Hello friends, hope you all are fine and enjoying good health In the previous posts we have seen the basic concepts and introduction of Induction motor, we did few calculations as well and now I am gonna discuss the torque speed characteristics of Induction motor.

This is a very important tutorial as it includes a lot of calculations and concepts to understand.I have really tried my best to pour everything in it yet if something’s left you guys can post in comments or can ask if something’s complicated.

I have divided this tutorial in nine parts and in the whole tutorials, we will cover all about Induction motor, how it works and its controlling factors etc and in the coming tutorials I will explain its controlling using microcontroller. These are the few parts in which I have divided this tutorial :

**A complete Tutorial on Induction Motor**

- Basic Concepts of Induction Motor
*(Part 3)*

- Types of Induction Motor
*(Part 4)*

The torque-speed relationship is examined first from a Physical Standpoint and then a general equation for torque as a function of slip is derived from the induction-motor equivalent circuit.

**Figure 1 : Induction-motor torque speed curve**#### Induced Torque from a Physical Standpoint

##### No Load condition

- At no load slip is very small, relative motion between magnetic field and rotor is also less, rotor frequency is again small, and current flow in rotor is also less because of less induced voltage in rotor bars.
- Because of small rotor frequency, the reactance of the rotor is almost zero and the maximum rotor current
is in phase with rotor voltage**IR****ER.** - Even at no load condition, stator current is quite large, since it must supply most of Bnet . That is why induction motors have large no load currents compared to other types of machines.
- The induced torque and its magnitude are is given by :

##### On Load condition

- Now suppose induction-motor is loaded down. As motor’s load increases its slip rises because of which the rotor speed falls.
- Difference between rotor and stator magnetic field increases.
- Greater relative motion produces a stronger rotor voltage ER which in turn produces a larger rotor current
.**IR** - Then the rotor magnetic field BR also increases. Since rotor slipis larger, rotor frequency rises
and rotor reactance increases**(fr = s fe )**. Therefore, rotor current lags further behind the rotor voltage.**(ωLR)** - Notice that angle sigma has increases.
- The increase in BR tends to increase the torque, while increase in sigma tends to decrease the

torque. - Since first effect is larger than the second one so overall torque increases to supply motor’s increased load.
- Induction-motor reaches pullout torque when the point is reached where as load on shaft is increased, the
term decreases more than**sin(sigma)**term increases.**BR** - At that point a further increase in a load decreases induced torque and motor stops. The angle sigma between the net and rotor magnetic fields can be expressed in a very useful way.

- This term is the power factor of rotor. The rotor power factor angle can be calculated as :

- Rotor magnetic field will increase as the rotor current will increase (provided that the rotor core is not saturated).
- Current flow will increase as slip increase (reduction in velocity).
- The angle sigma will increase as slip rises. Hence the
value will reduce until as such**sin(sigma)**

that the reduction ofwill be greater than the increase of*sin(sigma)*(pullout torque).**BR** - Since sigma is greater than 90 degrees, as such that :

- Combining the characteristics of all these elements would give induction motor’s torque-speed curve.
- The torque speed curve may be divided into 3 regions of operations:
- Linear region or low slip region.
- Moderate slip region located until the pullout torque level.
- High slip region.

#### Induction Motor Induced Torque Equation

Previously we looked into the creation of the induced torque graph, now we would like to derive the Torque speed equation based upon the power flow diagram of an induction-motor. We know that :

- Pag is air gap power which is absorbed by R2. Pag for one phase of motor can be seen to be :

- Therefore the total air gap power is :

- Magnitude of this current is :

- The air gap power is given by :

- Induction-motor induced torque equation will be :

Hi,

Can you please tell me how to find the slip at minimum torque? is there any formula ? thansk