EE362-Electromechanical Energy Conversion-II

class: center, middle

# Rotating MMF Concept and AC Excitation

## Ozan Keysan

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

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

---
# Induction in a Coil
--

## How many ways to induce voltage?
--

- ## Time variation of flux (e.g. AC excitation)
--

- ## Due to conductor movement in a stationary field
--

- ## Rotation (\\(\vec{B}.dA\\) changes)

---
# Example in an Electric Machine

--
<img src="./images/ee362/salient_alternator.jpg" alt="Drawing" style="width: 500px;"/>

<!--

# Electric Machine Parts

# Electric Machine Parts

-->
---

# WHY 3 PHASE? (but not 2 or 5?)
--

---
# WHY 3 PHASE? (but not 2 or 5?)
--

---

# WHY 3-PHASE?

- # More power per unit wire length.

--
- # Constant Power
[Power Graphs](https://docs.google.com/spreadsheets/d/1RP-MsrHwybAG6J3CFTbdLOCTvGdIdkaWUkhRuAHPWd0/edit?usp=sharing)

--
- # Rotating MMF
(wait until EE362)

---
# Rotating Magnetic Field !!
## The most important term for EE362

## A few basic examples:

### [Coca-Cola Motor](https://www.youtube.com/watch?v=cIf9iPskgJs)

### [Simplest AC Motor](https://www.youtube.com/watch?v=vbh_yR9Ngc0)

---
# Single Phase AC: A time varying signal

# \\(I=sin(\omega t)\\)

### X-axis: Time
---
# MMF created by a single coil

### If excited by DC:

## \\(MMF=F_m cos(\theta)\\)

---

### What happens if the coil is excited with AC?
--

### DC excitation waveform multiplied with a time varying sinusoid: \\(sin(\omega t)\\)

### \\(MMF=F_m cos(\theta) sin(\omega t)\\)
--

### A Standing Wave!

### X-axis: position (or angle), animation frames: time

---
<img src="https://quotefancy.com/media/wallpaper/800x450/6361070-Nikola-Tesla-Quote-If-you-want-to-find-the-secrets-of-the-universe.jpg" alt="Drawing" style="width: 800px;"/>

---
# Three Phase AC

## Invented by Nicola Tesla in 1880s

### was independently invented by [Galileo Ferraris](https://en.wikipedia.org/wiki/Galileo_Ferraris), [Mikhail Dolivo-Dobrovolsky](https://en.wikipedia.org/wiki/Mikhail_Dolivo-Dobrovolsky), [Jonas Wenström](https://en.wikipedia.org/wiki/Jonas_Wenstr%C3%B6m) 
---
## 3 Phase Voltage Phasors

### X-axis: time
---
## Three Phase AC Magneto-motive Force (MMF)

### X-axis angular position, each animation frame is a time-shot

---
# Three Phase AC: Rotating MMF

<img src="http://www.ece.umn.edu/users/riaz/animations/vecmovieslow.gif" alt="Drawing" style="width: 500px;"/>
---
# Three Phase AC: Rotating MMF

---
# Let's derive it:
## Yes it is boring, but quite important.
### [Simplest AC Motor](https://www.youtube.com/watch?v=vbh_yR9Ngc0)
--

#### You have three coils, separated with \\(2 \pi/3 \\) radians and excited with 3-phase current.

## \\(I\_A (t) = I\_m cos (\omega t )\\)
## \\(I\_B (t) = I\_m cos (\omega t - 2\pi /3 )\\)
## \\(I\_C (t) = I\_m cos (\omega t - 4\pi /3)\\)

---
### \\(F\_A (t) = F\_m cos (\theta) cos (\omega t )\\)
### \\(F\_B (t) = F\_m cos (\theta - 2\pi/3) cos (\omega t - 2\pi/3))\\)
### \\(F\_C (t) = F\_m cos (\theta- 4\pi/3) cos (\omega t - 4\pi/3)\\)
--

## \\(F\_{total} (t) = F\_A + F\_B + F\_C \\)
--

## \\(F\_{total} (t) = \dfrac{3}{2}F\_m cos (\theta - \omega t) \\)

- #### [Animation](https://andymikeknight.github.io/machines/fundamentals/f_ac_rotation.html)

---
# Rotation MMF

## \\(F\_{total} (t) = \dfrac{3}{2}F\_m cos (\theta - \omega t) \\)

### Generalized solution:
--

## N-phase

## \\(F\_{total} (t) = \dfrac{N\_{phase}}{2}F\_m cos (\theta - \omega t) \\)

---
# Fundamental Idea of all AC Machines
--

<img src="./images/ee362/donkey.jpg" alt="Drawing" style="width: 700px;"/>
---
# Rotating MMF

---
<img src="https://s-media-cache-ak0.pinimg.com/originals/92/86/54/9286549c76feba31890b5cce45690e0d.jpg" alt="Drawing" style="width: 500px;"/>

### [Nikola Tesla vs Thomas Edison. Epic Rap Battles of History](https://www.youtube.com/watch?v=gJ1Mz7kGVf0)
<!--

### [Nikola Tesla vs Thomas Edison. Epic Rap Battles of History](https://www.youtube.com/watch?v=gJ1Mz7kGVf0)
-->
---
## You can download this presentation from: [keysan.me/ee362](http://keysan.me/ee362)