Speed-torque control of induction motors

A MATHEMATICAL analysis was made to determine the effect of symmetrical series reactance in the supply lines upon the speed-torque relation, the power factor, and the efficiency of standard induction motors. The analysis showed that torque, the speed for pull-out torque, and the power factor are functions of the added reactance. The efficiency, however, is a function of the machine constants and speed only, and is, therefore, not affected by the added reactance. The nature of the speed-torque and power-factor variation is as follows, if the supply voltage is assumed constant. The expression for the speed at pull-out is actually an expression for impedance match between stator and rotor. The addition of a small series capacitive reactance into each phase reduces the impedance of the machine, thus increasing the current and also the torque. The impedance match between the windings, however, occurs at a lower speed, thus reducing the speed for pull-out. Addition of more capacitive reactance depresses the speed for pull-out and increases the magnitude of pull-out torque until a critical value of series reactance is reached. At this critical value, series resonance and pull-out occur at the same speed, and the impedance match for pull-out becomes a resistance match. Therefore, this critical value of series reactance determines the maximum value of pull-out torque that can be obtained from the machine at constant voltage. Furthermore, the speed for pull-out has been reduced to its minimum value, since it is limited by the ratio of rotor to stator resistance.