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This paper analyzes the effects of injecting additional signals in induction machines for the purpose of speed control. A new saturation model able to correctly model the interaction between the added signal and saturation of the motor core due to the main torque-producing flux is presented. The introduction of a variable saturation factor is used to model the variation of the saturation level due to the additional signal. A third harmonic rotor circuit is also introduced to take account of the third harmonic component of the air-gap flux, due to saturation. An additional balanced voltage set is added to the normal supply to analyze the effects of such signals on a saturated induction motor. Simulation results of such a model both at no load and full load are presented together with experimental measurements.