EE361-Electromechanical Energy Conversion

class: center, middle

# EE-361
# VOLTAGE REGULATION

## Ozan Keysan

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

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

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# Voltage Regulation

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### A transformer's ability to keep its output voltage constant.

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# Ideal transformer: 
## \$V\_{out}\$ at No Load = \$V\_{out}\$ at Full Load

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# Practical transformer: 
### \$V\_{out}\$ under load is generally smaller than \$V\_{out}\$ at No Load

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# Voltage Regulation

## $$\frac{V\_{2(No\;Load)}-V\_{2(Full\;Load)}}{V\_{2(Full\;Load)}}$$
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## Smaller regulation is better.

## Regulation of an ideal transformer = 0

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# Voltage Regulation with Phasors

### Neglect the parallel branch (for now)

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# Voltage Regulation

### Regulation can be calculated at any load.

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# Voltage Regulation

- ## Inductive: \$V_{reg}>0\$

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- ## Resistive: \$V_{reg}>0 \$

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- ## Capacitive: \$V_{reg} = ?\$
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# Voltage Regulation

![](voltage_regulation.png)

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# Voltage Regulation

### [Burdur GES](https://goo.gl/maps/JF91W3KiWgH2)
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## [Effects to Electric Grid](https://en.wikipedia.org/wiki/Voltage_regulation)

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# Example:
## For the same transformer(1000 VA) used in the previous problem, calculate the voltage regulation at:

## a) 0.8 pf lagging rated current
## b) 1.0 pf rated current
## c) 0.8 pf leading rated current

### if the output voltage of the transformer is adjusted to be 115 V, under the given load condition.

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# Transformer Efficiency

# $$\mathrm{Efficiency (\eta) = \frac{Pout}{Pin}}$$

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## $$\mathrm{Efficiency (\eta) = \frac{Pout}{Pout+\mathrm{Losses}}}$$

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# Transformer Efficiency

# $$\mathrm{Efficiency (\eta) = \frac{Pout}{Pin}}$$

## $$\mathrm{Efficiency (\eta) = \frac{Pin - Losses}{Pin}}$$

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# Transformer Efficiency

- ## Constant Losses: Core Losses (Eddy, Hysteresis)

### $$\frac{V_1^2}{Rcore}$$
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- ## Variable Losses: Copper Losses
### $$I_1^2 (R_1 + R_2')$$
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# Best Power Transformer

- ## Efficiency as high as possible
- ## Voltage Regulation as low as possible
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# Temperature Effect

### How does the resistance change with time?

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# Temperature Effect

## Temperature Coefficient
## $$R(T) = R(T_0)(1 + \alpha\Delta T)$$

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# Resistivity of copper increases by 30 % from 20 C to 100 C.

## For copper $$\alpha = 0.393 \%$$ per degree C

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# Losses and Cooling
<img src="http://www.amesimpex.com/images/oil_cooled_002.jpg" alt="Drawing" style="width: 600px;"/>

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# Losses and Cooling: Small Transformers
<img src="http://www.globalspec.com/ImageRepository/LearnMore/201210/EI-Transformer-for-Electric-Tool484de69d1e254262a778c635653aa340.png" alt="Drawing" style="width: 500px;"/>

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# Losses and Cooling: Large Transformers
<img src="http://ogrforum.ogaugerr.com/fileSendAction/fcType/0/fcOid/23252098522776349/filePointer/23252098522776380/fodoid/23252098522776373/imageType/LARGE/inlineImage/true/Power-Transformer%2004.jpg" alt="Drawing" style="width: 500px;"/>
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# Losses and Cooling: Large Transformers
<img src="http://upload.wikimedia.org/wikipedia/commons/8/80/Drehstromtransformater_im_Schnitt_Hochspannung.jpg" alt="Drawing" style="width: 300px;"/>
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# Losses and Cooling: Large Transformers
<img src="http://upload.wikimedia.org/wikipedia/commons/thumb/a/a3/Trafostation_Alter_Hellweg_IMGP4722.jpg/1280px-Trafostation_Alter_Hellweg_IMGP4722.jpg" alt="Drawing" style="width: 750px;"/>

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<img src="http://blog.sciencescore.com/media/elephant-ears1.jpg" alt="Drawing" style="width: 850px;"/>

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### [Who’ll Freeze First? A Puzzle About Size and Staying Warm](http://noticing.co/on-size-and-warmth/)
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### [Who’ll Freeze First? A Puzzle About Size and Staying Warm](http://noticing.co/on-size-and-warmth/)

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### [Who’ll Freeze First? A Puzzle About Size and Staying Warm](http://noticing.co/on-size-and-warmth/)

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### [Who’ll Freeze First? A Puzzle About Size and Staying Warm](http://noticing.co/on-size-and-warmth/)

###[Size and Metobolism](http://noticing.co/on-size-and-metabolism/)
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## (Heat \$\propto\$ Mass, Heat Dissipation \$\propto\$ Surface Area)
<img src="https://upload.wikimedia.org/wikipedia/commons/4/43/Angry_elephant_ears.jpg" alt="Drawing" style="width: 500px;"/>

### [Square-Cube Law by Prof. Walter Lewin](http://www.youtube.com/watch?v=qoM17ikreio)

### [Square-cube law, small is mighty](https://www.youtube.com/watch?v=qzq710aOHjE)
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## (Heat \$\propto\$ Mass, Heat Dissipation \$\propto\$ Surface Area)
<img src="http://noticing.co/wp-content/uploads/2015/08/elephant-with-tail.gif" alt="Drawing" style="width: 500px;"/>

[Small is mighty](https://www.youtube.com/watch?v=qoM17ikreio)
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# What about in humans?
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<img src="http://noticing.co/wp-content/uploads/2015/05/512px-volume_surface.svg.png" alt="Drawing" style="width: 600px;"/>
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# What about in humans?

<img src="http://noticing.co/wp-content/uploads/2015/05/saami_family_1900.jpg" alt="Drawing" style="width: 800px;"/>
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# What about in humans?

### [Bermann's rule](https://en.wikipedia.org/wiki/Bergmann%27s_rule), [How insects breathe?](http://noticing.co/how-insects-breathe/)
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# Example:
## For the same transformer(1000 VA) used in the previous problems, calculate the efficiency at rated current and 0.8 pf lagging (assuming output voltage is 115 V).

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#Question:
## What is the point that the transformer has maximum efficiency?

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- ## Full Load?

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- ## Half Load ?

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- ## No Load ?

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# Efficiency Graph
![](http://www.bomara.com/powerware/images/wp_efficient_transformers3.jpg)

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# A transformer has maximum efficiency when:

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# Copper Losses = Core Losses

# But, Why?
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## You can download this presentation from: [keysan.me/ee361](http://keysan.me/ee361)