EE462-Utilization of Electtrical Energy

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# EE-462 UTILIZATION OF ELECTRICAL ENERGY

# DC Motor Drives

## Ozan Keysan

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

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

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# Motor Drives
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## Torque Control (Current Control)

## Speed Control

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# Motor Drives

<img src="./images/ee462/motor_drive_control.png" alt="Drawing" style="width: 700px;"/>
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# Motor Drives

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# DC Motor Drives wrt Supply
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# DC/DC Drives
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# AC/DC Drives
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# 3Ph AC/DC Drives

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#DC/DC Drives: Simplest PWM Generator

<img src="./images/ee462/simple_pwm.png" alt="Drawing" style="width: 800px;"/>
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## A few definitions:

### D: duty cycle, fs: switching frequency, T: period

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#DC/DC Drives: Simplest PWM Generator

## \\(V\_{dc}= \dfrac{t\_{on}}{T}V\_s = D V\_s\\)

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#DC/DC Drives: Simplest PWM Generator

### What is the problem with this configuration as a DC motor drive?
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### Inductive Load! Solution: add a frewheeling diode

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#One-Quadrant DC Motor Drive

## Chopper with Freewheeling Diode

<img src="./images/ee462/one_quadrant_dc_drive.png" alt="Drawing" style="width: 800px;"/>
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#One-Quadrant DC Motor Drive

### Forward Motoring Mode
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### \\(V_s = L_a \dfrac{di_a}{dt}+R_a i_a + E_a\\)
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### Frewheeling Mode
### \\(0 = L_a \dfrac{di_a}{dt}+R_a i_a + E_a\\)

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#One-Quadrant DC Motor Drive
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<img src="./images/ee462/one_quadrant_continuous.png" alt="Drawing" style="width: 400px;"/>
### Continuous Mode of Operation

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#One-Quadrant DC Motor Drive
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#### Armature time constant: \\(\tau_a =\dfrac{L_a}{R_a}\\)
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#### Forward Motoring Mode:

###\\(i_a(t) = I_1 e^{(-t/\tau_a)}+ \dfrac{V_s-E_a}{R_a} (1- e^{(-t/\tau_a)})\\)
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### If \\(T<<\tau_a\\),  using Taylor series approximation:

###\\(i_a(t) \approx I_1 (1- \dfrac{t}{\tau_a}) + \dfrac{V_s-E_a}{L_a} t\\)

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### Freewheeling Mode:
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The magnitude of current at the beginning of the freewheeling cycle:

###\\(I_2 = I_1 e^{(-dt/\tau_a)}+ \dfrac{V_s-E_a}{R_a} (1- e^{(-dT/\tau_a)})\\)
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###\\(i_a(t) = I_2 e^{(-t/\tau_a)} - \dfrac{E_a}{R_a} (1- e^{(-t/\tau_a)})\\)
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#### If \\(T<<\tau_a\\),  using Taylor series approximation:

###\\(i_a(t) \approx I_2 (1- \dfrac{t}{\tau_a}) - \dfrac{E_a}{L_a} t\\)

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## Continuous Mode of Operation

### Reading for Derivations [Ch10](http://onlinelibrary.wiley.com/book/10.1002/9781118524336)

### Current Ripple: \\(\Delta I = I_2 - I_1\\)

### Current Ripple: \\(\Delta I = \dfrac{V_s}{R_a} \Bigg[\dfrac{1-e^{-dT/\tau_a} + e^{-T/\tau_a} - e ^{-(1-d)T/\tau_a}}{1-e^{-T/\tau_a}}\Bigg]\\)

### Max. current ripple occurs when:
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\\(d=0.5\\)
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### Max. ripple \\(\approx \dfrac{V_s}{R_a}tanh(\dfrac{T}{4\tau_a})\\)

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## Discontinuous Mode 
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## Discontinuous conduction may occur when:
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## - Ea is high
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## - Load is light (small Ia)
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## - T is long (small switching frequency)
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## - \\(\tau_a\\) is small (low inductance)
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## Discontinuous Mode

## Group Exercise:
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# Plot Ia, Is, Id, Va

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## Discontinuous Mode

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## Discontinuous Mode

### \\(\beta = \dfrac{\tau_a}{T} ln (\dfrac{V_s-E_a}{E_a} (1-e^{-dT/\tau_a})+1) \\)
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### Chopper gets into discontinuous mode when:

### \\( 1-d-\beta > 0 \\)
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### \\(d_c = \dfrac{\tau_a}{T} ln ( 1+ \dfrac{E_a}{V_s} (e^{T/\tau_a})-1) \\)

### If \\(d \lt d_c \rightarrow \\) discontinuous mode

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## Discontinuous Mode

### Approximate method

### If \\(T << \tau_a\\)
### \\(\beta \approx \dfrac{(V_s - E_a)d}{E_a}\\)

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### Chopper gets into discontinuous mode when:

### \\( 1-d-\beta > 0  \rightarrow d V_s \lt E_a\\)

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## DC Chopper

### Averaging Method
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### If \\(T << \tau_a\\)

### \\(V\_{dc} = d V\_{s}\\)

### \\(I\_{av}= \dfrac{V\_{dc}-E\_a}{R\_a}\\)

### \\(T\_{av}= K I\_{av}\\)

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# First Quadrant Chopper

### Positive Torque & Positive Speed
### Positive Current & Positive Voltage
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# Second Quadrant Chopper

### Negative Torque & Positive Speed
### Negative Current & Positive Voltage
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# Two-Quadrant Chopper

### Combine the previous choppers 
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# Two-Quadrant Chopper

### Forward Motoring: T1, D4
### Regenerative Braking: T4, D1

<img src="./images/ee462/two_quadrant.png" alt="Drawing" style="width: 600px;"/>
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# Alternative Two-Quadrant Chopper

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# Four-Quadrant Chopper
## Combine double two-quadrant choppers

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# Four-Quadrant Chopper
## Operating Modes

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## Exercise

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# Control of Four-Quadrant Choppers
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## PWM control
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<img src="https://qph.ec.quoracdn.net/main-qimg-5aaab7d90b562ccbe1a65aaf75f06c9b-c" alt="Drawing" style="width: 600px;"/>
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# Control of Four-Quadrant Choppers

## PWM control

- ### Switching Frequency: Fixed at Carrier Freq.
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- ### Speed Response: Fast
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- ### Ripple Current: Fixed
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- ### Filter Size: Usually Small

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# Control of Four-Quadrant Choppers

## Hysteresis Control

<img src="https://au.mathworks.com/help/physmod/sps/powersys/ug/gs_fig_19.gif" alt="Drawing" style="width: 450px;"/>
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# Control of Four-Quadrant Choppers

## Hysteresis Control

- ### Switching Frequency: Varying
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- ### Speed Response: Faster
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- ### Ripple Current: Adjustable
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- ### Filter Size: Depends on current hysteresis

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# Motor Drives

- [Control Tutorials - DC Motor PID Controller](http://ctms.engin.umich.edu/CTMS/index.php?example=MotorSpeed§ion=ControlPID)

- [PID without a PhD](http://m.eet.com/media/1112634/f-wescot.pdf)

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# Input to the Chopper
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## Diode Rectifier

<img src="./images/ee462/chopper_input.png" alt="Drawing" style="width: 700px;"/>
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# Input to the Chopper

## Diode Rectifier
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## Advantages:

- ### Near Unity Power Factor
- ### No Control Input
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## Disadvantages

- ### No Regenerative Braking

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# Input to the Chopper

## How to enable bi-directional power flow?
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<img src="https://puserscontentstorage.blob.core.windows.net/userimages/cf3e2b5d-8391-4350-a2c8-acb324804778/5b75fc3f-dc2c-4996-8467-42a9ab850178image19.png" alt="Drawing" style="width: 500px;"/>
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# Input to the Chopper

## Regenerating Converter

- ### Converter is operated with a firing angle close to 180 degree

- ### Only when \\(V\_s > 1.35 V\_{l-l(rms)}\\) regenerating is possible
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# Conclusions

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