EE462-Utilization of Electtrical Energy

class: center, middle

# EE-462 UTILIZATION OF ELECTRICAL ENERGY

# Induction Motor Drives

## Ozan Keysan

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

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

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# Speed Control Problems

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# Voltage Control Techniques

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## SCR Based AC Voltage Controller

### Generates sinusoidal voltages and hence only preferred in small motors (with fan loads)

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## SCR Based AC Voltage Controller

### AC voltage is chopped, so that RMS value is reduced

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## SCR Based AC Voltage Controller

### AC voltage is chopped, so that RMS value is reduced

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## Speed Control by Rotor Resistance Control

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## Speed Control by Rotor Resistance Control

### Duty cycle of the chopper can be adjusted to control the equivalent resistance.

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## Speed Control by Rotor Resistance Control

<img src="./images/ee462/resistance_control3.png" alt="Drawing" style="width: 300px;"/>
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### Power dissipated in resistor:
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\\(P\_{av}=I\_d^2 R\_{ex} (1-D)\\)
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### \\(P\_{av}=3 I\_{2(rms)}^2 R\_{ex-eq}\\)
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### \\(R\_{ex-eq}=\dfrac{1}{2} (1-D) R\_{ex}\\)
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## Speed Control by Rotor Resistance Control

### \\(P_{ag}=T \omega_s\\)
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### \\(P\_{rotor} = s P\_{ag} \approx V\_d I\_d = \dfrac{3\sqrt{6}}{\pi} s E\_2 I\_d\\)
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## Speed Control by Rotor Resistance Control

### \\( s P\_{ag} = s T \omega_s = s \dfrac{3\sqrt{6}}{\pi}  E\_2 I\_d\\)

### \\(T \propto I_d\\)

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## Rotor Slip Energy Recovery

### Instead of dissipating return to source

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## Rotor Slip Energy Recovery

### For torque control measure Id and vary firing angle
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## Speed Control via Line Frequency Control

### \\(T\_e = \dfrac{3 V\_{th}^2}{(R\_{th}+\dfrac{r'\_2}{s})^2 + (X\_{th}+X'\_2)^2}\dfrac{r'\_2}{s \omega\_s}\\)

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# Linear Approximation of Torque
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## Accurate torque expression
### Valid for all values of slip

### \\(T\_e = \dfrac{3 V\_{th}^2}{(R\_{th}+\dfrac{r'\_2}{s})^2 + (X\_{th}+X'\_2)^2}\dfrac{r'\_2}{s \omega\_s}\\)

### However, under steady-state conditions, slip is usually very small (<5%)
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# Linear Approximation of Torque

## \\(s < 0.05\\)
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## \\(\dfrac{r\_2'}{s} >> R\_{th}, X\_{th}, X\_{2}'\\)

### Torque equation becomes
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### \\(T\_{e} \approx \dfrac{3 V\_{th}^2 s}{r'\_2 \omega\_s}\\)
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# Linear Approximation of Torque

## \\(T\_{e} \approx \dfrac{3 V\_{th}^2 s}{r'\_2 \omega\_s}\\)

## \\(T\_{e} \approx k s\\)

## (only valid for small values of s)
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# Speed Control via Line Frequency Control

## What happens if we reduce f, with constant V?
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## \\(\Phi\\) increases, core will saturate

## Not desirable!
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## How can we keep \\(\Phi\\) constant?

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# Speed Control via Line Frequency Controls

## Constant V/f (or Constant Flux) Operation 
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# Constant V/f Operation

### Alternative representation of linear torque expression

### \\(T\_{e} \approx \dfrac{3 V\_{th}^2 s}{r'\_2 \omega\_s}\\)
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\\(= \dfrac{3 V\_{th}^2 s}{r'\_2 \omega\_s} \dfrac{\omega\_s}{\omega\_s}\\)
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## \\(T\_{e} \approx \dfrac{3}{r'\_2} {(\dfrac{V\_{th}}{\omega\_s})}^2 \omega\_{slip}\\)

## Torque is proportional to slip speed!

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# Constant V/f Operation

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# Example
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## 3-Phase, 440 V, 60 Hz, 10 hp, 1746 rpm, 4-pole induction motor is driven by constant flux operation.
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### a) Plot torque-speed curve (linear portion) for the stator terminal frequencies of 60 Hz and 45 Hz.
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### b) For a squared-power load, which requires rated torque at rated speed, calculate the operating speeds.

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### Use a Variable Voltage-Frequency Source

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# Constant Flux Operation

### \\(T\_{max}\\) is constant  
<img src="http://www.scielo.br/img/revistas/jbsmse/v29n1/a04fig01.gif" alt="Drawing" style="width: 400px;"/>
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### What happens if the speed is increased beyond rated speed under V/f control?

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# Flux Weakening Range

### If the torque is kept constant at high speeds, power limit will be exceeded
### Even if you wanted to increase, there may be a limit on the input voltage level

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# Constant Flux Operation

<img src="http://www.ece.umn.edu/users/riaz/animations/vf3.gif" alt="Drawing" style="width: 400px;"/>
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# Flux weakening

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# Constant V/f Operation

## Remember, we assumed \\(V\_1 \approx E\_1\\)
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## This assumption is less valid when:
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- ### High loads (I is high)
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- ### Lower speeds (voltage drop on R is more visible)
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## Need to boost the voltage to neutralize this effect! 
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# Constant V/f Operation with Voltage Boost

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# 3-Phase Voltage Source Inverter (VSI)
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## Two level VSI

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# 3-Phase Voltage Source Inverter (VSI)

## Operating Principle

### Do not close:

- ### S1 and S4
- ### S3 and S6
- ### S2 and S5

## never at the same time!

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## Square wave

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## PWM with Two-Level VSI

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## PWM with Two-Level VSI

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## PWM with Two-Level VSI

### Amplitude modulation index

## \\(m\_a=\dfrac{\hat{V}\_m}{\hat{V}\_{cr}}\\)

### Frequency modulation index

## \\(m\_f=\dfrac{f\_{cr}}{f\_m}\\)

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## PWM with Two-Level VSI

### For modulation index: 0 <m <1:

## \\(V1\_{ll} = \dfrac{\sqrt{3}}{2\sqrt{2}} m\_a V\_d = 0.612 m\_a V\_d\\)

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## Typical Voltage-Current Waveforms

<img src="./images/ee462/vsi_pwm3.png" alt="Drawing" style="width:600px;"/>
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## Overmodulation (m>1)

<img src="./images/ee462/vsi_pwm4.png" alt="Drawing" style="width:550px;"/>
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## Overmodulation (m>1)

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## VSI Controller

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## Drive Topologies
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### PWM-VSI with a Diode Rectifier

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## Drive Topologies

### Square Wave-VSI with a Controlled Rectifier

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## Drive Topologies

### Current Source Inverter

<img src="./images/ee462/converter3.png" alt="Drawing" style="width:750px;"/>
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## Drive Topologies

### Current Source Inverter

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# Challenges of Variable Frequency Drives
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## High Dynamic Performance
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## Low Inertia Rotor

### But beware of natural frequencies (especially at high speeds)

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# Thermal Challenges
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## Variable Speed vs. Cooling

### Induction Motor Internal Fan
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## Variable Speed vs. Cooling

### Motor with External Fan
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## Variable Speed vs. Cooling

### Inverter driven motors usually equipped with PTC thermistors
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## Variable Speed vs. Cooling

### Inverter driven motors usually equipped with PTC thermistors
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# Additional Losses
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- ## Stator-rotor copper losses

## \\(P\_{loss}=3 \sum_{k=1}^{\infty} (R\_s + R\_r') I^2_k  \\)

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- ## Core losses!

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## Derating of a general purpose motor

### \\(HVF = \sqrt{ \sum_{k=5}^{\infty} (\dfrac{V_n}{n})^2}  \\)

#### More info: [WEG-Inverter Driven Motors](http://ecatalog.weg.net/files/wegnet/WEG-induction-motors-fed-by-pwm-50029350-technical-article-english.pdf)
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# Challenges: Life-time
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## High dv/dt!

### With IGBT it can be around 3000V/μS
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## Reduces the insulation lifetime
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## Introduce additional losses (core)
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## Puts a limit on the motor cable length

[More info-ABB](https://library.e.abb.com/public/fec1a7b62d273351c12571b60056a0fd/voltstress.pdf)

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# High dv/dt filters
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#### A few commercial products:

[Eagtop](http://www.passivedevice.com/5-8-dvdt-filters.html), [MTECorp](http://www.mtecorp.com/pages_lang/wp-content/uploads/INSTR-019Rel041119dVdTFilterSeriesA440-600VACUserManual.pdf), [Schaffner](http://www.schaffner.com/products/power-magnetics/dvdt-filters/)

#### A better but more expensive product is [sine wave filters](http://chziri.com/en/Catalogue/Sine-Wave-Filter-24.html)
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# Challenges: Life-time

## Bearing/Shaft Currents
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#### [Further Info](http://www.kyservice.com/wp-content/uploads/2017/03/EASA-Shaft-Bearing-Currents.pdf)
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# Challenges: Life-time

## Bearing/Shaft Currents

#### [Further Info](http://www.kyservice.com/wp-content/uploads/2017/03/EASA-Shaft-Bearing-Currents.pdf)
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# Challenges: Life-time

## Bearing/Shaft Currents

#### [Further Info](http://www.kyservice.com/wp-content/uploads/2017/03/EASA-Shaft-Bearing-Currents.pdf)
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# Challenges: Life-time

## Bearing/Shaft Currents

#### [Further Info](http://www.kyservice.com/wp-content/uploads/2017/03/EASA-Shaft-Bearing-Currents.pdf)

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## Bearing/Shaft Currents
### Reduction: Use Symmetrical multi-core cable

### Use HF Bonding Strap

#### [Further Info-ABB Application Note](https://library.e.abb.com/public/8c253c2417ed0238c125788f003cca8e/ABB_Technical_guide_No5_RevC.pdf)
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## Bearing/Shaft Currents
### Reduction: Use Common Mode Chokes

#### [Common Mode Chokes](http://www.mhw-intl.com/applications/by-solution/cmc/)
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## Bearing/Shaft Currents
### Reduction: Use Ceramic Bearing

### Ceramic is not conducting, hence no bearing currents

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# Harmonics Effects

<img src="https://www.mathworks.com/help/physmod/sps/ref/pwm_generator_three_phase_three_level_model_plot.png" alt="Drawing" style="width:700px;"/>
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# Inverter Harmonics
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### Torque due to higher frequency current harmonics

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# Inverter Harmonics

## Over-modulation range

### Would you prefer Wye or Delta connection to reduce harmonics?
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### Would you prefer Wye or Delta connection for higher speed operation?

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## Motor Harmonics

<img src="./images/ee462/torque_pulsations.png" alt="Drawing" style="width:750px;"/>
### Torque Pulsations
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## Crawling Speed

<img src="http://www.eeeguide.com/wp-content/uploads/2016/10/Cogging-and-Crawling-1.jpg" alt="Drawing" style="width:650px;"/>
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### Cogging Torque
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### Why does the rotor is skewed?

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# Acoustic Noise
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: Fan Blades

## Can you guess the frequency of the noise?
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## \\(f= N\_{blades}*f\_{rotor}\\)
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# Acoustic Noise
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: Magnetic Pull

## Can you guess the frequency of the noise?
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## Most dominant: \\(2*f\_{switching}\\)

### Avoid noise around 2 kHz ([Online Tone Generator](http://onlinetonegenerator.com/))
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# Dunning-Kruger Effect
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<img src="https://media.licdn.com/mpr/mpr/shrinknp_800_800/AAEAAQAAAAAAAAgdAAAAJDZjNzZlZWRlLTNiZWYtNGI3OS05YWEwLThhNWMwNjY1YjViZQ.jpg" alt="Drawing" style="width:500px;"/>
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# Dunning-Kruger Effect

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