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<!DOCTYPE html>
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<head>
<title>EE462-Utilization of Electtrical Energy</title>
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class: center, middle
# EE-462 UTILIZATION OF ELECTRICAL ENERGY
# AC to DC Motor Drives
## Ozan Keysan
## [keysan.me](http://keysan.me)
### Office: C-113 <span class="meta">•</span> Tel: 210 7586
---
# Review:
--
## Half-wave Controlled Rectifier?
--
<img src="https://kullabs.com/uploads/image024.gif" alt="Drawing" style="width: 800px;"/>
---
# 1-Ph AC Input DC Motor Drives
--
## Single Phase Full-wave Rectifier
<img src="./images/ee462/single_phase_full_wave.png" alt="Drawing" style="width: 500px;"/>
### Reference [Ch11](http://onlinelibrary.wiley.com/book/10.1002/9781118524336)
---
## Single Phase Full-wave Rectifier
<img src="./images/ee462/single_phase_full_wave2.png" alt="Drawing" style="width: 700px;"/>
---
## Single Phase Full-wave Rectifier
## \\( V\_d = \dfrac{1}{\pi} \int\_{\alpha}^{\pi + \alpha} \sqrt{2}V_s sin(\omega t) d(\omega t)\\)
--
## \\( V\_d = \dfrac{2\sqrt{2}}{\pi} V\_s cos (\alpha)\\)
--
## \\( V\_d = 0.9 V\_s cos (\alpha)\\)
#### Ref: Mohan Chapter-6: Single Phase Converters
---
## Single Phase Full-wave Rectifier
<img src="./images/ee462/Vd_full_wave_rectifier.png" alt="Drawing" style="width: 750px;"/>
#### Ref: Mohan Chapter-6: Single Phase Converters
---
## Single Phase Full-wave Rectifier
### Harmonics on the Source Side
<img src="./images/ee462/single_phase_rectifier_harmonics.png" alt="Drawing" style="width: 550px;"/>
#### Fourier expansion of a square wave
---
## Single Phase Full-wave Rectifier
### with Non-zero Line Inductance (\\(L_s\\))
<img src="./images/ee462/single_phase_full_wave_Ls.png" alt="Drawing" style="width: 500px;"/>
### Implies non-zero commutation period
---
## Single Phase Full-wave Rectifier
### Implies non-zero commutation period
<img src="./images/ee462/single_phase_rectifier_commutation
.png" alt="Drawing" style="width: 750px;"/>
#### Ref: Mohan Chapter-6: Single Phase Converters
---
## Application as a DC Motor Drive
<img src="./images/ee462/single_phase_thyristor_drive
.png" alt="Drawing" style="width: 500px;"/>
---
## Application as a DC Motor Drive
### Can you plot the waveforms?
--
<img src="./images/ee462/single_phase_thyristor_drive_cont.png" alt="Drawing" style="width: 800px;"/>
### Continuous Conduction Mode
---
## Application as a DC Motor Drive
### Continuous Conduction Mode
## \\( V\_d \approx 0.9 V\_s cos (\alpha) - \dfrac{2}{\pi} \omega L\_s I\_{d(min)} \\)
---
## Application as a DC Motor Drive
<img src="./images/ee462/single_phase_thyristor_drive_discont.png" alt="Drawing" style="width: 800px;"/>
### Discontinuous Conduction Mode
---
# 3-Phase Thyristor Rectifiers
<img src="./images/ee462/3ph_thyristor_rectifier.png" alt="Drawing" style="width: 500px;"/>
#### Reference: Mohan Chapter 6
---
# 3-Phase Thyristor Rectifiers
<img src="./images/ee462/3ph_thyristor_rectifier_simplified.png" alt="Drawing" style="width: 500px;"/>
#### Reference: Mohan Chapter 6
---
# 3-Phase Thyristor Rectifiers
## Can you plot the waveforms?
### for a firing angle of 0 degrees.
---
<img src="./images/ee462/3ph_thyristor_voltage.png" alt="Drawing" style="width: 750px;"/>
---
# 3-Phase Thyristor Rectifiers
<img src="./images/ee462/3ph_thyristor_voltage2.png" alt="Drawing" style="width: 750px;"/>
### What is the relation between Vd and Vll?
---
# 3-Phase Thyristor Rectifiers
<img src="./images/ee462/3ph_thyristor_voltage2.png" alt="Drawing" style="width: 750px;"/>
### \\(V\_{do}= \dfrac{3\sqrt{2}}{\pi}V\_{l-l} = 1.35 V\_{l-l}\\)
--
### \\(V\_{d\alpha}= \dfrac{3\sqrt{2}}{\pi}V\_{l-l} cos (\alpha)= 1.35 V\_{l-l} cos (\alpha)\\)
---
# Output Voltage vs. Firing Angle
<img src="./images/ee462/3phase_thyristor_0.png" alt="Drawing" style="width: 800px;"/>
---
# Output Voltage vs. Firing Angle
<img src="./images/ee462/3phase_thyristor_30.png" alt="Drawing" style="width: 800px;"/>
---
# Output Voltage vs. Firing Angle
<img src="./images/ee462/3phase_thyristor_60.png" alt="Drawing" style="width: 800px;"/>
---
# Output Voltage vs. Firing Angle
<img src="./images/ee462/3phase_thyristor_90.png" alt="Drawing" style="width: 800px;"/>
---
# Output Voltage vs. Firing Angle
<img src="./images/ee462/3phase_thyristor_120.png" alt="Drawing" style="width: 800px;"/>
---
# Output Voltage vs. Firing Angle
<img src="./images/ee462/3phase_thyristor_150.png" alt="Drawing" style="width: 800px;"/>
---
# Output Voltage vs. Firing Angle
<img src="./images/ee462/3phase_thyristor_180.png" alt="Drawing" style="width: 800px;"/>
---
## Input Current Waveform
<img src="./images/ee462/3ph_thyristor_input_current.png" alt="Drawing" style="width: 500px;"/>
### No 3rd order harmonics
#### Comparison: <a href="https://www.google.com.tr/?gfe_rd=cr&ei=XqrmWLLjEc-z8weYuJvgDA&gws_rd=ssl#q=sin(x)%2Bsin(3x)/3%2Bsin(5x)/5%2Bsin(7x)/7%2Bsin(9x)/9%2Bsin(11x)/11%2Bsin(13x)/13%2Bsin(15x)/15%2Bsin(17x)/17">Single Phase</a>, <a href="https://www.google.com.tr/?gfe_rd=cr&ei=warmWK-gCM-z8weYuJvgDA&gws_rd=ssl#q=sin(x)-sin(5x)/5-sin(7x)/7%2Bsin(11x)/11%2Bsin(13x)/13-sin(17x)/17-sin(19x)/19">Three Phase</a>
---
# Effect of Supply Reactance
--
### Introduces a voltage drop on the rectified side
- ### Single Phase: \\(\dfrac{2\omega L_s}{\pi}I_a\\)
--
- ### Three Phase: \\(\dfrac{3\omega L_s}{\pi}I_a\\)
--
- ### Resultant voltage in a 3-ph rectifier:
### \\(V\_{d\alpha}= \dfrac{3\sqrt{2}}{\pi}V\_{l-l} cos (\alpha) - \dfrac{3\omega L_s}{\pi}I_a \\)
---
# Applications as DC Motor Drives
<img src="./images/ee462/3ph_thyristor_motor_drive.png" alt="Drawing" style="width: 650px;"/>
---
# Applications as DC Motor Drives
### Continuous Current Conduction
<img src="./images/ee462/3ph_thyristor_motor_drive2.png" alt="Drawing" style="width: 800px;"/>
---
# Applications as DC Motor Drives
### Discontinuous Current Conduction
<img src="./images/ee462/3ph_thyristor_motor_drive3.png" alt="Drawing" style="width: 800px;"/>
---
# Applications as DC Motor Drives
## Pros and Cons?
--
<img src="./images/ee462/3ph_thyristor_motor_drive_current.png" alt="Drawing" style="width: 800px;"/>
---
# Applications as DC Motor Drives
## In which quadrants can the drive operate?
<img src="./images/ee462/3ph_thyristor_motor_drive.png" alt="Drawing" style="width: 450px;"/>
### Ref: Mohan Chapter 13 DC Motor Drives
---
# Applications as DC Motor Drives
## Two Quadrant Operation
## Forward Motoring (Ea>0, Ia>0)
## Reverse Braking (Ea<0, Ia>0)
---
# Applications as DC Motor Drives
## How can you obtain four quadrant operation?
--
## Cheap Way: Use a contactor
<img src="./images/ee462/3ph_thyristor_motor_drive_contactor.png" alt="Drawing" style="width: 650px;"/>
---
# Applications as DC Motor Drives
## How can you obtain four quadrant operation?
## Proper Way: Use two back-to-back rectifiers
<img src="./images/ee462/3ph_thyristor_motor_drive_regenerative.png" alt="Drawing" style="width: 450px;"/>
---
## You can download this presentation from: [keysan.me/ee462](http://keysan.me/ee462)
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