EE361-Electromechanical Energy Conversion

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# EE-361 ELECTROMECHANICAL ENERGY CONVERSION

## Ozan Keysan

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

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

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# B-H Characteristics

## $$\vec{B} = \mu \vec{H} $$

## Linear Materials

- ## Air

## Non-linear Materials

- ## Iron
- ## B limit => Saturation

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# Magnetic Saturation

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# Magnetic Saturation

## Residual Magnetism
<img src="https://upload.wikimedia.org/wikipedia/commons/thumb/f/f0/Compactcassette.jpg/1920px-Compactcassette.jpg" alt="Drawing" style="width: 320px;"/>
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<img src="./images/ee361/ego_karti.jpg" alt="Drawing" style="width: 350px;"/>

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# Hysteresis Loss
<img src="https://www.electronics-tutorials.ws/wp-content/uploads/2018/05/electromagnetism-mag19.gif" alt="Drawing" style="width: 500px;"/>

#### [How do magnets work?](https://youtu.be/hFAOXdXZ5TM?t=4m24s)
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# Hysteresis Loss
<img src="https://qph.fs.quoracdn.net/main-qimg-ac943b670cbcf5b5ced59b7e9bff9075" alt="Drawing" style="width: 750px;"/>

#### [How do magnets work?](https://youtu.be/hFAOXdXZ5TM?t=4m24s)
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## Hysteresis Loss \$\propto\$ Frequency
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# Hysteresis Loss

## Variable Hmax
<img src="./images/ee361/B-H_loop.png" alt="Drawing" style="width: 700px;"/>

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# Lenz's Law

## Why there is a negative sign?
## \$e = -\frac{d \Phi}{dt}\$

### An induced electromotive force (emf) always gives rise to a current whose magnetic field opposes the original change in magnetic flux.

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# Eddy Current Losses
### Created by Induced Voltage in a Conductor

### [Magnet in a Copper Tube](http://www.youtube.com/watch?v=keMpUaoA3Tg)

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# Transmission Lines
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## Why are the conductors (grouped)?

![](http://i.stack.imgur.com/vCf6K.png)

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# Transmission Lines
## Why are the conductors (grouped)?

![](http://i.stack.imgur.com/Icgxw.png)

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# Transmission Lines
## Why are the conductors (grouped)?

![](http://i.stack.imgur.com/ZiMjy.png)
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# Side Question
### What are red balls on transmission lines?

![](http://66.media.tumblr.com/c709447a8d8ab4a8a1237b336a0bb860/tumblr_inline_nfkavn3fjk1rmzke4.jpg)

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# Side Question
### What are red balls on transmission lines?

#### [Installation of marker balls](https://www.youtube.com/watch?v=dC_izlGm28c)
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# AC Resistance vs DC Resistance
## Which one is higher?

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- ## AC Resistance > DC Resistance
- ## Why?

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# Skin Depth
# Distribution of Current in a Wire
![](http://upload.wikimedia.org/wikipedia/commons/thumb/6/61/Skin_depth.svg/450px-Skin_depth.svg.png)
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# Skin Depth

### Due to circulating eddy currents
![](http://upload.wikimedia.org/wikipedia/commons/thumb/c/c7/Skineffect_reason.svg/293px-Skineffect_reason.svg.png)

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# Skin Depth

## Current Distribution: \$ J = J_S e ^{-d/\sigma}\$

## Skin depth: \$\sigma = \sqrt{\frac{2 \rho}{\omega \mu_r \mu_0}}\$

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# Skin Depth for Copper:
- ## 50 Hz --> 9.3 mm

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- ## 1 kHz --> 2.1 mm

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- ## 10 kHz --> 0.66 mm

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- ## 100 kHz --> 0.21 mm

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- ## 1 MHz --> 66 um

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## How to increase conductor area without increasing thickness?

## Bundled Conductors

### Also helps to reduce [Corona discharge](http://www.electricaleasy.com/2016/07/corona-discharge.html)
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## How to increase conductor area without increasing thickness?

## Foil Conductors
<img src="https://kllaminates.si/wp-content/uploads/2015/03/image002.jpg" alt="Drawing" style="width: 600px;"/>

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## Hollow Conductors
<img src="http://sub.allaboutcircuits.com/images/52013.jpg" alt="Drawing" style="width: 400px;"/>
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# AC Resistance

## AC Resistance [Calculator](http://www.clemson.edu/ces/cvel/emc/calculators/Resistance_Calculator/round.html)

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## Rule of Thumb: For 50 Hz power systems
## $$Rac \simeq 1.1 Rdc$$
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## Power Dissipated due to Eddy Currents

# \$P= \frac{ V \pi^2 B_{peak}^2 d^2 f^2}{k \rho}\$

## Notice the \$f^2\$ element
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#Magnetic Losses

# Hysteresis Loss \$\propto\$ Frequency

# Eddy Loss \$\propto\$ Frequency\$^2\$

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### Several Applications

- [Eddy Current Brake](https://www.youtube.com/watch?v=lywaL2tpLB0)

- [Eddy Current Science](https://www.youtube.com/watch?v=ezXVzc64qRE), [Eddy Current Seperator2](https://www.youtube.com/watch?v=zlwpEzcamcc)

- [Levitating Coil](http://www.youtube.com/watch?v=VydPQuLyEns)

- [Induction Heater](http://www.youtube.com/watch?v=aOsbIP3y2Wg), [Induction Cooking](https://www.youtube.com/watch?v=T3AI1eQ50iE), [Electroboom Eddy Curents](https://www.youtube.com/watch?v=u7Rg0TcHQ4Y)

- [Electromagnetic Retarder](https://www.youtube.com/watch?v=5FMoUEmSsdE), [Rötarder Sesi](https://www.youtube.com/shorts/kQygTyy1p08)
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## You can download this presentation from: [keysan.me/ee361](http://keysan.me/ee361)