EE362-Electromechanical Energy Conversion-II

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# EE-362 ELECTROMECHANICAL ENERGY CONVERSION-II

# Induction Machines

## Ozan Keysan

[keysan.me](http://keysan.me)

Office: C-113 <span class="meta">•</span> Tel: 210 7586

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# Induction Motors
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## Operation Principle: Lenz Law and Eddy Currents

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## Operation Principle: Lenz Law and Eddy Currents

### [What happens if I rotate a magnet over an aluminium disk?](https://youtu.be/H5O0DJ65RdA?t=40s)

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### How to obtain the same effect without any moving parts?

## Rotating MMF with 3-phase: [Coca Cola Motor](https://youtu.be/cIf9iPskgJs)
 
 <iframe width="600" height="350" src="https://www.youtube-nocookie.com/embed/cIf9iPskgJs" title="YouTube video player" frameborder="0" allow="accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture" allowfullscreen></iframe>
 
 ## or even a [simpler version](https://www.youtube.com/watch?v=P-eTLmJC2cQ)
 
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## Induction Motors

### [Invented by](https://en.wikipedia.org/wiki/Induction_motor) Nicola Tesla, and [Gallieo Ferraris](https://en.wikipedia.org/wiki/Galileo_Ferraris)

#### [Who invented the induction motor?](https://hackaday.com/2017/09/21/inventing-the-induction-motor/)

#### Tesla [Patent-1](https://patents.google.com/patent/US416195A/en), [patent-2](https://patents.google.com/patent/US381968)

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## Rotating MMFs
###  $$\mathcal{F\_R} = \dfrac{3}{2}\mathcal{F\_{max}}cos(\theta - \omega t)$$

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# Induction Motors

- ## Robust, Simple Structure

- ## No electric brushes --> no-maintenance

- ## No expensive magnets --> Inexpensive

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## 90 % of the motors used in industry are induction motors

### and also the motors of [Tesla Model S](https://youtu.be/KA18tusTgE4?t=1360), [Audi E-tron](https://www.youtube.com/watch?v=UuraNOlh-Vk)

### [Tesla Motor Production](https://www.youtube.com/watch?v=v66vBb1FK2k), [Audi Motor Production](https://www.youtube.com/watch?v=uWBEPEspbWI)

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# Induction Motor: Stator Side

## 3-phase double-layer distributed winding (exactly same with synchronous machines)
## Excited with balanced 3-phase AC currents

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# Induction Motor: Rotor Side
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## 1) Wound Rotor:

###Three-phase winding similar to the stator, and terminals are carried out with slip-rings.

<img src="https://f.ptcdn.info/805/024/000/1414088335-BWOU1-o.jpg" alt="Drawing" style="width: 400px;"/>
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# Induction Motor: Rotor Side

## 2) Squirrel Cage Rotor:

## Short-circuited aluminium bars, no slip-rings!

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# Induction Motors

# Squirrel Cage

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# Squirrel Cage Rotor

## Short-circuited aluminium bars

[How does an induction motor works?](https://youtu.be/LtJoJBUSe28?t=24s)

[Induction Motor Assembly](https://www.youtube.com/watch?v=bZnC6JlOFD4)

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# Some Definitions
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## Synchronous Speed:
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 Speed of the stator excitation
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## Electrical speed:
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\$\quad \omega_e = 2 \pi f_s \$ rad/s
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## Mechanical speed:
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\$\quad \omega_m = \dfrac{\omega_e}{p/2} = \frac{2\pi f_s}{p/2}\$
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## Mechanical speed:
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\$\quad n_s = \dfrac{120 f_s}{p} \$ RPM

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# Slip:
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 Difference between rotor speed and stator speed in per unit.
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# \$s = \dfrac{\omega_s - \omega_r}{\omega_s}\$
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# \$s = \dfrac{n_s - n_r}{n_s}\$

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# Slip

## If \$s = 1\$, then
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 rotor is not rotating (\$n_r = 0 \$)
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## If \$s = 0\$, then
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 rotor is rotating at synchronous speed (\$n_r = n_s \$)
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## \$\omega_r = (1-s) \omega_s\$

## \$n_r = (1-s) n_s\$

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# Frequency of the induced rotor currents: \$f_r\$
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## What happens to \$f_r\$ when the rotor is stationary?
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> ## The motor is just like a transformer:  \$f_r = f_s\$
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## What happens to \$f_r\$ when the rotor is rotating at synchronous speed?
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> ## No relative speed between rotor and stator, no induced voltage:  \$f_r = 0\$

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# Frequency of the induced rotor currents: \$f_r\$
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# \$f_r = s f_s\$
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## What is the torque generated at synchronous speed?
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# Torque when (\$s=0\$) is zero!
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# Induction motors can't run at synchronous speed
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# Thus, they are also called asynchronous motors.
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# Exercise:

## A three-phase 50 Hz, 6-pole induction motor rotates at a slip of 5% (0.05). Calculate:

### a) Electrical synchronous speed in rad/s

### b) Mechanical synchronous speed in rpm

### c) Actual rotor speed in rpm

### d) Frequency of induced rotor current in Hz

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## You can download this presentation from: [keysan.me/ee362](http://keysan.me/ee362)