Lesson 32 Torque-Slip (speed) Characteristics of Induction Motor (IM) Version 2 EE IIT, Kharagpur
Instructional Objectives •Derivation of the expression for the gross torque developed as a function of slip (speed) of Induction motor •Sketch the above characteristics of torque-slip (speed), explaining the various features •Derive the expression of maximum torque and the slip (speed) at which it occurs •Draw the above characteristics with the variation in input (stator) voltage and rotor resistanceIntroduction In the previous, i.e. third, lesson of this module, starting with the formulas for the induced emfs per phase in both stator and rotor windings, the equivalent circuit per phase of the three-phase induction motor (IM), has been derived. The relation between the rotor input, rotor copper loss and rotor output (gross) are derived next. Finally, the various losses −copper losses (stator/rotor), iron loss (stator) and mechanical loss, including the determination of efficiency, and also power flow diagram, are presented. In this lesson, firstly, the torque-slip (speed) characteristics of IM, i.e., the expression of the gross torque developed as a function of slip, will be derived. This is followed by the sketch of the different characteristics, with the variations in input (stator) voltage and rotor resistance, along with the features. Lastly, the expression of maximum torque developed and the slip (speed) at which it occurs, are derived. Keywords: The equivalent circuit per phase of IM, gross torque developed, torque-slip (speed) characteristics, maximum torque, slip at maximum torque, variation of the characteristics with changes in input (stator) voltage and rotor resistance. Gross Torque Developed The current per phase in the rotor winding (the equivalent circuit of the rotor, per phase is shown in Fig. 31.1) is (as given in earlier lesson (#31)) 222222222)()/()()(xsrExsrEsIrr+=⋅+⋅=Please note that the symbols used are same as given in the earlier lesson. In a similar way, the output power (gross) developed (W) is the loss in the fictitious resistance in the equivalent circuit as shown earlier, which is ()()()2222222222222220)()()1(3)()(/)1(3/)1(3xsrssrExsrssrEsssrIPrr⋅+−⋅⋅⋅=⋅+−⋅⋅⋅=−⋅⋅=The motor speed in rps is srnsn⋅−=)1(The motor speed (angular) in rad/s is srsωω⋅−=)1(The gross torque developed in mN⋅is Version 2 EE IIT, Kharagpur
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