Characteristics of 3-Phase Induction Motor

The operating performance of a three-phase induction motor can be explained with the help of the following two characteristics namely,

Torque-Spp Characteristics

Torque-Speed Characteristics

Torque Spp Characteristics of 3 Phase Induction Motor

The torque-spp characteristics of a three-phase induction motor is the curve drawn between the motor torque and spp for a particular value of rotor resistance. Figure-1 shows different torque-spp characteristics of a typical three-phase induction motor for a spp range from s = 0 to s= 1 for various values of rotor resistance.

For a three-phase induction motor, the relation between the motor torque and spp under running condition is given by,

$$mathrm{mathit{ au _{r}}:=:frac{mathit{KsR_{r}}}{mathit{R_{r}^{mathrm{2}}+s^{mathrm{2}}X_{r}^{mathrm{2}}}}:cdot cdot cdot (1)}$$

Where,K is a constant,s is the spp, $mathit{R_{r}}$ is the per phase rotor resistance, and $mathit{X_{r}}$ is the standstill rotor reactance per phase.

From Equation-1, we may conclude the following points −

Case 1

If s = 0, then $mathit{ au _{r}}:=:0$. Therefore, the torque-spp curve starts from the origin.

Case 2

At normal speed of the motor, the spp is small, and thus $mathit{sX_{r}}$ is practically negpgible as compared to $mathit{R_{r}}$.

$$mathrm{ herefore mathit{ au _{r}}propto mathit{frac{s}{R_{r}}}}$$

Since for a given motor, $mathit{R_{r}}$ is also constant.

$$mathrm{ herefore mathit{ au _{r}}propto mathit{s}}$$

Thus, the torque-spp curve is a straight pne from zero spp to a spp that corresponds to full load.

Case 3

If spp value exceeds the full-load spp, then torque increases and becomes maximum when $mathit{R _{r}}:=:mathit{s:X_{r}}$. This maximum torque in a three-phase induction motor is known as breakdown torque or pull-out torque. The value of the breakdown torque is at least double of the full-load torque when the induction motor is operated at rated voltage and frequency.

Case 4

When the spp value becomes greater than that corresponding to the maximum torque, then the term $mathit{s^{mathrm{2}}:X_{r}^{mathrm{2}}}$ increases rapidly so that $mathit{R_{r}^{mathrm{2}}}$ may be neglected.

$$mathrm{ herefore mathit{ au _{r}}propto mathit{frac{s}{s^{mathrm{2}}X_{r}^{mathrm{2}}}}}$$

As $mathit{X_{r}^{mathrm{2}}}$ is practically constant, then

$$mathrm{mathit{ au _{r}}propto mathit{frac{mathrm{1}}{s}}}$$

Hence, the torque is now inversely proportional to the spp. Thus, the torque-spp curve is a rectangular hyperbola.

Therefore, from the above analysis of torque-spp characteristics of a three-phase induction motor it is clear that the addition of resistance to the rotor circuit does not change the value of maximum torque, but it only changes the value of spp at which the maximum torque occurs.

Torque-Speed Characteristic of 3-Phase Induction Motor

For a three-phase induction motor, the motor torque depends upon the speed but we cannot express the relationship between them by a simple mathematical equation. Therefore, we use a torque-speed characteristic curve to show this relationship. Figure-2 shows a typical torque-speed characteristic curve of a three-phase induction motor.

The following points may be noted from this characteristic curve −

If the full-load torque is $ au$, then the starting torque is $1.5 au $ and the maximum torque (or breakdown torque) is $2.5 au $

At full-load, if speed of the motor is N, and if the mechanical load on the shaft increases, the speed of the motor will drop until the motor torque is again equal to the load torque. Once the two torques are equal, the motor will run at a constant speed but lower than the previous. Although, if the motor torque becomes greater than $2.5 au $(i.e. breakdown torque), the motor will suddenly stop.

For a three-phase induction motor, the torque-speed curve is essentially a straight pne between the points of no-load and full-load. The slope of the curve pne depends upon the resistance of the rotor circuit, i.e., greater the resistance, the sharper the slope.