EE464-Static Power Conversion-II

class: center, middle

# EE-464 STATIC POWER CONVERSION-II

# Other PWM Techniques

## Ozan Keysan

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

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

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# Hysteresis (Bang-Bang) PWM
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## You already implemented in the first semester

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# Hysteresis (Bang-Bang) PWM

### If your current is higher than your reference, reduce the current (switch off), if not increase the current (Switch ON)

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# Hysteresis (Bang-Bang) PWM

### For an inverter, just change your reference current to a sinusoidal waveform instead of a constant reference.

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# Hysteresis (Bang-Bang) PWM
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- ## The switching frequency is varying
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- ## Difficult to design filter (because of varying fs)
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- ## Can induce side-band harmonics
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- ## Simple control and implementation

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# Hysteresis (Bang-Bang) PWM

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# Field Oriented Control (FOC)
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- ### [What is FOC?](https://www.youtube.com/watch?v=Nhy6g9wGHow)
- ### [Field oriented Control of PM Motors](https://www.youtube.com/watch?v=cdiZUszYLiA)
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## How to aim to a moving target?
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# A Few 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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### Main Idea: 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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##How do you define the resultant (black) phasor?

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# Clarke Transformation

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# Clarke Transformation

<img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/36e05ba56ec15de753eb9f3c60983bc874e31370" alt="Drawing" style="width: 750px;"/>
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# Park Transformation
## (or D-Q Transformation)

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# Park Transformation in Space

### i.e. [Interstellar - Docking Scene](https://www.youtube.com/watch?v=c4tPQYNpW9k)

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# Park Transformation
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## From rotating frame to stationary frame
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## Instead of dealing with sinusoidal signals, just  use the magnitudes.
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## When re-constructing signals use the rotor position information

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# Park Transformation

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# Park Transformation
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<img src="./images/ee462/park_transform.png" alt="Drawing" style="width: 400px;"/>
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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

# Id: Proportional to flux in the air-gap

# 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

<img src="https://in.mathworks.com/help/sps/powersys/ug/electric_drives223.gif" alt="Drawing" style="width: 600px;"/>
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# Summary

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# Further Reading

### [Vector Control for Dummies](https://www.switchcraft.org/learning/2016/12/16/vector-control-for-dummies)

### [What is Field Oriented Control?](https://www.eetimes.com/document.asp?doc_id=1279321)

### [Field Oriented Control](http://mycourses.aalto.fi/pluginfile.php/1055633/mod_resource/content/12/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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# 3-Phase Two-Level Inverter
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### Anti-parallel diodes are not shown.

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# 3-Phase Two-Level Inverter

## Each leg has two positions: 
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top switch closed (1)

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# 3-Phase Two-Level Inverter

## Each leg has two positions: 
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bottom switch closed (0)

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# [Voltage Vectors](https://www.switchcraft.org/learning/2017/3/15/space-vector-pwm-intro)
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### 000 - \\(v_0\\) (zero vector)
### 001 - \\(v_1\\) (Phase +U)
### 010 - \\(v_2\\) (Phase +V)
### 011 - \\(v_3\\) (Phase -W)
### 100 - \\(v_4\\) (Phase +W)
### 101 - \\(v_5\\) (Phase -V)
### 110 - \\(v_6\\) (Phase -U)
### 111 - \\(v_7\\) (zero vector)

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# Voltage Vectors: V0

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# Voltage Vectors: V1

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# Voltage Vectors: V2

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# Voltage Vectors: V3

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# Voltage Vectors: V4

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# Voltage Vectors: V5

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# Voltage Vectors: V6

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# Voltage Vectors: V7

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# Square Wave Operation

### [BLDC Drive with square wave](https://www.youtube.com/watch?v=IiY01xIKg28)

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## What about the vectors in between?
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## What about the vectors in between?

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## What about the vectors in between?

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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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## SPWM vs SVPWM
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#### Phase Voltages
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## SPWM vs SVPWM
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- ## Space Vector PWM generates less harmonic distortion
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- ##  Space Vector PWM utilizes input voltage more \\(1/2\\) vs \\(1/\sqrt{3}\\) (15% more)

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### What is the max. possible phase voltage with SPWM (Sinusoidal PWM)?
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<img src="./images/ee464/spwm.jpg" alt="Drawing" style="width: 400px;"/>
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### \\(\hat{V}\_{p-n}=\dfrac{V\_{DC}}{2}\\)

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### What is the max. possible phase voltage with SPWM (Sinusoidal PWM)?
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### The inverter is connected to 400 \\(V\_{l-l}\\) grid with a 3-ph diode rectifier:

<img src="./images/ee464/vfd.jpg" alt="Drawing" style="width: 500px;"/>
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### \\(V\_{DC}=\\)
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\\(\dfrac{3\sqrt{2}}{\pi} V\_{l-l} \\)
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\\(= 1.35 V\_{l-l} = 540 V\\)

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### What is the max. possible phase voltage with SPWM (Sinusoidal PWM)?
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<img src="./images/ee464/vfd.jpg" alt="Drawing" style="width: 500px;"/>
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### Maximum motor phase voltage:
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### \\( V\_{phase-rms} = \dfrac{V\_{DC}}{2 \sqrt{2}}= 190 V\\)

### which is quite low for standard motors!

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## How can you increase the output voltage beyond the DC-link voltage limit?
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