EE463-Static Power Conversion-I

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# EE-463 STATIC POWER CONVERSION-I

# Basic Concepts

## Ozan Keysan

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

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

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## Let's start with a simple DC-DC Converter
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<img src="./images/ee463/simple_dc_dc.png" alt="Drawing" style="width: 800px;"/>

## Can you design this converter?

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## Resistive Voltage Divider

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# Series Regulator (Transistor in linear mode)

### Efficiency= 50% !
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# Use an Ideal (Two Position) Switch

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## With L-C (Low-Pass) Filter

## Notice high efficiency

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## A more realistic example (Buck converter)

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# Generating AC: Single-Phase Inverter

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# Common Points
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## Avoid lossy elements!

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# Ideal Switch

<img src="./images/ee463/ideal_switch.png" alt="Drawing" style="width: 400px;"/>
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# Which factors make a switch ideal?

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# Ideal Switch
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- ## No voltage drop in the on-state
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- ## Zero switching time
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- ## No leakage current in the off-state
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- ## Infinite breakdown voltage and current capacity

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# What happens if you turn off a inductive load?
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# or

# What happens if turn-on with a capacitive load?

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# Practical Switch
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- ## Conduction losses (voltage drop, leakage current)
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- ## Finite switching time
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- ## Switching losses
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- ## Limited current and voltage capacity
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- ## Limited dv/dt and di/dt rating

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# General Rules in Power Electronics
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## Do not short circuit voltage sources (Unless V=0)
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## Do not open (turn-off) current sources (Unless I=0)
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## Inductors behave like current sources
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## Capacitors behave like voltage sources

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# Inductors in Steady-State Operation
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## a.k.a. Inductor Volts-Seconds Balance
### Average value of inductor voltage is zero in steady-state

### (Positive and negative areas of inductor voltage cancel each other)

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# Capacitors in Steady-State Operation

## a.k.a. Capacitor Charge (or Ampere-seconds) Balance 
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### (Positive and negative areas of capacitor current cancel each other)

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# Performance Parameters for Waveforms
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## i.e. How do you decide an output is better than another?
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## For example, can you tell which one of the DC supply voltage is better?

- ### [5 + 0.5sin(x)](https://www.google.com.tr/search?client=ubuntu&hs=a00&channel=fs&dcr=0&q=plot+%285+%2B+0.5*sin%28x%29%29&oq=plot+%285+%2B+0.5*sin%28x%29%29&gs_l=psy-ab.3...8005.8005.0.8351.1.1.0.0.0.0.111.111.0j1.1.0....0...1.1.64.psy-ab..0.0.0....0.14FW91dDBMU)

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### or

- ### [5+0.25*sin(x)+0.25*sin(10*x)](https://www.google.com.tr/search?client=ubuntu&hs=nKs&channel=fs&dcr=0&sxsrf=ALeKk01hPIMt3M_xlJsWnnme8lTzW-kinA%3A1602792352635&ei=oKuIX8aDJuXyqwGb0KuACQ&q=plot+%285+%2B+0.25*sin%28x%29%2B+0.25*sin%2810x%29%29&oq=plot+%285+%2B+0.25*sin%28x%29%2B+0.25*sin%2810x%29%29&gs_lcp=CgZwc3ktYWIQAzoHCAAQRxCwA1CbsRFY-8ERYPLPEWgBcAB4AIABiQOIAewLkgEFMi0zLjKYAQCgAQGqAQdnd3Mtd2l6yAEIwAEB&sclient=psy-ab&ved=0ahUKEwjG087msrfsAhVl-SoKHRvoCpAQ4dUDCAw&uact=5)

<img src="./images/ee463/sin2.png" alt="Drawing" style="width: 700px;"/>
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## Or can you tell which "more sinusoidal"?
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- ### [sin(x) + 0.3sin(3x)](https://www.google.com.tr/search?client=ubuntu&channel=fs&dcr=0&q=plot+%28sin%28x%29%2B0.3sin%283x%29%29&oq=plot+%28sin%28x%29%2B0.3sin%283x%29%29&gs_l=psy-ab.3...399088.399088.0.399490.1.1.0.0.0.0.283.283.2-1.1.0....0...1.1.64.psy-ab..0.0.0....0.zn-Ff1RFWRY)

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### or

- ### [sin(x) - 0.3sin(3x)](https://www.google.com.tr/search?client=ubuntu&channel=fs&dcr=0&q=plot+%28sin%28x%29-0.3sin%283x%29%29&oq=plot+%28sin%28x%29-0.3sin%283x%29%29&gs_l=psy-ab.3...4386.5198.0.5884.3.3.0.0.0.0.420.683.2-1j0j1.2.0....0...1.1.64.psy-ab..1.0.0....0.DUWQhKX7g00)
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<img src="./images/ee463/sin3.png" alt="Drawing" style="width: 700px;"/>
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# RMS
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(Root Mean Square)
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## \\(I_{RMS}= \sqrt{\dfrac{1}{T}\int_0^T i^2(t) dt}\\)
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## What is the physical meaning?
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## Average power dissipated if connected to \\(1 \: \Omega\\) resistor

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# RMS (Root Mean Square)

## What is the RMS of a signal with harmonics?

## \\(I= I_1 + I_2 + I_3 ...\\)
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## \\(I\_{RMS}= \sqrt{I\_{1\_{RMS}}^2+I\_{2\_{RMS}}^2+I\_{3\_{RMS}}^2...}\\)

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# Form Factor (FF)

## Ratio of RMS to average value

## \\(FF= \dfrac{V\_{RMS}}{V\_{average}}\\)

### Example: What is the form factor of a rectified sine?

# Crest Factor (or Peak Factor)
## Ratio of peak value to RMS Value

## \\(CF= \dfrac{V\_{peak}}{V\_{RMS}}\\)

# Crest Factor

## Higher CF means, higher energy in higher frequency harmonics

# Some Examples

-->

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# Distortion Factor
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## Ratio of Fundamental RMS to Total RMS
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## \\(DF=\dfrac{I\_{1\_{RMS}}}{I\_{s\_{RMS}}}\\)

## Quick Question: What is the DF for a square wave?
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# Displacement Power Factor
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## Power factor for the fundamental component

## i.e. DPF=\\(cos(\phi)\\) , where \\(\phi\\) is the phase difference between the FUNDAMENTAL components of V and I.

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# (True) Power Factor
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## Ratio of Real Power (P) to Apparent Power (S)

# \\(PF = \dfrac{P}{S}\\)

## True Power Factor includes all harmonics, whereas DPF includes only the fundamental component.

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# (True) Power Factor

# For perfect sine wave
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# DF = 1 and DPF = PF
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# For distorted waves
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# DF<1 and PF<DPF

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## For this waveform:

## displacement power factor (DPF) = 1
## but true power factor is < 1
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# THD
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 (Total Harmonic Distortion)
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## Ratio of the RMS of the harmonics (excluding the fundamental) to RMS of the fundamental component
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## \\( THD= \dfrac{\sqrt{\sum\limits_{h=2}^{\infty}I_h^2}}{I_1}\\)

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## i.e. ratio of power in harmonics to power in the fundamental component

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# THD (Total Harmonic Distortion)

## Very important for power quality, and limited by many standards.
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### [Used to be less than 5% for LV](https://www.aadc.ae/img/41f76c6a-90c5-46e4-aabc-1414e6e4896b.pdf)
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### In 2014, it was [increased to 8%](https://ieeexplore.ieee.org/document/6826459). Why?

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# THD (Total Harmonic Distortion)

### \\( THD= \dfrac{\sqrt{\sum\limits_{h=2}^{\infty}I_h^2}}{I_1}\\)
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 \\( = \dfrac{\sqrt{I_s^2-I_1^2}}{I_1}\\)

### Distortion factor can be expressed in terms of THD

## \\(DF=\dfrac{1}{\sqrt{1+THD^2}}\\)

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## Quick Question: Derive the THD of a square waveform

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## You can download this presentation from: [keysan.me/ee463](http://keysan.me/ee463)