied for a drive equipped with an incremental encoder and commanded with a constant flux. Using the position information delivered by the encoder, a suitable representation of the current model is formulated that makes the drive operation feasible at true zero speed. Operating with a constant flux command, the variations in the rotor time constant dominate over the other parameters; their effect on the drive behavior is analyzed in steady state founding that the motor flux and torque are deviated from the references of a quantity, which is a function of the torque reference. Experimental results are given to substantiate both the capabilities of the scheme of developing the full torque at a standstill and the theoretical findings on the drive behavior under rotor time constant mismatch.