EE362-Electromechanical Energy Conversion-II

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# EE-362 ELECTROMECHANICAL ENERGY CONVERSION-II

# Equivalent Circuit of Synchronous Machines

## Ozan Keysan

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

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

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# Review: Torque in Synchronous Machines
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# \\(T = K \Phi\_f \Phi\_R sin (\delta)\\)

### \\(K\\): Constant (we'll see what it is in the following weeks)

### \\(\Phi_f\\): Field generated flux (rotor-side)

### \\(\Phi\_R\\): Resultant (or Air-gap) flux (\\(\Phi\_R = \Phi\_f + \Phi\_{ar}\\))

## \\(\delta\\): Load-angle (very important!)

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# Torque vs Load Angle

## \\(\delta > 0 \\): Generating Action

## \\(\delta < 0 \\): Motoring Action

## \\(\delta = \pm \dfrac{\pi}{2} \\): Maximum torque point

## \\(\delta = 0 \\): Zero Torque (Donkey eats the carrot)

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# Torque vs Load Angle

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# Simple Equivalent Circuit

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# Equivalent Circuit

## The armature windings has some resistance: \\(R_a\\)

### Ra is usually around <5% of jXs so can be ignored
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## Motoring and Generating Convention
### Remember synchronous machines are mostly used as generators.

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# Most important definitions

- ## Load Angle (\\(\delta\\)): Angle between phase voltage and field voltage

- ## Power Factor Angle (\\(\theta\\)): Angle between phase voltage and current.
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# Load Angle and Power Factor

### Neglect \\(R\_a\\) for now.

### [Voltage and Current Waveforms](https://docs.google.com/spreadsheets/d/1K7vG-rez29gQ3fhGt3pZCsy4OtRYml2UaPSoeRor9wI/edit?usp=sharing)
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# Full Equivalent Circuit with Field Circuit

<img src="./images/synch_full_circuit.png" alt="Drawing" style="width: 800px;"/>
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### \\(L\_f\\) can be neglected at steady state (DC) conditions

## Remember \\(I\_f\\) can be controlled to adjust \\(E\_f\\)

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# Operation Modes: Standalone Generating

### Assume you have a single diesel generator supplying a load
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<iframe width="560" height="315" src="https://www.youtube.com/embed/LqpQZd9XxJM" frameborder="0" allowfullscreen></iframe>

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# Standalone Generating

# Challenge:
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- ## Keep the terminal voltage constant
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- ## Keep the frequency of the electricity constant
	
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# Standalone Generation
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## Assume we have a resistive load (unity pf)
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## Assume the field current and speed is kept constant and see what happens to terminal voltage as we increase the load.

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## Standalone Generation with Unity Power Factor

### Speed is kept constant.
### \\(I_f\\) is kept constant and hence magnitude of \\(E_f\\) constant

## As load increases, \\(V_t\\) slightly decreases. [Animation](http://people.ucalgary.ca/~aknigh/electrical_machines/synchronous/stand_alone/sa_phasors.html)

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## Standalone Generation with Lagging Power Factor

### Magnitude of \\(E_f\\) constant
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### As load increases, \\(V_t\\) considereably decreases. [Animation](http://people.ucalgary.ca/~aknigh/electrical_machines/synchronous/stand_alone/sa_phasors.html)

### [Animation](http://people.ucalgary.ca/~aknigh/electrical_machines/synchronous/sg_standalone.html)

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# Leading Power Factor

### As load increases, \\(V_t\\) slightly increases. [Animation](http://people.ucalgary.ca/~aknigh/electrical_machines/synchronous/stand_alone/sa_phasors.html)

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# Voltage Regulation
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## \\(V\_{reg}= \dfrac{V\_{no-load}-V\_{full-load}}{V\_{full-load}}\\)

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## In a standalone power system, we want to keep the frequency and voltage constant.
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# Solution?
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## Control Field Current to adjust \\(E_f\\) so that constant \\(V_t\\) magnitude can be achieved

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# AVR?
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 : Automatic Voltage Regulator
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![](http://www.chinageneratoravr.com/wp-content/uploads/2012/03/15A-AVR.jpg)
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# What does this device do?

![](http://www.findsminimodelhotbulbengines.dk/boksermotor%202.JPG-for-web-LARGE.jpg)
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![](http://www.eagleridgetech.com/images/Centrifugal_governor.png)
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## Speed Governor: 
## Centrifugal Flyball System works as a speed controller

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# Watt's  Steam Engine

### [We're still using the same technology](https://www.youtube.com/watch?v=1VqS74JJ17U)
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# Speed control ensures constant frequency

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## Full Control Scheme of a Diesel Generator

<img src="https://api.intechopen.com/media/chapter/44431/media/image1_w.jpg" alt="Drawing" style="width: 750px;"/>
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## You can download this presentation from: [keysan.me/ee362](http://keysan.me/ee362)