## Introduction

The basic expression relating the speed of an induction motor and its frequency is N = 120f/P. From this expression, many facts can be derived and understood. And this expression is also helpful in understanding starting and full load torques of an induction motor. In this article, let us explore in-depth, of what happens to an induction motor if the supply frequency and supply voltage is varied.

## Effect of Change in Supply Voltage on Torque and Speed

As already discussed in my article on speed control of induction motors, it is evident that the torque (T) of an induction motor is directly proportional to the square of the supply voltage. During starting, the supply voltage is kept to minimum, so that the torque is also minimum. When the supply voltage is gradually increased, the torque increases following the relation:

T α s * V^2.

Where T = torque,

s = slip and

V = the supply voltage.

So it is evident from the above equation that the torque at any speed is proportional to the square of the applied voltage. If the stator voltage is decreased by 10%, then the torque decreases by 20%. This decrease in torque, due to decrease in supply voltage will not only happen during starting of the motor, but also during running conditions. It should be appreciated that when the supply voltage V decreases, then the torque T also decreases. But there is a load connected to the motor and it requires a constant torque all the time. Thus in order to maintain a constant torque during reduced supply voltage, as a compensation, the speed of the motor decreases.

It should be understood by referring to the torque equation, “T α s * V^2”, as the supply voltage is reduced, the slip increases to maintain a constant torque. As the slip increases the speed of the motor reduces.

## Effect of Change in Supply Frequency on Torque and Speed

The change in supply frequency hardly occurs in large distribution systems used on land. If there are some major disturbances or very heavy load fluctuating continuously, then there might be a minimal frequency variation. But large frequency variations are possible on electrical systems used on board ships and emergency supply systems for factories and hospitals. Such large frequency variations are possible on low power systems where diesel engines and gas turbines are used as prime movers.

As already mentioned, the relation between the speed of the motor and its frequency is given by the expression N = 120f/P.

From this expression, it is evident that the speed of the motor is directly proportional to the supply frequency. Thus any decrease or increase in frequency will affect the speed of the motor. Let us now analyze what exactly happens when a motor of 50Hz made to run with 60Hz supply and vice-versa.

*Analysis 1:*

When a 50 Hz motor is made to run on 60 Hz supply:

It is general practice in several countries to have all house-hold items and equipments rated for 50 Hz supply. So when such small domestic devices are connected to a 60 Hz supply, they cause a severe problem. For better understanding, let us visualize this small calculation:

[(60Hz – 50 Hz)/ 50 Hz] * 100 = 20 %. Thus all such equipments run 20 % faster than their normal rated speed. This is not safe for the equipment as the insulations may be rated for lesser capacity and windings may burn-out. To run safely, we either require a reduction gear or an expensive 50 Hz source.

Also this 50 Hz motor will operate perfectly on a 60 Hz supply provided its supply voltage is stepped-up.

60 Hz/ 50 Hz = 6/5 * 100 = 120 %.

*Analysis 2:*

60 Hz motor connected to 50 Hz supply:

It is same as the above, but instead of stepping-up the supply voltage, it is necessary to step-down the supply voltage.

50Hz/ 60 Hz = 5/6 * 100 = 80 %.