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<!DOCTYPE html>
<html>
<head>
<title>EE462-Utilization of Electtrical Energy</title>
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class: center, middle
# EE-462 UTILIZATION OF ELECTRICAL ENERGY
# Basics of the Field Oriented Control
## Ozan Keysan
## [keysan.me](http://keysan.me)
### Office: C-113 <span class="meta">•</span> Tel: 210 7586
---
# Background Information Reading Material
### [Vector Control for Dummies](https://www.switchcraft.org/learning/2016/12/16/vector-control-for-dummies)
### [What is Field Oriented Control?](http://www.copleycontrols.com/Motion/pdf/Field-Oriented-Control.pdf)
### [Field Oriented Control](https://mycourses.aalto.fi/pluginfile.php/155905/mod_resource/content/4/Lecture10.pdf)
### [Field Oriented Control of AC Motors](http://www.ti.com/lit/an/bpra073/bpra073.pdf)
### [Sensorless PMSM Field Oriented Control](http://cache.nxp.com/assets/documents/data/en/reference-manuals/DRM148.pdf)
### [Space Vector PWM](https://www.switchcraft.org/learning/2017/3/15/space-vector-pwm-intro)
---
# Three Phase AC
<img src="http://www.ece.umn.edu/users/riaz/animations/sinwaves0.gif" alt="Drawing" style="width: 750px;"/>
---
# 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
<img src="http://www.ece.umn.edu/users/riaz/animations/sinvec.gif" alt="Drawing" style="width: 800px;"/>
---
# Fundamental Idea of all AC Machines
<img src="http://wrightresults.com/wp-content/uploads/2014/04/donkey-and-carrot.jpg" alt="Drawing" style="width: 600px;"/>
### Field Oriented Control (FOC) is keeping the carrot exactly at the optimum distance (i.e. 90 degrees)
---
# Some Useful Mathematical Tools
--
- ## Clarke Transformation
- ## Park Transformation
---
# [Clarke](https://en.wikipedia.org/wiki/Edith_Clarke) Transformation
## (a-b-c) to \\(\alpha \beta \\) Transformation
## From three-phase to two orthogonal phase transformation
--
### Note: In a balanced three-phase system, \\(I_a + I_b + I_c =0\\) so there is redundant information and system can be reduced to two variables.
---
# Clarke Transformation
<img src="https://www.keil.com/pack/doc/CMSIS/DSP/html/clarke.gif" alt="Drawing" style="width: 600px;"/>
---
# Clarke Transformation
<img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/36e05ba56ec15de753eb9f3c60983bc874e31370" alt="Drawing" style="width: 750px;"/>
---
# Park Transformation
--
## From stationary frame to rotationary frame
--
## Instead of dealing with sinusoidal signals, just use the magnitudes.
--
## When reconstructing signals use the rotor position information
---
# Park Transformation
<img src="https://static1.squarespace.com/static/584729023e00bebf8abd6ba0/t/58664f0f2994ca78b5145f29/1483099927549/?format=750w" alt="Drawing" style="width: 750px;"/>
---
# Park Transformation
--
## \\(I\_d = I\_\alpha cos(\theta) + I\_\beta sin (\theta)\\)
--
## \\(I\_q = I\_\beta cos(\theta) - I\_\alpha sin (\theta)\\)
--
<img src="./images/ee462/park_transform.png" alt="Drawing" style="width: 400px;"/>
---
## Reference Frames
<img src="./images/ee462/reference_frames.png" alt="Drawing" style="width: 750px;"/>
---
## Clarke and Park Transformations
<img src="https://static1.squarespace.com/static/584729023e00bebf8abd6ba0/t/5866535e414fb5c4d35ed4cb/1483101083243/ClarkePark_Animation?format=500w" alt="Drawing" style="width: 500px;"/>
---
# Torque and Flux Control
--
# Id: Proportional to flux in the airgap
--
# Iq: Proportional to torque generated
---
# Inverse Transforms
--
## Required to apply reference voltage and current waveforms (sinusoidals)
--
- ## Inverse Park Transform
- ## Inverse Clarke Transform
---
# Inverse Park Transform
--
## From rotation frame to stationary frame
--
## \\(I\_\alpha = I\_d cos(\theta) - I\_q sin (\theta)\\)
--
## \\(I\_\beta = I\_q cos(\theta) + I\_d sin (\theta)\\)
---
## Inverse Clarke Transform
### From two-axis orthogonal plane to 3-phase stationary frame.
<img src="http://e2e.ti.com/cfs-file/__key/communityserver-discussions-components-files/171/3750._F764D653_.JPG" alt="Drawing" style="width: 500px;"/>
---
## Whole Workflow
<img src="https://static1.squarespace.com/static/584729023e00bebf8abd6ba0/t/58c88acd579fb3efb64797c9/1489537751460/?format=1000w" alt="Drawing" style="width: 750px;"/>
---
# Classical Vector Control Diagram
<img src="http://3l4sbp4ao2771ln0f54chhvm.wpengine.netdna-cdn.com/wp-content/uploads/2016/07/Vector-Block-Diagram.gif" alt="Drawing" style="width: 600px;"/>
---
# Vector Control in PMSM
<img src="http://www.mdpi.com/sensors/sensors-17-00973/article_deploy/html/images/sensors-17-00973-g007.png" alt="Drawing" style="width: 750px;"/>
---
# Vector Control in Induction Motors
<img src="https://www.mathworks.com/help/physmod/sps/powersys/ug/electric_drives223.gif" alt="Drawing" style="width: 600px;"/>
---
# SVPWM
--
## Space Vector Pulse Width Modulation
--
<img src="https://www.mathworks.com/help/physmod/sps/powersys/ref/svpwmgenerator2level_sectors.jpg" alt="Drawing" style="width: 500px;"/>
### Approximate the reference voltage by a combination of 8 switching patterns
---
# Two-Level Inverter
<img src="https://static1.squarespace.com/static/584729023e00bebf8abd6ba0/t/58fe88ba3a04117b78eda510/1493076202195/?format=1000w" alt="Drawing" style="width: 800px;"/>
---
# [Voltage Vectors](https://www.switchcraft.org/learning/2017/3/15/space-vector-pwm-intro)
--
### There are 8 combinations (\\(2^3\\)) (Note that, you can't open the top and bottom switches simultenously).
<img src="./images/ee462/voltage_vectors.png" alt="Drawing" style="width: 450px;"/>
---
# For example: \\(V_4\\): 100
--
<img src="https://static1.squarespace.com/static/584729023e00bebf8abd6ba0/t/58fe8b655016e163f2febb78/1493076844542/?format=1000w" alt="Drawing" style="width: 750px;"/>
---
# For example: \\(V_5\\): 101
--
<img src="https://static1.squarespace.com/static/584729023e00bebf8abd6ba0/58fe97e82994caa7f860f9a7/58fe97e9d1758e34037dfacc/1493080117024/PowerElectronics-101.png?format=1000w" alt="Drawing" style="width: 750px;"/>
---
# Voltage Vectors
### 000 - V0 (zero vector)
### 001 - V1 (Phase +U)
### 010 - V2 (Phase +V)
### 011 - V3 (Phase -W)
### 100 - V4 (Phase +W)
### 101 - V5 (Phase -V)
### 110 - V6 (Phase -U)
### 111 - V7 (zero vector)
---
# Voltage Synthesizing
<img src="https://static1.squarespace.com/static/584729023e00bebf8abd6ba0/t/58fea6c8ebbd1a25ce89c905/1494287982183/Basic-Vectors-with-reference.png?format=500w" alt="Drawing" style="width: 500px;"/>
---
# Voltage Synthesizing
<img src="https://static1.squarespace.com/static/584729023e00bebf8abd6ba0/58fea923197aea4f7f28f61a/58fea9286a49632401d63e94/1493084598485/SVPWM-1.png?format=1000w" alt="Drawing" style="width: 700px;"/>
---
# PWM Generation
<img src="https://static1.squarespace.com/static/584729023e00bebf8abd6ba0/t/59110ff0ebbd1a1c7143886d/1494290426838/?format=1000w" alt="Drawing" style="width: 700px;"/>
---
# PWM Generation
<img src="https://static1.squarespace.com/static/584729023e00bebf8abd6ba0/t/59111028c534a5947d523098/1494290481944/?format=1000w" alt="Drawing" style="width: 550px;"/>
### Switching Sequence: 000-001-011-111
---
# PWM Generation
## Switching Sequence:
- ## Zero Vector (000)
--
- ## Basic Vector (i.e. 001)
--
- ## Basic Vector (i.e. 011)
--
- ## Zero Vector (i.e. 111)
--
## Only one switch position is changed at each step!
---
# PWM Generation
<img src="https://static1.squarespace.com/static/584729023e00bebf8abd6ba0/t/58feacf5d482e9da38497463/1493085606567/?format=1000w" alt="Drawing" style="width: 700px;"/>
---
# Multi Level SVPWM
<img src="http://www.merl.com/publications/images/TR2013-005.jpg" alt="Drawing" style="width: 600px;"/>
---
# Voltage Limits
### Magnitudes of each basic vector:
--
\\(V\_{DC}\\)
--
<img src="https://static1.squarespace.com/static/584729023e00bebf8abd6ba0/t/59067c66f7e0ab758917712d/1493597294454/?format=500w" alt="Drawing" style="width: 350px;"/>
--
#### \\(V\_{max,RMS}= V\_{DC} cos(30) \dfrac{1}{\sqrt{2}}\\)
#### [Detailed Example](https://www.switchcraft.org/learning/2017/3/15/space-vector-pwm-intro)
---
# Third Harmonic Injection
--
<img src="https://static1.squarespace.com/static/584729023e00bebf8abd6ba0/t/590687ddff7c50866d9f4f1d/1493600229378/?format=1000w" alt="Drawing" style="width: 800px;"/>
---
# Third Harmonic Injection
<img src="https://static1.squarespace.com/static/584729023e00bebf8abd6ba0/t/59068b67725e256add1f37f5/1493601135313/?format=1000w" alt="Drawing" style="width: 800px;"/>
---
# Third Harmonic Injection
<img src="https://static1.squarespace.com/static/584729023e00bebf8abd6ba0/t/59068e15e6f2e142b4adbe4f/1493601820281/?format=1000w" alt="Drawing" style="width: 800px;"/>
---
# Third Harmonic Injection
<img src="https://static1.squarespace.com/static/584729023e00bebf8abd6ba0/t/590691aed1758ec4d7664141/1493602742473/ThirdHarmonics.png?format=500w" alt="Drawing" style="width: 600px;"/>
---
## You can download this presentation from: [keysan.me/ee462](http://keysan.me/ee462)
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