# Torque speed relationship of induction motor

### Electrical Machines - Induction Motor Torque Speed Curve Torque-Speed Characteristics of Three Phase Squirrel Cage An induction motor compared to a dc motor has some major advantages such as - Absence of . The torque produced by three phase induction motor depends upon the following Speed Control of Induction Motor Using Static Devices. Figure 1 showed a plot of induction motor torque vs speed from zero to synchronous speed. This curve is called the torque-speed characteristic curve. We can.

## Torque Speed Characteristic of an Induction Motor

In the absence of a computer, this is a tedious process at best. Multiple solutions of the above equation for torque at different slips can be made simpler by simplifying the equivalent circuit model.

Consider the per-phase equivalent circuit diagram in Fig. Induction Motor per-phase equivalent circuit The stator part of the equivalent circuit together with the magnetising branch can be replaced by a Thevenin equivalent circuit. Note that if power or efficiency calculations are needed, the full equivalent circuit model should be used not the Thevenin version. Torque Speed Curve General Curve Using the Thevenin torque equation it is relatively easy to calcaulte the torque as a function of slip.

This plotted is in Fig. This operations is also called plugging.

### Torque Equation of Three Phase Induction Motor

This mode of operation can be used to quickly stop a machine. If a motor is travelling forwards it can be stopped by interchanging the connections to two of the three phases.

Switching two phases has the result of changing the direction of motion of the stator magnetic field, effectively putting the machine into braking mode in the opposite direction. This is the most common mode of operation. In this case, power flows from the mechanical system, to the rotor circuit, then across the air gap to the stator circuit and external electrical system. Motoring Torque Characteristic The motoring region of the induction machine torque-speed curve is the region of greatest interest. The plots below show a number of different torque speed curves, due to differences in the motor designs. Common features of interest are noted and discussed below.

The rated torque of the machine. This is the design operating point. Figure 2 showed the equivalent circuit for the stator. Looking back into the stator circuit, we find the magnetizing reactance in parallel with the stator winding impedance: Figure 4 shows the rotor circuit coupled to the Thevenin equivalent of the stator and magnetizing branches. Because this circuit consists of two impedances in series, we can easily calculate the rotor current in terms of V1e and thus V1.

Using the rotor current, we can then calculate the torque directly as a function of the slip. Clearly, the current will be given by the source voltage divided by the total impedance in the circuit of Figure 4. Thus, reducing the voltage applied to a motor will cause it to develop substantially less torque, or to operate at a higher value of slip for a given load. However, it is also rated to operate from a V supply.

If one were to operate the motor at V.

## Torque Equation of Three Phase Induction Motor

Although equation 7 appears formidable, it is relatively simple to program it using a spreadsheet. With the spreadsheet, the slip can be varied over a wide range to obtain the complete torque-speed characteristic.

Motor Region The motor region, which we have already considered, occurs for slip between 0 and 1. Generator Region The slip is negative in the region to the right of the motor region, which implies the rotor is rotating faster than the stator field.

This can only occur if the rotor is mechanically driven. The torque in this region is opposite to the direction of rotation, indicating generator action. Induction generators are seldom used because they require reactive power either from the power system or from an external capacitor bank. The induction generator, however, does not have to operate at only one speed like the synchronous machine and is thus useful for applications where the speed of the machine will vary.

One such application is for wind generators. Braking Region The region to the left of the motor region in Figure 6 is one in which the slip is greater than 1, which implies that the rotor is rotating in the opposite direction of the stator field. Thus, this is called the braking region. This is done by switching two of the leads on the three-phase supply to the stator.

Braking is used when it is necessary to stop the motor very quickly; however, braking is very hard on the motor as the currents during braking are very high, causing heating of the windings.

### INDUCTION MOTORS:INDUCTION MOTOR TORQUE-SPEED CHARACTERISTICS | electric equipment

The stored energy of the rotating rotor is also dissipated in the form of heat. The motor region of the torque-speed curve The accuracy of the induction motor model has limitations, and the actual torque-speed characteristic is somewhat more complicated than the model predicts.

Figure 7 shows the torque-speed characteristic as it might actually appear. For many induction motors, the average torque drops a bit as it accelerates and then rises to a peak value of torque, known as the pull-out or breakdown torque. The normal operating region for the induction motor is the nearly linear portion between rated speed and synchronous speed, shown by the heavy line. Note that the negative slope of the operating region provides stable operation, because an increase in load slows the machine down, causing the motor to develop more torque.

The maximum torque that the motor can produce is called the breakdown torque.