EE462-Utilization of Electtrical Energy

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

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# 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)

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# Three Phase AC

<img src="http://www.ece.umn.edu/users/riaz/animations/sinwaves0.gif" alt="Drawing" style="width: 750px;"/>
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# Three Phase AC: Rotating MMF

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

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# Fundamental Idea of all AC Machines

### Field Oriented Control (FOC) is keeping the carrot exactly at the optimum distance (i.e. 90 degrees)
 
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# Some Useful Mathematical Tools
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- ## Clarke Transformation
- ## Park Transformation

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# [Clarke](https://en.wikipedia.org/wiki/Edith_Clarke) Transformation
## (a-b-c) to \\(\alpha \beta \\) Transformation

## From three-phase to two orthogonal phase transformation
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### 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.

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# Clarke Transformation

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# Clarke Transformation

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# Park Transformation
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## From stationary frame to rotationary frame
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## Instead of dealing with sinusoidal signals, just  use the magnitudes.
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## When reconstructing signals use the rotor position information

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# Park Transformation

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# Park Transformation
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## \\(I\_d = I\_\alpha  cos(\theta) + I\_\beta sin (\theta)\\)
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## \\(I\_q = I\_\beta  cos(\theta) - I\_\alpha sin (\theta)\\)
--

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## Reference Frames

<img src="./images/ee462/reference_frames.png" alt="Drawing" style="width: 750px;"/>
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## Clarke and Park Transformations

<img src="https://static1.squarespace.com/static/584729023e00bebf8abd6ba0/t/5866535e414fb5c4d35ed4cb/1483101083243/ClarkePark_Animation?format=500w" alt="Drawing" style="width: 500px;"/>
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# Torque and Flux Control
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# Id: Proportional to flux in the airgap
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# Iq: Proportional to torque generated

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# Inverse Transforms
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## Required to apply reference voltage and current waveforms (sinusoidals)
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- ## Inverse Park Transform
- ## Inverse Clarke Transform

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# Inverse Park Transform
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## From rotation frame to stationary frame
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## \\(I\_\alpha = I\_d  cos(\theta) - I\_q sin (\theta)\\)
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## \\(I\_\beta = I\_q  cos(\theta) + I\_d sin (\theta)\\)

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## Inverse Clarke Transform

### From two-axis orthogonal plane to 3-phase stationary frame.

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## Whole Workflow

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# Classical Vector Control Diagram

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# Vector Control in PMSM

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# Vector Control in Induction Motors

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# SVPWM
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## Space Vector Pulse Width Modulation
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### Approximate the reference voltage by a combination of 8 switching patterns

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# Two-Level Inverter

<img src="https://static1.squarespace.com/static/584729023e00bebf8abd6ba0/t/58fe88ba3a04117b78eda510/1493076202195/?format=1000w" alt="Drawing" style="width: 800px;"/>
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# [Voltage Vectors](https://www.switchcraft.org/learning/2017/3/15/space-vector-pwm-intro)
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### There are 8 combinations (\\(2^3\\)) (Note that, you can't open the top and bottom switches simultenously).

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# For example: \\(V_4\\): 100
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<img src="https://static1.squarespace.com/static/584729023e00bebf8abd6ba0/t/58fe8b655016e163f2febb78/1493076844542/?format=1000w" alt="Drawing" style="width: 750px;"/>
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# For example: \\(V_5\\): 101
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# 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)
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# 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;"/>
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# Voltage Synthesizing

<img src="https://static1.squarespace.com/static/584729023e00bebf8abd6ba0/58fea923197aea4f7f28f61a/58fea9286a49632401d63e94/1493084598485/SVPWM-1.png?format=1000w" alt="Drawing" style="width: 700px;"/>
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# PWM Generation

<img src="https://static1.squarespace.com/static/584729023e00bebf8abd6ba0/t/59110ff0ebbd1a1c7143886d/1494290426838/?format=1000w" alt="Drawing" style="width: 700px;"/>
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# PWM Generation

### Switching Sequence: 000-001-011-111
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# PWM Generation

## Switching Sequence:

- ## Zero Vector (000)
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- ## Basic Vector (i.e. 001)
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- ## Basic Vector (i.e. 011)
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- ## Zero Vector (i.e. 111)
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## Only one switch position is changed at each step!

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# PWM Generation

<img src="https://static1.squarespace.com/static/584729023e00bebf8abd6ba0/t/58feacf5d482e9da38497463/1493085606567/?format=1000w" alt="Drawing" style="width: 700px;"/>
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# Multi Level SVPWM

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# Voltage Limits

### Magnitudes of each basic vector:
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\\(V\_{DC}\\)  
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<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)
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# Third Harmonic Injection
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# Third Harmonic Injection

<img src="https://static1.squarespace.com/static/584729023e00bebf8abd6ba0/t/59068b67725e256add1f37f5/1493601135313/?format=1000w" alt="Drawing" style="width: 800px;"/>
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# Third Harmonic Injection

<img src="https://static1.squarespace.com/static/584729023e00bebf8abd6ba0/t/59068e15e6f2e142b4adbe4f/1493601820281/?format=1000w" alt="Drawing" style="width: 800px;"/>
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# Third Harmonic Injection

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## You can download this presentation from: [keysan.me/ee462](http://keysan.me/ee462)