EE464-Static Power Conversion-II

class: center, middle

# EE-464 STATIC POWER CONVERSION-II

# DC/AC Converters (Inverters)

## Ozan Keysan

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

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

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# DC/AC Converters
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# Inverters

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# Block Diagram

### AC Motor drive with unidirectional power flow
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<img src="./images/ee464/inverter_unidirectional.png" alt="Drawing" style="width: 800px;">
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# Block Diagram

### AC Motor drive with bidirectional power flow
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### Back-to-Back Converter, Active Front-End Converter, Variable Frequency Drive (VFD)
<!--
# Operating Quadrants

# Operating Quadrants

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# Single Leg Inverter
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### Building block for almost all inverter types
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# PWM Generation
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## Sinusoidal PWM (SPWM)

- ## The most common type

- ## There are many different PWM techniques (wait 2 weeks)

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# Sinusoidal PWM (SPWM)

### Compare a sinusoidal wave with a carrier triangular wave

<img src="./images/ee464/svpwm1.png" alt="Drawing" style="width: 600px;">
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# Sinusoidal PWM
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# Sinusoidal PWM
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<img src="./images/ee464/analog_svpwm.png" alt="Drawing" style="width: 700px;">
### Analog generation of SPWM

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# PWM in one leg inverter

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# Some Definitions
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## Frequency Modulation Ratio
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## \\(m_f = \dfrac{f_s}{f_1}\\)

## \\(f_s\\): Switching frequency
## \\(f_1\\): Fundamental frequency of AC output
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# What is \\(m_f\\) for this case?

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## \\(m_f\\) selection
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## Preferred to have a high value (\\(m_f>21\\))

- ### i.e 2 kHz for 50 Hz: \\(m_f=40\\)
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- ### May not be possible for larger power applications
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- ### Be aware of [audible noise](http://onlinetonegenerator.com/) (not only fs, but also its harmonics)
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- ### Asynchronous PWM can be used but not preferred
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## Synchronous PWM

### \\(f_s\\) is an integer multiple of  \\(f_1\\)

<img src="./images/ee464/svpwm_one_leg.png" alt="Drawing" style="width: 300px;">
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- ### \\(m_f\\) is integer
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- ### If not (asynchronous PWM), subharmonics of \\(f_1\\) is generated
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## \\(m_f\\) selection
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## Small Frequency Modulation (\\(m_f<21\\))

- ### Synchronous PWM should be used
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- ### \\(m_f\\) should be an odd integer

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# Some Definitions
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## Modulation Index
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## (Amplitude Modulation Ratio)
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## \\(m\_a=\dfrac{\hat{V}\_{control}}{\hat{V}\_{triangle}}\\)
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## Linear region: \\(m_a<1\\)
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## Overmodulation: \\(m_a>1\\)

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# Linear Region
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### Fundamental voltage magnitude varies linearly with \\(m_a\\)
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### \\(\hat{V}\_{ao1}= m\_a \dfrac{V\_d}{2}\\)
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### \\(V\_{ao}= \dfrac{v\_{control}}{\hat{V}\_{triangle}} \dfrac{V\_d}{2}\\)
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### Other harmonics does NOT change linearly with \\(\hat{V}\_{ao1}\\)
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# PWM Harmonics
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## FFT in linear region
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## Notice the sidebands

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# [PWM Harmonics](https://www.google.com.tr/search?ei=fVW5Wpm9G6Lg6ATYtquYCg&q=plot+0.8*sin%28x%29%2B0.22*sin%2837*x%29%2B0.818*sin%2839*x%29%2B0.22*sin%2841*x%29%2B0.314*sin%2877*x%29%2B0.314*sin%2879*x%29%2B0.139*sin%2881*x%29%2B0.139*sin%2875*x%29%2B0.013*sin%2883*x%29%2B0.013*sin%2873*x%29%2B0.171*sin%28117*x%29%2B0.176*sin%28119*x%29%2B0.176*sin%28115*x%29%2B0.104*sin%28121*x%29%2B0.104*sin%28113*x%29%2B0.105*sin%28155*x%29%2B0.105*sin%28157*x%29%2B0.115*sin%28153*x%29%2B0.115*sin%28159*x%29%2B0.016*sin%28143*x%29%2B0.016*sin%28131*x%29&oq=plot+0.8*sin%28x%29%2B0.22*sin%2837*x%29%2B0.818*sin%2839*x%29%2B0.22*sin%2841*x%29%2B0.314*sin%2877*x%29%2B0.314*sin%2879*x%29%2B0.139*sin%2881*x%29%2B0.139*sin%2875*x%29%2B0.013*sin%2883*x%29%2B0.013*sin%2873*x%29%2B0.171*sin%28117*x%29%2B0.176*sin%28119*x%29%2B0.176*sin%28115*x%29%2B0.104*sin%28121*x%29%2B0.104*sin%28113*x%29%2B0.105*sin%28155*x%29%2B0.105*sin%28157*x%29%2B0.115*sin%28153*x%29%2B0.115*sin%28159*x%29%2B0.016*sin%28143*x%29%2B0.016*sin%28131*x%29&gs_l=psy-ab.3...48885.70566.0.71020.15.15.0.0.0.0.0.0..0.0....0...1c.1.64.psy-ab..15.0.0....0.-PE9gd4ffFo)
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<img src="./images/ee464/pwm_harmonics_table.png" alt="Drawing" style="width: 550px;">
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# PWM Harmonics

## Advantages of choosing \\(m_f\\) as odd integer:

- ### Results in odd symmetry (\\(f(-t)=-f(t)\\))

- ### Results in half-wave symmetry (\\(f(t)=-f(t+T/2)\\))

- ### No even harmonics are present

- ### Only sine components exist (no cosine harmonics component)

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## Over-modulation in SPWM
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### Control signals gets bigger than the triangle waveform

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## Over-modulation in SPWM

### Possible to create higher magnitude, but induce harmonics of \\(f_1\\)
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## Over-modulation in SPWM

## Worst Case?:
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Square Wave

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## Over-modulation in SPWM

## Square Wave Harmonics

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## Over-modulation in SPWM

## Square Wave Peak Voltage?
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### \\(\hat{V}\_{ao1}= \dfrac{4}{\pi} \dfrac{V\_d}{2} = 1.273 \dfrac{V\_d}{2}\\)
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## Fundamental harmonics:

### \\(\hat{V}\_{aoh}= \dfrac{\hat{V}\_{ao1}}{h}\\)

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# Over-modulation Index Variation

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# Single-Phase Half-Bridge Inverter

### In order to have equal capacitor voltage, io cannot have a DC component

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# Single-Phase Full-Bridge Inverter

### Voltage level is twice of the half bridge inverter

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# Bipolar PWM

## Same with the full-bridge DC/DC converter 
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### \\(T\_{A+}\\) and \\(T\_{B-}\\) are turn on and off together
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### \\(T\_{A-}\\) and \\(T\_{B+}\\) are complimentary of \\(T\_{A+}\\) and \\(T\_{B-}\\)
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## Can give \\(V\_d\\) or \\(-V\_d\\)

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# Bi-polar Voltage Switching

<img src="./images/ee464/bipolar1.png" alt="Drawing" style="width: 600px;">
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# Bi-polar Voltage Switching

<img src="./images/ee464/bipolar2.png" alt="Drawing" style="width: 700px;">
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# Bi-polar PWM

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# Bi-polar PWM
### Voltage level is twice of the half bridge inverter
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## Linear Region

### \\(\hat{V}\_{o1}= m\_a V\_d\\)
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## Over-modulation

### \\(V\_d < \hat{V}\_{o1} <   \dfrac{4}{\pi}  V\_d\\)
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# Bi-polar PWM

## Same harmonics

<!--
# Source Side Current

# Source Side Current

## Has DC and AC (with \\(2f_1\\)) component.

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# Unipolar PWM

## Same with the full-bridge DC/DC converter

### \\(T\_{A+}\\) and \\(T\_{B+}\\) are controlled seperately

### \\(T\_{A-}\\) and \\(T\_{B-}\\) are complimetary of \\(T\_{A+}\\) and \\(T\_{B+}\\)
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## Can give \\(V\_d\\), \\(0\\), \\(-V\_d\\)

## \\(V\_o = 0 \\) if \\(T\_{A+}\\) and \\(T\_{B+}\\) are ON
## \\(V\_o = 0 \\) if \\(T\_{A-}\\) and \\(T\_{B-}\\) are ON

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# Uni-polar Voltage Switching

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# Uni-polar Voltage Switching

<img src="./images/ee464/unipolar2.png" alt="Drawing" style="width: 700px;">
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# Uni-polar PWM Sine Output
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<img src="./images/ee464/unipolar_sine.png" alt="Drawing" style="width: 600px;">
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# Uni-polar PWM Sine Output
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<img src="./images/ee464/unipolar_sine2.png" alt="Drawing" style="width: 800px;">
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# Uni-polar PWM Harmonics
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## Harmonics of twice the switching frequency.
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<img src="./images/ee464/unipolar_pwm_harmonics.png" alt="Drawing" style="width: 800px;">
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## Harmonics Comparison

### Bipolar PWM

### Unipolar PWM
 <img src="./images/ee464/unipolar_harmonics2.png" alt="Drawing" style="width: 800px;">

<!--
# Unipolar PWM DC Side Current

<img src="./images/ee464/unipolar_dc_current.png" alt="Drawing" style="width: 800px;">
-->
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# Inverter Connected to R-L Load
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# Inverter Connected to R-L Load

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# Inverter Connected to R-L Load

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# Inverter Connected to R-L Load

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## Sinusoidal Generation by Voltage Shift
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### Generate Square wave with controllable off periods

<img src="./images/ee464/pwm_square.png" alt="Drawing" style="width: 600px;">
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## Sinusoidal Generation by Voltage Shift
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### Generate Square wave with controllable off periods
### Van and Vbn has overlapping regions

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## Sinusoidal Generation by Voltage Shift
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### Generate Square wave with controllable off periods
### Van and Vbn has overlapping regions

<img src="./images/ee464/square_off2.png" alt="Drawing" style="width: 650px;">
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## Sinusoidal Generation by Voltage Shift

### What about harmonics?
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### For curious students: SHE: [Selective Harmonic Elimination](https://pdfs.semanticscholar.org/7f9a/8313ba8b0988e9e6657cf1e4d21878e0abe2.pdf)

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### Example 8.8 (Hart-Power Electronics)
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### A full-bridge inverter is used to produce a 60 Hz voltage across a series R-L load using bi-polar PWM.
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### DC input is 100 V, amplitude modulation is 0.8, frequency modulation is 21. R=10 Ω, L= 20 mH.
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### a) Find the 60 Hz component of the voltage and current

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### Example 8.8 (Hart-Power Electronics)

### A full-bridge inverter is used to produce a 60 Hz voltage across a series R-L load using bi-polar PWM.

### DC input is 100 V, amplitude modulation is 0.8, frequency modulation is 21. R=10 Ω, L= 20 mH.

### b) Power absorbed by the resistor (refer to Table 8-3).
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<img src="./images/ee464/harmonics_example.png" alt="Drawing" style="width: 750px;">
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### Example 8.8 (Hart-Power Electronics)

### A full-bridge inverter is used to produce a 60 Hz voltage across a series R-L load using bi-polar PWM.

### DC input is 100 V, amplitude modulation is 0.8, frequency modulation is 21. R=10 Ω, L= 20 mH.

### c) THD of the load current
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### [Load Current](https://www.google.com.tr/search?q=plot+6.39*sin%28x%29%2B0.15*sin%2819*x%29%2B0.52*sin%2821*x%29%2B0.13*sin%2823*x%29&sxsrf=ALiCzsbdxyfjozNpyA-bOdmdiSNXuYDZBw%3A1652162874950&ei=OgF6YoPMOaOGxc8Pg72NoAo&ved=0ahUKEwiD0ZaqotT3AhUjQ_EDHYNeA6QQ4dUDCA0&uact=5&oq=plot+6.39*sin%28x%29%2B0.15*sin%2819*x%29%2B0.52*sin%2821*x%29%2B0.13*sin%2823*x%29&gs_lcp=Cgdnd3Mtd2l6EANKBAhBGAFKBAhGGABQilNY5_sFYKGABmgBcAB4AIABhQGIAYUBkgEDMC4xmAEAoAEBwAEB&sclient=gws-wiz)

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## You can download this presentation from: [keysan.me/ee464](http://keysan.me/ee464)