EE362-Electromechanical Energy Conversion-II

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# EE-362 ELECTROMECHANICAL ENERGY CONVERSION-II

# Real & Reactive Power, V-Curves of Synchronous Machines

## Ozan Keysan

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

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

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# Synchronous Machines Power:

## \\(P = 3 V_t I_a cos (\theta)\\) Watts
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### or

## \\(P = \dfrac{3 V\_t E\_f sin(\delta)}{X\_s}\\)

### when \\(R_a\\) is neglected
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## What about Q (Reactive power)?
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## \\(Q = 3 V_t I_a sin (\theta)\\) VAR 
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## \\(Q = \dfrac{3 V\_t (E\_f cos(\delta)-V\_t)}{X\_s} \\)

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## What about Q (Reactive power)?

## Formal derivation

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# Direction of P, Q?

## Power (P) flows from leading side to lagging side
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## Reactive Power (Q) flows from over-excited to under-excited side.

## Lagging pf generator supplies Q, lagging pf motor absorbs Q
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## Power-Reactive Power Directions

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## Power-Reactive Power Directions

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### Direction of P, Q Summary

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# Standalone Operation:

### Let's draw output voltage vs. load

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# Standalone Operation:

### \\(P\_{mech}\\) and \\(I\_f\\) must be controlled for constant \\(V_t\\) and f.

### Automatically done by the AVR (Automatic Voltage Regulator)

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## Synchronous Generator Connected to Infinite Bus

## Constant terminal voltage and speed
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## Synchronous Generator Connected to Infinite Bus

# \\(\vec{E\_f} = \vec{V\_t} \pm (R\_a + j X\_s)\vec{I\_a}\\)

## \\(+\\): Generating

## \\(-\\): Motoring

## \\(V\_t\\): Constant (when connected to infinite bus)

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## Synchronous Generator Connected to Infinite Bus

### There exists two main operating modes:

- ## Constant Excitation, Variable Load (Circle Diagram)

- ## Constant Power, Variable Excitation

## [Animation](https://andymikeknight.github.io/machines/synchronous/sg_p_infinite_bus.html)

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# Constant Power, Variable Excitation

## From geometry: \\(E\_f sin (\delta) = X\_s I\_a cos (\theta)\\)  = Constant

## \\(E_f\\) moves on horizontal line
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## For a generator connected to infinite bus:

### Draw \\(I\_f\\) vs \\(I\_a\\) if the power kept constant (= constant \\(E\_{f}sin(\delta)\\).
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<img src="./images/ee362/generator_v_curve.png" alt="Drawing" style="width: 600px;"/>
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# V-Curves: Generating Mode

### In generating mode, excess \\(I\_{field}\\) makes pf. lagging, and generator supplies reactive power to the grid.

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#V-Curves: Motoring Mode

## Phasor under constant power for the motoring mode

<img src="./images/ee362/motor_v_curve.png" alt="Drawing" style="width: 800px;"/>
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#V-Curves: Motoring Mode

### Different characteristics for motoring and generating modes

### In motoring mode, excess \\(I\_{field}\\) makes pf. leading.
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# Some Useful Animations

### [Infinite Bus Operation Animation](https://andymikeknight.github.io/machines/synchronous/sg_p_infinite_bus.html)

### [V-curves of a synchronous motor](http://www.ece.umn.edu/users/riaz/anim/synchronous_motor_Vcurves.html)

### [Synchronous generator capability curves](http://www.ece.umn.edu/users/riaz/anim/sm_V.html)

### [Video Animations for Rotating MMF](https://www.youtube.com/@bingsen/videos)

### [Other Animations](http://www.ece.umn.edu/users/riaz/animations/listanimations.html)
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# Synchronous Condenser
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## A Synchronous motor operating at no-load

### Used to deliver or to absorb VAR by controlling \\(I_f\\)
### Can behave as a capacitor or an inductor!
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# Synchronous Condenser

## Any difference compared to a motor?

<img src="https://teletype.in/files/0d/0dcf01b2-14e7-46d9-8be2-2d285e2e93ac.jpeg" alt="Drawing" style="width: 600px;"/>
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## Largest Synchronous Condenser

### 100 MVAr, 300 tons,  built in 2014 by [WEG](http://www.weg.net/us/Media-Center/News/Products-Solutions/WEG-Manufactures-Mega-Synchronous-Condensers) for the Brasil Grid. [Manufacturing Video](https://www.youtube.com/watch?v=8g6CssH5iWo)

#### For curious students: [Rise of renewables leads to synchronous condenser revival](https://new.abb.com/motors-generators/synchronous-condensers/rise-of-renewables-leads-to-synchronous-condenser-revival), [An old tool rediscovered to address new grid challenges](http://search.abb.com/library/Download.aspx?DocumentID=9AKK107258&LanguageCode=en&DocumentPartId=&Action=Launch)

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# Losses in Synchronous Machines

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# Operating Limits of Synchronous Machines
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## What are the factors that limit the power output from the synchronous generator?
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# Operating Limits of Synchronous Machines

- ## Stator Heating: \\(\propto I_a^2\\)
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- ## Rotor Heating: Limited \\( I_f\\) = Limited \\( E_f\\)
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- ## Mechanical Power Input Limit
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- ## Stability Limit \\(\delta < 90 \\)
### Most cases it is much smaller for extra safety

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# Operating Limits of Synchronous Machines
<img src="./images/synch_limits.png" alt="Drawing" style="width: 650px;"/>
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# Real Data

### [Source:Cummins Generators](http://power.cummins.com/sites/default/files/literature/technicalpapers/PT-6001-ImpactofPowerFactorLoads-en.pdf)

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## Example:
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## 500 MVA, 3-phase, 4-pole, Y-connected synchronous generator connected to 22 kV infinite bus.
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## Prime mover power (i.e. mechanical power) is set to 300 MW.
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### a) Find E and load angle for a power factor of 0.8 lagging.
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### b) Double check the load angle from the power expression.
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### c) The field current is changed, and the power factor is adjusted to unity at 300 MW. Calculate the new load angle and the E.
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## You can download this presentation from: [keysan.me/ee362](http://keysan.me/ee362)

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# Excluded Slides

# Synchronous Machine Tests

## Open-Circuit Characteristics (OCC)

### At open-circuit friction and core losses can also be estimated.

# Short-Circuit Characteristics (SCC)

## Armature windings short circuited, a small If is applied

# OCC vs SCC

# Determination of Xs

## If \\(R_a\\) is small:

# \\(X\_s = \dfrac{V\_{(OC)}}{Ia\_{(SC)}}\\)

### For better approximation measure \\(R\_{a(dc)}\\) when the machine is stationary.

# Determination of Xs

## \\(X\_s\\) can be calculated both for saturated and unsaturated regions

-->