EE362-Electromechanical Energy Conversion-II

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# EE-362 ELECTROMECHANICAL ENERGY CONVERSION-II

## Ozan Keysan

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

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

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# Review:
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## Distributed Winding

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# Review:

## Three Phase Winding
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# A
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, -C
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, B
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, -A
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, C
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, -B

[Rotating MMF animation with discrete windings](http://people.ucalgary.ca/~aknigh/electrical_machines/fundamentals/f_ac_rotation.html)

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# Review: Number of Poles

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#Review

###Electrical Angle is not equal to Mechanical Angle!

## \\(\theta\_{elec} = (\dfrac{p}{2}) \theta\_{mech} \\)

### \\(p\\) : Number of poles (always even number)

### \\(\dfrac{p}{2}\\) : Number of pole pairs

### \\(\omega\_{elec} = (\dfrac{p}{2}) \omega\_{mech} \\) (radians/second)

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# Winding Factors

### Two constants that help to estimate induced voltage characteristics in the machine windings analytically.
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- ## Distribution Factor (\\(k_d\\))
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- ## Pitch Factor (\\(k_p\\))

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# Distribution Factor

<img src="https://raw.githubusercontent.com/ozank/ozank.github.io/master/presentations/images/distributed_coil.png" alt="Drawing" style="width: 500px;"/>
 
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# Distribution Factor

## Vector sum of voltages in a distributed coil is less than the algebraic sum of the voltage in each coil.
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## \\(k_d = \dfrac{\mathrm{Vector\,Sum\,of\,Voltages}}{\mathrm{Algebraic\,Sum\,of\,Voltages}}\\)

[Animation](http://cusp.umn.edu/electric_drives/animations/electric_drives_animation_1_distributed_winding.php)
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# Distribution Factor

### Q1: What is the distribution factor of a concentrated coil?
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### Q2: What is the distribution factor of two coils seperated by \\(\pi/3\\)?
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### Q3: What is the distribution factor of three coils seperated by \\(\pi/6\\)?
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### Generalized equation

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# Distribution Factor

## \\(k_d = \dfrac{sin(q \dfrac{\alpha}{2})}{q sin(\dfrac{\alpha}{2})}\\)

## \\(q\\): Number of coils
## \\(\alpha\\): Angle between each coil (electrical angle!)

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# Pitch-Factor
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## Review of Definitions:

- # Full-pitched (= \\(\pi\\) electrical)
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- # Under-pitched (< \\(\pi\\) electrical)
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- # Over-pitched (> \\(\pi\\) electrical)
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## A 2-pole machine with sinusoidal \\(B_{gap}\\)

<img src="https://raw.githubusercontent.com/ozank/ozank.github.io/master/presentations/images/2pole_mmf.jpg" alt="Drawing" style="width: 450px;"/>
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# Can you plot:
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- ## Airgap flux density?
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- ## Flux Linkage in the coil?
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- ## Induced voltage?

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## A 2-pole machine with sinusoidal \\(B_{gap}\\)

<img src="https://raw.githubusercontent.com/ozank/ozank.github.io/master/presentations/images/2pole_voltage.jpg" alt="Drawing" style="width: 800px;"/>
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# Full-pitched vs Fractional-pitched Coil

- ## Full-pitch = 180 degrees (\\(\pi\\))
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- ## Under pitch < 180 degrees (\\(\pi\\))
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- ## \\(V\_{full-pitch} > V\_{under-pitch}\\)
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- # If so, what is the point?

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# A big Paranthesis

## Fourier Series
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> ## All waveforms, no matter what you scribble or observe in the universe, are actually just the sum of simple sinusoids of different frequencies.

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# Fourier Series

![](http://media.giphy.com/media/Km4XeiMqFNCDK/giphy.gif)

[Fourier Series using Circles](https://www.youtube.com/watch?v=LznjC4Lo7lE), [Complex Orbits](https://www.youtube.com/watch?v=QVuU2YCwHjw), [Useful applets](http://www.falstad.com/fourier), [Fourier examples](http://ptolemy.eecs.berkeley.edu/eecs20/week8/examples.html)

[More Useful Links on Fourier Series](http://keysan.me/explained/)
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# Fourier Series

[Google Plot](https://www.google.com/search?q=square+wave+fourier+transform&ie=utf-8&oe=utf-8#q=plot+%28sin%28x%29%2B0.25*sin%283*x%29%2B0.1*sin%285*x%29%29)

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- ## Let's see what happens with a 2/3 under pitched coil?
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- ## Under-Pitched coils are very useful for the elimination of harmonics
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#Pitch Factor

## Voltage in a short-pitched coil is less than a full-pitched coil

## \\(k_p = \dfrac{\mathrm{Short-Pitched\;Coil\;Flux}}{\mathrm{Full-Pitched\;Coil\;Flux}}\\)
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#Pitch Factor

# \\(k_p = sin(\dfrac{\lambda}{2})\\)

# \\(\lambda\\): Coil-pitch in electrical degrees
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# Pitch and Distribution Factor for Harmonics
## For harmonic number n:

## \\(k_p(n) = sin(\dfrac{n\lambda}{2})\\)
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## \\(k_d(n) = \dfrac{sin(q n \dfrac{\alpha}{2})}{q sin(\dfrac{n\alpha}{2})}\\)
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# Winding Factor:
## is the combination of distribution and pitch factor 
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#\\(k_w = k_d \times k_p\\)
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## gives an idea about the magnitude of the coil voltage (or MMF) compared to concentrated and full-pitched winding.

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