EE361-Electromechanical Energy Conversion

class: center, middle

# EE-361
# 3-PHASE SYSTEMS

## Ozan Keysan

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

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

---
## Electric Plugs & Sockets

### [Why some countries use different voltage, frequency?](https://www.quora.com/Why-does-India-use-230-V-50HZ-while-the-USA-uses-120V-60HZ)
---

## Electric Plugs & Sockets
<img src="https://www.szapphone.com/wp-content/uploads/2024/10/World-of-Power-Plug-Standards.webp" alt="Drawing" style="width: 800px;"/>

[Different plugs around the world](https://www.iec.ch/world-plugs),  [but WHY?](https://www.quora.com/Why-does-India-use-230-V-50HZ-while-the-USA-uses-120V-60HZ)
---

## Electric Plugs & Sockets
<img src="https://imgs.xkcd.com/comics/standards.png" alt="Drawing" style="width: 800px;"/>

---
# Introduction to Three Phase
## Industrial Electric Plugs

<img src="https://rukminim1.flixcart.com/image/832/832/k3t21zk0/wire-joint-connector/b/x/r/2-industrial-plug-and-socket-32-a-x-5-pin-415v-weatherproof-ip44-original-imafmuxqgpym6hzx.jpeg" alt="Drawing" style="width: 450px;"/>
---
# Introduction to Three Phase
## Industrial Electric Plugs

---
## Industrial Electric Plugs

### [IEC 60309 industrial standard](https://www.plugsocketmuseum.nl/IEC60309_2.html)
---
# Expired 3-Phase Color Code (Before 2011)

---
# New 3-Phase Color Code (Since 2011)

---
# Electric Vehicle Chargers

### [What are all these pins for?](http://tesla.o.auroraobjects.eu/Design_Guide_Combined_Charging_System_V3_1_1.pdf)
---
# CCS: Combined Charging System

---
# Introduction to Three Phase
## Offshore Power Plugs
--
<img src="http://i.kinja-img.com/gawker-media/image/upload/s--lCQmivgV--/c_fit,fl_progressive,q_80,w_636/yvnjg8sxmbvgya1luf6n.jpg" alt="Drawing" style="width:800px;"/>

---
# Introduction to Three Phase
## Offshore Power Plugs

<img src="http://i.kinja-img.com/gawker-media/image/upload/s--Mb48YYZM--/c_fit,fl_progressive,q_80,w_636/vs2m6ydklatpy6u0ngje.jpg" alt="Drawing" style="width:700px;"/>
---
# Introduction to Three Phase
## Transmission Lines

---
# Introduction to Three Phase
## Transmission Lines

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

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

---
# WHY 3-PHASE?
--

- ## Less conductor material for the same power.

--
- ## Constant Power
[Power Graphs](https://docs.google.com/spreadsheets/d/1RP-MsrHwybAG6J3CFTbdLOCTvGdIdkaWUkhRuAHPWd0/edit?usp=sharing), [3-Phase Animations](./interactive/three_phase_explorer.html)

--
- ## Rotating MMF
### [3-phase](http://people.ece.umn.edu/users/riaz/animations/sinwaves0.gif), [phasor](http://people.ece.umn.edu/users/riaz/animations/vecmovieslow.gif)(wait until EE362 for details)

---
# Voltages & Currents

## \\(Va = V_{max} \mathrm{sin} (\omega t)\\)
## \\(Vb = V_{max} \mathrm{sin} (\omega t - 2 \pi /3)\\)
## \\(Vc = V_{max} \mathrm{sin} (\omega t - 4 \pi /3)\\)

### Note that \\( V_{max}\\) is the peak value, but we still use RMS values in phasors!

---
# Voltages & Currents
![](3phase_phasors.png)

---
# 3 Phase Phasors

<img src="./images/ee361/three_phase_phasor.gif" alt="Drawing" style="width: 800px;"/>
---
### Explore: 3-Phase Waveforms, Phasors & Power
<iframe src="interactive/three_phase_explorer.html?embed" width="790" height="500" style="border:0"></iframe>

#### Try it yourself: [keysan.me/presentations/interactive/three_phase_explorer.html](https://keysan.me/presentations/interactive/three_phase_explorer.html)

---
# Balanced 3-Phase System
## \\(\vec{V\_{a}} + \vec{V\_{b}} + \vec{V\_{c}} = 0 \\)

## \\( \vec{I\_{a}} + \vec{I\_{b}} + \vec{I\_{c}} = 0\\)
--

## So the neutral current is zero → the neutral wire can be thin or omitted
--

### Phase sequence: abc (positive) or acb (negative)
### Swap any two wires → sequence reverses → a 3-phase motor turns the other way

---

# How to measure voltage & currents?

<img src="https://upload.wikimedia.org/wikipedia/commons/4/48/3-phase_flow.gif" alt="Drawing" style="width: 800px;"/>
---
# How to measure voltage & currents?

<img src="3phase_voltages.png" alt="Drawing" style="width: 800px;"/>
---
# How to measure voltage & currents?

## \\(\vec{V\_{ab}}=\vec{V\_{an}} + \vec{V\_{nb}} = \vec{V\_{an}} - \vec{V\_{bn}}  \\)

## If \\(\vec{V\_{an}} = V \angle 0^∘ \\)

--
## \\(\vec{V\_{ab}}= \sqrt 3 V \angle 30^∘\\)
---
### Where do √3 and 30° come from?
<iframe src="interactive/line_phase_explorer.html?embed" width="790" height="500" style="border:0"></iframe>

#### Try it yourself: [keysan.me/presentations/interactive/line_phase_explorer.html](https://keysan.me/presentations/interactive/line_phase_explorer.html)

---
# What is the Grid Voltage Level?

## Used to be 220 V
--
(line-to-neutral RMS)

## Peak (line-to-neutral) \\(= 220 \sqrt{2} = 311 \\) V

## RMS (line-to-line) \\(= 220 \sqrt{3} \approx 380 \\) V 
---
# What is the Grid Voltage Level?

# NOW  [the standard is 230 V](http://www.schneider-electric.co.uk/en/faqs/FA144717/) 
## ± 10% (line-to-neutral RMS)

--
### IEC 60038 harmonised Europe's 220 V and the UK's 240 V into a single 230 V standard
### Turkey's grid has run synchronously with the [European system (ENTSO-E)](https://www.entsoe.eu/data/map/) since 2010

---
# What is the Grid Voltage Level?

# NOW  [the standard is 230 V](http://www.schneider-electric.co.uk/en/faqs/FA144717/) 
## ± 10% (line-to-neutral RMS)
## Peak (line-to-neutral) \\(= 230 \sqrt{2} = 325 \\) V

## RMS (line-to-line) \\(= 230 \sqrt{3} \approx 400 \\) V

---
# Star/Wye (Y) & Delta (\\(\Delta\\)) Connections 
<img src="https://www.electricalvolt.com/wp-content/uploads/2023/11/image-67.png?ezimgfmt=ng:webp/ngcb1" alt="Drawing" style="width: 800px;"/>

---
# Wye(or Star) Connection (Y)
<img src="./images/ee361/3_Phase_Power_Connected_to_Wye_Load.png" alt="Drawing" style="width: 500px;"/>

### \\( |V\_{line-to-line}| = \sqrt{3} \; |V\_{phase}|\\)
### \\( |I\_{line}| = |I\_{phase}|\\)

#### \\( \vec{V\_{ab}} = \sqrt{3}\,\vec{V\_{an}} \angle 30^∘\\) (line voltage leads phase voltage by 30°)
---
# Delta Connection (\\(\Delta\\))

### \\( |V\_{line-to-line}| = |V\_{phase}|\\)
### \\( |I\_{line}| = \sqrt{3} \; |I\_{phase}|\\)

---
#Power Relations
--

## Regardless of the connection type

## \\(  |S| = 3V\_{phase}I\_{phase}\\)
--

## or

## \\( |S| = \sqrt{3}V\_{line-to-line}I\_{line}\\)

#### [Review of three phase AC circuits](http://www.egr.unlv.edu/~eebag/EE%20340%20-%20Review%203-Phase%20Ckts.pdf)
---
#Power Relations

## Regardless of the connection type

## \\(  P = 3V\_{phase}I\_{phase} cos (\theta)\\)

## or

## \\( P = \sqrt{3}V\_{line-to-line}I\_{line}cos (\theta)\\)

## Careful: \\(\theta\\) is always the angle between \\(V\_{phase}\\) and \\(I\_{phase}\\)

#### [Review of three phase AC circuits](http://www.egr.unlv.edu/~eebag/EE%20340%20-%20Review%203-Phase%20Ckts.pdf)

---
# Impedance Transformation

## \\(Z_{\Delta} = 3 Z\_Y \\)
---
# Per-Phase Analysis (balanced systems)

## 1. Convert any \\(\Delta\\) to an equivalent Y (\\(Z\_Y = Z\_\Delta/3\\))

## 2. Solve **phase a** only: a single-phase circuit, line-to-neutral

## 3. Phases b and c: same magnitude, shifted by \\(-120^∘\\) and \\(+120^∘\\)

## 4. Total power = 3 × phase power

---
# Examples

- ### [AC Power Solved Problem](./files/ee361-ac-solved1.pdf)
- ### [AC Power Solved Problem 2](./files/ee361-ac-solved2.pdf)
- ### [3 Phase Power Solved Problem](./files/ee361-3phase-solved.pdf)

---
## You can download this presentation from: [keysan.me/ee361](http://keysan.me/ee361)